If there was one store a kilometer from where you live and another store four kilometers from where you live, you would naturally describe the furthest store as being four times the distance from where you live as the closer store. If you were comparing the weight of two objects, you might say that one object is 2.13 times as heavy as the other. If you wanted to tell someone how long it took you to complete a task, you may possibly say that it took one hour and ten minutes.
These are examples of quantification, or using numbers to express a quantity, which is what numbers are for.
Now, let me ask you a question. If you had two machines, one more complex than the other, and someone asked you how much more complex the one was than the other, what would you answer? You would most likely say that "The one machine is quite a bit more complex than the other." You might use other terms such as "a lot more complex" or "somewhat more complex".
Have you ever wondered why human beings use numbers, quantification, for expression of all kinds of things, but when we want to express or compare complexity, we invariably use subjective terms instead of numbers? Just why is it that we do not express something as primal to life as complexity in numbers and units as we do distance, time, temperature or, weight? I have really put quite a bit of thought into this.
Complexity is a conservative quantity in being simply the amount of information in something, which is why I believe that we could and should quantify it, that is express it as a number instead of in the vague and subjective terms that we tend to use now. The quantification of complexity would be a great advantage in all that human beings do, particularly in science and engineering. It seems to me that the increasing use of complex documents like computer programs, blueprints and, product specifications in recent decades has prepared us to begin the expression of complexity with precise numbers.
We live in a world and universe that consists of matter in space. This matter can form many, many different patterns. This is what brings complexity into existence. The people of long ago were very much affected by complexity, just as we are today. But they did not have the knowledge to quantify it and got in the habit of expressing it in subjective terms, which we still do today.
The quantification of complexity does not require and kind of measuring device. It does, however, require a new way of thinking. I have developed some general rules of complexity to get us started.
THE RULES OF COMPLEXITY
Any type of measurement, unless it is a comparison, requires units. What does the number 17.33 mean? The answer is that it means absolutely nothing until it is used with a unit, such as meters or ounces.
The unit of complexity will be the "level". A level is anything that is quantified, which can be expressed in numbers. If you have a box, you can describe the box with three levels, that of it's length, width and, height. We could say that the box, basically, has a complexity of three levels.
It was the writing of my book, "The Theory of Primes" that led me to the idea of quantifying complexity. Every domain in existence can be differentiated from every other domain by it's levels. This makes it possible for complexity to be expressed by simply the number of levels that is manifested by a domain.
RELEVANCE
In the expression of complexity, a level must be expressed if there is any possible alternative to what that level is now that would affect the purpose for the measurement of the complexity. This is the great factor that we must work around in the quantification of complexity, that it's expression will be done for a variety of different reasons and that not all levels that can be expressed will be relevant to a measurement of complexity for a specific purpose.
To give an example, if a meteorologist is measuring snowfall, the complexity of the measurement does not normally need to include the patterns in the snowflakes. For another example, measurement of the temperature of an object can be expressed as one level and does not normally need to include the trajectories of the fast-moving atoms and molecules that create heat. We can describe these as "irrelevant" levels.
REDUNDANCY
The domains with the least complexity is a line, circle, cube or, sphere requiring only one number, one level, to describe it. It is important that, in measurement of complexity, there be no redundancy in the levels expressed. Redundant levels are those levels that are unnecessary because the quantities can be found by other listed levels. There must be only the minimum required information.
For example, we do not need to include the level for the volume of a cube if that can be found by it's length, width and, height which are already listed. It also does not matter which level, out of a choice of several, is included if it can describe the domain without the others. As an example of this, a circle can be described by any one of several criteria, radius, diameter, curvature or, area. Only one would be necessary and to include more than one in a measurement of complexity would bring redundancy.
SYSTEMS AND REPETITION
A so-called "system" is a domain consisting of at least two sub-domains. Such a system would be more complex than would the complexity of the separate sub-domains added together. This is simply because in the system, not only do the sub-domains have to be described but it also has to be described by additional levels how the sub-domains relate to each other by location or function in the larger domain.
Thus, we could say that the combining of sub-domains into a larger domain increases complexity by the number of levels it would require to describe how the sub-domains relate to each other in the larger domain.
On the other hand, any type of repetition in a large domain reduces complexity. In any arrangement of identical units, the complexity of the unit counts only once. An arrangement of twenty identical cars is only a little bit more complex than one of the cars would be. In addition, even if the cars were not identical, the arrangement could be described by first describing one car and then describing how the other cars differ from the first, if that would require less information, and thus fewer levels, than describing each car individually.
So, we could say that in any system or domain consisting of sub-domains, any repetition or similarity between sub-domains decreases complexity.
Remember that complexity consists of the minimum amount of information that can describe a domain, any redundancy must be eliminated for a true measure of complexity. The domain of which we are measuring complexity is defined by the relevance for which we are taking the measurement.
MAXIMUM AND MINIMUM COMPLEXITY
In any system or domain, there is a minimum and a maximum possible complexity. If you arrange pennies on a table top, you lower the complexity by simply arranging them in a circle. You maximize the complexity by spelling out words with the pennies in single file. We go back to minimum again by scattering the pennies in a meaningless, random pattern.
Basically the number of units, such as pennies, multiplied by the possible arrangement of each, gives us the potential complexity of a system. To reach the maximum possible complexity, the arrangement must have no repetition or randomness. Motion, or potential motion, in a system will obviously drastically increase complexity. Theoretically, there can be neither zero nor infinite complexity in the universe.
INTRICACY
Complexity can also be expressed by the ratio of actual complexity to the maximum or minimum possible complexity. At this point, we should also compare and contrast intricacy and complexity. Intricacy, as opposed to complexity, is just such a ratio. A system that is intricate will be closer to it's maximum potantial complexity than a system that is not intricate, regardless of how complex it is.
A lawnmower engine may be more complex than a watch mechanism but the watch is more intricate because, given the amount of metal in the watch, because it is much closer to it's maximum possible complexity. A comparison of intricacy requires a common denominator of the given, while complexity does not.
RANDOMNESS
The patterns of complexity have no effect on it's quantification, only the numbers of levels. Neither does the amount or quantity of each level have any effect on the complexity of a system, only the number of levels. A ton of sugar is no more complex than a pound of sugar as long as it has no special arrangement.
In taking a measurement of complexity, it is necessary to define or understand what will be considered as randomness. Such as the meteorologist being unconcerned with documenting the patterns of the crystals in each snowflake. He would leave that undocumented and it would be considered as randomness. Thus, randomness is a form of irrelevance.
This is the reason that we have never gotten around to quantifying complexity, that not all levels are relevant to whatever reason we would be taking the measurement of complexity.
Anything that is done to an object, such as cutting it into pieces, that requires more levels to be manifested, will increase complexity. This is only if it is deemed necessary to describe the dimensions and gaps between the pieces, that they are not to be considered as random. Likewise, anything that reduces the number of levels reduces complexity.
Randomness is not complexity. Random arrangements are not to be classified as complexity. Randomness is a state in which any arrangement has about as much meaning as any other arrangement, given the purpose for which that the complexity is being measured. Thus, any random permutations can be considered as of equal complexity. In pure randomness, positions can be expressed as a concentration, the actual positions or arrangements of sub-domains are not expressed and are not considered as increasing complexity.
A fundamental rule of the quantification of complexity is that, if the number of levels necessary to describe a system can be determined either by a direct description of that system or a description of the forces that created that system, the complexity of that system is the lesser number of levels. Thus, we could say that a system can be effectively described by a description of the forces that brought it about, but only if it can be done with less information than a direct description of the system. The rule is that the complexity of a system is the least information necessary to describe it.
Random scattering could be described by describing the forces that brought about the scattering. An obvious way to see if complexity can be reduced is to look for a formula that can describe a system. A formula can thus be described as a tool to reduce complexity.
NUMERICAL AND VERBAL EXPRESSION
In the quantification and expression of complexity, it is only numerical levels that count, not verbal descriptions. Words are a human creation, the real universe operates by numbers, which form the levels by which we are going to measure complexity. Descriptions are for our use only.
Our verbal definitions of systems are fuzzy and imprecise and are not the same as absolute numerical definitions. To measure complexity, the levels are represented by numbers or statements equivalent to numbers, no matter how a description is stated.
LEVELS OF OBSERVATION
The reason for relevance and irrelavance in measurements of complexity, including randomness is that we can observe our sorroundings from many different levels. Even the nature of our observation of complexity is thus expressed in levels. The lowest level from which we can make observations is that of sub-atomic particles. The highest level is to observe the universe as a whole all at once.
You may notice that the higher we get in our observation level, the more is considered as random. At the lowest level of observation, nothing is random, the position of every electron in every atom counts. At the highest level, the level of the entire universe, almost everything is random such as the orbits of planets around stars.
Thus at the highest level of observation, the entire universe is no more complex than a single atom at the lowest observation level but there is far more randomness. We can see that the amount of randomness, the number of levels that do not need to be included in the measurement, in a measurement of complexity will be proportional to the height of our observation level.
Of course, we see this way because we are human beings. The way God sees the universe, there is the absence of any irrelevance or randomness in the view at the lowest observational level when he views the universe at the highest observational level, that of the entire universe. A formula can be described as the reduction in complexity at a lower level of observation by viewing the system from a higher level.
COMPARISON OF COMPLEXITY
This is why our present expressions of complexity are so subjective. So many present levels are irrelevant to our measurements. However, in considering whether we should begin quantifying complexity, we must also consider that the main purpose for which human beings would do so would not be so much for direct measurement but for comparison purposes.
Measurement of comparitive complexity is much simpler than measurement of absolute complexity. We do not need to know or measure everything about the systems whose complexity we are measuring and comparing as long as the levels that we do not measure are the same for both and the unmeasured levels will cancel each other out.
We can never be sure of the real complexity of any system or domain because we do not know all there is to know. But it is logical to believe that any undiscovered properties in measurement of complexity for the purpose of comparison will cancel out. Any inefficiencies in measurement and expression will also cancel out since the main purpose of measurement of complexity will be the comparison of the complexity of two or more systems.
THE LIMITS OF COMMUNICATION
I now think that I understand how we have managed to miss the tremendous benefit that could come with being able to put a number on complexity, which is what "quantification" means. The reason is not complex at all, in fact it is very simple.
Suppose that you had an object of some kind and wanted someone far away to understand the object. You would most likely take a photo or make a drawing of the object and send it to them. This is where the problem lies, for it is the use of visual representation which conceals complexity from us.
Suppose now that you only had words with which to describe the object to someone who was completely unfamiliar with it. The length of the text required to thoroughly describe the object, without comparing it with any other objects, would be an effective measure of the complexity of the object.
Take an object and thoroughly describe it, or the aspects of it that are relevant, by sentences without illustration or comparison and contrast to other objects. The number of sentences, or more precisely the number of descriptions in the sentences, since some sentences are compound, is actually equal to the complexity of the object.
The use of numbers in description makes it even easier to quantify complexity. Each number used to describe the object represents one unit of it's complexity. This is easier to deal with since it requires more care to parse verbal descriptions.
Similarity between objects is found when, in an effort to describe an object or event or situation, it becomes more efficient to describe it by starting with the description of a similar object (or event or situation) and then describing only what is different, rather than starting a description from the beginning. The degree of similarity can easily be expressed as the proportion of the description saved by starting with the description of the similar object (or event or situation) for which a description already exists. This means that the complexity of an object, such as a vase or rocket, can be described in terms of variation from standard geometric shapes such as circle and rectangle.
My conclusion is that if humans had never developed drawing, painting, or other such artwork, we would have long since been expressing complexity in numbers, instead of vague and general descriptions. The lack of illustration would have been a great disadvantage, but the quantification of complexity would have been of immeasurable benefit. Computer coding makes it somewhat easier to quantify complexity since everything, including illustrations, are written as lines of code.
Saturday, July 11, 2009
Complexity, Patterns And, Energy
I would like to bring together two topics that I have been writing about here. Patterns and complexity are not two separate subjects but are actually one and the same thing. The number of patterns that are manifested by any given system is a numerical quantification of the absolute complexity of that system. This means that grasping the underlying patterns that are to be found everywhere will also enable us to put a number on complexity, with all the advantages that will bring.
I have found that complexity is a lot like energy in that it cannot be created or destroyed but only transformed. In fact, when we transform energy in any way, we are also transforming complexity. This must be true since energy is manifested as either motion or potential motion and motion rearranges reality and thus, complexity. Energy, patterns and complexity are three manifestations of the same thing.
It is important to remember that we view complexity through our own lenses. We have words such as "random" and "chaos", when in absolute reality there is no such thing. Randomness and chaos, as seen by us, are the result of our incomplete knowledge and limited vision.
Work is required to transform complexity, just as it is to transform energy. But we can never increase or decrease either. We can concentrate or disperse complexity. When we concentrate it, we get what is known as intricacy. My definition of intricacy is the concentration of complexity.
I have also reasoned that complexity must operate like hot and cold when two systems are brought into contact. Indeed this should not surprise us since heat is energy and energy is a different facet of complexity. Since the sun is giving off energy in the form of radiation, we know that it's internal complexity, the total number of patterns manifested by it's innards, must be decreasing. The energy released by the sun comes from leftover energy when smaller atoms are crunched together into larger ones. This reduces the complexity because the larger atom has only one trajectory which contains information, instead of the previous two or more.
The molecules concentrated in our bodies increases the complexity there, but at the expense of complexity elsewhere. The molecules of food are broken down, thus reducing their complexity so that the complexity can be applied elsewhere. Our bodies are highly intricate but a birth must make the inanimate world somewhat more disperse. (Let's refer to the opposite of intricacy as "dispersity").
Remember that complexity, like energy, can be transformed or concentrated but cannot be created or destroyed. Likewise the total number of patterns manifested by the universe always stays the same, although in continuous flux as we move through time.
To understand how complexity is like energy in that it can only be transformed but never change in quantity, remember that two identical cars are only slightly more complex than one car. Repetition lowers complexity. Human beings are complex but more human beings in the world does not increase the world's complexity in proportion to the numbers because human beings have so much in common.
Living things are very complex, so what if every thing that is alive died? Would that decrease complexity? The answer is no, at least at the most basic level of inanimate reality, because the movement of the living things while they were alive would drastically rearrange the atoms in the world and thus increase complexity.
However we look at it, complexity just cannot be created or destroyed but only transformed. When a living thing is born, it concentrates complexity as intricacy and when it dies, the intricacy is dispersed. But the overall complexity, the total number of underlying patterns that are manifested, always remains the same, at least depending on what we look at as random.
When we learn we are not really increasing complexity, at least at the universal level, because we are only mirroring what we see in the world around us in our minds and remember that repetition decreases complexity. When we make or build something we are not really increasing absolute complexity either because we are only mirroring the complexity in our minds, which in turn is only a mirror of the complexity around us.
Technology is just copies of what we have seen in nature. The complexity of a new model of car is merely a reflection of the complexity in the designer's mind from which it arose. We cannot create complexity and more than we can create energy because the two are the same thing. Complexity can be concentrated into intricacy but never increased or decreased. Remember that the total complexity of any technology or building also actually includes our nature and the purpose in the larger scheme of society that it will be used for.
We seem to be increasing complexity by building a city where there was once a wilderness. But that is only from our point of view. The very act of imposing order reduces complexity, such as cutting trees and planting crops in less-complex rows. There is the apparent complexity as seen by us but also an absolute complexity that we can transform but cannot change. Yet we cannot reduce complexity by imposing order on nature because in doing so, we increase our experience and thus complexity always balances out.
When you think about this, it is really amazing. I spent hours trying to think of ways to either increase or decrease absolute complexity, to no avail. It operates by the same rules as energy because the two are one and the same.
There is no better illustration of how my theory of complexity operates than the structure and life processes of living things.
The bodies and structures of all living things on earth are composed of cells. Have you ever wondered why? My rules of complexity can explain it.
The cellular structure of living things drastically lowers their complexity in comparison to what it would be if living things consisted of one large cell. All life begins with a seed of some type, and the finished product might be thousands or millions of times the size of the original seed.
If the mature living thing had the same complexity per volume as it's seed, that would mean that it's complexity would have to increase by thousands or millions of times and, according to my rule that complexity is like energy in that it cannot be created or destroyed, but only changed in form, that is impossible.
It is the cellular structure of living things that make them no more complex than their seeds, except for the influence of environmental factors. A seed is essentially a packet of information, and the structure of the living thing at maturity can be no more complex than the information contained in the original seed.
According to the rules of complexity that I explained, any number of duplicates are only slightly more complex than one of them. And the complexity of two systems, which share some similarities, is equal to the complexity of one of the systems, plus the complexity of the differences between it and the second system. The only thing that makes any number of an entity more complex than one of the entity is that their arrangement adds to the complexity. Remember that copying complexity does not increase it.
This means that, in living things composed of cells, the original seed must contain the information for the layout of a cell, the differences of the other types of cell from this cell and, the arrangement of the cells. Without the cell structure of living things, this would violate these rules of complexity, and thus living things as we know them would not be possible.
COMPLEXITY AND EVOLUTION
Now, onto some implications of this. If cannot change the complexity of the world around us but can only transform it, this must mean that the motions of inanimate matter must not be able to transform it either.
The development of living things on the earth as described in evolutionary theory requires a temendous increase in the complexity in the world in comparison with the inanimate world before the supposed development of life. The great complexity of living things in evolutionary theory is supposedly provided by the fact that random mutation will make survival to reproductive age either more or less likely. But where did this evolutionary complexity come from in the first place?
Random mutations cannot, on the average, make a system that is more complex than it's sorroundings, more complex still. The average of random mutations can only bring a system, such as a living thing, closer to the complexity level of it's environment.
Remember that complexity operates in a way analogous to hot and cold, average random mutations must bring the complexity of a complex system down to the complexity level of it's sorroundings. This is why a dead body breaks down from intricacy to dispersity.
So if the presence of even the simplest forms of life dramatically increaes the complexity of the world and if the complexity of a given system can be transformed from inside but never increased or decreased, what does that tell us about how life must have originated? The mind-boggling complexity of living things must have been put into the world from outside, since nothing like this complexity existed on the bare earth before living things.
Put simply, life must have been created by God. If we could quantify complexity, we would have seen all of this sooner. The nature of our energy usage shows, in another way, my hypothesis that energy and complexity ultimately comes down to the same thing.
ENERGY USE AND COMPLEXITY
The laws of physics tell us that energy can never be lost or destroyed, but only changed in form. So why can't we keep on reusing energy, why is it lost to us once it is used?
A moving vehicle, for example, plows air aside from in front of it. The energy that it took to move the air, and the vehicle, is then lost to us. Why can't we reuse the energy to move the next vehicle along?
Energy is used to propel a jet aircraft. But once it has been used, it cannot be retrieved and used to propel another jet. Why is this the case if energy can never be lost or destroyed?
We lose the energy that we use, but the surrounding environment never loses it's energy. In nature if energy is not used for one thing then it will be used for something else, if only dissipating the energy as heat. It can never be lost. Why can't it be the same way when it comes to our use of energy?
The answer to this unfortunate dilemma lies in complexity. We are of a higher level of complexity than our inanimate surroundings. That simply means that there is more information encoded within us as to how we came to be. When we make or build things, we are imposing our higher level of complexity on the surrounding reality of lower complexity.
The irrecoverable loss of energy, when the laws of physics state that it supposedly cannot be lost, is the result of the difference in the level of complexity between us and our inanimate surroundings. We use this energy in our technology and skilled work, but we add information to it and this information represents our higher complexity by providing instructions on how the energy is to be used.
After the energy has been used by us, it has not really been lost but it has returned to the lower complexity level of the surrounding inanimate reality so that it is of no further practical use to us. If we are on some elevated platform, and drop something so that it falls to the ground, it is not entirely lost but it is lost to our level. So it is with the energy that we use.
The more difference there is between the levels of complexity, the more easily energy will be lost to us and the more valuable it will be. If we were at the same level of complexity as the surrounding inanimate reality, we would not be losing any energy in this way because all energy would be readily reusable.
A similar example concerns entropy. Because we are on a higher level of complexity then our inanimate surroundings, it is much easier to spill something than it is to put it back into the container. This is because it is easier to drop from a higher to a lower level of complexity then vice versa. This brings us back to how complexity is related to energy because, in exactly the same way, it easier to drop from a high to a low energy state, such as the kinetic energy of altitude, than it is to climb from a low to a high energy state.
I have found that complexity is a lot like energy in that it cannot be created or destroyed but only transformed. In fact, when we transform energy in any way, we are also transforming complexity. This must be true since energy is manifested as either motion or potential motion and motion rearranges reality and thus, complexity. Energy, patterns and complexity are three manifestations of the same thing.
It is important to remember that we view complexity through our own lenses. We have words such as "random" and "chaos", when in absolute reality there is no such thing. Randomness and chaos, as seen by us, are the result of our incomplete knowledge and limited vision.
Work is required to transform complexity, just as it is to transform energy. But we can never increase or decrease either. We can concentrate or disperse complexity. When we concentrate it, we get what is known as intricacy. My definition of intricacy is the concentration of complexity.
I have also reasoned that complexity must operate like hot and cold when two systems are brought into contact. Indeed this should not surprise us since heat is energy and energy is a different facet of complexity. Since the sun is giving off energy in the form of radiation, we know that it's internal complexity, the total number of patterns manifested by it's innards, must be decreasing. The energy released by the sun comes from leftover energy when smaller atoms are crunched together into larger ones. This reduces the complexity because the larger atom has only one trajectory which contains information, instead of the previous two or more.
The molecules concentrated in our bodies increases the complexity there, but at the expense of complexity elsewhere. The molecules of food are broken down, thus reducing their complexity so that the complexity can be applied elsewhere. Our bodies are highly intricate but a birth must make the inanimate world somewhat more disperse. (Let's refer to the opposite of intricacy as "dispersity").
Remember that complexity, like energy, can be transformed or concentrated but cannot be created or destroyed. Likewise the total number of patterns manifested by the universe always stays the same, although in continuous flux as we move through time.
To understand how complexity is like energy in that it can only be transformed but never change in quantity, remember that two identical cars are only slightly more complex than one car. Repetition lowers complexity. Human beings are complex but more human beings in the world does not increase the world's complexity in proportion to the numbers because human beings have so much in common.
Living things are very complex, so what if every thing that is alive died? Would that decrease complexity? The answer is no, at least at the most basic level of inanimate reality, because the movement of the living things while they were alive would drastically rearrange the atoms in the world and thus increase complexity.
However we look at it, complexity just cannot be created or destroyed but only transformed. When a living thing is born, it concentrates complexity as intricacy and when it dies, the intricacy is dispersed. But the overall complexity, the total number of underlying patterns that are manifested, always remains the same, at least depending on what we look at as random.
When we learn we are not really increasing complexity, at least at the universal level, because we are only mirroring what we see in the world around us in our minds and remember that repetition decreases complexity. When we make or build something we are not really increasing absolute complexity either because we are only mirroring the complexity in our minds, which in turn is only a mirror of the complexity around us.
Technology is just copies of what we have seen in nature. The complexity of a new model of car is merely a reflection of the complexity in the designer's mind from which it arose. We cannot create complexity and more than we can create energy because the two are the same thing. Complexity can be concentrated into intricacy but never increased or decreased. Remember that the total complexity of any technology or building also actually includes our nature and the purpose in the larger scheme of society that it will be used for.
We seem to be increasing complexity by building a city where there was once a wilderness. But that is only from our point of view. The very act of imposing order reduces complexity, such as cutting trees and planting crops in less-complex rows. There is the apparent complexity as seen by us but also an absolute complexity that we can transform but cannot change. Yet we cannot reduce complexity by imposing order on nature because in doing so, we increase our experience and thus complexity always balances out.
When you think about this, it is really amazing. I spent hours trying to think of ways to either increase or decrease absolute complexity, to no avail. It operates by the same rules as energy because the two are one and the same.
There is no better illustration of how my theory of complexity operates than the structure and life processes of living things.
The bodies and structures of all living things on earth are composed of cells. Have you ever wondered why? My rules of complexity can explain it.
The cellular structure of living things drastically lowers their complexity in comparison to what it would be if living things consisted of one large cell. All life begins with a seed of some type, and the finished product might be thousands or millions of times the size of the original seed.
If the mature living thing had the same complexity per volume as it's seed, that would mean that it's complexity would have to increase by thousands or millions of times and, according to my rule that complexity is like energy in that it cannot be created or destroyed, but only changed in form, that is impossible.
It is the cellular structure of living things that make them no more complex than their seeds, except for the influence of environmental factors. A seed is essentially a packet of information, and the structure of the living thing at maturity can be no more complex than the information contained in the original seed.
According to the rules of complexity that I explained, any number of duplicates are only slightly more complex than one of them. And the complexity of two systems, which share some similarities, is equal to the complexity of one of the systems, plus the complexity of the differences between it and the second system. The only thing that makes any number of an entity more complex than one of the entity is that their arrangement adds to the complexity. Remember that copying complexity does not increase it.
This means that, in living things composed of cells, the original seed must contain the information for the layout of a cell, the differences of the other types of cell from this cell and, the arrangement of the cells. Without the cell structure of living things, this would violate these rules of complexity, and thus living things as we know them would not be possible.
COMPLEXITY AND EVOLUTION
Now, onto some implications of this. If cannot change the complexity of the world around us but can only transform it, this must mean that the motions of inanimate matter must not be able to transform it either.
The development of living things on the earth as described in evolutionary theory requires a temendous increase in the complexity in the world in comparison with the inanimate world before the supposed development of life. The great complexity of living things in evolutionary theory is supposedly provided by the fact that random mutation will make survival to reproductive age either more or less likely. But where did this evolutionary complexity come from in the first place?
Random mutations cannot, on the average, make a system that is more complex than it's sorroundings, more complex still. The average of random mutations can only bring a system, such as a living thing, closer to the complexity level of it's environment.
Remember that complexity operates in a way analogous to hot and cold, average random mutations must bring the complexity of a complex system down to the complexity level of it's sorroundings. This is why a dead body breaks down from intricacy to dispersity.
So if the presence of even the simplest forms of life dramatically increaes the complexity of the world and if the complexity of a given system can be transformed from inside but never increased or decreased, what does that tell us about how life must have originated? The mind-boggling complexity of living things must have been put into the world from outside, since nothing like this complexity existed on the bare earth before living things.
Put simply, life must have been created by God. If we could quantify complexity, we would have seen all of this sooner. The nature of our energy usage shows, in another way, my hypothesis that energy and complexity ultimately comes down to the same thing.
ENERGY USE AND COMPLEXITY
The laws of physics tell us that energy can never be lost or destroyed, but only changed in form. So why can't we keep on reusing energy, why is it lost to us once it is used?
A moving vehicle, for example, plows air aside from in front of it. The energy that it took to move the air, and the vehicle, is then lost to us. Why can't we reuse the energy to move the next vehicle along?
Energy is used to propel a jet aircraft. But once it has been used, it cannot be retrieved and used to propel another jet. Why is this the case if energy can never be lost or destroyed?
We lose the energy that we use, but the surrounding environment never loses it's energy. In nature if energy is not used for one thing then it will be used for something else, if only dissipating the energy as heat. It can never be lost. Why can't it be the same way when it comes to our use of energy?
The answer to this unfortunate dilemma lies in complexity. We are of a higher level of complexity than our inanimate surroundings. That simply means that there is more information encoded within us as to how we came to be. When we make or build things, we are imposing our higher level of complexity on the surrounding reality of lower complexity.
The irrecoverable loss of energy, when the laws of physics state that it supposedly cannot be lost, is the result of the difference in the level of complexity between us and our inanimate surroundings. We use this energy in our technology and skilled work, but we add information to it and this information represents our higher complexity by providing instructions on how the energy is to be used.
After the energy has been used by us, it has not really been lost but it has returned to the lower complexity level of the surrounding inanimate reality so that it is of no further practical use to us. If we are on some elevated platform, and drop something so that it falls to the ground, it is not entirely lost but it is lost to our level. So it is with the energy that we use.
The more difference there is between the levels of complexity, the more easily energy will be lost to us and the more valuable it will be. If we were at the same level of complexity as the surrounding inanimate reality, we would not be losing any energy in this way because all energy would be readily reusable.
A similar example concerns entropy. Because we are on a higher level of complexity then our inanimate surroundings, it is much easier to spill something than it is to put it back into the container. This is because it is easier to drop from a higher to a lower level of complexity then vice versa. This brings us back to how complexity is related to energy because, in exactly the same way, it easier to drop from a high to a low energy state, such as the kinetic energy of altitude, than it is to climb from a low to a high energy state.
Complexity, Humans And, Living Things
I have introduced the possibility and advantages of applying numbers to complexity as we do with distance, time, weight, temperature, etc. This posting is about the tremendous advantages that we would gain from applying numbers to the concept of complexity instead of continuing to describe it in vague and subjective general terms. Quantifying complexity would upgrade our whole way of thinking and of making decisions.
Human beings are generally adept at making judgements concerning distance, weight and, temperature. In my view, that is because we are accustomed to measuring and quantifying these.
When people make poor decisions, it is very often because we have misjudged complexity. Even when we make a misjudgement concerning time, it is usually complexity that we have actually misjudged. We measure time more often than all other quantities combined and so are closely familiar with it. It is not so much that we have underestimated the time as that we have underestimated the complexity involved.
Whenever any type of life decision is made, it inevitably involves an assessment of complexity. So, wouldn't it be better to be able to express this with concrete numbers instead of vague terms such as "more complex", "very complex" or, "relatively simple". This would make us much more proficient at assessing all manner of consequences and ramifications while making decisions.
It is my feeling that we underestimate complexity more than we overestimate it when making difficult decisions. Underestimation of complexity is comparable to looking at a scene on a computer monitor with fewer pixels than is necessary to completely render it. Sometimes we make a situation more complex than it really is by worrying about it.
We especially underestimate complexity in our relationships with others. It is good, when dealing with inanimate matter, to be able to break everything down into simple formulae. But this does not work as well in the world of people. Our minds are much better at handling complexity than our emotions.
There are so many ways that we understate complexity in handling life and the world around us. We tend to zig-zag through history instead of moving in a more efficient straight line. This is because every new system or ideology we come up with tends to be a reaction against what came before. We distort the situation with our emotions and move too far in the opposite direction until a reaction forms against that and the process repeats.
The primary reason for this zig-zag through history is oversimplification, in other words poor handling of complexity. We tend to take what would be good advice at one point in time and harden it into dogma. We oversimplify by taking advice that should be written in sand and making into ideology written in stone. One way to improve the situation is to get a better grasp of complexity.
Another way that we sometimes destructively oversimplify in times of conflict or competition is to group everyone into one of two pigeon holes. Those that are for us and those that against us. The situation is most likely far more complex with some that are with us and some that are against us but a vast range of people or nations somewhere in between.
Simplistic pigeon-holing is, of course, another form of understating and poor handling of complexity. Anyone who lives in a country other than the one in which they were born is familiar with how people tend to think that all people from the old country are much more alike than they actually are and that the move from one country to another is tantamount to the stepping from one simple pigeon-hole into another. Students have long been pigeon-holed as either primarily academic, athletic or, vocational. It is so much easier to think of people in broad groups rather than as individuals, but this invites misjudgement of complexity.
We would get much better at evaluating complexity, and would thus make better decisions, if we got used to quantifying it. Measurement of complexity requires some creativity since it is not something that we can just place a ruler against or place on a scale.
For example, one day I got to thinking how we could measure how much people are alike as opposed to how much they are different. The solution that I came up with was to count the number of words in the dictionary, eliminate redundancies and then divide the world's population by that number. That would give us a "Sameness Ratio", we would be that number of times more the same than different.
Quantification of complexity would also enable us to add new categories to the record books. For example, what is the world's greatest coincidence? We cannot, at present, evaluate this question in any other than subjective terms. Putting numbers on complexity would certainly lead us to discover patterns in reality that we had not noticed before.
Let's have a look at how we think in terms of patterns. We have a certain "pattern vocabulary", patterns that we are familiar with, and this affects all that we do.
On my cosmology blog, I explained that to really understand the universe, we have to understand that we see it not only because of what it is, but also what we are. This concept also applies to how we interact with the world around us. We see the world the way we do not only because of what it is but because of what we are.
We are composed of organs, which accomplish various tasks. We have internal organs like the stomach, intestines, kidneys, liver, heart, lungs, brain, etc. And also external organs like the legs, arms and, eyes. Our own structures are the most fundamental source of patterns for our pattern vocabulary.
Have you ever noticed that we invariably tend to organize everything in ways closely resembling that of our bodies? It is not that there is not other ways of organizing things, it is just that we do not readily see any other way because we are bound to see the world as we do not only because of what it is, but also because of what we are. Let's suppose that we had all of the same capabilities that we do, but that we consisted of an "imaginary homogenous medium" without the internal structure organized into various organs.
What about the way we organize knowledge? We organize it as a virtual mirror image of the organ structure of our bodies. There is not just "knowledge", it is organized into categories such as science, history, philosophy, religion, technology, and so on. If we were not organized the way we are, we would not organize our knowledge the way we do.
We cannot help it because these are the patterns that we are familiar with. If we were structured differently, we would be familiar with a different set of patterns and would organize our knowledge differently, although we cannot now imagine how that would be.
Consider how we divide up labor (labour). We assign workers different tasks that are organized in a way that, like knowledge, mirrors the way that our bodies are structured. If we did not have this organ structure, but consisted of some "imaginary homogenous medium", the way we organize work would be completely different. Although, we cannot imagine what it might be simply because it is outside our pattern vocabulary.
How about the rooms in a house? This also bears a very close resemblence to the structure of the organs in our bodies. It is not that there are not other possibilities for the layout of a house, it is just that we are constrained by our pattern vocabulary from imagining those possibilities.
The same thing with the various departments in stores. We see and organize our sorroundings the way we do because of what we are, and we inevitably try to shape those sorroundings into extensions of ourselves. It is not that there are no other ways, it is just that we are unable to see those other ways.
Even when designing vehicles, we cannot get away from how we are organized. Cars and trucks, like their makers, are organized into components which accomplish various tasks. It is said that anyone who creates something inevitably leaves a part of themselves in the creation, the concept of limited pattern vocabulary explains why.
The economy is composed of various industries, and governments of different ministries, that work together, much like the workers doing different tasks within those industries, in the same way that the organs of our bodies do. The leader of some enterprise is even referred to as "the head", and the center as "the heart". It would be much different if we consisted of an imaginary homogenous medium, but we cannot imagine that reality because of how we are structured in this reality.
We are fortunate that our bodies are as complex as they are, even though complexity means more things to go wrong. If we were simpler, even with the same level of intelligence, we would have an even more limited pattern vocabulary than we do.
In all that we do, it is not that there are not other ways to do it, it is just that we cannot see those other ways because of the patterns that we are familiar with. Just as a radio is tuned in to a certain wavelength, we are "tuned in" to a certain selection of patterns and any patterns outside this selection go unnoticed.
The entire set of patterns is determined by the nature of matter. The primary value of art and sports is that it "transmits" patterns that can then be adapted by us to other uses. The patterns that are outside our pattern vocabulary are not completely beyond our reach because all possible patterns can be broken down into the fundamental four that I refer to as "primes", for "primary", as described in "The Most Basic Pattern".
Have you ever noticed something about life concerning difficulty and complexity? Life can be made easier, but only at the expense of becoming more complex. If we could put an actual measurement on difficulty and complexity, we would have noticed this previously. But we can only express such things in vague and subjective terms.
Ancient people had a much simpler life, but at the expense of being more difficult. The natural state of life is difficulty without complexity. Making use of the mind is tantamount to replacing difficulty with complexity. Difficulty is represented by the body, while complexity is represented by the mind.
It is technology that makes life so much easier, but the price is complexity. It must be designed and maintained, and requires skill to use.
Tools are the first and most obvious step in substituting complexity for difficulty. Tools make all manner of manual work much easier. But the tools themselves must, in most cases, be carefully made and their use requires skill, which is complexity. Tools are the simplest and most widespread example of exchanging difficulty for complexity.
My reasoning is that if difficulty and complexity can be readily interchanged, it can only mean that the two must be different manifestations of the same thing. In the patterns blog, we already established that energy and complexity must be different forms of the same thing, since neither can be created or destroyed, but only changed in form. Since energy overcomes some difficulty, we should not be surprised that difficulty is a part of the interchange also.
One way that I have thought of to put a measurement on the complexity of a society is the total number of different occupations that the people work at.
The point is that there must be a difficulty plus complexity sum which remains constant, at least on a large scale, for all of human life. We cannot access or express this sum because we cannot attach numbers to entities like difficulty and complexity, but can only express them in the usual vague and subjective terms.
This interchangeability between difficulty and complexity only applies on a large scale. For example, upon retirement life usually gets both less complex and less difficult. So, when someone's life becomes both less complex and less difficult due to retirement, we can be sure that there must be a corresponding increase in both somewhere else.
I have really been doing some thinking lately about how complexity relates to the structures of living things, and there is a conclusion that I think we can safely arrive at. When a system arises that interacts with it's surrounding environment, and is completely dependent on that environment, it cannot logically be more complex than that environment.
This can only mean that while plants are far more intricate than the natural environment, intricacy is concentrated complexity but not more complexity, they cannot be more complex in structure than the sum total of the complexity of the natural environment in which they live.
A good example of intricacy is a watch and an engine. The watch is far more intricate than the engine, because it contains more complexity per unit of material, but is not more complex than the engine. Complexity can be defined as the number of levels in a system, or as the minimum volume of information required to construct that system.
Plants are certainly complex in their structures. But remember that all of the information necessary to construct a plant is contained in the seed of the plant. Most of the structure of the plant is repetition of the basic cells, and recall that repetition is not complexity. For example, six identical cars are only one level of complexity more complex than one such car and that is only because we require another piece of information to express how many cars there are.
Let's consider what is meant by the sum total of the environment in which plants live. This would include the patterns in the wind that affects the plant, the energy from the sun on which the plant depends, the composition and density of the air, the soil and it's nutrients, the plant's interactions with insects such as bees, interactions with birds and animals, the change between day and night, the changes of the seasons, impurities in the air and soil, variations in water, variations in temperature, the force of falling rain and, cloud cover.
Just consider what sense it would make for plants to be more complex than the natural environment in which they live. It would make no sense whatsover. Therefore I feel safe in concluding that plants, while extremely intricate in structure, can never have a meaningful complexity greater than that of the sum total of the complexity of their natural environment.
But then what about humans and animals? Maybe plants cannot be more complex than the totality of their environment. But humans, particularly our brains, are far more complex than the environment in which we live. How can we explain that?
The answer lies in something that humans and animals have that plants don't, with regard to complexity. We have what is known as free will. My conclusion is that for a living thing to be more complex in structure than it's natural environment, it must be able to exercise free will. To exercise free will, a living thing must be able to move or to move things, or both. Free will makes up for the complexity gap between being and environment so that a more complex system, such as a human, can operate in a less complex sorrounding environment.
You may notice that the smaller a living thing is, such as an insect, generally the less intellect and free will it requires to operate in it's environment. This is simply because it's environment is more limited, and thus less complex. The various species of plants do, as a whole, manifest a kind of collective free will by trial and error in "deciding" where to grow. This is because the species, on the whole, matches the complexity of a larger-scale environment while a single plant matches the complexity of the local-scale environment, which is less complex. In this way, evergreens "choose" to live in high latitudes rather than in the tropics, while palm trees make the opposite choice.
The fact that we are more complex than our surrounding environment can be seen in two ways that I described in the posting "True And False, Words And Numbers", on this blog. Because the surrounding environment cannot match our complexity, we see "truth possibilities". Some of these truth possibilities turn out to be true, others to be false. If we were equal in complexity to the environment in which we live, there would be no truth possibilities because everything that we could conceive of would have to be true. Thus, free will would be meaningless and unnecessary.
Likewise, there is not enough complexity in the sorrounding environment for everything that we could conceive of to exist. This is why we use both words and numbers to communicate. If we were equal in complexity to our environment, words to differentiate what actually exists from what could possibly exist but doesn't would be unnecessary because everything could be described with numbers. The difference between words and numbers is that numbers are continuous, but words aren't. That is why there are new words as time goes on, but no new numbers.
Let's add another manifestation of the difference in the level of complexity between us and our natural environment. Life is about dealing with two levels of complexity and the dynamic tension between the two. The result is the opposites that we refer to as construction and destruction. Construction is to make something, destruction is to destroy it. Construction represents the higher level of our complexity while destruction represents the lower complexity level of the natural environment.
When we make or build something from materials which are available in the sorrounding environment, we are imparting our level of complexity onto that of the environment. The skills involved in making and using something is part of the complexity imparted onto it.
When the thing that we have made is destroyed, it is returning to it's former level of complexity. Of course, it is true that complexity can never be lost or destroyed at a universal level. On our level, involving complexity that is meaningful to us, the object would have returned to the complexity of the natural environment.
It is clear that birth is construction, while death represents destruction by a returning of the atoms of the body to their former level of complexity in the natural environment. If our complexity was the same, or less, than that of the natural environment, there would be no such thing as technology. We could never learn anything because we could never conceive of anything that was not true. This means that free will would be unnecessary and of no use, and we would logically live like plants.
Complexity is the level of information that is stored within some system, in how the system is put together and how it operates. There are two fundamental levels of complexity on earth, that of living things with free will and that of the surrounding environment. We saw how plants, while being far more intricate than the surrounding environment, are no more complex overall than that environment. This is why plants, while living things, do not require the free will that other living beings have.
For our purposes here, I define a plant as a living thing with no free will and without getting into the biology of whether mushrooms, fungus and, lichens are technically plants.
A living thing must have some type of separation from the surrounding environment, such as skin or cell walls, and cannot be less complex than the sum total of the surrounding environment. The most efficient living thing will be greater in intricacy, which is the concentration of complexity, but equal in complexity to that of it's surrounding environment. This is why plants comprise by far the vast majority of living things on earth, above that of single cells.
(By the way, this is also a creation issue that I covered on the blog about creation. It simply does not make sense for plant life to evolve into animals when plants are by far the most efficient of the two).
A living thing that is more complex than the surrounding environment will see truth possibilities that cannot all be true, because there will not be enough complexity for all to be true, so it will have to have the free will necessary to decide which are true and which are not. Having free will makes no sense unless the living thing also has senses to receive information, as well as the ability to move and possibly to move things. There must be more than one way of doing things for free will to make sense. It is easy to see that complexity in living things is very high-maintenance.
A living thing that is much more complex than the surrounding environment will have more capacity to learn about that environment, but will also have a greater capacity to make mistakes because a higher proportion of the truth possibilities that it sees will have to be false simply because there is not enough complexity available in the environment for all to be true.
The two basic levels of complexity on earth, the higher level of beings with free will and the lower level of the surrounding environment are manifested in another way, as construction and destruction. When we impose our complexity on the surrounding environment in some way, we engage in construction by adding information to it so that it is brought closer to our level of complexity. When that complexity is effectively eliminated in some way, it results in the process of destruction by bringing the environment back to it's effective original level of complexity.
So much about life-truth possibilities, use of words, health, aging, diet and, labor (labour) result from the difference in complexity between ourselves and the surrounding environment. The purpose of all work is to bridge this complexity gap.
I have established how work and complexity is interchangeable, meaning that they must be the same thing. We can make life easier for us, primarily through technology and organization, but only at the expense of making it more complex. Labor (labour) is required of any being that is more complex than their environment, but none is required of plants because they are equal in complexity (although far greater in intricacy) than the surrounding environment.
In the environment of inanimate matter, there is quantity but not quality. Quality make sense only for living things. In geometric terms, quantity is simply a slope or a straight line. But quality shows as a peak formed by more than one line because it is more complex than simple quantity. Plants are not more complex than the sum total of their environments, but manifest this peak pattern due to their greater intricacy. This peak of quality is the optimum living conditions of living things. I defined life, on the patterns and complexity blog, as a manifestation of this peak factor which is not found in inanimate matter.
Organization is information, and thus complexity. Whenever we organize elements of the environment around us, we bring it closer to our own complexity level in order to approach our peak of quality. A less complex being, relative to the surrounding environment, would organize less while a more complex being would organize more. We can see this in how much of the organization that we impose on the environment is meaningless to animals and insects.
If we could bring the complexity level of the surrounding environment up to our level, by construction and organization, there would be no more truth possibilities that would not be true and thus no more need for more knowledge. This is theoretically impossible, because to do so we would have to be "smarter than ourselves", but it means that we can define paradise in terms of complexity as bringing the surrounding environment up to our level of complexity by construction and organization so that we can effectively live like plants, with no need for work or benefit from more knowledge.
We have seen that the primary pattern that defines living things, in contrast to inanimate matter, is the peak. A peak is manifested in any situation where there can be either too much or too little of something. The optimum amount is at the peak.
A few obvious examples, with regard to human beings, is food, sleep and, temperature, and also the balance between work and relaxation. This pattern has no meaning in the universe of inanimate matter. In fact, I regard this as the very definition of life as described in "The Definition of Life" on this blog.
Progress, the moving forward of civilization in improvement, can be readily expressed in terms of complexity as a bringing of our surrounding environment, which is at a lower level of complexity than we are, up to our level of complexity.
This complexity, of either ourselves or our native environment, is simply the information contained within it as to how it came to be and how it operates. All death and destruction can also be expressed in terms of complexity, simply as a reverting back to the lower level of the surrounding environment.
In imposing our complexity on the surrounding environment during progress, it must be remembered that we are dependent on this environment. Imposing our complexity must take the nature of our complexity into account. Progress forms a peak and the peak of progress is neither too much or too little.
For example, imposing our complexity on a tree does not necessarily mean that it's wood will be carved into something complex but possibly that it will be arranged so that it is in the most desirable location in the larger scheme of society.
As explained previously, the fact that we are more complex than our surrounding environment brings about truth possibilities. As we look at our environment, there is not enough complexity available for everything that we can conceive of to be true. This opens the possibility that we could believe some things to be true that are, in fact, false or, we may believe some things to be false that are actually true.
In other words, this disparity in complexity means that we can make mistakes. If we were of the same or lesser complexity than our surrounding environment, we could not even conceive of anything that was not true in our surrounding environment and so this would not be an issue. This is where the learning comes in which is necessary to progress, finding out just what is true and false in our surroundings.
We do work or labor (labour) to bring our surroundings up to our level of complexity in order to make progress. We usually define progress as having the maximum of what we want being achieved with the minimum of work. My theory is that when a being of a given level of complexity succeeds in completely imposing it's complexity on it's surrounding environment then labour (labor) will no longer be necessary.
In my complexity theory, plants are equal in complexity to the surrounding environment although they are far greater in intricacy (defined as the concentration of complexity or complexity per unit of matter or given). This is why plants have no need to do any work, all that they require comes right to them.
There are two broad types of labor (labour) that we do, physical and mental. These represent the two different levels of complexity that we are dealing with. If there could be pure physical labour (labor), with no mental component at all, it would be solely of the lower level of complexity of the surrounding environment.
(Let's just alternate the two global spellings of labor and Labour).
I define the difference in the two complexity levels, ours and that of the surrounding environment, as experienced by us while seeking progress to be: total labor = physical labour x mental labour. The total labor required must always remain constant, but as we make progress the mental labour increases as the physical labor diminishes.
This is actually another way of stating my doctrine that we can make life physically easier by use of technology, but only at the expense of making it more complex. We can never, on a large scale, make life both physically easier and simpler.
The real basis of progress is that mental labor can be replicated, while pure physical labour cannot. We can replicate physical labor using machines, but the design of those machines is mental labour. Someone doing the physical labor of planting his crops does not plant the crops of others as well, but someone figuring out how to plant crops figures it out for others as well.
Technology begins with tools, which are synthetic extensions of ourselves and our senses. Tools are the result of using mental labor to make physical labour easier and more efficient. Machines are a kind of complex tool that attempts to replicate physical labor.
Just as machines are complex tools, and a step upward from tools, computer technology is a step upward from writing. Written words can be described as tools to store and replicate information. Computer technology is a step upward from this, and is a kind of complex book which replicates skill rather than just information. Instruction naturally flows from highest to lowest technology, you still have to tell a computer what to do because it is less complex than you.
But everything that we do while making progress must ultimately bear the imprint of the surrounding environment in which we exist. Our universe is one of spatial dimensions that pervade everything about us. We can look at progress, then, in terms of dimensions. One dimensional tools can be combined into multi-dimensional machines. One dimensional books can have their information combined into multi-dimensional computer technology.
Human beings are generally adept at making judgements concerning distance, weight and, temperature. In my view, that is because we are accustomed to measuring and quantifying these.
When people make poor decisions, it is very often because we have misjudged complexity. Even when we make a misjudgement concerning time, it is usually complexity that we have actually misjudged. We measure time more often than all other quantities combined and so are closely familiar with it. It is not so much that we have underestimated the time as that we have underestimated the complexity involved.
Whenever any type of life decision is made, it inevitably involves an assessment of complexity. So, wouldn't it be better to be able to express this with concrete numbers instead of vague terms such as "more complex", "very complex" or, "relatively simple". This would make us much more proficient at assessing all manner of consequences and ramifications while making decisions.
It is my feeling that we underestimate complexity more than we overestimate it when making difficult decisions. Underestimation of complexity is comparable to looking at a scene on a computer monitor with fewer pixels than is necessary to completely render it. Sometimes we make a situation more complex than it really is by worrying about it.
We especially underestimate complexity in our relationships with others. It is good, when dealing with inanimate matter, to be able to break everything down into simple formulae. But this does not work as well in the world of people. Our minds are much better at handling complexity than our emotions.
There are so many ways that we understate complexity in handling life and the world around us. We tend to zig-zag through history instead of moving in a more efficient straight line. This is because every new system or ideology we come up with tends to be a reaction against what came before. We distort the situation with our emotions and move too far in the opposite direction until a reaction forms against that and the process repeats.
The primary reason for this zig-zag through history is oversimplification, in other words poor handling of complexity. We tend to take what would be good advice at one point in time and harden it into dogma. We oversimplify by taking advice that should be written in sand and making into ideology written in stone. One way to improve the situation is to get a better grasp of complexity.
Another way that we sometimes destructively oversimplify in times of conflict or competition is to group everyone into one of two pigeon holes. Those that are for us and those that against us. The situation is most likely far more complex with some that are with us and some that are against us but a vast range of people or nations somewhere in between.
Simplistic pigeon-holing is, of course, another form of understating and poor handling of complexity. Anyone who lives in a country other than the one in which they were born is familiar with how people tend to think that all people from the old country are much more alike than they actually are and that the move from one country to another is tantamount to the stepping from one simple pigeon-hole into another. Students have long been pigeon-holed as either primarily academic, athletic or, vocational. It is so much easier to think of people in broad groups rather than as individuals, but this invites misjudgement of complexity.
We would get much better at evaluating complexity, and would thus make better decisions, if we got used to quantifying it. Measurement of complexity requires some creativity since it is not something that we can just place a ruler against or place on a scale.
For example, one day I got to thinking how we could measure how much people are alike as opposed to how much they are different. The solution that I came up with was to count the number of words in the dictionary, eliminate redundancies and then divide the world's population by that number. That would give us a "Sameness Ratio", we would be that number of times more the same than different.
Quantification of complexity would also enable us to add new categories to the record books. For example, what is the world's greatest coincidence? We cannot, at present, evaluate this question in any other than subjective terms. Putting numbers on complexity would certainly lead us to discover patterns in reality that we had not noticed before.
Let's have a look at how we think in terms of patterns. We have a certain "pattern vocabulary", patterns that we are familiar with, and this affects all that we do.
On my cosmology blog, I explained that to really understand the universe, we have to understand that we see it not only because of what it is, but also what we are. This concept also applies to how we interact with the world around us. We see the world the way we do not only because of what it is but because of what we are.
We are composed of organs, which accomplish various tasks. We have internal organs like the stomach, intestines, kidneys, liver, heart, lungs, brain, etc. And also external organs like the legs, arms and, eyes. Our own structures are the most fundamental source of patterns for our pattern vocabulary.
Have you ever noticed that we invariably tend to organize everything in ways closely resembling that of our bodies? It is not that there is not other ways of organizing things, it is just that we do not readily see any other way because we are bound to see the world as we do not only because of what it is, but also because of what we are. Let's suppose that we had all of the same capabilities that we do, but that we consisted of an "imaginary homogenous medium" without the internal structure organized into various organs.
What about the way we organize knowledge? We organize it as a virtual mirror image of the organ structure of our bodies. There is not just "knowledge", it is organized into categories such as science, history, philosophy, religion, technology, and so on. If we were not organized the way we are, we would not organize our knowledge the way we do.
We cannot help it because these are the patterns that we are familiar with. If we were structured differently, we would be familiar with a different set of patterns and would organize our knowledge differently, although we cannot now imagine how that would be.
Consider how we divide up labor (labour). We assign workers different tasks that are organized in a way that, like knowledge, mirrors the way that our bodies are structured. If we did not have this organ structure, but consisted of some "imaginary homogenous medium", the way we organize work would be completely different. Although, we cannot imagine what it might be simply because it is outside our pattern vocabulary.
How about the rooms in a house? This also bears a very close resemblence to the structure of the organs in our bodies. It is not that there are not other possibilities for the layout of a house, it is just that we are constrained by our pattern vocabulary from imagining those possibilities.
The same thing with the various departments in stores. We see and organize our sorroundings the way we do because of what we are, and we inevitably try to shape those sorroundings into extensions of ourselves. It is not that there are no other ways, it is just that we are unable to see those other ways.
Even when designing vehicles, we cannot get away from how we are organized. Cars and trucks, like their makers, are organized into components which accomplish various tasks. It is said that anyone who creates something inevitably leaves a part of themselves in the creation, the concept of limited pattern vocabulary explains why.
The economy is composed of various industries, and governments of different ministries, that work together, much like the workers doing different tasks within those industries, in the same way that the organs of our bodies do. The leader of some enterprise is even referred to as "the head", and the center as "the heart". It would be much different if we consisted of an imaginary homogenous medium, but we cannot imagine that reality because of how we are structured in this reality.
We are fortunate that our bodies are as complex as they are, even though complexity means more things to go wrong. If we were simpler, even with the same level of intelligence, we would have an even more limited pattern vocabulary than we do.
In all that we do, it is not that there are not other ways to do it, it is just that we cannot see those other ways because of the patterns that we are familiar with. Just as a radio is tuned in to a certain wavelength, we are "tuned in" to a certain selection of patterns and any patterns outside this selection go unnoticed.
The entire set of patterns is determined by the nature of matter. The primary value of art and sports is that it "transmits" patterns that can then be adapted by us to other uses. The patterns that are outside our pattern vocabulary are not completely beyond our reach because all possible patterns can be broken down into the fundamental four that I refer to as "primes", for "primary", as described in "The Most Basic Pattern".
Have you ever noticed something about life concerning difficulty and complexity? Life can be made easier, but only at the expense of becoming more complex. If we could put an actual measurement on difficulty and complexity, we would have noticed this previously. But we can only express such things in vague and subjective terms.
Ancient people had a much simpler life, but at the expense of being more difficult. The natural state of life is difficulty without complexity. Making use of the mind is tantamount to replacing difficulty with complexity. Difficulty is represented by the body, while complexity is represented by the mind.
It is technology that makes life so much easier, but the price is complexity. It must be designed and maintained, and requires skill to use.
Tools are the first and most obvious step in substituting complexity for difficulty. Tools make all manner of manual work much easier. But the tools themselves must, in most cases, be carefully made and their use requires skill, which is complexity. Tools are the simplest and most widespread example of exchanging difficulty for complexity.
My reasoning is that if difficulty and complexity can be readily interchanged, it can only mean that the two must be different manifestations of the same thing. In the patterns blog, we already established that energy and complexity must be different forms of the same thing, since neither can be created or destroyed, but only changed in form. Since energy overcomes some difficulty, we should not be surprised that difficulty is a part of the interchange also.
One way that I have thought of to put a measurement on the complexity of a society is the total number of different occupations that the people work at.
The point is that there must be a difficulty plus complexity sum which remains constant, at least on a large scale, for all of human life. We cannot access or express this sum because we cannot attach numbers to entities like difficulty and complexity, but can only express them in the usual vague and subjective terms.
This interchangeability between difficulty and complexity only applies on a large scale. For example, upon retirement life usually gets both less complex and less difficult. So, when someone's life becomes both less complex and less difficult due to retirement, we can be sure that there must be a corresponding increase in both somewhere else.
I have really been doing some thinking lately about how complexity relates to the structures of living things, and there is a conclusion that I think we can safely arrive at. When a system arises that interacts with it's surrounding environment, and is completely dependent on that environment, it cannot logically be more complex than that environment.
This can only mean that while plants are far more intricate than the natural environment, intricacy is concentrated complexity but not more complexity, they cannot be more complex in structure than the sum total of the complexity of the natural environment in which they live.
A good example of intricacy is a watch and an engine. The watch is far more intricate than the engine, because it contains more complexity per unit of material, but is not more complex than the engine. Complexity can be defined as the number of levels in a system, or as the minimum volume of information required to construct that system.
Plants are certainly complex in their structures. But remember that all of the information necessary to construct a plant is contained in the seed of the plant. Most of the structure of the plant is repetition of the basic cells, and recall that repetition is not complexity. For example, six identical cars are only one level of complexity more complex than one such car and that is only because we require another piece of information to express how many cars there are.
Let's consider what is meant by the sum total of the environment in which plants live. This would include the patterns in the wind that affects the plant, the energy from the sun on which the plant depends, the composition and density of the air, the soil and it's nutrients, the plant's interactions with insects such as bees, interactions with birds and animals, the change between day and night, the changes of the seasons, impurities in the air and soil, variations in water, variations in temperature, the force of falling rain and, cloud cover.
Just consider what sense it would make for plants to be more complex than the natural environment in which they live. It would make no sense whatsover. Therefore I feel safe in concluding that plants, while extremely intricate in structure, can never have a meaningful complexity greater than that of the sum total of the complexity of their natural environment.
But then what about humans and animals? Maybe plants cannot be more complex than the totality of their environment. But humans, particularly our brains, are far more complex than the environment in which we live. How can we explain that?
The answer lies in something that humans and animals have that plants don't, with regard to complexity. We have what is known as free will. My conclusion is that for a living thing to be more complex in structure than it's natural environment, it must be able to exercise free will. To exercise free will, a living thing must be able to move or to move things, or both. Free will makes up for the complexity gap between being and environment so that a more complex system, such as a human, can operate in a less complex sorrounding environment.
You may notice that the smaller a living thing is, such as an insect, generally the less intellect and free will it requires to operate in it's environment. This is simply because it's environment is more limited, and thus less complex. The various species of plants do, as a whole, manifest a kind of collective free will by trial and error in "deciding" where to grow. This is because the species, on the whole, matches the complexity of a larger-scale environment while a single plant matches the complexity of the local-scale environment, which is less complex. In this way, evergreens "choose" to live in high latitudes rather than in the tropics, while palm trees make the opposite choice.
The fact that we are more complex than our surrounding environment can be seen in two ways that I described in the posting "True And False, Words And Numbers", on this blog. Because the surrounding environment cannot match our complexity, we see "truth possibilities". Some of these truth possibilities turn out to be true, others to be false. If we were equal in complexity to the environment in which we live, there would be no truth possibilities because everything that we could conceive of would have to be true. Thus, free will would be meaningless and unnecessary.
Likewise, there is not enough complexity in the sorrounding environment for everything that we could conceive of to exist. This is why we use both words and numbers to communicate. If we were equal in complexity to our environment, words to differentiate what actually exists from what could possibly exist but doesn't would be unnecessary because everything could be described with numbers. The difference between words and numbers is that numbers are continuous, but words aren't. That is why there are new words as time goes on, but no new numbers.
Let's add another manifestation of the difference in the level of complexity between us and our natural environment. Life is about dealing with two levels of complexity and the dynamic tension between the two. The result is the opposites that we refer to as construction and destruction. Construction is to make something, destruction is to destroy it. Construction represents the higher level of our complexity while destruction represents the lower complexity level of the natural environment.
When we make or build something from materials which are available in the sorrounding environment, we are imparting our level of complexity onto that of the environment. The skills involved in making and using something is part of the complexity imparted onto it.
When the thing that we have made is destroyed, it is returning to it's former level of complexity. Of course, it is true that complexity can never be lost or destroyed at a universal level. On our level, involving complexity that is meaningful to us, the object would have returned to the complexity of the natural environment.
It is clear that birth is construction, while death represents destruction by a returning of the atoms of the body to their former level of complexity in the natural environment. If our complexity was the same, or less, than that of the natural environment, there would be no such thing as technology. We could never learn anything because we could never conceive of anything that was not true. This means that free will would be unnecessary and of no use, and we would logically live like plants.
Complexity is the level of information that is stored within some system, in how the system is put together and how it operates. There are two fundamental levels of complexity on earth, that of living things with free will and that of the surrounding environment. We saw how plants, while being far more intricate than the surrounding environment, are no more complex overall than that environment. This is why plants, while living things, do not require the free will that other living beings have.
For our purposes here, I define a plant as a living thing with no free will and without getting into the biology of whether mushrooms, fungus and, lichens are technically plants.
A living thing must have some type of separation from the surrounding environment, such as skin or cell walls, and cannot be less complex than the sum total of the surrounding environment. The most efficient living thing will be greater in intricacy, which is the concentration of complexity, but equal in complexity to that of it's surrounding environment. This is why plants comprise by far the vast majority of living things on earth, above that of single cells.
(By the way, this is also a creation issue that I covered on the blog about creation. It simply does not make sense for plant life to evolve into animals when plants are by far the most efficient of the two).
A living thing that is more complex than the surrounding environment will see truth possibilities that cannot all be true, because there will not be enough complexity for all to be true, so it will have to have the free will necessary to decide which are true and which are not. Having free will makes no sense unless the living thing also has senses to receive information, as well as the ability to move and possibly to move things. There must be more than one way of doing things for free will to make sense. It is easy to see that complexity in living things is very high-maintenance.
A living thing that is much more complex than the surrounding environment will have more capacity to learn about that environment, but will also have a greater capacity to make mistakes because a higher proportion of the truth possibilities that it sees will have to be false simply because there is not enough complexity available in the environment for all to be true.
The two basic levels of complexity on earth, the higher level of beings with free will and the lower level of the surrounding environment are manifested in another way, as construction and destruction. When we impose our complexity on the surrounding environment in some way, we engage in construction by adding information to it so that it is brought closer to our level of complexity. When that complexity is effectively eliminated in some way, it results in the process of destruction by bringing the environment back to it's effective original level of complexity.
So much about life-truth possibilities, use of words, health, aging, diet and, labor (labour) result from the difference in complexity between ourselves and the surrounding environment. The purpose of all work is to bridge this complexity gap.
I have established how work and complexity is interchangeable, meaning that they must be the same thing. We can make life easier for us, primarily through technology and organization, but only at the expense of making it more complex. Labor (labour) is required of any being that is more complex than their environment, but none is required of plants because they are equal in complexity (although far greater in intricacy) than the surrounding environment.
In the environment of inanimate matter, there is quantity but not quality. Quality make sense only for living things. In geometric terms, quantity is simply a slope or a straight line. But quality shows as a peak formed by more than one line because it is more complex than simple quantity. Plants are not more complex than the sum total of their environments, but manifest this peak pattern due to their greater intricacy. This peak of quality is the optimum living conditions of living things. I defined life, on the patterns and complexity blog, as a manifestation of this peak factor which is not found in inanimate matter.
Organization is information, and thus complexity. Whenever we organize elements of the environment around us, we bring it closer to our own complexity level in order to approach our peak of quality. A less complex being, relative to the surrounding environment, would organize less while a more complex being would organize more. We can see this in how much of the organization that we impose on the environment is meaningless to animals and insects.
If we could bring the complexity level of the surrounding environment up to our level, by construction and organization, there would be no more truth possibilities that would not be true and thus no more need for more knowledge. This is theoretically impossible, because to do so we would have to be "smarter than ourselves", but it means that we can define paradise in terms of complexity as bringing the surrounding environment up to our level of complexity by construction and organization so that we can effectively live like plants, with no need for work or benefit from more knowledge.
We have seen that the primary pattern that defines living things, in contrast to inanimate matter, is the peak. A peak is manifested in any situation where there can be either too much or too little of something. The optimum amount is at the peak.
A few obvious examples, with regard to human beings, is food, sleep and, temperature, and also the balance between work and relaxation. This pattern has no meaning in the universe of inanimate matter. In fact, I regard this as the very definition of life as described in "The Definition of Life" on this blog.
Progress, the moving forward of civilization in improvement, can be readily expressed in terms of complexity as a bringing of our surrounding environment, which is at a lower level of complexity than we are, up to our level of complexity.
This complexity, of either ourselves or our native environment, is simply the information contained within it as to how it came to be and how it operates. All death and destruction can also be expressed in terms of complexity, simply as a reverting back to the lower level of the surrounding environment.
In imposing our complexity on the surrounding environment during progress, it must be remembered that we are dependent on this environment. Imposing our complexity must take the nature of our complexity into account. Progress forms a peak and the peak of progress is neither too much or too little.
For example, imposing our complexity on a tree does not necessarily mean that it's wood will be carved into something complex but possibly that it will be arranged so that it is in the most desirable location in the larger scheme of society.
As explained previously, the fact that we are more complex than our surrounding environment brings about truth possibilities. As we look at our environment, there is not enough complexity available for everything that we can conceive of to be true. This opens the possibility that we could believe some things to be true that are, in fact, false or, we may believe some things to be false that are actually true.
In other words, this disparity in complexity means that we can make mistakes. If we were of the same or lesser complexity than our surrounding environment, we could not even conceive of anything that was not true in our surrounding environment and so this would not be an issue. This is where the learning comes in which is necessary to progress, finding out just what is true and false in our surroundings.
We do work or labor (labour) to bring our surroundings up to our level of complexity in order to make progress. We usually define progress as having the maximum of what we want being achieved with the minimum of work. My theory is that when a being of a given level of complexity succeeds in completely imposing it's complexity on it's surrounding environment then labour (labor) will no longer be necessary.
In my complexity theory, plants are equal in complexity to the surrounding environment although they are far greater in intricacy (defined as the concentration of complexity or complexity per unit of matter or given). This is why plants have no need to do any work, all that they require comes right to them.
There are two broad types of labor (labour) that we do, physical and mental. These represent the two different levels of complexity that we are dealing with. If there could be pure physical labour (labor), with no mental component at all, it would be solely of the lower level of complexity of the surrounding environment.
(Let's just alternate the two global spellings of labor and Labour).
I define the difference in the two complexity levels, ours and that of the surrounding environment, as experienced by us while seeking progress to be: total labor = physical labour x mental labour. The total labor required must always remain constant, but as we make progress the mental labour increases as the physical labor diminishes.
This is actually another way of stating my doctrine that we can make life physically easier by use of technology, but only at the expense of making it more complex. We can never, on a large scale, make life both physically easier and simpler.
The real basis of progress is that mental labor can be replicated, while pure physical labour cannot. We can replicate physical labor using machines, but the design of those machines is mental labour. Someone doing the physical labor of planting his crops does not plant the crops of others as well, but someone figuring out how to plant crops figures it out for others as well.
Technology begins with tools, which are synthetic extensions of ourselves and our senses. Tools are the result of using mental labor to make physical labour easier and more efficient. Machines are a kind of complex tool that attempts to replicate physical labor.
Just as machines are complex tools, and a step upward from tools, computer technology is a step upward from writing. Written words can be described as tools to store and replicate information. Computer technology is a step upward from this, and is a kind of complex book which replicates skill rather than just information. Instruction naturally flows from highest to lowest technology, you still have to tell a computer what to do because it is less complex than you.
But everything that we do while making progress must ultimately bear the imprint of the surrounding environment in which we exist. Our universe is one of spatial dimensions that pervade everything about us. We can look at progress, then, in terms of dimensions. One dimensional tools can be combined into multi-dimensional machines. One dimensional books can have their information combined into multi-dimensional computer technology.
Complexity And Cosmology
COMPLEXITY AND COSMOLOGY
I wonder what we might be able to tell about the Big Bang, the tremendous explosion which began the universe as we know it, just by looking at the universe as it is. I am also near-obsessed with the concept of complexity, and the possibility of quantifying it. But, it seems that we do not do well at even defining complexity.
I have defined complexity as the total number of levels manifested by a given system. The complexity of any system is not the same thing as the definition of the boundaries of that system. This is because complexity can be defined as the sum total of all factors that may affect the system, in other words the amount of information within the system.
These factors may be either inside or outside the boundaries of the system. As an example, a party held outdoors is more complex than one held indoors because the one outdoors may be affected by rain, even though the weather is not actually an element of the party.
If we are dealing with man-made machines, the boundaries of a system include a definition of what it will be used for. The operation of a refrigerator may be affected if it was taken into outer space with no air and zero gravity. But since it is highly unlikely that the buyers of a new refrigerator intend to take it into outer space, this can be safely excluded when setting the defintition of the system that is the refrigerator.
When considering the factors which may affect a given system, and thus affect it's complexity, we must remember that a factor will only affect the complexity of a system if it changes the total number of levels within that system, but not if it changes what those levels are.
The number of different permutations of the elements of a system which we define may or may not be the number of levels in the system, and thus the complexity of the system. It depends on the relationships between the elements of the system. If the elements of the system are independent of one another, as the planets of the Solar System essentially are, then the complexity is equal to the number of elements. This could be referred to as a "loose" system.
If the planets were closer together, so that the position of a planet was significantly affected by the gravity of the other planets as they orbited the sun at different rates, then the relationship of each planet to each other planet would also be elements of the total system. This could be referred to as a "tight" system and would be much more complex than the loose system. But the complexity is always the sum of information within the system.
I wonder what we might be able to tell about the Big Bang, the tremendous explosion which began the universe as we know it, just by looking at the universe as it is. I am also near-obsessed with the concept of complexity, and the possibility of quantifying it. But, it seems that we do not do well at even defining complexity.
DEFINING COMPLEXITY
I have defined complexity as the total number of levels manifested by a given system. The complexity of any system is not the same thing as the definition of the boundaries of that system. This is because complexity can be defined as the sum total of all factors that may affect the system, in other words the amount of information within the system.
These factors may be either inside or outside the boundaries of the system. As an example, a party held outdoors is more complex than one held indoors because the one outdoors may be affected by rain, even though the weather is not actually an element of the party.
If we are dealing with man-made machines, the boundaries of a system include a definition of what it will be used for. The operation of a refrigerator may be affected if it was taken into outer space with no air and zero gravity. But since it is highly unlikely that the buyers of a new refrigerator intend to take it into outer space, this can be safely excluded when setting the defintition of the system that is the refrigerator.
When considering the factors which may affect a given system, and thus affect it's complexity, we must remember that a factor will only affect the complexity of a system if it changes the total number of levels within that system, but not if it changes what those levels are.
The number of different permutations of the elements of a system which we define may or may not be the number of levels in the system, and thus the complexity of the system. It depends on the relationships between the elements of the system. If the elements of the system are independent of one another, as the planets of the Solar System essentially are, then the complexity is equal to the number of elements. This could be referred to as a "loose" system.
If the planets were closer together, so that the position of a planet was significantly affected by the gravity of the other planets as they orbited the sun at different rates, then the relationship of each planet to each other planet would also be elements of the total system. This could be referred to as a "tight" system and would be much more complex than the loose system. But the complexity is always the sum of information within the system.
THE UNIVERSE IN TERMS OF COMPLEXITY
I find that the concept of complexity, which I would really like us to begin expressing in quantitative terms, sheds valuable new light on the structure of the universe. This will form a link between my complexity theory and my cosmological theory, as described on my cosmology blog.
Let's consider the conservation of complexity, which I described in the posting "Complexity, Patterns And, Energy". We saw there how complexity is like energy in that it cannot be created or destroyed, but only changed in form.
This can only mean that the complexity of the entire universe, and of the many individual systems within the universe cannot exceed the complexity of the Big Bang, meaning the information within it, which began the universe.
Have you ever noticed that all of the fundamental organizational units of the universe; atoms, molecules, stars, solar systems, galaxies and, galactic groups all have roughly the same, relatively low, level of complexity? This does not, however, include living things on earth, which I believe to be the special creation of God.
We must remember that the number of elements in such a system does not affect this universal complexity. Two identical systems are not twice as complex as one such system, but only slightly more complex and this also goes for multiple identical systems. This means that a plutonium atom is only marginally more complex than a helium atom.
There can be repetition of complexity without violating the law of conservation of complexity, but there cannot be interrelationships which would require more complexity because there is only so much information available. This level of complexity, which is found in all of the basic units of the inanimate matter of the universe, is a reflection of the complexity of the Big Bang, which got everything started.
Atoms are the first structural building block of matter in the universe. Stars and planets are the second and, galaxies are the third. Molecules, solar systems and, galactic groups can be considered as three secondary structural elements associated with the primary elements. All have a similar, and relatively low, level of complexity because this repetition of structure lessens complexity and there is only the limited amount of information from the Big Bang available. Complex molecules are synthesized by living things and are not really complex in that they are multiple repetitions of a basic pattern.
What can this level of complexity be except a reflection of the complexity level of the Big Bang?
Boundaries must be maintained between the basic fundamental units of structure in the universe. The positions of electrons in the individual atoms in stars cannot affect the large-scale operation of the star. The internal processes of the star cannot affect the orbits of the planets around the star.
There cannot be a permanent, complex solar system in which all of the planets affect each others' orbits. Moons around planets cannot affect the other planets and their moons. Positions of individual planets in solar systems cannot affect the arrangements of stars or the rotation of the entire galaxy. The rotational positions of individual galaxies in a galactic group cannot affect the movement of the entire group.
If any of the above took place, it would make those systems more complex and so violate the conservation of complexity. The numerical ratios that comprise the structures of the universe, such as how many atoms it requires to make a star and how many stars to make a galaxy, are as they are to avoid violating the conservation of complexity because there is only so much information available. Distances in space are also set to maintain this necessary separation of matter structural elements, in order to keep a limit on the resulting complexity.
(Note-concerning the relative sizes of planets and stars, you might like to read "The Chemical-Nuclear-Astronomical Relationship" on my physics and astronomy blog, http://www.markmeekphysics.blogspot.com/ ).
The extreme complexity of living things is far greater than any of these universal structual elements and does not come remotely close to fitting into this pattern. I say that this complexity of living things must therefore have been introduced from outside the universe, namely by God. The things made by human beings are also highly complex because they are a reflection of the complexity in our brains.
The number of dimensions affects complexity, two dimensions are twice as complex as one. The conventional model of the Big Bang, a simple and sudden explosion, is not complex enough to account for the structures of atoms, molecules, stars, solar systems, galaxies and, galactic groups.
This can only mean that there must be more to the Big Bang, in more than the three spatial dimensions that we can see. My model of the two-dimensional sheet of orphan space folding until the dimensional bonds in one of it's dimensions disintegrated, leaving strings of matter arcoss the universe, gives us just about the right amount of complexity necessary to account for the primary structural elements of matter in the universe today.
Can you see how useful this concept of measuring complexity is? For one thing, it has given us a new way of looking at the fundamental structure of the universe.
Body Temperature And Complexity
The human body is an extraordinarily complex system which operates down to the level of atoms and molecules. It is unlike anything else that we know in it's sheer complexity. We cannot even conceive of how complex the human brain is because we are processing the information with our own brains and to do that, we would have to be smarter than ourselves, which is impossible.
Today, I would like to use the body as an example of how an extremely complex system involving the peak pattern, as described on this blog, will manifest a sharper peak than a less complex system. This means that one way to get a measurement of the complexity of a system involving a peak pattern is the sharpness of the peak.
One prominent fact about the body is it's strict operating temperature, 98.6 degrees Fahrenheit or 37 degrees Celsius. This is unlike any other machine or system known to us. All warm-blooded creatures have a narrow operating temperature, cold-blooded life forms like insects and snakes are sluggish at cold temperatures.
I have explained that gaining the ability to measure complexity will require us to come up with some creative ways of measuring. As one example, it seemed to me that we could get a good idea of the complexity of the human body by the number of diseases and ailments by which it could possibly be afflicted.
My logic was that the more complex a system or operation is, relative to the surrounding inanimate environment, the more the possible things that can go wrong with it. Thus, the total number of diseases and ailments, and their variations, in a medical textbook, from the flu to cystic fibrosis, becomes an effective measurement of the complexity of the body and brain.
Now, let's have a look at how the strict and narrow operating temperature range of the body is another tool by which it's complexity might be measured. Heat is the kinetic energy of moving atoms and molecules within an object or environment. The atoms and molecules continuously collide with one another and, in doing so, impart and take energy from each other.
Imagine two baseball or cricket players standing opposite one another in a school hallway, on opposite sides of the hallway. The two are trying to perform a difficult stunt consisting of each throwing a ball at the same instant in the same direction down the hallway. The object is to have each ball bounce off the floor once and then collide with the other ball in the air in the middle of the hallway. The balls will then bounce off one another and impact the walls of the hallway at the same height off the floor and exactly opposite each other.
The stunt would be extremely difficult to achieve. It would require endless practice (practise) and would be worthy of Youtube fame if it succeeded. This scenario is so difficult because a ball can travel at any speed and the speed of both balls would have to be exactly equal to bring this about.
But suppose that the laws of physics were different so that a ball could travel at only one possible speed. Then this stunt would be much easier to achieve.
Let's go back to moving atoms. Heat is actually the velocity of the moving atoms and molecules but it is much easier for us to measure the general level of kinetic energy present and express is as temperature than to measure the velocities of individual atoms.
Suppose that we had a vast number of atoms and molecules that were part of a very complex system. In the system, the atoms and molecules must interact with great precision. They continuously collide and bounce off one another.
Such a very complex system involving moving things like this would be far more simple if the atoms and molecules all move at the same speed. This is why the human body has such a finely-defined operating temperature. Just imagine how much more complex and how much more difficult the operation of the body would be if the participating atoms and molecules were moving at different speeds.
Since the benefit of maintaining a carefully-controlled temperature is proportional to the complexity of the body, the sharpness of the acceptable temperature range is an effective measurement it's complexity. The optimum operating temperature is the top of the peak pattern that is manifested.
Today, I would like to use the body as an example of how an extremely complex system involving the peak pattern, as described on this blog, will manifest a sharper peak than a less complex system. This means that one way to get a measurement of the complexity of a system involving a peak pattern is the sharpness of the peak.
One prominent fact about the body is it's strict operating temperature, 98.6 degrees Fahrenheit or 37 degrees Celsius. This is unlike any other machine or system known to us. All warm-blooded creatures have a narrow operating temperature, cold-blooded life forms like insects and snakes are sluggish at cold temperatures.
I have explained that gaining the ability to measure complexity will require us to come up with some creative ways of measuring. As one example, it seemed to me that we could get a good idea of the complexity of the human body by the number of diseases and ailments by which it could possibly be afflicted.
My logic was that the more complex a system or operation is, relative to the surrounding inanimate environment, the more the possible things that can go wrong with it. Thus, the total number of diseases and ailments, and their variations, in a medical textbook, from the flu to cystic fibrosis, becomes an effective measurement of the complexity of the body and brain.
Now, let's have a look at how the strict and narrow operating temperature range of the body is another tool by which it's complexity might be measured. Heat is the kinetic energy of moving atoms and molecules within an object or environment. The atoms and molecules continuously collide with one another and, in doing so, impart and take energy from each other.
Imagine two baseball or cricket players standing opposite one another in a school hallway, on opposite sides of the hallway. The two are trying to perform a difficult stunt consisting of each throwing a ball at the same instant in the same direction down the hallway. The object is to have each ball bounce off the floor once and then collide with the other ball in the air in the middle of the hallway. The balls will then bounce off one another and impact the walls of the hallway at the same height off the floor and exactly opposite each other.
The stunt would be extremely difficult to achieve. It would require endless practice (practise) and would be worthy of Youtube fame if it succeeded. This scenario is so difficult because a ball can travel at any speed and the speed of both balls would have to be exactly equal to bring this about.
But suppose that the laws of physics were different so that a ball could travel at only one possible speed. Then this stunt would be much easier to achieve.
Let's go back to moving atoms. Heat is actually the velocity of the moving atoms and molecules but it is much easier for us to measure the general level of kinetic energy present and express is as temperature than to measure the velocities of individual atoms.
Suppose that we had a vast number of atoms and molecules that were part of a very complex system. In the system, the atoms and molecules must interact with great precision. They continuously collide and bounce off one another.
Such a very complex system involving moving things like this would be far more simple if the atoms and molecules all move at the same speed. This is why the human body has such a finely-defined operating temperature. Just imagine how much more complex and how much more difficult the operation of the body would be if the participating atoms and molecules were moving at different speeds.
Since the benefit of maintaining a carefully-controlled temperature is proportional to the complexity of the body, the sharpness of the acceptable temperature range is an effective measurement it's complexity. The optimum operating temperature is the top of the peak pattern that is manifested.
Coincidences And Complexity
I have developed a method for measuring the complexity in very complex systems. This method is based on what we refer to as "coincidences".
We are all familiar with coincidences. Suppose that a five-dollar bill or a five-pound note caught your attention because it's serial number was exactly the same as your phone number. That would indeed be a coincidence.
Coincidences, of course, vary in magnitude. Suppose you were in a small town on the day that there was a market in the town. You happened to pass a certain person as you were shopping in the market. On your way home, you stop at a store in the town to get something that was not available in the market and you happen to encounter the same person again by random chance. This would be a coincidence.
Now suppose you were in a big city. You went to the other side of the city to shop at a market and you passed a certain person in the market. On your way home, far away from the market, you stopped at a store and encountered the same person again. This would not only be a coincidence but a far greater coincidence than the one that occurred in the small town.
The reason it would be a greater coincidence is that the chances of it happening in the big city would be much slimmer than in the small town. Of course, for this to be so, it must be a genuine coincidence and cannot be encounters between two people travelling on the same bus or where one is following another.
One reason that complexity is so tricky to measure is that we often do not see a system in it's real complexity. That is, there may be a difference between actual complexity and apparent complexity. The way that complexity is related to coincidence is that a coincidence can be defined as a random reduction in apparent complexity. When you experience the coincidence of meeting the same person in the city or town, the "system" (the city or town) is made to seem as if it were much smaller, in other words much less complex, than it really is.
Suppose you are calling for tech support or some kind of customer service to a call center that has a hundred operators, but you do not know that. If you by a one-in-a-hundred chance got the same operator twice, it would be a coincidence and would make it seem that the call center must be much smaller, less complex, than it really is. Such a coincidence would thus be described as a random reduction in apparent complexity.
This means that there is also such a thing as a "reverse coincidence". If you had a company that called the call center a hundred times and just by random chance got a different operator on each call, it would seem like there would have to be many thousands of operators there, making the call center seem much bigger, more complex, than it really is.
I have noticed something about coincidences. If we were to make a given type of system much more complex, the average number of coincidences will remain the same but will be greater in magnitude.
Suppose that the residents of a small town go out and randomly select ten names from their town and the residents of a big city do the same. The average number of people in the town and the city that selected each other will average out the same. This is because each person in the city has much less chance of being in such a coincidence than each person in the town, but this is cancelled out because there are so many more people in the city than in the town.
I should point out that not all complex systems have coincidences. For example, in a car engine there is nothing that we could easily measure that could be termed a coincidence. But in the more complex systems, such as the flow of money in an economy, there are measurable coincidences. A person could get the same bill with the same serial number twice by random chance.
Let's term those complex systems which we may wish to measure but do not manifest measurable coincidences "closed" or "integrated" complex systems. Let's term those systems which do manifest coincidences that we can measure "open" or "non-integrated" complex systems.
The good news is that closed complex systems tend to be simpler and easier to measure by other means, as I described in my other postings on this subject. Closed complex systems will tend to be man-made machines. In the world of coincidences, we could say that one is actually zero since there is no coincidence until the same unit is encountered twice.
The great thing about this coincidence method is that numbers of observed coincidences can give us a lot of information about a complex system without us knowing the size or all of the details about the overall system. In a perfectly fluid system, the size of the system can be estimated by the coincidence rate multiplied by the size of the control group.
An example of perfect fluidity would be a unit of currency in an economy flowing equally through all areas of the country. Think of all that could be discerned about a country's economic system, for example, if a given number of observers (the control group) recorded the serial numbers of all the given monetary units that passed through their possession during normal activity in the course of a year.
The total number of recordings in each geographical area would be recorded and then all the serial numbers that occurred only once would be discarded. The remaining data of coincidences, those numbers occurring two or more times, would tell us a vast amount about the complexity and operation of the economy that would be very difficult to learn any other way.
The first thing to do to measure the complexity of any given system is to find one or more types of coincidence that take place and then measure those coincidences. This will enable us to put an exact measure on the most complex of systems and can be done with incomplete knowledge of the system. Using this method, we can use the random reductions in the apparent complexity of a complex system, that we refer to as coincidences, to measure the actual complexity of the system.
You have probably heard of the Guinness Book of World Records. You can read more about it on Wikipedia if you like. It is a book of records which is revised yearly. The book contains hundreds of categories of world records such as the longest-lived person, the tallest and, who could eat the most chocolate cakes.
I have thought of a record which anyone could possibly break at any time, without even trying. Unfortunately, this record is not categorized in the book as of yet. But maybe someday it could be.
Coincidence involves the set of all potential results in comparison with those results which actually do happen. If the actual results make the set of all potential results appear to be less than it actually is, we have a coincidence. If more than it actually is, we have a reverse coincidence.
Coincidence involves a valley of odds between two hills of higher odds on either side. One hill represents coincidence, the other represents reverse coincidence. We distribute points, representing every event that happens. Odds are that each point will fall in the valley, but some happen to fall on the coincidence hill and some on the reverse coincidence hill.
An obvious example of a great coincidence would be the same person winning a lottery twice. Minor coincidences and reverse coincidences happen to us all of the time, but that is not what we are concerned with here. I think that the ultimate world record would be the greatest coincidence ever.
At this point, we are not really capable of measuring coincidences other than subjectively. We must carefully define the system involved, since all coincidences happen within some system. Two neighbors meeting, by chance, on the opposite side of the city would be considered as a coincidence. But it is much less of a coincidence if they rode there on the same bus or were there for the same reason. The scale of a coincidence is equivalent to the size of the system in which it takes place.
I define coincidence as a random reduction in apparent complexity. But this definition says that coincidences do not really exist in absolute reality. In the entire universe as a whole, there is actually no such thing as a coincidence, everything has a definite cause and effect.
"Random" and "apparent" are words associated with our perspective. There appear to be coincidences in systems that we define because we do not have complete information and our system is not as definite as we think it is. Coincidences are related to chaos, of which there is really no such thing. The occurrence of coincidences and reverse coincidences can only mean that we have incomplete understanding of the systems involved. Of course, due to our incomplete understanding, there are many "coincidences" that we are unaware of.
Coincidences are a manifestation of complexity. To be able to measure coincidences, which will reveal a lot about the operation of the reality around us, we must first be able to measure complexity. A the present time we are unable to measure complexity, except to describe it in general subjective terms, so we cannot actually measure coincidences.
This is unfortunate because the world gets more complex every day in terms of communications, interconnections and, population. Anyone could become a part of the greatest coincidence ever simply by going about their ordinary daily business.
Suppose you were at an amusement park as a child, standing in line to go on a ride. There is an odd number of people in your group and the group in front of yours also has an odd number of people, so that you end up sitting in the ride with a child you do not know.
Years later, in your twenties, you order a book to be mailed to you. Although you are both unaware of it, the person who packs your book order is the child who was once on the amusement park ride with you.
Years after that, while you are in your forties, you are driving across the country and you find yourself in a minor traffic accident. Although either of you have no way of knowing it, the driver of the other car is the neice of the child that you were on the ride with and the one who packed your book order years before.
Such is what we could call a "multiple coincidence", a random reduction in the apparent complexity of the world we live in.
Just imagine the possibilities if we could measure complexity, as I am trying to get us doing on my patterns blog, and thus coincidences. There would be a world record category for the greatest coincidence ever documented, and verified to have happened beyond the control of those involved. There could be a "Book of Coincidences".
Even if we could effectively measure coincidences, there would still likely be some subjectivity involved because some coincidences will surely be more important to us than others, regardless of the actual magnitude.
We are all familiar with coincidences. Suppose that a five-dollar bill or a five-pound note caught your attention because it's serial number was exactly the same as your phone number. That would indeed be a coincidence.
Coincidences, of course, vary in magnitude. Suppose you were in a small town on the day that there was a market in the town. You happened to pass a certain person as you were shopping in the market. On your way home, you stop at a store in the town to get something that was not available in the market and you happen to encounter the same person again by random chance. This would be a coincidence.
Now suppose you were in a big city. You went to the other side of the city to shop at a market and you passed a certain person in the market. On your way home, far away from the market, you stopped at a store and encountered the same person again. This would not only be a coincidence but a far greater coincidence than the one that occurred in the small town.
The reason it would be a greater coincidence is that the chances of it happening in the big city would be much slimmer than in the small town. Of course, for this to be so, it must be a genuine coincidence and cannot be encounters between two people travelling on the same bus or where one is following another.
One reason that complexity is so tricky to measure is that we often do not see a system in it's real complexity. That is, there may be a difference between actual complexity and apparent complexity. The way that complexity is related to coincidence is that a coincidence can be defined as a random reduction in apparent complexity. When you experience the coincidence of meeting the same person in the city or town, the "system" (the city or town) is made to seem as if it were much smaller, in other words much less complex, than it really is.
Suppose you are calling for tech support or some kind of customer service to a call center that has a hundred operators, but you do not know that. If you by a one-in-a-hundred chance got the same operator twice, it would be a coincidence and would make it seem that the call center must be much smaller, less complex, than it really is. Such a coincidence would thus be described as a random reduction in apparent complexity.
This means that there is also such a thing as a "reverse coincidence". If you had a company that called the call center a hundred times and just by random chance got a different operator on each call, it would seem like there would have to be many thousands of operators there, making the call center seem much bigger, more complex, than it really is.
I have noticed something about coincidences. If we were to make a given type of system much more complex, the average number of coincidences will remain the same but will be greater in magnitude.
Suppose that the residents of a small town go out and randomly select ten names from their town and the residents of a big city do the same. The average number of people in the town and the city that selected each other will average out the same. This is because each person in the city has much less chance of being in such a coincidence than each person in the town, but this is cancelled out because there are so many more people in the city than in the town.
I should point out that not all complex systems have coincidences. For example, in a car engine there is nothing that we could easily measure that could be termed a coincidence. But in the more complex systems, such as the flow of money in an economy, there are measurable coincidences. A person could get the same bill with the same serial number twice by random chance.
Let's term those complex systems which we may wish to measure but do not manifest measurable coincidences "closed" or "integrated" complex systems. Let's term those systems which do manifest coincidences that we can measure "open" or "non-integrated" complex systems.
The good news is that closed complex systems tend to be simpler and easier to measure by other means, as I described in my other postings on this subject. Closed complex systems will tend to be man-made machines. In the world of coincidences, we could say that one is actually zero since there is no coincidence until the same unit is encountered twice.
The great thing about this coincidence method is that numbers of observed coincidences can give us a lot of information about a complex system without us knowing the size or all of the details about the overall system. In a perfectly fluid system, the size of the system can be estimated by the coincidence rate multiplied by the size of the control group.
An example of perfect fluidity would be a unit of currency in an economy flowing equally through all areas of the country. Think of all that could be discerned about a country's economic system, for example, if a given number of observers (the control group) recorded the serial numbers of all the given monetary units that passed through their possession during normal activity in the course of a year.
The total number of recordings in each geographical area would be recorded and then all the serial numbers that occurred only once would be discarded. The remaining data of coincidences, those numbers occurring two or more times, would tell us a vast amount about the complexity and operation of the economy that would be very difficult to learn any other way.
The first thing to do to measure the complexity of any given system is to find one or more types of coincidence that take place and then measure those coincidences. This will enable us to put an exact measure on the most complex of systems and can be done with incomplete knowledge of the system. Using this method, we can use the random reductions in the apparent complexity of a complex system, that we refer to as coincidences, to measure the actual complexity of the system.
You have probably heard of the Guinness Book of World Records. You can read more about it on Wikipedia if you like. It is a book of records which is revised yearly. The book contains hundreds of categories of world records such as the longest-lived person, the tallest and, who could eat the most chocolate cakes.
I have thought of a record which anyone could possibly break at any time, without even trying. Unfortunately, this record is not categorized in the book as of yet. But maybe someday it could be.
Coincidence involves the set of all potential results in comparison with those results which actually do happen. If the actual results make the set of all potential results appear to be less than it actually is, we have a coincidence. If more than it actually is, we have a reverse coincidence.
Coincidence involves a valley of odds between two hills of higher odds on either side. One hill represents coincidence, the other represents reverse coincidence. We distribute points, representing every event that happens. Odds are that each point will fall in the valley, but some happen to fall on the coincidence hill and some on the reverse coincidence hill.
An obvious example of a great coincidence would be the same person winning a lottery twice. Minor coincidences and reverse coincidences happen to us all of the time, but that is not what we are concerned with here. I think that the ultimate world record would be the greatest coincidence ever.
At this point, we are not really capable of measuring coincidences other than subjectively. We must carefully define the system involved, since all coincidences happen within some system. Two neighbors meeting, by chance, on the opposite side of the city would be considered as a coincidence. But it is much less of a coincidence if they rode there on the same bus or were there for the same reason. The scale of a coincidence is equivalent to the size of the system in which it takes place.
I define coincidence as a random reduction in apparent complexity. But this definition says that coincidences do not really exist in absolute reality. In the entire universe as a whole, there is actually no such thing as a coincidence, everything has a definite cause and effect.
"Random" and "apparent" are words associated with our perspective. There appear to be coincidences in systems that we define because we do not have complete information and our system is not as definite as we think it is. Coincidences are related to chaos, of which there is really no such thing. The occurrence of coincidences and reverse coincidences can only mean that we have incomplete understanding of the systems involved. Of course, due to our incomplete understanding, there are many "coincidences" that we are unaware of.
Coincidences are a manifestation of complexity. To be able to measure coincidences, which will reveal a lot about the operation of the reality around us, we must first be able to measure complexity. A the present time we are unable to measure complexity, except to describe it in general subjective terms, so we cannot actually measure coincidences.
This is unfortunate because the world gets more complex every day in terms of communications, interconnections and, population. Anyone could become a part of the greatest coincidence ever simply by going about their ordinary daily business.
Suppose you were at an amusement park as a child, standing in line to go on a ride. There is an odd number of people in your group and the group in front of yours also has an odd number of people, so that you end up sitting in the ride with a child you do not know.
Years later, in your twenties, you order a book to be mailed to you. Although you are both unaware of it, the person who packs your book order is the child who was once on the amusement park ride with you.
Years after that, while you are in your forties, you are driving across the country and you find yourself in a minor traffic accident. Although either of you have no way of knowing it, the driver of the other car is the neice of the child that you were on the ride with and the one who packed your book order years before.
Such is what we could call a "multiple coincidence", a random reduction in the apparent complexity of the world we live in.
Just imagine the possibilities if we could measure complexity, as I am trying to get us doing on my patterns blog, and thus coincidences. There would be a world record category for the greatest coincidence ever documented, and verified to have happened beyond the control of those involved. There could be a "Book of Coincidences".
Even if we could effectively measure coincidences, there would still likely be some subjectivity involved because some coincidences will surely be more important to us than others, regardless of the actual magnitude.
Opposites And Complexity
Today, I have something that I think is really profound. I have been giving some thought to the nature of opposites. I mean things which are opposite from one another, like night and day. My conclusion is that opposition, or the concept of opposites, could be a powerful tool for measuring complexity and also reveals much about what we have to learn about the nature of the universe.
Opposites are not something to which most people usually give much thought. So, let's do a quick review of what opposites are. We often confuse opposites and pairs. Day and night, male and female, matter and antimatter, salt and pepper. The most fundamental opposite is, of course, negative and positive electric charges.
These are opposites, but they are also pairs. My definition is that pairs are the simplest and most fundamental type of opposite. We will deal mainly with more complex opposites here.
The true definition of a set of opposites involves the reflection of a mirror. When you look in a mirror, you see yourself as you really look with the exception that your left side is the right side of your mirror image, and vice versa. In other words, you and your mirror image are opposites.
Opposition, in my definition, does not mean completely different. Opposition is actually a relationship between two entities. They are not unrelated at all, but are the reverse permutations of the same thing.
Two things that have absolutely nothing to do with each other are not opposites. Consider the following statement: "Mangoes are the opposite of lacrosse". It just sounds nonsensical because the two have nothing to do with each other. Mangoes are tropical fruit, while lacrosse is a native American Indian sport.
To be a meaningful concept, opposition must be concise. The vast majority of words in the dictionary have nothing to do with most of the other words in the dictionary. So, having nothing to do with something cannot be the defintion of opposite. Such a defintion would be so broad as to be meaningless.
Have you ever wondered if the systems of measurement that we use are failing to keep up with advances in science and technology? I have described what a tremendous benefit it would be if we were able to put a number on complexity, to quantify it, instead of describing it in the vague and subjective ways we do at present. Complexity is the total amount of information in a given system. Instead of describing something as "much more complex" or "a little bit less complex" than something else, we could be precise about it and say that this is 2.35 times as complex as that.
The reason we have not yet gotten to that point is that complexity cannot be measured in the traditional ways. It is not possible to quantify it with a ruler, a clock, a thermometer or, a voltmeter.
To get the great benefits that measurement of complexity would bring, we must come up with some creative ways of measuring it. I have already described how the complexity of a dynamic system (meaning in motion) could possibly be measured by keeping track of the coincidences that occur in the system. It is also true that is is sometimes possible to measure complexity directly, by counting the number of levels involved. If a system can be broken down into a formula, or a number of formulae, it also serves as a direct measurement of the system's complexity.
Some other ways of measuring complexity that I have thought of include the Sameness Index. We know that all people are different, but they are more the same than they are different. The Sameness Index is simply the population of the world divided by the number of entries in a comprehensive encyclopedia and dictionary, after eliminating redundancies. The total number of entries represent how different we are, but in comparison with the world's population, we might be 100 times more the same than we are different.
A creative way of measuring the complexity of the human body, in comparison with the background environment of inanimate matter, is to look at a medical library. We know that the more complex a dynamic (moving) system is, the more likely something will go wrong. So, my reasoning is that the total number of diseases, ailments and, injuries which can afflict human beings, including the variations of each, can be used as an effective measurement of the complexity of the human body.
Now, back to the concept of opposites. Opposition is a very useful concept for the measure of complexity. To undertake such a measurement, we would first define two opposites within the system to be measured. This method would be useful whether the system is static or dynamic and the opposites do not have to actually exist, as long as we can be certain of what they would be if they did exist.
The reasoning behind this opposites method is the fact that the more complex a given system is, the more different from one another will be the opposites produced within that system. So, if we can put a measurement on how different the opposites are from one another, we can effectively measure the complexity of the system. Since opposition is a mathematical concept, that should not be too difficult to do.
This concept is analogous to measuring the diameter of a circle. The opposites are represented by diametrically opposite points on the circle while the complexity of the system is represented by the size of the circle. In a simple system, a small circle, the opposites must be close together, or similar to one another. In a complex system, the opposites are far apart, or dissimilar.
Let's consider a simple example. Suppose there is a program, or other system, which generates random strings of letters. The opposite of the string "ABCD" can only be "DCBA". We know that in a simple system, a pair of opposites as defined by the system cannot be very different from one another. In this system, the two opposite strings of letters are exactly the same except that they are reverse permutations of each other. Therefore, this system is simple. It takes a complex system to produce opposites which are very different from each other.
Another simple system is a line of numbers starting at zero and proceeding as positive numbers in one direction and negative numbers in the other direction. The opposite of 241 can only be -241. The two numbers are the same except for the sign in front of them. Therefore, the system in which they are defined as opposites must be simple and it is.
As stated previously, the simplest of systems are those in which the system revolves around a pair, which are also considered as opposites. The fundamental negative and positive charges are such a simple system, as is the rotation of the earth producing night and day.
The important thing about measurement of complexity is whether the measurement proves useful. The accuracy of measurements such as these depends on the accuracy of our definition of the system itself that we are trying to measure. If we do not get this definition perfect when we deal with very complex systems, then our measurement of the complexity of the system cannot be expected to be perfect. But a wondeful thing about measurement of complexity is that it can still be very useful, without being perfect.
There are a couple of ground rules that I came up with concerning measurement of complexity using opposites. The first is that if a number is attached to an object, the number must be considered before the object. If we have 5 pies, the opposite of that would be -5 pies. We would not go into trying to determine the opposite of a pie.
Another ground rule also concerns numbers. If we have both negative and positive numbers in the system, the opposite of a positive number is a negative number. If there are no negative numbers in the system, the opposite of a number is it's reciprocal.
Now, for the part that I consider as really profound. We can see that in simple systems, every entity has an opposite, whether or not it actually exists. Since complex systems are only combinations of simple systems, that can only mean that any entity in a complex system must also have an opposite. Thus, everything in the universe has an opposite.
To determine opposition, which is a mathematical concept, we must completely understand the system. At this point, we cannot identify the opposite of a rock simply because we do not completely understand the universe. By the way, the opposite of a rock which I am referring to is not an identical rock made of antimatter. Matter and antimatter are opposites at the sub-atomic level, but there must be an opposite of a rock whether it is made of matter or antimatter.
To define what this opposite of a rock is, whether or not it actually exists, we would have to understand everything about the universe. To thoroughly understand something means to understand not just what exists, but what does not exist, meaning what could possibly exist but doesn't.
Opposites are not something to which most people usually give much thought. So, let's do a quick review of what opposites are. We often confuse opposites and pairs. Day and night, male and female, matter and antimatter, salt and pepper. The most fundamental opposite is, of course, negative and positive electric charges.
These are opposites, but they are also pairs. My definition is that pairs are the simplest and most fundamental type of opposite. We will deal mainly with more complex opposites here.
The true definition of a set of opposites involves the reflection of a mirror. When you look in a mirror, you see yourself as you really look with the exception that your left side is the right side of your mirror image, and vice versa. In other words, you and your mirror image are opposites.
Opposition, in my definition, does not mean completely different. Opposition is actually a relationship between two entities. They are not unrelated at all, but are the reverse permutations of the same thing.
Two things that have absolutely nothing to do with each other are not opposites. Consider the following statement: "Mangoes are the opposite of lacrosse". It just sounds nonsensical because the two have nothing to do with each other. Mangoes are tropical fruit, while lacrosse is a native American Indian sport.
To be a meaningful concept, opposition must be concise. The vast majority of words in the dictionary have nothing to do with most of the other words in the dictionary. So, having nothing to do with something cannot be the defintion of opposite. Such a defintion would be so broad as to be meaningless.
Have you ever wondered if the systems of measurement that we use are failing to keep up with advances in science and technology? I have described what a tremendous benefit it would be if we were able to put a number on complexity, to quantify it, instead of describing it in the vague and subjective ways we do at present. Complexity is the total amount of information in a given system. Instead of describing something as "much more complex" or "a little bit less complex" than something else, we could be precise about it and say that this is 2.35 times as complex as that.
The reason we have not yet gotten to that point is that complexity cannot be measured in the traditional ways. It is not possible to quantify it with a ruler, a clock, a thermometer or, a voltmeter.
To get the great benefits that measurement of complexity would bring, we must come up with some creative ways of measuring it. I have already described how the complexity of a dynamic system (meaning in motion) could possibly be measured by keeping track of the coincidences that occur in the system. It is also true that is is sometimes possible to measure complexity directly, by counting the number of levels involved. If a system can be broken down into a formula, or a number of formulae, it also serves as a direct measurement of the system's complexity.
Some other ways of measuring complexity that I have thought of include the Sameness Index. We know that all people are different, but they are more the same than they are different. The Sameness Index is simply the population of the world divided by the number of entries in a comprehensive encyclopedia and dictionary, after eliminating redundancies. The total number of entries represent how different we are, but in comparison with the world's population, we might be 100 times more the same than we are different.
A creative way of measuring the complexity of the human body, in comparison with the background environment of inanimate matter, is to look at a medical library. We know that the more complex a dynamic (moving) system is, the more likely something will go wrong. So, my reasoning is that the total number of diseases, ailments and, injuries which can afflict human beings, including the variations of each, can be used as an effective measurement of the complexity of the human body.
Now, back to the concept of opposites. Opposition is a very useful concept for the measure of complexity. To undertake such a measurement, we would first define two opposites within the system to be measured. This method would be useful whether the system is static or dynamic and the opposites do not have to actually exist, as long as we can be certain of what they would be if they did exist.
The reasoning behind this opposites method is the fact that the more complex a given system is, the more different from one another will be the opposites produced within that system. So, if we can put a measurement on how different the opposites are from one another, we can effectively measure the complexity of the system. Since opposition is a mathematical concept, that should not be too difficult to do.
This concept is analogous to measuring the diameter of a circle. The opposites are represented by diametrically opposite points on the circle while the complexity of the system is represented by the size of the circle. In a simple system, a small circle, the opposites must be close together, or similar to one another. In a complex system, the opposites are far apart, or dissimilar.
Let's consider a simple example. Suppose there is a program, or other system, which generates random strings of letters. The opposite of the string "ABCD" can only be "DCBA". We know that in a simple system, a pair of opposites as defined by the system cannot be very different from one another. In this system, the two opposite strings of letters are exactly the same except that they are reverse permutations of each other. Therefore, this system is simple. It takes a complex system to produce opposites which are very different from each other.
Another simple system is a line of numbers starting at zero and proceeding as positive numbers in one direction and negative numbers in the other direction. The opposite of 241 can only be -241. The two numbers are the same except for the sign in front of them. Therefore, the system in which they are defined as opposites must be simple and it is.
As stated previously, the simplest of systems are those in which the system revolves around a pair, which are also considered as opposites. The fundamental negative and positive charges are such a simple system, as is the rotation of the earth producing night and day.
The important thing about measurement of complexity is whether the measurement proves useful. The accuracy of measurements such as these depends on the accuracy of our definition of the system itself that we are trying to measure. If we do not get this definition perfect when we deal with very complex systems, then our measurement of the complexity of the system cannot be expected to be perfect. But a wondeful thing about measurement of complexity is that it can still be very useful, without being perfect.
There are a couple of ground rules that I came up with concerning measurement of complexity using opposites. The first is that if a number is attached to an object, the number must be considered before the object. If we have 5 pies, the opposite of that would be -5 pies. We would not go into trying to determine the opposite of a pie.
Another ground rule also concerns numbers. If we have both negative and positive numbers in the system, the opposite of a positive number is a negative number. If there are no negative numbers in the system, the opposite of a number is it's reciprocal.
Now, for the part that I consider as really profound. We can see that in simple systems, every entity has an opposite, whether or not it actually exists. Since complex systems are only combinations of simple systems, that can only mean that any entity in a complex system must also have an opposite. Thus, everything in the universe has an opposite.
To determine opposition, which is a mathematical concept, we must completely understand the system. At this point, we cannot identify the opposite of a rock simply because we do not completely understand the universe. By the way, the opposite of a rock which I am referring to is not an identical rock made of antimatter. Matter and antimatter are opposites at the sub-atomic level, but there must be an opposite of a rock whether it is made of matter or antimatter.
To define what this opposite of a rock is, whether or not it actually exists, we would have to understand everything about the universe. To thoroughly understand something means to understand not just what exists, but what does not exist, meaning what could possibly exist but doesn't.
True And False, Words And Numbers
THE NATURE OF TRUE AND FALSE
Today, let's have a look at another way in which complexity affects us. Why is it that some things are true and some are false? The answer lies in what we could refer to as our "complexity perspective".
In any finite realm, there is not enough complexity available for everything to be true that could possibly be true. Therefore some "truth possibilities", as we will call them, must be false. Actually, the way we see it, there are many times the truth possibilities that are false than there is those that are actually true. A truth possibility is simply a statement that may or may not be true, such as "Points A, B and, C form a straight line".
This true and false perspective is entirely the result of complexity, or more accurately the complexity perspective of beings that are more complex than their sorrounding inanimate matter. We are more complex than our inanimate sorroundings. So, we see truth possibilities that are not true.
We see our less complex inanimate sorroundings through the lenses of our more complex brains. The sorroundings do not have enough complexity to match our complexity. The result is that we perceive some truth possibilities that turn out to be false.
We can thus define a "Truth Possibility Ratio". This ratio defines the truth possibilities we perceive that are not true, in relation to those that are true, and is equal to the ratio of our complexity to that of our inanimate sorroundings.
If we were less complex, we would see a higher proportion of truth possibilities that actually are true. If we were more complex, we would see a higher proportion of truth possibilities that are false. No falseness at all would be seen by beings that happened to be somehow less complex than their sorroundings.
This does not mean that a being of one level of complexity would see something as true, while a being of another level of complexity would see it as false. It means that the more complex being, if in the same sorrounding reality, would see more truth possibilities as false. Animals see a higher proportion of truth than we do.
If we could have a realm of infinite complexity, everything would be true and nothing would be false. If we lived in such an infinitely complex realm, we could be no more complex than our sorroundings, and so would see every truth possibility as true. In a "zero realm", meaning a realm that does not exist and is not even defined, nothing is true and any truth possibility must be false. In a finite realm, such as our universe, there is the possibility of perceiving both truth and falseness.
A characteristic of a complex realm is that statements tend to have some degree of self-fulfillment. In a realm such as our economy, if enough people keep warning that there will be a recession then that in itself tends to bring about the recession, making it self-fulfilling. This means that in an infinitely complex realm, not only would all truth possibilities have to be true but any statement would be true because it would be self-fulfilling.
This complexity perspective with regard to true and false is yet another example of how we see the universe not only because of what it is, but also because of what we are.
THE NATURE OF WORDS AND NUMBERS
Have you ever wondered why we need both words and numbers to describe the reality around us? The answer is related to that in true and false.
The difference between words and numbers is that all possible numbers exist, but not all possible words exist. There is no gap in the sequence of numbers, every number exists even if it is not manifested.
Most cosmologists believe that reality actually is mathematics being manifested. But yet the reality that we see, unlike the number system that we use to describe it, is not continuous. There are definite gaps in reality in that only a fraction of what could potentially exist or happen actually does.
This is where words come in. Words define and describe that which exists against the background of that which does not. Words operate in the same way as numbers in that they differentiate the one against the many (There is a posting by that name on this blog). But, unlike numbers, the reality described by words is discontinuous. All numbers exist, but not all possible words exist because not all possible things that words describe exist.
This relationship of words and numbers is rooted in our complexity perspective. Our brains are more complex than our sorrounding reality, and we see this reality through our complexity. There is not enough complexity in the sorrounding inanimate reality to match the complexity through which we view it, and the result is the apparent gaps in reality as we see it. Unlike numbers, which do not have to be actually manifested to exist, words are used only for that which does exist, or at least can be imagined to exist.
As in true and false, the proportion of things which we see that potentially could exist or happen, but do not, equals the proportion of our level of complexity to that of the sorrounding inanimate reality.
If we were of equal, or less, complexity than our sorrounding reality, we would not require words to describe it, but only numbers. Nothing that we could see would be false or non-existent so that it could all be described with continuous numbers.
Words are actually codes, which is why we have dictionaries for words but not for numbers. A word serves to differentiate something that exists from everything else, this fits with that all-pervasive pattern that I termed "The One And The Many", as described in the posting by that name.
Since we are more complex than our inanimate matter sorroundings, there is not enough complexity for everything that we could conceive of to actually exist. So, words also define for us that which does exist from that which doesn't. This is why we require words, as well as numbers, only a fraction of what could exist, from our complexity perspective, actually does exist.
Words, as codes, are far more complex than numbers. Although it may not seem like it, there is a vast amount of complexity packed into each and every word. All of the complexity of the pre-agreed upon meaning is contained in a word.
Numbers differ from words in that everything is basically numbers being manifested. They exist in the universe of inanimate space and matter, while words don't. Numbers are less complex than words, but are not required to differentiate that which exists from that which doesn't as words are. Since numbers act as an addressing system, a manifestation of The One And The Many pattern, any number must necessarily be as complex as the entire set of numbers since a number is defined by the numbers that it is not, the total complexity must include all numbers.
Theoretically, anything that can be described with words can also be described with numbers, and vice-versa. Words hold vastly more complexity than numbers, but the number of words is finite while the number of numbers is infinite. The two must ultimately be equal in complexity.
We must completely understand something in order to describe it with numbers, although that is not the case with less-precise words, which are views of reality from our perspective. (In "The Progression Of Knowledge", on the progress blog, I explained how this can give us an idea of where we stand as far as how the volume of knowledge that we have now compares with all that we can possibly know).
The calendar is an example of how something that was once science, the orbit of the earth around the sun, has been reduced to mathematics because it is more or less completely understood. The periodic table of the elements, which follows exactly the same pattern as the calendar, is a more recent example of something that was once science, meaning partially understood, is now the realm of mathematics. We can now describe the elements, as well as their isotopes and electron orbitals, with numbers alone, without really needing words.
Everything is really numbers being manifested, as in the periodic table of the elements or the calendar, but only down to a certain extent. We get down to a level where we cannot use numbers for description. In my original Theory of Primes, where I broke all patterns down into four basic primes, numbers are part of LEVEL, which is the second prime. The first prime is DOMAIN, which may not be able to be described with numbers.
Consider subatomic particles such as electrons, for example. We can describe the properties and orbitals of electrons with numbers, but we cannot describe what electrons are themselves with numbers. We will always arrive at a point where numbers can no longer be used, and we have to resort back to words.
We cannot determine the complexity of the words that we must fall back on because if we could, we could continue our description of reality with numbers and would not need the words. We know what words mean, or else they would not be useful, but we do not know how much actual complexity the word contains in it's meaning because if we did, we could express it's meaning with numbers and would no longer really need the word.
Our lack of complete understanding of reality is reflected in the fact that a number by itself is utterly meaningless. Suppose that you saw the number 36. What would it mean? It could mean 36 Elm Street, or 36 liters of water, or 36 kilometers.
From our perspective, a number is incomplete. It has no meaning until it is either manifested by something, such as 36 stars in a constellation, or paired with some unit or non-numerical definition. Numbers, and all mathematics, is a tool that requires words as a starting point. But this is another example of how we see the universe, and all of reality, not only because of what it is but also because of what we are. If we completely understood everything, we would be able to express it with numbers alone and the only non-numerical domain would be the entire cosmos.
Today, let's have a look at another way in which complexity affects us. Why is it that some things are true and some are false? The answer lies in what we could refer to as our "complexity perspective".
In any finite realm, there is not enough complexity available for everything to be true that could possibly be true. Therefore some "truth possibilities", as we will call them, must be false. Actually, the way we see it, there are many times the truth possibilities that are false than there is those that are actually true. A truth possibility is simply a statement that may or may not be true, such as "Points A, B and, C form a straight line".
This true and false perspective is entirely the result of complexity, or more accurately the complexity perspective of beings that are more complex than their sorrounding inanimate matter. We are more complex than our inanimate sorroundings. So, we see truth possibilities that are not true.
We see our less complex inanimate sorroundings through the lenses of our more complex brains. The sorroundings do not have enough complexity to match our complexity. The result is that we perceive some truth possibilities that turn out to be false.
We can thus define a "Truth Possibility Ratio". This ratio defines the truth possibilities we perceive that are not true, in relation to those that are true, and is equal to the ratio of our complexity to that of our inanimate sorroundings.
If we were less complex, we would see a higher proportion of truth possibilities that actually are true. If we were more complex, we would see a higher proportion of truth possibilities that are false. No falseness at all would be seen by beings that happened to be somehow less complex than their sorroundings.
This does not mean that a being of one level of complexity would see something as true, while a being of another level of complexity would see it as false. It means that the more complex being, if in the same sorrounding reality, would see more truth possibilities as false. Animals see a higher proportion of truth than we do.
If we could have a realm of infinite complexity, everything would be true and nothing would be false. If we lived in such an infinitely complex realm, we could be no more complex than our sorroundings, and so would see every truth possibility as true. In a "zero realm", meaning a realm that does not exist and is not even defined, nothing is true and any truth possibility must be false. In a finite realm, such as our universe, there is the possibility of perceiving both truth and falseness.
A characteristic of a complex realm is that statements tend to have some degree of self-fulfillment. In a realm such as our economy, if enough people keep warning that there will be a recession then that in itself tends to bring about the recession, making it self-fulfilling. This means that in an infinitely complex realm, not only would all truth possibilities have to be true but any statement would be true because it would be self-fulfilling.
This complexity perspective with regard to true and false is yet another example of how we see the universe not only because of what it is, but also because of what we are.
THE NATURE OF WORDS AND NUMBERS
Have you ever wondered why we need both words and numbers to describe the reality around us? The answer is related to that in true and false.
The difference between words and numbers is that all possible numbers exist, but not all possible words exist. There is no gap in the sequence of numbers, every number exists even if it is not manifested.
Most cosmologists believe that reality actually is mathematics being manifested. But yet the reality that we see, unlike the number system that we use to describe it, is not continuous. There are definite gaps in reality in that only a fraction of what could potentially exist or happen actually does.
This is where words come in. Words define and describe that which exists against the background of that which does not. Words operate in the same way as numbers in that they differentiate the one against the many (There is a posting by that name on this blog). But, unlike numbers, the reality described by words is discontinuous. All numbers exist, but not all possible words exist because not all possible things that words describe exist.
This relationship of words and numbers is rooted in our complexity perspective. Our brains are more complex than our sorrounding reality, and we see this reality through our complexity. There is not enough complexity in the sorrounding inanimate reality to match the complexity through which we view it, and the result is the apparent gaps in reality as we see it. Unlike numbers, which do not have to be actually manifested to exist, words are used only for that which does exist, or at least can be imagined to exist.
As in true and false, the proportion of things which we see that potentially could exist or happen, but do not, equals the proportion of our level of complexity to that of the sorrounding inanimate reality.
If we were of equal, or less, complexity than our sorrounding reality, we would not require words to describe it, but only numbers. Nothing that we could see would be false or non-existent so that it could all be described with continuous numbers.
Words are actually codes, which is why we have dictionaries for words but not for numbers. A word serves to differentiate something that exists from everything else, this fits with that all-pervasive pattern that I termed "The One And The Many", as described in the posting by that name.
Since we are more complex than our inanimate matter sorroundings, there is not enough complexity for everything that we could conceive of to actually exist. So, words also define for us that which does exist from that which doesn't. This is why we require words, as well as numbers, only a fraction of what could exist, from our complexity perspective, actually does exist.
Words, as codes, are far more complex than numbers. Although it may not seem like it, there is a vast amount of complexity packed into each and every word. All of the complexity of the pre-agreed upon meaning is contained in a word.
Numbers differ from words in that everything is basically numbers being manifested. They exist in the universe of inanimate space and matter, while words don't. Numbers are less complex than words, but are not required to differentiate that which exists from that which doesn't as words are. Since numbers act as an addressing system, a manifestation of The One And The Many pattern, any number must necessarily be as complex as the entire set of numbers since a number is defined by the numbers that it is not, the total complexity must include all numbers.
Theoretically, anything that can be described with words can also be described with numbers, and vice-versa. Words hold vastly more complexity than numbers, but the number of words is finite while the number of numbers is infinite. The two must ultimately be equal in complexity.
We must completely understand something in order to describe it with numbers, although that is not the case with less-precise words, which are views of reality from our perspective. (In "The Progression Of Knowledge", on the progress blog, I explained how this can give us an idea of where we stand as far as how the volume of knowledge that we have now compares with all that we can possibly know).
The calendar is an example of how something that was once science, the orbit of the earth around the sun, has been reduced to mathematics because it is more or less completely understood. The periodic table of the elements, which follows exactly the same pattern as the calendar, is a more recent example of something that was once science, meaning partially understood, is now the realm of mathematics. We can now describe the elements, as well as their isotopes and electron orbitals, with numbers alone, without really needing words.
Everything is really numbers being manifested, as in the periodic table of the elements or the calendar, but only down to a certain extent. We get down to a level where we cannot use numbers for description. In my original Theory of Primes, where I broke all patterns down into four basic primes, numbers are part of LEVEL, which is the second prime. The first prime is DOMAIN, which may not be able to be described with numbers.
Consider subatomic particles such as electrons, for example. We can describe the properties and orbitals of electrons with numbers, but we cannot describe what electrons are themselves with numbers. We will always arrive at a point where numbers can no longer be used, and we have to resort back to words.
We cannot determine the complexity of the words that we must fall back on because if we could, we could continue our description of reality with numbers and would not need the words. We know what words mean, or else they would not be useful, but we do not know how much actual complexity the word contains in it's meaning because if we did, we could express it's meaning with numbers and would no longer really need the word.
Our lack of complete understanding of reality is reflected in the fact that a number by itself is utterly meaningless. Suppose that you saw the number 36. What would it mean? It could mean 36 Elm Street, or 36 liters of water, or 36 kilometers.
From our perspective, a number is incomplete. It has no meaning until it is either manifested by something, such as 36 stars in a constellation, or paired with some unit or non-numerical definition. Numbers, and all mathematics, is a tool that requires words as a starting point. But this is another example of how we see the universe, and all of reality, not only because of what it is but also because of what we are. If we completely understood everything, we would be able to express it with numbers alone and the only non-numerical domain would be the entire cosmos.
Subscribe to:
Posts (Atom)