Beyond the Absolute: Limits to Knowledge
By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/COMP Theory/Model; 14 Mar. 2014
“There are more things in heaven and earth, Horatio,
than are dreamt of in your philosophy.” From “Hamlet” by William Shakespeare
“A society which cannot escape from its current abstractions is doomed to stagnation after a limited period of growth.”
“Almost anything which jogs us out of our current abstractions is a good thing.”
—Alfred Whitehead, co-author of “The Principia Mathematica”
“I hold that a little rebellion now and then to be a good thing.”
—President Thomas Jefferson
1. No absolutes in events in existence, no absolute space or time, no infinities, certainties, perfections or other absolutes.
2. No complete models, astronomical models as solid evidence; Incomplete models of physics
3. Sphericity of the earth shown by imposing flat, 2-D surveying street grids
4. Exponential barrier of particle physics now reached, expon bars of velocity of light (cee) and absolute zero, incompleteness of human knowledge.
5. Gödel’s incompleteness theorem (AKA Gödel’s Proof), empirical evidence confirming the theorem.
6. The Structure/Function approach to knowledge’ structure but not function, or the converse method.
7. Structure/function incompleteness of the Human Genome Project showing power of the S/F method; A number of practical ways to find the missing functions of known genes; comparing normal gene to abnormal gene gives solutions to the problem.
8. S/F problem of missing information in Gödel’s Theorem.
9. Examples of Incompleteness of math/logic
10. Exponential barriers, Heisenberg’s Uncertainty Principle as a form of ExponBar;
11. Comparison Process can go beyond limits of math/logic and related forms: Examples of the Taxonomies of living species; medical conditions also based upon comparison observations, history, examination, differential diagnoses and treatment plans, beyond mathematics: Plate tectonics and languages and taxonomies of languages and their relationships; etc.
12. Non-logical systems descriptions: emotions, delusions, rationalizations, the Mythos of gods/goddesses, animistic beliefs;
13. Source of both logic and the illogical, of math and emotions, the comparison process.
14. The one way street. Language can express all math, but math cannot express very much of language in exact, meaningful symbology. The extreme limits of math: poetry, literature, religious statements; language and linguistics. Gödel’s proof gives no clues about what specifically those incompletenesses are, where located, or their natures.
15. The alinearity of complex systems; the epistemological shift to complex systems using the comparison process. 15a. The ignoratio ignorationis problem and related.
16. The Exclusion Principle and the origin and limits of the negative; the negative as the source of incompleteness” Godel not necessarily applicable to logics of exclusion.
17. Examples of implicit and explicit(the global negative) exclusions
18. Many examples of incompleteness of knowledge.
19. The value of the structure/function approach to incomplete knowledge.
20. The primacy of observational/visual organized systems
21. Approximations and series’ approximation methods. Recursivity evidences.
22. The kinds of ignorances as causes of incompleteness and limits to knowledge.
23. Exclusion principle and the internal consistencies of biological systems not logical/mathematical; ideas excluding other ideas, implicitly or explicitly; idealism as a very large part of the problem of incompleteness.
24. Exponential growth of the sciences and knowledge still largely incomplete despite this, as an example of how much humans do NOT know, yet.
25. Incompleteness of the general categories, the ontologically implicit incompleteness of categories, etc.
26. Human brain outputs do NOT necessarily correspond to events in existence to any considerable degree. Models of events are not the events outside of the brain. The fatal flaw of idealisms. Historical suppressions of empirical investigation by idealisms.
27. General ignoring of most all data on a daily basis.
28 Multi-tasking methods to improve how we deal with events in existence; escaping limits by these methods. The simultaneity of 2-3 brain operations method.
28. Categories and hierarchies. The comparison process creates those and allows us to navigate up and down them, by reading them. Math cannot follow, it can mostly work inside one category, but not, as can language, move up or down. It can’t scale like language/comparison processes can.
1. Previously the idea that there is no absolute space and time has been discussed. That there is probably no such events in existence as perfection, infinity or absolutes, has also been shown to be the case by trying to describe/measure perfection and showing that it cannot, like infinity, be shown to exist. In fact, most anything which we measure does not have a finite number to describe it. Most all empirical lengths are very likely irrational, because there is not a final digit. And any attempt to find that last digit is empirically as well as theoretically very likely an impossible task, because we go up the exponential barrier, that greased slide of increasing slope and height, until we run out of energy, time and money, effectively. Also called the law of diminishing returns. These are both empirical and theoretical limits. The Heisenberg Uncertainty Principle, where the spin and location of the electron cannot both be accurately determined is the case. But is it not true, that we cannot determine EITHER the position or the spin to a final digit of certainty?
In the case of the orbits of the planets, Kuhn’s brilliant analysis in “The Structure of Scientific Revolutions” showed that the circular orbits of Ptolemy were not complete by comparing the data to perfect circles, and had to be “adjusted” by using smaller circles called epicycles. This approximated the later elliptical orbits. Copernicus showed that a simpler system put the planets in orbits, circular, around the sun. Kepler was not convinced and when he finally got Tycho Brahe’s data, and compared the figures with what Mars’ orbit was, he showed that an ellipse was the orbit of the planets, but only just. Because as we know now the orbits, by comparison with the data, are in 3-D and cannot be elliptical, either. And the orbit of Mercury also rosettes around the sun, in both space and altered time due to relativistic influences. So, currently we use elements of orbits, which Kuhn also addressed. But these are only good for 50K-100K years of theoretical accuracy, and then become useless. Of course, this 50-100K estimate has NOT been checked & cannot be at this time. No one has actually measured them. Thus even there we find a limit to measurement.
There is the finding that trans-Neptune plutoids, bodies, which are from a few kilometers to a few 1000’s kms. in size and mostly watery, rocky metallic composition like Pluto and Charon, move in highly eccentric orbits quite out of the plane of the ecliptic and some with orbits as long as 1000’s of years. Because they were so distant and so far out of the ecliptic, they were missed until astronomers could spend weeks long viewing times, using CCD’s for higher light gathering power, and the money and time to do the searching. Now they number in the scores, and probably in the 1000’s to say the least. Again, limits to knowledge, any new knowledge. Astronomy is Still incomplete.
2. Given the new ideas and findings in physics, not only was Aristoteles’ knowledge incomplete, but so was Galileo’s and as Einstein and quantum mechanics showed so was classical physics. Relativity does not seem to necessarily apply on the quantum level, because it’s a deterministic theory, not a probabilistic and stochastic one, like quantum mechanics, which so far has been shown to be the case whenever it can be tested. Sadly, QM is so complex and many of the calculations are impossible to solve using even today’s advanced supercomputers. Finding answers using the QM wave functions is simply & often impractical and unhelpful. So in a very real sense, those are real, palpable and important limits to the usage of QM, as valuable and correct as it has been shown to be.
3. In each case we have the same process. From the apparent flatness of the earth being shown to be a special case where the circularity, spheroidal shape of the earth gave the illusion of flatness. And this could have been dispelled 1000’s of years ago, simply by creating on the earths surface a planar grid pattern and then seeing that regular, clear error because the north going lines on a planar grid will diverge too much on either side of the grid, if it’s extended too far east and west. Longitudinal lines on a sphere tend towards the north or south pole, and meet, whereas on a 2-D grid plane, they do NOT meet. The planar grid does NOT compare well with the spheroidal model.
And this also applies to the space-time geometry of the universe. Thought to be 3-D, it’s in fact not Euclidean, not linear at all. There is also a divergence when 3-D is compared to the actual universe. By comparison, the model does not fit. None of these models fits completely, either.
4. When the Higgs boson was finally believed to be found, but NOT confirmed by at least two other sites/teams, because it was so expensive to do so, it marked the point, again, it should be said, that the exponential barrier was being climbed, until it was so expensive to do, it’s not likely to be tested that way again. Again, limits to knowledge using standard, scientific measuring methods, which have been shown time and again to be comparison process and methods.
But the point is this, using description and the mathematical method of description, measurement, we will most always be climbing the Expon Bar, eventually, no matter what we do. We cannot find perfection nor infinity, which have no reality. There is not absolute space nor time. We cannot reach the light barrier of Cee using normal acceleration. At the other end of the speeds of particles, viz. ultra low temperatures, we cannot reach absolute zero, where the cost of reaching it becomes greater and greater with each approaching millidegree or even more so a microdegree. There is a limit to our human knowledge, both Empirically and scientifically, as well as theoretically, mathematically and logically. The exponential barriers of measurement show us the physical reality of this limit, as does a special case of that barrier, the Heisenberg Uncertainty Principle.
So what is going on here? If both description and measurement have such limits, then most all knowledge, either theoretical(mathematics and logics) and empirically obtained is unlikely to be complete, necessarily. There is NOT absolute knowledge, either theoretically or empirically. NO verbal descriptions nor intensely worked out, pursued and highly accurate measurements can give us this. There is a natural limit to most all our knowledge, at least in a practical sense, which we cannot at this time easily overcome.
5. Let us take this point further. Godel’s Proof showed logically that and necessarily all such logical, recursive systems were incomplete. Comparing this to the current methods of the sciences and most all measurement, indicates that the ExponBar may be a physically testable form of the same thing. Thus not only is mathematics and logic incomplete, but using the Comparison processes, which create description and measurements, most all such theories cannot either be complete. There is most always something which is going to be left out. We cannot attain absolute, final, logically consistent systems, and when we try to measure and describe events in existence using such systems, there is also the same outcome. Most All of our models are therefore incomplete. The ExponBar is a physical measurement showing the reality of the limits of most all methods using the comparison process, which are provably as recursive in an empirical way as are Godel’s abstractions.
6. Using the structuralist approach of the Structure —-> Function model (S/F), a lot more becomes clear. We knew from Einstein that E=MCsquared. But there was no real way to prove that, either. We had the Function, above, but not how to do it, the S. That is, the theoretical knowledge, but not any practical way of doing it. Just like Cristaforo Colon knew that the earth was round, he had to show it was so, as he partly showed by sailing west and then Magellan and Drake showed further in making a complete circumnavigation of the earth. So with the finding of nuclear fission of uranium yielding a chain reaction and energy, and then nuclear fusion doing the same, the left side of the S/F relationship was discovered. This model fits with most all discoveries and their subsequent explanations, although it doesn’t necessarily tell us what’s going on, specifically. It DOES show the limits of knowledge, the incompleteness, which is the point.
6. Human knowledge is incomplete. We often see the S/F relationship, one side or the other. We have the structures, that is the superconductor(SC), but we don’t know how it works, the theoretical. The SC’s were found at low temps, but no one knew how those worked, until it was found later and got a Nobel Prize. Those models were still incomplete because no one knew why or how the superconductivity phenomenon was gained or lost due to temperature rise and fall, either. And then the higher temp SC’s were found which astonished everyone again. Recently some major progress in understanding those has been found. And yet again, they can create an understanding of how the High Temp SC ( HTSC) worked, but they can’t easily make more SC’s which work at higher temps, because again, the “S” side of the relationship is not fully understood. So here we have with superconductivity research and findings the incompleteness of scientific knowledge coming out not once, but THREE times more, easily understood with the S/F model!!
7. There has been a serious problem with getting useful information out of the Human Genome Project. This has resulted from, very clearly, having the Structure of the genes, but not the functions. There is nothing in gene which necessarily states or ID’s what it does, specifically. So while we have almost all the human genes, we do NOT know what a large majority of them do. This is why the Genome has not delivered on its promise, very clearly highlighted by the Structure/Function method.
Essentially, we need to understand the comparison process and how it’s used. For this begin at the introduction to the comparison process, part 1.
Scroll down about 60% of the slide bar to find:
“Any kind of error, be it a genetic error creating a disorder, or other conditions, creates a new opportunity to compare that genetic disorder to the normal. ”
This is the solution to the entire problem, in fact. If we think about it. Those who are not creative won’t see it. Those who are, well, they will create these innovations.
Create a new, synthetic allele of the gene whose function is not known. See what it does to the cells in a human cell culture. Insert it into a mouse and see what it does to the mouse genome. Does the mouse die, or does it have a serious, observable or metabolic problem? Using a chimp would be even better, though.
Compare the known human genes whose functions are well known, and the classes of genes to which they belong, be it structural, enzymes, polypeptides, regulatory, and so forth. Build up a database of what those genes’ characteristics are in each category, then begin to compare the unknown genes’ functions and find the similarities. Once those are known, then a lot more can be found.
This will require a big database, and will allow computer’s early AI to recognize similarities among the genetic DNA base code sequences and codons to make identification of the gene’s functions easier. And computers can do the job of comparison of gene functions a LOT faster than can humans, and might often find whole series of base pairs and codons strings, which are very similar to other genes, which functions we do not know. And it might even show that enzymes are created from other enzymes, simply by using chunks of DNA to become incorporated into new enzymes with new functions, too. Sort of a higher level genetics, which allows play around with the genes to create solutions to real problems. Sort of an epigenetic system, too.
Lastly, but by no means all of the methods which can be created by the comparison process, DNA hybridization. This was how the Myostatin gene was found in other species than mice, the primary species where it was ID’d. Simply take the unknown human gene, and use DNA hybridization to find it’s chromosomal location in mice, rats, chimps, and other species whose genomes are fairly well worked out. If it compares to one of those which is known, then we can surely tell a great deal more about what it does.
All of this by the method of comparison, you see. Next compare the effects of new, synthetic alleles in unknown genes to what happens to cell cultures and observable effects in functioning animals, too. There are an indefinitely large number of comparison methods capable of creating solutions to the structure/function problem now rife with the human genome.
8. And now we see the Godel’s incompleteness theorem, this important point. We have the right sided Function, but not the left sided S, Structure, which confirms it, do we not? Or do we? The huge problem with Godel was that he stated that math/logic of a recursive type was incomplete, but few have Yet given any real evidence which is convincing of that, either. Nor did the proof state WHERE and WHAT to look at or for or how to find that missing knowledge. How is this any different from E=MCsqu.? We knew it was likely to be the case, but it took until mid 1940’s before Einstein’s theory was found to be correct, too. Again, the F but not the S.
9. What then is likely shown here are some limits to math and logic, what they cannot do and are therefore incomplete about, thus beginning to complete the S/F relationship which Godel created by now providing some empirical, measurable evidence of the limits to logic/math using the COMP tool. And why moving on to a complex systems approach is both becoming successful, practical and necessary to further human understanding. That is, getting away from linear methods, to finding more of those which go beyond the absolutes of linear, mathematical thinking.
We know that our models of the solar system have been incomplete by historical evidences from Kuhn’s “The Structure…”. Here is yet more evidence of it. In the same way, math/logic and other linear methods cannot describe/understand complex systems, nor the human emotions, nor a good many other events in existence. The Comparison process is a way/tool/method to significantly advance the search to reduce those ignorances.
10. Expon barriers are likely measurable, empirical tests of the universality of these limits to current human, scientific knowledge. As stated before the Heisenberg Uncertainty Principle is very likely yet another form, and element of the category of the exponential barriers to complete knowledge. They are likely real and solid evidence that most all human knowledge, in some way or another, or in many ways, is incomplete. That last digit of most all events cannot ever be found no matter what we measure, nor theoretically and practically, we can’t measure it, either. Is this not a union of theory and facts based upon empirically testable events? When we exhaustively compare measurement and theory, we find these ExponBars. The Comparison Process describes measures and tests events in existence by comparing events to one another.
11. Can the COMP go beyond the limits of logic and mathematics, the latter of which cannot describe verbal concepts very well, but which math itself CAN be described by words, as well as logic? It’s likely possible. Using the descriptions of words of living systems and their relationships, something which math cannot do, for instance, in the medical history and physical exam plus the differential diagnoses and testing/treatment protocols; in plate tectonics; in descriptions of psychiatric states, (the DSM series); in descriptions of the relationships of languages to each other, the language diagrams, the entire virtually totally verbal taxonomy of all known, millions of species, etc. These suggest an approach which is superior to mathematics, that is, uses verbal descriptions to go where mathematics cannot go. The existence of the above may indeed allow us to go where mathematics cannot dsecribe as it has provably done so. These may well be solid evidences that, yet again, structures have their limits and capabilities, and of these, Godel’s proof is a part of that. Most all of our models are incomplete.
Using the body of knowledge of the “Tree of Life”, the connections among most all of the species to one another organized in hierarchical form, comprising what is called the Taxonomies of the species. This is based upon the relationships created by OBserving living species and comparing them to the others. It’s not based upon logic, nor upon mathematics, unless it be measuring, which is very limited, and for that alone it’s subjected to Godel’s limits, but not necessarily other descriptions. Therefore complex systems understanding might well lie outside of the mathematics which cannot solve the N-body problem, but which verbal descriptions using the comparison process have and can describe, but which are largely forbidden to mathematics. This shows yet again, empirical evidence for the incompleteness theorem of Godel. Or as Stanislas Ulam, the father of complex systems investigation, once stated Mathematics must become far more developed to be useful in understanding and describing complex systems.
12. Emotional systems are irrational. The comparison process shows how those arise, the delusions, the not logical rationalizations, excuses and violations of the rules of logic, including the Mythos, by which our ancestors used to explain so much of their world using gods, goddesses and animistic beliefs, and so forth. Therefore to the extent the COMP describes them, it lies outside of logic, which the emotions are definitely. Thus emotions and the ability to describe them is a not-logical description which can act outside of formal math/verbal logics, by the very nature of its descriptive existence. The limited linearity of systems can be shown logically, but necessarily incompletely. Those systems which are complex, are necessarily not completely logical and Godel’s proof does not necessarily apply, as mathematics and logic do not apply. Although, linear systems may approximate some aspects of complex systems.
13. The COMP shows itself as both the origin of logic, both mathematical and verbal logics, as well as the delusional, irrational beliefs, and the mythos of earlier religious explanations, and superstitions as well. Thus from it arises both the logical and the irrational, reason and the emotions, no mean achievement, either, for the comparison process model.
Clearly, quite something else is going on, which is outside of logical, formally logical, mathematical systems. This then shows the limits of logic and mathematics, can be breached and overcome by the comparison process in actual, empirical fact. The comparison process can create mathematics, and it can create logics, but it’s not necessarily subject to them, either, or to Godel’s proof.
14. To be more precise, language and words can express all mathematical statements. But mathematical symbology cannot express very much of verbal descriptions. Viz. these examples prove the case. It goes the one way, words speaking math, but not back again, math being largely UNable to describe language of most all types.
“How shall I compare thee to a summers day? Thou art more lovely and more temperate…” –Shakespeare.
“Blessed are the meek for they shall inherit the earth” –Beatitudes.
“When I was 16, my parents didn’t know very much. When I got to be 25, I was surprised to see how much they’d learned.” –Mark Twain.
Shall we then expect mathematics to explain a great deal more of what is going on with these rather serious limits? Especially linguistics and the unlimited hierarchies of the languages and living systems? Can it describe the reductionist model, going from particles, protons and electrons, up to atoms and isotopes, and then onto molecules, and thence to organic chemistry, thence biochemistry and metabolism. Thence up to the living cell, the collections of cells called colonial forms, then multicellarity, etc., until we finally come to the human brain, and the cortical cell columns, from which the mental functions arise, creating the mind and consciousness? It cannot. This will be dealt with later, to explain the limits of linear mathematics and logics being unable to comprehend or model those systems.
There is no necessity that by observing events, that Godel’s proof can be tested, either. Observations of themselves do not necessarily show that Godel’s proof, which confined itself to human mental functions/processes of the mathematical and logic type, do not necessarily apply, because those observations ARE not linear, and are capable of describing complex systems, not describable by math. A further problem with Godel’s incompleteness theorem is that it gives NO clues as to what has been left out, that is, the specifics of what those omissions creating the incompleteness are. How are we to know where to look? This article is an attempt to begin that discovery of the omissions of knowledge, that incompleteness and its nature and its types within formal systems. An attempt to complete some of the structure/function relationship of Gödel’s Proof.
Simply using mathematical symbology, state the Beatitudes or one of Shakespeare’s more famous sonnets, “Thou art more beautiful than a summer’s rose…” clearly, not logical, not mathematics, but still in an emotional, mental way, comprehensible to most normal persons. Godel’s proof does not necessarily then apply to comparison process functions and descriptions which CAN in part describe such complex systems, which math and logic cannot describe, that is specifically, language with emotional and complex system content. This might well explain why complex system methods are being more and more widely used and complex system approaches are going well beyond what can be achieved with the linear, N= 2, logical, mathematical approaches. Math can approach in some cases, by approximations, and mathematical series, just as the circular orbits when modified by epicycles approached the elliptical model of Kepler. But it cannot pass over that abyss, and solve the N body problem, either.
15. For complex systems, A doesn’t always yield B. A can yield B, C, d’, phi, Xi prime and a lot of other outcomes, very similarly to the dopamine receptors, which have about 10 distinctive receptor types/functions, thus showing once again, that Godel does not necessarily apply to such complex systems. Their logic, if anything exists, more likely their organizations, their structure/functions relationship are NOT logical, but complex interactions and relationships, in fact, which can be understood in part by complex system thinking, that is, more like the comparison processes of observations.
To use a most simple and day to day event to demonstrate this complex system characteristic, suppose we walk down the street and say hello to the first person who comes by. They may say hello, but others can say, allo, or Buenas Dias, or nothing at all, to “How ya doin?”, and a virtually unlimited number of responses, in one or unlimited numbers of languages. They are are not predictable, but they ARE not linear, and instead complex systems, where there are huge number of interactive factors. Simple observation allows us to see that fact. It’s not logical, but it is organized, and the frequency of the responses can be given a probability by observing these systems working. Again, comparison process observations and methods can allow us to get information about not logical, not mathematical events and learn a LOT more about how they work.
15a. The ignoratio ignorationis problem is that of not knowing that one does not know. Ignorance of most events, concepts and mental training is a real problem. For instance, if a physician doesn’t know of a medical condition, how can he possibly make a diagnosis of it, and will miss it to the grief and too often death of his patient. Again, the cluelessness. If a person doesn’t know of the major logical fallacies, how can he avoid committing them? Overall, a good education will largely remove a good deal of this ignorance, and although it’s impossible to know everything, if one is trained broadly, generally and well, most of those kinds of problems will not occur, and the person, being well trained, will be well of aware of his limitations and most of the time be seeking to know those limits, and exceed them.
This is also a plea for far, far better education in the major nations, esp. in North America. Because not only is knowledge good because it creates wisdom, but also because it gives the comparitors in the human cortex more to work with to compare against all else. Knowledge is the deepest resource of the mind, and has been shown before, the more there is to compare, the more comparisons can be made which are useful and fruitful. And then because there is more found by those comparisons, then more can be compared against the newer knowledge and the comparison system exponentiates.
It’s simply too bad that in the USA so few have any real understanding or training in the sciences, because this is the most useful, reliable, practical and valuable knowledge known. Yet only about 5% of the US student graduate with any real understanding of their now 99% technological culture, which, with increasing computerization everywhere, only will continue to become ever more so. This is a great tragedy, because in the Eurasian nations, a 50/50 mix of math-science/humanities is required for graduation in most cases of secondary education and university degrees. It means that Eurasian graduates will simply run all over most all Americans. And that means in the long run, the US education system has simply failed to compete to the point where it must fail, weakening the entire nation vis a vis our Eurasian competitors.
Another problem is those who insist upon linear concepts and methods. They state dualities exist, without realizing the above logical fallacy of the false dichotomy. “There are always two sides to an issue.”, which false claim is yet another aspect of this problem. In complex systems, which are virtually everything in our universe, there are usually MANY sides to most all issues, and real dichotomy is more rare than common. The insistence upon the dialectic, which again has limited value due to the false dichotomy it commits, is yet another problem. Dividing events and ideas into dualities, while ignoring the continuum, upon which most dualities are in fact a part of, has been discussed before in ” The Continuum, dualities, Yin, Yang, etc. below.
Events are largely complex systems, and insisting upon dualities, dichotomies, and linear methods, where A almost always results in B, is not going to work very well. And is as shown above, yet another limit to knowledge, being the failure to understand complex systems, their characteristics, ubiquity, and how they work.
This is in fact, very likely the superiority of the COMP. It gives rise to the logics and mathematics, but it’s not subject necessarily to the same limits by the very means by which it creates the irrational emotions, as an aspect of more rational ways of doing things. It’s more effective because it has more capabilities, due to its very structure. This represents a massive epistemological shift away from strict, logical determinism to a comparison process way of thinking about anything, which can include logics as well as mathematics, but is not bound, necessarily by them. The COMP can compare anything to other events, because any event, whether internal to the brain and sensory report of the body, or externally existing events can be compared to much else, besides. There is no limit to what events can be compared to others, either. And in creating more outputs using the COMP, those also can be compared to other events, producing yet another form of unlimited functions, compound interest at work, i.e. the exponential capabilities of the comparison process.
Language also is NOT logical or rational or mathematical, and has so far resisted understanding it. But if we understand language on its own terms as being comparison processes and comparison methods, it becomes much more understandable as has and can be further shown. No mathematics can describe and give partial meaning to languages. Yet language can include and create mathematics and are expressible, describable, using language. The relationship of languages to mathematics as its parent in even found in the brain, where the math centers are located abutting the language centers from which math arose. There is no question but that language preceded mathematics. But the capabilities of math/logic do not go both ways. It can be created by the human brain, but it cannot necessarily fully comprehend it, otherwise emotions and language would be readily and easily understood, just any modern language easily states math and logic. Get away from logic, and math and use observations of what events in existence, just like in the taxonomies of the species of animals, just as medical professionals and engineers use observation of real events to understand them, etc. This very likely shows the superiority of the innate processes inside the brain, too, to describe and comprehend an irrational world, because we cannot find that last digit…… Godel was right, math and logic cannot understand many events in existence, for the obvious reasons.
16. Much more can be understood by means of the Exclusion Principle (EP), and its extension from physics into thinking. As stated before, the Exclusion Principle can be applied to motor vehicular laws and shows to be the one, basic rule largely underlying most all of it. Two fermions of normal matter, cannot occupy the same space at the same time. The electron repulsion of the EP prevents it. We see this daily that two trees cannot occupy the same space as they fall over and may push the other aside. Same for two rocks and so forth.
In the same way a comparison process exclusion principle is also acting, and this will show very simply how Godel’s Proof comes about and how the negative is created. We cannot stand or sit at the same time. Nor can we sleep or be awake at the same time. Many states preclude other states. We cannot sit, nor walk at the same time. We cannot speak, nor swallow at the same time, nor speak and hold our breaths at the same time. Thus there are in a very real way, actions which exclude other actions, states which exclude other states, and in a very real way, our language expresses and recognizes IMPLICITLY these exclusions in the ways we use words, showing the real modeling of words compared to the events to which they refer, but do not exactly nor fully describe, either. It is this implicit knowledge of exclusion, manifested by the mental exclusion principle, which gives rise to the explicit negative. The negative arises directly from the exclusion principle, a fact which has heretofore been widely ignored. This is the origin of the negative.
17. So we state he does Not run. But this tells us nothing about what he IS doing, does it? It excludes in fact, globally. The negative is often a global exclusion. There is a huge omission of data, is there not? But when we say he is running, by the very nature of both the model and reality, we know he is not sleeping, not walking, not sitting, not driving a car safely, etc., etc., etc. Which is more descriptive and complete? The negative, or the implied exclusion? Obviously the latter. And this is likely the problem with the negative, which Godel found. It eliminates too much information, virtually all of it. Using a logic of exclusion, which is what the comparison process uses, far, far more is kept into the description and thus is then more complete. Observations of events such as living species do this. Observations of the physical exam and history do this. Observations of plate tectonics also do this. Math uses the negative. So does logic. and here is the point, the comparison process doesn’t, and thus is capable of understanding much more than the math/logical linear methods can. The logic of implied exclusion is what is going on here, and that is the comparison process in most cases, and thus is far, far more capable of dealing with events in existence in terms of verbal descriptions than is formal math and logics.
In fact, was not the very phrase, “This statement is NOT true.” or a form of it, how Godel’s proof was created? By the use of the negative, again. Is this a coincidence? Not likely. The limits of using a logic and math in which the negative is used likely created the problem. Created the incompleteness. A logic of exclusion, such as used in observed systems, will likely not have the same limits as math/logic found by Godel.
By comparing directly what math can do with what words can do, we see this contrast. This may be a part of the solution to the problem of the limits to math/logic and linear methods. And it’s shown very, very clearly by using the same tool, the comparison process, which our brains use to create language, and which we have ignored far too long.
18. Essentially, there many aspects of the limits to knowledge of many kinds. Once the comparison process and its multiplicit and open ended characteristics are known, then much more can flow. Godel’s incompleteness theorem shows the logical, mathematical basis that such systems were incomplete. But simply because a statement is logical, does not mean it compares highly to events which exist. We must test those statements for completeness by comparing them to events in existence, which is the scientific method in a nutshell. It escapes beyond the limits of logic/math to find events to which those do not apply. It may be why scientific method is superior to pure thought alone, too. The mind trap of logic and idealisms.
If some other limits to empirical knowledge can be shown, which are based upon mathematics and the sciences, which are heavily mathematized, then some hitherto unspecified by Godel’s theorem, “kinds” of incompleteness would give support to it.
The Exponential barrier has been shown to be such an empirical limit to measurement. That there is no absolute space or time, nor perfections infinities, or certainties, or ultimates or absolutes of any kind, including immortalities of individuals, is very likely the case as has been shown by the limits of mathematical measurements, and it likely may also be the case for most verbal descriptions based upon language entirely.
That many statements in language CANNOT be expressed using mathematical symbolisms and methods, shows, clearly, the limits to math/logical statements stated by Godel’s theorem of incompleteness. This has been addressed before in detail and need not be shown again. That the taxonomies of the species cannot be expressed using math, nor logic by themselves, altho those can help, but is established by observations and comparisons massively is very likely the case. And this shown yet again, by comparison, the difference between descriptions verbal and mathematical descriptions or measurements. The limits of the the former are not necessarily the limits of the latter, and vice versa.
19. Essentially, we now invoke the structuralist approach. Most everything has structure, and that means the structure —-> function/output approach. For every structure there is a describable and/or measurable output, or outcome. This is essential to understanding complex systems, such as those biological and physical, too. And the premise that most all structure/function relationship have their capabilities as well as their limits. That this fits well into the findings of Godel’s theorem is clear. But the implications are as wide ranging as our understanding biological as well as physical complex systems. It’s yet another comparison process tool, i.e., a comparison method for understanding events around us, far, far better than linear, mathematical methods.
20. Whereas the logical, mathematical process builds up systems based upon concepts and ideas, the observational approach builds up systems based upon constant calls to events in existence. The taxonomies of the species, the periodical table of the elements, the IUPAC listing and organization of the compounds; the listing of all known biological proteins, enzymes, etc., much the same; the Hertzsprung Russell diagram of all known stars; the classification astronomical of all known galaxies, from the dwarf irregulars to the elliptical galaxies, to the various kinds of spiral galaxies, to the dwarf to the massive low surface brightness galaxies; and the nebulae; the planets from the asteroids to the rocky planets, to the gas giants, to the plutoids and so forth. These are most ALL classified NOT by logical forms, but by comparisons. In that sense they are NOT logical forms, nor mathematical, although those tools can be helpful, but in a limited form. These are all of different types, including the receptor sites method in pharmacology and the differential diagnoses methods plus the classification of all known human disease states, etc. But each of them has a physical basis which math and logic do not have, necessarily. Nor can they easily be described by math/logic of a linear kind, but only approximated.
21. And those approximations, which Kuhn showed were characteristic of the Ptolemaic perfect circles, then with epicycles; the sun centered solar system models, the elliptical model of same by Kepler, and the elements of orbits now used, all approximated, by the others, yet, the progression is never ending. It’s the approach by approximation which shows the exponential barrier being seen as a limit to knowledge. Again, these all show limits to knowledge, by the COMP. When we compare these as did Kuhn, we recognize the patterns above, also. Those approximations are the limits to knowledge, the incompletenesses also which are stated, but not identified as specific instances by Godel’s theorems.
As and aside, Gödel’s theorem applied to recursive systems, such as logic and mathematics. It should be pointed out that the comparison process is necessarily recursive and massively so, given the ability to think about thinking, understand understanding, writing about writing, recognizing recognition, ultimately from comparing a comparison without limit, this become very clear. This once again, the recursivity of the COMP shows a relationship to Gödel.
22. Have also addressed the limits of humans in terms of insights, from cortical blindness to lack of insight by many both normal and abnormal mental states. Of the neglect syndromes. Of the inability of animals to see the outcomes of their actions as can we, although not all humans can. These kinds are all of the same, limits to knowledge based upon structural limits of the methods being used.
Section 18: the ignoratio ignorationis problems.
23. The exclusion principle is also the case either specifically or explicitly. The consistencies of the complex biochemistry biological organisms can be seen as this, in fact, which both include and exclude specific capabilities and so forth. A poison can be seen as a biochemical inconsistency which can damage or kill the organism. Those processes of aging can be seen in the same light. The consistencies biochemical of living species are a logic all their own, observed and real. There are tasks they can do and which they cannot. They are the biochemical sum of their capabilities and limits, as well. The many truths can be seen in the same light, limits and capabilities of mathematical, scientific, logical, moral, historical, and spiritual truths, etc., each with their limits and capabilities.
Ideas and beliefs may implicitly and/or explicitly exclude other ideas. There is emotional exclusion where we simply do not like something. There is the ignoratio ignorationis exclusion which persons do not literally know what they do not know. There is the exclusion of knowledge by limited intellect, by dementias, by stupidity, by the above lack of knowledge by inadequate education, or ignorance of intellectual tools. There are many ways in which belief and ideas can be excluded directly or indirectly, such as brute force method, too commonly used, “If you don’t do/believe this, you will be shot.”
There are many other points to be made about many other aspects of this insight. Idealisms will exclude empirical methods, because the word/idea is held to be superior to events in existence, which are held to be, classically, mere shadows of the Ideal. Of course, the big pot, the universe does not go into the little pot, the brain, which shows how silly and foolish Platon’s idealistic beliefs were. We humans fit into the universe and are subject to it, not vice versa, and it was not until these exclusive, mind trapping idealisms were exposed as egocentric, homocentric, geocentric nonsense, that modern sciences came about and began their exponential expansion.
24. This also gives insights. If medical & scientific knowledge has been expanding exponentially, doubly about every 5-6 years, for the last many decades, and it seems very likely, and we still don’t know all which we need to know, is this not yet again another case of the limits to our knowledge? Having seen scientific knowledge very rapidly expanding exponentially yet we are not yet able to fully model even the brain, or complex biological systems, let alone a single cell, and much else, including living systems. Does this not also provide more evidence of the essential incompleteness of our knowledge, even though we know vastly more about our universe, compared to what was known 500 years ago, alone.
Language, like so many complex systems is unlikely to be fully understood without recognizing that linear, logical, mathematical methods are inadequate to the task. Once this realization is made, using the comparison process, then we can make real progress in understanding language and thus linguistics.
25. What are some of the other, more easily seen limits to knowledge? Let us take, as have so many times, the word, Tree. What does this have in comparison to that oak tree in my front yard? Does it give the size and structure of the roots, the size and shape of the trunk, the many branches, their locations of sizes and shape? Does it tell us about the genetics or physiology of it? Does it tel us the shape of the leaves, how they are growing or not, budding processes, or how many and where all those leaves are on the tree, or how they move in the wind, the rustling of the leaves as the poets state? No. It leaves that all out. No wonder our knowledge is incomplete!!! For these and most every other events in existence, our ideas/words are inadequate to the task. Then we wonder why our knowledge is incomplete? Gut Gott im Himmel!! It’s so obvious. Yet very much like not seeing the forest for the trees, again, by NOT comparing what we do, to what we observe, we miss the limits of ideas/words, language and math.
26. As Korzybski, the founder of general semantics, stated so many years ago, “The Word is NOT the thing.” In more general terms, the idea/word is NOT the event in existence to which it compares/refers. By confusing the two, ideas/words, brain products, with events in existence, there is the trouble. This harkens back to the philosophical idealism of Platonistic idealisms, which stated that ideas/words were the “ultimate absolutes”, and that events in existence were mere shadows of those absolute realities of ideas. We can see very quickly today, from the standpoints of our highly successful and exponentiating empirical sciences, that Platonists had it exactly ass backwards. It’s in psychiatric terminology of personality disorders, exactly the use of Projection, accusing others of those bad deeds which the disorder is doing itself. This unmasks the problem with the idealistic, self-centered, almost puerile in its origins, mind trap at last. There exists an external universe of events in existence, independent of our limited, small brains and ideas. It’s the Idea/words which are the merest shadows of events in existence, not the converse. Or as Dr. Johnson did, upon hearing of Berkeley’s absurd idealism, “I refute it thus” and kicked at him symbolically.
And is this not yet again, another implicit means of exclusion of ideas? Was not Galileo’s suppression and ignoring by the Scholasticists yet another example of how and why our ideas are incomplete? They looked away as the large and small spheres he dropped from his sedcond story where they could see them land at the same time, events contradicting Aristoteles very clearly. The Scholasticists refused even to look into his telescope where the moons of Jupiter clearly circled it, thus showing that by comparison, by extension that the earth could also orbit a much larger sun. Idealisms of all sorts are diametrically opposed to empirical observations, holding the scientific beliefs mistaken, when quite the opposite is the case, by simple observations a child could do.
27. Look once more this time carefully, at how we go about our daily business. We go over to a grocery store, and know where it is by comparing to our internal map, either by using a grid, or by comparing to landmarks, which eventually gets us there. (That some persons cannot read maps is most always shown by their inability to find north or south, or know where they are relatively, by comparing to a map. Instead they compare sites to their own idiosyncratic landmarks and few others can figure out those, so they can’t give good directions to others, either. Again, the comparison process gone badly wrong!!) But in going to the store do we see everything about us, the stores, the houses, etc.? Most of the time if you asked a person what was three doors down from a local shop they frequented, they couldn’t tell you. And there are endless numbers of examples of this, too. We miss most all the details. We deliberately ignore almost all of the universe, because of the fact we cannot remember it all due to limits of memory and processing information at less than 3-4 subjects at the same time. We are not good multitaskers for N =/> 3.
And this shows what’s going on in our day to day lives. We ignore most all of the details. We haven’t the capacity in our memories, either. And no wonder our models are incomplete!! Further, we cannot attend easily to more than about 2-3 things going on at the same time. There are limits to our awarenesses, too. This is easily shown in a practical sense by what happens when people drive and try to use their cell phones. They have about 4 times the number of accidents compared to those who don’t drive, if they use phones simultaneously. Therefore a good deal of our ignorance is not only memory capacity but channel capacity as well. Those are yet further instances of why most all our models are incomplete, as well.
28 In order to get around those limitations, let us employ the tool, the Structure/function model again. We have seen any number of people in our experience who are good multi-taskers. They can take those same tasks which many do and do a lot more in the same time and often better than most others. This is nothing new nor surprising. When Julius Caesar was dictating his Gallic war work, he had two scribes, one on each side of him. He’d dictate to the one to the point where his speaking rate was faster than the scribes writing rate, stop and then pick up where he left off with the other scribe, and repeated the process. Thus doing a lot, multitasking in the same way. Both dictating as well as composing what he would be dictating to the other. I had a college chemistry prof who not only would lecture to us in class about a subject which he knew well, but was simultaneously planning ahead about how his experiments would be done later that afternoon. He knew of others who could do the same. Many of us have.
I knew of a ward clerk who could finish up here work at about twice the rate of the other clerks in the same and other hospitals, tho her work load was not on average any more than the others. Someone in administration should have studied her, figured out how she did it, and taught the methods to the others. Not surprisingly that hospital closed 2 years later. To think that such a person could do that task so fast and well, & could be extended to other tasks in the hospital might have kept it open. Least energy rules.
Now why are these, known multitasking and brain dual tasking capabilities not being studied and then adapted to teaching others how to do it accurately and capably on a wide scale basis? Surely many others have seen and heard of the above abilities? Why stand so many here idle? The ability to double even quadruple our output by learning and having the self-discipline to learn these methods while still young is not to be scoffed at or ignore.
Let us proceed to another important issue relevant the above limits of human knowledge.
Categories and the Hierarchies
Herein, let us briefly explore how catergories come about using the comprisin process which both creates the categories, fills them in many cases with similarly structured/functioning elements and this then leads necessarily to the higher abstraions and categories of the hierarchies. Udnerstanding this relationship, and how the COMP can create and read the structure of this type, just as it both creates and reads maps, indices, dictionaires, encyclopeidas, phone book, directories, paginations, etc. It organizes the data creatively, thus building up an efficient, effectively, least energy method, which favors the creation of such organized forms.
Math cannot follow these categorical, hierarchically arranged transitional movements. The comparison process can navigate up and donw and among these changing levels, these epiphenomenological changes. The COMP can recognize, create and read them. Math can’t do this. Within categories, it can measure and count, and its other tasks. But math is ever the maid servant of verbal descriptions, not its master, which may explain some of the failures of math to describe most complex systems in the universe as well as complex systems of living species. Mathematics can describe to a limited extent within the categories, but it cannot scale up to the next. Words and the comparison process can, and this is another major limit to mathematics.