Thread: the limitations of mathematical results

1. Greetings forum members,

I am a great follower of all mathematical posts, but I am still haunted by the notion that mathematics relies on principaled observation, and not necessarily what their equations result to.

Of course mathematics can prove phenomena physics can not put better into words as mathematics can do with numbers, but can the use of mathematics actually lead us on linear chases of formula that can actually mislead physics into making words out of numbers that really do not state actual facts of observed phenomena?

Has this ever happened in the history of mathematical exercise?

2.

3. Originally Posted by theQuestIsNotOver
Greetings forum members,

I am a great follower of all mathematical posts, but I am still haunted by the notion that mathematics relies on principaled observation, and not necessarily what their equations result to.

Of course mathematics can prove phenomena physics can not put better into words as mathematics can do with numbers, but can the use of mathematics actually lead us on linear chases of formula that can actually mislead physics into making words out of numbers that really do not state actual facts of observed phenomena?

Has this ever happened in the history of mathematical exercise?
Mathematics is not physics.

Physics is not mathematics.

Mathematics cannot "prove phenomena" at all. The connection between mathematical models and physical phenomena, i.e. the validity of the model, is a matter of physics. It has nothing to do with mathematics.

4. yes sir.

(I have to say that I am surprise you didn't "get that" in my trasncript though)

Thank you for reminding me.

(btw)

Apologies for making your aquaintance out of season.......(and you are?).

No, seriously, thank you. If anyone asks me about any such a question, I will refer them to you.

Thank you again.

(lol)

For anyone else not in the mood to bark, could you please be relevant to the question and perhaps provide answers relevant to historical examples........um, any.

5. mathematics relies on principaled observation
No! mathematics never relies on observations , But it is the nature of mathematics that ti always fits in observations.

6. Math is amenable to the regularities in nature.

On the other hand: The Yang-Mills equations so much describe gluon behavior that we don’t even have to try to experimentally look at them to gain the same empirical information. Amazingly, the equations even came first, before the gluons’ discovery!

On yet some other hand (gleaned from Lee Smolin):

At the Bottom of it All

The last watch fire, that of mathematics, lights the shadows of the universe, telling us much about its machinery; and, yet, there is a kind of mysticism about this and its platonic forms and ideals of perfection; so, although no one has been killed in its name, it requires a kind of faith in what magic lies beneath it; but, perhaps, what is really there beneath and at the bottom of all, are statistics and probabilities averaged over large numbers of small events, which, though math-like come to be, are not exactly the root mathematical formulas; so, perhaps math is not at the bottom of all although it is very much amenable to the emergent and secondary patterns that we observe and measure thereafter, being very effective in describing that “real” world.

It’s just that, as Lee Smolin sort of said once, about platonic forms being underlying, “a flower is not a dodecahedron”. Is the universe, and even more so the world a reflection of some perfect mathematical form? Or does the world rest on the kind of statistical methodologies that underlie our understanding of biology?

Physicists, unlike biologists, wrestle not with reality but with mathematical representations of it. This is a great and masterly art, as is that of a painting artist, the high beauty obtained not from reproducing nature, but from representing it, with the addition that a physicist’s greatest creations may even truly capture some of the deep and permanent reality behind mere transient experience. There can be moments of blissful clarity, a rare combination, indeed, such as when one really comprehends Newton’s laws, and realizes simultaneously that what one has grasped mentally is a logic that is realized in each of the countless things that move in the world. And, yet, neither Newton’s nor Euclid’s laws completely capture the world, but are still a fine mirror of it, although not the finest and truest mirror of reality; plus, there are areas that can’t be completely captured by math. And, thus, what is both wonderful and terrifying is that there is absolutely no reason that nature at its very deepest level must have anything to do with math directly.

In many cases, there is a simple, non-mathematical reason that an aspect of the world follows a mathematical law on a subsequent plane. some systems have an enormous number of parts, such as why the air is spread uniformly in a room, no mystery or symmetry being required, or how the force on a rubber band increases proportionally to the distance stretched, this reflecting nothing deep, as the rubber band force we feel is a sum of an enormous number of small forces between the atoms. Each of which may act in a complicated, even unpredictable way, to the stretching.

A Platonist nightmare, then, would be that, in the end, at the bottom, all of our laws will be like this, all the regularities turning out to be more statistics, beyond which lies only randomness or irrationality. It must always come to this, as we already see in biology: that the tremendous beauty of the living world is but, in the end, merely a matter of randomness, statistics, and frozen accidents—for which the capture of there can be no one, single, and beautiful equation.

7. I can't be bothered reading this last post, but I strongly suspect it is gibberish.

But since you mentioned the Yang-Mills equations, perhaps you would care to write them down and explain them.

8. Originally Posted by questor
Physicists, unlike biologists, wrestle not with reality but with mathematical representations of it. This is a great and masterly art, as is that of a painting artist, the high beauty obtained not from reproducing nature, but from representing it, with the addition that a physicist’s greatest creations may even truly capture some of the deep and permanent reality-----------------------------. And, yet, neither Newton’s nor Euclid’s laws completely capture the world, but are still a fine mirror of it, although not the finest and truest mirror of reality; plus, there are areas that can’t be completely captured by math. And, thus, what is both wonderful and terrifying is that there is absolutely no reason that nature at its very deepest level must have anything to do with math directly.
I don't feel this is "gibberish" but maybe that is because I am not a mathematician.
Probably it should have been posted in another sub forum.
Of course mathematics is the language of science but often the non-mathematician gets the impression that with maths (as another poster said) one is looking at an extremely accurate map, but not the actual territory.
The map may give the most accurate information available, but does not necessarily show the complete picture.

9. questor, where exactly did those quotes come from?

It is not mathematics...but I feel it's not gibberish if one takes it philosophically.

10. Lee Smolin wrote an essay in one of those recent Best Science Stories compendiums that come out every year.

I guess it is still an open question of whether math underlies reality or not.

11. Originally Posted by questor
I guess it is still an open question of whether math underlies reality or not.
To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once. – Richard P. Feynman in The Character of Physical Law

12. My own view, as in my First Philosophy thread, is that Totality must be a single perfect mathematical equation, where the buck stops—since cause and effect cannot regress forever downward.

13. Originally Posted by DrRocket
Originally Posted by questor
I guess it is still an open question of whether math underlies reality or not.
To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once. – Richard P. Feynman in The Character of Physical Law
A summary update on CP. Snow’s idea, from the so-called Reality Club spokesman, I forget who, in that same Best Science Story compilation:

The essence of science is conveyed by its latin etymology: Sceintia, meaning knowledge. Science itself is then the body of knowledge obtained by using suitable practices for its fields. Science has spread into many areas, even psychology and the social sciences, and has become essential, for science is the most accurate way of obtaining knowledge about anything and everything.

Scholars who spurn science end up with inaccurate results, such as Marx, Freud, etc., and they and the religious scholars preach blah, blah, blah—as it’s all up in the air, empirically ungrounded. The traditional intellectual is being replaced, for science-oriented investigation now renders visible the deeper meanings and states beneath our being, redefining who and what we are.

The arts and science are now combining into an enlightened ‘third culture’ of a new intellectual landscape—a reality club of the new humanists. There are revolutionary developments everywhere. The wonderful whole-like approaches, such as those of the long-gone giants of Leonardo, Newton, Michelangelo, Darwin, and Einstein encompassing all. The previous incomprehensible humanism with an ignorance of science is fading fast away. The previous culture that dismissed science is soon to become a fossil of the past. The self-referential disciplines go nowhere, being most often concerned with the exegesis of earlier thinkers, in which one reflects on and recycles the ideas of others, with no real expectation of any systematic progress. They just get further away from reality.

Science poses questions to elicit answers. And the more science you do, the more there is to do. Reality is the final check and balance. There are no fixed, unalterable positions. Life plays an ever greater role in the future of the universe. Science is involved in all the humanities now. Subject matter is discussed, not intellectual style. Scientists talk about the universe, unlike many old style humanities academicians—who only talk about each other. Those disdaining science are doomed to be left behind.

Certainly, human nature is fixed, but its behavior isn’t, for it is sensitive to the environment, being endlessly variable and diverse. Change the environment for the good and behavior will then improve. There is no real need to fiddle with genes. The fixed rules of human nature can give rise to an inexhaustible range of outcomes. To know what changes to the environment would be appropriate and effective, you have to know the Darwinian rules. We only need to understand human nature, not to change it.

So, something radically new is in the air: new ways of understanding physical systems, new focuses that lead to our questioning of many of our foundations. A realistic biology of the mind, advances in physics, information technology, genetics, neurobiology, engineering, the chemistry of materials; all are questions of great importance with respect to what it means to be human.

(By some coincidence, after I read this, ‘Scientific American’ restated the theme and has therefore listed the ten recent great scientific contributors to humanity.)

15. Originally Posted by DrRocket

16. Originally Posted by Ophiolite
Originally Posted by DrRocket
There is little in common between mathematics and philosophy, other than formal logic. I am a mathematician and know a LOT of othere mathematicians. I don't know any mathematician who pays attention to philosophers (excluding logicians like Tarski). I don't even know anyone who knows anyone who ...

17. While the claim of an equivalency between mathematics and philosophy would be erroneous, there are some clear intersections. ()
http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes

18. Originally Posted by GiantEvil
While the claim of an equivalency between mathematics and philosophy would be erroneous, there are some clear intersections. ()
http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes
Except for formal logic there are no meaningful intersection within the last hundred years (more likely last 200 years but I am comfortable with a century +).

Decartes died in 1650.

In the very distant past science was "natural philosophy", but in modern times philosophy has been of, at best, questionable value to science, and less so to mathematics (ignoring the intersection in formal logic).

http://depts.washington.edu/ssnet/Weinberg_SSN_1_14.pdf

19. Originally Posted by DrRocket
There is little in common between mathematics and philosophy, other than formal logic. I am a mathematician and know a LOT of othere mathematicians. I don't know any mathematician who pays attention to philosophers (excluding logicians like Tarski). I don't even know anyone who knows anyone who ...
What about Descartes, Leibniz, Berkeley, Pascal, Arnauld, and van Nierop amongst others?

20. Originally Posted by Ellatha
Originally Posted by DrRocket
There is little in common between mathematics and philosophy, other than formal logic. I am a mathematician and know a LOT of othere mathematicians. I don't know any mathematician who pays attention to philosophers (excluding logicians like Tarski). I don't even know anyone who knows anyone who ...
What about Descartes, Leibniz, Berkeley, Pascal, Arnauld, and van Nierop amongst others?
Their work in philosophy is not useful to mathematicians. Remember also the "last century" restriction on what I said.

21. Originally Posted by DrRocket
I don't know any mathematician who pays attention to philosophers (excluding logicians like Tarski). I don't even know anyone who knows anyone who ...
Your academic ancestor did, and he is more competent at mathematics than anyone you know.

"Nothing can be loved or hated unless it is first understood."

--Leonardo da Vinci

22. Originally Posted by Ellatha
Originally Posted by DrRocket
I don't know any mathematician who pays attention to philosophers (excluding logicians like Tarski). I don't even know anyone who knows anyone who ...
Your academic ancestor did, and he is more competent at mathematics than anyone you know.

"Nothing can be loved or hated unless it is first understood."

--Leonardo da Vinci
If you go back far enough, all science was "natural philosophy" and the best scientists knew essentially all of mathematics and science. Newton was one of them. da Vinci was another, and also an artist. But that was then and this is now.

23. Originally Posted by DrRocket
Originally Posted by questor
I guess it is still an open question of whether math underlies reality or not.
To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once. – Richard P. Feynman in The Character of Physical Law
Werner Heisenberg said "what we observe is not nature itself, but nature exposed to our method of questioning".
That statement suggests that he had doubts "whether math underlies reality" despite the fact that mathematics, as the tool and language of physics, probes the deepest questions in nature.

24. Originally Posted by Halliday
Werner Heisenberg said "what we observe is not nature itself, but nature exposed to our method of questioning".
I agree with this. It is a self-evident statement.

Originally Posted by Halliday
That statement suggests that he had doubts "whether math underlies reality" despite the fact that mathematics, as the tool and language of physics, probes the deepest questions in nature.
I have no idea what this is supposed to mean.

25. I believe it's referring to the question of whether physical phenomena arise from mathematics, or if mathematics is simply the language that we view such phenomena with, with the physical not being dependent on the mathematical.

26. Originally Posted by AlexP
I believe it's referring to the question of whether physical phenomena arise from mathematics, or if mathematics is simply the language that we view such phenomena with, with the physical not being dependent on the mathematical.
No one has ever claimed that physical arise from mathematics -- how could they?

What has been claimed and thoroughly supported with evidence, is that natural phenomena can me described by mathematical models of great generality, which entails predictive power, and which enable deep insight.

To think that mathematics creates physical phenomena is tantamount to believing in witchcraft.

It is really quite simple. Mathematics is the study of order. Nature appears to be orderly.

27. Originally Posted by DrRocket
Originally Posted by Halliday
Werner Heisenberg said "what we observe is not nature itself, but nature exposed to our method of questioning".
I agree with this. It is a self-evident statement.

This statement, which may be self-evident, concerns epistemology - the central tenant of philosophy. Does math need concern itself with epistemology?

Also, I thought Alan Turing, highly regarded in philosophy, was a well respected mathematician?

28. Originally Posted by DrRocket
Originally Posted by AlexP
I believe it's referring to the question of whether physical phenomena arise from mathematics, or if mathematics is simply the language that we view such phenomena with, with the physical not being dependent on the mathematical.
No one has ever claimed that physical arise from mathematics -- how could they?

What has been claimed and thoroughly supported with evidence, is that natural phenomena can me described by mathematical models of great generality, which entails predictive power, and which enable deep insight.

To think that mathematics creates physical phenomena is tantamount to believing in witchcraft.

It is really quite simple. Mathematics is the study of order. Nature appears to be orderly.
I do not subscribe to that view myself, but I believe some do - the whole "the universe is one big equation" idea. I agree with what you just said.

29. Originally Posted by Prometheus
Originally Posted by DrRocket
Originally Posted by Halliday
Werner Heisenberg said "what we observe is not nature itself, but nature exposed to our method of questioning".
I agree with this. It is a self-evident statement.

Originally Posted by Prometheus
[This statement, which may be self-evident, concerns epistemology - the central tenant of philosophy. Does math need concern itself with epistemology?
no

Mathematics is derived from a small set of postulates that are accepted without proof (Zermelo Fraenkel axioms of set theoy plus the Axiom of Choice in almost all cases). The rest is just definitions and logic. I have never heard any discussion of epistemology among mathematicians regarding mathematical knowledge.. I do not expect that I ever will.

Science requires evience from nature, and epistemology applies. But scientists have their own views in the subject and there is little influence in practice from professional philosophers. The debates tend not to be on epistomology, but rather on the accuracy of the data and the analysis of the data.

Epistomologists analyze the work of physicists. Physicists ignore epistomologists. http://depts.washington.edu/ssnet/Weinberg_SSN_1_14.pdf

Originally Posted by Prometheus
[Also, I thought Alan Turing, highly regarded in philosophy, was a well respected mathematician?
I specifically noted the interest of mathematicians in formal logic and set theory. In that sense Turing is regarded as a mathematician He was educated as as a mathematician (a student of Church at Princeton). The same comment applies to Tarski.

Academic joke: A new university was being established. The Board of Regents decided that they neededat least one prestigous department, but had a limited budget. Said one member: "Let's invest in a first rate mathematics department. All the mathematicians need are pencils, paper and vwaste baskets." Responded a second member : "How about a Philosophy department ? They don't need waste baskets."

30. Originally Posted by DrRocket
If you go back far enough, all science was "natural philosophy" and the best scientists knew essentially all of mathematics and science.
This was largely the case in the time of Aristotle or Plato, but Galileo Galilei developed the modern notion of physics, thus leading Einstein to call him the "father of modern physics." As you know, Galileo's time is before that of Newton's. I.e., in Newton's time science had been established to be separate from natural philosophy.

Originally Posted by DrRocket
Newton was one of them. da Vinci was another, and also an artist. But that was then and this is now.
da Vinci was also an inventor, architect, geometer, biologist, sculptor, musician, geologist, anatomist, and cartographer amongst the list of topics included in the enormous universality of his genius.

The fact is that science owes a huge debt to philosophy, yet despite many problems related to the scientific method it considers philosophy unworthy of consideration. Science relies on the scientific method, which states that scientists can only develop theories related to observed phenomena, which limits the depth of knowledge of reality to a great extent. On the other hand, mathematics is based on logical propositions rather than materialistic observations (the Cartesian divider of the material and mental world referred to as dualism). Even Einstein's work in physics borders on the line of philosophy (in particular metaphysics).

The reason philosophy is not a critical part of the extent educational curriculum (disregarding the theory of knowledge course provided to some advanced programs) is that it doesn't aid in the development of practical technology to as great an extent as science (or mathematics). That is, research is funded on the basis of increasing technology or solving problems with applications that would result in an increase in technology. Since philosophy, while it allows us to ask among the more sublime problems that relate to our universe, is inferior to both mathematics and science in this respect receives and as a result little attention from the academic community. On the other hand, philosophy has essentially broken down all of its sub-branches to different parts of academia for which they can be found: for example, morals and ethics are often related to the subject of law and government policy, logic, which was originally studied in parallel with philosophy is now a subject of large discussion in mathematics, and social philosophy is largely studied in sociology as another example.

A scientist that understands philosophy is better than a scientist that doesn't, and similarly a mathematician that understands philosophy is better than a mathematician that doesn't. This is because philosophy provides a cybernetic understanding of problems and the algorithms and logic that should be used in solving them.

Such scientists and mathematicians that attack philosophy do not understand philosophy, nor do they understand that the subjects of study they have undertaken were once essentially branches of philosophy. For example, you often use the satirical question of "does a horse exist" at an attempt of downgrading the questions raised by philosophers. On the other hand, such a question is a profound one that is more relevant than many of the questions raised by mathematicians and scientists. Namely, such a question does not address the pragmatic question of "does a horse exist" but a deeper, existentialism question of is our world mental or material in nature? The question was answered by Descartes long before science and mathematics were the dominant branches of technical academic study.

31. The Music of the Primes

…order to bring harmony within the human-world-system.

The music closest to the TOE is the harmony of the TOE itself, a symphonic orchestra consisting of the universal, galactic, and solar sections all playing in concert; yet, all their instruments are still separate, no one sound rising above the others, such as the pattern between the patterns arising to make the prime number keys, much like a string plucks its harmonics of 1/2, 1/3, 1/4, etc. It’s not quite the music of the spheres, yet, they, too, resonate to it, flinging it down from the father sky to our mother earth.

So, the songs of life, too, are sung to it, yet they are vibrations of it, and all music repeats it. It is the pattern outside of the patterns, the primes conducting all the rest of the musical numbers. (The proof may remain incomplete even into the year 1,000,000, yet it remains “conditionally” true.)

Of the seven wonders of the old world, only the Giza pyramid remains, the rest having succumbed to fire and earthquakes. The life of some things approaches forever. The prime numbers march on, never ending, as we will see, although the non-primes ever chip away at the prime real estate.

Alien beings from Vega beam a series of prime numbers to earth…
Primes are the atomic elements of arithmetic, from which all the non-primes can be formed. What is the secret of their pattern? It would seem that only the non-primes have a pattern, those being their nth instances.

How then can can there be an unobviously unpatterned pattern between the patterns in these leftover spaces in between? The even numbers already cut the prime potential in half, but for ‘2’, which is the only even prime. The multiples of ‘3’ then remove another swath, although less than a third, ‘4’ doing nothing, and ‘5’, some more, and so on, these few numbers alone already consuming perhaps over 70% of the numerical realm. Yet, there will ever be more primes, some even so-called “twins”, like 1,000,000,009,649 and 1,000,000,009,651, for, the harmonics may only approach 100% but never get to it.

Bertrand Russell once wrote and thought that “mathematics possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” however, in later life, Bertrand dismissed his youthful rhapsodizing as “largely nonsense”, writing “mathematics has ceased to seem to me nonhuman in its subject matter. I have come to believe, though very reluctantly, that it consists of tautologies.”

Will math become even more trivial than six of the seven wonders? Primes seem to be special since they cannot be split into smaller factors. All the unspecial non-primes can be obtained by multiplying primes together, for example, ‘666’ is 2 x 3 x 3 x 37, this being called the “fundamental theorem of arithmetic”.

How many primes are there? There are an “infinite” number, as Euclid shows, for, if they were a finite number, then one could always obtain another by multiplying the primes together and adding ‘1’. What then the pattern of the “primal” scattering, seeming more as random weeds sprouting? Are we in the presence of one of the inexplicable secrets of creation? Are they of a complex and timeless reality that is independent of our minds? Are they transcendently mysterious? No, for they obey a law.

The Law of Primes

Here we must climb the edifice of mathematics that rises above the humble counting numbers, the fractions, and the real numbers—all the way up to the complex numbers with “imaginary” parts. Here we find the Riemann zeta hypothesis that holds the secrets of the primes, after an ascent taking over two millennia. If true, then there is a hidden harmony to the primes, one that is rather beautiful. In 1900, David Hilbert included it on his list of the 23 most important problems in mathematics. It is the only one that remains.

Computers have thrown zillions of numbers at it and yet it holds, never failing; but, what would it do further on in its path toward “infinity”? If it ever fails, even once, then all the thousands of theorems of higher mathematics “conditioned” on its hypothesis will collapse into a heap of meaninglessness. What, then, and where, are the ever shrinking recesses in which primes can grow forever?

The zeta functions has its origins in music, the vibrating violin string creating all the overtones of the note, know as the “harmonic series” of 1/2 + 1/3 + 1/4 +…

If we take every term in this series and raise it to the variable power ‘s’, we get the zeta function, introduced by Euler, around 1740:

Zeta(s) = (1/2)**s + (1/3)**s +, etc.

He then noted that this infinite sum could be rewritten as an infinite product:

Zeta(s) = 1/(1-1/2**s) x 1/(1-1/3**s) x …

However, he didn’t fully grasp the potential of his infinite product formula, writing that the human mind would never penetrate the mystery of the sequence of the prime numbers.

In 1792, Gauss noted that one could estimate how many primes there were up to a given number by dividing that number by its natural logarithms, the percentage of error heading toward zero as the number got larger. This, then, was “the coin that nature tossed to choose the primes.” Again, it might not hold unto infinity, nor does it predict any primes. It was Reimann who would dispel any lingering illusion of randomness/mystery.

The Prime Hypothesis

In 1859, Reimann cracked the mystery.

He began with the zeta function, enlarging it to take in the complex numbers, those having both a real and an “imaginary” part involving ‘i’, the square root of ‘-1’. The complex numbers are two-dimensional, so they can be graphed on a plane. In effect, Reimann created a vast imaginary zeta landscape, consisting of mountains, hills, and valleys that stretched forever in every direction. The sea-level points, those with zero altitude that yielded the zeta output zero, were the most interesting, for they showed exactly how the infinity of primes arranged themselves in the number sequence.

There was no longer random noise in the primes, for now there was a way to hear their music. Each zero of the zeta function, when plugged into Reimann’s prime formula, produced a wave resembling a pure musical tone. When these pure tones are all combined, they reproduce the structure of the prime numbers, the particular location of any given zero in the zeta landscape determining the pitch and volume of its corresponding musical note, and, very importantly, the farther east it was, the greater the loudness. With all the zeroes lying in a fairly narrow longitudinal strip of the zeta landscape, and only if, can the orchestra of the primes play in balance, with no instrument drowning out the others. But Reimann went further.

After navigating just a tiny portion of the infinite zeta landscape he asserted that all of its zeroes were precisely arrayed along a “critical line” running from north to south—and it is this claim that became known as the Reimann zeta hypothesis.

Epilog

The ebb and flow of the primes, then, is the pattern of each instrument playing, but combining together with the others so perfectly that the patterns cancel themselves out. We may predict that long before the year 1,000,000 A.D., mathematicians will awaken from their collective Platonist dream, noting, like Bertrand, “you are only symbolic convenience.”

While even the Giza pyramid may crumble, along with the magic of numbers, we will still have laughter—the so-called hardest problem of the primes then becoming a somewhat broad joke of a trivial tautology to the schoolchildren of some distant time.

32. Originally Posted by Ellatha
A scientist that understands philosophy is better than a scientist that doesn't, and similarly a mathematician that understands philosophy is better than a mathematician that doesn't. This is because philosophy provides a cybernetic understanding of problems and the algorithms and logic that should be used in solving them.
I have no idea whom you are parroting. Probably some philosopher, since what you have is a positive assertion, with no data that makes no sense. I can think of no meaning of "cybernetic" that makes the last sentence true, or even meaningful. It just this sort of meaningless drivel from philosophers that reinforces the understandable tendency of scientists and mathematicians to ignore them in their professional work.

Originally Posted by Ellatha
Such scientists and mathematicians that attack philosophy do not understand philosophy, nor do they understand that the subjects of study they have undertaken were once essentially branches of philosophy.
More likely because they understand this better than do you. Science grew from Natural Philosophy, but Natural Philosophy is no longer a viable branch of what has become modern philosophy. Modern philosophers study the work of modern scientists, but the reverse is not true in their professional work..

Originally Posted by Ellatha
For example, you often use the satirical question of "does a horse exist" at an attempt of downgrading the questions raised by philosophers. On the other hand, such a question is a profound one that is more relevant than many of the questions raised by mathematicians and scientists. Namely, such a question does not address the pragmatic question of "does a horse exist" but a deeper, existentialism question of is our world mental or material in nature? The question was answered by Descartes long before science and mathematics were the dominant branches of technical academic study.
You have got to be kidding. Even philosophers think solipsism is a bad joke. Materialism vs idealism is a false dichotomy, and debating one against the other is silly.

33. Originally Posted by DrRocket
I have no idea whom you are parroting. Probably some philosopher, since what you have is a positive assertion, with no data that makes no sense.
There is an explanation for your first sentence. Let A be the individual who wrote the original statements. Let B be the individual who regurgitated the information. If A = B, than there is no unique "parrot-er" in the conventional sense, namely my writing is original.

Originally Posted by DrRocket
I can think of no meaning of "cybernetic" that makes the last sentence true, or even meaningful.
Science, mathematics, and philosophy are all subjects of study that relate to one goal: accumulating descriptions, i.e., theories, regarding the universe.

All three are unique in some fashion. For example, scientists follow the scientific method: namely, their theories are derived from empirical measures. However, in being in compliance with the scientific method, scientists cannot make theories relating to phenomenon that occurs outside of the senses. In the problematic resolution to the mind-matter problem of philosophy, scientists suggests that reality is materialistic in essence.

Mathematicians are fairly different in their approach: rather than basing their theories on observations, they choose to derive them via a collection of self-evident statements called axioms or postulates and from logical propositions ramify theories that are in agreement with the necessary, initial conditions. In other words, rather than basing their theories on materialistic events, mathematicians base their work on the mental picture of reality and from that derive their conclusions.

Originally Posted by DrRocket
It just this sort of meaningless drivel from philosophers that reinforces the understandable tendency of scientists and mathematicians to ignore them in their professional work.
One can similarly say that scientists and mathematicians ignore one another in their professional work (up to a certain extent, science borrows from mathematics as much as all branches of study borrow from philosophy). There is a logical reason for this: let A = science, B = mathematics, C = philosophy,

Originally Posted by DrRocket
More likely because they understand this better than do you. Science grew from Natural Philosophy, but Natural Philosophy is no longer a viable branch of what has become modern philosophy. Modern philosophers study the work of modern scientists, but the reverse is not true in their professional work..
I do not believe that most scientists and mathematicians understand philosophy better than me. I've read and thought quite a bit relating to this subject.

http://en.wikipedia.org/wiki/Edmund_Husserl
http://en.wikipedia.org/wiki/William_Whewell

Originally Posted by DrRocket
You have got to be kidding. Even philosophers think solipsism is a bad joke. Materialism vs idealism is a false dichotomy, and debating one against the other is silly.
I was referring to the issue of materialism as opposed to idealism (and I'm aware that this problem is generally regarded as solved to date). Solipsism is a form of skepticism rather than a mainstream theory with regard to certain philosophical debates.

Philosophy is not merely based around any branch with the suffix "-ism." It's a much more sophisticated topic of discussion than that; to understand philosophy one must first understand the topics of discussion of philosophy (such as the argument for the existence of God, the counterargument related to the existence of evil, the problem of freewill, existence, morals and ethics and et cetera). Afterward, a philosopher must study logic and formal proofs (with the philosophy of mathematics, special and general relativity, and quantum mechanics), followed by the history of philosophy (with an emphasis on Cartesian principles, and the philosophy of Pascal, Spinoza, Hume, and Kant). Advanced courses consist of advanced logic, linguistics and semantics, epistemology, and afterward a reading related to various philosophical ideas (which mostly consist of ideas with the suffix "-ism").

As a generality, we all have a philosophy of some sort, in this specific instance yours could be considered "anti-philosophy" (at least with respect to certain subjects of discussion).

34. Originally Posted by Ellatha
As a generality, we all have a philosophy of some sort, in this specific instance yours could be considered "anti-philosophy" (at least with respect to certain subjects of discussion).
Of course scientists have a philosophy. They philosophisize -- much better than do philosophers.

35. Originally Posted by DrRocket
They philosophisize -- much better than do philosophers.
No, they don't. And neither does your posse.

36. Originally Posted by Ellatha
Originally Posted by DrRocket
They philosophisize -- much better than do philosophers.
No, they don't. And neither does your posse.

Yes, they do.

This is not to say that there are not a few bright philosophers out there. They do exist. But they are irrelevant to the progress of science and mathematics.

Wittgenstein remarked that "nothing seems to me less likely than that a scientist or mathematician who reads me should be seriously influenced in the way he works." -- from Dreams of a final Theory by Steven Weinberg

37. Originally Posted by Ellatha
There is an explanation for your first sentence. Let A be the individual who wrote the original statements. Let B be the individual who regurgitated the information. If A = B, than there is no unique "parrot-er" in the conventional sense, namely my writing is original.
Too bad. There goes the option of blaming it on someone else.

38. Originally Posted by DrRocket
Yes, they do.

This is not to say that there are not a few bright philosophers out there. They do exist. But they are irrelevant to the progress of science and mathematics.

Wittgenstein remarked that "nothing seems to me less likely than that a scientist or mathematician who reads me should be seriously influenced in the way he works." -- from Dreams of a final Theory by Steven Weinberg
I'm not impressed.

Originally Posted by DrRocket
Too bad. There goes the option of blaming it on someone else.
Yes; the totality of the blame belongs to me.

39. Mathematics, philosphy, and physics.

Mathematics is the use of numbers, which as a tool can be applied to conepts of space-time. On it's own, it is the use of numbers, real or unreal, finding patterns between numbers using equations, and so on.

Physics is the study of space-time, putting to words observed phenomena. Explaining physics with mathematics is physics employing mathematics as a tool.

Mathematics has been used to predict outcomes for physics. That is the current trend of physics, to employ mathematics. For, without mathematics, physics can only "propose" ideas that have yet to be confirmed, and on that front, in the absence of using mathematics, they employ a type of philosophy; hypothesis, prediction, possibility.

My question asked what the limitation of mathematics was. By the development of the responses, the ensuing arguments, it seems the limitation of mathematics is the philosophy of argument. Would anyone agree?

40. Originally Posted by theQuestIsNotOver
Mathematics, philosphy, and physics.

Mathematics is the use of numbers, which as a tool can be applied to conepts of space-time. On it's own, it is the use of numbers, real or unreal, finding patterns between numbers using equations, and so on.

Physics is the study of space-time, putting to words observed phenomena. Explaining physics with mathematics is physics employing mathematics as a tool.

Mathematics has been used to predict outcomes for physics. That is the current trend of physics, to employ mathematics. For, without mathematics, physics can only "propose" ideas that have yet to be confirmed, and on that front, in the absence of using mathematics, they employ a type of philosophy; hypothesis, prediction, possibility.

My question asked what the limitation of mathematics was. By the development of the responses, the ensuing arguments, it seems the limitation of mathematics is the philosophy of argument. Would anyone agree?
You are being rather narrow in your conclusion (there is much more to it than this), however what you have said is not incorrect. For example, all of science borrows from mathematics (for example, biostatistics and and biophysics). Mathematics has been shown to hold internally consistent but externally inconsistent systems by Kurt Godel, and as a result we are not able to use mathematics alone to understand the entirety of reality.

Although, some individuals excel at certain subjects over others. For example, I have a greater aptitude in philosophy than mathematics or science, while I know others that pose terrible philosophical arguments but are excellent at science, while being only average at mathematics. Therefore, one should not necessarily pursue philosophy as a subject of study, but whichever branch they are most interested and competent in, as they all have advantages with regard to certain subjects (for example, because science concerns itself with the senses, it allows us to progress technology rather rapidly as opposed to mathematics and certainly philosophy).

Unfortunately for me, philosophers are not in high-demand because of the aforementioned reason as opposed to mathematicians and scientists. This is largely because funding money is provided by the government, which decides that "technological advancement" will provide greater happiness for its people than philosophical wisdom (by making their lives easier). On the other hand, what the top of the socio-economic and political ladder don't understand is that by providing materialistic goods to their people they are only stimulating their mental responses, so one can just as much gain happiness from philosophy as they can from the technological advancements in mathematics and science (and even to a more direct extent).

41. Without being too narrow as a conclusion, would it be right to suggest that in the absence of mathematics being able to fill the great gaps of scientific logic, as what mathematics cannot offer science, could philosophy better explain or should I say better "provide" as an explanation (that which mathematics can't explain with consistent equations)? For instance, mathematics has yet to provide a link between gravity and electro-magnetism, but we know one exists, because we perceive the two to exist in this one reality.

42. Originally Posted by theQuestIsNotOver
Mathematics, philosphy, and physics.

Mathematics is the use of numbers, which as a tool can be applied to conepts of space-time. On it's own, it is the use of numbers, real or unreal, finding patterns between numbers using equations, and so on.
wrong

Originally Posted by theQuestIsNotOver
Physics is the study of space-time, putting to words observed phenomena. Explaining physics with mathematics is physics employing mathematics as a tool.
wrong

Originally Posted by theQuestIsNotOver
Mathematics has been used to predict outcomes for physics. That is the current trend of physics, to employ mathematics. For, without mathematics, physics can only "propose" ideas that have yet to be confirmed, and on that front, in the absence of using mathematics, they employ a type of philosophy; hypothesis, prediction, possibility.
not even wrong

Originally Posted by theQuestIsNotOver
My question asked what the limitation of mathematics was. By the development of the responses, the ensuing arguments, it seems the limitation of mathematics is the philosophy of argument. Would anyone agree?
perhaps some fool somewhere

There are too many false assumptions to be worth addressing this mess in detail. Try reading the essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene Wigner.

http://www.dartmouth.edu/~matc/MathD...ng/Wigner.html

43. Originally Posted by theQuestIsNotOver
Without being too narrow as a conclusion, would it be right to suggest that in the absence of mathematics being able to fill the great gaps of scientific logic, as what mathematics cannot offer science, could philosophy better explain or should I say better "provide" as an explanation (that which mathematics can't explain with consistent equations)? For instance, mathematics has yet to provide a link between gravity and electro-magnetism, but we know one exists, because we perceive the two to exist in this one reality.
The theories of philosophy are broader than those of mathematics or science, and as a result philosophers have built the reputation of questioning everything (as they should). An excellent textbook for an introduction to philosophy is Reason and Responsibility, 12 edition, by Joel Fernberg and Russ-Shafer-Landau. However the price is rather high.

Feel free to message me or create a thread for other questions related to the subject philosophy (in the philosophy sub-forum, of course, although I must say most members in that particular forum are rather under-competent at the subject [nor should I expect otherwise, after all, this is a science forum]). You can find much better philosophy forums by using a search engine.

44. Mmmm. I think I have incorrectly given you the idea I am in support of philosophy filling a gap either mathematics or physics cannot.

In returning to the initial subject of the possible limitation of mathematics, maybe I should re-phrase the question: does mathematics consider itself to "have" a limitation; if so, what is it, if not, how so?

45. Originally Posted by theQuestIsNotOver
Mmmm. I think I have incorrectly given you the idea I am in support of philosophy filling a gap either mathematics or physics cannot.

In returning to the initial subject of the possible limitation of mathematics, maybe I should re-phrase the question: does mathematics consider itself to "have" a limitation; if so, what is it, if not, how so?
In that case this is a purely mathematical question (and therefore science and philosophy shouldn't be discussed); the limitations of mathematical knowledge is not a mathematical question, therefore mathematicians recognize no limit.

46. Originally Posted by Ellatha
Originally Posted by theQuestIsNotOver
Mmmm. I think I have incorrectly given you the idea I am in support of philosophy filling a gap either mathematics or physics cannot.

In returning to the initial subject of the possible limitation of mathematics, maybe I should re-phrase the question: does mathematics consider itself to "have" a limitation; if so, what is it, if not, how so?
In that case this is a purely mathematical question (and therefore science and philosophy shouldn't be discussed); the limitations of mathematical knowledge is not a mathematical question, therefore mathematicians recognize no limit.

For the record, I wasn't the one who went off track with the initial question. My aim was to find in mathematical terms what the limit to mathematical utility was/is/is-perceived-to-be.

In following up your position though, if the idea of "mathematics not knowing it's limitation, not accepting one" is a standard set of values of mathematical expression of values/tenets/processes, what great mathematician in history, or contemporary if the case may be, has put this eloquently enough to be considered an ambassador of this truth?

47. Originally Posted by Ellatha
Originally Posted by theQuestIsNotOver
Mmmm. I think I have incorrectly given you the idea I am in support of philosophy filling a gap either mathematics or physics cannot.

In returning to the initial subject of the possible limitation of mathematics, maybe I should re-phrase the question: does mathematics consider itself to "have" a limitation; if so, what is it, if not, how so?
In that case this is a purely mathematical question (and therefore science and philosophy shouldn't be discussed); the limitations of mathematical knowledge is not a mathematical question, therefore mathematicians recognize no limit.
Rubbish

Mathematical "knowledge" is based upon that which may logically be deduced from accepted axioms, normally the Zermelo Fraenkel axioms plus the Axiom of Choice. Any relationship between what follows from those axioms and the natural world is a question for science, not for mathematics -- which is an inherent limitation.

Moreover, as one sees from the Godel incompleteness theorems, there are limitations on that which can be logically inferred from the axioms. There are true statements that cannot be proved via formal logic within the axioms. That is most certainly a limitation.

Mathematicians, of which I am one and you are not, recognize those limitations and work within them.

48. Originally Posted by DrRocket
Originally Posted by Ellatha
Originally Posted by theQuestIsNotOver
Mmmm. I think I have incorrectly given you the idea I am in support of philosophy filling a gap either mathematics or physics cannot.

In returning to the initial subject of the possible limitation of mathematics, maybe I should re-phrase the question: does mathematics consider itself to "have" a limitation; if so, what is it, if not, how so?
In that case this is a purely mathematical question (and therefore science and philosophy shouldn't be discussed); the limitations of mathematical knowledge is not a mathematical question, therefore mathematicians recognize no limit.
Rubbish

Mathematical "knowledge" is based upon that which may logically be deduced from accepted axioms, normally the Zermelo Fraenkel axioms plus the Axiom of Choice. Any relationship between what follows from those axioms and the natural world is a question for science, not for mathematics -- which is an inherent limitation.

Moreover, as one sees from the Godel incompleteness theorems, there are limitations on that which can be logically inferred from the axioms. There are true statements that cannot be proved via formal logic within the axioms. That is most certainly a limitation.

Mathematicians, of which I am one and you are not, recognize those limitations and work within them.

So, the logical question here is, "can the natural limitations of mathematics clearly state to science why their own utility can no longer be of service to explaining types of observed phenomena that would circumscribe an axiomatic mathematical limitation"? Or, more precisely, "what aspects of science would mathematics agree they cannot be appled to, as based on their natural axiomatic limitation"?

49. Originally Posted by theQuestIsNotOver

So, the logical question here is, "can the natural limitations of mathematics clearly state to science why their own utility can no longer be of service to explaining types of observed phenomena that would circumscribe an axiomatic mathematical limitation"? Or, more precisely, "what aspects of science would mathematics agree they cannot be appled to, as based on their natural axiomatic limitation"?
That is not a logical question at all, and it has nothing whatever to do with any axiomatic limitation. You have missed the point entirely.

The fact that nature appears amenable mathematical descriptions is an issue for svience, not mathematics.

Mathematics states nothing to science. Science employs mathematics to describe nature. Given a mathematical model, mathematicians can deduce logical consequences of that model, but science and only science determines if the model is an accurate description of nature.

50. Originally Posted by DrRocket
Rubbish

Mathematical "knowledge" is based upon that which may logically be deduced from accepted axioms, normally the Zermelo Fraenkel axioms plus the Axiom of Choice. Any relationship between what follows from those axioms and the natural world is a question for science, not for mathematics -- which is an inherent limitation.

Moreover, as one sees from the Godel incompleteness theorems, there are limitations on that which can be logically inferred from the axioms. There are true statements that cannot be proved via formal logic within the axioms. That is most certainly a limitation.

Mathematicians, of which I am one and you are not, recognize those limitations and work within them.
This is a complete and utter waste of American English. You have said nothing that is not already known or relevant.

51. Originally Posted by DrRocket
Originally Posted by theQuestIsNotOver

So, the logical question here is, "can the natural limitations of mathematics clearly state to science why their own utility can no longer be of service to explaining types of observed phenomena that would circumscribe an axiomatic mathematical limitation"? Or, more precisely, "what aspects of science would mathematics agree they cannot be appled to, as based on their natural axiomatic limitation"?
That is not a logical question at all, and it has nothing whatever to do with any axiomatic limitation. You have missed the point entirely.

The fact that nature appears amenable mathematical descriptions is an issue for svience, not mathematics.

Mathematics states nothing to science. Science employs mathematics to describe nature. Given a mathematical model, mathematicians can deduce logical consequences of that model, but science and only science determines if the model is an accurate description of nature.

Agreed that it wasn't a logical question, as the context of the question was not agreed on a shared platform of intertest held on a set of common variables of interest. It appears to be a perceived difference though for the time being.

In though replying to your actual comment, mathematics states nothing to science, agreed. Science employs mathematics to explain nature, agreed. Mathematical models deducing consequences, agreed. Science deducing if a mathematical model is suitable to nature, agreed.

Mathematics clearly is no God, but it still "is what it is" nonetheless, right?

52. Originally Posted by Ellatha
Originally Posted by DrRocket
Rubbish

Mathematical "knowledge" is based upon that which may logically be deduced from accepted axioms, normally the Zermelo Fraenkel axioms plus the Axiom of Choice. Any relationship between what follows from those axioms and the natural world is a question for science, not for mathematics -- which is an inherent limitation.

Moreover, as one sees from the Godel incompleteness theorems, there are limitations on that which can be logically inferred from the axioms. There are true statements that cannot be proved via formal logic within the axioms. That is most certainly a limitation.

Mathematicians, of which I am one and you are not, recognize those limitations and work within them.
This is a complete and utter waste of American English. You have said nothing that is not already known or relevant.
It is quite relevant, and equally apparent that you don't understand it. What is a waste of time are your comments, which reveal a rather poor grasp of both mathematics and science, typical of someone with an inflated ego but lacking in understanding of the subject matter.

Pascal you ain't.

53. Originally Posted by theQuestIsNotOver
Mathematics clearly is no God, but it still "is what it is" nonetheless, right?
One cannot disagree with a tautology.

Did you read Wigner's essay ?

54. Originally Posted by DrRocket
It is quite relevant, and equally apparent that you don't understand it. What is a waste of time are your comments, which reveal a rather poor grasp of both mathematics and science, typical of someone with an inflated ego but lacking in understanding of the subject matter.
How unfortunate that over twenty years of professional mathematics has only provided you with a rudimentary understanding of it. Than again I suppose that slow people learn slow.

Originally Posted by DrRocket
Pascal you ain't.
Nor do I need to be to know that I easily possess more aptitude in the field of mathematics than you.

55. Originally Posted by Ellatha
Originally Posted by DrRocket
It is quite relevant, and equally apparent that you don't understand it. What is a waste of time are your comments, which reveal a rather poor grasp of both mathematics and science, typical of someone with an inflated ego but lacking in understanding of the subject matter.
How unfortunate that over twenty years of professional mathematics has only provided you with a rudimentary understanding of it. Than again I suppose that slow people learn slow.

Originally Posted by DrRocket
Pascal you ain't.
Nor do I need to be to know that I easily possess more aptitude in the field of mathematics than you.
Seriously, you need professional help.

56. Originally Posted by DrRocket
Originally Posted by theQuestIsNotOver
Mathematics clearly is no God, but it still "is what it is" nonetheless, right?
One cannot disagree with a tautology.

Did you read Wigner's essay ?

I think I know what you mean, but I'll take a look nonetheless. My remark though aimed to highlight that there is not necessarily a tautology at work, but it's opposite; although the "is what it is" phrase could be interpreted as a "god is nonsense" idea (and thus support a tautology), I was highlighting a duality instead at work, a schism of operation, that mathematics is falsely trying to be a God, and thus my initial question as to what limit such a course has found itself contained within.

57. Originally Posted by theQuestIsNotOver
a schism of operation, that mathematics is falsely trying to be a God, and thus my initial question as to what limit such a course has found itself contained within.
ridiculous

58. Originally Posted by DrRocket
Originally Posted by theQuestIsNotOver
a schism of operation, that mathematics is falsely trying to be a God, and thus my initial question as to what limit such a course has found itself contained within.
ridiculous

But, if there were to be a tautology present, you would need someone like Alan Turing to explain it, to suggest how a mathematical model could "explain itself".

59. Originally Posted by theQuestIsNotOver

But, if there were to be a tautology present, you would need someone like Alan Turing to explain it, to suggest how a mathematical model could "explain itself".

There are always tautologies present.

No useful model explains itself.

You hardly need Turing to understand this stuff.

You are just spewing typical philosophical obfuscations. Junk.

60. Originally Posted by DrRocket
Originally Posted by theQuestIsNotOver

But, if there were to be a tautology present, you would need someone like Alan Turing to explain it, to suggest how a mathematical model could "explain itself".

There are always tautologies present.

No useful model explains itself.

You hardly need Turing to understand this stuff.

You are just spewing typical philosophical obfuscations. Junk.

Yes, there are always tautologies present, but ultimately we are getting at the idea of tautology-set-A and tautology-set-B presuming to equal one another to be an overall tautology, when the only way that can happen is as Turing rightly suggested tautology-set-A explains tautology-set-B and vice-versa. That maybe word salad to some people in your own tautology of life, but I am not of the "word salad" opinion on the matter of what Turing insightfully presented on the case of mathematics at the time, which lead to the development of computer technology nonetheless, near-AI cases of mathematical equations calibrating itself. But, as my initial question aimed to reach, "with limits", not as perfect as it "could be".

Turning designed a mathematical model that interfaced with the operation of a machine, yes. And we are forever in his debt for that. But he only went that far. He didn't go to the level of using that type of mathematics to interface with the operation of space-time. If he went that far, he could have designed a way to explain how the so-called equilibrium in space-time works (aka gravity).

I am therefore a firm believer that some type of Turing-styled mathematical "symmetry" is required to explain gravity in regard to atomic-phenomena. And as you pointed out, Wigner touched on this his own way. But the mathematics required for that symmetry may require a different application of mathematics to theories of space-time to make that work and thus to make it useful to technology. To make it work, we need to know the limits of mathematics, be honest about that, and work with that in the construction of any required mathematical models of space-time symmetry.

.

61. Originally Posted by theQuestIsNotOver

Yes, there are always tautologies present, but ultimately we are getting at the idea of tautology-set-A and tautology-set-B presuming to equal one another to be an overall tautology, when the only way that can happen is as Turing rightly suggested tautology-set-A explains tautology-set-B and vice-versa. That maybe word salad to some people in your own tautology of life, but I am not of the "word salad" opinion on the matter of what Turing insightfully presented on the case of mathematics at the time, which lead to the development of computer technology nonetheless, near-AI cases of mathematical equations calibrating itself. But, as my initial question aimed to reach, "with limits", not as perfect as it "could be".

Turning designed a mathematical model that interfaced with the operation of a machine, yes. And we are forever in his debt for that. But he only went that far. He didn't go to the level of using that type of mathematics to interface with the operation of space-time. If he went that far, he could have designed a way to explain how the so-called equilibrium in space-time works (aka gravity).

I am therefore a firm believer that some type of Turing-styled mathematical "symmetry" is required to explain gravity in regard to atomic-phenomena. And as you pointed out, Wigner touched on this his own way. But the mathematics required for that symmetry may require a different application of mathematics to theories of space-time to make that work and thus to make it useful to technology. To make it work, we need to know the limits of mathematics, be honest about that, and work with that in the construction of any required mathematical models of space-time symmetry.

.
more meaningless word salad seasoned with misconceptions

not even a hint of a serious thought

62. Originally Posted by DrRocket
Originally Posted by theQuestIsNotOver

Yes, there are always tautologies present, but ultimately we are getting at the idea of tautology-set-A and tautology-set-B presuming to equal one another to be an overall tautology, when the only way that can happen is as Turing rightly suggested tautology-set-A explains tautology-set-B and vice-versa. That maybe word salad to some people in your own tautology of life, but I am not of the "word salad" opinion on the matter of what Turing insightfully presented on the case of mathematics at the time, which lead to the development of computer technology nonetheless, near-AI cases of mathematical equations calibrating itself. But, as my initial question aimed to reach, "with limits", not as perfect as it "could be".

Turning designed a mathematical model that interfaced with the operation of a machine, yes. And we are forever in his debt for that. But he only went that far. He didn't go to the level of using that type of mathematics to interface with the operation of space-time. If he went that far, he could have designed a way to explain how the so-called equilibrium in space-time works (aka gravity).

I am therefore a firm believer that some type of Turing-styled mathematical "symmetry" is required to explain gravity in regard to atomic-phenomena. And as you pointed out, Wigner touched on this his own way. But the mathematics required for that symmetry may require a different application of mathematics to theories of space-time to make that work and thus to make it useful to technology. To make it work, we need to know the limits of mathematics, be honest about that, and work with that in the construction of any required mathematical models of space-time symmetry.

.
more meaningless word salad seasoned with misconceptions

not even a hint of a serious thought

I know, even to me it is pre-amble compared to the hard-core mathematics awaiting the attention of anyone interested enough to taker the pre-amble a step further.

But the point here being made, and thank you for your input, was the limitation of mathematics, and how that cross-references with theories of space-time. You have made some excellent suggestions (include here your explanation of the axioms of mathematics and of course the work of Wigner, who I will be taking a closer look at in regard to possible mathematical models of atomic symmetry).

Thank you.

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