Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as π, E=mc^{2}, and even something as simple as using abstract integers to count real-world objects. Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its "mother tongue," and that this mathematics has its own existence that is out there waiting to be discovered? This point of view on the nature of the relationship between mathematics and the physical world is called Platonism, but not everyone agrees with it.

Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the *Proceedings of the IEEE* in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality.

This argument is not new. In fact, Abbott estimates (through his own experiences, in an admittedly non-scientific survey) that while 80% of mathematicians lean toward a Platonist view, engineers by and large are non-Platonist. Physicists tend to be "closeted non-Platonists," he says, meaning they often appear Platonist in public. But when pressed in private, he says he can "often extract a non-Platonist confession."

So if mathematicians, engineers, and physicists can all manage to perform their work despite differences in opinion on this philosophical subject, why does the true nature of mathematics in its relation to the physical world really matter?

The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.

And that is Abbott's main point (and most controversial one): that mathematics is not exceptionally good at describing reality, and definitely not the "miracle" that some scientists have marveled at. Einstein, a mathematical non-Platonist, was one scientist who marveled at the power of mathematics. He asked, "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?"

In 1959, the physicist and mathematician Eugene Wigner described this problem as "the unreasonable effectiveness of mathematics." In response, Abbott's paper is called "The Reasonable Ineffectiveness of Mathematics." Both viewpoints are based on the non-Platonist idea that math is a human invention. But whereas Wigner and Einstein might be considered mathematical optimists who noticed all the ways that mathematics closely describes reality, Abbott pessimistically points out that these mathematical models almost always fall short.

What exactly does "effective mathematics" look like? Abbott explains that effective mathematics provides compact, idealized representations of the inherently noisy physical world.

"Analytical mathematical expressions are a way making compact descriptions of our observations," he told *Phys.org*. "As humans, we search for this 'compression' that math gives us because we have limited brain power. Maths is effective when it delivers simple, compact expressions that we can apply with regularity to many situations. It is ineffective when it fails to deliver that elegant compactness. It is that compactness that makes it useful/practical ... if we can get that compression without sacrificing too much precision.

"I argue that there are many more cases where math is ineffective (non-compact) than when it is effective (compact). Math only has the illusion of being effective when we focus on the successful examples. But our successful examples perhaps only apply to a tiny portion of all the possible questions we could ask about the universe."

Some of the arguments in Abbott's paper are based on the ideas of the mathematician Richard W. Hamming, who in 1980 identified four reasons why mathematics should not be as effective as it seems. Although Hamming resigned himself to the idea that mathematics is unreasonably effective, Abbott shows that Hamming's reasons actually support non-Platonism given a reduced level of mathematical effectiveness.

Here are a few of Abbott's reasons for why mathematics is reasonably ineffective, which are largely based on the non-Platonist viewpoint that math is a human invention:

• Mathematics appears to be successful because we cherry-pick the problems for which we have found a way to apply mathematics. There have likely been millions of failed mathematical models, but nobody pays attention to them. ("A genius," Abbott writes, "is merely one who has a great idea, but has the common sense to keep quiet about his other thousand insane thoughts.")

• Our application of mathematics changes at different scales. For example, in the 1970s when transistor lengths were on the order of micrometers, engineers could describe transistor behavior using elegant equations. Today's submicrometer transistors involve complicated effects that the earlier models neglected, so engineers have turned to computer simulation software to model smaller transistors. A more effective formula would describe transistors at all scales, but such a compact formula does not exist.

• Although our models appear to apply to all timescales, we perhaps create descriptions biased by the length of our human lifespans. For example, we see the Sun as an energy source for our planet, but if the human lifespan were as long as the universe, perhaps the Sun would appear to be a short-lived fluctuation that rapidly brings our planet into thermal equilibrium with itself as it "blasts" into a red giant. From this perspective, the Earth is not extracting useful net energy from the Sun.

• Even counting has its limits. When counting bananas, for example, at some point the number of bananas will be so large that the gravitational pull of all the bananas draws them into a black hole. At some point, we can no longer rely on numbers to count.

• And what about the concept of integers in the first place? That is, where does one banana end and the next begin? While we think we know visually, we do not have a formal mathematical definition. To take this to its logical extreme, if humans were not solid but gaseous and lived in the clouds, counting discrete objects would not be so obvious. Thus axioms based on the notion of simple counting are not innate to our universe, but are a human construct. There is then no guarantee that the mathematical descriptions we create will be universally applicable.

For Abbott, these points and many others that he makes in his paper show that mathematics is not a miraculous discovery that fits reality with incomprehensible regularity. In the end, mathematics is a human invention that is useful, limited, and works about as well as expected.

For those who seek something more practical out of such a discussion, Abbott explains that this understanding can allow for greater freedom of thought. One example is an improvement of vector operations. The current method involves dot and cross products, "a rather clunky" tool that does not generalize to higher dimensions. Lately there has been a renewed interest in an alternative approach called geometric algebra, which overcomes many of the limitations of dot and cross products and can be extended to higher dimensions. Abbott is currently working on a tutorial paper on geometric algebra for electrical engineers to be published in the near future.

**Explore further:**
Belgian wins Norway's $1 million Abel math prize

**More information:**
More information: Derek Abbott. "The Reasonable Ineffectiveness of Mathematics." *Proceedings of the IEEE*. To be published. DOI: 10.1109/JPROC.2013.2274907

## HannesAlfven

"In retrospect, it seems clear that Alfvén considered his early theoretical assumption of frozen-in magnetic fields to be his greatest mistake, a mistake perpetuated first and foremost by mathematicians attracted to Alfvén's magnetohydrodynamic equations. Alfvén came to recognize that real plasma behavior is too "complicated and awkward" for the tastes of mathematicians. It is a subject "not at all suited for mathematically elegant theories." It requires hands-on attention to plasma dynamics in the laboratory. Sadly, he said, the plasma universe became "the playground of theoreticians who have never seen a plasma in a laboratory. Many of them still believe in formulae which we know from laboratory experiments to be wrong.""

[...]

## antialias_physorg

while I agree with him that maths is something we conjured up this question seems to go past the point:

We make the math to fit the application (before anyone misconstrues this: no, we do not make the SOLUTION to fit the problem - we merely invent the tools that we think are helpful for a certain set of problems and then try out whether they are actually useful.)

So while a current set of matehematical methods may not be effective at solving an issue another set of matehmatics may well be. The author makes it out as if mathematics were something static. Far from it.

The real central point of using math, however is this idea:

We perceive (and believe) the universe to be self consistent. Math is also self consistent. So we try to map the one onto the other.

## antialias_physorg

This seems to be an unreasonable criticism. That math maps onto the universe does not mean that all the universe has to map onto math (i.e. that for every possible expression of a mathematical/physical theorem there has to be a corresponding reality...that would be Platonism)

It does exist. It's just too hard to compute (simulation is way faster). The author's distinction of what makes a simple/elegant formula and what doesn't seems rather arbitrary. That a formula is bigger than one can keep in mind does not make it less elegant than a shorter one.

WTF?

## HannesAlfven

"Again and again Alfvén reiterated the point: the underlying assumptions of cosmologists today "are developed with the most sophisticated mathematical methods and it is only the plasma itself which does not 'understand' how beautiful the theories are and absolutely refuses to obey them.""

---

That said, I do still wonder if cosmologists/astrophysicists were to include the observed behavior of laboratory plasmas in their inferences for cosmic plasmas, perhaps machine learning algorithms could nevertheless sort out much of the confusion. We're still at a point in cosmology where most infer velocities for radio redshifts centered near critical ionization velocities without much thought put into the inherent politics of such inferences -- even when those inferred velocities are anomalous.

If each time an inference is made, the tool of mathematics is only used to support the existing theory, then the tool of mathematics becomes subordinate to our own pre-existing expectations.

## antialias_physorg

Ah. Captain Obvious strikes.

However we still don't know whether the universe is, at its core, quantized. So I wouldn't count out the possibility of countability just yet.

But that there is no natural boundary that distinguishes THIS from THAT is rather trivial. It is one of the aspects of using SOME math based models. There are plenty of math based models that don't use integers. For a lot of issues that are useful to us integer based models are good enough.

It's like the puddle (math) and the pond (the universe). You develop the math that fits the universe. The longer you fiddle with it the better it fits.

How much it's limited depends on how much you fiddle with it.

## flashgordon

http://wwwscienti...cal.html

Some more thought that just came to me is that based on Jacob Bronowski's findings, mathematics starts from our current perspectives. It is also about overcoming our current perspective limitations. I actually don't get into this part of Jacob Bronowski's "Origins of Knowledge and Imagination" in my article linking some remarkable connections in James Burke's "Connections" and Jacob Bronowski's ideas in his "Origins" book already mentioned. Jacob gets much more into the biology in the book.

## HTK

It's our human limitation that binds us to the belief that a perfect fit does not exist.

## kochevnik

## HannesAlfven

This might be the most important claim in the article. Part of the problem of our university system (and even websites/forums like this one) is that there is no ongoing effort to systematically catalog all of this claimed cherry-picking. Each time that a problem is raised, the models are simply made more complex, and those who point to competing ideas which might better explain the observation are ostracized/ridiculed.

In any other endeavor, this would be considered defensive behavior. When "thinking like a scientist" is no longer simply a set of human virtues and methodologies, but also includes ideologies, then assumptions go unquestioned, and mathematics becomes a weapon which is used to both confirm that ideology and destroy competitors.

## indio007

Thank goodness for Steinmetz who simplified the mathematical model enough for practical application.

## infogulch

I've tried and failed many times to describe this. Thank you for these words!

## scottfos

says the guy that KNOWS plasma cosmology to be true, and the "proof" is that it's so obnoxious, serious thinkers ignore it...proving that "mainstream science" is a false dichotomy since they won't take your obnoxiousness seriously...

## rkolter

I laughed because it's just not true. A given volume of bananas would not condense into a black hole. The math is basically this:

A 1.4 solar mass black hole (2.8x10^30 kg) has a diameter of 30km (14 trillion cubic meters). These are the vital statistics for the smallest black hole, give or take, that you can make just by letting stuff fall in on itself.

A banana weighs 0.125kg and has a density of 0.2 (much less than water). It takes 11.2 x10^30 bananas to equal 1.4 solar masses. That's 7x10^30 cubic liters. And that volume of bananas fills a sphere roughly 23.8 million kilometers in diameter.

No Black Hole.

## rtrader

You get this type of straw man arguments when you have engineers mess with philosophy of science. The aim of physics is a ToE via the use of mathematics. The only missing part is quantum gravity and a ToE is possible. This means that every conceivable phenomenon will be described by these ToE. This is not an issue of Platonists versus constructivists. This is a strawman argument. The issue is whether gravity can be quantized. All else is senseless argumentation. If gravity is an "outside force" then our math will never describe this reality because it is a computer simulation http://t.co/jwS8lxlc

## GSwift7

I would like to point to my previous sentence as evidence to support itself. No, I'm not kidding. If my sentence was effective, then it would describe everything perfectly.

If you agree with him, then there is no such thing as a colloseum. His example says that one math should describe all situations. If so, then one single colloseum should seat all people for all events, and everyone should have a good seat. Oh, and since The Colloseum in Rome isn't all there, then it's totally useless; bulldoze it down.

Geometry and numerical relationships are there whether people discover and name them or not. It's human interpretation of math that is lacking or incomplete, not the natural numerical relationships that exist with or without us.

Geometric proofs, chords, harmonics, discrete objects, etc. all exist whether there are people to name them and use them or not. This guy is a loone.

## Eikka

In other words, while math can provide a perfect representation of reality like you can draw a perfect map, the perfect map would be a 1:1 replica of the territory, and as such would be perfectly useless.

## ArtVandelay

Damn, they plagiarized my banana theory,... which was to compete with AWT.

## axemaster

Oh, and I'm a physicist. I'd love to meet some of these so-called "closeted non-Platonist" physicists, but I suspect they're actually few and far between, and that Dr. Abbott is mostly inventing his crowd of supporters.

## beleg

A language becomes effective. This is how you will label reality.

## scottfos

oh, they exist. but the further away models get from daily life, the harder it is from some to appreciate. everyone gets 2+2, because you can count out 4 apples, but you cannot count Ď� apples, let alone imaginary #'s like i. are models *perfect* for explaining nature? usually not. doesn't make them "wrong". same thing here, i'd suggest.

in other words, verbal wanking semantics. and i basically just plagiarized Cryptonomicon :)

## beleg

## TheGhostofOtto1923

Physicists cant just sit and do math all day, they have to experiment with complex and expensive machinery built by, well, engineers. It can be frustrating and we can understand if physicists will become irrational some times and start writing poetry or something.

Math never failed to describe something where words only made it worse.

## Noumenon

I think what Einstein was referring to was the analytic / synthetic distinction. An analytic proposition is one that is logically certain, but in which we can not learn anything new (the predicate in contained in the subject),.... while a synthetic proposition is one that is not certain, but one for which we can learn new things.

⇒

## Noumenon

Analytic propositions are a-priori (knowledge prior to and independent of experience) and are dependent upon our definitions (axioms). Synthetic propositions are a-postori and are contingent upon a conjunction of empirical observations.

How is it possible then that mathematics works so well in describing reality? What's the connection between the analytic and synthetic distinction? .....

We must have evolved a-priori synthetic intuitions,... intellectual faculties that determine the form of experience, and so the conditions for the understanding. For example, space and time are a-priori intuitions necessary for a synthesis of experience to be possible. It is a means the mind has evolved to order experience. Our choice of logical axioms may likewise be guided automatically in our intuitions.

That the mind evolved to operate on empirical reality is unique in that reality informs the mind of what faculties will be necessary to do so,.... so they are 'guaranteed' to work.

## Lurker2358

Wow, I don't know where to begin with this absurdity.

Math is a sub-set of Logic. You don't discard a sub-set of knowledge just because it either doesn't apply to a specific situation, or just because you don't understand it.

Points 1, 2, and 3 near the end of the article are all arguments from absurdity.

In the case of a "cloud" i.e. distributed organism, the numbers are still "real" whether or not you have the ability or patience to actually count them, just as the number of people in a crowd at a rally or protest is real, whether or not you have the intelligence, tools, time or care to count them properly.

Your will is not required for math to be real.

## Lurker2358

Just because a problem is difficult, or even impossible for man to solve through mathematics, does not mean that the underlying math of the situation is a fabrication of man's will.

Ignorance doesn't disprove the validity of math as an actual law of the universe and logic.

Let's take biochemistry for an example.

At some point in the distant past, people didn't know what atoms and molecules were. They just knew sugar was sweet.

Then they later learned sugar was a molecule made of atoms.

Then they later learned it's actual structure and could count the atoms and the arrangement.

The last statement was always true and always involved math, even before humans discovered it. Math isn't a fabrication of man. That's absurd.

## Noumenon

Dear dear GhostofOtto1923, you know not even what you profess to hate.

The Platonist view of mathematics IS a metaphysical one,... that there are abstract mathematical objects whose existence is independent of us and our language,.. existing "out there" independent of imperfect things of experience.

## Noumenon

The Fermi-Dirac statistics and the Einstein-Bose statistics were formulated precisely because of the inability of enumerating indistinguishable particles, even in principal, while their wavefunctions overlap.

## Lurker2358

But the fact that we use so-called "abstracts" every day proves that they in fact exist.

A rule which limits the scope of a logical operation or of an entire branch of knowledge does not invalidate that operation or branch of knowledge.

For example, division by zero being "undefined" doesn't make division useless. It just means division only applies to other instances. It may be that division by zero does not exist at all in reality, or it may be that it does exist and we just haven't discovered it. After all, "Imaginary numbers" were actually proposed before a physical use for them was discovered, but they are now used in describing Neutrinos.

## Lurker2358

Yet even that is not a fabrication, if anything it actually proves that mathematics is somehow fundamental to the universe itself, because the same mathematical operation was found in nature after it was hypothesized in pure mathematics. It wasn't a matter of discovering something in nature and then proposing a model. It was a matter of extrapolating mathematics people already understood into a realm not previously understood, and then that relationship was discovered in reality anyway.

The point here is that math can predict the universe, within the limits of our understanding, because the universe is mathematical.

Limited knowledge: Garbage in Garbage out.

## Noumenon

Now, my posts priori to that WAS designed to refute Platonism (metaphysics) in placing mathematical truth and its applicability to reality in the 'hardwiring' of the mind, informed by physical reality in its evolution.

## Lurker2358

A water molecule exists because hydrogen "wants" to form one bond, and Oxygen "wants" to form two bonds, therefore two hydrogen and one Oxygen combine to make a new molecule. the math is real, else the molecule would not exist, and even if it could somehow exist without math, we would have no way to describe it.

Once you try to claim math is a fabrication of man, then you'd have to discard it just like Unicorns and Leprechauns, and resort to what? Topology only? Well the reason math exists is because Topology cannot describe reality. Math is required. Even topology actually requires math because you can have more than one object, and more than one hole in a single object.

## Noumenon

But those molecules don't exist on the basis of knowing that. The molecules are not asking that question,... how many covalent bonds. They just are. Man comes along and constructs a model, and in so doing asks about bonds and relations between observable things, and only then do those relations have meaning. Relations between things are not themselves physical entities, but rather only questions.

I'm not exactly saying that 'math is a fabrication of man'. I'm saying that the axioms of math are informed by our a-priori intuitions, which were in turn informed by reality during the evolution of the mind,..... probably.

The logical positivist mathematicians say that mathematical axioms are dependent upon our definitions and language.

## Lurker2358

The author, i.e. Abott, not Lisa Zyga, claims that computer models are used when mathematics can't describe something. Yet computers function on pure mathematics, so you can't claim a computer model is producing something which is not mathematical. In fact, everything a computer does is ultimately mathematical.

Now you are saying math is an emergent property, which is silly. You are made of water molecules, among a lot of other molecules, and all of them are based on mathematics.

Human consciousness is based on mathematics, even in the case of humans who are ignorant of math, because the molecules of the brain and body are based on mathematics.

Self awareness is not a fundamental property of mathematics, but rather an emergent property.

## BigPink

## Noumenon

Regarding "Taking out the trash". Who are you to judge anyone's post while you make no counter argument nor comments to be judged yourself?

To click on so many 1's so persistently and mindlessly, demonstrates your profound mental disturbance more so than any critique of a post could.

If you are not a 14 year old half-wit, please seek help.

## Noumenon

Nope, a knowledge-of or model-of those things are based on mathematics, not the things in themselves.

## Moose Dr_

However, we will have huge swaths of mathematics in common. Certainly the alien species will have a total match for "integer", though they are likely not to use base 10 as their default base. I bet, however, that they will have a "base x" system as part of their mathematical model. They will have decimals, fractions, even a direct calculus equivalent. They will have the same numeric sequence (base factored in) for pi, and e. They will most likely recognize that e^(pi*i)=-1.

If the alien would have the same math as we have (though they might have some we haven't discovered yet and vice versa) then math is a discovery, not an invention.

## Ober

Having said all this, I do hate when brilliant theories need to NORMALISE in order to yield useful results. This, to me, demonstrates that maths still has a long way to go.

P.S. Einstein used maths from a book which gathered dust on a library shelf for apx 60 years. Until Einstein used it, the maths it contained were considered quite interesting but of no useful application.

## antialias_physorg

The brain may be able to explain the brain. Similarly a computer simulation may be able to simulate that simulation (e.g. by mapping the time dimension into a space dimension or vice versa. A concrete example of this would be simulating a massive parallel construct in series. This requires far less computing power at the cost of a lot more time)

The only thing that is certain is that a simulation cannot simulate itself in realtime (e.g. the brain cannot fully grasp ALL that is going on in itself in realtime. But it could do so if it grasps parts one after another for a desired time interval.).

So we'll never get something that will give us all the results for everthing all the time - continuously. But that is hardly needed.

## rtrader

True but there are some problems according to Gödel's incompleteness theorems. In the article I mentioned> it is claimed that we can determine experimentally whether our world is a virtual reality. However, if that is the case then a full description of reality may never be available from inside the simulation. Think of the cave analogy in Plato. Actually, Plato never said a Platonic world provides a full explnation of everything. This is a misunderstanding of the author of the mentioned paper.

## rtrader

True but there are some problems according to Gödel's incompleteness theorems. In the article I mentioned (http://www.digita...er-game) it is claimed that we can determine experimentally whether our world is a virtual reality. However, if that is the case then a full description of reality may never be available from inside the simulation. Think of the cave analogy in Plato. Actually, Plato never said a Platonic world provides a full explnation of everything. This is a misunderstanding of the author of the mentioned paper.

## antialias_physorg

Sure. Unless we start talking to the 'guys outside' and come to an agreement to step into their reality.

But that's sort of metaphysical to the point whre it doesn't matter. If there's a reality you can't know then there's no real point bothering about it.

## Pattern_chaser

## brt

I think the good professor is wasting his time, because this should be (and mostly is) obvious. The only people that don't think this way are usually those who are trying to capitalize off of scientific philosophy; should read: popular science books/films.

## MrVibrating

What's so beguiling however is that all around us, we see inanimate matter performing precise mathematical operations. Thus therein lies the question; of whether there's any fundmanetal distinction between how WE process numbers, and how the universe does. Mathematical axioms certainly occupy a realm independent of physical constraints, yet the physical world appears bound by them all the same - arbitted by things like dimensional symmetries and conservation laws etc...

Just playing devil's advocate here... (i'm in the non-Platonist camp)

## Szkeptik

Our logic and math came to be as our brain, generation after generation, formulated an approximation of the nature of reality in order to allow for better prediction and reaction to our environment. It is only an approximation, but it does aproximate reality, as if it wasn't we would have gone extinct.

Reality must be self consistent across all phases, times and scales. If this weren't so, inconsistent parts of reality would surely generate destructive effects that would have long since destroyed it. So laws of logic can change, but there must be some manner of logic. Since our math and logic was developed by a brain adopted to the "middle world" as Dawkins puts it, we may face challenges making sense of the quantum and galactic scale worlds. That's why the equations get long and convoluted. But they still work.

## antialias_physorg

I'm not so sure about that. Inconsistent parts may simply 'split off' (multi world hypothesis?). And it's really only at the interfaces of consistent to inconsistent parts that you'd get any effects at all.

So if inconsistency isn't fundamental - but 'occasionally allowed' - it may not be the demise of the universe.

(Note: I do think the universe is consistent. We havent observed anything that would argue otherwise. I just think it's almost impossible to prove it from within the universe)

## TheGhostofOtto1923

Yah nou we have sat here before. I do not have to know how to speak philo to know that it is worthless. Just like you I rely on experts. Only my experts are scientists as yours are poets.

'Philosophy is dead.' -hawking

'Philosophy is useless.' -Feynman

'Philosophers make me laugh.' -Kraus

'What is a Kant?' -most postdocs Why because Plato is a dead philo? His theory of forms is an obvious absurdity. The use of the word is only an unfortunate symptom of the poison of religion. Philosophy was invented to wean intellectuals off god; a placebo. The metaphysical has no more validity than the hereafter, and is certainly no more useful to science as a concept.

It has absolutely no meaning whatsoever. As Feynman says, you can ask questions using such words to get any answers you want.

'You can get no information from the metaphysical' -nou

-So then what the fuck good is it?

## tadchem

P.A.M. Dirac's Quantum Mechanics is an excellent example of non-Platonic application. He simply summarized the observed characteristics of sub-atomic entities and their interactions, formalizing them in a customized mathematics. The model was designed according to the observation, and therefore must agree with them.

Far too many modern theoreticians confound their beloved models with observed reality, and find themselves misled thereby.

## tadchem

P.A.M. Dirac's Quantum Mechanics is an excellent example of non-Platonic application. He simply summarized the observed characteristics of sub-atomic entities and their interactions, formalizing them in a customized mathematics. The model was designed according to the observation, and therefore must agree with them.

Far too many modern theoreticians confound their beloved models with observed reality, and find themselves misled thereby. Models are chosen by how well they IMITATE reality, but they are always just an imitation. The best models, such as general relativity, imitate reality very well.

## barryk

Platonism is a relation between 'mathematics' and 'existence'.

It is literally senseless to argue about Platonism without first defining 'mathematics' and 'existence'.

## Noumenon

This entire discussion is a philosophical one. Logic is a branch of philosophy. Epistemology, the question of the nature and possibility of knowledge, is a philosophical one. While the core of QFT, QM remains validated via experimentation, it remains of interpretation of what the theory tells us about physical reality. IOW, interpretations of qm are philosophical.

Your theory of AWT is no more than philosophical musings if it is contingent upon intuition at the expense of lacking predictive power.

## barryk

If you separate the symbolic representation of mathematics from the underlying mathematical structures and relations, and treat mathematics simply as a self-generating way to compose existence directly from the potential difference relations between energy and virtual energy fields, then the Platonists are correct.

Mathematics is 'unreasonably effective' because existence is a complete and consistent base ONE mathematical system that is based on the axiom of identity, instead of being based on predicate calculus, and the definition of the set membership, and set equality operators.

## SolidRecovery

## Noumenon

Your ignorance of philosophy is not an argument against it.

The philosophy of physics and the philosophy of mathematics ARE in fact legitimate branches of philosophy, irrespective of your personal aversion to them.

I proved to you in a previous thread that this quote is taken out of context. He was not speaking of modern philosophy of physics. In fact he has written on philosophy, in terms which coincide with what I post on the matter.

"There is no way to remove the observer us from our perception of the world, which is created through our sensory processing and through the way we think and reason. Our perception and the observations upon which our theories are based are shaped by a kind of lens, the interpretive structure of our human brains." - S. Hawking

## Noumenon

But I only need to post one prominent physicist who disagrees to refute your claim, yet there are many;

"We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning." - Werner Heisenberg, Physics and Philosophy

"Any sound scientific theory, whether of time or of any other concept, should in my opinion be based on the most workable philosophy of science: the positivist approach put forward by Karl Popper and others" - Stephen Hawking.

"How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? [..] Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as 'necessities of thought,' 'a priori givens,'" - Albert Einstein

## TheGhostofOtto1923

These wanderings may cause a stir in the philo world and in public perception but they have no effect on how these guys do their science.

## JulioMarco

Whether or not mathematics have an onthologically independent existence (which I think it has not, what classifies me as a "non-platonist"), the contents of our models are far from being mathematical. Instead, we populate our models with our views of the World, our ideas, our preferences and our technical (and even personal) experience - that is what exists in our models and is written in mathematical symbols, which are ruled by the laws of Mathematics just as this text is ruled by the laws of the English Language.

Our models fail when our hypotheses and tests fail and they succeed when our hypotheses and tests succeed.

## no fate

## brt

I think the basic proof of what you and Abbott are saying is that you can't point to "5" in nature. You can point to a "quantity of 5", but there is no such than as a "5". Numbers are a concept and we only created them in order to understand the concept of limits. "Limits" being a concept which begins to break down when we move into quantum mechanics.

## drhoo

## drhoo

Mathematics is logic. And logic is not an approximation.

## nEc2

## nEc2

## GSwift7

Define "effective"

Define "describe"

Define "world"

Then it might make sense to discuss the answer to the question. The body of his article even hints at conflicting definitions of the terms in his question.

I think the real question here should have been more like 'Is mathematics an effective way to describe a guy with too much spare time on his hands?'

## Noumenon

You don't know what your talking about, nor does your post contain any refutation of anything I stated here, just your dopy "opinion". I can't even tell whether you understood anything I wrote.

## christophe_galland1

Quantum mechanics seems to give a clear physical meaning to integers, as a number of quanta of energy, momentum, etc. Abbott's reference to continuum physics is ignoring this important point.

## Noumenon

I think it wouldn't serve him to define too much. The above article doesn't even mention "predictions",.... obviously if a mathematical theory allowed one to make predictions, then clearly it is effective.

## nEc2

## kevin_hingwanyu

So the math and theories are invented?

## kevin_hingwanyu

Scientists can find their reading/articles on nature.com ... etc. A layperson may not understand the systematical catalog, magnetic motors, cold fusion and similar stuffs. With Internet, are there some websites/forums where laypersons can find those systematic catalog, precious data and those experimental results which mostly are ineffectively mathematical applicable ?

## kevin_hingwanyu

I speculate the dividing the micrometers the decreasing the denominator, the former neglected effects would require more variables and awesome steps of computations.

## Tipped

Of course. Now for a question of philosophy: If a model is indistinguishable from that which it models, is there any difference between the two?

I would argue no, and base my claim on the reflexive property. It would be like arguing over what the difference between 2 and the square root of 4 is. There may be different ways of modeling the object, including through the use of the thing itself, but they will all be equivalent.

Q.E.D., the universe is mathematics. Or, perhaps more accurately, the universe is a subset of mathematics.

## brt

If this is true then why do we run into the measurement problem and uncertainty principle? Quantification is our approximation of what is happening. It may just be that whatever is going on beyond that point has such an insignificant impact on our macroscopic experience that it isn't worth including such a fine (enormous) amount of detail in our macroscopic calculations and models.

## cijbm

## brt

When I say that "it may be", I mean that it is actually exactly what scientists do. If you can design a model that is correct 99.999999% of the time in our macroscopic experience of the universe, then you don't really need to quadruple the size of your calculation just to add a few more nines on the end of that unless you are proving a theory.

## main_h_don_5

atechplanet.com

upcomingfashions.com

## antialias_physorg

What it all boils down to is that we wish to draw information from observations. Now this is an inherent 'human bias', as a fully connected universe doesn't really do the information thing.

Information, at its core, requires a delineation into separate parts (and here's where the human bias comes in). This is required because humans have limited brain capacity - and we already do the delineation on the most fundamental level: the self vs. everything else.

So while math and information may not be the ultimate way of going about understanding the universe it IS the ultimate way if we stick to our human roots. (If we ever achieve unlimited brain capacity that may change - as then a holistic approach may be feasible)

## ubavontuba

Mathematics is an excellent tool for describing relatively simple systems and interactions, however it is less useful when it comes to complex systems and interactions, and the nuances of concepts related to esthetics.

So it's a useful tool in the toolbox, but it's not the only tool.

## TheGhostofOtto1923

## TheGhostofOtto1923

The brain is a machine. There is nothing non-physical about it.

Words are entirely inadequate in describing physical phenomena which is why science turned to math to describe them.

## Q-Star

Ya can not find the nuances without first doing the maths. Unless ya think "just a shade darker than fire engine red" is a proper scientific concept.

No it's not the only tool,,, but useful?

It's indispensable. Ya can't do science without it. Unless ya use the Zephyr method of discovering intuitive truths, the AWT doesn't require or become bogged down with the maths.

It is the only tool which is required,, the others are all optional to greater or lesser degrees. It's the only tool that will reliably indicate self-consistency.

## antialias_physorg

You have to allow that he's never tested his ideas.

It's always the same. Someone has a grand, overarching concept - but when you get to the details it falls apart.

You'll notice this with armchair coaches, generals, politicians, ... even parents.

(...and also scientists, BTW. There is not a single scientists who had his first stab at an issue turn out exactly right)

Stuff that 'sounds good' or is 'intuitive' just doesn't mean anything in science. If the numerical(!) predictions match the numerical(!) measurements - then it's good. Otherwise it's worthless.

## TheGhostofOtto1923

## Noumenon

The use of symmetry in physics is not motivated by aesthetic considerations as much as a purely mathematical result, in Noether's theorem.

## antialias_physorg

Well, since I never championed string theory you might want to get your head checked (and I seem to have told you this before).

String theory is elegant - but that doesn't mean a thing as to whether it's true or not. When it starts making good predictions (and when the degrees of freedom are seriously collapsed) is when it'll become interesting.

Then why are you championing AWT and cold fusion? Neither of which fit that bill. Both are singuarly spectacular examples of obfuscation/fuzzification tactics.

## Noumenon

The use of 'transparent' to define intuition is a bit redundant. Intuition means that one is able to form representations that are analogous to previous experience **. The question is why would this be possible for the qm realm, when it is clear we have evolved to synthesize experience only at the macroscopic realm. This is why qm is non-intuitive for example. History has shown that mind dependent intuition is too restrictive for physics to continue to make progress, at other scales.

** [or that is an a-priori form of thought necessary for experience given the nature of mind]

## Q-Star

What else to say? Well ya might have added that he was talking about the AWT.

## Noumenon

IOW, if conservation laws have physical reference to you, then via Noether's theorem, 'symmetry' would have a physical motivation and not aesthetic one.

## brt

Abstraction. http://en.wikiped...traction

Abstraction guides us in the right direction. When we get into higher levels of math that are extremely complex, the direction we are guided in is much more accurate.

## brt

I always picture Borat speaking when I read his comments.

## brt

You say AWT relies on particle systems, yet you also say that Quantum Mechanics and fields are nonsense. So AWT is correct because it's just like a particle system, but particle systems are nonsense. How could you ever be wrong with logic like that?

It's like you're angry at your spouse for snooping on your phone & finding nude pictures from an affair.

## antialias_physorg

Exactly right

en.wikipedia.org/wiki/Artifact_(error)

Quote: "In natural science and signal processing, an artifact is any error in the perception or representation of any visual or aural information introduced by the involved equipment or technique(s)."

..since you already admit it yourself...

Case closed.

## brt

Just because you don't understand it does not mean that it is incorrect. You are championing the idea of "Good Enough" because the path to a better future is too difficult for you to understand; whether or not you are aware that you don't understand is really the only thing up for debate.

## brt

What does it say when you try to save face by jumping to a conspiracy theory or abandoning the topic by jumping from quantum mechanics to astronomy? It says that your mouth is writing checks that your ass can't cash.

## Q-Star

Ah, Zeph, there only one eeny teeny problem with this profound thing ya say,,,,

Five generations have passed through the great halls of science since Lodge was on the scene,,,, so according to Planck's Law of Emerging Ideas things have gone amiss, because ya are the only one who got the memo about aether outliving it's detractors and taking it's proper place in science..

## rug

The basics of math are numbers. Based on that very primitive example it would seem humans only gave words and symbols for something that was already there. We didn't invent the number 1 we just gave a name and a symbol for it. The simplest of math problems is addition. 1+1=2. Once you have given some names and symbols to these numbers then it would make sense they would add up like that. One will always be one no matter what name you call it. Uno, une, een, ein, or amháin it is still 1 in most languages.

It seems to me that our universe is a logical universe. Granted that might only be because we are part of the universe so it seems logical to us. Either way, it means we should be able to understand the universe and these numbers and symbols are simply how we chose to make sense of it.

## TheGhostofOtto1923

Right now much of the objective info I've seen leads me to believe that rossis e-cats are being independenty validated as we speak. But then I've read about slow neutrons so that helps you know?

## lomed

## lomed

For my contribution to this discussion I define mathematics as the deduction of statements from axioms. Logic is a part of these axioms (the part that allows deduction). Which axioms one uses is determined by the statements one wishes to make. If the title of the article means "do there exist axioms from which all reasonably desired statements about physical observables can be deduced accurately in a reasonable amount of time", I would say that that is an open question. It is easy to infer from many successful cases of finding accurate models that such axioms exist, but there is no way to prove that any given set of axioms is the desired set (it is possible to disprove some sets if "accurate", "reasonably desired", and "reasonable amount of time" are well defined).

## lomed

## Q-Star

Hey Zeph, your dreams time picture reminded of something,,, what ever happened seneca, cato, and xerox?

## rug

First off, you completely and utterly wrong. They can be counted it's simply we don't have the ability to count them in the time frame of their existence. You take a picture of the waves and they can be counted within that frame. Bosons can be counted, the hard part is detecting them in the first place to be able to count them.

Second, what exactly does that have to do with anything anyway?

## ubavontuba

## rug

## Captain Stumpy

@rug you took the words right out of my mouth...

...and whose wonder do you refer to? the child's or the hypothetical observer...

## ubavontuba

Sure, you can quantify the concept, "fire engine red." And you can quantify the concept, "a shade darker." But you can only do so under quantifiably defined and uniform lighting.

Even then, it's only an approximation, as the parameters of the receptor to perceive the reflected light isn't defined. The angle of incidence isn't defined, texture isn't defined... and so on. And once the standard, uniform lighting is taken away, all mathematical definitions become meaningless.

In this case, what we perceive as "a shade darker" actually retains more meaning in simple language than it does mathematically.

So in this case, which model of the world is actually more correct? The one with the well defined standards, or the aesthetic?

...I know which I would choose.

## rug

## ubavontuba

## Captain Stumpy

## ubavontuba

## ubavontuba

And I dare say, you cannot convey the definition of the phrase mathematically, nearly so expediently. Ergo linguistic descriptors are more efficient in complex circumstances.

## Captain Stumpy

Isn't it obvious? ...Both. After all, beauty is in the eye of the beholder.

but that is not necessarily a repeatable and quantifiable answer. empirical evidence may be synonymous with the outcome of an experiment. In this sense, an empirical result is a unified confirmation and since you cannot have consensus on "beauty" then it is not an accurate descriptor. Just as "wonder" is defined by the observer, the answer would be malleable depending on point of view. the answer is too malleable and subjective

## rug

## rug

## Captain Stumpy

hyperbole intended

## ubavontuba

This is a good point. The logic is recognizably "fuzzy." But it's certainly more accurate than the same can be defined mathematically.

Frankly, these complex concepts cannot be explained mathematically in a compact enough form for the human mind to hold. However, linguistically, they fit right in.

## ubavontuba

## rug

That is not what I'm saying. What I am saying is, emotional aspects of an abstract idea is not a physical state. Then again, if you could read you would have know that already.

## ubavontuba

Or even in some cases: 1 + 1 + 1 = 1.

But what you probably mean to imply is there's no mathematical proof there is a god. This is correct. But equally so, there is no mathematical proof for most any emotional concept, yet generally, we all feel emotions and generally understand each other when we describe our emotions. Ergo emotions are real, yet not well defined by mathematical models.

## Captain Stumpy

you are forgetting that mathematics is the same all over, whereas linguistics has rules, semantics, grammar, syntax... all that crap, all subjective to the user, the language AND the year, as language use differs slightly between generations, and WIDELY over longer periods. that means it is malleable and abstract, unlike math. and therefor subjective, and cannot be considered empirical even though, right now, you may get the basic idea, but for how long?

you cannot be specific enough to define the moment for all time without a universal language: mathematics IMO

## rug

Nope, that math is all kinds of wrong.

Correct, thanks for understanding my poorly stated point

Once again, math is used to describe physical states. Not emotional aspects of an abstract idea.

## ubavontuba

What I'm saying is, just because something is too complex to be conveniently stated mathematically, doesn't mean it cannot be expressed efficiently, at all.

## rug

Even though it's rhetorical I'm going to take a stab at it. The abstract idea of thought is not a physical state. Now if you want to get into the workings of the mind then it's nothing more than an electrical state of the neurons in a brain. That electrical state can be represented with math. However, the questions remains due to lack of evidence, is that really what a thought is? Don't know yet. Until science can reproduce that exact state in another brain we will not have clear evidence of that.

## ubavontuba

Wouldn't these be equivalent to mathematical order and signs?

Making it all the more better to describe abstract ideas.

People could forget math and its symbology just as easily.

How about using a picture?

## Captain Stumpy

but what you are also saying is that the complexity and convenience of language is subjective to the time, place, observer, period, dialect etc, etc... therefor it is NOT universal, and therefor mathematics is a better tool for passing on information (or describing things) in a universal manner that allows all parties to understand the concepts in the same way, at the same time, regardless of the time spread between speakers, language differences, etc. which is what the article asks! isnt it? what we want to communicate through the ages should not be "interpreted" as we interpret ancient Greek, Aramaic, etc. there will inevitably be flaws.

## ubavontuba

Good thing you didn't try to describe it mathematically. ;-)

So you're saying the wonder of a child holding a ladybug is not a physical state? How then might we ever progress to artificial intelligence, if we ourselves deny our consciousness is a physical state? How can we create that which isn't real?

And it's not just philosophical concepts that can't easily be explained mathematically, many complex physical systems are just as hard to describe. For instance, is the deformation of a rubber ball on a bounce better described mathematically, or with a single photograph?

## Captain Stumpy

but math is the same... we had NO problems interpreting the math from ancient times... it is the syntax and language that is all subjective.

whereas symbols CAN be forgotten, math proofs are logic, pure and simple. and any steady investigation into the subject will give you the same results. that is why you can send math from one continent to another and it will always work out the same (as long as you use the same increments of measurement- metric and SAE dont always translate the same... because it is LANGUAGE the math is the same, the measurements are just due to language and abstract ideas of what is "better")

## ubavontuba

Isn't it interesting a complex thought itself can easily be defined and understood by all ,even though we don't understand the mechanics of it?

## ubavontuba

Pictures and recordings then, are the only best solution.

## Captain Stumpy

i understand your argument. i even agree with some of your points. but it also comes down to time... long stretches of time. something that "language" has proven to fail us. we can get a general idea of what is being said in our translations, but not a specific, logical all-encompassing detailed analysis and comprehencive translation of the idea in question. Math does transcend that issue, and HAS... and i also believe that all things, given time, will be mathematically explained. it is the blessing/curse of humans to break things down into the simplest, most logical definition.

## rug

Sure, some people might look at it that way. However, if you had read all of my post you would have seen that's not really the case.

That is what language is good at, but unless it gets translated it can't be understood by lots and lots of people. Keep in mind though sometimes there isn't a direct translation. Have you ever heard the phrase. Looses something in translation?

## ubavontuba

## Captain Stumpy

no... math is math. cubit and feet are units of measure, and subject to definition, but 1+1 will always be 2 , whether you use cubits or feet.

the difference between cultures are because of ideology and language ... not because of math. math is the same across the board.

## ubavontuba

I disagree. Just because we figured out some ancient symbols, doesn't mean that we have and will always be able to interpret other culture's mathematical symbols.

And I'm arguing that math isn't always the most efficient tool.

## Captain Stumpy

the limitations of our understanding are just showing. my 9 year old grandson has some girls he "likes", but cannot adequately describe what he actually feels... our understanding of math is the same. just because we are in our "terrible two's" , or whatever, does not mean there is a limitation to math, because math is pure logic, and in time, it will be able to adequately communicate whatever we wish through a universal set of logical steps.

this is the power of math (as much as i hate it). the power to describe logically over spans of time. this is what makes an effective tool. that is my argument, that it will be the most effective tool over time, because it HAS been the most effective tool over time.

## ubavontuba

You feel the answere is always yes, I feel the answer is only sometimes.

That is what language is good at, but unless it gets translated it can't be understood by lots and lots of people. Keep in mind though sometimes there isn't a direct translation. Have you ever heard the phrase. Looses something in translation? Which is why in many fields and applications, language has been (and is being) standardized.

## rug

That I will agree with. However, efficiency isn't always the most important thing.

I never said this.

## ubavontuba

This is not correct. Even 1 + 1 does not always necessarily equal 2. For instance, 1 particle plus one antiparticle, equals what, exactly?

## ubavontuba

I apologize that I misunderstood.

## Captain Stumpy

sorry. still math logic.... and it would be 1-1 which is 0. one is positive, one negative, and they cancel each other out. or you could write it (pos) 1 plus a (neg) 1 which equals zero... same same.

## Captain Stumpy

## ubavontuba

However, it would sure be interesting if it turns out antiparticles have antigravity properties...

## ubavontuba

Stay safe.

## Captain Stumpy

as for anti-particle properties... I would love to know more. :-)

## Captain Stumpy

PEACE

## ubavontuba

## ubavontuba

## Captain Stumpy

i wonder what a physicist would say about that though... perhaps a particle and an anti-particle orbiting a sufficiently large mass that could keep them separate. the kicker would be keeping them separate... that is the only way you could count them both. the absolute value would be two but the combination is still zero.

## Torbjorn_Larsson_OM

So platonists et cetera philosophers needs to test their ideas of something more.

You can't predict and test for something more, so that fails.

[tbctd]

## Torbjorn_Larsson_OM

There is a recourse to a testable constraint of Tegmark though. He posits that a multiverse where mathematical objects (theories) is the universal substrate would be a simpler hypothesis. In his hypothesis mathematics (perhaps only sometimes) maps to physics, especially where we live. He argues for the identity mapping as the simplest. This would presumably be tested if selection bias (weak anthropicity) can be tested valid and with the testable exclusion of everything else.

But compared with the empirical null hypothesis it isn't simpler, because Tegmark doubles his objects. Mathematical objects is a class, physical objects is another, and he sets up a mapping in between even if he chooses the identity mapping. One way to interpret it is that they have different properties before merging - physics is testable, for one. So this fails too, whether it is testable or not.

Hence a skeptic must be an aplatonist.

## beleg

Languages become extinct too.

## rug

Here is a conundrum for you.

1+1=10 (Binary)

9+1=A (Hex)

7+1=10 (Oct)

When you change the base it's still valid math but from a base ten perspective we are use to the results seem all kinds of odd.

## Spaced out Engineer

Partial differential equations of continuous or discrete contextually dependent or independent random variables

Done.

Subjects in and of themselves are self defining things. Keys hide in no one thing.

Is that nonsense or does it accurately describe some phenomena? As our measuring tools improve and our statistical correlations of data increase we will find the crease within the singularity or perhaps the empty set {} that is the nature of all or nothing. Anticipate, believe, but do not expect my fellow discoverers. Tolerate exploration on all frontiers and assist those you can in finding the universe's or perhaps multiverse's gears. She will sing to us if we but seek the time/space...... Nothing is impossible. I'm possible and so are you. We will be... The self knowing mind whether it is self, society, or some construct others refer to as God is unfolding. :)

Unknown unknowns hold no bounds, but do require context.

## JohnGee

Ubavontuba also believes in perpetual motion machines and thinks he can engineer starships from his basement without math. Don't indulge the morons. Just call them morons and move on.

He also thought the LHC was so dangerous it should be moved off world over concerns of planetary destruction. But climate change... nah...

## rug

When you don't understand math even the simple equations become complex.

hmmm that's odd, we can create black holes that will suck up the whole earth but we have no affect on the climate. Interesting premise. Completely crazy of course but interesting in a neurological kind of way.

## lomed

## pete1513

In addition, it could be that the universe vanishes 5 minutes from now, even though our models don't predict any such occurrence. It would be extremely embarassing, however, to claim that this possibility makes it highly likely that our models are wrong. Just so, mathematics might not describe the universe adequately in some ways, but as of now, is has passed all the tests. Platonism for the win.

## pete1513

## kevin_hingwanyu

## kevin_hingwanyu

'a product of the human imagination' & just a mental construct? I don't understand, human effectively links mathematics and world, different persons at different places and time can find same answers/numbers.

Math is not the source of the ineffectiveness.

I wonder it finds no magnetic motor (free energy) on phys.org or instructables.com.

## Noumenon

What is rather horrendous is that seemingly scientifically minded people fall for such metaphysical fallacy as Platonism.

It makes zero rational sense to suggest that the universe is intrinsically 'mathematical', independent of its conceptualization in thought. That's what would qualify as Platonism,... ontologically independent of thought.

The universe of itself (noumenal reality), does not have need of relating things, nor of measuring things, nor of redundently constructing models of itself. Mathematics therefore does not exist in any fashion independent of mind asking such questions.

It is why Einstein had to take an Operational pov with general relativity.

## meBigGuy

Since when does using the right tool for the job become cherry picking? Having a set of wrenches, why would I try to build a computer? No, I'd just cherry pick the loose nut jobs and the real nut jobs could publish an article on the ineffectiveness of wrenches.

Math is a modeling language, and is as good as the understanding of what it is being used to model. Models are created with inherent limitations. The limitations are either in understanding of what is being modeled, or a result of the size/complexity of the problem,or the suitability for matematical modeling.

## IronhorseA

Obviously, this EE forgot to use probability to count the bananas instead of using an accountant ;P

## ArtVandelay

## Lurker2358

I don't think a universe need necessarily be mathematical. However, the universe which was created, in which we actually exist, is definitely mathematical.

Does math describe everything in our universe? Maybe. Maybe not. We'd need to know everything, or at least nearly everything, about our universe in order to answer the question absolutely.

All known phenomena seem to be describable in some form of mathematics.

Yet it is possible to prove that it is mathematically impossible for a temporal being or civilization to ever know everything about our universe. For starters, just imagine how many molecules are required by our brain to store memory of the location of just one molecule. Obviously you can't map the location of everything in the universe, because you can't make a memory large enough; even if you only hit the high notes, I doubt Earth could store a map of every star and planet in the universe.

## Lurker2358

If math does not exist how do objects "know" how much force (or space-time warp,etc) is being applied to them by gravity or other forces?

Our universe would not exist as it does without mathematics being a part of it's very construction.

The fact that the universe can contain intelligent beings such as ourselves, who are then able to produce self-referencial models of both themselves and the universe, should tell you something.

The universe is created by a mind, so it comes as no surprise that it would bear the markings of a mind.

If it looks like a mind, and acts like a mind, then it probably is a mind, or was created by a mind.

## beleg

Platonism offers you choice. Be part or platonic.

## beleg

## Noumenon

It would be redundant for an object to be both itself and to be it's own model of itself. That is what "to know" means afterall, ... to reproduce reality in an abtract conceptual form. Reality apart from mind knows nothing, it just is. Like space and time, mathematics are not entities existing independent of their application in relating and ordering things. Platontism is metaphysics.

## Lurker2358

You don't understand the question, though you thought you did.

If mathematics is not "real" then the inverse squared relationship would not exist. Why would the objects' orbits exist, if they were not being pulled with a precise force, or following a precisely warped path?

You have a model of yourself, and we call this model the "self image" it is a combination of what you know and what you believe about yourself.

However, as regarding inanimate matter, I used the word "know" generically in a sense that did not require self intelligence.

In Newton's gravity "M" and "m" mean something...

## Lurker2358

They represent the larger mass and the smaller mass (though they can be equal), and "r" means something as well, namely the distance between them.

Change any one variable in the formula, and the opposite mass "feels" less or more force, accordingly, referencing Newtonian Dynamics anyway.

How would you express that fact, which we know to be true, without using mathematics?

If the observation and the mathematics are identical, or at least nearly identical, then it stands to reason that the universe is mathematical.

Are you claiming that all similarities between mathematical models and the universe itself are coincidental?

The mathematical model works because the universe is mathematical.

Math isn't something humans made up, it was discovered by man, not invented by man, though formal language has standardized it into what we call mathematics today. The relationships always existed; to say otherwise is completely absurd.

## eric96

"You therefore cannot describe the universe in any language."

"Furthermore, you cannot describe something infinite (true infinity in space and time) in math because in math whatever you describe has a focus (is finite), and the universe is infinite."

## Lurker2358

There is no evidence to suggest that the universe is infinite in either space or time.

The second law of thermodynamics forbids the universe to be infinite in time, because it would have already reached a state of maximum entropy.

The universe can't be infinite in space, because growing to that size would require an infinite amount of time.

## ubavontuba

## ubavontuba

So deliberate misinterpretation and just making stuff up is the best argument you can make?

Okay, you're a moron.

More out of context B.S.. Is this the best argument you can make?

When did I supposedly state we cannot affect the climate?

So what's with all the bullying? Perhaps you suffer from an inferiority complex?

## ubavontuba

Was that too complex for you still, or are you getting it?

So baby-shit bullying is the best you can do too?

## ubavontuba

## rug

That is correct, however, that is not what you said. Here is what you did say and

Both of these statements are completely incorrect. Making the normal base 10 assumption. Even when dealing with particles of matter and antimatter. Antimatter by definition is a negative. Therefore, you equation should have been 1-1=0 or -1+1=0 or maybe |1|+|1|=2 as has already been explained to you. I thought you had understood. Judging by your correction of the formulas I see you did.

My statement was perfectly correct. When you don't understand math even the simple equations become complex. I'm glad you now understand the math behind it so you don't make any more erroneous equations.

## rug

Once again, my statement is completely correct. There would have to be some kind of neurological disorder (crazy for short) to not see the failure of the logic. You see this as bullying, I see it as calling a rock a rock. You stated you never said we can't affect the climate. Well, then I guess it doesn't apply to you now does it? Judging by this response you obviously believe we could make black holes and we can't affect the climate. Which your statement about not saying it was pointless.

## ubavontuba

This gets downright metaphysical: If I own one matter apple and one antimattter apple, Do I own two apples ...or nothing?

continued....

## ubavontuba

So it's your contention that if you don't understand the logic it's necessarily bad?

continued...

## rug

Can you give me a example of this? I've never seen it, read it, nor can I conceive of one instance where this could possibly be true.

This gets downright metaphysical: If I own one matter apple and one antimattter apple, Do I own two apples ...or nothing?

You would have two apples if the do not come into contact with each other. This is where the |1|+|1|=2 comes in. There is not anything metaphysical about it. It's pretty straight forward math.

## ubavontuba

Where did you read that in my response?

Clearly, I was responding to your name-calling, innuendo, and aspersions (aka bullying). To pretend otherwise is clearly dishonest.

## rug

That is where the absolute values come in.

Yes, if someone can't understand logic they are either refusing to think or have a neurological disorder. When people refuse to think they agree to be dumbasses. An accrual neurological disorder might be treatable but at least understandable.

## ubavontuba

This gets downright metaphysical: If I own one matter apple and one antimattter apple, Do I own two apples ...or nothing?

You would have two apples if the do not come into contact with each other. This is where the |1|+|1|=2 comes in. There is not anything metaphysical about it. It's pretty straight forward math. It's still 1 + 1 = 2. The special separators are irrelevant, especially when simply discussing the mass.

## ubavontuba

So you're admitting then that since you didn't understand my logic, you're either a dumbass or you have a neurological disorder?

Does it ever occur to you that maybe, sometimes, people just misunderstand the issues?

## rug

## rug

And this is exactly why you can't things that are not alike. One of the first fundamentals in math.

That is because you are using the absolute values which is indicated by |1|

## ubavontuba

Again, you're being disingenuous. Knock it off.

## Captain Stumpy

this is not a matter of adding masses, but objects. what you are confusing is the object and the negative object... and absolute value. either add absolute value or not.

this is a simple situation of misunderstanding. you are not understanding basic math or science, and are using a metaphysical or semantic argument (depending) to get your point across.

there is no magic. just logic. 1+1 only equals more than two when the condom breaks. and that is biology, not math

## rug

This is not correct. Due to the fact one is a negative charge so you must use a negative value.

You're logic was flawed. No one can understand flawed logic.

That does seem to be the case with you currently. It happens all the time and is not a big deal. However, when that misunderstanding is cleared up and yet the person still perpetuates the misunderstanding then my original statement is clearly case.

## ubavontuba

No, when i'm discussing the mass, as the sign for the mass in either case is normally positive, I technically don't need to use the absolute value to write the formula. And absolute values when added, do not sum to zero (at least they're not suppose to).

But is would be correct to write: |1| + |1| = |-1 + 1|

## Captain Stumpy

matter and anti-matter are NOT the same, one is Pos, one Neg. but their absolute value is always Pos,

therefore it MUST be

EITHER

1+1=2

OR

-1+1=0

## ubavontuba

## ubavontuba

My logic is impeccable.

But you're the one perpetuating the misunderstanding, therefore your statement must apply to you.

## rug

After this long discussion with your clear misunderstanding after being corrected multiple times from more than one person I am forced to end the discussion. I refuse to argue the logic about illogical statements.

## ubavontuba

Now you're confusing charge with mass.

## Captain Stumpy

in your mass argument, you do state two particles (one the anti-particle of the other) orbiting a suffucient mass (paraphrased).

for get about mass for a moment. in our current known universe, and from observation and testing, form everything i can read, i dont think even a black hole would be able to separate the particles enabling them to co-exist. especially since we live in a universe populated by matter, and not anti-matter. there could not be the ability for an anti-particle to exist without interacting with normal matter.

then there is the whole quantum mechanics thing... even empty space does not have a zero charge...

## JohnGee

## ubavontuba

I suppose that not understanding the logic certainly would make it appear illogical...

## Captain Stumpy

sigh* but you CHOSE to use the ANTI-particle, because you thought it would help your argument. therefore my logic stands. and you are wrong.

again... not confusing it at all. just using YOUR argument ... mass is NOT the issue. anti + reg matter was the logical issue, and again, I stand by my argument.

this is miscommunication. I am trying to talk math and science, you are trying to invent a hypothetical situation to support your belief. not the same thing. apples and oranges. we will not be able to come to any agreement.

## ubavontuba

## ubavontuba

## rug

Only when you are doing it wrong. Which you have been this entire time.

The math is sound, it's your knowledge that is the flawed. (This has been said before as well)

Thank you for proving you really are a dumbass and ignore the logic after it's been explained to you. THIS time and ONLY this time was malice intended. Dumbass

## ubavontuba

## ubavontuba

I guess i should have simply described two masses in orbit, and not told you one was antimatter until much later then?

Okay. It's been nice chatting with you again.

## Captain Stumpy

this is the realm of science fiction, not science fact.

and even given two masses in orbit, it is still 1+1=2 until you put a charge into them. period. in order for your argument to work it MUST be science FICTION because when two masses orbit, which occurs regularly, they are 1+1=2. when you state, for ANY reason that one is an anti-particle, then regardless of mass, charge comes into play. because one is the OPPOSSITE of the other, therefore a NEGATIVE. mass is not the issue in this case anymore. the fact that the anti-particle cannot co-exist with the particle becomes the issue.

you should have kept with the interpretation of math as a language, in such instances, semantics can and would have been great. you simply chose an issue that you did not fully understand.

## ubavontuba

Fine. Prove it. Show me any well known math formualtion where mass is in absolute values.

So you really are just a crybaby bully. I guess it must be frighteningly frustrating when the logic is too advanced for you...

## ubavontuba

## Captain Stumpy

we seem to be at an impasse. you do not understand, or perhaps just refuse to capitulate to lack of knowledge about certain science issues, and i am trying to explain, but obviously i am failing. i am not able to sufficiently explain to your liking and therefore this discussion is not capable of progressing. You are arguing semantics and science fiction, not math and logic. whereas there are times when there can be a lack of knowledge, i have tried to explain it above, to the best of my ability. i apologize for the inconvenience, i am a simple mountain man, not a physicist.

PEACE

## ubavontuba

.

## Noumenon

Actually it is you who don't understand the difference between knowing something, requiring a mind in conceptualizing it, and the thing as it exists in itself. Conceptualizing reality with use of mathematics is a human endeavor. Yes 'phenomenal reality' is mathematical but only because by definition it contains a mind dependent component.

Exactly, you couldn't EXPRESS that fact independently of knowledge. Expressing facts is what mathematics if for.

## Noumenon

Platonism is pure metaphysics. Metaphysics has no place in science. I'm not exactly suggesting that mathematics is 'made up' subjectively....

I mentioned epistemology above somewhere,... in the study of what knowledge IS and how the mind acquires it, one could say that mathematics (& space and time, etc) are a-priori forms of thought, a hardwired means of ordering experience given the nature of mind and how mind operates on experience.

This is why such concepts SEEM like their "real" even though they are not tangible. It is very hard to get out of our own intellectual way. Even among pure mathematicians it is not clear and there is widely differing camps about this subject. IMO it, along with why qm is non-intuitive, will remain unclear until we understand how the mind works itself,..

## Noumenon

This is a Physical discovery, that some of our concepts must then be artifacts of thought, and NOT a real structure existing independently of mind. In QM there is a discontinuity between the mathematical formulation and an observation,... in fact measurement in some way produces the result that was not there before hand, the wavefunction is a collapse into concepts.

Relationships don't exist as things independently of us, nor do paths. They're questions about things and where things will be expected at next observation, not things in themselves independent of observation.

## beleg

Proponents of emergence do not accept descriptions where information is conserved.

## beleg

Typo correction for the above.

## Q-Star

Zeph, thank ya for my morning dose of water rippling through the aether on low-dimensional surface model (maths). As edifying as always.

But if I may digress for a moment. In October I'll be visiting your neck of the water surface (so to speak) and was wondering if we might get together for a pint and discussion face to face on the deeper issues confounding modern physics. I don't know if ya are close to Plzen, I'm going there, but would be happy to make a side trip.

## Protoplasmix

Yes, bananas sums up this work quite well.

Ah, so instead of maths it's best to use maths. Brilliant.

## visionabler

I think you have that exactly backwards. Think of a concept that has nothing to do with the universe, and you will be the first. Even the impossible, including the paradox, all comes from our universe (virtual particles, particles existing in two places at once, concept of zero which doesn't actually exist, etc).

## Q-Star

Is that far from Pilzen? If it's under an hour drive I could probably do it.

## ryggesogn2

Discussion of the Method

Billy Koen

http://www.me.ute...OUP.html

## Q-Star

Ya are confusing me,,, is Lubos Motl part of Pilzen? Are ya saying that ya (Zephyr) is right there? In Pilzen? Or in Lubos Motl?

Zeph, ya must be patient with me, I am clueless on the geography of the area.

I can't follow the Facebook link, I'm down in one of the labs, and Facebook is blocked from the computers down here. (To keep the students from being distracted.)

## Diogenes Tha Dogg

"In mathematics everything is algorithm and nothing is meaning; even when it doesn't look like that because we seem to be using words to talk about mathematical things."

Also I liked what the other German guy said about the distinction between infinite and indefinite (progressus/regressus in indefinitum/infinitum)

## Macrocompassion

## brt

What about a circle? or a sphere? Circumference is an infinite distance which can only be described by an infinite number (pi) which is the result of a mathematical relation. Sounds like Math wins again.

## AlumnodeVerum

## rug

Don't forget about i (i = sqrt(-1)) (EDIT: I think this is an infinite number....reasearch time! woohoo!)

Math always wins, even when people do not understand or care to understand the logic behind it. Just like science, just because someone refuses to believe it, doesn't make it any less true.

## Diogenes Tha Dogg

circles don't exist in nature.

## rug

Really? Guess you never had ring worm. http://img.webmd....lder.jpg

## rug

## AlumnodeVerum

What??? How do you figure models must apply to the world but the mathematics used to construct and refine them must not? That makes no sense whatsoever

## AlumnodeVerum

## rug

True

False, most people might not be able to do the math that is required for such a complex structure but the math itself still works. While Newton had problems figuring it out with the math and theories that were available to him and then gave up. It has since been worked out. That was one of the achievements done by general relativity. While it is very complicated it is solvable....

## rug

There is also the fact that many people are simply illogical. Such people have little use for complex mathematics because they do not understand. Math is pure logic and therefore takes a logical mind to comprehend.

Complete fabrication out of over exaggeration. Math is not a first language for anyone. Therefore, math will never be the preferred method of communication for most people.

## Captain Stumpy

@AlumnodeVerum - this is the heart of my argument! thank you, very well said.

@teech2

[p] On the other hand the mathematics doesn't allow model even the system of six gravitating bodies in deterministic way - such a system is too complex for it. [/p]

like rug says - just because WE cant do the math, doesn't mean the math is not capable. besides, what more is there to learn that we don't know?

## rug

If you want to talk about models then, yes you are basically right they don't always work and are simplified for ease of use. They are only generalizations not precise instruments.

Math on the other hand, with all the valid data available and enough time to be worked out the math will always workout.

If you had all the data, the data be perfect, and enough time to do so. A perfect model of the universe could be created. Since none of our data is perfect with the fact we tend to not have all of it combined with the general time crunch everyone lives with every day this will never happen.

Once you start talking about the same thing maybe there can be a logical discussion.

## rug

"Intuitive reasoning" fails all the time. Since it's not based on data. Intuitive reasoning is used for a hypothesis possibly but not in the logic needed need understand the results. If you are using "Intuitive reasoning" for basis of theories then the theories fail more times than not.

Come to think about it......that explains a lot of what you have said and believe.

## rug

However, that is not always the case. Like in mass and energy. This is a very complex relationship and yet described with a deceivingly simple equation. E=MC2 (squared). Another example, Ohm's law V=IR it's the basis of all electronics. It's a very complex relationship and yet this equation is extremely simple.

The Universe or Multiverse (string theory) it's extremely complex and well huge. There is a lot more to deal with and therefore it alot more complex. Orders of magnitude complex. The math has to be more complex in order to describe it. The thought is however that once we understand enough the equations will be simplified.

## Captain Stumpy

emergent logics like: numerology? cabala?

really?

"in numerology and cabala the math is literally unbeatable" i am not sure how you can make that statement with a straight face... prove to me the math is "literally unbeatable"... please.

and i stand by my arguments posted above... please READ THEM ALL above before coming back to me on that, unless you can prove something with numerology that i need to know. i am not arguing that math is difficult... or about models, which may or may not contain all the needed data. models are a shortcoming of US, not the math!

thanks.

## rug

Correct.

Then it's not intuitive. However, seeing the results of your reasoning I would have to say it fails you more often than you realise.

I do understand emergent logic. It has nothing to do with models or math.

Really? Fictional characters is the best you can do? Sadly, you have even misrepresented what they did. They took evidence most people would not notice and used them to construct a working theory. Since they are fictional it worked more times than not. In the real world it fails more often than not.

## rug

I think Steven Weinberg said, Nature is not here to make physicists happy.

If physicists are not happy with how it works then why should you be?

I don't pretend to understand quantum mechanics. The whole thing just gives me a headache. What I do know is the smaller the things we look at get the stranger it becomes.

## rug

## rug

## rug

That is pretty simple. Some people don't seem to understand that math works and always works. A lot of people are illogical and so they cannot understand the logical foundations of mathematics.

We have made a full circle of your "logic" and it seems impossible for you to have a logical discussion without bringing irrelevant information into it.

The only possible conclusion... Choose one.

1 ) Math needs to be taught better in schools. Taught to understand how math works and how to use it to understand how things work. Not just numbers and equations to memorise. Everyone finds that boring and we end up with people that think math is not effective. Like you.

2 ) You are not logical. You do not understand the basic concepts the of science or mathematics.

3 ) You're a dumbass.

I leave the choice up to you....

## AlumnodeVerum

Ok First- just because we don't see examples of some mathematical predictions here doesn't mean they don't exist. Second- people use math all the time in common speech. Have you never been to the grocery store?

## AlumnodeVerum

## rug

## misterx

## rug

## beleg

Is mathematics an effective way to describe the world?

Yes and No.

https://www.simon...physics/

Amplitudes of particle spectra reduced to high school math.

New geometric object removes the need of Feynman diagrams and removes locality and unitarity. This is a world (math) where relativity and quantum mechanics emerge naturally from it.