The physical models often enable to derive the predictions, which are difficult to handle (or even to express) by formal math, for example the order of Venus phases from heliocentric model (after all, how we can express mathematically the simple information, the Earth revolves around Sun and not vice-versa?). At such cases, the picture of geometry is much more illustrative.
From this point of view it's not accidental, the common illustrations of modern physical theories (like string theory) are mostly quite schematic and pathetic. Such drawings illustrate nothing, but the fact, their authors have no true physical insight into real situation - so they cannot imagine/picture even their own models.
But here are more substantial objections against formal approach in physics. The true is, the consecutive ("step-by-step") logic of formal math describes the heavily parallelized physics of multiparticle systems poorly. Even the gravitational system of five bodies is (nearly) impossible to describe by formal math and the resulting description would be so complex, so that nothing useful can be derived from it. This is the reason, why we have no deterministic description of phenomena in multiparticle system, like the turbulence. This forces the formally thinking physicists to use the probabilistic interpretation instead - like at the case of quantum mechanics - although such system remains deterministic apparently - it's just more complex, then the consecutive formal math can handle (while we know already, we can model the quantum mechanics phenomena by discrete particle models, even experimentally).
By such way, the formally thinking physicists are effectively mentally blocked from understanding, our Universe can be interpreted by multiparticle system for last two hundred years. Their formal math and way of thinking is simply incompatible with this trivial idea - even at the case, the illustrative understanding of such system can be quite simple. This is dual approach to philosophy, which cannot describe some connections by using of formal math, even at the case, such description can be quite simple. It's evident, the optimized approach in reality understanding should involve both strategies (the formal and non-formal one) in balanced ratio.
Of course, the above problem just illustrates the limits of math and formal thinking - not the limits of AWT concept. We should simply face the fact, here exists a wide group of phenomena and geometries, the handling of which by formal math is noneffective with respect to their understanding - that's all. This doesn't say, the formal math is nonsense - it's simply inappropriate tool for deterministic / reproducible description of such systems.
From general perspective, the AWT is extrapolation of free fermion models of string field theories to zero dimension. These models are nothing very new in physics, as some physicists have assumed already, the strings are composed from more fundamental particles (so called preons) already. The one-dimensional strings are just the lowest number of dimensions, which the formal math can handle without problem, while avoiding the singularities. The concept of environment composed from zero dimensional particles is naturally singular from formal math perspective, so the formal math cannot use it. It can be replaced by concept of one or more-dimensional strings partially - but here's a technical problem: such approximation leads to landscape of 10E+500 possible solutions (which roughly corresponds the number of 0D particles involved in this model of observable Universe) - so it's unusable from practical reasons. But the system of many particles can be handled without explicit models, for example by computer simulation:
From such particle model is evident, the system enables the only single way of Aether compactification, leading to dynamic foam of higher-dimensional density fluctuations (i.e. "strings" and "branes") naturally - so no giant landscapes of possible solutions, no ad-hoc assumption of strings, no assumption of (unexplained yet) relativity and quantum mechanics postulates is required here at all - and we can derive all these postulates from geometry of simple particle concept instead. By such way, AWT is highly motivated approach, which follows Occam razor criterion, minimizing the number of postulates in theory.
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Aether Wave Theory models & explains observable Universe by nested density fluctuations of dense particle gas, aka Aether and it explains, why fact, that reality is observable still doesn't mean, such reality must remain computable in sense of formal math in contradiction to Max Tegmark hypothesis of "Mathematical Universe". Therefore "Unified theory of everything" (TOE) probably isn't possible.
David H. Wolpert logically proved two Wolpert's theorems of inference :
a) For every machine capable of conducting strong inferences on the totality of the laws of physics there will be a second machine that cannot be strongly inferred from the first one.
b) Given any pair of such machines, they cannot be strongly inferred from each other.
Does mathematical reality trump physical reality?
IMO the theories of Universe would converge to the model, which would enable survival of as high number of theorists, as possible..
Here you can find whole dedicated web in Java, which illustrates, what is possible to compute just by using of particle, statistical and LBM models. In most cases, these situations couldn't be modelled by using of formal math at all because of their complexity and low stability of formal solution. With compare to formal models, numerical models are very stable, robust and suficiently fast in most cases. They can handle situations like vortex and singularity formations, where formal models tends to become unstable.
http://mike1336.web.fc2.com
The main point of Aether theory is, you're not required to derive and solve various equations, if whole observable reality is composed of particles anyway. So it can be modelled by particle simulations from very befinning.
Eric Zaslow: Physmatics
"I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce." [Freeman Dyson, Missed Opportunities, 1972]
Formally rigorous derivations are self-evident tautologies instead:
Albert Einstein in [Geometry and Experience, 1921]:
"As far of the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
Therefore we shouldn't argument with pure formal model at physical forums, with infinity or zero values the less as the physics doesn't operate with unmeasurable quantities. We should use nonformal logical models instead.
As Hume correctly said, building physical theory has two parts:
1. By applying induction on what we observed, we bang out extra-logical axioms of the theory, called laws of physics. This process can be understood as "proof by examples" for the laws banged out. There is nothing better physicists can do on this. This is essentially a process of speculation. From limited experiences, we stretch out to claim laws of physics. Empiricism is to govern this most disturbing part of building physical theories. It is not a process of finding truth but it is a process of reaching to agreement among us.
2. Once the axioms are bunged out, the deduction (prediction) process of the physical theory is precisely that of formal logical reasoning. This means that physical theories succumbs to the laws of logic in prediction process. This is where physicists often have no understanding at all.
Stephen Hawking: "Someone told me that each equation I included in the book would halve the sales."
In dense aether theory the reality is gradient density driven and it appears like density fluctuations in dense gas. You cannot see that gas - only density fluctuations of it. It means, observable reality is inconsistent and dispersive by its very nature - if it wouldn't, we would see it at all.
AWT describes math theories with implicate geometry model. The theories are formed with density fluctuations in casual space, which are connecting scalar points (scalar axioms) with density gradients (vector, tensors) represented with implications. It means, the casual structure of math theories is similar to structure of universe and it appears like foam. After then we are facing the very same inconsistency problem: every theory must consist from at least pair of postulates, which are defining it's implication vector and enabling their extrapolation (i.e. testable prediction) along line. But if these postulates would be fully consistent, we could replace them with single one and whole theory would change into tautology. You cannot extrapolate a line from single point in unique way In such way, every formal theory must remain inconsistent at least a bit - or it would change into tautology without true value. It just seems, math theory, the Peano algebra in particular is no exception. On this trivial insight the Goedel's incompleteness theorems are based, too.
Therefore it's not quite true, physical theories are irrelevant with respect to mathematical conclusions, because formal math and geometry is not quite abstract. Formal math is atemporal and it cannot derive/handle the time concept, for example. But concept of natural numbers is derived from concept of countable colliding objects (fermionic particles), which cannot penetrate mutually. And concepts of differential math are derived from physical gradients of inertial environment. It has it's own deep consequences regarding the [larger number hypothesis](Dirac large numbers hypothesis), theory of prime numbers, theory of monstrous group and number of dimensions of observable Universe, incompleteness theorems and implicate geometry and inconsistency principle of math theories.
Mathematicians could learn a lot from physics, not just vice-versa.
While the slogan "Shut up and calculate!" is sometimes attributed to Paul Dirac or Richard Feynman, it is in fact due to the lesser known David Mermin
Dehumanized: When math and science rule the school
In AWT it corresponds the perspective of the interaction of the bubble sitting at the water surface with its neighborhood via surface ripples. For small or large ripples the water surface is behaving like system of infinitely many particles, which is relatively easy to formalize with formal math, because the dispersive effects of the (hidden dimensions of) underwater can be neglected (relativity) or considered dominant (quantum theory).
But with increasing distance from the dimensional scale of the bubble the chaotic character of underwater will manifest again and the formal models will become useless because of their complexity. IMO this perspective basically corresponds the current stage of physics in its attempt for formal description of the Universe.
Albert Einstein: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality".
Has the Einstein Revolution Gone Too Far?
A slight paradigm shift, so to say:
Max Tegmark, a MIT teacher: The Mathematical Universe
http://arxiv.org/abs/0704.0646
versus
Alan P. Lightman, a MIT teacher: We are living in a universe uncalculable by science.
http://www.harpers.org/archive/2011/12/0083720
Derivation of the Fine Structure Constant
http://en.wikipedia.org/wiki/Ashkenazi_Jewish_intelligence http://www.otaulc.com/text/1262.htm
Richard Feynman: "Physics is to mathematics like sex is to masturbation. Sure, it may give some practical results, but that's not why we do it."
The Overuse of Elegant Mathematics
Is Nature unnatural? Decades of confounding experiments have physicists considering a startling possibility: the universe might not make sense
Max Tegmark: Shut up and calculate! "I advocate an extreme "shut-up-and-calculate" approach to physics, where our external physical reality is assumed to be purely mathematical. This brief essay motivates this "it's all just equations" assumption and discusses its implications."
The “Unnatural” Standard Model
The problem with reductionism, Laughlin says, is that it’s susceptible to “Dark Corollaries”, which obscure the inconclusive nature of many experiments. One of these corollaries he has dubbed ‘the Deceitful Turkey’, to describe the phantom breakthrough that feels so tantalisingly close but will always be beyond one’s grasp, no matter what computer power or technology is at hand.
Is mathematics an effective way to describe the world? 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.
Politics wrecks your ability to do math. New research suggests that people even solve math problems differently if their political ideology is at stake.
"Shut up and let me think": Quantum foundations vs the "shut up and calculate" attitude.
Liping Ma: "Knowing and Teaching Elementary Mathematics", "A
Critique of the Structure of U.S.Elementary School Mathematics"
Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Einstein. They chose to look for reality only in terms of abstract mathematics instead of
the physical imagery given to us by the reality of what we can see and touch.
Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."
Albert Einstein: "Books on physics are full of complicated mathematical formulas, but thought and ideas are the beginning of every physical theory"
In formal rigor, when two systems of equations are providing different results for the same set of parameters, they're mutually inconsistent and they share no common solution. At the case of quantum mechanics and general relativity theories such a results is a vacuum density, for example - but we can find even much more trivial example.
For example, the quantum mechanics of free massive wave packet predicts, that such packet will expand into infinity with speed of light. This is simply a solution of Schrodinger/Dirac equations and you can do anything with it. But the general relativity predicts instead, that every massive object will collapse into singularity. This is indeed a quite opposite result and you cannot do anything with it again. This is simply, how the general relativity works.
So it's evident, that at the formal level both systems of equations are mutually inconsistent and they cannot be never reconciled by means of strictly deterministic formal rigor. This is one of reasons, why I introduced the AWT and its dense aether model. And this is the reason, why string theory leads into landscapes of 10E+500 solutions.
If the string theorists would be just a bit more clever and familiar with principles of formal rigor, they could save their forty years of analysis and tax payers money with the same zero result and do something more meaningful. Instead of it, they're getting millions of dollars in various ad-hoced prices from similar fraudster for their incoherent nonsense.
In AWT the classical world results from averaging of quantum mechanics and general relativity theories. So if you're seeking for quantum corrections to general relativity, then the classical world cannot be omitted. The classical forces apply to the dimensional scale which is exactly BETWEEN dimensional scales of general relativity and quantum mechanics, so that every quantum gravity theory must consider (actually predict) them as well. You may call this logics AWT and ignore as such, but this logics is still here.
scheme
For me it's completely clear, that the physicists have their math models developed for particular situations, but they have absolutely no idea, how they should be combined into testable models. They cannot see the forests through their woods of equations, because they were actually never trained to think outside of formal rigor, i.e. in nonformal way. Without their equations they're simply lost and cannot understand anything about their models like toddlers. Actually from my experience with reddit is evident, the nonformal thinking is not only taught at schools, but even prohibited and ridiculed. It's not therefore very difficult to play a role of complete genius and idiot here at the same moment.
The Voyager probes would need to use codewords whose sequences were distinct enough to be recognizable even with a few corrupted bits. But using less distinct codewords would provide more possibilities within the 24-bit limit, enabling faster data transmission. These competing needs translated into a geometry problem in which the bits corresponded to spatial coordinates, with each codeword the center point of a sphere in 24-dimensional space. If the spheres overlapped, the associated codewords would no longer be uniquely recognizable. To optimize the amount of data that could be transmitted and then corrected, the question became: How densely could spheres be packed in 24-dimensional space?
Invest in minds not maths to boost the economy
Max Tegmark argues that we have to get rid of equations in physics that aren’t just based on finite and discrete quantities. Nature history: "Shut up and calculate!" The nuclear weapon research contributed significantly not just for the social statut of physicists but for credit of computational methods and formal approach in physics too - because the nuclear weapon design requires lotta calculations.
Hartry Field’s Science Without Numbers: A Defence of Nominalism which shows you can do Newtonian physics without math.
Lee Smolin has written a whole book about the problem with the timeless math
You can't do the math without the words: Many tribal nations don't use
calculus at all. They're still use a language. Also, many animals can count, but they use nonverbal language only, not calculus.
V.I. Arnold, On teaching mathematics
Do you have calculations showing this?
Do you have calculations proving you're real? Only the contemporary physicists believe, everything must be calculable - or it cannot exist. For example, they believe, that the cold fusion cannot be computed from existing models, so it's denied by the whole century. In another words, the belief in calculability, which is promoted by existing priests of science at universities has replaced the medieval religion and belief in God. The concept of mathematical universe is an economical theorem - rather than something else. In fact it only provides the social credit and job for these people in the same way, like the belief in God provided an income for medieval priests.
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