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 thinki*

*ng 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.

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.

OdpovědětVymazatDavid 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.

Concerning the math and art relation, it's well known, many brilliant mathematicians were good artists, too. But the best artists were usually very bad in formal math. Knowledge of math at the level, which is learned at schools could be algoritmized easily and it's merely just a technical skill. But at its abstract level it could be very creative technique. IMO now we are living in era of mathematical education, which is analogous era of assembly language programming of 60's. Now nearly nobody is required to know assembly language to be able to work with computer. The contemporary high-level math will be handled by software packages like Matlab or Mathematica. The knowledge of math will be limited to few specialists and future engineers will learn, how to run heavilly parallelized simulations instead. BTW Does knowledge of math help or prohibit us in solving of paradoxes like this one 1 2?

OdpovědětVymazatIn reality, simulation is key to math education, says Stanford mathematician.

OdpovědětVymazatHere 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.

OdpovědětVymazathttp://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:

OdpovědětVymazatPhysmatics"

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:

OdpovědětVymazatAlbert 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:

OdpovědětVymazat1. 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: "

OdpovědětVymazatSomeone 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.

OdpovědětVymazatAWT 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.