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onsdag 16 oktober 2024

Science or Magic?


What is the difference between science and magic? Is there less magic and more science in our modern technological society ultimately geared by Human Intelligence HI? Let' see, with connection to recents posts. 

This years Nobel Prizes in Physics and Chemistry were given to Artificial Intelligence AI and not HI as all previous years, which can be seen as an expression of the crisis of modern theoretical physics witnessed by leading physicists in popular science media/web. 

Modern theoretical physics was born 100 years ago in the form of Quantum Mechanics QM for atomic microscopics without gravitation and Einstein's General Theory of Relativity GR for macroscopic gravitation, still today serving as foundation, although incompatible.  

Both QM and GR introduced new elements of magic into theoretical physics, in classical form carried by logic and clarity in the spirit of Leibniz and Euler, as expressed by Nobel Laureates: 

  • If quantum theory is correct, it signifies the end of physics as a science. (Einstein 1921)
  • If you can fathom QM without getting dizzy, you don't get it. (Bohr 1922)
  • It seems clear that the present quantum mechanics is not in its final form. Some day a new quantum mechanics will be discovered ....determinism in the way that Einstein wanted. (Dirac 1933) 
  • I don't like QM, and I'm sorry I ever had anything to do with it. (Schrödinger 1933)
  • Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. Such weighty views cannot be ignored. (Born 1954)
  • It was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness. (Wigner 1963)

  • Nobody understands QM. (Feynman 1965) 
  • Many people probably felt relieved when told that the world could not be understood except by Einstein and a few other geniuses who were able to think in four dimensions. (Alfven 1970)
  • QM is wrong. QM makes absolutely no sense.(Penrose 2020). 

Nevertheless QM is viewed to have, then apparently by magic, delivered wonders like the atomic bomb and the computer and all physicists confess to GR even if its "four dimensional curved space time" is pure magic.  

We are led to conclude that modern science ultimate based on QM + GR has very strong elements of magic. To this picture we can now add AI as something magical beyond understanding, because the computational optimisation process behind AI is too complex to be inspected and understood. 

The essence of science in a classical sense is to be understandable by HI, while magic is not understandable by HI. Understanding is important because that opens for constructive improvement/advancement, while shear magic does not.  

The crisis of modern theoretical physics can thus be seen as an expression of the difficulty of advancing science based on magic. QM and GR has not evolved since birth 100 years ago and science without advancement is dead science. 

Origin of the mystery of QM.   

QM is based on Schrödinger's Equation SE presented in 1925 for the hydrogen atom with one electron, and then formally extended to atomic systems with $N>1$ electrons, with solutions named wave functions  denoted by $\Psi$ depending on $N$ three-dimensional spatial coordinates altogether $3N$ coordinates and a time coordinate. Theoretical physicists like to speak about $\Psi$ as offering a full description of the World, unfortunately maybe way beyond the imagination of a general public. 

The mystery of QM introduced by Born, is that the wave function $\Psi$ has a meaning only as probability and not as actuality, and since physics concerns actuality the wave function lacks physical meaning. In addition it is uncomputable because computational work scales exponentially with $N$. The effect is that QM describes  physics in terms of wave functions without direct physical meaning, which in addition are uncomputable. The wave function carries information about all possibilities but no single actuality and as such is an uncomputable monster which cannot be used constructively.

In this hopeless situation, physicists compute solutions to simplified SE and adjust computations until fit with experiments. The mantra then reads that QM always gives exact agreement with observation as evidence that QM is a complete success (and as such truly magical). 

The probability interpretation of QM appeared as a necessity from a trivial formal mathematical generalisation of SE for one electron with physical meaning, into a canonical SE for many electrons without physical meaning. Non-physical formality thus dictated resort to probability instead of physical actuality, and the result was mystery beyond HI.

Is there then no hope? Yes, there is a different generalisation from one to many electrons based on physics into a deterministic model in the form of classical continuum mechanics, which we refer to as Real Quantum Mechanics RealQM. This model is understandable and computable and as such can open to advancement of fundamental science. Take a look.  

PS Note that science as magic is not the same as science fiction, which is based on physics albeit fictional.


söndag 11 november 2018

Turbulence Riddle Solved by AI as Automated Computational Mathematical Modeling ACMM

The (super)human intellect of Euler (1707-83) formulated Euler's equation for fluid flow.
The information society is based on computational mathematical modeling with Automated Computational Mathematical Modeling ACMM now emerging as a form of Artificial Intelligence AI.

The FEniCS Project is software for ACMM in a setting of (partial) differential equations (mathematical models of physical systems) offering automation of discretisation and computational solution. 

Unicorn/FEniCS is a unified solver for solid and fluid dynamics, which offers a solution to the major unsolved problem of mathematical modeling of turbulent fluid flow in the form of an automated turbulence model as the product of best possible computational solution of Euler's equations for fluid flow. 

This is presented by Johan Jansson in edX courses on High Performance Finite Element Modeling Part I and Part II. Take the courses and see yourself! This is a high-light of the educational program DigiMat carrying from basic school to university bringing ACMM to the people!

The turbulence model is the result of AI in the form of a computational procedure for finding a best possible solution to a set of partial differential equations formed by the Human Intelligence HI of Euler as the sharpest mind of the scientific revolution. Here HI sets the goal and ACMM is the factual process to reach the goal.

The solution of the riddle of turbulence thus comes out from a combination of HI and AI in a setting where HI showed to be too weak to give an answer, as witnessed by 

Werner Heisenberg:
  • When I meet God, I’m going to ask him two questions: why relativity? And why turbulence? I really believe he’ll have an answer for the first.
Horace Lamb:
  • I am an old man now, and when I die and go to heaven, there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. About the former, I am really rather optimistic.
Turbulent flow (video) around a jumbojet in landing as best possible solution of Euler's equations.
We here view AI as an extension of HI and not (merely) as a replacement as in self-driving cars,
recalling that after all driving a car does not need much intelligence. But predicting turbulent flow does and requires both HI and AI.

Notice that AI is beyond full understanding of HI since AI is a self-learning system and not a system taught by HI. In particular the automatic turbulence model offered by ACMM is beyond full understanding by HI as a the result of a self-learning adaptive computational procedure, generating the turbulent viscosity which showed to be evasive for HI alone.

Notice further that once turbulent fluid motion can be simulated by ACMM, computational fluid environments can be set up for testing of airplane designs, training of pilots or self-learning of flying vehicles as a combined vehicle-environment application of AI.