The Accumulation of Understanding

This essay is eloquently written and reflects a broad knowledge of how science works and the history and philosophy of science. But it is profoundly conservative. Instead of answering "How could science be different?" the essay answers "Why should science continue to be the same?".

Of course, there are many achievements that science can claim. I'm proud to be a scientist, and proud of the community of scientists. There has never in the history of humanity been a more reliable arbiter of truth than the world community of scientists.

And yet, there are big questions that science has not answered. Some of these are not just missing pieces in the puzzle -- some of them seem to imply that we have reached dead ends. We need new foundations, new paradigms, new ways of understanding how the world works.

A few examples...

• Monica Gagliano has demonstrated that plants sense sound in the environment without ears or even a nervous system. Plants learn and remember. Plants strategize and make educated guesses about the future. We associate all these activities with synapses and neural networks. Plants do these things in a fundamentally different way.

• The 30-year legacy of Robert Jahn and Brenda Dunne demonstrates with 6-sigma certainty that human intention in the abstract can influence events at the quantum level. Why are there no physicists seeking to incorporate their experimental results into a new formulation of QM?

• The study of life's pre-Darwinian origin has made much progress in synthesizing biochemical precursors from abiotic starting materials, and yet it is becoming clear that a self-reproducing system ("hypercycle") is elusive. This is the prerequisite for the beginning of a Darwinian process, so we can't attribute it to natural selection. We may have to face the fact that our current understanding of physics and chemistry is incompatible with life's origin.

• There are dozens of labs around the world that have demonstrated cold fusion, and yet their research is excluded from mainstream publications in physics and engineering. Understanding cold fusion as a new bulk quantum phenomenon has the potential to offer solutions to most major environmental problems, and a new perspective on many-particle quantum phenomena. But the subject remains a backwater because of scientific taboos.

• The Pyramids of Giza could not have been built by any technology we know today. Full stop.

There is a compelling need for new scientific paradigms. We need to re-establish the open-minded attitude that Niels Bohr epitomized when he said, "We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct."

Yaakov Fein
You are absolutely right that normal scientific activity is critical for progress. However, I believe science administrators are fully in favour of the normal research -- indeed, research grants are given almost exclusively to "normal" research, you would be exceptionally lucky to get a grant for doing something that no one (including yourself) has done yet! The public hopes for, and notices, revolutionary research, but scientists keep doing what they have always done, only occasionally straying out. Funders almost never support the unknown. In my essay "Efficient funding produces better science" I have tried to suggest a solution that would help both kinds of research -- just in case you might be interested.

Yaakov Fein Ok, that is a fair explanation of your position. Thank you!

quote
While such open questions indicate that we are still far from a complete description of nature, it
is impossible to deny our successes, and in particular the success of mathematics in science. The
reason for this deep connection is far from obvious and is a recurring subject among scientists
and philosophers. The theoretical physicist Eugene Wigner explores this connection in his
widely-discussed essay, The Unreasonable Effectiveness of Mathematics in the Natural Science
(Wigner, 1960). He readily acknowledges that the correspondence is not one-to-one, since only a
small fraction of mathematical concepts are employed in the context of physical theories. Despite
this, Wigner sees a strong indication that the connection is more than coincidence based on the
incredible ability, particularly obvious in physics, to extrapolate a mathematical description far
beyond its original domain: “… the mathematical formulation of the physicist’s often crude
experience leads in an uncanny number of cases to an amazingly accurate description of a large
5
class of phenomena. This shows that the mathematical language has more to commend it than
being the only language which we can speak; it shows that it is, in a very real sense, the correct
language.
end of quote
While I like this essay I wish to point out that we have a long way to go in terms of optimization of mathematical analysis
quote
Differential Dyson–Schwinger equations for quantum chromodynamics
Marco Frasca
The European Physical Journal C volume 80, Article number: 707 (2020) Cite this article

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A preprint version of the article is available at arXiv.

Abstract
Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The ’t Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.

1 Introduction
The main difficulty of quantun chromodynamics (QCD) is that, at low energies, the theory is not amenable to treatment using perturbation techniques. This implies that some non-perturbative methods should be devised to solve them. The most widespread approach is solving the equations of the theory on a large lattice using computer facilities. This permitted to obtain, with a precision of a few percent [1, 2], some relevant observables of the theory. This method improves as the computer resources improve making even more precise the comparison with experiment. Use of numerical techniques is a signal that we miss some sound theoretical approach to compute observables.

A similar situation is seen for the correlation functions of the theory. Studies on the lattice of the gluon and ghost propagators, mostly in the Landau gauge, [3,4,5] and the spectrum [6, 7] proved that a mass gap appears in a non-Abelian gauge theory without fermions. Theoretical support for these results was presented in [8,9,10,11,12,13] providing closed form formulas for the gluon propagator. Quite recently, the set of Dyson–Schwinger equations for this case was solved, for the 1- and 2-point functions, and the spectrum very-well accurately computed both in 3 and 4 dimensions [13,14,15]. Confinement was also proved to be a property of the theory [14, 16].

Indeed, the Dyson–Schwinger equations were considered, since the start, the most sensible approach to treat a non-perturbative theory like QCD at low-energies [17,18,19] and, more recently, [20]. In any case, the standard technique is to reduce the set of equations, that normally are partial differential equations, to their integral form in momentum space. Some years ago, Bender, Milton and Savage [21] proposed to derive the Dyson–Schwinger equations and treat them into differential form. This way to manage these equation was the one used to find the exact solution [13]. This technique appears more general as it permits to work out a solution to a quantum field theory also when a background field is present. This is a rather general situation when a non-trivial solution of the 1-point equation is considered. Such a possibility opens up the opportunity of a complete solution to theories that normally are considered treatable only through perturbation methods. The idea is that, knowing all the correlation functions, a quantum field theory is completely solved.

The aim of this paper is to derive the Dyson-Schwinger equations for QCD in differential form.
end of quote
Let me run this by you, so you can see it. QCD is, according to this abstract NOT particularly well solved by PERTURBATION THEORY

Why is this so important ? There have been cases of series solutions of the QCD equations having very large contribution from terms way down in the line of series expansion solutions

It means that there is more work to do.

In about 100 years from now if we have not killed ourselves off, our solutions to many of these equations may look very different

You say: "we consider successful scientific paradigms to be the ones best suited, compared to
competing paradigms, to describe our observations of nature." [p.3] I do not think Kuhn would agree with that at all. Kuhn's main argument was that the accepted scientific paradigms are not any better than the competing ones. You say that your essay is a "Kuhnian approach", but it is the opposite.

Yaakov Fein Kuhn claimed that the new paradigms were incommensurable with the old. Scientists might prefer the new to the old, but not for any good measurable or rational reasons. He portrayed scientists as irrationally jumping from one fad to another, without making progress.
You say: " Copernicus’ heliocentric model was not a dramatic improvement on Ptolemy’s geocentrism based on the data available at the time". Yes, that seems to be what drove Kuhn's view. The rest of the history of science does not match what he says at all.

Hello MalachitePony. Your essay:
"In other words, judging it to be "ultimate" or not may well be beyond our capabilities, but I believe this is distinct from the question of whether it would be a worthwhile scientific program to attempt to falsify it when a functional understanding of all natural phenomena has already been achieved".

You have to think big!
It is known that Newton determined the gravitational coefficient through the parameters of the orbits of the planets of the solar system. If the gravitational coefficient is determined in a similar way from the parameters of the orbits of electrons in the Hydrogen atom, then the gravitational coefficient of the planetary system of the Hydrogen atom becomes 40 orders of magnitude greater than in the solar system. Then the Planck parameters of the Hydrogen atom are the parameters of an electron with its radius equal to the radius of the Compton wave of the electron. Those. each level of fractal matter has its own “Planck parameters”, and the generally accepted Planck parameters are an abstract delusion and have no real meaning at all. Indeed, what relation does the gravitational coefficient from the parameters of the Solar system have to the parameters of the planetary system of the Hydrogen atom? None!!!

You have to think big!
The fine structure constant can be easily calculated with an accuracy of up to 7 digits, assuming that all elements of matter have a fractal structure. Then, therefore, "black holes" do not exist, and there is no event horizon. Those. inside putative "black holes", there is deterministic matter that obeys the simple quantum laws of fractal matter, which unify gravity and quantum phenomena of the deterministic functioning of matter on all scales of the universe [ appendix: https://s3.amazonaws.com/fqxi.data/data/essay-contest-files/16/reference_id_2304.pdf
https://qspace.fqxi.org/competitions/entry/2304#control_panel ].