Optimism is much needed these days. I hope I also transmitted this feeling in my essay, entitled ""More diversity and creativity for a different science". I invite you to take a look at https://qspace.fqxi.org/competitions/entry/2330#control_panel.
Admin Comment: Please respect other entrants and don’t just reply to advertise your own essay. Please keep on topic.
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."
Amitabha Lahiri Thank you for your comment!
I readily accept your criticism that my suggestions in the latter half of the essay (regarding how we can best pursue a scientific agenda) were a bit vague. I believe we require a restructuring of how we (both scientists and the public) approach normal science, to eliminate the misconception that only revolutionary science is a worthwhile pursuit: revolutions only result from a breakdown of a paradigm developed to its breaking point, making normal scientific activity absolutely critical for progress. I mainly wanted to emphasize this shift in perspective, which can then be implemented in a number of different ways (e.g., a restructuring of the hierarchy in research institutions or a rethink of publication practices).
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.
Amitabha Lahiri I think we may be referring to somewhat different concepts with the expression "normal science". I mean it in the very specific Kuhnian sense, that is, science guided by a given paradigm. While this can sometimes involve incremental progress building closely upon previous research (which I think is what you had in mind), this is not necessarily the case- seminal discoveries which lead to the downfall of a paradigm (for example, the Michelson-Morley experiment) I would still consider as part of a normal scientific agenda, since the experiment could only have been conceived in the framework of the time.
Perhaps the term "normal" science is problematic, since it sounds so negative and conservative compared to "revolutionary" science- maybe "paradigmatic" would be a better term. In any case, while funding agencies may be willing to fund some types of normal science (like the safer, incremental kind you describe in your essay), they are more resistant to explore higher-risk normal science (the kind really probing the limits of a paradigm) without some technology or application as an additional societal bonus.
I will certainly have a closer look at your essay, it looks very interesting!
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
761 Accesses
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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
I enjoyed reading your well-written and engaging essay. You nailed it by pointing out that breakthrough discoveries require risk-making and supporting new ideas with an open mind. As you said, We should be confident enough to retreat in our ideas, even at the cost of explanatory power, and be willing to approach new ideas with open minds.
Another issue that I believe has been overlooked in academia is that universities and research institutes mainly hire graduates of the top universities of first-world countries. Well, it is the safest decision because the graduates of the top universities are among the best in the world. But overdoing it (the way it is happening) is destructive for science. We all have our own knowledge & vision boxes, formed by our backgrounds and alma maters. When academia highly focuses on top-rated universities, it may impede the exploration of out-of-the-box ideas and hinder breakthrough discoveries. Someone with a different background and educational system can bring new perspectives and ideas.
I should also mention I liked FQXi's anonymity rule.
I raised related ideas in my essay and would be happy to have your opinion on them.
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.
Thank you for your comment! This is a point I am happy to discuss.
Indeed, in this section from which you quoted, I begin to depart from Kuhn's views, as I say at the start of the preceding paragraph:
"Notably, Kuhn himself would protest to this aspect of the analogy. In comparing the development of scientific paradigms to natural selection, he emphasizes that it is a process which proceeds without an external guiding hand and
without any defined end goal (Kuhn, 1962)..."
I don't think Kuhn would object that each new paradigm offers some form of advantage over previous ones- he himself uses natural selection as an analogy, implying that successful paradigms are somehow better suited to survival (not the same as "better", and perhaps this is really the point) than their competitors. The new paradigm may not even agree better with the data than the old one, but something about it makes it more "promising" to the scientific community, leading to its acceptance. However, Kuhn firmly distanced himself from the idea that this implies progress toward some grand ultimate theory. In my essay, I make the claim that an evolutionary progression of paradigms does lead in the direction of some sort of ultimate theory, albeit in a weighted random walk sort of way. However, you are completely right that Kuhn (and likely many others!) would not agree with this.
I wrote that my essay follows a "Kuhnian approach" because I work in the framework of his paradigm model and use his divisions of eras like "normal science" and "crisis" throughout my essay.
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.
Roger Schlafly I think we are mostly on the same page, but I'd like to clarify two points (not defending my own position, just clarifying what I have understood to be Kuhn's position):
As you say, Kuhn did not believe that paradigms progressed in a cumulative fashion (like "normal science"), and that a new paradigm is only selected from among its incommensurable peers as a result of persuasion. However, such "persuasion" is not necessarily based on irrational ideas, as Kuhn writes in his postscript to The Structure of Scientific Revolutions:
"Nothing about that relatively familiar thesis implies either that there are no good reasons for being persuaded or that those reasons are not ultimately decisive for the group. Nor does it even imply that the reasons for choice are different from those usually listed by philosophers of science: accuracy, simplicity, fruitfulness, and the like."
What I suspect you find disconcerting (as I do!) is that he regards such reasons as "values", making it ultimately a rather subjective affair, which would seem on the surface to inhibit any form of progress through paradigms.
However, Kuhn did not entirely deny the notion of scientific progress (although not in a sense leading toward some ultimate scientific truth), as he writes in the same postscript where he is discussing how one could perform a "genealogy" of scientific theories if one did not know their history a priori:
"...it should be easy to design a list of criteria that would enable an uncommitted observer to distinguish the earlier from the more recent theory time after time. Among the most useful would be: accuracy of prediction, particularly of quantitative prediction; the balance between esoteric and everyday subject matter; and the number of different problems solved. ... Those lists are not yet the ones required, but I have no doubt that they can be completed. If they can, then scientific development is, like biological, a unidirectional and irreversible process. Later scientific theories are better than earlier ones for solving puzzles in the often quite different environments to which they are applied. That is not a relativist’s position, and it displays the sense in which I am a convinced believer in scientific progress."
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 ].