The essay compares the history of science with its fundamental achievements and truths. It is shown, by referring to some exemplary cases, that the former could be different, and better, from what it is, if it hadn't been – and still wasn't, in many contexts and in many countries – strongly conditioned by discrimination, despotism, prejudices, bigotry. The latter, on the other hand, could not substantially change, because it is very difficult to imagine an approach to scientific research different from the one that was established in the direction traced by Galileo in the 17th century. That approach is based on two pillars, the mathematical language and the experimental method, which can be improved but not replaced.

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    5 days later

    It is a very clear essay, indeed it "seems" as if mathematics and experience are the only pillars of science. They were in the past but in the future? Will new technology like AI invent maybe a third pillar?

    Thank you very much for your kind appreciation and interesting questions!
    I don't know whether mathematics and experience are and will also be in the future the "only" pillars of science. Certainly they have been and are two pillars of it, and I find it hard to imagine a science - that is, objective and verifiable knowledge - without them, even if some AI or aliens will be producing it. But I could also be wrong.
    Best regards!

    An interesting and well written essay that shows that the acceptance of new scientific and mathematical ideas can depend on the current environment of ideas prevailing at the particular historic time. And acceptance of new ideas can also depend on attitudes to the person who proposed the new idea, e.g. women’s ideas might not be as readily accepted as men’s ideas. A more recent 2002 example details how “human, all too human” interactions are relevant. What are now seen as true ideas, or ideas that were on the right track, can often only be seen with the benefit of hindsight, not at the historic time, when they were not seen as true ideas. I.e., truth is the daughter of time.

    The author concludes that: “science could have developed in a different way, and certainly better, if in its ordinary practice, in the evaluation and sharing of its results, factors outside the sphere of knowledge had not often prevailed.” And I agree. But I feel obliged to point out that science itself, in particular physics, claims that every single outcome is either necessary (due to the impersonal laws of nature) or random (due to impersonal quantum randomness): despite surface appearances, what happens has nothing whatsoever to do with human beings, according to physics.

    Thank you very much for your appreciation and your detailed comment, which shows that you read the essay with interest!
    I make just one thought about the second part of the comment.
    I am well aware that - as you also rightly observe in you interesting essay - on the basis of two of the most entrenched dogmas in the history of philosophy and physics, everything that happens in the universe is either necessary (according to the principle of causal determinism), or is random (according to a certain way of interpreting quantum mechanics).
    But these are precisely two dogmas, which may be conceptually tenable, but are not verified or verifiable scientific theories. Were it not so, the theme of this competion, with its counterfactual question ("How could science be different?"), would also make little sense. And it would be impossible to admit free will, which is probably impossible to prove (as e.g. Kant, who was convinced of its existence, knew), but we can only act and live as if it were there.

    Giovanni Prisinzano
    An excellent essay that makes us think about the future paths of science in connection with the modern conceptual-paradigm crisis of the metaphysical / ontological basis of fundamental science (mathematics, physics, cosmology, logic), which manifests itself as a "crisis of understanding" ("J. Horgan "The End of Science", Kopeikin K.V. "Souls" of atoms and "atoms" of the soul : Wolfgang Ernst Pauli, Carl Gustav Jung and "three great problems of physics"), "loss of certainty" (Kline M. "Mathematics : Loss of Certainty", D. Zaitsev "True, following and modern logic"), "crisis of interpretation and representation" (Romanovskaya T.B. "Modern physics and contemporary art - parallels of style") , "trouble with physics" (Lee Smolin "The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next")
    In this regard, I have questions.
    You write:
    <<We limit ourselves to the assumption that a non-mathematical science of nature is impossible, because space and time, the two dimensions in which everything happens, are of a mathematical nature.>>

    Theoretical physicist Carlo Rovelli in the article "Physics Needs Philosophy / Philosophy Needs Physics” outlined a list of issues and topics currently being discussed in theoretical physics. You can see that most of the issues relate to the field of philosophical ontology. And this list is not complete. The first question in the list: "What is space?" Second: "What is time?"

    Have you ever dealt with the problem of "hundred-year-old beard" - the ontological foundation of mathematics?
    What is the nature of mathematics (ontological status), if we proceed from the philosophical testament of John Archibald Wheeler:
    “We are no longer satisfied with insights only into particles, fields of force, into geometry, or even into time and space. Today we demand of physics some understanding of existence itself."

    D. Bukin makes the following conclusion in the article "The Crisis of the Foundations of Mathematics as a Crisis of Ontology":

    "The crisis of the foundations of mathematics is, first of all, the crisis of ontology, the essence of which is the inability to describe objects, the fact of being or becoming of which goes beyond the usual ideas about the world. The way out of such a crisis should be sought not so much in improving the methods of mathematics itself, but in updating the cognitive means of ontology, which do not deny the classical paradigm, but can go beyond it. In this sense, dialectics is a historically proven method of comprehending the existence of a mathematical object in its development and relationship with objective reality."

    Then maybe Whitehead is right: “A precise language must await a completed metaphysical knowledge”,
    Morris Kline:
    <<But isn't there a power that can impose a ban on the mass production of new results on the grounds that, before moving on, it is necessary to put things in order in the foundations of mathematics?>> (Maurice Kline. "Mathematics. Loss of Certainty")
    and Alexander Zenkin: "truth should be drawn..."
    ("SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS")

    Dear Vladimir,
    thank you very much for your reply and your kind appreciation!

    Referring to your questions, I say at once that I am very far from the perspective of splitting science from philosophy. In ancient times they constituted a single discipline, and the great founders of modern science, from Galileo to Newton, called "Philosophia Naturalis" what we now call "Physics." The separation begins only after Kant, in the nineteenth century, but still in the twentieth century several very great scientists, such as Einstein, Schroedinger, Bohr, Heisenberg, Dirac, Russell, Goedel, Tarski, Monod, to name only those who now come to mind, explicitly recognized the relevance of philosophy in their intellectual journey and made important contributions to it.
    I also believe, following the example of Pascal - another great scientist-philosopher - that some fundamental concepts of science, such as space, time, and number, cannot be defined and understood only by the "esprit de géométrie," but also require a philosophical foundation.

    8 days later

    quote
    During and despite these developments, women everywhere remained in social and legal
    inferiority, with their participation in the development of science denied or confined to marginality,
    just as it had been in the ancient world. There were extraordinary exceptions, such as
    mathematicians Sophie Germain and Sofya Kovalevskaya, to name but two examples. But one of
    the best known names, among female scientists who were heavily penalized simply for being
    women, is that of Emmy Noether (1892-1935), Jewish and German, surely one of the greatest
    mathematicians of the 20th century. Determined to become a mathematician like her father, she
    studied at the universities of Erlangen (her hometown) and Göttingen as an auditor, as she was not
    allowed, as a woman, to attend in her own right. After obtaining her doctorate, she taught in
    Erlangen for seven years without any pay; then in 1915, at the invitation of Hilbert and Klein, who
    had to face opposition from some faculty members, she moved to Göttingen, then probably the best
    center of mathematical studies in the world, and taught there until 1923 always without any pay,
    even after formulating her most famous theorem, one of the most important of the twentieth
    century, which establishes a close correlation between the symmetries of a physical system and
    conservation laws. The theorem was presented in 1918 to the Society of Science in Göttingen by
    Klein and not by Noether herself, who was not a member of the Society. Expelled from Germany in
    1933 as a result of the rise of Nazism and of the anti-Jewish laws, she emigrated to the U.S. like so
    many of her colleagues and obtained a grant to Bryn Mawr College, Pennsylvania, where she died
    only two years later from cancer.
    We have recalled, although it is rather well known, the story of Emmy Noether, because it
    highlights in an exemplary way the condition of exclusion from academia and the scientific
    community experienced by women, in the West as in the rest of the world, until less than a century
    ago. It should also be pointed out that exclusion from scientific society does not automatically mean
    exclusion from science itself, for Emmy Noether succeeded, at the cost of great sacrifice and
    renunciation, in doing mathematics at the highest level. Nor should it be forgotten that the same or
    similar conditions of marginalization that existed everywhere a century ago for women continue to
    exist today in many parts of the world, and that the only way to escape them, for those who have the
    opportunity, is to migrate to more inclusive countries
    end of quote
    I will say it right here. the persecution of women scientists is linked to certain board brains whom think that women should be breeders and that they have no business not being baby factories.

    Emmy Noether scared men whom could not conceive that she, GASP, had a really great scientific intellect.

    You would think that progress has been made in this area? Sadly no. In CONUS< USA,> The GOP is doing everything it can to insure that women cannot have birth control and to turn half the population into baby factories.

    In terms of science, it is beyond insane that half the peoples in countries are stigmatized due to having ovaries. not a scrotum

    The loss of such scientific potential can have real life implications. One Black woman was essentially the magic sauce which made the Apollo Moon program a success instead of a suicide mission. She is celebrated today.

    Likely the Apollo program would have FAILED without this one
    'quote
    Did you mean: black mathematician who helped apollo 11

    Katherine Johnson | Space race mathematician at NASA | New ...
    Katherine Johnson was a NASA mathematician whose calculations helped the US get an astronaut into orbit for the first time. She also played a crucial role in calculations for the first moon … landing.
    end of quote

    Oh Dear me, i.e. today we would see TED CRUISE demanding that she be FIRED from NASA.

    But again, due to the GOP citing a bastardized version of RELIGION, its time for all those women whom would
    DARE learn , GASP, CALCULUS and Differential equations, to be knocked up, pregnant and far away from alpha males in the research centers

    I do not know what it will take to reign in this totally idiotic self defeating mentality

      Andrew Beckwith

      Thank you for reading my essay and responding by reporting an extensive excerpt from it on such an emblematic case of discrimination, "just" because she was a woman, of a great figure in science!

      Having read your essay, which considers similar issues, I intend to post a somewhat more articulate response in the thread related to it.

      Here I say only that I understand your indignation at the discriminatory tendencies that persist - or re-emerge - even in so-called advanced societies, and that, looking at what is happening in my own country and around the world, I am sadly not at all optimistic.

      it goes way beyond that. Here is an example of what we need more of
      quote
      Hubble Tension: The Evidence of New Physics
      Jian-Ping Hu, Fa-Yin Wang
      The ΛCDM model provides a good fit to most astronomical observations but harbors large areas of phenomenology and ignorance. With the improvements in the precision and number of observations, discrepancies between key cosmological parameters of this model have emerged. Among them, the most notable tension is the 4σ to 6σ deviation between the Hubble constant (H0) estimations measured by the local distance ladder and the cosmic microwave background (CMB) measurement. In this review, we revisit the H0 tension based on the latest research and sort out evidence from solutions to this tension that might imply new physics beyond the ΛCDM model. The evidence leans more towards modifying the late-time universe.
      end of quote
      What we need is more of this foundation investigation. Much more. And then we can go ask fundamental issues once this one is seriously entertained. As an example, the problem of time, and where it really started.

      5 days later

      Hi CrimsonQuail,
      I appreciate your essay in an effort to look at the root of the problems:
      “What can be the fundamental reasons for such enduring success of an erroneous theory? Certainly neither the fact that it responds most directly to empirical evidence”.
      “More problematic is the question of whether, along with history, the results, the truths so far achieved by science could also be substantially different from what they are”.
      “Science aims in large part to understand nature, and it cannot legitimize itself without a feedback, in nature, of its hypotheses and predictions”.
      My essay is devoted to the key facts that lead to new key laws that are not noticed by the generally accepted concept. But these laws may form a new science of studying reality without studying abstractions. I think you will also be interested in the elements of the deterministic functioning of the quantum solar system on the new laws that are given in the appendix, and which are similar to the quantum laws of the functioning of the Hydrogen atom.
      I wish you success!

      17 days later

      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 ].

      17 days later

      "The issue is enormous in scope and we certainly cannot address it in this essay. We limit
      ourselves to hypothesizing that a non-mathematical science of nature is impossible because space
      and time, the two dimensions in which everything happens, have a mathematical nature. It is very
      difficult to verify this hypothesis, because space and time, if they are of a mathematical nature, are
      not empirical realities, but we think that there are solid reasons, both theoretical and historical,
      which lead to this conclusion. "
      There is another view different of yours. In GR eventhought in empty space there is always energy which fill all the space with negative pressure. So space , time and energy have mathematical nature and empirical realities.
      I can proove it as follows:
      4-vector momentum= universal constant times 4-vector wave-vector (duality wave-corpuscle)
      Split the duality wave-corpuscle in two dualities:
      4-vector momentum= universal constant times 4-vector identity
      4-vector wave-vector= universal constant times 4-vector identity
      What is 4-vector identity?:
      4-vector identity= (inertial time times celerity of light, inertial time times speed of corpuscle)
      What is inertial time ?:
      Inertial time=Inertia of the corpuscle/universal constant
      What is inertia of the corpuscle ?:
      Inertia of the corspucle= Energie of the corpuscle/square speed of light
      Don't think that the universal constant in the definition of inertial time is equal to c3/G: it can be different, it can be a new universal constant and gives a 5th dimension for the corpuscle.

        Alaya Kouki

        Thanks for your response and interesting thoughts!

        Yes, it is possible that you are right in thinking that space and time are both empirical and mathematical. After all, twentieth-century scientific-philosophical reflection suggests that some pairs of concepts that ancient and modern Western traditions judged to be opposites (matter-vacuum, wave-corpuscle, analytic-synthetic, body-mind, energy-mass) are actually closely related or, in some respects, equivalent. So it is possible that the empirical-mathematical alternative, as suggested by GR and, in part, also by QM, is also to be overcome.
        The fact remains that space and time, as, for example, Kant said in the second half of the eighteenth century or, in a different way, Leibniz a few decades earlier, are not directly experienceable realities. We can observe objects and phenomena that are in space-time, but not space and time as such.

        I will also try to reflect on your other considerations and other posts of yours, if I can.
        All the best

        René Descartes said "I think so I am" in 1650 . From this date there is separtion between the object and the subject: there is no influence of the subject on the object. I can study the motion of the object as sequences on a theatre: time is absolute and it reflects only changes. By 1900 there is changes: To resolve the black body radiation problem Planck had adpated that energy is discrete and he introduces two constants the Planck constant h which have the dimension of an action i.e. a momentum times time and the Boltzmann constant k which denotes a classical mean energy of an oscillator. By Planck constant h energy and time are linked and we can't speek about an isolate object: the subject can influence the object by means of its intruments and the notion of material point in the classical model have no meaning. The object becomes a wave-corpuscle entity and it depends which we want to test: the wave behaviour or the corpuscle behaviour. Of course the notion of absolute time remains the same because it reflects only changes but we should introduce another time the inertial time which denotes the minimum rate of energy exchanges: we can't loose or gain energy in a time equal to zero. To resolve this problem it should exist a new universal constant which the dimension of a power i.e. of energy divided by time: theoritically this cosntant is predictable by Planck theory heat radiation in 1911 when he explain its constant as the integral of action of an oscillator: multiply the Planck integral by the constant K/L where K is the stifness of the spring and L the mass of socillating point and so directly you deduce the existance of the new universal constant.

        17 days later

        If we are assigning familial rankings, truth could be part of time, and is incorporated within it as a coveted product that secures symbiosis. Trust could be the daughter of Truth, as symbiotic relationships form trust over long periods, using truth as the guide. She is definitely going to check your sock drawers, before accepting the ring.

        Interestingly, if we examine ancient calendars, which track biology or holistic systems, we find that depending on the cycle, it has a product that is distinct. A child if you will.

        There is a mathematical element of time, in the periodicity, and in the close examination of the particles it helps to produce, and there is a quantum element that mathematics will find to be too laborious for human hands. This is the point of our next likely step in evolution. The mathematics is helpful in understanding, and elucidating that periodicity and its stages, but the Big application will likely come from developing a new sense of time. Or retrieving one we had already.

        In the 20 day calendar, combined with the 13 day calendar, the product is in one descriptor "faithful loyal companions', which I understand to be symbiosis. It is also the day of squaring the circle, mathematics.
        For the ancient Chinese, it is the day which sees, the subject, chewing a bone until it is clean and all is revealed.
        Truth, as the great great grandmother who vetted her partners well, set out as a component of time.
        A comforting guide perhaps. At every turn, she is there waiting to be found.

        Time, and how we perceive and utilize it, according to our specific location, will be how we are vetted or how we proceed , into a new place or time, intact. On the 20th day, it is often seen, a doorway, and the choice to proceed and what can be brought along. An evaluation of product or integrity. We churn in a repeated chain of flavors and components, like the periodic table, until we produce truth and faithful loyal companions.

        Look how the cute little elements all snuggle next to each other, all finding their places, happy and securely fit for travel.

        Time is a conductor on the train for the family of truth. It is said, 'father time", but this does not appear in any observable fashion. It is in appearance, non binary, and machine like. Itself has truth as a component.

        I conjecture, that Symbiosis is the daughter of Truth, and Time was the bus driver who diligently waited outside the hotel, circling the block until she came out. (it never parks)

        Incidentally, Hypatia may well have been one of the last teachers of the 260 day calendar in Egypt.

        They did not likely violate her because they disagreed, but because they coveted what she taught and sought to own it for themselves, using it to their advantage. Much later, they did the same to the Maya. To their shock and horror, these people knew the same thing, and the dispatch was sent, and the order given.

        Let the day come, when the noblewomen of science, and the truth of time are returned, and the family all rides the bus together again. In wisdom and truth we proceed on the bus of time toward symbiosis of our choosing.

        6 days later

        123
        Thanks for your post!
        The title, of course, takes up a famous quote from Francis Bacon's Novum Organon: "For truth is rightly named the daughter of time, not of authority ."
        I chose the interrogative form because the relationship between truth and time (historical time, in this case) is complex, and the question cannot be answered peremptorily either yes or no.
        In summary, I would say that the discovery of truth is definitely a product of time, because it occurs at a particular historical moment and depends on a set of contingent factors: the author’s life and genius, the cultural context, social and political conditions, and so on; however, a part of scientific truths as such, once achieved, are indisputable truths, in the sense that they can no longer be denied, at least as long as nature and the universe remain as we know them. To give a few examples, the atomic structure of matter, the composition of DNA, and the Earth’s motion are now assured truths beyond reasonable doubt.
        This does not mean that these are absolutely necessary truths, because the earth and the entire solar system have not always been there and will not be there forever; and even the matter we know and are made of, having been formed over time during the evolution of the universe, could change its structure or dissolve altogether.
        In short, all scientific truths concerning matters of fact or "states of affairs" are based, as Hume had seen well in the eighteenth century, on the principle of the uniformity of nature, which is a postulate and not a provable truth.
        A separate argument must be made for logical and mathematical truths, which seem to have a status of necessity completely independent of any temporal condition. The Pythagorean theorem, for example, in the context of Euclidean geometry is and always will be true, regardless of the historical circumstances of its discovery; just as it is absolutely true that even numbers and prime numbers are countably infinite.
        But even in mathematics it is necessary to relativize and distinguish. Geometric truths, in fact, are valid only within the system in which they are proved, so the theorems of Euclidean geometry, such as that of Pythagoras, are no longer true, or must be appropriately modified, within other geometries. Less relative seem to be arithmetic truths, or at least some of them. The infinity of prime numbers or the value of the square root of 2 to all the billions of decimal places for which it has been calculated so far are truths whose negation seems impossible for us to imagine.
        In principle, it would be possible to conceive and construct an arithmetic that completely excludes the notion of infinity, but it (unlike, for example, a non-Euclidean geometry) would be uninteresting, useless, and therefore anti-scientific. Suffice it to say that the mathematical science of nature was solidly established only with the development of infinitesimal calculus, whose enormous effectiveness, after nearly four centuries, is there for all to see.

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