Three Flukes Made Modern Science Possible

I like how you looked for the good influences that steered science in the western world.

I often look for those things which are MOST certain, and organize related things around most certain ones.
Your assertion that Mathematical truths are forever. is a certainly a good candidate.
Also, central tenant of Christianity is to seek truth above all else.
Shakespeare said it too, "To thy own self be true." Suddenly I'm reminded of this poem, I hope you find it a source of encouragement:

Keep asking and you shall receive,
Keep seeking and you will achieve,
Keep knocking and doors will open wide,
Respect others, let love be your guide.

Love your neighbor as you love yourself,
Love God with all that you have felt,
Your existence is an unchanging fact,
Everything's here and now, so act.

One is all, all is one, so true,
What you give, comes back to you,
These fine laws will never shift,
Everything else is in constant drift.

Ask and the universe will provide,
Answers will come from the source inside,
Receive without resistance, just let go,
Master this step, blessings will flow.

No matter the circumstance, stay upbeat,
This positive attitude, always keep,
Weave these ideas into your life's theme,
And watch your dreams turn to a reality stream.

For indeed Euclid laid the foundations of his famous geometry. However, my profound discovery isthat the whole universe is a Hyperspherical Hologram -- an ever-expanding Event Horizon that we call our universe. Time is the polar coordinate of the quantum-thin onion layers of time.)

Please read the essay: "What if we knew 123 year ago what we know now?" Hope you like it.

How do you explain this one ?
quote
Japanese mathematics (和算, wasan) denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term wasan, from wa ("Japanese") and san ("calculation"), was coined in the 1870s[1] and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 yōsan).[2]

In the history of mathematics, the development of wasan falls outside the Western realm. At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western mathematical technique, and this led to a decline of interest in the ideas used in wasan.

History

The soroban in Yoshida Koyu's Jinkōki (1641 edition)
The Japanese mathematical schema evolved during a period when Japan's people were isolated from European influences, but instead borrowed from ancient mathematical texts written in China, including those from the Yuan dynasty and earlier. The Japanese mathematicians Yoshida Shichibei Kōyū, Imamura Chishō, and Takahara Kisshu are among the earliest known Japanese mathematicians. They came to be known to their contemporaries as "the Three Arithmeticians".[3][4]

Yoshida was the author of the oldest extant Japanese mathematical text, the 1627 work called Jinkōki. The work dealt with the subject of soroban arithmetic, including square and cube root operations.[5] Yoshida's book significantly inspired a new generation of mathematicians, and redefined the Japanese perception of educational enlightenment, which was defined in the Seventeen Article Constitution as "the product of earnest meditation".[6]

Seki Takakazu founded enri (円理: circle principles), a mathematical system with the same purpose as calculus at a similar time to calculus's development in Europe. However Seki's investigations did not proceed from the same foundations as those used in Newton's studies in Europe.[7]

Mathematicians like Takebe Katahiro played and important role in developing Enri (" circle principle"), a crude analog to the Western calculus.[8] He obtained power series expansion of

{\displaystyle (arcsin(x))^{2}} in 1722, 15 years earlier than Euler. He used Richardson extrapolation in 1695, about 200 years earlier than Richardson.[9] He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation.[10]
end of quote
It is not that you are wrong, you are not considering parallel developments.
People all over the WORLD were doing mathematics. Consider your suppositions

If Mathematics truths are eternal then why is the Riemann hypothesis still unsolved ?
Seems like the converse is true.
Mathematics "facts" are eternal if PROVED.
And are you aware of the so called solution to the four color problem ?
quote
The proof was refined in 1996 by a team of four mathematicians: Robertson, Sanders, Seymour, and Thomas, but they still relied on computer code to complete their proof. In 2010, Steinberger offered another variation. However, there is still no completely satisfying answer as to why the 4-colour theorem is true.Nov 24, 20
end of quote
What constitutes a PROOF in Mathematics ? The answer is still not clear in all cases. And a computer assisted "proof" is by definition assisted by technology

Regarding as to mathematics as physics, The limitations of observing math ie 'physics,' are not fully integrated into intuition. For instance, the 3 spatial dimensions cannot have the same characteristics, the same inner structure, because if they did, they would be indistinguishable, and we would observe them as only one dimension. This notion lends weigh to the idea that the four dimensions of space-time are just the four nicely normed infinitely divisible algebras: **R, C, H, and O.** The differing inner structures of these algebras seem to dovetail nicely with the different particles and constriants of Standard Model. (Yes. Details to be worked out. Anyway.) And again, with the Hamiltonian and Octonion algebras, we have symmetries in the three and seven imaginary dimensions respectively. So to figure out observational statistics from first principle, the combinatorics of those algebras would have to be worked out.

Nice to see Euclid get a little extra love. (JBTW: The 5th of Euclid's "Common Notions," which precede his postulates, like his 5th postulate itself, also seems to admit to alternative (If also counterintuitive) possibilities for further insight.)

Roger Schlafly

Before giving you feedback on your essay, I just want to mention some thoughts of mine about what you wrote about commenting and critizising.

I not (yet) voted your essay nor did I post a comment on your essay page. But I already read your essay twice. And I read your latest comment and think you are on to something. Notwithstanding that your 21 ratings could amount to a high or a low appreciation for your essay, many voters seem to think that the voting comments are sufficient to make their points, without aiming at some feedback from the author for possible misunderstandings or overseen aspects of own reasonings.

Moreover, the first bunch of submitted essays obviously – at least in part – granted each other the priviledge to be amongst the essays that have more than 10 votes – and according to the rules therefore are subject to expert judgement.

The essays that came later are still not sufficiently voted, be it because the voters take their time until doing it immediately before the deadline, or they see no sense in voting since mathematically they assume there is an asymmetry of voting others essays and not having their own essay voted. That is at least what my point of view is – why should I vote a certain essay when even my comments don't get any replies (with minor exceptions!)?

Shouldn't it be the other way round: an author should reply and clarify if needed when there are critical arguments raised on what he has written. It seems to me that the whole discussion about judges, arxiv and the like does somewhat repeat in this contest on the same level the opponents of peer review are eager to argue against. What a mess that would be in adapting a double standard and then complaining about double standards.

Now to your essay. You wrote that certain historic lines in the evolution of science have been contingent. This can only be true when the universe we live in is not fully deterministic. Although we do not (yet) understand how a not-so-deterministic universe should look like, we nonetheless can deduce what a fully deterministic one looks like: it does not leave any room for the evolution of science to have been other than it was and therefore any speculation about an alternative history of science would be ill-defined.

Note that I do not presume you to having adopted that strictly deterministic world view. Since you also wrote about Darwinian evolution, the latter will also be suspicious to be ill-defined for the case that it is true that we live in a fully deterministic universe. Because then the reasons for Darwinian evolution to have happened (in every unknown detail) was pre-programed into the initial conditions exacly in the way it happened – up to the last bit of mutation – and therefore no “selection” ever took place in a strictly deterministic world!

Thus, believing in the big bang and also in a strictly deterministic universe poses the question about very, very, very special initial conditions. If we additionally assume that a black-box science will some day discover a “theory of everything” - then we would really live in a very special universe – wouldn't we? Even if there are myriads of other universes, each with slightly different initial conditions, our universe would arguably be a special one regarding the propper configuration to obtain the “full truth” about the universe. In other words, its configuration then would be such that its information processing would be perfectly set up to determine the “full truth”.

From the point of view that there could be many independent universes “out there”, this result of “speciality” may not be more than a simple computational truth, and there would be nothing to wonder about. But wait a minute, we do not at all know whether or not there does exist such a “theory for everything”, and if such a theory nonetheless would be possible, we do not know at all whether or not WE will ever be able to find it: according to a strictly deterministic world view, that information is hidden and totally inaccesible within the initial conditions of the universe (or if we believe that the universe has no origin in time, it is hidden in what globally happens “now” with every particle / wave in the universe while I type these lines of reasoning).

My whole argument amounts to the question whether or not those initial conditions themselves must be considered as contingent or not. You wrote about the eternal truth of mathematical relationships. I agree that there must be something about reality that truly is eternal. There should be some eternal truths, since otherwise truths would come and go randomly and no logical thinking would be reliable and we could stop here. I think one of these truths is that in a strictly deterministic universe where Darwinian evolution only seems to be governed by randomness, but in fact would be governed by some unimaginably “fine-tuned” initial conditions, the latter do not allow for any examination an especially not for any prediction of whether or not Artificial Intelligence will be able to produce further insights into the question whether or not our universe is deterministic or not!

Since if it would be strictly deterministic, mine and also your thoughts about these issues would be strictly determined – but the latter would not guarantee that our thoughts would also be determined to reflect any fundamental truth about the bigger picture of reality. And the same would then also be true for any kind of AI-governed black-box science – since the very assumption of some very special but in-principle unknowable initial conditions in a fully deterministic world would already be the ultimate black-box that no AI could ever hack since it lacks a complete description of all the particles / waves in our universe at any time!

Roger Schlafly
Responding to your call for comments, I thought I would read your essay. But I couldn’t get past the first paragraph before disagreeing with the essay:

“...you have to accept the universality of mathematical truths and be receptive to the idea that we live in a clockwork universe where nature behaves in an orderly way.”

No. In fact, “you have to accept the universality of” relationships that can be represented using mathematical symbols; a very different thing to “mathematical truths”.

Yes, clearly “nature behaves in an orderly way” due to the abovementioned relationships. But no: the abovementioned relationships do not imply that “we live in a clockwork universe”, because it is apparent that, in the real physical world, the numbers are very often refusing to play ball. The problem of the misbehaving numbers is not some error or misunderstanding on the part of physicists, it is just a fact.

Dreary, dreary, dreary (from my point of view). Then I got to the absolute drivel, and absurd ideas about computers/ AIs, on page 6:

“They may even get to the artificial intelligence singularity, and people might become slaves to super-intelligent robots that take over the world. The laws of physics would become implicit in the trillion-parameter models being used. The computers could deduce everything we can with our theories and much more, but the poor mortals would have no conceptual understanding of how the world works.”

The above irrational imaginings are seemingly due to not knowing how computers work. In fact, binary digits don’t even exist, except in the human imagination. The technical article “Logic Signal Voltage Levels” (https://www.allaboutcircuits.com/textbook/digital/chpt-3/logic-signal-voltage-levels ) explains the connection between voltage and binary digits/ “logic states” in computers. If you read this technical article will notice that there is no necessary connection between voltage (a measurable aspect of the world) and binary digits, which are not a measurable aspect of the world. In other words, binary digits/ “logic states” are merely an idea that human beings have imposed on voltages, where the whole setup including circuits and transistors makes the idea work. Binary digits only exist in the human imagination, and there is no actual logic being performed by computers/ AIs.

Roger Schlafly
No matter what some scientists in the past thought, “quantum randomness” gives the lie to any idea of a clockwork universe. This “randomness” is not due to some error or misunderstanding on the part of physicists, it is an integral part of how the universe works.

The point about the linked article is that binary digits don’t exist, except in the human imagination: what exists is voltage, which is a measurable aspect of the real physical world.

“Every time a computer adds two numbers”

A computer is not adding two numbers: there are no numbers, and there is no addition.

There are no numbers, there are only voltages used to represent numbers:

1. Different number systems (hexadecimal or binary) can be used to represent the same number. In other words, two completely different arrays of voltages can represent the same number.
2. In addition to this, binary numbers are symbolically represented by arrays of higher and lower voltages. In general the higher voltage will represent the binary digit one, but in fact the lower voltage can also be used to represent the binary digit one. Once again, depending on the setup, two completely different arrays of voltages can represent the same number, where “101” and “010” could represent the very same number.
3. In addition to this, binary digits can be represented using different voltage ranges. In the case where the higher voltage is used to represent the binary digit one, the binary digit one does not correspond to a particular voltage number.
4. In addition to this, there are no numbers, there are just arrays of interconnected voltages.

There is no addition:
A computer is not adding two numbers. People who knew the properties of voltages, transistors and circuits, created computers using voltages, transistors and circuits to symbolise the adding of two numbers.

Roger Schlafly
What does this have to do with your essay? I am refuting what you say in your essay.

I have just explained why there are no numbers in computers, and why computers are not doing addition, and I might well have added that “logic gates” are not doing logic. “Logic gates” / transistors are useful because they can be used to symbolise logic, if you place them in the right setting of circuits and voltages, and with the right computer program.

“Everybody knows about number representations”

Do they? What are numbers? The real world, including bodies, brains and the physical correlates of consciousness, is built out of real-world categories (examples would be mass, energy, position), real-world lawful relationships, and real-world numbers. Numbers representing the real world are obtained from measurement of the real world (e.g. by physicists). People use symbols to represent these real world numbers, but the real world numbers are not in any way implied by the symbols that are used to represent them (except from the point of view of pre-existing educated human beings), and the symbols of numbers don’t reverse-engineer themselves and transmogrify into real-world numbers.

The voltages, circuits, and transistors in computers, that might well be used to represent real-world numbers, real-world categories, and real-world lawful relationships (possibly including the physical correlates of consciousness), don’t reverse-engineer themselves and transmogrify into real-world numbers, real-world categories, and real-world lawful relationships, and real-world consciousness.