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Old 05-08-2020, 04:03 PM
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How long did it take scientific theorems/laws to catch on?


Ironclad laws and theorems such as: Newton's laws of "for every action there is an equal and opposite action" or "energy can be neither created nor destroyed," or the Pythagorean Theorem, or e=mc^2.

Did the scientific community say "yeah, there we go" and embrace these discoveries quickly, or did Newton, Pythagoras, Einstein have to do some intellectual arm-wrestling with them for a long while in order to get them to buy into it?

Last edited by Velocity; 05-08-2020 at 04:04 PM.
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Old 05-08-2020, 04:18 PM
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What makes you say they are "ironclad"? That might give you a hint to your answer.
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Old 05-08-2020, 04:55 PM
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I am sure it varies based on the field, how much the discovery goes against established belief, how advanced communication technology is, etc.

I think there is a 20 year gap in between scientific research and clinical practice in medicine.

In the middle ages, it was far longer sometimes. For example the idea that limes could combat scurvy was known off and on for hundreds of years before becoming canon.

then again, didn't the guy who theorized blood was circulated have his theory taken seriously almost instantly? edit: I looked it up, it took 20 years for that to be accepted.

https://en.wikipedia.org/wiki/William_Harvey#Reception

Germ theory and the washing of hands took a while to be accepted by the medical community.
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Old 05-08-2020, 06:01 PM
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For example the idea that limes could combat scurvy was known off and on for hundreds of years before becoming canon.
Of course, it wasn't limes specifically, but vitamin C, which is found in lots of fresh fruits and veggies, and also (in limited quantities) in some fresh meat.

Citrus fruits are excellent sources, but limes are actually far from the best - oranges and lemons are better.
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Old 05-08-2020, 07:44 PM
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Of course, it wasn't limes specifically, but vitamin C, which is found in lots of fresh fruits and veggies, and also (in limited quantities) in some fresh meat.

Citrus fruits are excellent sources, but limes are actually far from the best - oranges and lemons are better.
Yeah, the fact that nobody knew what vitamin c was until the 1930s didn't help.

I think some ships thought it was the acid in limes that prevented scurvy so they tried vinegar to no avail. Some thought limes that were pre cut would work, but those lose vitamin c due to oxidation. I think there were also issues with pipes destroying vitamin c of some fruit based beverages.

There were so many unknowns that probably stopped adoption.

There was a documentary about developing world diseases. Some researcher discovered that kids who got vitamin A supplements had lower death rates from infectious diseases.

The idea wasn't taken too seriously until someone discovered that vitamin A plays a role in the immune system. Without an easy to explain mechanism, people seem to be more likely to reject the new idea.
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Old 05-08-2020, 05:04 PM
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There's no general rule.

Darwin's Theory of Evolution by Natural Selection was widely embraced by many scientists shortly after it was proposed in 1859, although there were holdouts. It fell somewhat out of favor as a mechanism (although evolution was accepted) later in the 1800s. It wasn't until the Neo-Darwinian Synthesis from the early 1900s to the 1940s that united natural selection and genetics that it came to be nearly universally accepted. So that's perhaps 80 years.

Einstein proposed general relativity in 1915, and tests confirming its prediction concerning the bending of light were conducted in 1919. The theory became widely accepted by scientists after that. So that's four years.

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Old 05-08-2020, 05:29 PM
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Einstein proposed general relativity in 1915, and tests confirming its prediction concerning the bending of light were conducted in 1919. The theory became widely accepted by scientists after that. So that's four years.
I find this the most astonishing example for quickly confirming a scientific theory I've heard of (given how revolutionary and outlandish the theory was), and I think that Eddington's achievement in this was almost as great as Einstein's. First thing I thought about when I read the OP.

ETA: a counterexample are Wegener's plate tectonics. Like Darwin, he didn't have an explanation for the process, so it took a long time to be confirmed.
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Old 05-08-2020, 05:43 PM
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ETA: a counterexample are Wegener's plate tectonics. Like Darwin, he didn't have an explanation for the process, so it took a long time to be confirmed.
Another good example of delayed acceptance. Like Darwin, who didn't know about genes or Mendelian genetics, Wegener had a theory but no good mechanism. He first proposed "continental drift" in 1912, but it didn't become widely accepted until 1965, after sea-floor spreading had been discovered. When I was in college in the early 1970s it was still considered a kind of flaky theory.

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Old 05-08-2020, 06:00 PM
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He first proposed "continental drift" in 1912, but it didn't become widely accepted until 1965, after sea-floor spreading had been discovered. When I was in college in the early 1970s it was still considered a kind of flaky theory.
Mrs. Cretin was baffled by this in her late 60's college days. She thought the theory was a slam dunk, obviously correct. In the mid 70's a (Scripps) oceanographer I knew told me that "nobody serious" was doubting it any more.
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Old 05-08-2020, 06:59 PM
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He first proposed "continental drift" in 1912, but it didn't become widely accepted until 1965, after sea-floor spreading had been discovered. When I was in college in the early 1970s it was still considered a kind of flaky theory.
I was in junior high in the late 70s, and I asked my science teacher if he believed in continental drift. He told me that it was established science. I'm not sure where I got the idea that some people accepted it and others didn't, but it's good to know that I wasn't completely off-base.
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Old 05-09-2020, 11:54 AM
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Another good example of delayed acceptance. Like Darwin, who didn't know about genes or Mendelian genetics, Wegener had a theory but no good mechanism.
Similarly, Ignaz Semmelweis, a Hungarian doctor practising in Vienna, proposal that doctors should wash their hands with a disinfectant, each time they were about to examine a woman who had just given birth.

He was able to show that doing so greatly reduced the spread of puerperal fever, which was a killer disease in hospital maternity wards, but he couldn't advance any reason for it. He was widely mocked and professionally ridiculed by other physicians who refused to accept that there could be transmission of disease in this way.

It wasn't until Pasteur published about germ theory that it was confirmed that hands could appear completely clean, and yet contain microscopic particles that could cause disease.

Pasteur's discovery came too late for Semmelwis: he'd been committed to an insane asylum, and died a couple of weeks later, from a gangrenous infection that was likely caused by a beating from the guards.
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Old 05-08-2020, 10:40 PM
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ETA: a counterexample are Wegener's plate tectonics. Like Darwin, he didn't have an explanation for the process.
I'm not following this. Darwin did have an explanation for the process: natural selection.
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Old 05-08-2020, 11:29 PM
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I'm not following this. Darwin did have an explanation for the process: natural selection.
As noted, Darwin didn't have a mechanism for the details of the process. Mendel's experiments were published in an obscure journal in German in 1866. They didn't become widely known until they were "re-discovered" in the early 1900s by several geneticists. Darwin had fallen back on pangenesis as a mechanism, which was not correct. It was the integration of Mendelian inheritance with natural selection that produced the modern synthesis starting in the early 1900s.

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Old 05-08-2020, 07:27 PM
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Einstein proposed general relativity in 1915, and tests confirming its prediction concerning the bending of light were conducted in 1919. The theory became widely accepted by scientists after that. So that's four years.
But this theory was a generalization of his 'special relativity' from 10 years earlier, which evolved from even earlier work by Lorentz. So scientists were kind of 'prepared' for this, and thus when experimental test seemed to confirm it, they mostly readily accepted it. In fact, even running tests that soon is an indication that the theory was being seriously considered. Some hypothesis sit untested for years because they are considered too weird.
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Old 05-08-2020, 05:59 PM
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It'll depend on what the state of knowledge was before the new discovery. For instance, it was known long before Pythagoras that a 3-4-5 triangle has a right angle, and probably also known for some other triples like 5-12-13. So when Pythagoras came up with a proof for the general rule, it would have been no surprise. Similarly, at the time of Darwin, many biologists suspected that organisms evolve from other organisms, based on the observed similarities and differences between them: Darwin merely provided the mechanism for how it happens.
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Old 05-10-2020, 02:11 AM
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For instance, it was known long before Pythagoras that a 3-4-5 triangle has a right angle, and probably also known for some other triples like 5-12-13.
No "probably" about it: it's incontrovertible that the general concept of a "Pythagorean" triple, including many different specific numerical triples was known to Old-Babylonian scholars nearly 4000 years ago.

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So when Pythagoras came up with a proof for the general rule, it would have been no surprise.
It's highly unlikely that Pythagoras himself (if that somewhat legendary philosopher ever actually existed) made any kind of breakthrough in "coming up with a proof for the general rule". Some sort of geometric rationale for the general rule was probably widely known for centuries or millennia before him, even if it didn't have the more rigorous form that it acquired in, e.g., the later Elements of Euclid.

Logical mathematical demonstration isn't something that a few named early Greek philosophers just suddenly invented out of nothing, even though later Greek historians sometimes described it that way.
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Old 05-10-2020, 05:21 AM
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No "probably" about it: it's incontrovertible that the general concept of a "Pythagorean" triple, including many different specific numerical triples was known to Old-Babylonian scholars nearly 4000 years ago.
...
Logical mathematical demonstration isn't something that a few named early Greek philosophers just suddenly invented out of nothing, even though later Greek historians sometimes described it that way.
The Pythagorean theorem was known in ancient Mesopotamia, ancient China, ancient India and ancient Egypt. Some of these ancient cultures could also solve quadratic equations, and so on. BUT the idea of theorems rigorously proved from axioms seems to have been an invention unique to classical Greece, beginning with Thales, the Pythagoreans, Hippocrates of Chios, Theaetetus, Euclid, etc. No?
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Old 05-10-2020, 12:21 PM
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It'll depend on what the state of knowledge was before the new discovery. For instance, it was known long before Pythagoras that a 3-4-5 triangle has a right angle, and probably also known for some other triples like 5-12-13. So when Pythagoras came up with a proof for the general rule, it would have been no surprise. Similarly, at the time of Darwin, many biologists suspected that organisms evolve from other organisms, based on the observed similarities and differences between them: Darwin merely provided the mechanism for how it happens.
I have often wondered about the 3,4,5 triangle. Was it really "known" or just considered an excellent approximation? Was the difference between the two understood?

Evolution was widely believed long before Darwin. His grandfather Erasmus Darwin was a strong advocate. What Charles proposed was natural selection as the mechanism. But he was also aware that under his quite natural assumption of graded inheritance (mate short peas with tall peas and get medium peas) even favorable mutations would take a long time to spread. Mendel showed otherwise and thereby inferred the existence of genes or something like them. After that it was widely accepted (except in Tennessee).

I would expect that Newtonian gravity was accepted almost immediately since it literally explained everything from the elliptical orbits to the falling apple. Anomalies like 43 seconds of arc per century in the perihelion of Mercury came later. In fact I have no idea how to go about measuring the perihelion of Mercury, let along how to measure .43 seconds per year, an incredibly small angle, about .0006 of a degree.

On the other hand, results in math are generally accepted almost immediately. Even the incredibly complicated argument in Wiles's theorem was fully accepted in under a year, once the original gap had been filled.
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Old 05-10-2020, 12:26 PM
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On the other hand, results in math are generally accepted almost immediately.
That's my impression. But some exceptions might include non-euclidean geometry and Cantor's work with infinite cardinalities. And, historically, it took a while before negative numbers (and, later, imaginary numbers) were generally accepted.
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Old 05-11-2020, 02:56 PM
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That's my impression. But some exceptions might include non-euclidean geometry and Cantor's work with infinite cardinalities. And, historically, it took a while before negative numbers (and, later, imaginary numbers) were generally accepted.
Things like Cantorian set theory and non-Euclidean geometry are not theorems; they are new ways of looking at things and subject to the same kind of social forces as everything else. When Arthur Cayley and John Joseph Sylvester created matrix theory in the mid 19th century it was widely derided as a kind of useless abstraction that could not possibly ever find any application. Until it did. My own spciality, category theory, is nearly 80 years old and still denounced, despite notable successes, by a great many mathematicians. But none doubt that the theorems are valid. Le garde meurt, mais il ne cède jamais.

Of course Cantorian set theory was inconsistent, as discovered by Russell, but that was not the objection to it. The basic objection was the consideration of actual infinities. There were also objections to the non-constructive methods which persist to this day, but that gets into the thicket of the philosopy of mathematics.
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Old 05-10-2020, 12:45 PM
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I would expect that Newtonian gravity was accepted almost immediately since it literally explained everything from the elliptical orbits to the falling apple. Anomalies like 43 seconds of arc per century in the perihelion of Mercury came later. In fact I have no idea how to go about measuring the perihelion of Mercury, let along how to measure .43 seconds per year, an incredibly small angle, about .0006 of a degree.
Newton developed the equations which described how gravity affects the interaction of objects, and Einstein described in terms of the curvature of space. Even after centuries, we still don't really know the mechanism by which gravity works.
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Old 05-08-2020, 07:48 PM
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I wonder if there is some deeper motivation to this question? Perhaps the OP has a hunch about some knowledge that they think the scientific community is wrongly dismissing?
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Old 05-08-2020, 09:35 PM
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Galileo got a lot of grief for some of his ideas for quite a long time.
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Old 05-08-2020, 09:47 PM
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What makes you say they are "ironclad"? That might give you a hint to your answer.
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I wonder if there is some deeper motivation to this question? Perhaps the OP has a hunch about some knowledge that they think the scientific community is wrongly dismissing?
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Let's not question the motivations for a question in GQ. Instead you should try to provide factual information. In particular, your first post wasn't really pertinent in this forum. If you can't contribute to answering a question, there is really no need for you to post in this thread.

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Old 05-08-2020, 09:59 PM
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Mrs. Cretin was baffled by this in her late 60's college days. She thought the theory was a slam dunk, obviously correct. In the mid 70's a (Scripps) oceanographer I knew told me that "nobody serious" was doubting it any more.
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I was in junior high in the late 70s, and I asked my science teacher if he believed in continental drift. He told me that it was established science. I'm not sure where I got the idea that some people accepted it and others didn't, but it's good to know that I wasn't completely off-base.
As I mentioned, the theory began to become widely accepted by geologists and other professional scientists around 1965. It took maybe 10 years for the message to reach the general public via high school and university courses. So acceptance became more generally from the late 1960s to the mid 1970s.
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Old 05-08-2020, 10:44 PM
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As I mentioned, the theory began to become widely accepted by geologists and other professional scientists around 1965. It took maybe 10 years for the message to reach the general public via high school and university courses. So acceptance became more generally from the late 1960s to the mid 1970s.
I took Earth Science 1965 - 1966 in junior high, and I don't think it was in our textbook. I did a paper on the accepted cause of mountain building at the time.
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Old 05-09-2020, 01:36 PM
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As I mentioned, the theory [continental drift] began to become widely accepted by geologists and other professional scientists around 1965. It took maybe 10 years for the message to reach the general public via high school and university courses. So acceptance became more generally from the late 1960s to the mid 1970s.
Just for kicks, and because I have a 1953 Compton's Encyclopedia, I looked up "continental drift." There was just one reference, tucked in the article titled "Earth," to wit:
Quote:
An American and an Austrian geologist suggested that the continents had drifted to their present positions. The Austrian, Alfred Wegener, pictured one huge early continent that began to break up about 230 million years ago. Its sections then moved over a fluid layer which might have been melted by radioactive heat. North and South America drifted westward; Africa pulled away from Europe; Antarctica went to the South Pole. Asia swung northward, while Australia drifted far to the east.

Each of these theories explains some facts, but fails to explain others; and objections can be found to all of them. The continental drift theory meets this objection, for example, that centrifugal force ought to have sent drifting masses toward the equator.
The other theories include a proposal that when the Earth was molten, heavier regions sank to become ocean bottom and lighter ones were pushed upward, forming continents. I guess that's not wrong, but not sufficient.

There is no entry in this edition under Sea Floor Spreading, Seafloor Spreading, or even Spreading which lends credence to Colibri's timeline of acceptance ca. 1965.
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Old 05-08-2020, 10:33 PM
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Old 05-08-2020, 10:41 PM
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When a new killer hypothesis comes forward it has to two things, which happen at different speeds and possibly to different audiences in the discipline.

Firstly, it has to explain known reality better than the existing theories, which means having to look at eminent Professor Plum's work and not just trashing it, but clearly explaining why New Theory has better explanatory power on the same evidence as Plum had, and why it can pick up/ explain/ categorise / count/ label evidence in a better way [and what 'better' actually means].

Secondly, it has to not just be neater on existing evidence, it has to be validated in some way on new data and to show that it has greater predictive ability and robustness for deriving new information.

Depending on the discipline this has to happen as existing multi-year programmed research agendas and career trajectories unfold, as Professor Plum decides he's only years from retirement and does not need this shit, as pushy young researchers look at opportunities to make reputations as they seek tenure.

Its not just the sheer force of the idea but a whole bunch of social and professional factors that influence the take-up of new ideas.
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Old 05-09-2020, 08:44 AM
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Einstein's Special Theory of Relativity was an idea whose time had come. It was surprising, but there was lots of groundwork there, in the works of Lorentz, Maxwell, Michelson, and many others (maybe also Minkowski; I'm not sure if any of his work was before Einstein's). But while General Relativity followed on from Special (and also from the work of Riemann), it was a much bigger leap. The eclipse of 1919 is often cited as the proof of the theory, but in fact, the error bars in the data were large enough to encompass both Newton and Einstein. I think that it was the fact that it explained the perihelion precession of Mercury that really nailed it down for most physicists, though that wasn't exactly a "prediction" of the theory: It was already known, and one of the puzzles of science, at the time that Einstein published (there's a tale, possibly apocryphal, that one of the great scientists of the turn of that century stated that the perihelion advance of Mercury and the blackbody spectrum were the only two puzzles remaining to physics, and that once we explained those, physics was a completed discipline).

And Kelvin's calculation of the age of the Sun was in conflict with Darwin's theory of evolution, but it was also inconsistent with what geologists of the time were starting to conclude about the age of the Earth. So it wasn't quite the slam-dunk refutation of evolution that it might appear to be.
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Old 05-09-2020, 09:43 AM
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There is no general answer, but when experimental or observed evidence repeatedly confirms the predicted values.
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Old 05-10-2020, 12:34 AM
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Just a note: Theories are not "promoted" to laws. A law is an equation.* A theory is a testable model supported by the preponderance of data. (Except legal "theories", but I won't go there.) A hypothesis lacks such support but invites exploration. Theories evolve as more data creeps in. As suggested, acceptance of new models may require "paradigm shifts" i.e. the old-school folks croak and the youngsters muddle drive on. See Kuhn. Also see a philosophical view of scientific change

* All equations are correct if elements are properly defined. Thus Ohm's Law: E=IR with known units of electrical potential, current, and resistance. And 1+1=3 for large enough values of 1.
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Old 05-10-2020, 07:39 AM
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The concept of proving things logically of course emerged gradually over the course of time. But for any individual mathematical theorem, there was still some single individual who first proved it. The guy who first proved what we now call the Pythagorean Theorem might or might not have been the leader of that weird cult, and he might or might not have been named Pythagoras, and it's quite possible that his true identity has been lost to history. But he was somebody. My guess would be that it was some lower-ranking member of Pythagoras' cult, but that's just a guess. And Euclid, the best-known of the classical Greek mathematicians, mostly just compiled the work of others whose names we mostly don't remember (though he probably had some novel ways of proving things that had already been proven in other ways, and he probably advanced knowledge in some other ways).

In any event, though, special cases of that equation were certainly known before that formal proof, and the general formula may well have been known, so the proof wasn't completely revolutionary.
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Old 05-15-2020, 09:38 AM
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There's a whole book about this


There is an outstanding book that covers this exact subject: The Structure of Scientific Revolutions by Thomas Kuhn. It was considered groundbreaking when it came out, and is still highly regarded.

The gist: The dominant paradigm in any scientific endeavor shifts only when there is overwhelming evidence of anomalies to the current way of thinking. Even then it's a struggle.

The downside to this is that it slows down advancement. The upside, however, is that it slows down and kills ideas that are ultimately proven wrong.
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Old 05-10-2020, 12:49 PM
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Actually, the observations of Mercury's orbit are even more impressive than that. 43 arcseconds per century is not the amount of Mercury's perihelion precession: The actual number is over twice that. But most of the precession was calculated as being due to the influence of the other planets-- 43 arcseconds per century was just what was left over once that was accounted for. And in fact, people did try to explain it (before Einstein) by assuming the existence of another planet, usually referred to as Vulcan, unobserved because it was too close to the Sun.
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Old 05-10-2020, 12:54 PM
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Even after centuries, we still don't really know the mechanism by which gravity works.
I'm not fond of statements like this. Anyone who's ever conversed with a three-year-old knows that you can always ask "why" of anything, and when you give an answer, it just leads to another "why". One might fairly say that curved space, as described by Einstein, is the mechanism by which gravity, previously described by Newton, works. It may be that we'll someday discover something even more fundamental, that we could describe as the mechanism by which mass curves space, but we still won't be done, because there could still be another mechanism underlying that one, and so on.
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Old 05-10-2020, 01:04 PM
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I'm not fond of statements like this. Anyone who's ever conversed with a three-year-old knows that you can always ask "why" of anything, and when you give an answer, it just leads to another "why". One might fairly say that curved space, as described by Einstein, is the mechanism by which gravity, previously described by Newton, works. It may be that we'll someday discover something even more fundamental, that we could describe as the mechanism by which mass curves space, but we still won't be done, because there could still be another mechanism underlying that one, and so on.
Let's just say that phenomena such as dark matter and dark energy have suggested to some that alternative theories of gravitation are possible. The nature of gravity is not really something that is firmly nailed down.
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Old 05-10-2020, 01:08 PM
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Let's just say that phenomena such as dark matter and dark energy have suggested to some that alternative theories of gravitation are possible. The nature of gravity is not really something that is firmly nailed down.
Isn't it the other way around - dark matter and dark energy are postulated (in part) because they explain anomalous phenomena while retaining the GR framework. Alternate theories of how gravity works (vice "what gravity is") were created to find a theory of gravity that didn't need dark matter/energy.
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Old 05-10-2020, 12:54 PM
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Even after centuries, we still don't really know the mechanism by which gravity works.
I'm not fond of statements like this. Anyone who's ever conversed with a three-year-old knows that you can always ask "why" of anything, and when you give an answer, it just leads to another "why". One might fairly say that curved space, as described by Einstein, is the mechanism by which gravity, previously described by Newton, works. It may be that we'll someday discover something even more fundamental, that we could describe as the mechanism by which mass curves space, but we still won't be done, because there could still be another mechanism underlying that one, and so on.
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Old 05-10-2020, 01:14 PM
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There have been attempts to explain away the evidence that suggests dark matter by means of differing models for gravity, but none of them work particularly well. And really, the lack of existence of dark matter is itself an unnecessary assumption: There's no reason there shouldn't exist fundamental particles without charge (in fact, we already know of some of them; there's just not enough of the known ones).

Dark energy is different. We have less than no idea of what it would be, and in fact, positing different laws for gravity is exactly mathematically equivalent to positing dark energy. The current consensus is that describing it as a sort of energy is in some sense more elegant, though I'm not at all sure that I agree with that.
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Old 05-10-2020, 01:17 PM
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There have been attempts to explain away the evidence that suggests dark matter by means of differing models for gravity, but none of them work particularly well. And really, the lack of existence of dark matter is itself an unnecessary assumption: There's no reason there shouldn't exist fundamental particles without charge (in fact, we already know of some of them; there's just not enough of the known ones).

Dark energy is different. We have less than no idea of what it would be, and in fact, positing different laws for gravity is exactly mathematically equivalent to positing dark energy. The current consensus is that describing it as a sort of energy is in some sense more elegant, though I'm not at all sure that I agree with that.
Thanks.
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Old 05-11-2020, 04:15 PM
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In some sense, mathematics is really just a game, or more precisely, a set of games. For each of those games, you come up with a set of rules, and then see what you can do according to those rules. Just as a naive American might look at a Canadian football game and say "They're doing it wrong", but a more knowledgeable fan would know that it's simply a slightly different game, played under different rules, so too a naive mathematician might look at a new branch of mathematics and say that it's "wrong", when it's really just a slightly different game. Alternately, a fan (or mathematician) might agree that something is a valid game (or form of mathematics), but argue that it's a boring or uninteresting game, especially as compared to their own game of choice.

Some mathematicians, in fact, are slightly disturbed by the fact that so much in mathematics ends up modeling so many different aspects of reality, and find it uncanny that games would have such real application. I don't think this perception of uncanniness is particularly well-founded, though. We humans are steeped in the real world, and it's only natural that the games we create would have some correspondence with the real world.
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Old 05-13-2020, 01:13 AM
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Ironclad laws and theorems such as: Newton's laws of "for every action there is an equal and opposite action" or "energy can be neither created nor destroyed," or the Pythagorean Theorem, or e=mc^2.
Sorry, but right there you have ALREADY fallen off the bus by completely misunderstanding what "laws of nature" are, *and* you have quoted inaccurate examples about it.

For starters, Einstein's formula is not "E=mc2". That is the collapsed form of the function when nothing is in motion. the actual equation is more like "E2 = p2c2 + m2c4"

and
Pythagorean Theorem. It works fine in a perfectly flat Euclidean space. Unfortunately real-world space is not perfectly Euclidian. Is *is* veryveryveryveryvery close, but not exactly.


"Laws of Nature" are merely the descriptions of how we understand the Universe to work. They are, to the best of our ability to test and prove, correct. But this does *not* make them ironclad! Indeed the very opposite is true. Theorems are subject to disproof, adjustment and refinement.
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Old 05-13-2020, 10:26 AM
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Originally Posted by MarvinKitFox View Post
Pythagorean Theorem. It works fine in a perfectly flat Euclidean space. Unfortunately real-world space is not perfectly Euclidian. Is *is* veryveryveryveryvery close, but not exactly.


"Laws of Nature" are merely the descriptions of how we understand the Universe to work. They are, to the best of our ability to test and prove, correct. But this does *not* make them ironclad! Indeed the very opposite is true. Theorems are subject to disproof, adjustment and refinement.
Einstein said, "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

Once a valid proof has been found for a mathematical theorem, it can be forever regarded as true: it is not subject to disproof or adjustment within the mathematical context in which it is stated and proved. What is subject to disproof or adjustment is how well that mathematical context matches physical reality (or whether the theorem would still apply in a different mathematical context).
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Old 05-13-2020, 08:30 AM
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Ironic that you would choose those two examples, because E2 = p2c2 + m2c4 is actually an application of the Pythagorean theorem (one that holds even in curved space, so long as it's locally flat).
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Old 05-13-2020, 01:08 PM
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And even when the mathematical context is fundamentally separated from reality, you can still get mathematicians arguing about which context is more interesting.

Neither the Continuum Hypothesis nor its negation could possibly have any relevance to "reality", and likewise for the Axiom of Choice. But you can do math with or without either of those, and get valid results either way (though sometimes different valid results).
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Old 05-17-2020, 03:46 AM
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About humans and human evolution.

1. I've discussed with persons who claim that humans are not animals. So it seems that the basic biological definition of animal is not ironclad truth.

2. Humans is one race and there are no other extant human races on Earth. But there still are people who think that humans is subdivided into races. So that species defining truth is not ironclad.

3. Wikipedia defines Aquatic ape hypothesis as pseudoscience even though there is fossile record from Somali coast of aquatic apes. So not all evidence is accepted even by scientists.
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Old 05-19-2020, 12:33 AM
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1. I've discussed with persons who claim that humans are not animals. So it seems that the basic biological definition of animal is not ironclad truth.
No biologist would define a human as anything other than an animal. There are non-scientific usages of the words which distinguish humans from animals. But this has nothing to do with the biological definition.

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2. Humans is one race and there are no other extant human races on Earth. But there still are people who think that humans is subdivided into races. So that species defining truth is not ironclad.
You are using "race" in two entirely different senses here. Many words can be used in different senses. That does not mean that the individual definitions are false. In the first instance, you are using "race" as equivalent to species. In the second instance, most scientists today would prefer to talk in terms of human populations rather than "races." The traditional races have no scientific validity. Human variation is essentially a continuum, rather than falling into a few simple categories.

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3. Wikipedia defines Aquatic ape hypothesis as pseudoscience even though there is fossile record from Somali coast of aquatic apes. So not all evidence is accepted even by scientists.
There are no fossils of aquatic apes. You have been misinformed. Please provide the name of the supposed fossil.

Last edited by Colibri; 05-19-2020 at 12:43 AM.
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Old 05-17-2020, 08:30 AM
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Evidence is weighted. One piece of extremely low quality evidence can be ignored in favor of large amounts of high-quality evidence.
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Old 05-19-2020, 12:12 AM
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Evidence is weighted. One piece of extremely low quality evidence can be ignored in favor of large amounts of high-quality evidence.
I do understand that, but to label as pseudosciece something that has evidence is IMHO very very very biased.
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