Thanks.
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.
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.
If scientific advances had proceeded differently, scientists would’ve realized the easy answer to the dilution of mutations is exactly the same as the problem of electrons falling out of orbit: quantization. Genes are quantized just as electronic orbitals are.
Mathematics is not empirical. A theorem is accepted once proved, because that’s that; there’s nothing more to show. On the other hand, scientific theories must be empirically tested, and are only ever provisionally accepted. There’s always the potential that future experiments will invalidate a scientific theory.
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=mc[sup]2[/sup]”. That is the collapsed form of the function when nothing is in motion. the actual equation is more like “E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup]”
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.
Ironic that you would choose those two examples, because E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup] is actually an application of the Pythagorean theorem (one that holds even in curved space, so long as it’s locally flat).
what WAS the accepted cause before plate tectonics / continental drift?
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).
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).
The reason that Doctors were going from dead mothers to deliveries was because they were training in an important new medical technology: forceps delivery. And they were using an important new training technology: extracting dead babies from dead mothers (who had died of puerperal fever in the lying-in hospital). Forceps delivery was actually a great medical advance, but the techniques require significant training: the first training models were dolls, leather,cloth,wood, metal, and training on corpses was a significant improvement.
So the objection wasn’t just the insult. They had important new medical technologies, with the means to save lives, and then this (crazy) doctor comes along with this ~ woo ~ woo ~ idea about invisible transfer of infection, by the laying on of hands that he’d more or less just invented himself …and he’s not attacking doctors: he’s attacking modern medical technology and modern medical understanding.
He was the crystal-pyramid anti-vaxxer of Vienna.
Not a fair assessment. The evidence for Dr. S’s claim became stronger over time, just a few years. Crystal-pyramid evidence has not improved over centuries. Anti-vax claims have been shown to be ludicrously wrong for decades.
If the Randi Million-Dollar Challenge had been around in 1847, and Semelweis’ claim accepted, he would have won it, (washed) hands down.
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.
About humans and human evolution.
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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.
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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.
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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.
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.
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.
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.
There are no fossils of aquatic apes. You have been misinformed. Please provide the name of the supposed fossil.
You shouldn’t be using what Wikipedia says or “what some people think” as your criteria as to whether something is true.
I wouldn’t call the Aquatic Ape Hypothesis pseudoscience myself, since those who advanced it cited what they regarded as evidence for it. However, scientists have considered the evidence and in general regard it as entirely insufficient to support the hypothesis. It was also advanced at a time when the human fossil was far more incomplete than it is now. Given the state of our knowledge now, it’s pretty much impossible that humans could have undergone an aquatic phase of the kind proposed. The hypothesis was based on ignorance rather than solid facts.