What is not real about theorical math models preceding and predicting such discoveries as special relativity, the Higgs boson and digital information transfer?
Why does that make them more than models?
In the past I started spouting off about isomorphic structures in math and reality.
Let's try this: there are models and there are working models that are actually applied in real world circumstances. These "embedded" models are more than strictly theory. What makes them more...............
That they work in actual practice, either physical practice -- or working in correct computational output.
ie: at a macro scale F = MA enables predictive answers, changing the real world probability of science to utilize natural structures in organized systems. In other words - the reduced uncertainty from the computation is a measuable negentropic part of a working thing, event or process.
I am only arguing for the natural place for computation and information in a casuative role in reality, instead of implying that what humans "think" about is some kind of "special" physics.
ie the assertions made that human reasoning is something different than computation, as a rebuttal to computation is part of science.
No, you've whizzed right by me again. What you wrote still sounds like "because they work well" to me.
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I think, for example, of Jack Horner's recent controversial hypothesis that Triceratops are in fact simply juvenile Torosauruses. This is a hypothesis based on non-computational comparative anatomy, and throwing math at the question isn't good to resolve it. I think there is plenty of reason to suppose Horner is wrong, but it is nevertheless a well-formed, contemporary example of a scientific hypothesis that resists the Procrustian mathematical box you'd like to force it into.
Germ is an informal term for a pathogen, particularly bacteria (as in germ warfare). One of the first people to postulate that some diseases were caused by the presence of some kind of very small 'seed' (the original meaning of 'germ') that germinated or multiplied in the body to produce the disease was Ignaz Semmelweis, a Hungarian doctor, practising in an obstetrics ward in the 1840s. He noticed that the death rate of the impoverished women attended by the nurse midwives was many times less than that of the wealthier women attended by the doctors. His observations led him to conclude that it was a matter of cleanliness.
Ambiguous and informal terms - are very problematic in logical computation. That's why in modern medicine accurate terms like pathogen, virus, bacteria and microorganism are used. Germ is still a term of science, in the correct and formal context, such as germ cell or in germination.
Please take note, that it is a quantity based analysis that was offered as the basis of Semmelweis's actual science, so many years ago. He had data. Further, it is another quantity based anlysis that leads us to have to reeducate people today - who kill "germs" with antibacterial soap as normative - when computational models tell us that it helps evolve resistant strains and over time can lead to a worse situation than just using soap and water. Here modern science is trying to overcome the problems of "germ theory" of the 1800's.
On a very positive note - I loved your "Procrustian mathematical box" I had to look it up to refresh the mythological reference!!
My instinct is for rebuttal - but just let me humbly say that - if you think I am proposing some limitation to science - imposed by math practice - I stand corrected.
Asto the Horner, conjecture - it points to a real conflict in science. If he could look at DNA samples and compute - he would have a trustworthy science answer. I am not saying that his data, as to measurements of fossils are not worthy efforts - just that computational work from DNA is a surer route, with a higher Sigma value. When both suggest similar models - then the amount of uncertainty is even lower.
This conflict is rampant in the origins of humans. Old-line fossil finders are having their theories upset on a regular basis by those geeky girls and guys in the bioinformatics labs. And the old-line folks, don't like it. The recent news is about a linguistics theory of the migration to the New World - that was disgarded by the fossil and artifact finders - has been rediscovered by genomic research.
No, you've whizzed right by me again. What you wrote still sounds like "because they work well" to me.
Amcolph,
It is me, not you. I am simply not to the task. It is all in the implication that computation is a lawful process - on the same basis as is a transfer of energy. The process of computation just happening in a different level of a multi-level reality, lies at the root of this. Even when Wigner wrote his famous paper on the subject; he called it "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".
He knew what he was talking about, far more than myself - and here 52 years later - the idea is still a curiousity in most quarters.
THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle." - E. Wigner
Asto the Horner, conjecture - it points to a real conflict in science. If he could look at DNA samples and compute - he would have a trustworthy science answer. I am not saying that his data, as to measurements of fossils are not worthy efforts - just that computational work from DNA is a surer route, with a higher Sigma value. When both suggest similar models - then the amount of uncertainty is even lower.
Surely, Horner (and other paleontologists) would love to get their hands on triceratops DNA. That would be an absolute treasure trove. But they don't have it, and quite possibly never will. That doesn't in any way make Horner's work "less scientific" or "not modern science." Not everything that can be studied scientifically is readily or usefully addressed mathematically.
I also think you're using the concept of "Sigma value" rather loosely. The sigma value (standard deviation) of a result is only a measure of the statistical unlikelihood that the result is caused by random chance (which is frequently the null hypothesis in an experiment). It does NOT measure the uncertainty that a hypothesis/model is incorrect (or, synonymously, certainty that it is correct), unless that model is the only POSSIBLE alternative to the null hypothesis.
No, you've whizzed right by me again. What you wrote still sounds like "because they work well" to me.
Amcolph,
It is me, not you. I am simply not to the task. It is all in the implication that computation is a lawful process - on the same basis as is a transfer of energy. The process of computation just happening in a different level of a multi-level reality, lies at the root of this. Even when Wigner wrote his famous paper on the subject; he called it "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".
He knew what he was talking about, far more than myself - and here 52 years later - the idea is still a curiousity in most quarters.
THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle." - E. Wigner
Another factoid which always intrigued me is, that if you let a river meander freely the ratio of the length of the river between two points to the straight-line distance between those two points will be approximately Π as well. Can't remember where I read that.
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No, you've whizzed right by me again. What you wrote still sounds like "because they work well" to me.
Amcolph,
It is me, not you. I am simply not to the task. It is all in the implication that computation is a lawful process - on the same basis as is a transfer of energy. The process of computation just happening in a different level of a multi-level reality, lies at the root of this. Even when Wigner wrote his famous paper on the subject; he called it "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".
He knew what he was talking about, far more than myself - and here 52 years later - the idea is still a curiousity in most quarters.
THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle." - E. Wigner
Another factoid which always intrigued me is, that if you let a river meander freely the ratio of the length of the river between two points to the straight-line distance between those two points will be approximately Π as well. Can't remember where I read that.
Hmm, I don't recall seeing anything like that in any of my fluvial geomorphology studies, I could be mistaken but what you posted doesn't sound corect. Stream/river sinuosity is a function of gradient, depth, velocity, substrate, etc.
Another factoid which always intrigued me is, that if you let a river meander freely the ratio of the length of the river between two points to the straight-line distance between those two points will be approximately Π as well. Can't remember where I read that.
Pi shows up a lot - as a built-in feature to natural processes. There is a wonderful book "An Imaginary Tale. The Story of the Square Root of -1. For some reason imaginary numbers like i; are all over electrical engineering.
I hope every one checks out the Higgs field blog by Amir Aczel. Its the link a couple of posts ago. He talks about Sigma and math.
But I have no idea whether Eugene Wigner was at all interested in anthropic arguments, and in any case, marveling about WHY mathematics works so magically well in physics and other sciences has nothing to do (in my opinion) with anything anthropic. My guess is that this is true regardless of whether you are Platonic or Kantian in your philosophy of mathematics. But I would welcome readers opinions on this.
Hmm, I don't recall seeing anything like that in any of my fluvial geomorphology studies, I could be mistaken but what you posted doesn't sound corect. Stream/river sinuosity is a function of gradient, depth, velocity, substrate, etc.
I found this "Back on Earth, pi controls the path of winding rivers from the Amazon to the Thames. A river's meandering is described by its sinuosity – the length along its winding path divided by the distance from source to ocean as the crow flies. It turns out the average river has a sinuosity of about 3.14."
No control, as would be a structural component -- just an average. I would want to see some real data. It refers to this actual paper. www.sciencemag.org/content/271/5256/1710...
ES -- how about fractals and sinuosity - are they in play with streams, as there are in coastlines?