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Post by freonbale on Jan 17, 2024 23:53:56 GMT
The foundation of all science is math. It is the language and structure that scientists use to describe the universe. In physics, sure. But physics is just one part of science. Much of biology has not been described particularly thoroughly by math. Yet we wiped out smallpox, discovered antibiotics, and so on. The parts of math that apply to the physical universe do, but there are parts that do not. Trying to prove something like the Riemann Hypothesis does not involve collecting data and hypothesizing about it. It involves making extremely complicated logical arguments based on the axioms of math. Very, very different from science. Having read arguments from many sides, I suspect the question is wrong. I don't think mathematics is based on transcendent, independently-existing objects, like Platonic forms. On the other hand, no sane person argues that 5 is less than 3, and this understanding appears to be hard-wired into how human minds construct our experiences from the data of our senses. Edit for formatting Respectfully, your first statement is truly naive. Ultimately, all sciences become Math. My training was in Biology, which depended on Chemistry and Physics, though I did take pure Math courses as well, especially on the computational side of Biology. Chemistry is dependent on Physics, though the Chemists must also take pure Math courses. And of course, as you say, Physics is based on Math. So your statement is wrong. ALL science is discovery, lol. And ALL science uses logic to prove accuracy. The scientific method does not require 'collecting data', though each attempt at trying to logically solve a problem of that nature IS data. The scientific method is just a process of hypothesis, experimentation, results analysis, iterating repetitively until a truth is logically determined. This ABSOLUTELY happens in Math. Thank you for answering my question, I had not considered it from that perspective. Freon |
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Post by DaveJavu on Jan 18, 2024 0:41:04 GMT
How many dimensions has the space consisting of all polynomials with real coefficients? Infinite. But that is a space, not a polynomial. The set of all mustards is not, itself, a mustard. I've already responded to this post but I have something to add. The dimension of a vector is not determined by the number of its non-zero coefficients but by the number of dimensions of the space that contains it. If you are in a space of three dimensions then all the vectors in this space will have three dimensions regardless of the specific values of their coordinates. Polynomials as it happens, are all in a space of infinite dimensions, so they are of infinite dimensions. The proof of that is that you can take any polynomial regardless of its specific values and add it to any other polynomial, and you couldn't do that if they were in different spaces. So they have to be in the same space, a space of infinite dimensions. QED. |
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Post by Running Deer on Jan 21, 2024 20:31:32 GMT
Infinite. But that is a space, not a polynomial. The set of all mustards is not, itself, a mustard. If you consider that zero is a number (you do, don't you?) then you must count the terms that have a zero coefficient in addition to the ones with a non-zero one. I don't see why I must. It's not necessary for anything that anyone does with a polynomial. |
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Post by Running Deer on Jan 21, 2024 21:01:38 GMT
In physics, sure. But physics is just one part of science. Much of biology has not been described particularly thoroughly by math. Yet we wiped out smallpox, discovered antibiotics, and so on. The parts of math that apply to the physical universe do, but there are parts that do not. Trying to prove something like the Riemann Hypothesis does not involve collecting data and hypothesizing about it. It involves making extremely complicated logical arguments based on the axioms of math. Very, very different from science. Having read arguments from many sides, I suspect the question is wrong. I don't think mathematics is based on transcendent, independently-existing objects, like Platonic forms. On the other hand, no sane person argues that 5 is less than 3, and this understanding appears to be hard-wired into how human minds construct our experiences from the data of our senses. Edit for formatting Respectfully, your first statement is truly naive. Ultimately, all sciences become Math. My training was in Biology, which depended on Chemistry and Physics, though I did take pure Math courses as well, especially on the computational side of Biology. Chemistry is dependent on Physics, though the Chemists must also take pure Math courses. And of course, as you say, Physics is based on Math. So your statement is wrong. Biology has not been reduced to mere chemistry, and chemistry has not been reduced to mere physics. That was once a hope of science, but it has not been remotely achieved, and there are good reasons to think it won't be. Saying that "all sciences become Math" is a quasi-religious belief; it doesn't describe actually-existing scientific practice. There are limits on how complicated mathematical equations can be before they're no longer useful. We then have to start approximating solutions - finding "good enough" answers - because it's too complicated to get an exact solution. This is numerical analysis, a branch of applied math, which studies how to find mathematical equations that are "good enough" for overly complicated problems, then solve them. Biological processes are often even more complicated than the problems we already can't exactly solve. This is good evidence that reducing biology to math simply won't happen. Nevertheless, we can still do useful biological work through the well-worn processes of collecting data, forming hypotheses, and testing those hypotheses against more data. This is all quite different than proving or disproving the Twin Primes Conjecture. |
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Post by freonbale on Jan 21, 2024 21:10:25 GMT
Respectfully, your first statement is truly naive. Ultimately, all sciences become Math. My training was in Biology, which depended on Chemistry and Physics, though I did take pure Math courses as well, especially on the computational side of Biology. Chemistry is dependent on Physics, though the Chemists must also take pure Math courses. And of course, as you say, Physics is based on Math. So your statement is wrong. Biology has not been reduced to mere chemistry, and chemistry has not been reduced to mere physics. That was once a hope of science, but it has not been remotely achieved, and there are good reasons to think it won't be. Saying that "all sciences become Math" is a quasi-religious belief; it doesn't describe actually-existing scientific practice. There are limits on how complicated mathematical equations can be before they're no longer useful. We then have to start approximating solutions - finding "good enough" answers - because it's too complicated to get an exact solution. This is numerical analysis, a branch of applied math, which studies how to find mathematical equations that are "good enough" for overly complicated problems, then solve them. Biological processes are often even more complicated than the problems we already can't exactly solve. This is good evidence that reducing biology to math simply won't happen. Nevertheless, we can still do useful biological work through the well-worn processes of collecting data, forming hypotheses, and testing those hypotheses against more data. This is all quite different than proving or disproving the Twin Primes Conjecture. I don't know you that well, but I just learned that you will double-down when you are wrong. You clearly are NOT a scientist, and do not have science training. I am (or was), and do. Believe whatever makes you happy, I guess. Freon |
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Post by DaveJavu on Jan 21, 2024 23:05:07 GMT
If you consider that zero is a number (you do, don't you?) then you must count the terms that have a zero coefficient in addition to the ones with a non-zero one. I don't see why I must. It's not necessary for anything that anyone does with a polynomial. You don't understand mathematics. This is not about practicality, it's about definitions. I've already told you more than I should have. You most likely are an autodidact and as such you probably are as stubborn and shortsighted as one. I don't have time to waste talking to a donkey. Have a nice day. |
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Post by Running Deer on Jan 27, 2024 17:51:05 GMT
I don't see why I must. It's not necessary for anything that anyone does with a polynomial. You don't understand mathematics. This is not about practicality, it's about definitions. I've already told you more than I should have. You most likely are an autodidact and as such you probably are as stubborn and shortsighted as one. I don't have time to waste talking to a donkey. Have a nice day. I've never seen a definition of polynomial fitting yours. Provide a link. |
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