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Is Mathematics There To Be Discovered Or Invented?
84 Answers
This is a question that I have pondered for some time.
Which numbers can be found in nature?
I raised a question two months ago asking -
Who invented binary numbers?
This led to the answers that I wanted and also to an interesting thread about the nature or lack of it of mathematics. So, I thought that I would put forward this question. If you are interested in the idea I would encourage you to look at the thread about Who invented binary numbers? which should not be too difficult to find. But please, do not continue that discussion on that thread. Start the new discussion here. Thanks.
So, this thread should be about whether mathematics exists and is to be discovered or whether it is an invention. If some mathematics exists and some must be invented then the thread may be about what exists mathematically and where can it be discovered.
And before we begin...
I hope that you enjoy this.
Which numbers can be found in nature?
I raised a question two months ago asking -
Who invented binary numbers?
This led to the answers that I wanted and also to an interesting thread about the nature or lack of it of mathematics. So, I thought that I would put forward this question. If you are interested in the idea I would encourage you to look at the thread about Who invented binary numbers? which should not be too difficult to find. But please, do not continue that discussion on that thread. Start the new discussion here. Thanks.
So, this thread should be about whether mathematics exists and is to be discovered or whether it is an invention. If some mathematics exists and some must be invented then the thread may be about what exists mathematically and where can it be discovered.
And before we begin...
I hope that you enjoy this.
Answers
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I agree with Bert. I am sure that Maths and Physics will ultimately be one unified whole. Complex Analysis for example is fundamental to the development and understanding of the quantum mechanical laws governing matter and also a central role in the relativistic laws governing the structure of space-time.
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@SandyRoe Pi is close to 22/7 but more interestingly it is not accurately described by a division or fraction. But division is important in this discussion because perhaps there is an operation in nature which is a real example of numeric division.
@Prudie I agree with you that mathematics is not just about measurement, (or at least I think I do, I have always felt that mathematics was much more interesting than that, but I am willing to be convinced otherwise). I can also add something to your observance of nature creating flowers that grow to a certain height. How do they do this? Some people might have an simplistic guess but I have also observed that dandelions that grow inbetween the concrete blocks that are used for creating surfaces for vehicle wheels whilst also encouraging plants (grass) to grow within spaces set in the concrete (feel free to fall asleep before I get to the end of the sentence) find that it is safer to flower with very short stems rather than sticking out high above the concrete "floor" at which height they would be crushed if they were run over. This to me suggests an intelligence is at work, but no-one has found a brain within a plant as far as I know.
@jim360 "it is probably a mixture of both" at this stage I am inclined to agree. The next step is to start finding out where the maths is to be discovered. I have already suggested that numbers do exist in nature. But what about the operations that we can make on numbers the simple operations being + - * and /? What about the boolean operations? Do any of these exist in nature? A simplistic answer might be to say "humans exist in nature and humans have found/invented numbers and operations" qed. But I want proof.
@3xTora thanks again for your answers to the previous question thread. Consider this as an idea. The integers can be written in any base as you suggest but they can also be considered to be in base infinity in which case ever number can have its own little symbol. Does nature use a base system? If not, are base systems a totally human invention?
@pixie373 & @WoofgangIf we cannot invent mathematics, what can we invent? I came to the opinion that mathematics is a language. The language of maths is one of the most powerful because it is agreed throughout the whole world. Spoken/written languages are never easy to translate because exact meanings are often difficult to ascertain. There are some differences in the ways that we codify (write) our maths even when you compare England and USA there are some differences. These few differences do not change the meaning of the underlying mathematics.
@EVERYONE Can anyone find examples in nature where mathematical operations are performed. Serious (or seriously amusing) answers only please. I was given a pair of underpants with "Go fourth and multiply". Now that joke has been done please try to restrain yourselves from repeating it.
Looking forward to hearing your suggestions. I will try to keep an eye on updates provided I am not lured away by the temptations of pub.
@Prudie I agree with you that mathematics is not just about measurement, (or at least I think I do, I have always felt that mathematics was much more interesting than that, but I am willing to be convinced otherwise). I can also add something to your observance of nature creating flowers that grow to a certain height. How do they do this? Some people might have an simplistic guess but I have also observed that dandelions that grow inbetween the concrete blocks that are used for creating surfaces for vehicle wheels whilst also encouraging plants (grass) to grow within spaces set in the concrete (feel free to fall asleep before I get to the end of the sentence) find that it is safer to flower with very short stems rather than sticking out high above the concrete "floor" at which height they would be crushed if they were run over. This to me suggests an intelligence is at work, but no-one has found a brain within a plant as far as I know.
@jim360 "it is probably a mixture of both" at this stage I am inclined to agree. The next step is to start finding out where the maths is to be discovered. I have already suggested that numbers do exist in nature. But what about the operations that we can make on numbers the simple operations being + - * and /? What about the boolean operations? Do any of these exist in nature? A simplistic answer might be to say "humans exist in nature and humans have found/invented numbers and operations" qed. But I want proof.
@3xTora thanks again for your answers to the previous question thread. Consider this as an idea. The integers can be written in any base as you suggest but they can also be considered to be in base infinity in which case ever number can have its own little symbol. Does nature use a base system? If not, are base systems a totally human invention?
@pixie373 & @WoofgangIf we cannot invent mathematics, what can we invent? I came to the opinion that mathematics is a language. The language of maths is one of the most powerful because it is agreed throughout the whole world. Spoken/written languages are never easy to translate because exact meanings are often difficult to ascertain. There are some differences in the ways that we codify (write) our maths even when you compare England and USA there are some differences. These few differences do not change the meaning of the underlying mathematics.
@EVERYONE Can anyone find examples in nature where mathematical operations are performed. Serious (or seriously amusing) answers only please. I was given a pair of underpants with "Go fourth and multiply". Now that joke has been done please try to restrain yourselves from repeating it.
Looking forward to hearing your suggestions. I will try to keep an eye on updates provided I am not lured away by the temptations of pub.
/I have also observed that dandelions that grow inbetween the concrete blocks that are used for creating surfaces for vehicle wheels whilst also encouraging plants (grass) to grow within spaces set in the concrete (feel free to fall asleep before I get to the end of the sentence) find that it is safer to flower with very short stems rather than sticking out high above the concrete "floor" at which height they would be crushed if they were run over. This to me suggests an intelligence is at work, but no-one has found a brain within a plant as far as I know. /
Dandelions only grow as high as they need to in relationshio to light levels. With all the other plants being crushes by wheels they don't have to compete.
Dandelions only grow as high as they need to in relationshio to light levels. With all the other plants being crushes by wheels they don't have to compete.
@ALL OF YOU (who did not get some sort of reply in my last message) keep thinking! I did not expect so many new replies when I started replying to the first ones.
@Bert - I like your example of gravitational speed. Can anybody determine whether this is an example of "squaring" or an example of "multiplication" or is it possibly neither (in which case try to give an explanation).
@Bert - I like your example of gravitational speed. Can anybody determine whether this is an example of "squaring" or an example of "multiplication" or is it possibly neither (in which case try to give an explanation).
@jomifl - is this proven or is it your own understanding? From what I see, there are other plants (mostly grass or other weeds) trying to grow. The dandelions are all doing the same thing, ie keeping their heads down, even in the places where the wheels do not go over them. This should probably be put to the biologists to see what they say. Perhaps you are a biologist jomifl.
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JustNotCricket - the "squaring" in that formula S = G * T^2 / 2 is by a unit increment of the exponent of T. The speed of the falling object is V = G * T, or G * T^1 to be more clear; and the distance is the integral of the speed; and mathematicians find that for whole-number exponents N, the integral of X^N is a multiple of X^(N+1). So it's as simple as 1 + 1 = 2!
Although we can scarcely suppose that nature knows anything of exponents or integrals, our invented mathematical notation and rules still match up with what we observe to happen.
Although we can scarcely suppose that nature knows anything of exponents or integrals, our invented mathematical notation and rules still match up with what we observe to happen.
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An apparent example of basic operations being performed in nature came up a few weeks ago. I don't know what to make of it myself, but I offer it up here:
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If you are looking for somewhere physical where maths exists to be discovered you might be disappointed. Even allowing for the discovery bit I mentioned earlier, I think most of that happens in our heads. That might make it an "invented discovery", I suppose.
I thought that i = root -1 was as intrinsic to electrical circuits as any other area in physics such as QM. In particular as soon as you get a waveform then an i comes attached with it somehow. Just as in QM, though, you square it away to get the physical results.
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If you are looking for somewhere physical where maths exists to be discovered you might be disappointed. Even allowing for the discovery bit I mentioned earlier, I think most of that happens in our heads. That might make it an "invented discovery", I suppose.
I thought that i = root -1 was as intrinsic to electrical circuits as any other area in physics such as QM. In particular as soon as you get a waveform then an i comes attached with it somehow. Just as in QM, though, you square it away to get the physical results.
-- answer removed --
JNC, aquatic biologist, been retired for a long time. Quite simply one of the things that make plants grow tall is light levels. If you have an area of mostly concrete with not many plants, any plants that manage to squeeze into the few cracks will not need to grow tall to get enough light because there aren't other plants to shade them. Lots of creatures and plants achieve what seems to be intelligent behaviour by having a few simple responses to external stimuli. A few simple responses with start and stop thresholds can make for some complicated behaviour.
metyl
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