Mathematics

[surreptitious57]

Mathematics is a discipline which exists entirely independent of
conception for while the symbols may be human it itself is not
But what do the honourable members here think of this though

 

[Loss Leader]

Just to be sociable, I'll take your word.

 

[Perpetual Student]

Mathematics is a discipline which exists entirely independent of
conception for while the symbols may be human it itself is not
But what do the honourable members here think of this though

I agree. I see mathematics as the basis for all relationships and action of the universe.
We have invented a language through which we discover and comprehend this action. That's what we call mathematics. So, the term "mathematics" refers to both the language and the study of the discovered relationships and action.

 

[Minoosh]

Mathematics is a discipline which exists entirely independent of
conception for while the symbols may be human it itself is not
But what do the honourable members here think of this though

Do you only want the opinion of the honourable members or can I respond?

By using the word "discipline," I believe you introduce a human element. There is probably a better word. "Mathematical relationships exist independent of conception" works better for me.

 

[annnnoid]

I agree. I see mathematics as the basis for all relationships and action of the universe.
We have invented a language through which we discover and comprehend this action. That's what we call mathematics. So, the term "mathematics" refers to both the language and the study of the discovered relationships and action.

That’s an incredibly sweeping claim to make…especially given that you cannot even begin to prove it. ‘Something’ may be the basis for all blah blah blah blah…but is it mathematics? Show me somewhere, anywhere…anywhere at all…where you can explicitly identify the existence of mathematics. The only place we can say, with any assurance, that it exists…is in our minds (and what kind of phenomenology does that constitute?). As for that…nobody has a clue…not a clue… how our minds come to create / discover the stuff. What is the relationship between ‘consciousness’ and the physical conditions that create it? How does a brain create the idea of a plus sign? What is the phenomenology of meaning?

Faith!

…but…if, as you say, mathematics is the basis for all relationships and action in the universe, that would make the universe informational. The processing (relationships / action) of information is typically regarded as a sign of intelligence. An intelligent universe.

…so mathematics is the anatomy of God!

 

[Perpetual Student]

That’s an incredibly sweeping claim to make…especially given that you cannot even begin to prove it. ‘Something’ may be the basis for all blah blah blah blah…but is it mathematics? Show me somewhere, anywhere…anywhere at all…where you can explicitly identify the existence of mathematics. The only place we can say, with any assurance, that it exists…is in our minds (and what kind of phenomenology does that constitute?). As for that…nobody has a clue…not a clue… how our minds come to create / discover the stuff. What is the relationship between ‘consciousness’ and the physical conditions that create it? How does a brain create the idea of a plus sign? What is the phenomenology of meaning?

Faith!

…but…if, as you say, mathematics is the basis for all relationships and action in the universe, that would make the universe informational. The processing (relationships / action) of information is typically regarded as a sign of intelligence. An intelligent universe.

…so mathematics is the anatomy of God!

I know of no counterexample to any aspect, in any place, at any level, at any scale of the universe behaving in any way but mathematically.

 

[annnnoid]

I know of no counterexample to any aspect, in any place, at any level, at any scale of the universe behaving in any way but mathematically.

Mathematics is something WE create. There is not a shred of evidence anywhere that explains the relationship between mathematics and the universe that it somehow represents (IOW…nobody has a clue how we create it). Just saying that it looks like everything has some kind of mathematical component…or that there does not exist (to our ignorant eyes) any other equivalent system of explanation…is nothing more than circumstantial. There is no explanation for mathematics. None. Until there is one, it is nothing but conditional.

So if the universe behaves so convincingly mathematically…how is it not then acceptable to conclude that some variety of intelligence orients the whole thing…given the (conditional) conclusion that information processing is a sign of intelligence?

 

[psionl0]

Is 1 + 1 = 2 a property of the universe or just a concept of our own creation?

 

[TheGnome]

Is 1 + 1 = 2 a property of the universe or just a concept of our own creation?

Ah but sometimes it is 0

 

[Roboramma]

Mathematics is something WE create. There is not a shred of evidence anywhere that explains the relationship between mathematics and the universe that it somehow represents (IOW…nobody has a clue how we create it). Just saying that it looks like everything has some kind of mathematical component…or that there does not exist (to our ignorant eyes) any other equivalent system of explanation…is nothing more than circumstantial. There is no explanation for mathematics. None. Until there is one, it is nothing but conditional.

Mathematics is just a way of defining the way things relate to each other.

Let's test those relationships and see if they apply to the real world. Here, I'll take an apple and put it in an empty bowl. Now I put another apple in the bowl. I look in the bowl and find two apples there, not five. I weigh the apples and bowl before putting the apples in and then weigh them after. I find that the total weight after equals the sums of the weights before...
Etc.

Of course things could have other relationships that have other mathematical descriptions. They would still be mathematical descriptions. The mathematics is really just a way of describing how one thing is related to another.

For instance, the apples in the bowl all together should actually weigh a tiny bit less than the total weight of the system when they are separate, because of the gravitational energy...

 

[Anerystos]

Is 1 + 1 = 2 a property of the universe or just a concept of our own creation?

Ah but sometimes it is 0.

But it can be 2, or 3, or even (but rarely) quads. See Wilt.

Maybe mathematics is but a useful way of describing some aspects of the universe.

The Raleigh distribution (aka, the bivariate normal distribution) (also aka crossed (single variate) normal distributions) is a useful way of describing the spread of arrows on a target - but that doesn't (necessarily) make it "true" (for some arbitrary value of "true").

 

[Anerystos]

See previous post.

Sorry, missed out 10.

 

[fuelair]

That’s an incredibly sweeping claim to make…especially given that you cannot even begin to prove it. ‘Something’ may be the basis for all blah blah blah blah…but is it mathematics? Show me somewhere, anywhere…anywhere at all…where you can explicitly identify the existence of mathematics. The only place we can say, with any assurance, that it exists…is in our minds (and what kind of phenomenology does that constitute?). As for that…nobody has a clue…not a clue… how our minds come to create / discover the stuff. What is the relationship between ‘consciousness’ and the physical conditions that create it? How does a brain create the idea of a plus sign? What is the phenomenology of meaning?

Faith!

…but…if, as you say, mathematics is the basis for all relationships and action in the universe, that would make the universe informational. The processing (relationships / action) of information is typically regarded as a sign of intelligence. An intelligent universe.

…so mathematics is the anatomy of God!

No, but good try and thanks for playing........ absent actual evidence/proof of a god(s) existence in any form or manner, positing that some feature of the universe/multiverse proves god is not rational, just wishful thinking.

 

[annnnoid]

Is 1 + 1 = 2 a property of the universe or just a concept of our own creation?

Obviously…1+1=2 is a property of the universe…because it is created by a brain that itself is a function of the universe. So far, no one has a clue what the relationship between the brain and 1+1=2 actually is. I think what you are asking is if mathematics exists somehow inherently in the structure of whatever-it-is that everything is.

Haven’t a clue….and neither does anyone else.

Mathematics is just a way of defining the way things relate to each other.

Let's test those relationships and see if they apply to the real world. Here, I'll take an apple and put it in an empty bowl. Now I put another apple in the bowl. I look in the bowl and find two apples there, not five. I weigh the apples and bowl before putting the apples in and then weigh them after. I find that the total weight after equals the sums of the weights before...
Etc.

Of course things could have other relationships that have other mathematical descriptions. They would still be mathematical descriptions. The mathematics is really just a way of describing how one thing is related to another.

For instance, the apples in the bowl all together should actually weigh a tiny bit less than the total weight of the system when they are separate, because of the gravitational energy...

….just ?!?!?!?!?!? As Perpetual Student quite accurately pointed out…mathematics somehow corresponds to, describes, represents, and / or predicts every fundamental feature of this universe we live in to one degree or another. It is not too much of a leap to wonder if mathematics actually IS this universe …except that no one anywhere has any idea how such a thing could be possible (then again…no one has any idea what this universe actually is)(except Pixy of course).

This also raises the question of whether mathematics is merely one of an infinite range of conceptual systems. One that is conducive to our particular ability to comprehend. But if it’s merely random how to explain the obvious fact that the mathematical systems that are discovered / created have such a vast range of practical applications (and there are so many features of the universe that implicitly or explicitly manifest mathematical ideas). There is a relationship between mathematics and the universe that it so effectively represents. Just because no one has a clue what that relationship is does not mean that it doesn’t exist.

No, but good try and thanks for playing........ absent actual evidence/proof of a god(s) existence in any form or manner, positing that some feature of the universe/multiverse proves god is not rational, just wishful thinking.

Did I say…anywhere…that anything anywhere anyhow proved that God exists? If I said such a thing…please point it out. Otherwise I will have to conclude that you simply do not know what you are talking about.

…and mathematics…BTW…is not just ‘some feature of our universe’. It is THE fundamental defining feature of our universe. It is implicated everywhere, in everything, all-the-time. Perpetual Student was quite accurate in pointing this out (however unavoidably metaphysical the conclusion actually is at this time). The OBVIOUS corollary (… obvious, that is, to anyone with any rudimentary capacity for elementary reasoning) is that the universe…if it is fundamentally mathematical (which was the argument PS was making)…is, by implication, intelligent (on however vast a scale). That you seem traumatized by such inherent realities is something you might consider taking up with a therapist.

 

[psionl0]

Obviously…1+1=2 is a property of the universe…because it is created by a brain that itself is a function of the universe.

So far, no one has a clue what the relationship between the brain and 1+1=2 actually is.

I didn't know there was a relationship (whatever that means).

I think what you are asking is if mathematics exists somehow inherently in the structure of whatever-it-is that everything is.

I would say that mathematics predicts that under certain conditions, you will always make the same observation about the universe - whether as a result of an action of yours or merely as a spectator. For example, if you bring two individual objects together then count how many objects you have ..........

 

[annnnoid]

I didn't know there was a relationship (whatever that means).


I would say that mathematics predicts that under certain conditions, you will always make the same observation about the universe - whether as a result of an action of yours or merely as a spectator. For example, if you bring two individual objects together then count how many objects you have ..........

I will rephrase:

The human brain exists in the universe and can thus be regarded as functioning according to principles embedded in this universe (principles which are currently believed to somehow be mathematical). Whatever the brain creates is, be extension, subject to the same conditions.

1+1=2 is created by brain activity. How? There must be some relationship between brain activity and whatever is created by it (in this case … 1+1=2). Currently, nobody has a clue what that relationship is (IOW…why does a certain variety of neural architecture generate the color red while another variety generates the color yellow...or the mathematical formula 1+1=2 ??? ….no one knows)

 

[Dinwar]

Mathematics is a discipline which exists entirely independent of
conception for while the symbols may be human it itself is not
But what do the honourable members here think of this though

I'm not sure how to translate this into English. That may be on my end, however.

Here's how I view math: It's a language. Any equation can be translated into any language (well....any language that includes numbers higher than five and the number zero, anyway). It's a very precise language, and often deals with very abstract concepts, but none the less, it is a language.

That in no way separates it from reality. Proper concepts are derived from perception, ultimately (though the number of steps between the two can approach infinity). Mathematical concepts can be thought of as the ultimate conceptualization--it deals with the inter-relationships between things, rather than things. y=mx+b is more a statement about how y, m, x, and b interact than it is anything else. And the precision adds certain value to the convesation--because it is so precise, one can do things with the mathematical language that a more organic language like English or French or Japanese simply can't, due to the error bars. Compare "when one goes up, the other goes down" with "y=1.75/x", for example.

As Perpetual Student quite accurately pointed out…mathematics somehow corresponds to, describes, represents, and / or predicts every fundamental feature of this universe we live in to one degree or another.

First, you can't say that with any certainty. We don't know the fundemental features of the universe we live in. If we did, to quote a comedian, science would stop.

Second, so what? English does the same thing. ANY living language MUST correspond to, describe, represent, and/or predict every known feature of the universe we live in--for the simple reason that if a language lacks a word or phrase that does so, one will be invented.

Third, this leaves entirely open the question of whether math is somehow a metaphysical reality (in the Aristotilian and Objecivist sense, not the Buhdist or mystical sense) or if it is merely an epistemological necessity. In other words, this does nothing to determine whether math is something inherent in reality, or something inherent in the human mind. (My standard caveat: I've no interest in discussing Objectivist philosophy here; I include it in the previous sentence merely to provide those curious with how I define "metaphysical" with the definition I'm using.)

…but…if, as you say, mathematics is the basis for all relationships and action in the universe, that would make the universe informational.

If math is, than yes, I'd agree. However, since math is the product of human cognition, we can't say that--at least, not without far more proof than we have thus far. I believe that ANY sufficiently precise language would result in the same advantages as math currently has.

 

[Perpetual Student]

<...>
Here's how I view math: It's a language. Any equation can be translated into any language (well....any language that includes numbers higher than five and the number zero, anyway). It's a very precise language, and often deals with very abstract concepts, but none the less, it is a language.

This an extremely one dimensional and naïve view of mathematics. The authors of the Wikipedia article did a fairly good job:

Mathematics is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8]

Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Certainly, mathematicians have developed a language to deal with their subject, but to reduce the subject itself to merely the language misses the point by a wide margin.
Mathematics can also be regarded as a complex and sophisticated extension of logic, since that is the fundamental tool of its development.

<..>

Third, this leaves entirely open the question of whether math is somehow a metaphysical reality (in the Aristotilian and Objecivist sense, not the Buhdist or mystical sense) or if it is merely an epistemological necessity. In other words, this does nothing to determine whether math is something inherent in reality, or something inherent in the human mind. (My standard caveat: I've no interest in discussing Objectivist philosophy here; I include it in the previous sentence merely to provide those curious with how I define "metaphysical" with the definition I'm using.)

If math is, than yes, I'd agree. However, since math is the product of human cognition, we can't say that--at least, not without far more proof than we have thus far. I believe that ANY sufficiently precise language would result in the same advantages as math currently has.

Let's take an example: The ratio of the circumference to the diameter of a circle in Euclidean space, which we have come to call pi (π). This relationship was discovered in antiquity and was further discovered to be true of all circles, regardless of size. It is a fundamental feature of Euclidean space! It has profound consequences and appears in disparate aspects of physics like the Schrödinger equation and Einstein's tensor equation of GR. Similarly, whether we are considering numbers or geometric relationships, these are discoveries about the reality of the universe; these relationships are not invented by man and his language of mathematics. This is why mathematics is the language of physics; there is no known aspect of the universe that does not behave mathematically.
This is what Einstein was referring to when he said, "The eternal mystery of the world is its comprehensibility."

 

[annnnoid]

I'm not sure how to translate this into English. That may be on my end, however.

Here's how I view math: It's a language. Any equation can be translated into any language (well....any language that includes numbers higher than five and the number zero, anyway). It's a very precise language, and often deals with very abstract concepts, but none the less, it is a language.

That in no way separates it from reality. Proper concepts are derived from perception, ultimately (though the number of steps between the two can approach infinity). Mathematical concepts can be thought of as the ultimate conceptualization--it deals with the inter-relationships between things, rather than things. y=mx+b is more a statement about how y, m, x, and b interact than it is anything else. And the precision adds certain value to the convesation--because it is so precise, one can do things with the mathematical language that a more organic language like English or French or Japanese simply can't, due to the error bars. Compare "when one goes up, the other goes down" with "y=1.75/x", for example.

First, you can't say that with any certainty. We don't know the fundemental features of the universe we live in. If we did, to quote a comedian, science would stop.

Second, so what? English does the same thing. ANY living language MUST correspond to, describe, represent, and/or predict every known feature of the universe we live in--for the simple reason that if a language lacks a word or phrase that does so, one will be invented.

Third, this leaves entirely open the question of whether math is somehow a metaphysical reality (in the Aristotilian and Objecivist sense, not the Buhdist or mystical sense) or if it is merely an epistemological necessity. In other words, this does nothing to determine whether math is something inherent in reality, or something inherent in the human mind. (My standard caveat: I've no interest in discussing Objectivist philosophy here; I include it in the previous sentence merely to provide those curious with how I define "metaphysical" with the definition I'm using.)

If math is, than yes, I'd agree. However, since math is the product of human cognition, we can't say that--at least, not without far more proof than we have thus far. I believe that ANY sufficiently precise language would result in the same advantages as math currently has.

First…not saying that we know the fundamental features of the universe (quite the opposite). Just that the vocabulary used to describe what we currently know of them (physics) is fundamentally mathematical in nature.

Second… math is the only vocabulary that seems to have some kind of ‘existence’ beyond the metaphysical. That is the issue. That it is an epistemological necessity is implicit (a lot of science would pretty much stop without it). But is it something else? It is clear that math is generated by human cognition (how and in response to what???). Just like every other vocabulary that we develop. But…unlike every other vocabulary that we develop we find mathematics ‘occurring’ everywhere all-the-time in one form or another. The structure and activity of this universe seems to be somehow mathematical. From the microscopic to the macroscopic. Mathematical principles either predict phenomenon; can be recognized in phenomenon, or both.

So…the question (so far unanswerable) is: What is the relationship between mathematics and the universe in which it occurs? There has to be one. At the very least there must be some way of explaining how a brain generates it (given the current state of neuroscience…that understanding is likely decades away at best). But…there also HAS to be some explanation for why we find mathematics….everywhere. It may well be that mathematics, as we know it, is nothing more than a vocabulary generated by our particular variety of consciousness (though we might ask: would a consciousness generated by a mathematical universe be somehow ‘conditioned’ to extracting that same mathematics? [purely speculative of course]).

Any claim that there is an explicitly mathematical component to the phenomenology of reality requires proof. Of which we have a grand total of zero. But what we have in uber abundance is the unmistakable and indisputable mathematical-seeming structure of…everything. We may have no idea what the relationship (between math and the structure of reality) is, but only an idiot would unequivocally insist that there isn’t one.

The fact that mathematics is a ‘vocabulary’ is worth repeating. But the issue is, as you have pointed out, the degree of precision, accuracy, and complexity involved. It achieves an explicit precision not just beyond any other language…but many many many many orders of magnitude beyond any other language. To the point that it leaves us wondering if math is somehow embedded within reality (there….English words describing something that math has no equivalent expression for…yet).

 

[Perpetual Student]

Logic and mathematics are manifested as the fundamental nature of the universe. The evidence for this is overwhelming. Logic and mathematics are not invented by humans; they are discovered. The vocabulary and language referred to above are the tools invented for this discovery. Let's not confuse the two.