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The Maths

calamity said:
It does all seem to click all of a sudden like. I still remember sitting in my first electrical circuits' analysis class and suddenly realizing why we had a natural log and Euler's number. It was a total Eureka! moment. My first thought though: "Why the **** do they not lay all this out for five minutes as a precursor to 8th grade Algebra instead of starting with all the 'X+Y equals what number' crapola? All that math and we had no freaking clue as to why."


I remember my astonishment when I learned that all shapes, like lines, circles, parabolas, etc. could be expressed as equations, and then combined with time to yield rates of change, which too could be plotted into fundamental shapes. That was what? 11th, 12th grade.

Man, it was really great because I was getting high back then too. The stuff fell right into place in my head. I'd be partying with friends and spout out something geeky crazy like, "Did you know that a flat line can become an incline and then a parabola just by differentiating it through time? Whoa....deep, Dudes."
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Solving quadratic equations! Why the hell are we doing these sir?

Ah, the beauty when you find out how to solve second order differential equations with them and critically damp that mechanism :)
 
William Rea said:
Solving quadratic equations! Why the hell are we doing these sir?

Ah, the beauty when you find out how to solve second order differential equations with them and critically damp that mechanism :)
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I forgot a lot about this stuff, but I certainly remember the joy of learning that you could solve a single equation with 4 unknowns by simply integrating it up or differentiating it down the food chain until you had 4 equations to work with...and usually one or more of them ended up being equal to zero or translated into a simple 2t = 5 of whatever.
 
calamity said:
From what I know, it only appears ordered because we filter out the noise. It's a function of evolution, a survival skill, if you will. If you throw in all the noise, nothing is ordered and it may all be happening at the same time---but, understanding the mechanics behind all that goes way beyond my pay grade.
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'Noise' is just another word for what we can't explain or properly observe. Much like quantum mechanics. They like to say that things start behaving differently at a small scale. Which isn't true. We simply can't observe things moving so quickly so we have to look at what happens over the time we can observe and the 'quantize' it. Everything is ordered. We just can't always observe the order to it.


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Aberration said:
'Noise' is just another word for what we can't explain or properly observe. Much like quantum mechanics. They like to say that things start behaving differently at a small scale. Which isn't true. We simply can't observe things moving so quickly so we have to look at what happens over the time we can observe and the 'quantize' it. Everything is ordered. We just can't always observe the order to it.


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I don't know if it's all ordered, the way galaxies are scattered and clustered seems rather disordered to me. Now, sure, once a force begins acting on things, the resulting behavior appears ordered. But...that could just be because forces acting on objects do yield similar results.

Gravity grabs a fast moving mass, it begins to orbit. Masses in the same orbit begin clumping together. We observe it, and we think we see a pattern. But, it's really not. It's just the result of the force of gravity. And, that result is consistent, and therefore can be described by a mathematical equation. It's not really a pattern; it is just consistent.
 
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calamity said:
I don't know if it's all ordered, the way galaxies are scattered and clustered seems rather disordered to me. Now, sure, once a force begins acting on things, the resulting behavior appears ordered. But...that could just be because forces acting on objects do yield similar results.

Gravity grabs a fast moving mass, it begins to orbit. Masses in the same orbit begin clumping together. We observe it, and we think we see a pattern. But, it's really not. It's just the result of the force of gravity. And, that result is consistent, and therefore can be described by a mathematical equation. It's not really a pattern; it is just consistent.
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Consistent is ordered.


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ashurbanipal said:
This is why I've become interested lately in Neoplatonism, a view that says (among other things) that the physical world is emmanated from other "higher" worlds, on which reside math and logic, and above them, gods and angels. Looks like a guy from Alexandria in 300 AD got at least the first part of that right.
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Before anything else, I am not a mathematicians but I know how to calculate as to arrive at the amount of tax I will pay, by first determining or assigning to myself how much I will pay, and then compute things so that I arrive at the figure of cash I will pay the government, and be ready to explain why and how I come to that figure, and perhaps or better in most instances I can out reason the government examiner.

Now, dear ashurbanipal, I see you to be into what I call the distinction between the:

1. Conceptival realm of things, and the
2. Objectival realm of things

Mathematics are all in the conceptival realm of things, i.e. they are concepts in our mind, and I submit we humans are very good with inventing concepts in our mind, even though they be absolutely nonsensical, but of course usually concepts are not nonsensical.

Things like the nose in our face, the rose in the garden, babies, they are all examples of things in the objectival realm of things, they exist outside and independent of our mind, so that if you lose your mind, i.e. gone crazy altogether, they exist just the same; and when mankind has extinguished itself totally so that there is no more man with a mind, I ask you where is mathematics then.

Dear ashurbanipal, I like very much you to answer me, when mankind has annihilated itself completely, so there is no more man's mind around, is there is mathematics?
 
Sanluis said:
Dear ashurbanipal, I like very much you to answer me, when mankind has annihilated itself completely, so there is no more man's mind around, is there is mathematics?
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Yes, I think so.

Welcome to DP.
 
ashurbanipal said:
Yes, I think so.

Welcome to DP.
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No there isn't.

The relationships that mathematics describes would remain but, the abstract language that we use to describe it would no longer actively exist; if the records still existed then it would exist in whatever way we had decided to record it. If some other intelligence came across the mathematics, I would suggest that they would not be able to comprehend it unless they went right back to the start and used basic geometry graphics to decode the abstract symbolism that represents the relationships. It is the abstract symbols that are mathematics, not the relationships it describes.
 
William Rea said:
Originally Posted by ashurbanipal View Post

Yes, I think so.

Welcome to DP.
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No there isn't.

The relationships that mathematics describes would remain but, the abstract language that we use to describe it would no longer actively exist; if the records still existed then it would exist in whatever way we had decided to record it. If some other intelligence came across the mathematics, I would suggest that they would not be able to comprehend it unless they went right back to the start and used basic geometry graphics to decode the abstract symbolism that represents the relationships. It is the abstract symbols that are mathematics, not the relationships it describes.
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Thanks for your reply, dear ashurbanipal and William Rea.

You say, dear William, that:
"The relationships that mathematics describes would remain but, the abstract language that we use to describe it would no longer actively exist; if the records still existed then it would exist in whatever way we had decided to record it."

I see that you are into what I call:
...the distinction between the:

1. Conceptival realm of things, and the
2. Objectival realm of things

Mathematics are all in the conceptival realm of things, i.e. they are concepts in our mind, and I submit we humans are very good with inventing concepts in our mind, even though they be absolutely nonsensical, but of course usually concepts are not nonsensical.

Things like the nose in our face, the rose in the garden, babies, they are all examples of things in the objectival realm of things, they exist outside and independent of our mind, so that if you lose your mind, i.e. gone crazy altogether, they exist just the same; and when mankind has extinguished itself totally so that there is no more man with a mind, I ask you where is mathematics then.

https://www.debatepolitics.com/phil...8104-maths-post1067297550.html#post1067297550 post #32
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Now, dear ashurbanipal and William, let us we three do some thinking together, on the question, 'Where' do the relationships of mathematics exist? or simply 'Where' does mathematics exist? when all man-made records whatsoever have gone out of material inscriptions in stone or in whatever medium of writing or record-keeping from man's invention?
 
William Rea said:
No there isn't.

The relationships that mathematics describes would remain but, the abstract language that we use to describe it would no longer actively exist; if the records still existed then it would exist in whatever way we had decided to record it. If some other intelligence came across the mathematics, I would suggest that they would not be able to comprehend it unless they went right back to the start and used basic geometry graphics to decode the abstract symbolism that represents the relationships. It is the abstract symbols that are mathematics, not the relationships it describes.
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You are confusing syntax and semantics. When people discuss the nature of mathematics they are discussing the nature of the semantic content of math, not the syntactic content. Obviously the syntax of math is an arbitrary convention established by humans (ie, we could just as easily have used the symbol ~ to indicate what we mean by addition instead of +). No one disputes this. The controversy, the discussion, surrounds the semantic content of math. To what does the symbol "2" refer? <--- That is the question.
 
the_recruit said:
You are confusing syntax and semantics. When people discuss the nature of mathematics they are discussing the nature of the semantic content of math, not the syntactic content. Obviously the syntax of math is an arbitrary convention established by humans (ie, we could just as easily have used the symbol ~ to indicate what we mean by addition instead of +). No one disputes this. The controversy, the discussion, surrounds the semantic content of math. To what does the symbol "2" refer? <--- That is the question.
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Right, Newton and Leibniz (and to an extent, Dirac) all came up with different notation for calculus but they describe the same underlying content that worked the same way in application.

That said, something like imaginary numbers are simply a useful tool to help us describe how various mathematical functions work. It's feasible that a different civilization might come up with a completely different tool/method to answer questions that we use imaginary number for (although I guess - if it came to the same answer then maybe it wouldn't be that different).

Angel said:
That the universe is mathematical in design and operation -- and that, before man invented the language of mathematics with which to measure and monitor the universe -- strongly suggests something other than accident and blind chance at work. :)
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How does it suggest that?
 
That the universe is mathematical in design and operation -- and that, before man invented the language of mathematics with which to measure and monitor the universe -- strongly suggests something other than accident and blind chance at work.
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Nilly said:
How does it suggest that?
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Mathematics is a rational construct. That the physical universe operates in accordance with a rational construct suggests the rationality of the universe.
Rationality implies mind and logic rather than accident or blind chance.
 
Angel said:
Rationality implies mind and logic rather than accident or blind chance.
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How does it imply that?

There are plenty of things that are rational that arise through accident or blind chance. The formation of a snowflake, a star, or evolution. We have examples of plenty of rational things happened before minds were around to comprehend them. To say that the existence of these things is evidence of a mind that predates us (or life) - or that by very nature of existing they are evidence that things aren't down to blind chance would seem like begging the question to me. There's no way to validate that.

So why does rationality require a mind?

https://en.wikipedia.org/wiki/Patterns_in_nature
 
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Nilly said:
How does it imply that?

There are plenty of things that are rational that arise through accident or blind chance. The formation of a snowflake, a star, or evolution. We have examples of plenty of rational things happened before minds were around to comprehend them. To say that the existence of these things is evidence of a mind that predates us (or life) - or that by very nature of existing they are evidence that things aren't down to blind chance would seem like begging the question to me. There's no way to validate that.

So why does rationality require a mind?

https://en.wikipedia.org/wiki/Patterns_in_nature
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The very concept of rationality derives from the human mind. That this concept applies to the universe is my point tout court. That the universe antedates the appearance of the human mind in the universe is no counterexample to the rationality of the universe, both before and after the concept was derived. The snowflakes and stars and evolution, both before and after the human mind took their measure, support the inference to a rational universe. There's no way to validate that blind chance or accident gave rise to rational order either, but as between the propositions rationality implies rationality and irrationality implies rationality, the former seems to me more coherent. Not to you?
 
calamity said:
That would be the implication. Yes. But then again, "look at that cloud, it looks like a giraffe."
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It only looks lie giraffe because of the fractal Fibonacci sequence causing variations in the structure of the cloud that give it a vague resemblance to a giraffe that is triggered by the massive amount of LSD you just took (seriously, that's an elephant if I ever saw one).
 
Angel said:
The very concept of rationality derives from the human mind.
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Rationality in the mathematical sense or in the common sense sense? I think we should probably be important with our definitions here. I'm essentially saying rationality in this case is synonymous with ordered/regular.

Angel said:
That this concept applies to the universe is my point tout court. That the universe antedates the appearance of the human mind in the universe is no counterexample to the rationality of the universe, both before and after the concept was derived. The snowflakes and stars and evolution, both before and after the human mind took their measure, support the inference to a rational universe.
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But their existence alone just as easily (more easily, in fact) supports the inference that rationality and order can arise without the mind. You need to be able to provide justification 'non-tout-court' (today I learnt what tout court means) for why the existence of rational things means there must be a mind behind it. Otherwise, your argument is little more than 'it is what it is, because that's what it is'.

Angel said:
There's no way to validate that blind chance or accident gave rise to rational order either,
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Except that we see it all the time in nature, through pattern, through emergent properties. You're just presupposing that nature is not blind chance at all in the first place - which is circular reasoning.

Angel said:
but as between the propositions rationality implies rationality and irrationality implies rationality, the former seems to me more coherent. Not to you?
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It may seem more aesthetically pleasing from a human perspective but that doesn't mean that it is more coherent/true.


Without knowledge of whether there is
 
Nilly said:
Rationality in the mathematical sense or in the common sense sense? I think we should probably be important with our definitions here. I'm essentially saying rationality in this case is synonymous with ordered/regular.
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I'm fine with "ordered."
Nilly said:
But their existence alone just as easily (more easily, in fact) supports the inference that rationality and order can arise without the mind.
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Rationality arose without the human mind, of course. I am not arguing any different.
Nilly said:
You need to be able to provide justification 'non-tout-court' (today I learnt what tout court means) for why the existence of rational things means there must be a mind behind it. Otherwise, your argument is little more than 'it is what it is, because that's what it is'.
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The only thing we know about rationality is that there is mind behind it -- our own. That's the basis of recognizing it in the universe.
Nilly said:
Except that we see it all the time in nature, through pattern, through emergent properties. You're just presupposing that nature is not blind chance at all in the first place - which is circular reasoning.
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What I see in nature is order. Pattern is order, as I understand it. Emergent properties emerge from order.
Nilly said:
It may seem more aesthetically pleasing from a human perspective but that doesn't mean that it is more coherent/true.

Without knowledge of whether there is
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Inferring rationality from rationality is more aesthetic perhaps, but it is also more logical, it seems to me. Inferring rationality from irrationality is incoherent, it seems to me. But I welcome instruction on the point.
 
The idea that math exists independent of man just doesn't add up.
 
ashurbanipal said:
Kurt Goedel, one of the most original mathematical minds of the 20th century, produced a series of proofs that didn't receive a lot of attention at the time. It was only later, after his death, that mathematicians and logicians began to take notice. One thing he proved is that no formal system complex enough to represent basic mathematics can be both sound and complete (where soundness and completeness are just properties of the system. Soundness, as a property of a system of mathematics, means that the system will never give you the wrong answer. Completeness means that the system will never give you a false negative--tell you an answer is wrong when it is correct).

This proof reinvigorated the debate over whether mathematics and logic are just mere formalism (a language we invented to describe things) or whether the objects of math and logic (operators, numbers, propositions, quantifiers, functions, etc) are real things. If it were just formalism, just games being played on a piece of paper with invented symbols, we'd expect to be able to make systems with any properties we want. Turns out, we cannot do that--there's something in the objects of math and logic that "push back," so to speak. If this argument goes through, the objects of math an logic are clearly abstract (they're certainly not physical), but they're also real, in much the same sense as physical things are real--abstract objects are just real in a different domain.
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Though math is abstract, it is entirely consistent. That's why any attempt to add to it (pardon the pun) is inherently difficult: Such an addition has to be checked against anything that's already there. Thus it is a perfect, self-contained, and most remarkably, human-created system.
 
Angel said:
Does not the universe have a physics independent of man?
Well, it's the same for mathematics. :)
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My take: the physics is independent, but the math used to describe it is an invention. I don't think the math was the discovery; the patterns math describes was though.
 
calamity said:
My take: the physics is independent, but the math used to describe it is an invention. I don't think the math was the discovery; the patterns math describes was though.
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Correct. Maths is completely abstract and in no way actually linked to anything physical. In fact, the maths is at best an approximation of reality. This is why proof exists in maths but not in science. This need to reify mathematics and somehow create a mystical aura about how it successfully describes many phenomena is just new age bull crap.
 
Angel said:
Does not the universe have a physics independent of man?
Well, it's the same for mathematics. :)
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No, the relationships exist.. The relationships are the territory, mathematics is a map of the territory.
 
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