Is the geometry of the world the source of what we call math ?

[2foolish]

Is the geometry of the world the source of what we call "math"?

I keep thinking about this lately, think about how we know this is different from that without having to consciouslly think about it.

For instance this T is different from the background it sits on. The only way we could know that is if we already did the comparisons unconsciously so we know there is inequality (or inequalities) on a surface, that is, a distinction.

Think about how we detect things, in order to think, or do anything, we first must be able to observe/detect something is there and get feedback from it in a feedback ring, binary logic, yes something is there or no, without binary logic we can't even have a single perception.

It seems that the act of detection between real world surfaces (energy/light/etc) in and of itself, is where we get the concept of object, and hence the concept of 1, or "one distinct object", this is not that.

It seems to me numbers are just shapes in the real world, but in our minds we call these distinct shapes "numbers". So there is an equivalence between geometric shapes and numbers in the real world, at least that seems to be the case to me.

 

[CRGreathouse]

I would be careful to distinguish numerals from numbers.

 

[granpa]

that would be a 'thing'. then 'things' break down into subthings. each subthing is a set of 'things' which resemble each other more closely than can be explained by chance. reptiles resemble other reptiles. mammals resemble other mammals. but there's not much in between reptiles and mammals.

its all about finding patterns that can't be explained by chance.

that 'T' in your example could have been a random stain on the paper. yet you know that it isnt. how?

 

[2foolish]

I would be careful to distinguish numerals from numbers.

Numerals are basically symbols of the 'alphabet' of the concept of one object though, when we say one, we say 'one object', that is distinct from all other objects.

When we look at two circles on a piece of paper, we call them 'circles' but they are merely two distinct shapes in the real world.

If it is an object, it has boundaries, and is distinct from other thoughts, so it must be a shape, because it is distinct from other concepts (not equal to).

 

[2foolish]

that would be a 'thing'. then 'things' break down into subthings.

Things are objects, i.e. they are distinct from other things, there is distinction between them, this thing is not that thing

that 'T' in your example could have been a random stain on the paper. yet you know that it isnt. how?

I think you misunderstood, what I'm saying is the concept of object in our minds, is an instance of distinction we get from the process of detection in the world, i.e. the t could be a random blob, but that doesn't make it NOT a distinct object.

 

[granpa]

I understood you.

how do we distinguish a 'thing' from another 'thing' or for that matter from a nonthing? that is the question.

a stain would certainly be a thing. but it wouldn't be a 'T'. and how would we distinguish a stain from a generally chaotic background?

furthermore each set of subthings has its own actions that they perform or that can be performed on them and has its own rules. in other words, its a field.

 

[2foolish]

I understood you. how do we distinguish a 'thing' from another 'thing' or for that matter from a nonthing? that is the question.

Self recursion, self-reflection, reality processing itself. i.e. we make distinctions because reality is constantly bombarding us with information about itself. Photons bounce off objects and hit our eyes, etc. That is the only way we could detect ourselves, not only that, if we don't believe it we undermine knowledge completely and should just give up. i.e. if you don't believe things "out there" exist or you "in there" exist, then why should anyone listen to that kind of person? right? Not only that your conception is based on a flawed understanding of "nothing" in reality, nothing as it was conceived was conceputalized before modern understandings of physics. Space is a surface of a kind, i.e. similar to the ocean. We could also prove it from logic: You can't throw a ball across a non-existent entity, therefore space exists, and nothing is merely 'empty-space-surface'

Consider if you were giving an object to another person at the bottom of the sea, the water between you still exists. There wouldn't technically be 'nothing'

 

[dodo]

This discussion reminds me of G. Spencer-Brown's "Laws of Form"; there he would recreate boolean logic starting from the concept of a boundary, where one of its sides has been deliberately marked to distinguish it from the other. See f.i. here,
http://www.lawsofform.org/ideas.html
or the Wikipedia page which is even more cryptic than the book.

 

[2foolish]

Check this out:

 

[atyy]

Maths is biology. If our brains were different, we might make different maths, or at least what we'd consider a natural construction might be different.

 

[dodo]

I wonder how the boy from the documentary would perform (or feel) doing arithmetic in a base other than 10.

 

[2foolish]

I wonder how the boy from the documentary would perform (or feel) doing arithmetic in a base other than 10.

I wonder that as well. I'd love to look at the research they did. But it goes to show we hardly know anything about the brain, i.e. people can have innate knowledge and abilities and not be able to explain the process of how it occurs.

Which rubs right against the scientific method.

 

[granpa]

Things are objects, i.e. they are distinct from other things, there is distinction between them, this thing is not that thing
I think you misunderstood, what I'm saying is the concept of object in our minds, is an instance of distinction we get from the process of detection in the world, i.e. the t could be a random blob, but that doesn't make it NOT a distinct object.

ok I get it. I don't know that I MISunderstood you and I don't think that what I said actually contradicts what you said but I did indeed miss your point.

so 'thing'=distinction? well I'll have to think about. it sounds possible but at the same time distinction to my mind is more about the process of distinguishing rather than that which is distinguished if that makes any sense. A 'thing' certainly gets distinguished, but is that what it 'is'? but you may be right though. I'll have to think about it.

BTW, as far as numbers being shapes, there is an interesting discussion on the successor function being the basis of numbers/math in this thread:
https://www.physicsforums.com/showthread.php?p=1857233&posted=1#post1857233

heres my take on it:
since the successor function is the basis of math then maybe we shouldn't think in terms of one, two, and three but rather first, second, and third. 2+3 becomes the second after the third. 2*3 becomes the second third. its just semantics but it might make the underlying fundamental idea clearer.

after all, what does three even mean anyway? thirdness?

 

[2foolish]

ok I get it. I don't know that I MISunderstood you and I don't think that what I said actually contradicts what you said but I did indeed miss your point.

so 'thing'=distinction? well I'll have to think about. it sounds possible but at the same time distinction to my mind is more about the process of distinguishing rather than that which is distinguished if that makes any sense. A 'thing' certainly gets distinguished, but is that what it 'is'? but you may be right though. I'll have to think about it.

Well here's how I think about it.. imagine you had a piece of paper over two lumps (bubbles) out of the same surface, the surface would be a single surface, and yet you'd have two bubbles (two humps), so we get the concept of object from inequalities, i.e. in this example it is the flat vs raise/height.

BTW, as far as numbers being shapes, there is an interesting discussion on the successor function being the basis of numbers/math in this thread:
https://www.physicsforums.com/showthread.php?p=1857233&posted=1#post1857233

http://www.boundarymath.org/

I know I'm doing research into computational logic. You may find this interesting:

http://www.lawsofform.org/aum/prolog.html

heres my take on it:
since the successor function is the basis of math then maybe we shouldn't think in terms of one, two, and three but rather first, second, and third. 2+3 becomes the second after the third. 2*3 becomes the second third. its just semantics but it might make the underlying fundamental idea clearer.

after all, what does three even mean anyway? thirdness?

Thirdness? - three distinct objects. But consider the "hidden" subtext - all 3 numbers are actually subdivisions of a dinstinct thought, not '3 separate thoughts', i.e. consider a fractal pattern, shapes within shapes, numbers within numbers. See this cool program, to sit and think on it for a bit. This is how I came around to these ideas, when I was thinking about the patterns in fractals.

http://www.ultrafractal.com/

I think we've got it backwards, for instance we observe the universe from 'outside' (pretend it's in a bubble), we are fractions of the universe, but when we look at 'objects', 'outside' of our minds, they are actually fractions of a single entity, i.e. part of a big fractal surface, but our senses give us the optical illusion that they are 'separate', but in the ultimate sense they are not, they are all part of one surface of reality.

 

[granpa]

or better still a surface with a great many bubbles of all sizes and shapes and 2 bubbles much larger than the rest. clearly the 2 stand out represent something distinct from the rest. they arent just random.

distinguishing things is exactly what I was talking about in post 6.

 

[granpa]

you are thinking in terms of real bumps while I am thinking in terms of bumps in a distribution. plot each of the random bubbles by its characteristics (shape, size) and most would fall into a Gaussian distribution but the other 2 (I should have made it many more than that) clearly fall outside that. that's a distinction. that's what I was talking about when I mentioned the random stains.

I know what 'three' means. I am suggesting that it is an 'empty' word, as the chinese say, derived in some bizarre and meaningless way from the root idea of being 'third'.

I tend to believe that only nouns, verbs, and possibly conjunctions are 'real' words. all others are derived from those or they are 'empty' words.

 

[Hurkyl]

If you want to discuss epistemology, then please do so in the philosophy forum (which is where I have moved this post). If you want to discuss a more scientific topic, such as the psychology of observation or the mathematics of detecting patterns in raw data, then please start a new thread on that topic, and try not to diverge into overly speculative posts.

(Of course, one must refrain from overly speculative posts in the philosophy forums as well)

 

[2foolish]

you are thinking in terms of real bumps while I am thinking in terms of bumps in a distribution.

The problem is you have it backwards, the bumps are what is real. Your distribution is a reflection (an image, a photograph) of what is i.e. think of the order of operations, photon bounces/is ejected from object (carrying information) hits your eye, eye translates the signal. The signal reaches your mind, mind derives a thought from the information your eye has received, therefore when you 'self generate' ideas, you got those ideas from the outside world first. Therefore in our minds we're really just manipulating 'holographic' reflections of what is on the outside. If you actually had to make your bumps in a distribution out of real stuff in the real world, you would find out things. This is why I always transport mathematical reasoning back into the 'real world' I think terms of "What would it be made of?".. if this is 'infinite' in terms of our thoughts (i.e. if we had infinite strings of data), but if we actually had to make say pi out of stuff in the real world. We would run out of stuff to make distinct numbers from, therefore. Pi is "infinite" only in imaginary space, in the real world, pi ends (i.e. when you make pi with stuff).

In a computer pi would have to be stored somewhere, pi would fill up any amount of memory, hard disk space, and processing power you could throw at it, therefore, pi in the real world is truncated, it eventually ends somewhere when you consider the real world is made of stuff.

 

[2foolish]

If you want to discuss epistemology, then please do so in the philosophy forum (which is where I have moved this post). If you want to discuss a more scientific topic, such as the psychology of observation or the mathematics of detecting patterns in raw data, then please start a new thread on that topic, and try not to diverge into overly speculative posts.

(Of course, one must refrain from overly speculative posts in the philosophy forums as well)

All science begins with thought, I fail to see how our discussion of detection is unscientific. i.e. if you don't think you can see stuff you can't move around objects, if you believe what you are seeing is subjective, you're getting an objective outcome (movement around an object) from a 'subjective' experience, seems a little off to me. Would you sit there thinking you were experiencing 'subjective hotness' and let your hand burn off? I wouldn't personally, the whole point in asking these questions is to discover errors in the philosophy of science and the method of science itself. Men conceived what we call 'science' if there are errors in conceptualizations, then there are errors in everyone who claims to know what 'science' is. Men derive their concepts from the world, if they conceptualized their concepts incorrectly we should demand these errors be exposed, that is the scientific way.

It is the duty of philosophy to destroy the illusions which had their origin in misconceptions, whatever darling hopes and valued expectations may be ruined by its explanations. My chief aim in this work has been completeness; and I make bold to say, that there is not a single metaphysical problem that does not find its solution, or at least the key to its solution, here. Pure reason is a perfect unity. (Immanuel Kant, Critique of Pure Reason, 1781)

 

[granpa]

anyway, my point was that the successor function, which is the basis of all mathematics, doesn't give us one, two, and three. it gives us first, second, and third. so the whole question of what is a 'number' may be meaningless.

for the record, I consider that very relevant to 'math'.you have to distinguish between 'types' and 'instances'. instances are real world objects. types are not. distinguishing an instance is in theory no different from distinguishing a type.

 

[2foolish]

anyway, my point was that the successor function, which is the basis of all mathematics, doesn't give us one, two, and three. it gives us first, second, and third. so the whole question of 'what is a number' may be meaningless.

for the record, I consider that very relevant to 'math'.you have to distinguish between 'types' and 'instances'. instances are real world objects. types are not.

The successor function is in fact what boolean logic is, I've been working on this, boolean logic is in fact the 'true math', our higher abstractions (arabic numerals, etc), if you go back to geometry, and represent numbers as a series of lines on a piece of paper (remmeber the 4 sticks then the cross on to represent 5?).

There is only one function there is not "0 and 1" it's -1 and +1, then the 0 "empty*, it's an existence/detection function --> yes it exists? --> yes it exists! Try expressing pi with simple shapes (i.e. 3 in 3.14) would be 3 boxes, then .1 would be 1/10 of a box, etc, and then represent each 1 within the number in binary notation, notice how the data is expanding and growing (i.e. self recursive).

The mayan's used shapes as their numerals, they didn't use our rather convoluted notation which compresses and masks mathematical truths (distinct shapes), when we write "3" we actually mean 1 and 1 and 1 (3 ones) or 3 sticks, or 3 distinctions.

 

[granpa]

I agree that math is an outgrowth of an even more basic field but geometry is an outgrowth of math. its 2 dimensional mathemetics (or rather, multidimensional mathematics). geometry therefore can't be as fundamental as your are thinking.

 

[2foolish]

I agree that math is an outgrowth of an even more basic field but geometry is an outgrowth of math. its 2 dimensional mathemetics (or rather, multidimensional mathematics). geometry therefore can't be as fundamental as your are thinking.

Incorrect, surfaces exist "out there", what we were taught as geometry is merely an instance of (reflection of) real world geometric surfaces, etc. Not only that the 'geometry' we were handed was conceived and handed down to us, i.e. we didn't come up with it ourselves, the whole point was to show that real-world geometry is in fact the source of math. you can't have a perception if you can't detect using binary, if something is there or not, yes it is there, no it is not, you can't have a single mathematical thought or perception without it. Colliding and interacting surfaces/energies comes before you can even think of a notion, conceive a mathematical system, etc. Perception is apriori to our conceived mathematics. Everything goes through a process of conceptualization, therefore, we examine the nature of how thoughts are derived from the world in the first place, to get the answers we are looking for. The time ordering of real world operations, remember.

 

[Hurkyl]

All science begins with thought, I fail to see how our discussion of detection is unscientific.

You are not applying the scientific method. You do not propose testable predictions, nor experiments to conform those predictions. Nor do you appear to be striving to achieve that standard. Thus, you are not being scientific.

 

[granpa]

Incorrect, surfaces exist "out there", what we were taught as geometry is merely an instance of (reflection of) real world geometric surfaces, etc. Not only that the 'geometry' we were handed was conceived and handed down to us, i.e. we didn't come up with it ourselves, the whole point was to show that real-world geometry is in fact the source of math. you can't have a perception if you can't detect using binary, if something is there or not, yes it is there, no it is not, you can't have a single mathematical thought or perception without it. Colliding and interacting surfaces/energies comes before you can even think of a notion, conceive a mathematical system, etc. Perception is apriori to our conceived mathematics. Everything goes through a process of conceptualization, therefore, we examine the nature of how thoughts are derived from the world in the first place, to get the answers we are looking for. The time ordering of real world operations, remember.

space is not geometry anymore than sheep are numbers even though they may often be counted.

it isn't clear to me what it is that you are arguing against.

 

[2foolish]

You are not applying the scientific method. You do not propose testable predictions, nor experiments to conform those predictions. Nor do you appear to be striving to achieve that standard. Thus, you are not being scientific.

logic (countable and uncountable; plural logics)

1. (uncountable) A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method.

Therefore, the scientific method reduces to and is rooted in logic, in fact hypotheses are logical statements in and of themselves, they are made and constructed using logic.

You're under the false notion that science is separate from thought, that is the whole point. Every act of detection you make to move around, is an act of science in and of itself. Is something there? yes/no, then move left/right. It is a logical operation that is tested - hypothesis is: Is something there -- yes? then... move left/right.

I am being quite scientific, since the act of detection is an act of observation and you cant' detect anything is there and do comparisons without logic.

 

[Hurkyl]

In a computer pi would have to be stored somewhere, pi would fill up any amount of memory, hard disk space, and processing power you could throw at it, therefore, pi in the real world is truncated, it eventually ends somewhere when you consider the real world is made of stuff.

This is patently false. pi can be represented, for example, as a symbolic constant, and thus requiring only a few bits of storage. And even if you insist on being able to retrieve individual digits of pi, you can do so with finite storage if you do something more clever than a lookup table algorithm.

As CRGreathouse advised in the first reply to your opening post:

I would be careful to distinguish numerals from numbers.​

 

[Hurkyl]

logic (countable and uncountable; plural logics)

1. (uncountable) A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method.

Yes, science makes use of logic. That does not imply that logic is synonymous with science.

 

[granpa]

The problem is you have it backwards, the bumps are what is real. Your distribution is a reflection (an image, a photograph) of what is i.e. think of the order of operations, photon bounces/is ejected from object (carrying information) hits your eye, eye translates the signal. The signal reaches your mind, mind derives a thought from the information your eye has received, therefore when you 'self generate' ideas, you got those ideas from the outside world first. Therefore in our minds we're really just manipulating 'holographic' reflections of what is on the outside. If you actually had to make your bumps in a distribution out of real stuff in the real world, you would find out things. This is why I always transport mathematical reasoning back into the 'real world' I think terms of "What would it be made of?".. if this is 'infinite' in terms of our thoughts (i.e. if we had infinite strings of data), but if we actually had to make say pi out of stuff in the real world. We would run out of stuff to make distinct numbers from, therefore. Pi is "infinite" only in imaginary space, in the real world, pi ends (i.e. when you make pi with stuff).
In a computer pi would have to be stored somewhere, pi would fill up any amount of memory, hard disk space, and processing power you could throw at it, therefore, pi in the real world is truncated, it eventually ends somewhere when you consider the real world is made of stuff.

you completely lose me at this point. how do you construe anything I said to imply that 'real' bumps arent real? and what does that have to do with anything?

 

[Hurkyl]

The successor function is in fact what boolean logic is,

I can't figure out what figurative meaning you could possibly intend by this comment. But I will point out that, taken literally, it is obviously false.

 

[granpa]

you seem to want to take abstract ideas like space and numbers and turn them into something concrete. either that or do away with them entirely. I'm not sure which.

theres something called 'mistaking the map for the territory'. I wonder if that's what is going on here?

 

[2foolish]

Yes, science makes use of logic. That does not imply that logic is synonymous with science.

Actually it is, an act of observation is an act of detection, is an act of interaction - contact. So it is logic, you can't detect something is there without logic. You can't escape the functional nature of detection and recursive feedback of the logic of detection.

There are different logics for different systems, you're confusing the misuse of logic with the proper use of logic.

Consider the question: Does the truth contain logic? Is existence truth? If the answers to those aren't yes. Then the whole of science collapses. The whole of science begins with things that exist, that you can sense. It begins with sensory experience, an act of sensation is an act of detection, the act of feedback, in that - this is not that. That's all I need to demonstrate you're not grasping what I said.

 

[2foolish]

I can't figure out what figurative meaning you could possibly intend by this comment. But I will point out that, taken literally, it is obviously false.

No it isn't, you just don't have the research background. You're thinking about one interpretation of boolean logic (the one you were taught), incorrect concepts (the interpretation of logic you were taught) must necessarily lead to incorrect judgments if what was taught was only half the story (partial understanding of boolean algebra). There are other expressions and understandings which are being worked on right at this very moment. Consider: http://www.lawsofform.org/aum/prolog.html

 

[2foolish]

This is patently false. pi can be represented, for example, as a symbolic constant, and thus requiring only a few bits of storage.

You're missing the point, if you were to calculate it out it would continue on forever, i.e. expanded the expression. for instance I can store 0.333 repeated in a computer as
1/3, but that does not make it's decimal expansion any less real.

As CRGreathouse advised in the first reply to your opening post:

I would be careful to distinguish numerals from numbers.​

Numerals are a form of object (one-ness) in and of themselves, you could simply use the representations to count i.e. the recursive nature of images (pictures within pictures), if what you were doing was stated.

 

[2foolish]

space is not geometry anymore than sheep are numbers even though they may often be counted.

"Time and space and gravitation have no separate existence from matter. ...
Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning."--Einstein

Relativity -- gravitational lensing, yes space is geometry, that is a surface of a kind, it's just a surface of a different nature (i.e. counter intuitive)