Mathematics, because it's completely unrelated to the real world, so usually you can't explain an advanced concept in the span of a conversation. Especially the really abstract stuff, like knot theory, category theory, or topology. Category theorists spout shit like "a monad is just a monoid in the category of endofunctors. What's the problem?"

>>16473
Which topic is best for my reasons? Or do you just learn all of them when you take the courses for advanced mathematics?

>>16473
Which topic is best for my reasons? Or do you just learn all of them when you take the courses for advanced mathematics?

>>16475
Topology is definitely part of a standard mathematics curriculum for a bachelor or masters degree. Knot and category theory are more likely to be optional subjects or part of a Ph.D. course.

Topology is weird but somewhat intuitive. Knot theory is so abstract it's completely useless (AFAIK), so definitely useful for your purposes. Category theory sees some use in computer science, but since what it does (IINM) is generalize relationships between various mathematical objects, it requires some background in order to even understand what is being discussed.

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>>16473
>Category theorists spout shit like "a monad is just a monoid in the category of endofunctors. What's the problem?"

Well, it is.

>>16475
If you have any Set theory under you, go with Category theory.

Mathematics probably has more complexity than physics, since not all math been found applicable to physics, and all physics is supported by math.

So the 'shit' is of equally mind-blowing complexity, except that Physics happens to deal in what we know to exist....much of math is many rabbit-holes and warrens distant from citeable physical examples.

So.... I'd go with math.

>>16472
Watch the 'numberphile' channel on jewtoob

When both physics and math get higher it's all written, so neither "sound" abstract.

This was done so mathamitions and physicists would be forced to talk about something else at cocktail parties.

This is such stupid shit, if you learn a lot of stuff you'll want people you can talk with about it, not to deliberately _not_ be able to talk about it.

Meh, fuck it.

Read this, and all of STEM will be within your grasp.

'Physics, Topology, Logic and Computation: A Rosetta Stone', John C. Baez, Mike Stay
https://arxiv.org/abs/0903.0340

Physics on account of exotic entities like black holes. Astrophysics is known as an exotic hard science, as is Cosmology. They just sound cool on the lonesome there of. Nuclear Physics and Particle Physics and Chemical Physics and Subatomic Physics just sound cool also. Muons, gluons, quarks, and the like also sound good. I do not know why, probably because I know more about it, but I believe Physics has more pizzazz than mathematics.

>16472
>Pic unrelated
Why not get into time travel? The good thing is the subject is an iceberg, on the surface it looks like a small subject but the majority is underneath.

Not only will you look autistic but everyone else will feel retarded. Double-win!

Theoretical mathematics is just people jerking off to fictional concepts that they made up on their own;
instead of trying to understand reality, they instead make classifications of abnormal phenomenons and then call it concept A and then just call it a day. Sure, it sounds smart but it's ultimately just retarded.

Physics is less so because there are actual practical elements in said field. But the theoretical mathematics syndrome is slowly creeping into the field so it's becoming another retarded field.

Which is why more people are more into engineering than just pure physics these days. Even though the latter was much more interesting.

>>17962
> Theoretical mathematics is just people jerking off to fictional concepts that they made up on their own;
instead of trying to understand reality, they instead make classifications of abnormal phenomenons and then call it concept A and then just call it a day. Sure, it sounds smart but it's ultimately just retarded.
Ever heard about fractal antennaes? That's why your cell phone doesn't have several antennaes:
https://en.wikipedia.org/wiki/Fractal_antenna

>Physics is less so because there are actual practical elements in said field. But the theoretical mathematics syndrome is slowly creeping into the field so it's becoming another retarded field.
As in string theory?

>Which is why more people are more into engineering than just pure physics these days. Even though the latter was much more interesting.
Source?

Fuck me, I replied in this thread seven years ago?

>>17962
There's no such thing as "theoretical mathematics" or "pure physics", retard, for the same reason there's no "experimental mathematics" (impossible) or "applied physics" (it's just engineering).

>>18770
>Fuck me, I replied in this thread seven years ago?
That's not so bad, I was here before cb9fa8 made the rounds.

>>18770
>There's no such thing as "theoretical mathematics" for the same reason there's no "experimental mathematics" (impossible)
Why not?
It isn't impossible for a mathematician to make a prediction for how some mathematical object would behave in a certain situation and then test his prediction in practice.

>>18851
No, that's not a prediction. A "prediction" in science means to run some numbers through a model of reality to reach some conclusion about how a real phenomenon will behave when experimented on under the same parameters. But mathematics doesn't have any real phenomena to predict with models and to run experiments on; it just has mathematical objects. There's no analog to empirical prediction in mathematics. If someone runs the first 10^30 naturals through the Collatz conjecture function then goes "*shrug* I guess the Collatz conjecture is true?", that person is not doing mathematics. That's not what the discipline is.

Now, empiricism is occasionally used in mathematics, specifically applied mathematics. Say you have some problem you need to solve and you find a paper from 1986 that would solve your problem, except no one has proven that the conjecture it uses is true for all R. But your domain space is not all of R, it's only, say, the first 2^256 naturals. After running some numbers you manage to figure out that if you exhaustively test the conjecture on a carefully picked subset of 2^32 integers, you have a 99% chance that the conjecture is true in your entire domain space, and this is good enough for your application. So you rent compute time on the cloud for one or two months and successfully prove that the conjecture holds for the subset you chose, and so conclude that it probably holds for 0 <= n < 2^256. To clarify: you're not actually any closer to proving the original conjecture from the paper. You've only managed to chip away at a (literally) infinitesimal portion of the problem.

>>18852
>But mathematics doesn't have any real phenomena to predict with models and to run experiments on; it just has mathematical objects.
But if mathematical objects aren't real, how can I see signs and traces of their existence everywhere? And why, after seeing them, am I supposed to conclude that mathematical objects don't exist when we do exactly the reverse for everything else?

>>18853
Because mathematics is an idea that exists in people's minds, and you're perceiving and interpreting the world using a mind that's already aware of mathematical memes. Like, you see two glasses holding 200 ml of water each, and you pour them into a third, empty glass and see that it now contains 400 ml. That makes intuitive sense, but it's an abstraction, and it's incorrect. First, during the pouring you invariably lost some water molecules to evaporation, and that's not even taking into account that the final volume may be measurably different if the third glass is at a different temperature. Second, while the mixing of liquids is modellable with (or interpretable as) addition, that doesn't mean that addition has literally taken place. Literally, was has happened in the physical realm? Some water molecules have moved from one place to another. At best we can say that they've moved generally closer, but that's really vague. At what point does addition take place? If I place the glasses next to each other, is that enough? The actual answer is, maybe. It depends on how you draw the analogy between the purely abstract idea of addition and what's supposed to happen in the real world.

Now, one valid question to ask is, if mathematics is so loosely coupled with reality, why is it that when mixing same liquids as above, the solution is close to the sum (at least if considering mass alone)? That's because addition was initially conceived to model precisely those kinds of situation. People saw a regularity in the world -- that if you put things together the total amount is equal to the sum of the separate amounts -- and thought of an abstraction that would let the reason about it. The reasons for the regularity are multiple; conservation of mass, first law of motion, etc. But it's not because mathematics suffuses the universe.

Simply put, mathematics is useful because we can't perceive reality in its rawest form, only through abstractions like "chair", "spoon", and "three". If we had the mind of a god we would just see the ultimate reality of whatever is in front of us and we would not need mathematics. We could just reason about the world in in the same physical and metaphysical rules that it follows, and we'd be nigh omniscient.

>>18854
Literally everything exists as an idea in people's minds... An idea, whose existence is the product of us noticing a system within the flow of our mind. And when we, normally, notice the existence of a new system like this, we give it a name and proclaim it a physical object. And yet, you insist we shouldn't do it with mathematics?
Mathematics, as a phenomenon, exists inside a human society and greatly influences its technological and scientific capabilities.
Mathematical objects, too...

>>18855
Everything else does not exist solely as an idea in people's minds. If you dispute this then please tell me where I can find literal, concrete mathematics in the real world. Is there a particle of mathematics? Can I collide the field axioms against the Peano axioms in a particle accelerator to see what happens? Can I build a chair out of the set of prime numbers and nothing else?

>>18856
Why are you ignoring the second part of my answer? It was composed to show you that math, also, does not exist solely as an idea in people's minds.
You can take a book filled with math, through it to some human society, and math from the book will physically interact with them.
Similar to how an apple is made of many particles, math is composed of many institutions and books and technology created with its help. They are its physical body.
And when you interact with its physical body, the idea of math forms in your consciousness, no different from how it is with every other physical phenomena. And if your idea says that math can maintain its existence at its current level with no material support, than your idea is wrong.
Now to the silly questions.
>Is there a particle of mathematics?
When people expected light to be continuous before learning that it is discrete, light wasn't considered not real.
>Can I collide the field axioms against the Peano axioms in a particle accelerator to see what happens?
Collide electromagnetism with gravity and you'll know the answer.
>Can I build a chair out of the set of prime numbers and nothing else?
The list of things you consider material but can't use for a chair approaches infinity; don't be like that.

>>18857
>You can take a book filled with math, through it to some human society, and math from the book will physically interact with them.
>Similar to how an apple is made of many particles, math is composed of many institutions and books and technology created with its help. They are its physical body.
Alright, you're giving me an answer composed of metaphors when I asked you to tell me where math can be found literally and concretely in the real world. I can't tell whether you don't realize you're doing or whether you I think I won't notice.
First of all, let's get this out of the way, mathematics is not "composed of institutions and books and technology". Mathematics is a system to deduce the non-contradiction of statements. If we must say that it is composed of anything, it's of axioms.

Institutions and society are human ideas. They would not exist if there were no human minds to believe in them.

A book may or may not be just an idea, depending on whether you're talking about its textual content or the physical object. The physical object is obviously physical, but doesn't contain mathematics. There's nothing you can do to it physically to extract the mathematics out of it (in the same way that you can pour out the contents of a bottle). You can read it, sure, but that doesn't change it physically.
The textual content does contain mathematics -- or rather, mathematical concepts -- but it's just an idea with no one-to-one correspondence to the real world. The content could be represented as a pattern of oxide particles on a metal platter, or as a pattern of colored pigment on a cellulose matrix. In other words, the textual content of a book is the same regardless of whether it's in ebook form or printed as a book. Any object that exists concretely could not exist as anything else other than what it is, without being something else.
Mathematics is not composed of the textual content of the books about it. You could burn all the books and erase all the hard drives and still reason mathematically.

Mathematics is certainly not composed of technology. What would that even mean?

>Now to the silly questions.
>>Is there a particle of mathematics?
>When people expected light to be continuous before learning that it is discrete, light wasn't considered not real.
>>Can I collide the field axioms against the Peano axioms in a particle accelerator to see what happens?
>Collide electromagnetism with gravity and you'll know the answer.
>>Can I build a chair out of the set of prime numbers and nothing else?
>The list of things you consider material but can't use for a chair approaches infinity; don't be like that.
You replied to the examples and not to the idea that the examples were meant to convey. Any thing that we can say exists concretely is either composed of matter or interacts with matter in some way (because if it didn't, we could not know about it). If mathematics is (or studies) a real phenomenon, then what is it? Where is it? Electromagnetism is detectable by the eyes; do we have an organ to detect mathematics in the universe?

>>18858
>Mathematics is a system to deduce the non-contradiction of statements.
And this system has a physical body. And when you interact with said physical body, you experience the idea of said system.
>Institutions and society are human ideas. They would not exist if there were no human minds to believe in them.
This is like claiming that cats don't exist and only their cells are real. A cell is a certain recognizable pattern within the flow of our mind. A cat is also a certain recognizable pattern. And both of them are as real as it gets. Even if you need a human to recognize their existence.
>Electromagnetism is detectable by the eyes; do we have an organ to detect mathematics in the universe?
Our eyes should be enough. You could look at, I don't know, a lightning bolt, and recognize it as electromagnetism, a sign of its existence and presence. You can know that electromagnetism is happening here.
Similarly, you can look at some writing on a blackboard and recognize it as math, a sign of its existence and presence. You can know that math is happening here.
This way, your encounter with math is as "literal and concrete" as your encounter with electromagnetism.
>Mathematics is certainly not composed of technology. What would that even mean?
Technology is designed to represent mathematical objects with... Ok, this idea might be a bit too complex, let's drop.

>>18859
>And this system has a physical body. And when you interact with said physical body, you experience the idea of said system.
Then you are agreeing that it is an idea, and that mathematics would not exist without people to have the idea? What are we arguing about, then?

>This is like claiming that cats don't exist and only their cells are real.
This is correct. A "cat" in an idea in a person's mind. This is what I was talking about being able to perceive reality in its rawest form. The delineation of the universe into distinct objects is a human-originated abstraction, separate from (but inspired by) ultimate reality. What that ultimate reality is, is difficult if not impossible to tell. At some level, we could that a "cat" is just some collection of subatomic particles that tend to consistently interact with each other over time, but even that is not entirely true.

>A cell is a certain recognizable pattern within the flow of our mind. A cat is also a certain recognizable pattern. And both of them are as real as it gets.
I disagree. Just like how the 200 ml glass of water was experiencing imperceptible changes in the configuration of its constituent matter, a cat is also experiencing such changes. A cat you pet today will have nothing in common with a cat you pet 10 years from now, despite you believing both are the same cat. That makes the cat a less real object than, say, an electron.

>Similarly, you can look at some writing on a blackboard and recognize it as math, a sign of its existence and presence. You can know that math is happening here.
>This way, your encounter with math is as "literal and concrete" as your encounter with electromagnetism.
This is the exact same problem as the distinction between a book and its contents. The eyes in this scenario are pretty irrelevant. I could take in the same message by having someone recite at me, and conversely, if I don't understand the mathematical notation then having eyes will not help me understand, even if I'm familiar with the concepts that the writing is meant to convey. Clearly the eyes are not the organs involved in the detection of math as a natural phenomenon.

>Technology is designed to represent mathematical objects with...
Well, I've already responded to this, then.
>You could burn all the books and erase all the hard drives and still reason mathematically.
Clearly technology is not the substance of mathematics, if you can destroy the former to no effect on the latter.

>>18860
>Then you are agreeing that it is an idea, and that mathematics would not exist without people to have the idea? What are we arguing about, then?
You're saying it's only true for mathematics. I'm saying this is true for every object that exists.
Whatever cannot influence your consciousness in any way does not exist for you. Whatever influences it systematically does exist and deserves a name.
>This is what I was talking about being able to perceive reality in its rawest form.
Its rawest form?
When some desire is present in your consciousness, energy shaped by that desire enters your body and flows through it.
This energy is what allows us to discuss phenomena that don't exist outside of our consciousness.
This desire-turned-energy is the source of all energy and matter, the rawest form of what you're calling reality.
You don't need godhood to understand this. Even if this understanding is the path to godhood.
>Clearly technology is not the substance of mathematics, if you can destroy the former to no effect on the latter.
You can destroy mathematics by attacking its physical body. You can damage it too.
Remove all books and institutions; will the idea of mathematics still form in your consciousness?
So, more physical than electromagnetism or gravity.
Also, if you erase all technology mathematics has helped develop, do you think it can preserve in this world at its current level without taking any damage?
>I could take in the same message by having someone recite at me, and conversely, if I don't understand the mathematical notation then having eyes will not help me understand, even if I'm familiar with the concepts that the writing is meant to convey.
Well, yeah? Mathematics can utilize many different things as its body. But if they aren't sufficient, it cannot exist.
>A cat you pet today will have nothing in common with a cat you pet 10 years from now, despite you believing both are the same cat.
You can't be serious. Come on.

>>18861
>I'm saying this is true for every object that exists.
Huh? Then how do humans exist? Humans are made of objects that exist, so if humans are required for those objects to exist, then there's a circular dependency.

>Whatever cannot influence your consciousness in any way does not exist for you. Whatever influences it systematically does exist and deserves a name.
I thought you were trying to argue that mathematics studies real phenomena. Now you're arguing that... I don't know, mathematical objects deserve names? They have names. That doesn't make them real in the same sense that the subjects of study of physics are real.

>Its rawest form?
>When some desire is present in your consciousness, energy shaped by that desire enters your body and flows through it.
>This energy is what allows us to discuss phenomena that don't exist outside of our consciousness.
>This desire-turned-energy is the source of all energy and matter, the rawest form of what you're calling reality.
>You don't need godhood to understand this. Even if this understanding is the path to godhood.
What? Are you on shrooms?

>You can destroy mathematics by attacking its physical body. You can damage it too.
>Remove all books and institutions; will the idea of mathematics still form in your consciousness?
>So, more physical than electromagnetism or gravity.
>Also, if you erase all technology mathematics has helped develop, do you think it can preserve in this world at its current level without taking any damage?
See, your problem is that you're confusing the symbolic manipulation game that is mathematics with the body of deduced theorems that have been proven throughout the years. Your question is like asking if burning all the English books would make people unable to communicate in English. It'd be a shame, because we'd have to re-write those books, and probably some theorems would be forgotten, but we wouldn't lose the ability to do math -- that is, to apply symbolic manipulation to abstract statements. That's all mathematics is. Well, sometimes it's also a game of rhetoric.

Also, what do you mean "more physical than electromagnetism or gravity"?

>Well, yeah? Mathematics can utilize many different things as its body. But if they aren't sufficient, it cannot exist.
That's precisely why it's not real. A hydrogen atom (1 proton, 1 neutron, 1 electron) cannot exist in multiple forms. Gravity cannot be transmitted orally. A hydrogen atom is not a representation of something else, it is the thing that it is. If you write "1+1=2" on a blackboard, all you did was scratch some chalk on a surface. The pattern of symbols is not itself mathematics or mathematical in nature. It doesn't even have any intrinsic meaning. The idea of addition does not become real in any sense by you simply writing down an equation. I think you have a real hard time distinguishing the thing from its representations.

You're still to answer my question: If mathematics is (or studies) a real phenomenon, then what is it? Where is it?

>You can't be serious. Come on.
Ship of Theseus. The atomic content of a living being is in constant flux.

>>18862
>Then how do humans exist?
Humans exist because they can interact with your consciousness.
And yes, this existence is a bit circular, in that something can't exist unless it is observed and nothing can be observed unless it exists, but this doesn't matter for us here.
Ultimately, any object only exists for you if it can interact with your consciousness. The end.

>I thought you were trying to argue that mathematics studies real phenomena.
Yes. By showing you that it has a physical body it uses to interact with the physical world, no different from any other physical phenomenon.

>What? Are you on shrooms?
I am perfectly lucid. If you carefully examine how your consciousness interacts with your body, you will notice a source of energy that is beyond the physical world. And once you notice it, everything becomes clear.

>Your question is like asking if burning all the English books would make people unable to communicate in English.
But of course, you'd also need to damage every English-speaking brain. And yes, English will vanish and die.
You can destroy a language by destroying everything it uses to interact with the physical world. You can destroy math the same way.

>but we wouldn't lose the ability to do math
So now you're defining math as an ability inherent to a healthy human body? It doesn't matter. For what I said should be true for every definition of math.
When math is defined like this, its "body" is the structure of the brain of every healthy human.
Kill them all, or change the structure - destroy the body math uses to exist - and math will vanish from this world.

>Also, what do you mean "more physical than electromagnetism or gravity"?
They are much harder to destroy. Thus, less physical. Math is much closer to an apple or a chair than to gravity or electromagnetism in this regard.

>A hydrogen atom (1 proton, 1 neutron, 1 electron) cannot exist in multiple forms.
There are different types of protons, neutrons, and electrons, and their amounts in an atom often vary. All of them also have various different properties that change over time. It doesn't matter, though.
You can notice physical signs of a certain hydrogen atom. You can unite these signs into a single idea, the idea of a hydrogen atom. And, guess what? I can do the same with math.
Then, you can notice a previously unnoticed sign that you decide to attribute to the same atom. And I can do the same with math.
And if you find a different hydrogen atom, with different properties, you won't deny that it's still a hydrogen atom. And I can do the same with math.

>If mathematics is (or studies) a real phenomenon, then what is it? Where is it?
Math creates and then studies mathematical objects. Their being artificially created doesn't make them any less real.

>Ship of Theseus. The atomic content of a living being is in constant flux.
It is. But living beings still exist. Be real.
Because if you refuse to accept it, then your use of words is so different from other people that understanding them is impossible for you, and communication becomes completely pointless.

>>18863
> If you carefully examine how your consciousness interacts with your body, you will notice a source of energy that is beyond the physical world.
No.

>You can destroy math [by damaging every math-doing brain].
Then you're agreeing that math is just an idea with reality independent of human minds. I ask again: What are we arguing about?

>So now you're defining math as an ability inherent to a healthy human body?
No, that's not what I said. What I said was that if you burn all the books and erase all the hard drives, people wouldn't lose the ability to do math. I don't know how you got from there to "math is defined as an ability inherent to healthy human bodies".

>They are much harder to destroy. Thus, less physical.
This is a very strange way to use "physical". They're literally half of the fundamental interactions.

>Math creates and then studies mathematical objects. Their being artificially created doesn't make them any less real.
Yes, it does. They are literally less real than physical objects, because they have fewer properties of real objects.

Does the object exist?
Gravity: yes
Matter: yes
Space: yes
Prime numbers: yes

Does the object exist independently of other objects? I.e. is it intrinsic to the universe?
Gravity: yes
Matter: yes
Space: yes
Prime numbers: no

Mathematics ceases to exist if there's no one to think about it, just like a file ceases to exist if you delete it. This is a much more tenuous form of existence than that of, say, a spoon.

>It is. But living beings still exist.
You moved the goalpost. Let me quote myself.
>A cat you pet today will have nothing in common with a cat you pet 10 years from now, despite you believing both are the same cat.
The point was, "a cat" that you perceive as a recognizable pattern is just an abstraction in your head. You perceive a continuity of the animal through time, but this is just an illusion of your senses because, again, you can't see reality in its rawest form. You can't see the cat exhale its little cat particles every time it breathes. The continuous turn-over of its matter means that your idea of "cat" is at least somewhat decoupled from the real state of affairs, so what does it even mean to say that "the cat is real"? "The cat" as in, the idea of it is real in your head? Yeah, sure. "The cat" as in, a single, sharply-delineated entity that exists continuously through time? That's far more dubious. And now I get to this other quote:
>Math is much closer to an apple or a chair than to gravity or electromagnetism in [that it can be destroyed].
This ties in well, because just like how the cat is a illusion of your senses, so is an apple or a chair. If you eat an apple you don't utterly obliterate the apple. All you do is transform the matter it's composed of into something else. The "apple" ceases to exist because it only existed as a distinct object in your mind, so the particular configuration of matter that composed the apple was destroyed, even though its matter wasn't.
Math, however, is an idea. Where an apple has substance that can be incorporated into other objects, math has no substance. If it's forgotten, it is utterly obliterated, with nothing that remains.

>>18864
>No.
Yes. Imagine a mountain. This mountain can't be found anywhere in this world. Yet it exists.
Suppose you need to describe this mountain. For this, your body would have to act in accordance with its structure. Which means the mountain, wherever it is, would have to influence your body. And such influence requires energy.
See? For you to describe the mountain, some energy would have to flow from wherever the mountain is into your body. Energy, whose properties are decided by the environment of that... Location. As easy as.

>Then you're agreeing that math is just an idea with reality independent of human minds.
Agreeing? I can't even understand what this sentence is supposed to mean.
But no. If you define math as an ability possessed by a human brain, dependent on its structure for its existence, then it isn't "just an idea."

>What I said was that if you burn all the books and erase all the hard drives, people wouldn't lose the ability to do math.
But their ability would be greatly reduced. Meaning you've damaged math by destroying a part of its body.
And if you damage the parts of their brains that were marked by math, their ability would be completely erased. Meaning you've killed math by fully destroying its body.
Even if it can be built again in the future. Similar to how a chair can be destroyed. Then built again in the future.

>Does the object exist independently of other objects?
>Gravity: yes
How about no? Without energy and matter, there is no gravity. At the very least.

>Mathematics ceases to exist if there's no one to think about it, just like a file ceases to exist if you delete it.
No. If you include a book as a part of its physical body, then it doesn't cease to exist. Through this book, math keeps interacting with the environment independent of your thoughts. Through this book, its properties keep changing over time. Even without any human involvement.

Feynman on Scientific Method
https://www.youtube.com/watch?v=EYPapE-3FRw
If it disagrees with experiment, then it's wrong. There is all that is to it.

>>18866
And then you reach the level when experiments become physically impossible to organize, and either give up or switch to predictive power.
Then again, predicting future with a theory and testing if it comes true can be seen as an experiment, some people just have reasons to not recognize it as such.

File 177013858171.jpg - (592.18KB , 2560x1841 , pipe.jpg )

>>18865
>Yet it exists.
You're using "exists" in a way that is different from the way people normally use the word. Like I said before, you have a hard time distinguishing a thing from its representation.
If I see an orange and I draw it, does the orange exist? Yes.
If I draw a vampire, does the vampire exist? No. The drawing of the vampire exists, as does the idea of it in my head, but that idea has no correspondence in reality.

>>18868
>You're using "exists" in a way that is different from the way people normally use the word.
What other way? We say a thing exists either because it systematically creates a certain pattern within our consciousness, or because it systematically interacts with some "common matter" we take as "the base of existence" instead.
Mental objects exist under both definitions. And "math" and "numbers" aren't even mental objects...

>If I see an orange and I draw it, does the orange exist? Yes.
>If I draw a vampire, does the vampire exist? No. The drawing of the vampire exists, as does the idea of it in my head, but that idea has no correspondence in reality.
Not quite?
The orange defined as a certain part of the image exists, it interacts with our consciousness and "common matter" in a systematic way. The orange defined as a certain idea within a human society also exists, it interacts with our consciousness and "common matter" in a systematic way. And an orange defined as a fruit that grows on a certain type of tree...
Similarly. The vampire defined as a certain part of the image exists. And the vampire defined as a certain idea within a human society also exists. Even if a vampire defined as a certain type of a magic being might not exist (I hope? I was forced to accept magic must be real recently, but magic vampires are still stupid).

>>18869
>We say a thing exists either because it systematically creates a certain pattern within our consciousness, or because it systematically interacts with some "common matter" we take as "the base of existence" instead.
What are you on about?? So a thing can fail to interact with matter in any way whatsoever, but somehow create ideas in people's minds? Are you a Platonist? Do you believe that when you form an idea in your mind you're accessing a world of pure ideas where everything that's ever been or ever will be thought exists?

No, that's not what people mean when they talk about things existing. If I say "vampires don't exist", that's a very different statement from "the idea of vampires doesn't exist". The latter is a contradictory statement (how am I formulating it without at least assigning the word some meaning?). What I mean is that there's nothing I can find in the real world to which the word "vampire" refers. Just like how the place at 91° S 0° E doesn't exist because the coordinates don't refer to anything, vampires don't exist because the word (and its idea) has no correspondent in reality. If we must concede that "vampires exist" because "the idea of vampires exists" then that makes language a much less useful tool, because it's unable to distinguish imaginary things from real things. Like, imagine this exchange:
-Hey, do you have a torx screwdriver?
-It's in the kitchen drawer.
(...)
-I just looked and there was nothing in the drawer.
-Yes, there is. There's all sorts of tools there.
-What are you talking about, dude? I have drawer here in my hand. It was completely empty.
-I imagine the drawer as having a torx screwdriver in it, so therefore there is one there. That's how I use "there is". Also, it's still in the kitchen, not in your hand.

Likewise, mathematical objects don't exist in this sense. There's no 2 anywhere in the universe as a distinct thing unto itself. There are pairs of things, there are ideas in people's minds, and there are symbols written down in various forms that refer to that idea, but there's no 2. If you actually are a Platonic realist this is as far as I'm going with this conversation. I have no interest in entertaining theories of metaphysics.

>>18870
>>We say a thing exists either because it systematically creates a certain pattern within our consciousness, or because it systematically interacts with some "common matter" we take as "the base of existence" instead.
>What are you on about?
I'm showing you how math and numbers exist under the two most common definitions of existence.

>If I say "vampires don't exist there"
It could mean that vampires don't exist on some planet, or on some image, or in some culture.

>how am I formulating it without at least assigning the word some meaning?
Because the idea might exist in your own culture, but not in some other country.

>Likewise, mathematical objects don't exist in this sense.
Which, again, is irrelevant. Since we only need for them to exist.

I'm done.

You guys sound like retards but in the unlikely case that you're not, consider what Kurt Godel held about math (which is what I personally align with) is that He was a mathematical platonist. In that our understanding of mathematics is limited, it's like we're interacting with the shadows of it, however it is a real thing out there so to speak and we are discovering it, not inventing it.

As well as many other smart ideas he had about mathematics, but I can't be bothered to read everything you guys wrote here so I'm not sure what you're even disagreeing on, but whatever it is, you're disagreement is not elegant on either of you's part so I'm reluctant to engage even if I agree with one of you.

>>18873
That reminded me, "Godel, Escher, Bach: an Eternal Golden Braid" was a good read. Also, yeah I'm in the same camp.

>>18873
Something that has the potential to be created is like an empty space that can be filled. An emptiness shaped by its borders, its existence is similar to a hole. And a hole whose borders are made of something often assumed to be necessary for us to exist may appear unusually special... Regardless.
Mathematics, at its core, is just information. Information that can be created and destroyed. It isn't much different from knowing that a river can be crossed by making a bridge and best practices for making one.
And of course, different ways to encode and process this information are something we absolutely can study and experiment with. As well as its natural properties.

>>18875
>Information
>The information of a heart falling into an abyss
>The sound of a heart falling into an abyss
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