Is math real?

For the discussion of math. Duh.

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Re: Is math real?

Postby doogly » Tue Mar 01, 2016 8:56 pm UTC

And people get weird about math for some reason.

Is soccer real?
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Re: Is math real?

Postby PsiSquared » Wed Mar 02, 2016 3:48 am UTC

jewish_scientist wrote:
PsiSquared wrote:
A weak point in this philosophy is that this means that the sentences, "I put an infinite sum into the campfire," and "I need to take the third root of my car," are logically and grammatically valid even though they are really confusing/ meaningless.


I don't really see this as a problem.

Just because mathematical objects are not physical objects, does not put their reality in to question.

Besides, you can't put gravity in your car either (not directly, anyway).

What I mean is, if I were to play Devil's Advocate and argue against this position, this is the area I would attack.


I got that.

I'm simply saying that even for a devil's advocate, it is hardly a promising line of attack.

jewish_scientist wrote:In 100 C.E., did calculus exist?


That's a bit like asking whether a stone statue existed in the rock before the sculptor made it or not.

The platonic structures that "calculus" deals with, always existed. However, the specific grouping of these specific structures into a coherent whole is a man-made thing.

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Re: Is math real?

Postby doogly » Wed Mar 02, 2016 4:26 am UTC

Platonism is the worst.
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Re: Is math real?

Postby jewish_scientist » Wed Mar 02, 2016 4:49 pm UTC

doogly wrote:No. Did you?

Depends on how you define 'you'.

LaserGuy wrote:
jewish_scientist wrote:In 100 C.E., did calculus exist? No one knows about it; no one has even heard the word. I am very curious as to what your answer will be.


Yes. Elements that make up modern calculus can be traced to ancient times. They didn't necessarily have all of the tools or language to describe it that we do today, of course, nor did they have a formalized system to describe all of the concepts.

That is kind of like saying that cars existed in 643 B.C.E., because the materials that make up cars existed in 643 B.C.E.

PsiSquared wrote:The platonic structures that "calculus" deals with, always existed. However, the specific grouping of these specific structures into a coherent whole is a man-made thing.

Here is an interesting hypothetical: If Earth is the only place where life exists, and we destroy all life on Earth with nuclear weapons, then does 1+1=2?
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Re: Is math real?

Postby doogly » Wed Mar 02, 2016 4:59 pm UTC

jewish_scientist wrote:
doogly wrote:No. Did you?

Depends on how you define 'you'.

Under what definition would you have existed in the year 100?
I certainly did not exist then. That sounds crazy. I will also not exist in a hundred years (unless medicine does some very exciting things.)
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Re: Is math real?

Postby jewish_scientist » Thu Mar 03, 2016 5:02 pm UTC

If you define self as your soul, and define souls so that they are immortal, then I could have existed back then.
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Re: Is math real?

Postby doogly » Thu Mar 03, 2016 5:14 pm UTC

If you believe in souls then your commitment to reality is already quite loose.
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Re: Is math real?

Postby moiraemachy » Thu Mar 03, 2016 10:45 pm UTC

PsiSquared wrote:
doogly wrote:We develop mathematical language based on what's important. I can write gravity as G=T and electromagnetism as d*F=J because we have loaded a whole lot into these symbols.

Fair point.

But still, even if you incorporated all the defintions along the way, I doubt the resulting statement would be more than a few pages long.
Here's Maxwell's "On Faraday's Lines of Force". Spoiler: it isn't 4 lines long.

Mapping physical concepts to your immediate reality is hard: force in newtonian mechanics is a number that we get from multiplying two other numbers that we assign to some things is certain situations by using an informal methodology filled with buts and ifs. You know these forces are equal because stuff doesn't move when you push it except wait that's torque this time. Force is how many of those things balance that other thing except how do you know the balance is right oh yes you can exchange the sides and it remains the same, wait that's not force that's mass because gravity and stuff, I guess force is the thing it is doing to the plates of the balance but wait it is torque again now damn also you didn't exchange those things right they must be at the same distance from the balance's pivot. Force is how much that spring is displaced time the constant of the spring's number k except the spring isn't really linear also how did you find out k? yes with the things in the balance and gravity and torque but since the manufacturer said it is reliable and scientist aren't yelling at me I can trust it I guess?... wait, how do I know those things you put in the balance have the same mass again?

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Re: Is math real?

Postby PsiCubed » Fri Mar 04, 2016 8:40 am UTC

moiraemachy wrote:
PsiSquared wrote:
doogly wrote:We develop mathematical language based on what's important. I can write gravity as G=T and electromagnetism as d*F=J because we have loaded a whole lot into these symbols.

Fair point.

But still, even if you incorporated all the defintions along the way, I doubt the resulting statement would be more than a few pages long.
Here's Maxwell's "On Faraday's Lines of Force". Spoiler: it isn't 4 lines long.


It is also over 90% fluff, most of which has absolutely nothing to do with physics. So all in all - a very poor example of what you were trying to prove.

Mapping physical concepts to your immediate reality is hard: force in newtonian mechanics is a number that we get from multiplying two other numbers that we assign to some things is certain situations by using an informal methodology filled with buts and ifs. You know these forces are equal because stuff doesn't move when you push it except wait that's torque this time. Force is how many of those things balance that other thing except how do you know the balance is right oh yes you can exchange the sides and it remains the same, wait that's not force that's mass because gravity and stuff, I guess force is the thing it is doing to the plates of the balance but wait it is torque again now damn also you didn't exchange those things right they must be at the same distance from the balance's pivot. Force is how much that spring is displaced time the constant of the spring's number k except the spring isn't really linear also how did you find out k? yes with the things in the balance and gravity and torque but since the manufacturer said it is reliable and scientist aren't yelling at me I can trust it I guess?... wait, how do I know those things you put in the balance have the same mass again?


You seem to be very intent on needlessly complicating everything. In reality, Newtonian mechanics are an exercise in simplicity:

1. F=ma (or more fundamentally: p=mv and F=dp/dt)
2. The gravitational force between two objects is MmG/r2.

In the F=ma equation, acceleration is a very straightforward concept: the rate of change in velocity. Mass is less intuitive, but nevertheless it can be rigorously defined by rule #2: The mass of an object is the acceleration induced by the object's gravitational pull at a unit distance (assuming a unit system where G=1), and it never changes (in Newtonian mechanics).

That's pretty much it.

Torque is nothing more than shorthand for r×F. You don't really need it to explain how balance scales work. All you need to do is to write down the forces which are applied to each weight (tension and gravity) and solve the equations, taking into account the geometrical constraint provided by the length of the arms of the scale. The concept of Torque gives you an alternative, faster and more elegant way to reach the same conclusion, but it isn't really necessary.

And F=kx isn't a fundamental law of Newtonian mechanics. It is an approximate property of springs which we observe empirically: Acceleration of an object tied to a spring is proportional to displacement. This is a nice and very useful bit of information which also provides us with a great practical way to measure weight (and therefore - mass). But neither weight nor mass are defined by the behavior of springs.


doogly wrote:If you believe in souls then your commitment to reality is already quite loose.


I'm curious: What is this concept of "soul" you speak of, when you argue against its existence? And what alternative definition of "self" do you propose?

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Re: Is math real?

Postby doogly » Fri Mar 04, 2016 1:34 pm UTC

PsiCubed wrote:
doogly wrote:If you believe in souls then your commitment to reality is already quite loose.


I'm curious: What is this concept of "soul" you speak of, when you argue against its existence? And what alternative definition of "self" do you propose?

EDITED TO ADD: I'm PsiSquared with a new username.

The soul is a popular thing in Abrahamic traditions, they have a pretty rich literature on it which can be interesting for some historical reasons if you happen to be into that. It can be fun. Taking these things seriously is crazy cakes though.

The self is your skin and spine and brain and liver and some extra bits. Maybe you can do without some of the bits. It's the whole thing.

These can't possibly be sincere questions, can they?
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Re: Is math real?

Postby moiraemachy » Fri Mar 04, 2016 4:30 pm UTC

PsiCubed wrote:You seem to be very intent on needlessly complicating everything. In reality, Newtonian mechanics are an exercise in simplicity:

1. F=ma (or more fundamentally: p=mv and F=dp/dt)
2. The gravitational force between two objects is MmG/r2.
These two, by themselves, say absolutely nothing about geometric constraints, or how forces are transferred through bodies (which you need in order to use torque in that particular example). Actually, you didn't say anything about forces other than gravity, not even the third law. Actually, in order for angular momentum to be conserved, you don't just need the third law: you need forces between objects to be in the same direction as the distance between them. Really, all you can get from these two statements is predict the shape of orbits.

Which, by the way, is hard to map to your immediate reality: you need telescopes and ways of recording time precisely and sometimes account for the delay light takes to get here.

My point is, maybe you linked all this context to these laws in your mind (I did), and that seems to be an useful way to think. But to suggest that all this context is contained in the statement of the laws is mystification.

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Re: Is math real?

Postby jewish_scientist » Fri Mar 04, 2016 4:43 pm UTC

doogly wrote:
PsiCubed wrote:
doogly wrote:If you believe in souls then your commitment to reality is already quite loose.


I'm curious: What is this concept of "soul" you speak of, when you argue against its existence? And what alternative definition of "self" do you propose?

EDITED TO ADD: I'm PsiSquared with a new username.

The soul is a popular thing in Abrahamic traditions...

I do not know a lot about Eastern religions, so I apologize if I misrepresent anything.
According to Hinduism, when a person dies they are born again in a new body, and no longer remember their previous life. This means that Hinduism's definition of self is not dependent on anything that is physical; there must be a non-physical entity that is what constitutes the self. This could be called the person's soul. In addition, the Allegory of the Cave demonstrates that Plato believed the self was independent of the body; rather, it is dependent on the cognitive activities of the person. This could be called the person's mind. It is clear that dualism (the school of philosophy that hold that man is made of a physical part, and a non-physical partl) has roots in cultures besides Judaism.

...Taking these things seriously is crazy cakes though.

The self is your skin and spine and brain and liver and some extra bits. Maybe you can do without some of the bits. It's the whole thing.

These can't possibly be sincere questions, can they

Almost every famous philosopher has taken this question seriously. This is because so much is dependent on what the self is. If is morally wrong to kill innocent people, then is it immoral to harvest organs from a human that is "brain dead"? The function of the government is to protect the rights of its people; if a person dies, do they still have right that the government can protect? If people can give consent, and drunk people cannot consent, then at what point does a human stop being a person? What is a person's consciousness? If a person is sleeping, and a person is running in a dream, then would Leibniz's law suggest that the person who is asleep is not the same person who is running in the dream.
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Re: Is math real?

Postby LaserGuy » Fri Mar 04, 2016 6:18 pm UTC

jewish_scientist wrote:Almost every famous philosopher has taken this question seriously. This is because so much is dependent on what the self is. If is morally wrong to kill innocent people, then is it immoral to harvest organs from a human that is "brain dead"? The function of the government is to protect the rights of its people; if a person dies, do they still have right that the government can protect? If people can give consent, and drunk people cannot consent, then at what point does a human stop being a person? What is a person's consciousness? If a person is sleeping, and a person is running in a dream, then would Leibniz's law suggest that the person who is asleep is not the same person who is running in the dream.


Spoiled for OT:

Spoiler:
If is morally wrong to kill innocent people, then is it immoral to harvest organs from a human that is "brain dead"?


I'm not sure what the first clause has to do with the second.

The function of the government is to protect the rights of its people; if a person dies, do they still have right that the government can protect?


What rights do you think that the dead have? In general, I'd say that the dead have no rights to speak of.

If people can give consent, and drunk people cannot consent, then at what point does a human stop being a person?


I think you're confusing legal personhood with consciousness.

If a person is sleeping, and a person is running in a dream, then would Leibniz's law suggest that the person who is asleep is not the same person who is running in the dream.


There is no person running in the dream. There is a person who is asleep, and their brain is conducting a simulation of the act of running. The runner is no more of a person than a character in a book is a person.

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Re: Is math real?

Postby jewish_scientist » Mon Mar 07, 2016 3:22 pm UTC

This is really long, so I put it in a spoiler.
Spoiler:
If is morally wrong to kill innocent people, then is it immoral to harvest organs from a human that is "brain dead"?

I'm not sure what the first clause has to do with the second.

If I left the word innocent out, then someone could argue that it is moral to kill some people; therefor the first clause is wrong. However, no one would argue that it is moral to kill innocent people. I just wanted to side-step that whole conversation.

The function of the government is to protect the rights of its people; if a person dies, do they still have right that the government can protect?

What rights do you think that the dead have? In general, I'd say that the dead have no rights to speak of.

You may not believe it, but there actually are some doctors who say that a person's right to decide what happens to their body ends with death; they are therefor allowed to use corpses to teach medical students without having to ask for anyone's consent. The same reason is why two museum exhibits which featured actually human bodies become controversial.

If people can give consent, and drunk people cannot consent, then at what point does a human stop being a person?

I think you're confusing legal personhood with consciousness.

The question I asked basically boils down to how does personhood compared to consciousness.

If a person is sleeping, and a person is running in a dream, then would Leibniz's law suggest that the person who is asleep is not the same person who is running in the dream.

There is no person running in the dream. There is a person who is asleep, and their brain is conducting a simulation of the act of running. The runner is no more of a person than a character in a book is a person.

That is an interesting answer. Are you saying that the self is defined solely in terms of the physical body?
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Re: Is math real?

Postby LaserGuy » Mon Mar 07, 2016 8:00 pm UTC

jewish_scientist wrote:This is really long, so I put it in a spoiler.


Spoiler:
If is morally wrong to kill innocent people, then is it immoral to harvest organs from a human that is "brain dead"?

I'm not sure what the first clause has to do with the second.


If I left the word innocent out, then someone could argue that it is moral to kill some people; therefor the first clause is wrong. However, no one would argue that it is moral to kill innocent people. I just wanted to side-step that whole conversation.


It's just not obvious to me how the two clauses are connected. I agree that it is morally wrong to kill innocent people, but if someone is already dead, then I do not have a problem in principle with harvesting their organs.

You may not believe it, but there actually are some doctors who say that a person's right to decide what happens to their body ends with death; they are therefor allowed to use corpses to teach medical students without having to ask for anyone's consent. The same reason is why two museum exhibits which featured actually human bodies become controversial.


Yes, we have certain rules in place governing how bodies are disposed, and likewise how the properties of the dead are dispersed. There's an old thread in SB that goes into the topic of mandatory organ donation in excruciating detail, so I don't think there's much benefit to rehashing that argument here. Generally speaking, I have no problem with the idea that the default option for your organs should be to donate them or put them to some other productive use, given that pretty much all of the current burial methods we use are, at best, wasteful, and at worst, actively harmful to the environment if nothing else. If people take particular exception to this default, allowing them to opt out is a satisfactory way of dealing with it. It is certainly useful to have a legal framework for dealing with the property (including the body) of a deceased person. From a legal point of view, it is worth noting that burial rights are conferred to the next of kin, not to the deceased directly.

The question I asked basically boils down to how does personhood compared to consciousness.


I mean here very strictly the legal definition of personhood. That is, a person is legally a person as long as they are alive (for whatever definition of alive is appropriate to your jurisdiction). During that period, that person may or may not be conscious at any given time, and thus may not be able to given informed consent to various activities.

There is no person running in the dream. There is a person who is asleep, and their brain is conducting a simulation of the act of running. The runner is no more of a person than a character in a book is a person.


That is an interesting answer. Are you saying that the self is defined solely in terms of the physical body?


Yes.

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Re: Is math real?

Postby PsiCubed » Tue Mar 08, 2016 12:49 am UTC

doogly wrote:The soul is a popular thing in Abrahamic traditions, they have a pretty rich literature on it which can be interesting for some historical reasons if you happen to be into that. It can be fun. Taking these things seriously is crazy cakes though.

These can't possibly be sincere questions, can they?


Yes, they are. And I'm asking these questions because people (both believers and non-believers) tend to use words like "soul" and "self" without actually stopping to think what they mean by it.

Case in point: Your statement of "the soul is a popular thing in Abrahamic traditions" is not a definition. I'm still at a complete loss in figuring out what is the exact "thing" you claim does not exist.

The self is your skin and spine and brain and liver and some extra bits. Maybe you can do without some of the bits. It's the whole thing.


Well, the "whole thing" changes all the time. Cells die and atoms are replaced... So what, exactly, is it that makes you "you"?

Nobody knows. Philosophers have been debating these issues for millennia, and there's still no consensus about the matter.

moiraemachy wrote:These two, by themselves, say absolutely nothing about geometric constraints, or how forces are transferred through bodies (which you need in order to use torque in that particular example). Actually, you didn't say anything about forces other than gravity, not even the third law.


You're right about the 3rd law. I should have added it to my list.

As for the other things you've said: Newton's theory was never meant to be a complete theory. Things like the laws of friction or F=kx are, really, nothing more than empirical (and approximate) laws. To actually derive something like F=kx from first principles, you need to delve into the structure of matter and the laws of electromagnetism, which was impossible in Newton's time.

Really, all you can get from these two statements is predict the shape of orbits.

Which, by the way, is hard to map to your immediate reality: you need telescopes and ways of recording time precisely and sometimes account for the delay light takes to get here.


It isn't "hard" to do these things. The steps required are pretty simple, and there aren't that many of them.

Perhaps what you meant to say is that doing this is counter-intuitive. And this is true. The laws of nature don't really jive with what we call "common sense". They do - however - fit well to our mathematical models.


My point is, maybe you linked all this context to these laws in your mind (I did), and that seems to be an useful way to think. But to suggest that all this context is contained in the statement of the laws is mystification.


I agree.

What I'm saying here is, that this "context" doesn't take as much additional space as you seem to think it does.

Sure, you can't really explain Maxwell's theory of electromagnetism in one Tensor equation. But you don't really need 76 pages, either. And even if you did need 76 pages, that's still incredibly compact when compared to the portion of the universe these pages describe.
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Re: Is math real?

Postby jewish_scientist » Wed Mar 09, 2016 1:59 pm UTC

LaserGuy wrote:
There is no person running in the dream. There is a person who is asleep, and their brain is conducting a simulation of the act of running. The runner is no more of a person than a character in a book is a person.


That is an interesting answer. Are you saying that the self is defined solely in terms of the physical body?


Yes.

That is why we disagree on many things; you are using a different definition of self than me. Unless one of us is willing to change their mind on what the self is for the purposes of this conversation, there is not really anything to talk about anymore. Still, this has been interesting. This website has a lot of thought experiments on these topics, in case you were interested. I did all of them except for "Peter Singer & The Drowning Child" (I hate Peter Singer), and "In The Face Of Death" (read the first question).
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I asked this question earlier, but I do not think anyone gave me an anwser: If Earth is the only place where life exists, and we destroy all life on Earth with nuclear weapons, then does 1+1=2?
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Re: Is math real?

Postby doogly » Wed Mar 09, 2016 2:50 pm UTC

Yeah, if you have non physical selfs running around, there may need to be another subforum in which to entertain the nonsense.

jewish_scientist wrote: If Earth is the only place where life exists, and we destroy all life on Earth with nuclear weapons, then does 1+1=2?

If we destroy all life on earth, does Kane recognize the sled at the end of the movie?
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Re: Is math real?

Postby PsiCubed » Wed Mar 09, 2016 5:51 pm UTC

doogly wrote:Yeah, if you have non physical selfs running around, there may need to be another subforum in which to entertain the nonsense.


Oh, I agree that everything is physical in the end. The word "supernatural" is a contradiction of terms, since everything that happens in the world is - by definition - natural.

Then again, modern physics has shown us that "physical" does not mean what we used to think it means. The solidity of the table in front of you is nothing more than an illusion created by countless quantum fields in flux. To tie this line of conversation back to the original topic of this thread: We have no idea what's "really out there", besides the mathematical equations that govern physical law.

So saying "the self is physical" - while true - doesn't get us anywhere. And it certainly doesn't mean that the self is forever tied to a single human body, or gives us any clue regarding what happens to it after the body dies. We can't even begin to investigate these questions scientifically yet, because we don't yet have a proper definition of "self" and "consciousness".

In short: nobody here has a definite answer to these questions, including you. So you might show a little more respect to differing opinions on the matter... at least until science manages to unlock these secrets (which will probably take at least half a century).

jewish_scientist wrote: If Earth is the only place where life exists, and we destroy all life on Earth with nuclear weapons, then does 1+1=2?


I really don't get this question. Why wouldn't it be?
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Re: Is math real?

Postby doogly » Wed Mar 09, 2016 7:32 pm UTC

PsiCubed wrote:And it certainly doesn't mean that the self is forever tied to a single human body, or gives us any clue regarding what happens to it after the body dies. We can't even begin to investigate these questions scientifically yet, because we don't yet have a proper definition of "self" and "consciousness".

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Re: Is math real?

Postby LaserGuy » Thu Mar 10, 2016 12:49 am UTC

jewish_scientist wrote:
LaserGuy wrote:
There is no person running in the dream. There is a person who is asleep, and their brain is conducting a simulation of the act of running. The runner is no more of a person than a character in a book is a person.


That is an interesting answer. Are you saying that the self is defined solely in terms of the physical body?


Yes.

That is why we disagree on many things; you are using a different definition of self than me. Unless one of us is willing to change their mind on what the self is for the purposes of this conversation, there is not really anything to talk about anymore. Still, this has been interesting. This website has a lot of thought experiments on these topics, in case you were interested. I did all of them except for "Peter Singer & The Drowning Child" (I hate Peter Singer), and "In The Face Of Death" (read the first question).



PsiCubed wrote:So saying "the self is physical" - while true - doesn't get us anywhere. And it certainly doesn't mean that the self is forever tied to a single human body, or gives us any clue regarding what happens to it after the body dies. We can't even begin to investigate these questions scientifically yet, because we don't yet have a proper definition of "self" and "consciousness".


Well, there are certainly a lot of things we can say about the self and consciousness. A few highlights:
-The self is intimately related to the brain. If the brain is damaged or altered in some way, it has direct consequences on the self. Depending on the nature of the incursion, this may or may not be reversible. There's several infamous examples of people who spontaneously became paedophiles as a result of brain tumors. We know that traumatic injury to the brain can result in significant changes to personality. We know that toxicological effects can lead to changes in memory and personality. There is no guarantee that any of the above effects are reversible.
-We know that memory is stored in the brain, and changes in the brain can result in changes to memories.
-We know that the self can be "split". Injury to the brain can result in the emergence of different personalities in an individual with different beliefs, values, and memories. In one famous example, a split brain patient's right brain believed in God, while his left brain was an atheist. The personalities are unaware of each other's existence, and confabulate memories on the fly to explain the behaviours of the other half.
-We know that dreams are a property of the brain, because stimulation of the brain can induce dreams.
-Likewise, we have the capacity, albeit only a very limited one at this point in time, to be able to figure out what someone is thinking about solely by looking at their fMRI scan.
-We know that stimulation, injury, or toxicology of the brain can also affect emotions.
-So called "near death experiences" and "out of body experiences" can be induced by electrical stimulation of the brain and/or toxicological effects.

If there's a non-physical part of consciousness or the self, whatever that means, we don't have any indication of what function it would have. The brain seems sufficient to explain consciousness, beyond the acknowledgement that the brain is profoundly complex and this field of research is still largely in its infancy.

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Re: Is math real?

Postby PsiCubed » Thu Mar 10, 2016 3:55 am UTC

Everything you said is true... under normal circumstances.

But consider the following scenarios:

1. I replace your neurons, one-by-one and one-step-at-a-time, with mechanical devices that simulate them perfectly. Will you still be "you"? (probably yes)
2. I transfer your brain-state into a computer and destroy the original body. Are you dead, or do you still live inside the computer?
3. I copy your brain-state into a computer and leave the original body and brain untouched. Which of the copies is "you"? Both of them? None of them?
4. I do #3 with a remote scanner and without your knowledge. Would you feel any different? (probably not)
5. Just after I did #4, you get hit by a car and die. Does your "self" vanish? If so, what about the copy running inside the computer?
6. Do Star Trek transporters transport you, or kill you?
7. If person A and person B switch brains, does the "self" of person B now occupy the body of person A and vica versa?
8. A person can live, mostly normally, with half a brain. If I put your left hemisphere in body A and your right hemisphere in body B, which one of them - if any - is "you"?

There seems to be no way to answer all these questions without running into a contradiction. Naively trying to extrapolate the maxim "my consciousness goes where my brain goes" to such extreme situations is bound to get us into trouble.

Of-course, none of these scenarios are realistic. But there is one extreme scenario which is realistic: When the brain - in it's entirety - stops functioning. Clearly, taking this massive 100 TeraByte, 10 PetaFlop computer out of the equation is a major game-breaker, don't you think? Not to mention the fact that you can't really extrapolate "X goes where Y goes" to a situation where Y doesn't exist.

So what happens to the "self" in this very extreme situation? Does it simply vanish? Maybe. Maybe not. I don't have a definite answer to this question and neither do you (or anybody else). All we have to go on is our intuition. And the problem is that different people reach different conclusions based on intuition alone.

And another thing:

These questions stir some primitive emotions and fears in every human being, so we are all bound to be extremely biased. We can't help it. But we can be aware of this fact, and realize that whatever notions we have about this issue - they are probably wrong.

At least until science finally resolves this question with some degree of certainty... hopefully before we learn the answer ourselves the hard way.

EDITED TO ADD:

I find it funny that we're having this discussion on a thread about the reality of mathematics. Right there you have an example of how an abstract platonic world interacts with the physical world. Perhaps the brain/self duality works in a similar way. It would be really ironic, if the thing that the traditionalists call "souls" is actually mathematical in nature. That would really turn the entire "mechanistic vs. spiritual" debate on its head. :)
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Re: Is math real?

Postby doogly » Thu Mar 10, 2016 4:16 am UTC

It's not like "Platonism" makes sense in math. Really what you're talking about is middle Platonism. Even fucking Plato figured this was all a bit too ridiculous.
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Re: Is math real?

Postby brenok » Thu Mar 10, 2016 1:39 pm UTC

PsiCubed wrote:Of-course, none of these scenarios are realistic. But there is one extreme scenario which is realistic: When the brain - in it's entirety - stops functioning. Clearly, taking this massive 100 TeraByte, 10 PetaFlop computer out of the equation is a major game-breaker, don't you think? Not to mention the fact that you can't really extrapolate "X goes where Y goes" to a situation where Y doesn't exist.

So what happens to the "self" in this very extreme situation? Does it simply vanish? Maybe. Maybe not. I don't have a definite answer to this question and neither do you (or anybody else). All we have to go on is our intuition. And the problem is that different people reach different conclusions based on intuition alone.
c, if the thing that the traditionalists call "souls" is actually mathematical in nature. That would really turn the entire "mechanistic vs. spiritual" debate on its head. :)

Wow, that's some really major selective skepticism. Where do movies go when you turn the tv off? Where does the fire go when you blow out a candle? Do they have a special "fire heaven" for flames that were well behaved? Maybe we should accept the possibility that yes, we are mortal and will die someday.

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Re: Is math real?

Postby jewish_scientist » Mon Mar 28, 2016 2:48 pm UTC

PsiCubed wrote:
jewish_scientist wrote: If Earth is the only place where life exists, and we destroy all life on Earth with nuclear weapons, then does 1+1=2?


I really don't get this question. Why wouldn't it be?

People invented cars, so if everyone is dead (and all cars have been destroyed) then cars do not exist. If people invented math, then math would stop existing when everyone died.

PsiCubed wrote:6. Do Star Trek transporters transport you, or kill you?

CGP Grey made a great Youtube video about this.

At least until science finally resolves this question with some degree of certainty... hopefully before we learn the answer ourselves the hard way.

The definition of 'self' is a question in philosophy, not science.

brenok wrote:Where do movies go when you turn the tv off?
That depends; is the souffle a souffle or is the souffle the recipe? If the souffle is a souffle, then you destroyed the movie; if the souffle is the recipe, then the movie is a series of bits stored magnetically somewhere.
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Re: Is math real?

Postby Carlington » Wed Mar 30, 2016 7:10 am UTC

jewish_scientist wrote:
PsiCubed wrote:
jewish_scientist wrote: If Earth is the only place where life exists, and we destroy all life on Earth with nuclear weapons, then does 1+1=2?


I really don't get this question. Why wouldn't it be?

People invented cars, so if everyone is dead (and all cars have been destroyed) then cars do not exist. If people invented math, then math would stop existing when everyone died.

I have bolded a parenthetical for emphasis, because it is key in your logic. Why must you add the requirement that all cars be destroyed to the first, when you needn't add the requirement that all maths be destroyed to the second?
Upthread, I made an analogy between mathematics as a formal metalanguage and natural languages. This analogy is useful here. We can just as well ask, if people invented a language (and I think it would be a good idea to say this is true), and all speakers of that language are dead, does that language still exist? We can say with a fair amount of certainty that Proto-Indo-European, for example, exists. Whether it matches what we imagine it to be today is another matter, but certainly all the parts of it are still around and could be assembled into a functional language. And even if it can't, there still must be some thing which we refer to as Proto-Indo-European. The word has a referent, ergo something exists.

There's a word for the idea that we project or construct our reality, but I can't remember it. It's something, I think, akin to idealism or solipsism or nihilism, but not quite the same thing. We can take a viewpoint like this to mathematics as well, in that we build ideas to match oue experience.

FakeEdit: I found it, it's constructivism I think. I'm not sure if I'm happy with this, or maybe I mean that I wouldn't necessarily take this view myself but it's valid.
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Re: Is math real?

Postby Bloopy » Thu Apr 07, 2016 2:34 am UTC

PsiSquared wrote:You cannot see, hear, smell, taste or touch gravity.

You can feel its effects manifest as weight or weightlessness. Unless we're being tugged at by some sort of Jedi mind power, it's a physical phenomenon, and the consensus seems to be that physical things are a subset of real things.

Having said that, I think mathematics is fairly real as well. It's almost impossible to imagine a universe without something mathematical going on. It would have to be some sort of randomly-acting soup-like environment where nothing had defined boundaries and you couldn't count or measure anything. No predictable behaviour or pattens to study, nothing to give rise to the field of mathematics or fluid dynamics or anything else.

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Re: Is math real?

Postby gmalivuk » Thu Apr 07, 2016 3:40 am UTC

I feel like fumbling attempts at doing philosophy of self are not really on-topic for this thread here in the math forum.
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Re: Is math real?

Postby PsiCubed » Mon Apr 18, 2016 3:15 am UTC

Bloopy wrote:
PsiSquared wrote:You cannot see, hear, smell, taste or touch gravity.

You can feel its effects manifest as weight or weightlessness. Unless we're being tugged at by some sort of Jedi mind power, it's a physical phenomenon...


Well, one could argue that gravity is nothing more than an abstract concept which humans use to model physical phenomena. If we see an apple that's falling down, that is an actual physical reality. But our generalizations and conclusions regarding such facts - which are embedded in the concept of "gravity" - is just a product of our human mind.

Of-course I don't adhere to this point of view. Not many people do... which doesn't stop the very same people from using a similar argument to claim that mathematics is "just a product of the human mind". And it is this inconsistency that bothers me. After all, we can see the effects of the laws of mathematics just as clearly as we can see the effects of gravity. So why the double standard?
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Re: Is math real?

Postby lorb » Wed May 18, 2016 12:00 pm UTC

PsiCubed wrote:Of-course I don't adhere to this point of view. Not many people do... which doesn't stop the very same people from using a similar argument to claim that mathematics is "just a product of the human mind". And it is this inconsistency that bothers me. After all, we can see the effects of the laws of mathematics just as clearly as we can see the effects of gravity. So why the double standard?


It is somewhat dependant on your definition of mathematics but here's what the difference would be: You can actually experience gravity with your senses. (See stuff fall down, feel weight etc.) The same is not possible for mathematics. Many of the things that you can experience can be modelled by mathematics, but they are not mathematics.
Also to reiterate a very important point: Have a look at the list of schools of thought that wikipedia has in the philosophy of mathematics article. The answer to many questions posed in this thread depend on which school you prefer.
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Re: Is math real?

Postby PsiCubed » Wed May 18, 2016 7:35 pm UTC

But that's exactly my point:

You cannot experience gravity with your senses. You can only experience events which we interpret as the result of gravity: Things falling down, feeling weight, the orbits of the planets.. Remember that it took the genius of Isaac Newton plus a great deal of mathematical modelling to realize that all these seemingly unrelated things are the result of one universal law (the medieval view on the matter, for example, was quite different).

And speaking of the orbits of the planets: The very fact that the Earth orbits the Sun is something that we cannot see with our senses. On the contrary: On the face of it, it sounds pretty ridiculous to believe that our world is spinning around at over 1000 kph, and whizzing around the Sun at 30 kilometers a second.

So why do we believe these outrageous claims? Because otherwise, the numbers don't add up: From Kepler's first calculation of the positions of the planets, through the effects of the Coriolis force, to modern application like GPS and interplanetary navigation. Any argument you can think of for the heliocentric view is based on the assumption that our mathematical models have a direct bearing on reality.

Do you believe that the earth really revolves around the Sun? Or do you regard this notion as nothing more than "a convenient model"?

If you pick the first option, then you've already conceded that our mathematical models are real enough to override what our senses tell us (which is: "I see and feel the earth and it doesn't seem to move").

And if you pick the second option, then you've just declared that some forms of gravity (specifically: the gravitational pull of the sun on the earth) to be unreal.

Either way my original assertion stands: Arguing that abstract physical concepts such as gravity are real while mathematics isn't, is not consistent.
(and of-course, very very few people would pick the second option. This alone should tell you something)
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Re: Is math real?

Postby lorb » Wed May 18, 2016 8:21 pm UTC

PsiCubed wrote:You cannot experience gravity with your senses.


Stand up and jump. Did you feel something in your legs when you landed? What was that, if not gravity? In that regard even the medieval and ancient greek views where correct: there is something that makes things fall down. What Newton did was not discover that there is gravity, but create a good model of it with a lot of math in it (which actually is this that you can't experience.)
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Re: Is math real?

Postby cyanyoshi » Wed May 18, 2016 8:42 pm UTC

lorb wrote:
PsiCubed wrote:You cannot experience gravity with your senses.


Stand up and jump. Did you feel something in your legs when you landed? What was that, if not gravity?

This gets into some hairy details, but you would have sensed the normal force from contact with the ground. Whether you're in free-fall or standing still, your motion can be modeled with a constant downward gravitational acceleration that you won't feel. Similarly, astronauts in the ISS are being pulled by Earth's gravity at roughly 9 m/s^2 from the Newtonian framework. Do they sense gravity?

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Re: Is math real?

Postby PsiCubed » Wed May 18, 2016 9:09 pm UTC

lorb wrote:Stand up and jump. Did you feel something in your legs when you landed? What was that, if not gravity?


That's missing the point, which is the fact that people gladly accept mathematical models as being real all the time, without even realizing it.

Here are two questions for you:

1. Do you believe that the earth goes around the sun? Or do you think it is merely "a useful mathematical model"?

2. Stand up on your feet and jump. Do you believe that the force that just pulled you to ground, is the same kind of force that's making the earth go around the sun? Or is this whole notion of universal gravity nothing more than "a useful mathematical model"?

cyanyoshi wrote:This gets into some hairy details, but you would have sensed the normal force from contact with the ground.


Nice catch. :)
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Re: Is math real?

Postby lorb » Wed May 18, 2016 10:13 pm UTC

Well, gravity being a force, it of course feels the same as any other force. You can run against a wall and feel basically the same as if you where falling onto the ground. The point is that this gives you a very clear sensory perception that there is a force which acts on your body. (Yes, technically the force is not gravity, but the floor stopping you, but gravity caused you to accelerate towards the floor in the first place.)

My point is that it's pretty easy to produce empirical data (sensory perception) that let's you in feel gravity, and everything else that is part of the physical world. It's not as easy however to do the same for something like the axiom of infinity.

Which doesn't mean to say that mathematics isn't real. It's just not possible to experience it in the same way as many other things.

As for your questions: I don't see a big difference between 1 and 2 except that number 2 is a lot harder/costlier to falsify/verify. And aside from semantics and technicalities about frames of reference both are of course true. It's very much observable that everything that has mass is attracted to each other, and mathematics can be used to create useful models that describe this behaviour. Which imho is the reason why we can say mathematics is real: it's indispensable to describe the real world in a scientific way.

edit: also the models of gravity can be falsified. the aforementioned axiom of infinity can by definition not be falsified, no matter what empirical data you can produce.
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Re: Is math real?

Postby PsiCubed » Wed May 18, 2016 10:45 pm UTC

lorb wrote:My point is that it's pretty easy to produce empirical data (sensory perception) that let's you in feel gravity, and everything else that is part of the physical world.


That's simply not true.

And I've already shown you why (the earth-around-the-sun example). Repeating a false statement a dozen times does not make it any more true.

It's not as easy however to do the same for something like the axiom of infinity.


Well, deducing facts about the real world from abstract concepts is often tricky.

But I still maintain that the axiom of infinity correlates much more directly with our senses, than the notion of the earth moving around the sun. The fact that numbers never end is so freaking obvious that most children deduce it on their own.

It's very much observable that everything that has mass is attracted to each other, and mathematics can be used to create useful models that describe this behaviour.


Nope.

The earth is moving around the sun in a circle, and the distance between them never changes.

And what about electrical repulsion? Magnets? Or that really nosey and irritating neighbor of mine, who causes me to back away every time I see him? He has a lot of mass, too. So what's all this foolishness about "everything that has mass is attracted to each other"?

See, you've got the order of things reversed: Without having a mathematical formulation first, the idea of "every mass attracts every other mass" doesn't make any sense. On the face of it, it seems to defy our day-to-day experience. It takes some really heavy mathematics (calculus, for one) to actually turn this seemingly crazy idea into something workable.
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Re: Is math real?

Postby LaserGuy » Wed May 18, 2016 10:52 pm UTC

cyanyoshi wrote:
lorb wrote:
PsiCubed wrote:You cannot experience gravity with your senses.


Stand up and jump. Did you feel something in your legs when you landed? What was that, if not gravity?

This gets into some hairy details, but you would have sensed the normal force from contact with the ground. Whether you're in free-fall or standing still, your motion can be modeled with a constant downward gravitational acceleration that you won't feel. Similarly, astronauts in the ISS are being pulled by Earth's gravity at roughly 9 m/s^2 from the Newtonian framework. Do they sense gravity?


You can definitely feel acceleration while falling. The human body is actually quite good at detecting small changes in acceleration--it's what you use for balance. What you can't do is tell if that acceleration is due to gravity or due to something else. In free fall, you feel "weightless", which is a very different sensation from being on solid ground.

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Re: Is math real?

Postby cyanyoshi » Thu May 19, 2016 12:13 am UTC

LaserGuy wrote:You can definitely feel acceleration while falling. The human body is actually quite good at detecting small changes in acceleration--it's what you use for balance. What you can't do is tell if that acceleration is due to gravity or due to something else. In free fall, you feel "weightless", which is a very different sensation from being on solid ground.

Right. I was being pedantic. My point was that our perception of gravity is entirely based on which mathematical model we use. All I know is that math is "real"ly useful at laying down a foundation for physics and the other sciences! :)

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Re: Is math real?

Postby lorb » Thu May 19, 2016 1:37 am UTC

PsiCubed wrote:
lorb wrote:My point is that it's pretty easy to produce empirical data (sensory perception) that let's you in feel gravity, and everything else that is part of the physical world.


That's simply not true.

And I've already shown you why (the earth-around-the-sun example). Repeating a false statement a dozen times does not make it any more true.


Please don't just say my statements are wrong. At least tell me why you think the example I gave is not an example of experiencing gravity. I don't understand from your answers why you think that. Also do you think that it is in principle possible to falsify the current theory in gravity? (In that it would in theory be possible to observe some datum that contradicts it. I already gave a link, but here it is again in case it's not clear what is meant by that: https://en.wikipedia.org/wiki/Falsifiability.

PsiCubed wrote:
It's not as easy however to do the same for something like the axiom of infinity.


Well, deducing facts about the real world from abstract concepts is often tricky.

Impossible imho. You have to allow for a priori knowledge if you want this to hold. Which is a valid position but not the kind of epistemology I subscribe to.

PsiCubed wrote:But I still maintain that the axiom of infinity correlates much more directly with our senses, than the notion of the earth moving around the sun. The fact that numbers never end is so freaking obvious that most children deduce it on their own.


If that is so, what sensory input would falsify the axiom of infinity? (See link above)

PsiCubed wrote:
It's very much observable that everything that has mass is attracted to each other, and mathematics can be used to create useful models that describe this behaviour.


Nope.

The earth is moving around the sun in a circle, and the distance between them never changes.

And what about electrical repulsion? Magnets? Or that really nosey and irritating neighbor of mine, who causes me to back away every time I see him? He has a lot of mass, too. So what's all this foolishness about "everything that has mass is attracted to each other"?

See, you've got the order of things reversed: Without having a mathematical formulation first, the idea of "every mass attracts every other mass" doesn't make any sense. On the face of it, it seems to defy our day-to-day experience. It takes some really heavy mathematics (calculus, for one) to actually turn this seemingly crazy idea into something workable.


Just because stuff isn't always behaving the same way doesn't mean you can't observe it. Sure it's hard to get a really good understanding on gravity just by looking at the world, but that's what science does. Collect a lot of empirical data and try deduce some laws from it. That's how we ended up with our current pretty complicated formulation of what gravity is, but you don't need that to experience it.

By the way, if you are using "children can deduce this on their own" as a test: while they may very often be able to deduce that numbers (theoretically) go on forever after one has educated them one what numbers are and how they work, even more children figure out that stuff falls down on their own without even anyone needing to tell them. Even 3 year olds that can't count to 5 have a primitive concept of gravity.

Edit: there is also absolutely no requirement to understand something in order to experience it. I can have 0 knowledge about electricity, and still get burned badly by it. Even if you think the force that makes the earth go round the sun, and the force that makes things fall down are totally different things, they both impact your senses a lot more than any math could ever do.
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Re: Is math real?

Postby Cauchy » Thu May 19, 2016 3:14 am UTC

There's a distinction between "gravity" and "the current scientific model of gravity". I can't directly observe that the earth goes around the sun instead of vise versa, and I can't directly observe that clocks up in satellites go faster than clocks down here. I can observe things moving to the ground when I let go of them, and I can feel a weird pressure on my butt as I sit here typing this post. Something is going on out in reality that makes those things happen, and "gravity" is the name I have for that. In that sense, it's very real.

PsiCubed wrote:1. Do you believe that the earth goes around the sun? Or do you think it is merely "a useful mathematical model"?


It's a useful mathematical model, of course. Here on Earth, it's also sometimes useful to model the sun as going around the earth, which is why we still have the terms "sunrise" and "sunset". We model the force of gravity as 9.8 m/s^2, even though it varies from height to height and even from place to place. These are both "true enough", in that the ways that they differ from reality are usually not extreme enough to mess with whatever we're doing at the moment. The same is the case for heliocentrism: the sun also moves slightly because of the gravitational effects of the Earth and other objects, but we say "close enough" and treat it as stationary for our model of everything going around the sun. (Or maybe for space travel, you can't actually say "close enough" about something like that and their models include it, I don't know.)

PsiCubed wrote:2. Stand up on your feet and jump. Do you believe that the force that just pulled you to ground, is the same kind of force that's making the earth go around the sun? Or is this whole notion of universal gravity nothing more than "a useful mathematical model"?


Both? I believe they're the same kind of force because universal gravitation is such a useful mathematical model. It's so useful, I'm willing to say "The things I call gravity are precisely the things universal gravitation talks about.".


"Gravity" describes some set of things in the universe. "Math" goes deeper, and attaches quantities and relations to those things (when it's used to talk about the real world). Both are obviously abstractions, but my line for "what counts as real" puts them on different sides of the divide: gravity is a real thing, and math is not.


By the by:

PsiCubed wrote:But I still maintain that the axiom of infinity correlates much more directly with our senses, than the notion of the earth moving around the sun. The fact that numbers never end is so freaking obvious that most children deduce it on their own.


The axiom of infinity does not say that "numbers never end". You get that much out of the other axioms just fine. The axiom of infinity says "there's a set that contains all the natural numbers". It's much harder to deduce that from observation, without using reasoning that leads you straight into Russell's Paradox.
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