What is the Nature of Mathematics?

[Mentat]

Originally posted by Alexander
Again you MISUNDERSTAND. Logic originates NOT because stuff exists, but because something exists. Sorry for poor english.

Logic originates not from objects but from an EXISTENCE itself. Anything which has the property "to exist" shall obey logic - simply because logic is derived from labeling an existence as "1", "+", "true", "yes", etc.

Thus, any object/subject/phenomenon which exists SHALL comply with logic (math). It shall interact with other objects only as logic (=math) allows.

This is exactly what we see in universe. Only allowed by math phenomena and objects can exist.

Say, math allows a wave to slosh in 3-dimensional 1/r potential hole only very certain way (called spherical harmonics, by the way). This is exactly what we see. We call such standing wave by label "atom" and label harmonics by a word "orbitals" . First allowed by math harmonics (n=1) is labeled by us as "s orbital",second allowed by math (n=2) harmonics - as "p orbital", etc. Shape, size, appearance, etc - all properties of these harmonics are governed by math.

Are you still preaching, Alexander? No offence, but I don't have any time for being preached at. It is just as logical to say that math is just an accurate description of reality, as to say that reality obeys math. In fact, the Hurdles that I have presented show some serious flaws in assuming the latter.

 

[Alexander]

Mentat, did you take atomic physics? Do you understand atom?

 

[Mentat]

Originally posted by Alexander
Mentat, did you take atomic physics? Do you understand atom?

Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?

I haven't gone to college yet, but I have a healthy understanding of physics for my age (15), I think.

 

[quantumdude]

Originally posted by Alexander
Mentat, did you take atomic physics? Do you understand atom?

Perhaps not, but I have and I say he is doing fine. Just answer his rebuttals, if you can.

 

[ahrkron]

You're doing great, Mentat.

I am a High Energy Physicist, and I think Alexander is not keeping up with your rebuttals to his faith.

 

[Mentat]

Thank you, Tom and Ahrkron. It didn't feel quite right for me to be debating with Alexander on my own.

 

[plus]

Originally posted by Mentat
Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?

I haven't gone to college yet, but I have a healthy understanding of physics for my age (15), I think.

Age should not come into question with this pure debate, although it does not seem necessary to have too high a level of understanding of physics for this argument.

 

[drag]

Greetings !

Purhaps at this partially "critical" stage
of the discussion it may be worth noting
that despite the apparent fact that math
is the best discriptive language we appear
to have so far for the type of observation
data we have - it's not that good at it's job !

Starting from the "simplest" problems of Newtonian
Mechanics and up to the most difficult problems of
modern physics, math is certainly not perfect.
The simplest example is the 3+ body problem that
appears to be unsolvable by mathematics. Also, every
time you use integrals, for example, you're making
approximations and these are often your only way
of adressing what you observe. I'm not even beginning
to discuss stuff like the Chaos theory according to
which we can only get multi-level approximations.

The point I'm trying to make, if that's not clear
enough yet, is that if math had a direct connection
to the Universe you'd expect it to be able to explain
it better, wouldn't you ?

Live long and prosper.

 

[Alexander]

Originally posted by Mentat
Truth is what complies with observation? Bull. Heard of Quantum Mechanics?

A little. What about it?

 

[Alexander]

Originally posted by Mentat
Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?

Which rebuttals? I don't see any. Please, 1)state clearly what you want to claim. 2) provide logical or factual substantiation.

I haven't gone to college yet, but I have a healthy understanding of physics for my age (15), I think.

Good. Tell me then wnat happens if you throw a wave into 1/r potential hole?

 

[ahrkron]

Tell me then wnat happens if you throw a wave into 1/r potential hole?

Do you mean a physical, real wave? or when you write down the equation for it?

 

[Alexander]

Originally posted by Tom
Perhaps not, but I have and I say he is doing fine.

That is interesting. So, one does not have to understand physics to judge what is correct in it and what is not?

Why do we have schools and colleges then, if anyone can just say that he does not need to know relativity theory simply because he has "healthy understanding" that relativity is wrong.

I radically disagree that ignorance is a proof.

 

[Alexander]

Originally posted by ahrkron
Do you mean a physical, real wave? or when you write down the equation for it?

Mathematical wave. Energy conservation law for a wave is called Shred equation.

 

[ahrkron]

Originally posted by Alexander
That is interesting. So, one does not have to understand physics to judge what is correct in it and what is not?

His arguments attack the logic of your claims. IMO, he is doing much better than you are in that department.

Why do we have schools and colleges then, if anyone can just say that he does not need to know relativity theory simply because he has "healthy understanding" that relativity is wrong.

This does not correctly capture the logic structure of what he said.

I radically disagree that ignorance is a proof.

Again, nobody is saying that "ignorance is a proof". You either need to read posts better, or be more careful with your logic.

 

[ahrkron]

Originally posted by Alexander
Mathematical wave.

OK, how do you produce a "mathematical wave", how do you "throw" such an object?

Energy conservation law for a wave is called Shred equation.

And that is relevant because... ?

 

[RuroumiKenshin]

Originally posted by Kerrie
i believe mathematics is human discovered but is the language of the universe, geometry especially in my opinion is extremely descriptive of our universe...

I agree with Kerrie. Mathematics is a language that describes the universe, but none the less is man made. We can't think outside of our number sense because its very natural for us to see relationships between physical objects. When you think about it(that is, when you think about the temporal lobe structures involved), it is a very fascinating sense.

 

[drag]

Greetings !

Alexander, how come you're not responding to
what I said. I mean, if math rules the Universe
it's just a tiny little bit strange that it
can't even precisely and directly discribe
a system of 3(or more, of course) bodies circling
each other ?

Live long and prosper.

 

[quantumdude]

Originally posted by Alexander
That is interesting. So, one does not have to understand physics to judge what is correct in it and what is not?

What are you talking about? No one is saying that. Mentat is talking about something far more fundamental than the Schrodinger equation or atomic physics.

You aren't even paying attention, and meanwhile everyone is running circles around you. Get in the game, man!

 

[jammieg]

I can still blow my nose without knowing calculus, but would I want to?

With sureness of communication, the more atypical a view and the more relevance that view has on things, the less people will listen to it sometimes even repel from it. If you want people to listen to your views, don't be so sure Alexander- leave a bit of room for being wrong and a bit for letting others fill in the blanks with their unique views and above all be honest. In less you are quite sure, but then you had better gives some good evidence or reasoning for it.

 

[Mentat]

Originally posted by Alexander
A little. What about it?

Well, if you accept the Uncertainty Principle, then you know that the exact state of a particle-wave is never exactly defined. So, while I (a being composed of wave-particles) appear to be sitting at my computer (this would be an "observation"), it is not entirely so.

 

[Alexander]

Originally posted by Mentat
Why are you side-stepping my rebuttals? Don't you believe in your hypothesis enough to combat my counter-arguments directly?

Which counter-argument(s)? You have not stated anyone yet. At least I can't find it in your recent posts.

If you did then I probably ovelooked it (or you have deleted it before I look at it), so please state it again and in clear and logical way, ok?

 

[Alexander]

Originally posted by Mentat
Well, if you accept the Uncertainty Principle, then you know that the exact state of a particle-wave is never exactly defined. So, while I (a being composed of wave-particles) appear to be sitting at my computer (this would be an "observation"), it is not entirely so.

You are wrong. You are soooooooo big (at least 50 kg, I assume), that you wave function spreads soooooooo negligibly even during maaaaaaaaany ages of our universe. You will be sitting practically there way after yior computer and everything around long decompose due to non-related to spread of wave function reason.

 

[Mentat]

Originally posted by Alexander
Which counter-argument(s)? You have not stated anyone yet. At least I can't find it in your recent posts.

If you did then I probably ovelooked it (or you have deleted it before I look at it), so please state it again and in clear and logical way, ok?

Well, first of all, if you look - in the "Hurdles" thread and this one - for my posts which contain a quote from you, you will find my "rebuttals" that I speak of.

In fact, I see no reason to restate all of the hurdles to your idea, just read them here: Hurdles thread.

Note: Also be sure to read the add-ons of Tom and wuliheron (and possibly others, those are just the two that I remember).

 

[Mentat]

Originally posted by Alexander
You are wrong. You are soooooooo big (at least 50 kg, I assume), that you wave function spreads soooooooo negligibly even during maaaaaaaaany ages of our universe. You will be sitting practically there way after yior computer and everything around long decompose due to non-related to spread of wave function reason.

You still have to defer to probability, no matter how negligible. Besides, my point is that not all is as it seems (or how it is "observed"). There may be a fourth spatial dimension. We may never actually "observe" it, but that doesn't mean that it doesn't exist.

 

[Mentat]

Just keeping the post up in the first page, and awaiting Alexander's response...

 

[Royce]

Your doing great mentat. Keep up the good work; but, you are fighting a futile battle that is impossible to win. If you can corner Aleander to the point that he actually has to answer a rebuttal he refuses to accept your answers or logic. But it is good exersize. Just don't butt your head against the brick wall named Alexander to long or hard.
You blew me away when you said you were 15. I would never have guessed from your writting or logic/philosophy that you were that yong. Well done, my friend.

 

[heusdens]

As to my answer (mathematics is a man made descriptive language) it was challenging to take the other alternative, that it is made by the universe.

The challenge is that we certainly claim that certain rules of mathematics are universal, that is they are the same to all inhabitants of the universe.

But in the same way we can state that the laws of physics are universal, cause they describe to the same physical world.

Physics is closely attacted to mathematics and extensively uses mathematical concepts.

 

[Alexander]

Originally posted by Mentat
Well, first of all, if you look - in the "Hurdles" thread and this one - for my posts which contain a quote from you, you will find my "rebuttals" that I speak of.


1) Non-physical Hurdle:

Mathematics has no physical presence (nor does logic, for that matter).

Define "physical presence".

 

[Alexander]

Anti"hurdles" continues. (Educating beginners about physics and math).

Originally posted by Mentat

You can say that electromagnetism (for example) is causal, because it can exert *physical* force on objects.

Mentat, next time when you claim something, make sure you know well what you are talking about, ok? Otherwise others have to waste their time explaining your errors in understanding how things actually work.

Force is not a "physical" object/subject. It is a pure mathematical phenomenon.

You need to learn origin of force (and ESPECIALLY of e/m force). It is all mathematical, there is no "physics" here. Force is just a time derivative of momentum: F=dp/dt. We simply label the rate of change of momentum by a symbol "F".

This labeleing does NOT mean that force "physically" exists. It does not.

Force has been eliminated out of list of "physical" objects since it was found that there are no forces in nature, but there are interactions of objects obeying certain mathematical symmetries (which we call conservation laws).

Mathematics, on the other hand, exists only in the metaphysical (or the realm of concepts).

Incorrect. Mathematics is way "physical" phenomena (like forces) and "physical" properties (like mass, for instance) emerge to existence. Say, if the rate of change of momentum in interactions would be zero, then there would be no "forces" in our world.

 

[ahrkron]

Originally posted by Alexander
Anti"hurdles" continues. (Educating beginners about physics and math).

Spare us the condescending comments. They don't make your position any less weak.

Force is not a "physical" object/subject. It is a pure mathematical phenomenon.

It is you who needs to straighten his definitions Alexander.

Directly from webster:

1a : having material existence : perceptible especially through the senses and subject to the laws of nature <everything physical is measurable by weight, motion, and resistance -- Thomas De Quincey> b : of or relating to material things.

If you want to say that force, mass, weight or heat are not perceptible through the senses, or that they are not subject to the laws of nature, go ahead; otherwise, you have to abide to the definition.

Forces, temperatures, speeds, frequencies, energy and the like are physical, whether you like it or not.

[Edit: a bracket, as usual]

 

[quantumdude]

Originally posted by Alexander
Mentat, next time when you claim something, make sure you know well what you are talking about, ok? Otherwise others have to waste their time explaining your errors in understanding how things actually work.

LOL

Alex, for someone who is totally lost in this discussion, you certainly have not lost your confidence.

Force is not a "physical" object/subject. It is a pure mathematical phenomenon.

You're begging the question here. Mentat is challenging you on this very point! Namely, that you are missing the distinction between abstract and concrete. The position he holds is that the mathematical relationship (an abstract object) describes the physical force (a phenomenon mediated by concrete objects).

You need to learn origin of force (and ESPECIALLY of e/m force). It is all mathematical, there is no "physics" here. Force is just a time derivative of momentum: F=dp/dt. We simply label the rate of change of momentum by a symbol "F".

That is just a definition. Again, you are confusing the label with the "real thing".

This labeleing does NOT mean that force "physically" exists.

Of course the label does not mean the force physically exists. The experimental evidence means that the force physically exists.

It does not.

It does so.

Force has been eliminated out of list of "physical" objects since it was found that there are no forces in nature, but there are interactions of objects obeying certain mathematical symmetries (which we call conservation laws).

The ability of humans to formulate mathematical descriptions of natural phenomena does not stop those phenomena from being natural (or "physical"). Nature does not care if we can do math. It exists independently of math.

Incorrect. Mathematics is way "physical" phenomena (like forces) and "physical" properties (like mass, for instance) emerge to existence. Say, if the rate of change of momentum in interactions would be zero, then there would be no "forces" in our world. [/B]

If you are lost in a desert and have not had water for a long time, a tall, cool glass of spherical harmonics will not save you. You need physical water for that.

No, Alex, mathematics is not "physical". At least, no one here has proven that it is.

 

[Alexander]

By the way, Tom, it occurred to me that you interrupted my conversation with Mentat and does not even let him talk to me. Why do you do that?

I recall that in the past you also did not let others to continue their reasoning.

Can you be more civilized about that and let other people to continue expressing their OWN opinion?

 

[Alexander]

Originally posted by Tom
No, Alex, mathematics is not "physical". At least, no one here has proven that it is.

LOL. ( )

Define "physical".

 

[Alexander]

Originally posted by ahrkron
Forces, temperatures, speeds, frequencies, energy and the like are physical, whether you like it or not.

Let's do some THINKING here (it never hurts).

Define "force", for example. (Feel free not to use laymann blah blah blah like: "something that pushes or pulls". We are in physics forum here, so adhere to accurate definition (as you advised by the way).

 

[Alexander]

Originally posted by Tom
You're begging the question here. Mentat is challenging you on this very point! Namely, that you are missing the distinction between abstract and concrete. The position he holds is that the mathematical relationship (an abstract object) describes the physical force (a phenomenon mediated by concrete objects).

What? Concrete objects? Virtual photons (and virtual gravitons) are "concrete" objects? Tell us about them. What is their origin? Why do they behave certain way?

Also, what makes you think that they are NOT mere mathematical consequences of deeper reality - as everything else with known origin is?