Lingusitics What is the Nature of Mathematics?

[Mentat]

Originally posted by drag
Hmmm...
Alexander doesn't want to play with me...

Yeah, I'm getting the same feeling.

 

[wimms]

Give him a break. Hes becoming impatient and took some time to chill.

Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?

When I first encountered Fourier series I was baffled, you can dismantle wavesignal of any shape whatsoever into finite number of components, that can sometimes be awfully compact equation. Any kind of patterns in signal results in reduction of complexity of equation. The more repetitions, the simpler it becomes. Complexity of equations increase only in case when signal approximates towards completely acausally random noise.

Math is so powerful these days, that they seek for methodology to actually find equation for any given photo of any complexity. Its all about compression ala DNA. Given space of nearly infinite possibilities, find equation that produces exactly that given image.

I guess one could describe in full detail, shape, colors, smell and all, actual bull's shjt floating in the waterpool with wave equations. Some QM is 'piece of cake' in comparison. Question is merely in finding which of infinite possible equations best fits observable reality. Thus impression creeps in, if math is so powerful that it can describe about anything, how can math be actually cause for anything? What then constrains its infinite flexibility? And most importantly, why in this particular way?

Then, equations are merely dormant relations, 'curvature'. To make them alive, one needs to put in some values, 'matter'. Only then can equations 'take off'. Only if 'matter' and 'curvature' were in mutual interaction, creating and changing each other, like mass and spacetime, could there be some justification to why we observe only small subset of possibilities. In that sense, theories of chaos are fascinating. As I understand it, they have capacity to actually create new math from dumbsimple initial conditions, upto complexification beyond imagination.

 

[wuliheron]

Originally posted by wimms

Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?

Paradox.

 

[drag]

Greetings !

Originally posted by wimms
Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?

Of course there are things math fails to
discribe. In fact, modern mathematics is
full of approximations of nature with few
direct discriptions. The simplest example
I offered Alexander and got no response is
that of 3+ bodies orbiting each other due to
the force of gravity.

Live long and prosper.

 

[Perspectives]

Math is a reflection and our mind the Mirror

The universe is an orderly and predictable environment that is reality. I’m sure the O and P statement will bring howls. Our attempt to emulate and capture the rules of the environment is through the discovery of the interrelationships that exist. We do this by creating symbolic relationships that when applied are predictive in nature, we call this mathematics. If math predicts in any reasonable manor the mechanics and mechanisms of the universe then we are merely illuminating that which is from the logic that is already there.

As regards what we call Reality, it is a subjective interpretation, verbal as much as logical, of our formal proofs. Half empty or half full, which is right?

 

[wuliheron]

Originally posted by Perspectives
The universe is an orderly and predictable environment that is reality. I’m sure the O and P statement will bring howls. Our attempt to emulate and capture the rules of the environment is through the discovery of the interrelationships that exist. We do this by creating symbolic relationships that when applied are predictive in nature, we call this mathematics. If math predicts in any reasonable manor the mechanics and mechanisms of the universe then we are merely illuminating that which is from the logic that is already there.

As regards what we call Reality, it is a subjective interpretation, verbal as much as logical, of our formal proofs. Half empty or half full, which is right?

Both are true, the glass is half empty and half full and that is the paradox. The universe is incredibly predictable and inordinately unpredictable else we would not be discussing the issue. Your argument is nothing less than a variation on the Anthropic Principle. That in itself is as humorous as it gets for the sciences and philosophy.

 

[Eh]

Why does this remind me of Lifegazer threads?

 

[Alexander]

Originally posted by Perspectives
Mathematics is an explanation of existence. Its complexity and level of relevance depends on need. Mathematics is to existence what the footprint is to the foot.

Small but impotrant correction: Behavior of existing objects is to mathematics what the footprint is to the foot.

 

[Alexander]

Originally posted by wuliheron
A bird in the hand is worth two in the bush
And, in turn, the two in the bush are (for all I can determine) worth an infinite number of mathematical white rabbits. [/I] [/B]

Wulli - no offense - how much expertise in math do you have?

The reason I am asking is that sometimes people with no or little expertise in some field try to judge that field and get wrong conclusion.

 

[Perspectives]

Mathematics any conclusions?

The qualifications for evaluation of the subject matter is elusive and every bit as consensus as the subject it’s self. We’re examining philosophy, theoretical physics, theology if you’re inclined, and of course mathematics.

I think, like the blind men each describing an elephant, the allegory fails to bring into account their area of expertise. It seems the most important part of the story is that they are blind, as if they could see they would immediately know what they see. Since all humans have some unique attributes that color their judgment each man would probably see something different. Scientific methodology tries to eliminate subjectivity from the evaluative process; therefore man should see the same thing. Yet we may have asked a subjective question, too unscientific to use an objective measure.

Mathematics without question is a methodology, just like a man is male. Math is a tool to assist our understanding of the Universe and a tool to assist us to build a house. We don’t care about the Universe when we build our house and we don’t think of houses when we consider the Universe. We just use it to justify our work. Especially at those levels we’re not standing far enough from the subject to illuminate it.

I believe that we have touched on many of the important points of the argument and as is equally important assisted each other in understanding individual perspective. At various levels we’re all right to some degree. This subject is important and not just an academic exercise since it’s conclusions could lead to innovation. Especially if one can get our mind around what Mathematics is. Then we can consider what it isn’t.

 

[Alexander]

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

 

[Mentat]

Originally posted by Alexander
Small but impotrant correction: Behavior of existing objects is to mathematics what the footprint is to the foot.

Step outside of your religious hold to this unproven idea, and you will realize that you are preaching against the definitive notion of mathematics itself. I've been doing research into what mathematics is, and it seems that everyone (including expert mathematicians) recognizes mathematics as a tool for understanding physical reality.

 

[Mentat]

Originally posted by Alexander
Wulli - no offense - how much expertise in math do you have?

The reason I am asking is that sometimes people with no or little expertise in some field try to judge that field and get wrong conclusion.

And herein lies one of your greatest character flaws. An Indian mand (from India), revolutionized Mathematics, after having only read a basic mathematics textbook (I forget his name, but I'm sure you're familiar with him). It doesn't take an extensive education in a field, to question an "expert's" of understanding of it.

 

[quantumdude]

Originally posted by Alexander
So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

This has nothing to do with anything in the discussion. No one is saying that accepted physical theories are "wrong".

 

[FZ+]

Originally posted by Alexander
So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

In an ideal would, they would nod in agreement, but not discard GR. Rather, they would agree that inevitably there would be improvements to the theory, but it's the best around at the moment.

 

[Perspectives]

Laymen and professionals

I agree with FZ

Of course not, But I would expect the layman to support his or her position. I suppose it depends on the physicist level of tolerance. The layman has clearly stated their level of competence is “Not an expert.” Having said that, he or she should defend their position and put it to the test. Experts are public targets for all to test and they should be ready to defend. I agree bearding the Lion in his own den is not prudent. Either the layman has a hypotheses, I would at least expect this level of challenge, or he will be shown the door. One does not need to be recognized in a discipline to participate just recognize that professionals don’t always play nice.

 

[Alexander]

Originally posted by Mentat
Step outside of your religious hold to this unproven idea, and you will realize that you are preaching against the definitive notion of mathematics itself. I've been doing research into what mathematics is, and it seems that everyone (including expert mathematicians) recognizes mathematics as a tool for understanding physical reality.

Goog. Keep searching. Learning is a wonderful process.

What is the origin of this "tool"?

 

[Mentat]

Originally posted by Alexander
Good. Keep searching. Learning is a wonderful process.

Yeah, you should try it sometime. Of course, that would mean letting go of your religious belief for a while... Oh well, I guess we should leave learning to us "laymen", as experts apparently have no use for it.

What is the origin of this "tool"?

An empirical pattern of behavior that one observes in the Universe. This pattern is not absolute (see my new thread), but it is deeply engrained in the human psyche, and set of beliefs.

 

[Alexander]

Originally posted by Tom
This has nothing to do with anything in the discussion. No one is saying that accepted physical theories are "wrong".

Incorrect. Some people here with little experience in math or in physics (or even in both!) try to JUDGE the RELATIONSHIP between math and physics. Not ask questions or suggest opinions, but to JUDGE.

Only those who not only do undestand (in reasonable depth) BOTH physics and math and have reasonable EXPERIENCE in mastering both physics and math, but also have good experience in dealing with RELATIONSHIPS and interconnections between them - only those can JUDGE about relationship of math and physics.

 

[quantumdude]

Jeez, you really don't get it.

You originally said:

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

I repeat: This has nothing to do with anything here. No one is suggesting that any physical theory is wrong or that any physical theory should be discarded.

Originally posted by Alexander
Incorrect. Some people here with little experience in math or in physics (or even in both!) try to JUDGE the RELATIONSHIP between math and physics. Not ask questions or suggest opinions, but to JUDGE.

That is not the same as what you said earlier.

Also, Mentat is asking questions and suggesting opinions. You are the only one doing the judging.

Mentat is reasoning, you are preaching.

 

[Alexander]

Originally posted by Mentat
Yeah, you should try it [learning] sometime.

I love it very much. I am even getting paid for it by government (being a full time scientist and educator).

Of course, that would mean letting go of your religious belief for a while...

Oh, no, that would be hard to do. My long experience in learning universe and solving many puzzles about it made me very closed minded believer in facts and logic.

Unlike some "wide open" minds.

 

[Hurkyl]

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what?

What if a layman walked into a physics conference and objected to someone's claim that "1 + 2 = 4"... would you still dismiss his objection based simply on the fact he's a layman?


The error you are accused of making is not up in the lofty stratosphere of scientific knowledge buried under such complicated equations that 10 years of study are required to even understand the equation in error. The error of which you are accused occurs down in the lower levels, in your philosophical interpretation of mathematical logic... a field outside of your primary field of study. I'm not sure why you keep bragging about being a government paid scientist, unless you're just trying to win the argument with the "I'm smarter than you" approach.

 

[drag]

Originally posted by Alexander
Goog. Keep searching. Learning is a wonderful process.

What is the origin of this "tool"?

What's the origin of a Monopoly game ?
Is it there because it is the fundumental
truth that discribes modern economics ?

Peace and long life.

 

[wimms]

Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations? (wimms)

Originally posted by wuliheron
Paradox.

Whats so hard about describing it? P = ~P

drag:
Of course there are things math fails to discribe. In fact, modern mathematics is full of approximations of nature with few direct discriptions. The simplest example I offered Alexander and got no response is that of 3+ bodies orbiting each other due to the force of gravity.

There is a difference between what humans are able to describe using math now, and what is possible to be described when sufficiently advanced. Math is developing.
What math doesn't do is explain. It helps finding relationships between descriptions, definitions.

Too often there are many ways to describe same thing. Take for eg square wave. Very simple thing, on-off switch with finite timing for each state. Simple formula would do. But if you dismantle it into Fourier series, it appears that there is one main harmonic sinusoid, and infinite amount of odd higher harmonics with decreasing amplitudes all summed. And if square wave were single on->off cycle, like when you switch off your lights? Then main harmonic is infinitely low frequency sinusoid.

So we can describe act of switching off the lights as 'spontaneous emitting of summ of infinite amount of odd harmonics of infinitely low frequency main sinusoid, where each consecutive harmonic has specifically decreased amplitude'. Yeah, that sure helps understanding act of pressing the button. Or even better, after detecting all that harmonic stuff, we deduce that math creates a peculiar event of infinite harmonics..

But if you can define anything, then you can do that in mathematical symbols, and its automatically inside math, relations describable at least, even if not yet resolvable or explainable.

 

[Mentat]

Originally posted by Alexander
I love it very much. I am even getting paid for it by government (being a full time scientist and educator).

That is not learning, that is teaching. They are, in fact, opposite sides of the coin. You are paid to teach, and this is good. But you should not have abandoned learning to pursue teaching.

Oh, no, that would be hard to do. My long experience in learning universe and solving many puzzles about it made me very closed minded believer in facts and logic.

While it's nice that you admit to being closed-minded, I don't much care for the implication that I am not using logic or facts. I (along with Tom and ahrkron) have used logic to counter your belief, but you have closed your mind to it (for some reason that I just don't understand).

 

[FZ+]

Originally posted by Tom
Jeez, you really don't get it.

You originally said:

So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?

I repeat: This has nothing to do with anything here. No one is suggesting that any physical theory is wrong or that any physical theory should be discarded.

Exactly. Only that if the layman describes the scientific theories as only a description of the universe that should be open to change as our knowledge develops, instead of an absolute law, he is completely correct. After all, that is what differentiates science from religion.

 

[Mentat]

Originally posted by Hurkyl
What if a layman walked into a physics conference and objected to someone's claim that "1 + 2 = 4"... would you still dismiss his objection based simply on the fact he's a layman?


The error you are accused of making is not up in the lofty stratosphere of scientific knowledge buried under such complicated equations that 10 years of study are required to even understand the equation in error. The error of which you are accused occurs down in the lower levels, in your philosophical interpretation of mathematical logic... a field outside of your primary field of study. I'm not sure why you keep bragging about being a government paid scientist, unless you're just trying to win the argument with the "I'm smarter than you" approach.

Hurkyl, how did you get so perfectly succinct? I am staggered every time I read one of your posts - wishing I could portray my thoughts so perfectly, in so few words, as you do. Kudos.

 

[Hurkyl]

I think it comes from years of participating in threads that look like this one on various forums. IMHO the only way to have any chance of getting through to the other side is to break things down to basic elements, so I've had practice.

 

[Alexander]

Originally posted by drag
Greetings !

Of course there are things math fails to
discribe. In fact, modern mathematics is
full of approximations of nature with few
direct discriptions. The simplest example
I offered Alexander and got no response is
that of 3+ bodies orbiting each other due to
the force of gravity.

Live long and prosper.

Sorry for missing your post. There are many other important things to do (research, paneling, teaching, etc) beyond PF in my life. Sometimes I have plenty of time and can respond to all posts, but sometimes unpostponable duties come across.

The above example given by Drag is typical example of misunderstanding mathematics and thus making wrong conclusion about mathematics.

While solution (for 3 and more bodies) exists and can be calculated say, using a computer, it does not have a specific name (like, say, r(t)=arctan(sin(1/t)), or Gudermannian function, or elliptical integral, etc).

We just say that the solution is not "analytical". In fact only very and very few solutions are analythical.

Some other kinds of solutions are catastrophic solutions, chaotic solutions, imaginary solutions, wave solutions, etc - many of which are considered by laymann to be "no solution" - just because they look unusual or suspicious to a laymann.

Finally, some equations may have NO solution (say, the system x=1, x²=2) or infinite number of solutions (say, equation (x²-1)=(x+1)(x-1)).

 

[Sting]

Mathematics - Description

Also an artform but my head is hurting so I won't go into any philosophical discussion