What is the Nature of Mathematics?

[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

 

[Alexander]

Originally posted by Mentat


[From] An empirical pattern of behavior that one observes in the Universe.

Not exactly. I would say, from empirical property "being able to exist" and "being able not to exist".

The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

Existence is logic, so to speak.

 

[Alexander]

Originally posted by Sting
Mathematics - Description

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

Description can't predict. Math can.

 

[Sting]

Description can't predict. Math can.

True, a description can't predict but I can see where mathematics both describes and predicts.

 

[Sting]

Wait, giving slightly more thought as not exacerbate my headache, isn't there a connection between description and prediction?

 

[Alexander]

Not much. Unless you use logic (=math).

 

[Hurkyl]

logic (=math)

Just curious how you justify the '=' in your statement, not to mention how logic alone can take you from description to prediction.

 

[Mentat]

Originally posted by Alexander
Not exactly. I would say, from empirical property "being able to exist" and "being able not to exist".

The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

Existence is logic, so to speak.

You are contradicting yourself. When will you see the contradiction. Let me spell it out for you:

First you said that the origin of logic is the labeling of the states of phenomena (which I agree with), then you said that everything existing obeys logic. This is a contradiction.

 

[Mentat]

Originally posted by Alexander
Description can't predict. Math can.

Math is a description.

 

[Mentat]

Originally posted by Sting
True, a description can't predict but I can see where mathematics both describes and predicts.

Prediction is just a form of description (particularly, the one that pertains to things that haven't happened yet).

 

[quantumdude]

The multiplicity of these threads is getting troublesome. I have already addressed the following comment, but not even I can find where!

Originally posted by Alexander
Description can't predict. Math can.

That is false. With mathematics, we can describe:

1. Physical states.
2. Time evolution of physical systems.

If we can accurately describe a physical state at one spacetime point, and if we can accurately describe the time evolution, then we can accurately describe the physical state at any spacetime point, including those in the future.

That sort of description is called a prediction.

 

[wimms]

Originally posted by Alexander
The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

You are talking about presence and absence. How can you label something that does not exist?? And then use as justification to fundamentals of logic itself? Absence or lack 'of it' presupposes existence of it and thus at least imaginable presence. And what does my absence from a party has to do with fundamentals and 'obeying logic'?
Where is the glue between 'existence' and 'obeying logic'??

Besides, what makes "0" fundamental logic/math entity? What makes "false" entity at all? Fundamental to math and logic is equivalence, '=' sign, validation operator. All else is endless crusade to get that '=' sign somewhere with maximum bang effect. Shuffling nicknames left and right doesn't make a reality, its just tailoring a suit to a shape of it. You are saying that suit makes a Man. Most say that suit fits a Man, and many suits fit.

 

[Sting]

Prediction is just a form of description (particularly, the one that pertains to things that haven't happened yet).

Yes, as soon as I posted that, I realized the ambigious nature of that statement (but the headache is gone and I can at least think logically )

 

[Mentat]

Originally posted by Tom
The multiplicity of these threads is getting troublesome. I have already addressed the following comment, but not even I can find where!

Imagine how that would be compounded if you and one other member were engaged in back-and-forth debate on two threads (at the same time) that had started to be about exactly the same thing. This is the situation that drag and I found ourselves in (on the "Purpose" thread and the "Cause-and-effect" thread).

 

[Mentat]

Originally posted by Sting
Yes, as soon as I posted that, I realized the ambigious nature of that statement (but the headache is gone and I can at least think logically )

It happens to the best of us (which is why it has yet to happen to me ).