What is the Nature of Mathematics?

[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[/color] 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[/color] 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?

 

[Mentat]

Originally posted by Alexander
Define "physical presence".

For a simple definition: The ability to exchange energy, and interact physically with other physical objects.

 

[Mentat]

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.

Why can't you just get to the point, without condesceding comments? If it's so simple to you, you should have no problem convincing me.

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

Force doesn't exist, but the curvature of spacetime does. According to a lot of the candidates for the T.O.E., all of the "forces" can be explained as curvatures of spacetime itself. That doesn't mean that it is only a mathematical phenomenon, it means that it requires different mathematics (Riemann Geometry, for example) to describe it.

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).

So what? The "interaction of objects" is still a physical process, that is described by mathematical symmetries.

Incorrect. Mathematics is way "physical" phenomena (like forces) and "physical" properties (like mass, for instance) emerge to existence.

I know that this is your opinion, but that doesn't mean it's true. In fact, you are contradicting yourself, as you said that there were no physical phenomena (just mathematical properties), and then you said that mathematics is the way that these "physical phenomena" came into existence.

Say, if the rate of change of momentum in interactions would be zero, then there would be no "forces" in our world.

No, if there were no "forces" in our Universe, then the rate of change of momentum would be zero.

 

[Mentat]

Originally posted by Alexander
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?

Why are you construing a "why" question as though it were scientific? Science doesn't answer "why" questions.

 

[Mentat]

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).

Thanks Tom! This is the biggest "hurdle", in my opinion, and cannot be overcome.

You see, Alexander, if you deny that there is a difference between the abstract and the concrete, then you make known that you are an idealist, not a scientist.

 

[Mentat]

Originally posted by Alexander
Let's do some THINKING here (it never hurts).

You don't need to weaken your position any further with these kind of comments, Alexander. Lifegazer was just recently banned, and he didn't start out so many of his posts with condescending comments, like you.

 

[Alexander]

You don't like thinking? I do. It never hurts to think, to analyse, to investigate in depth cause(s) and reason(s) things behave certain way.

Say, what is the definition of a force?

 

[ahrkron]

Originally posted by Alexander
You don't like thinking? I do. It never hurts to think, to analyse, to investigate in depth cause(s) and reason(s) things behave certain way.

Drop the attitude.

 

[Perspectives]

Mathematics and its relivance

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. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.

 

[wuliheron]

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. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.

Mathematics is symbolic of the footprint itself from a classical viewpoint. No matter how accurate our mathematical description of something might be, we cannot prove beyond a shadow of a doubt the thing itself really exists except by pointing our finger at it. When all is said and done, we can only point to a real footprint to prove they exist. Mathematics alone cannot prove anything exists in reality, thus it is considered symbolic.

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.

 

[Perspectives]

Mathematics, the object and Reality

Mathematics in its finest detail are composed of symbols and relationships between them. It is truly an expression of the tangible. However, most proven things cannot be held in the hand or seen by the eye but due to things in existence that can, we believe. These things are a model of what is from our perspective and while they are not the things, they like an echo are a part of it. Our existence is composed of all the things that are and the Mathematics are revealed to describe them. Without an object to examine we cannot apply math to it.

 

[Royce]

Ever notice how when Alexander feels he's being ganged up on and he thinks he's losing and arqument or debate he starts getting insulting. Very mature for a materialistic scientist, don't you think.

 

[FZ+]

Royce: It is also immature to make wry comments as to someone else's maturity from the sidelines.

Hmm...
(FZ+, now aged 4 [mental age])

 

[Mentat]

Originally posted by Alexander
You don't like thinking?

I don't like someone's insinuating that I, or any other member here, is not doing so. Insulting others, in this way, serves absolutely no purpose, except to irritate others.

 

[Mentat]

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. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.

Very good post. I like the analogy (of the foot and the footprint) too. I've been trying to defend a similar position against the belief that mathematics can actually "tell the Universe how to behave", or that there is no physical reality, but rather just mathematics.

 

[Perspectives]

Mathematics, Existence and Reality

What is possible and not is an enigma. I’m not speaking of why a person cannot flap its arms and fly like a bird. That we know is not possible. Why? We’re not equipped to do so and no one has reported it. Surely I would shout at the top of my lungs, ”I can fly like a bird, if I could.”

No, this is about the impossible being created out of nothing. On the one hand something that has not been discovered before, or should I say created, is new. Since it is new and a construct of the mind. Can we claim it never was therefore it is ours, created out of nothing? If we say YES, then we can say we operate outside of that which has been divined as ours back yard, our existence. If we say NO it has always been and it is predefined and impossible not to find if we exercise our mental ability.

When a lion drags down a deer, it does not empirically measure the deer’s health, size or weight. For the lion it is food and it will last how ever long it lasts. That is the lions existence and it’s mental extension to food. We on the other hand have selected the entire world as our food stores. We select a 32 oz. Steak, a baked potato, sour cream and a salad. That’s supper and we are satisfied. We check our mental pockets or our actual pockets and know how much money we have. We can eat till Thursday and we get paid Friday therefore we have a day of hunger or we can eat less expensive meals. I guess we should have had a hot dog instead of that large steak. We think of these things, our food supply in abstract terms days, money, where and what we eat. We developed these concepts out of want, not need. We could have still bartered or been self-sufficient. But we wanted more therefore we developed a system and nurtured friendly relations. We developed concepts that are extensions of more primitive existences. Families of Hippos allow little birds to pick parasites from their bodies, cooperation.

Where do we draw the line between saying “I did this out of nothing, it never was and it never could be at this time in this place except by me?” I claim this victory for myself at this point in existence. All may be true, except and it was specified, someone else could have discovered it, somewhere or sometime different.

But the essential point is not that it was discovered but that “what claim may be made regarding its preexistence?” Did these things exist before creation or were they there to create?

Mathematics is an expression of our existence as is physically portrayed through the universe. We merely model and explain what it is doing. If we developed a model of something that never was, or could not ever have been and has no relevance in existence then it can never be.

I believe existence and our comprehension of it as is called Reality, is only limited by our ability to emulate it through our mental constructs and exposure to others for consideration.

 

[wuliheron]

Originally posted by Perspectives
Mathematics in its finest detail are composed of symbols and relationships between them. It is truly an expression of the tangible. However, most proven things cannot be held in the hand or seen by the eye but due to things in existence that can, we believe. These things are a model of what is from our perspective and while they are not the things, they like an echo are a part of it. Our existence is composed of all the things that are and the Mathematics are revealed to describe them. Without an object to examine we cannot apply math to it.

Mathematics is meaningless unless we translate it into natural language. Ask yourself, "What is five?" Without reference to natural language concepts and the ability to physically point to "five" of something the word has no meaning. Thus the interpretation of mathematics and, indeed, logic itself has no meaning outside of natural language.

Natural language is repleate with vague terms and contradictions. Unless you can clarify these terms and contradictions, at least those that apply to mathematics and logic, any assertions you can make about mathematics and how it applies to the real world are pure speculation. Considering the evidence of the last century especially, the idea that any single view of mathematics covers everything is patently absurd.

 

[Perspectives]

Mathematics in all its form reveals all

While it is true mathematics is the chosen tool for the formal expression of physical phenomena, to most if it ‘s implications and indeed it’s implied consequences are not revealed through words and a story then it will not matter. I am most familiar with Einstein’s Special Theory of Relativity in both the math and his eloquent verbal expression of it. However his General Theory of Relativity is Mathematically beyond me at present and after that the implications that I must derive from it and finally I will not be able to express it verbally till I get the other two straight.

So considering the bridge that must be created between the abstractions of mathematics to the verbalization of its consequences, I agree with you. We do need to be able to properly express in non-mathematical terms the things revealed by mathematics.

Regarding why mathematics can be used to express all phenomena, I hold despite the many varied branches that may be needed, mathematics is a tool that is intrinsic to humans. And that it is very much applicable to all physical phenomena. We may need to create new abstract tools in the future that are mathematical in nature but nonetheless they will be mathematics. I therefore submit, formally expressed notation will be used that abstractly represent the relations in nature and it will perform the service of revealing nature’s inner workings. Mathematics and only mathematics in all its form is necessary and implicit in discovering nature’s mechanisms.

 

[wuliheron]

Originally posted by Perspectives
Regarding why mathematics can be used to express all phenomena, I hold despite the many varied branches that may be needed, mathematics is a tool that is intrinsic to humans. And that it is very much applicable to all physical phenomena. We may need to create new abstract tools in the future that are mathematical in nature but nonetheless they will be mathematics. I therefore submit, formally expressed notation will be used that abstractly represent the relations in nature and it will perform the service of revealing nature’s inner workings. Mathematics and only mathematics in all its form is necessary and implicit in discovering nature’s mechanisms.

Mathematics can be highly accurate and precise, but whether or not this implies it reflects reality in some sense is unknown. Its a bit like saying my yardstick is highly accurate and precise, therefore existence must be a yardstick, and everything must be capable of being measured by a yardstick. I should be able to measure my mother's love for me using my yardstick, or even the value of life itself.

Note that within mathematics itself, there is no clearly superior form of mathematics which describes reality better than another. In physics, Quantum Mechanics does a good job but only on a statistical basis that does not make any conclusive statement about the ultimate nature of existence. In other words, the evidence is against the idea no matter which way you turn. The only way available currently for this idea to hang on by a toe nail, is through the undifferentiated or indeterminate nature of existence we observe. If we cannot determine the precise nature of reality, then at least a small chance exists all our other observations are misleading due to our limited perspective.

 

[Perspectives]

Math, Man and Reality

Post from: Wuliheron

“Mathematics can be highly accurate and precise, but whether or not this implies it reflects reality in some sense is unknown.”….

”Note that within mathematics itself, there is no clearly superior form of mathematics which describes reality better than another.”…

“The only way available currently for this idea to hang on by a toe nail, is through the undifferentiated or indeterminate nature of existence we observe.”…

“If we cannot determine the precise nature of reality, then at least a small chance exists all our other observations are misleading due to our limited perspective.”…
___________________________________________________________________

I agree with you, we cannot know the precise nature of Reality since it is variable and interpreted from our perspective. Indeed our interpretation of Reality is subjective though the use of our Mathematics.

Mathematics can be the cause of two forms of interpretation, one a perspective and two a thoroughly incorrect application. I’m not sure there is much difference between them but there is a surety involved here, our observation of Reality in itself affects the outcome.

The interpretation of Reality is one point in the search and Mathematics is the other. It is difficult enough to, by some mystical event, discover a new or corrected view of reality, prove it in-principle through formal methodology, and then interpret what you’ve got. Lesley Groves has been quoted as having said upon viewing the first detonation of the atomic bomb, “ We’ve won the war, we have the biggest stick on the block,” whereas Robert Openheimer was quoted as reciting a passage from the Gita Bhagwat, “ I am become death…”

This is not math or science but a demonstration of perspectives regarding a pivotal event in history. After all the math and science two men regard the result from two entirely different perspectives.

There are times Mathematics, Reality and Humankind are as disparate as wind, rain, and Earth and sometimes, maybe as close as the tree that gains the benefits of the three.

 

[drag]

Hmmm...
Alexander doesn't want to play with me...