Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**All_Is_Number****Member**- Registered: 2006-07-10
- Posts: 258

Ricky wrote:

In mathematics, there is no concept of a hypothesis (which is what I believe you mean by assumption) being true or false. Whether the hypothesis leads to your conclusion or not depends upon your conclusion. In science however, there is a concept of a hypothesis (sciences call this an assumption) being wrong. That is, whether or not that hypothesis (assumption) holds true in the universe.

If you put it like that, scientific theories are never proven to be incorrect. They are just reclassified as pure mathematics, i.e. from one branch of science to another.

and the problem that arises when trying to find the precise distinction between the two.

Why would you expect a precise distinction between the two? The very nature of applied mathematics implies that it is a dynamic collection of mathematics, not a static one.

*You can shear a sheep many times but skin him only once.*

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

If you put it like that, scientific theories are never proven to be incorrect. They are just reclassified as pure mathematics, i.e. from one branch of science to another.

Could you please explain how the endosymbiont theory could be reclassified as pure math?

Why would you expect a precise distinction between the two? The very nature of applied mathematics implies that it is a dynamic collection of mathematics, not a static one.

Indeed, this is true with many subjects, science and pure mathematics included. But dynamic does not mean that demarcation is impossible. And I don't think I ever expected one.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**All_Is_Number****Member**- Registered: 2006-07-10
- Posts: 258

Ricky wrote:

Could you please explain how the endosymbiont theory could be reclassified as pure math?

There's nothing like a red herring when your argument can't stand on its own merit.

Setting aside for a moment the fact that biology is still quite young in its development, and has very little mathematical reconciliation, something that was pointed out earlier in the discussion, I think you'll find that biology has not wholly abandoned endosymbiotic theory. There is simply not enough evidence to say conclusively whether the theory is correct or not.

Indeed, this is true with many subjects, science and pure mathematics included. But dynamic does not mean that demarcation is impossible. And I don't think I ever expected one.

Right. That demarcation is quite clear. Mathematics which are applied outside of the science of mathematics belong to *applied mathematics*. It's rather ironic a pure mathematician would be in denial about the implications of the very evidence that supports the assertion that studying mathematics for mathematics' sake is beneficial to society.

*You can shear a sheep many times but skin him only once.*

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

There's nothing like a red herring when your argument can't stand on its own merit.

Please explain how asking how a scientific theory could hypothetically be reclassified as pure mathematics is a red herring. And I was hoping that it would have been obvious that it was indeed a hypothetical.

There is simply not enough evidence to say conclusively whether the theory is correct or not.

The evidence is amazingly strong in favor of it. I don't know of any controversy over it in the scientific community.

But as you think that scientific theories can be reclassified as pure mathematics, all I asked was a specific example. And indeed, I think it shows that this specific example shows what you suggested to be a bit absurd.

Mathematics which are applied outside of the science of mathematics belong to applied mathematics.

I have given three examples of pure mathematics that have been applied, and yet they remain pure. How do you account for this?

It's rather ironic a pure mathematician would be in denial about the implications of the very evidence that supports the assertion that studying mathematics for mathematics' sake is beneficial to society.

I do not deny that they are applied to something, I deny that they would be categorized as "applied mathematics". Again, you are being overly literal in your interpretation of "applied mathematics", as was I when talking about a "horse fly".

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**All_Is_Number****Member**- Registered: 2006-07-10
- Posts: 258

Ricky wrote:

Please explain how asking how a scientific theory could hypothetically be reclassified as pure mathematics is a red herring.

Do you *really* need someone to explain how a non-mathematical theory is completely irrelevant to a discussion about mathematics?

The evidence is amazingly strong in favor of it. I don't know of any controversy over it in the scientific community.

It has its problems, at least according to Wikipedia. Having said that, if the problems are of the same kind that evolution supposedly has (i.e. are fabricated by those who lack understanding of the theory), then that would be yet another reason why it is a topic wholly irrelevant to this discussion.

But as you think that scientific theories can be reclassified as pure mathematics, all I asked was a specific example. And indeed, I think it shows that this specific example shows what you suggested to be a bit absurd.

Your methodology is wholly devoid of logic.

I have given three examples of pure mathematics that have been applied, and yet they remain pure. How do you account for this?

Two possibilities: 1) There is overlap between pure mathematics and applied mathematics; or 2) those three examples are no longer in the realm of pure mathematics, despite your claim.

I do not deny that they are applied to something, I deny that they would be categorized as "applied mathematics".

You're still having trouble understanding the implications of the descriptor *applied*, I see.

*You can shear a sheep many times but skin him only once.*

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Your methodology is wholly devoid of logic.

Then explain. You claimed that under my view, falsified scientific theories could be reclassified as pure mathematics. I named a scientific theory and supposed hypothetically that it was falsified. If you can't explain how it can be reclassified as pure maths, then your claim is at the very best baseless, if not demonstrated to be false.

It has its problems, at least according to Wikipedia. Having said that, if the problems are of the same kind that evolution supposedly has (i.e. are fabricated by those who lack understanding of the theory), then that would be yet another reason why it is a topic wholly irrelevant to this discussion.

You make the same mistake that Creationists do, in conflating "problem" with "has an error". It is a problem that our knowledge of the world millions of years ago is incomplete. This does not imply that there is an error in what we currently think. The endosymbiotic theory has multiple lines of supporting evidence, each fairly independent. The only problem that wikipedia lists can be entirely explained by evolution, and indeed is expected to happen. This is the best we can hope to do, and so it is regarded as being true.

Two possibilities: 1) There is overlap between pure mathematics and applied mathematics; or 2) those three examples are no longer in the realm of pure mathematics, despite your claim.

Certainly there is an overlap between pure and applied mathematics, I don't believe anyone questions that. But group theory is almost universally regarded as a very pure math. If you are going to say that group theory is in the overlap, then virtually every pure math has to be in the overlap.

And as for your suggestion that (for example) group theory may not be a pure math, I can only refer you to the thousands of mathematicians that call it pure. I'd be quite surprised if it wasn't, considering that I've studied it for 2+ years and am greatly considering specializing my doctoral degree in it.

And I can continue giving examples. Functional Analysis, much like analysis itself, is used heavily in statistics, which of course are applied. Algebraic geometry is used in parts of organic chemistry, though I have no idea for what (I was told this by the head of the department at Virginia Tech). Commutative algebra and Ideal theory are both used heavily in Algebraic geometry. Representation theory is used in differential geometry, which I already showed was used in differential equations which in turn is used in classical and quantum physics. Field theory is used in algebraic correcting codes which are involved in every bar code that you've ever seen scanned.

Yet again, all of there are pure mathematics. Except for perhaps Functional Analysis which may be one of areas which is in between pure an applied, it's hard to say because I haven't studied it in any detail.

You're still having trouble understanding the implications of the descriptor applied, I see.

You still don't recognize the fact that just cause something has a name does not mean it is represented by the literal interpretation of that name. I suppose you think "death traps" are set by someone and "piggy-back rides" can only take place on a farm.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

Offline

**All_Is_Number****Member**- Registered: 2006-07-10
- Posts: 258

Ricky wrote:

Your methodology is wholly devoid of logic.

Then explain. You claimed that under my view, falsified scientific theories could be reclassified as pure mathematics. I named a scientific theory and supposed hypothetically that it was falsified. If you can't explain how it can be reclassified as pure maths, then your claim is at the very best baseless, if not demonstrated to be false.

You should check up-thread where I said that my comments didn't pertain to biology, since Biology has not yet been formulated mathematically. Thus, your example is a red herring, irrelevant to the discussion at hand.

You make the same mistake that Creationists do

Hardly. I readily admitted that I was not familiar with the theory, and offered up the source of my limited research, pointing out that the information could, in fact, be incorrect. But again, biological theories are irrelevant to our discussion.

Certainly there is an overlap between pure and applied mathematics, I don't believe anyone questions that.

Well, there you go. If (pure mathematics) ∩ (applied mathematics) ≠ ∅, then you should have no problem acknowledging that mathematics used in other science disciplines are applied mathematics.

But group theory is almost universally regarded as a very pure math. If you are going to say that group theory is in the overlap, then virtually every pure math has to be in the overlap.

That would be far more logical than trying to redefine *applied* so that a subset of mathematicians can feel exclusive.

And as for your suggestion that (for example) group theory may not be a pure math

I must admit that it's surprising that someone as good at maths as you can be so poor at logic. We just established that applied maths and pure maths have overlap. Therefore, saying something is a part of applied maths does not imply it is not a part of pure maths.

You're still having trouble understanding the implications of the descriptor applied, I see.

You still don't recognize the fact that just cause something has a name does not mean it is represented by the literal interpretation of that name. I suppose you think "death traps" are set by someone and "piggy-back rides" can only take place on a farm.

*Death-trap* is an appropriate term for things deemed to be dangerous or deadly due to poor design, poor maintenance, etc. *Piggy-back* is a word that has gradually evolved from the word *pickpack* (or *pickback*, according to some). But go ahead and keep the red-herrings coming. They seem to be the mainstay of your argument lately.

*Last edited by All_Is_Number (2008-11-05 11:56:51)*

*You can shear a sheep many times but skin him only once.*

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

You should check up-thread where I said that my comments didn't pertain to biology, since Biology has not yet been formulated mathematically. Thus, your example is a red herring, irrelevant to the discussion at hand.

Fine, then I take it you are acknowledging your previous statement:

If you put it like that, scientific theories are never proven to be incorrect. They are just reclassified as pure mathematics, i.e. from one branch of science to another.

To be incorrect. I would like you hear you qualify it however, because you appear as if you are still under the opinion that a derivative of it is true.

Well, there you go. If (pure mathematics) ∩ (applied mathematics) ≠ ∅, then you should have no problem acknowledging that mathematics used in other science disciplines are applied mathematics.

This is a straw man. I have never stated that mathematics used in other science disciplines are not applied. Indeed, *many* are. I argued that just because a mathematical theory is used to do something useful does not make it applied.

That would be far more logical than trying to redefine applied so that a subset of mathematicians can feel exclusive.

You should study the history of a term before you try to decide the reasons it came about.

Therefore, saying something is a part of applied maths does not imply it is not a part of pure maths.

This statement, in general, is correct. However, in the case of group theory, group theory is very strictly a pure mathematics.

Death-trap[i] is an appropriate term for things deemed to be dangerous or deadly due to poor design, poor maintenance, etc. [i]Piggy-back is a word that has gradually evolved from the word pickpack (or pickback, according to some). But go ahead and keep the red-herrings coming. They seem to be the mainstay of your argument lately.

You are using a literal interpretation of a phrase, and I am giving you other examples where you would be making the same error. Where is the herring, exactly?

Offline

**All_Is_Number****Member**- Registered: 2006-07-10
- Posts: 258

Ricky wrote:

Fine, then I take it you are acknowledging your previous statement To be incorrect. I would like you hear you qualify it however, because you appear as if you are still under the opinion that a derivative of it is true.

Like I said, go up-thread and you'll see where I specifically excepted Biology. If you have a *relevant* point to make, I'll be happy to address it. Your red-herrings, however, are getting old.

This is a straw man. I have never stated that mathematics used in other science disciplines are not applied.

You've been throwing out red-herrings in attempt to counter my claims that they are precisely that. If you don't think they're not, why are you disputing the assertion?

I argued that just because a mathematical theory is used to do something useful does not make it applied.

That's like saying something isn't blue, it just reflects electromagnetic waves of the same wavelength as those reflected by blue items.

You should study the history of a term before you try to decide the reasons it came about.

LOL. Please, share with us the history of the term *applied*.

This statement, in general, is correct. However, in the case of group theory, group theory is very strictly a pure mathematics.

If it is used outside of mathematics, then it is, quite literally, a part of *applied* mathematics. It doesn't matter if it's only taught to pure track maths majors, or even what the most eminent mathematicians claim. The definition of *applied* is clear.

You are using a literal interpretation of a phrase, and I am giving you other examples where you would be making the same error. Where is the herring, exactly?

They are in your posts.

You are trying to argue the point that because a word has a literal meaning, then any compound word containing that word must have a definition that is an exact combination of the literal definitions of the component words. That is not necessarily the case. For example, a *bookend* is not the end of a book. However, it is quite easy to understand the reasoning behind combining the words *book* and *end* to describe that object.

*Applied mathematics*, however, is not a compound word. It is a plural noun modified by an adjective. Are you suggesting that those who decided to use *applied* to describe the mathematics to which they wanted to refer were unaware of the meaning of the adjective *applied*? Did they just open a dictionary up to a random page and pick the first adjective they saw? Is it only by dumb luck that we don't call applied mathematics *insane* mathematics? Why do you suppose they would use the word *applied* if that wasn't what they meant? Is it just an obscure exception to mathematicians' obsession with precise definitions?

Can we refer to any set without many elements as the empty set? If a function is defined at a few places, without too many interruptions on a given interval, can we call it a continuous function on that interval?

*You can shear a sheep many times but skin him only once.*

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Like I said, go up-thread and you'll see where I specifically excepted Biology. If you have a relevant point to make, I'll be happy to address it. Your red-herrings, however, are getting old.

So you now mean "All sciences but biology"? I think you will soon mean "all sciences but biology and geology", because I would like you to hypothetically assume that continental drift is false and reclassify it as a pure mathematics.

And just so this doesn't take forever, let's eliminate some other fields as well from your meaning:

Chemistry: Atomic theory

Astronomy: heliocentrism.

Physics: Wave particle duality

You continually propose that "applied mathematics" means "mathematics which is applied", and you won't have it any other way. There is no reason that this is particularly wrong, but when ever in a discussion, one must first agree upon definitions before any meaningful discussion can take place. And because virtually everyone who uses the term "applied mathematics" as a discipline as I have, then it would probably be best to use the same meanings.

You don't seem to acknowledge that there is a discipline of thousands of people who call themselves "Applied mathematicians". If you want to poke fun at the term, by all means, do so. But realize nothing you do will change the term itself.

Applied mathematics, however, is not a compound word. It is a plural noun modified by an adjective.

No, it is a phrase. It is a phrase that has a meaning of its very own. Like "Quantum physics". Indeed, "Quantum physics" does not mean "an amount of physics".

Why do you suppose they would use the word applied if that wasn't what they meant?

Because the term "Studies that a mathematician pursues to be applied outside of mathematics" was just a tad too long. So it was shorted to "Applied mathematics".

Can we refer to any set without many elements as the empty set? If a function is defined at a few places, without too many interruptions on a given interval, can we call it a continuous function on that interval?

You're just laughing at yourself, because all you're doing is committing the same exact error all over again: You're using a definition that virtually *no one else accepts*.

*Last edited by Ricky (2008-11-08 08:25:48)*

Offline

**Dragonshade****Member**- Registered: 2008-01-16
- Posts: 147

To me, Math is not science

Science is the study of this world

but you CANT find math in the world , cant find a matter called "2"

It only exists in the world conceptual in our brains

leads to , does consciousness , thoughts count as substance?

Math is like coming from some other world only connects with our consciousness?

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,640

Good points, Dragonshade.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**sameer mishra****Member**- Registered: 2010-08-27
- Posts: 64

my openion about this is

Mathmatics is the perfect science

Offline