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Author Topic:   Objective reality
Straggler
Member
Posts: 10285
From: London England
Joined: 09-30-2006


Message 136 of 172 (560588)
05-16-2010 9:41 AM
Reply to: Message 124 by cavediver
05-14-2010 3:50 AM


Mathematical Elegance
Cavediver writes:

This is a huge, deep, and very interesting topic in its own right, and lies at the heart of my own turn towards a pseudo-Platonism.

I wanted to ask you about the role of mathematical elegance. As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant.

Now I am frankly too mathematically ignorant to even really know what is meant exactly by "mathematical elegance". Also "elegance" by it's very nature would seem to be a highly subjective quality. But this approach does seem to have borne much fruit. Einstein and Dirac spring to mind as two obvious examples of those who have achieved an immense amount with this abstract and highly non-empirical approach.

Now I am not saying that ultimately empirical verification can be anything but the ultimate arbiter of reality. If the maths says one thing but empirical reality says another then empirical reality wins (would you agree with that?) BUT having said that.......

It is my understanding that with one postulate (the constancy of the speed of light), an assumption of the universality of the equivalence principle and a notion of mathematical elegance it is possible to derive the whole of relativity (special and general) along with all of the predictions of relativity (Big Bang, black holes, gravitational time dilation etc. etc. etc.) just by sitting in a room manipulating equations. No need for a single observation or experiment or even for our mathematician in a room to have ever even expereinced gravity himself. Is that right?

Now Einstein didn't exactly do that. Practicalities of human endevour are never that black and white. But he did revoloutionaise science with his approach. An approach that strongly suggests that maths can lead the investigation rather than simply model observations. And that is where this more platonic view of reality is derived from.

Is that how you see it?


This message is a reply to:
 Message 124 by cavediver, posted 05-14-2010 3:50 AM cavediver has responded

Replies to this message:
 Message 139 by nwr, posted 05-16-2010 10:43 AM Straggler has responded
 Message 143 by Son Goku, posted 05-16-2010 3:26 PM Straggler has responded
 Message 147 by cavediver, posted 05-17-2010 7:50 AM Straggler has not yet responded
 Message 150 by Phage0070, posted 05-18-2010 4:46 AM Straggler has responded

  
nwr
Member
Posts: 5585
From: Geneva, Illinois
Joined: 08-08-2005


Message 137 of 172 (560591)
05-16-2010 9:48 AM
Reply to: Message 135 by Straggler
05-16-2010 6:01 AM


Re: "Shared Subjectivity" - What Do You Mean Exactly?
Straggler writes:
Rather than just be an arse about this I am going to attempt to be constructive by helping you work out more specifically what you do mean.

In other words, you are going to be an ass about it (I'm using the American spelling for "arse").

Straggler writes:
Consider the following questions:

The Straggler inquisition begins. I would suggest that you consult a shrink about your obsession with conducting these inquisitions.

Incidentally, none of your questions actually has very much to do with "shared subjectivity", but I'll accept that you think they do. You won't like my responses. You will think I am being evasive, though I am not.

Straggler writes:
1) Do you think there is a material world that exists regardless (i.e. even in the absence of) intelligent conscious lifeforms able to subjectively experience it?

I don't think we are conjuring up a world out of nothing.

One problem with the way you word the question, is that we don't really know what we mean by "material". A second problem is that many Berkeley idealists could respond "yes" to your question, as explained in that limerick usually attributed to Ronald Knox.

There was a young man who said, "God
Must think it exceedingly odd
If he finds that this tree
Continues to be
When there's no one about in the Quad."

Dear Sir:
Your astonishment's odd:
I am always about in the Quad.
And that's why the tree
Will continue to be,
Since observed by
Yours faithfully,
GOD.

Straggler writes:
If humanity (and any other lifeforms in the universe) were wiped out would the universe continue to expand, planets continue to orbit etc. etc. etc.?

Whatever it is that the Andromeda galaxy is doing now, it will continue to do that even if the sun expands to a red giant and wipes out all life on earth.

Straggler writes:
Is there an objective material reality that exists independently of and seperate to subjective experience in your view?

The words "objective", "material" and "reality" are human words that have meanings only on account of how humans use the words. The question is not meaningful unless you can come up with definitions for those terms that are not inseparably connected to their use by humans.

Straggler writes:
2) As conscious beings with limited perceptory apparatus do you consider it impossible for us to experience any objective material reality that may exist anything but subjectively?

That depends on what you mean by "experience". If a person were unconscious under anesthesia, and somebody put a bullet through that person's head, then the person could be said to have experienced death with no subjective involvement. That's one meaning of "experience". On a different meaning, the person would be said to have died but to have experienced nothing.

Straggler writes:
3) We both agree that dreams are wholly subjective experiences - Yes?

They may be wholly subjective, but I doubt that they are wholly experienced.

Straggler writes:
Can we share dreams in the sense of both experiencing the same dream?

No.

Straggler writes:
Can we objectify dreams?

That depends on what you mean by "objectify". Presumably I could provide a written report that purports to be a description of my dream. And one could say that the written report is objective.

Straggler writes:
What is the difference between a dream and the material objective reality which we seem able to co-exist in, scientifically invenstigate and "share" in such a way as to consider aspects of it to have been objectified?

One obvious difference is that dreams are incoherent.

Straggler writes:
What is the difference between a dream and the material objective reality which we seem able to co-exist in, scientifically invenstigate and "share" in such a way as to consider aspects of it to have been objectified? What is the difference between wholly subjective experience (like dreams) and aspects of reality that are considered to exist in some snes ethat we are able to "share"?

WTF!

You are asking me to compare incomparables.


This message is a reply to:
 Message 135 by Straggler, posted 05-16-2010 6:01 AM Straggler has responded

Replies to this message:
 Message 138 by Straggler, posted 05-16-2010 9:55 AM nwr has responded

  
Straggler
Member
Posts: 10285
From: London England
Joined: 09-30-2006


Message 138 of 172 (560594)
05-16-2010 9:55 AM
Reply to: Message 137 by nwr
05-16-2010 9:48 AM


Re: "Shared Subjectivity" - What Do You Mean Exactly?
Straggler writes:

What is the difference between a dream and the material objective reality which we seem able to co-exist in, scientifically invenstigate and "share" in such a way as to consider aspects of it to have been objectified? What is the difference between wholly subjective experience (like dreams) and aspects of reality that are considered to exist in some sense that we are able to "share"?

Nwr writes:

WTF

You are asking me to compare incomparables.

No. I am asking you why you think they are incomparable.

So?

Edited by Straggler, : No reason given.


This message is a reply to:
 Message 137 by nwr, posted 05-16-2010 9:48 AM nwr has responded

Replies to this message:
 Message 140 by nwr, posted 05-16-2010 10:46 AM Straggler has responded

  
nwr
Member
Posts: 5585
From: Geneva, Illinois
Joined: 08-08-2005


Message 139 of 172 (560600)
05-16-2010 10:43 AM
Reply to: Message 136 by Straggler
05-16-2010 9:41 AM


Re: Mathematical Elegance
Straggler writes:
I wanted to ask you about the role of mathematical elegance.

You addressed your question to cavediver, but I'll add my two cents so that you can have more than one opinion.

Straggler writes:
As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant.

If physicists believe that, then they are mistaken.

Straggler writes:
Now I am frankly too mathematically ignorant to even really know what is meant exactly by "mathematical elegance". Also "elegance" by it's very nature would seem to be a highly subjective quality. But this approach does seem to have borne much fruit. Einstein and Dirac spring to mind as two obvious examples of those who have achieved an immense amount with this abstract and highly non-empirical approach.

One of the things Dirac did, was to use a notion of generalized functions. I think many mathematicians would view that as inelegant and half-baked. The Theory of Distributions, due to Laurent Schwartz, provides a far more elegant way of doing this. Likewise, I suspect that many mathematicians would consider Einstein's treatment of GR as somewhat inelegant.

The mathematical analysis as described by Bourbaki is far more elegant than the same analysis as described by Titchmarsh, even though they are presenting the same analysis. You should think of mathematical elegance as an artistic quality that is appreciated by many, but not all, mathematicians.

Straggler writes:
It is my understanding that with one postulate (the constancy of the speed of light), an assumption of the universality of the equivalence principle and a notion of mathematical elegance it is possible to derive the whole of relativity (special and general) along with all of the predictions of relativity (Big Bang, black holes, gravitational time dilation etc. etc. etc.) just by sitting in a room manipulating equations.

I am inclined to say that is wrong.

For one thing, Einstein didn't start with just those assumptions. He also had Newtonian mechanics, which had proved highly effective. I look at it as finding a way to modify Newtonian mechanics to incorporate the new assumptions. It's a while since I looked over the history of that era, but I seem to recall that there were several proposed ways of modifying Newton, and I would guess that any of them could have been done in ways that were mathematically elegant.

There are serious conceptual changes involved in going from Newtonian mechanics to Relativity, and there was a lot of resistance. I would guess that finding changes that could be sold to other physicists was one of the important influences on the direction that Einstein took.

Straggler writes:
Now Einstein didn't exactly do that. Practicalities of human endevour are never that black and white. But he did revoloutionaise science with his approach. An approach that strongly suggests that maths can lead the investigation rather than simply model observations. And that is where this more platonic view of reality is derived from.

It ought to be obvious to anyone who seriously examines science, that mathematics is used for more than modeling observations. But you can find that as much with Newton as with Einstein.

Straggler writes:
And that is where this more platonic view of reality is derived from.

I can't comment on that, since I have never held a platonic view of reality. It has always seemed to me that the world (i.e. the universe) is a messy, disorderly place.
This message is a reply to:
 Message 136 by Straggler, posted 05-16-2010 9:41 AM Straggler has responded

Replies to this message:
 Message 145 by Straggler, posted 05-16-2010 7:25 PM nwr has acknowledged this reply
 Message 146 by cavediver, posted 05-17-2010 6:02 AM nwr has acknowledged this reply

  
nwr
Member
Posts: 5585
From: Geneva, Illinois
Joined: 08-08-2005


Message 140 of 172 (560601)
05-16-2010 10:46 AM
Reply to: Message 138 by Straggler
05-16-2010 9:55 AM


Re: "Shared Subjectivity" - What Do You Mean Exactly?
Straggler writes:
Nwr writes:

WTF

You are asking me to compare incomparables.

No. I am asking you why you think they are incomparable.


Comparison is a perceptual operation. We do not perceive dreams. We "experience" them in some sense, but we are not perceiving them. So comparison is out of the question.
This message is a reply to:
 Message 138 by Straggler, posted 05-16-2010 9:55 AM Straggler has responded

Replies to this message:
 Message 141 by Straggler, posted 05-16-2010 11:06 AM nwr has responded

  
Straggler
Member
Posts: 10285
From: London England
Joined: 09-30-2006


Message 141 of 172 (560603)
05-16-2010 11:06 AM
Reply to: Message 140 by nwr
05-16-2010 10:46 AM


Re: "Shared Subjectivity" - What Do You Mean Exactly?
We do not perceive dreams.

OK. So what is an example of something that we do perceive?

We "experience" them in some sense, but we are not perceiving them.

What is it that makes some things able to be experienced as a result of perception and some things (like dreams) not?

So comparison is out of the question.

You seem to be simply making the rather obvious statement that objective reality is necessarily perceived subjectively. A statement I would wholly agree with.

Except that cannot be the case because you have previously made it quite clear that is not what you mean by "shared subjectivity".

Straggler writes:

Are you simply saying that objective reality is necessarily perceived subjectively?

I did not think I was saying that. Message 397

Straggler writes:

In which case you once again appear to be making the inarguable and largely inane observation that objective reality is necessarily perceived subjectively.

No, that is not what I have been saying. Message 404

The question remains - What do you mean by "objectivity is just shared subjectivity"?

Or are you going to just continue to state what it is you don't mean?

Edited by Straggler, : No reason given.


This message is a reply to:
 Message 140 by nwr, posted 05-16-2010 10:46 AM nwr has responded

Replies to this message:
 Message 142 by nwr, posted 05-16-2010 12:04 PM Straggler has responded

  
nwr
Member
Posts: 5585
From: Geneva, Illinois
Joined: 08-08-2005


Message 142 of 172 (560609)
05-16-2010 12:04 PM
Reply to: Message 141 by Straggler
05-16-2010 11:06 AM


Re: "Shared Subjectivity" - What Do You Mean Exactly?
Straggler writes:
So what is an example of something that we do perceive?

Straggler writes:
What is it that makes some things able to be experienced as a result of perception and some things (like dreams) not?

If you think those are useful questions, then it is no wonder that we are miscommunicating.

You seem to be in the thrall of epistemology, and are attempting to apply epistemology's definition of rationality to everything. In particular, you seem to try to expose cases where people do not appear to adhere to that view of rationality.

By contrast, I think epistemology is mostly bullshit.

We are pretty much guaranteed to miscommunicate.


This message is a reply to:
 Message 141 by Straggler, posted 05-16-2010 11:06 AM Straggler has responded

Replies to this message:
 Message 144 by Straggler, posted 05-16-2010 5:53 PM nwr has acknowledged this reply

  
Son Goku
Member
Posts: 1121
From: Ireland
Joined: 07-16-2005


Message 143 of 172 (560627)
05-16-2010 3:26 PM
Reply to: Message 136 by Straggler
05-16-2010 9:41 AM


Simplicity
I know this is addressed to cavediver, but I'll give it a go.

Straggler writes:

I wanted to ask you about the role of mathematical elegance. As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant.


I think when physicists say this, they mean something quite different to what a mathematician means. Simply because a lot of physics is not very tidy mathematically.

The best way to describe it would be that we would like to derive physics as the consequence of simple but powerful ideas. Ideas that are quite short to write down mathematically, but contain a wealth of information about the physical world. An example would be Quantum Chromodynamics. If you say you want a theory which is:
1. Quantum
2. Relativistic
3. Makes sense (not self-contradictory)
4. Matches a certain experimental value (one single experiment), by getting a factor of three correct.

Then basically only one theory can possibly obey this. No fixing, no real tuning, no "why wasn't it this, instead of that?". The whole of nuclear physics from three principles and one experimental constraint. That's what we want.

Physics and reality gets more complicated the higher up you go, but at the deepest, lowest levels it is shockingly simple. Abstract and difficult to understand, but simple. As you mentioned, exploring the possibility that we should have simpler and less starting assumptions has lead to advancement.

It's why we have the standard model. In the 1960s particle physics was in a mess, with no way to relate the observations or what they had to do with each other. However by requiring 1-3 above, only one type of theory could possibly be write, "Yang-Mills field theory". All of particle physics is based on this.

If the maths says one thing but empirical reality says another then empirical reality wins (would you agree with that?)

Definitely.

Edited by Son Goku, : Spelling.


This message is a reply to:
 Message 136 by Straggler, posted 05-16-2010 9:41 AM Straggler has responded

Replies to this message:
 Message 148 by Straggler, posted 05-17-2010 10:53 AM Son Goku has not yet responded

  
Straggler
Member
Posts: 10285
From: London England
Joined: 09-30-2006


Message 144 of 172 (560639)
05-16-2010 5:53 PM
Reply to: Message 142 by nwr
05-16-2010 12:04 PM


Re: "Shared Subjectivity" - What Do You Mean Exactly?
Nwr initially writes:

quote:
"Some (including me) would argue that objectivity is just shared subjectivity anyway".

Yet in two threads we have seen no argument in support of this statement and no explanation of this somewhat paradoxical phrase. Instead we have seen a great deal of squirming around evading the issue and a fair degree of philosophical name dropping.

Straggler writes:

What is the difference between wholly subjective experience (like dreams) and aspects of reality that are considered to exist in some senss that we are able to "share"?

Nwr writes:

We do not perceive dreams. We "experience" them in some sense, but we are not perceiving them.

Straggler writes:

What is it that makes some things able to be experienced as a result of perception and some things (like dreams) not?

If you think those are useful questions, then it is no wonder that we are miscommunicating.

You are the one that raised perception as the defining difference between subjective experiences that cannot be shared and those that you apparently believe can be shared. This would seem to be rather key to the notion of objectivity as "just shared subjectivity". No?

Nwr writes:

In particular, you seem to try to expose cases where people do not appear to adhere to that view of rationality.

No. You seem unable to explain what you mean with your seemingly meaningless statement. I think this is something of a trend in your contributions here. My bullshit detector combined with a propensity for tenacious arsiness compels me to expose this.

Nwr writes:

By contrast, I think epistemology is mostly bullshit.

Then why do you keep throwing philosophical name-drops into your posts (Wittgenstein, Kant) and participating (even starting!) threads that are philosophical and epistemological in nature?

Nwr writes:

We are pretty much guaranteed to miscommunicate.

Is this your latest evasion tactic? I thought with you having identified perception as a key factor we were at last getting somewhere. I guess you are unable to follow that line of thought without contradicting your previous statements of what you didn't mean. Oh well.


This message is a reply to:
 Message 142 by nwr, posted 05-16-2010 12:04 PM nwr has acknowledged this reply

  
Straggler
Member
Posts: 10285
From: London England
Joined: 09-30-2006


Message 145 of 172 (560652)
05-16-2010 7:25 PM
Reply to: Message 139 by nwr
05-16-2010 10:43 AM


Re: Mathematical Elegance
Nwr writes:

For one thing, Einstein didn't start with just those assumptions.

Whether he did or not the question is could the whole of relativity be derived in that manner? It also seems that this was more so in Einstein's case than you are allowing for.

Link on SR writes:

Einstein's paper is remarkable for the different approach it takes. It is not presented as an attempt to explain experimental results, it is presented because of its beauty and simplicity.

Link on SR writes:

The whole theory is based on two postulates:-

1. The laws of physics take the same form in all inertial frames.
2. In any inertial frame, the velocity of light c is the same whether the light is emitted by a body at rest or by a body in uniform motion

SR Link

And now (so I understand) if we add in the equivalence principle the whole of GR can be derived from Special Relativity. So with 2 postulates and the equivalanece principle it is mathematically possible to derive large swathes of modern cosmology from the Big Bang to black holes and the predicted effects of gravity. I find that friggin amazing!

Nwr writes:

One of the things Dirac did, was to use a notion of generalized functions. I think many mathematicians would view that as inelegant and half-baked.

Dirac is probably the best example (or at least the most quotable) of a physicist who held elegance and beauty in high esteem - Dirac writes

quote:
"I think there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment. .... If seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the result of one's work and experiment, one should not allow oneself to be toodiscouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory..."

Nwr writes:

It ought to be obvious to anyone who seriously examines science, that mathematics is used for more than modeling observations. But you can find that as much with Newton as with Einstein.

I don't think maths leading the investigation into nature rather than following it really occurred until Einstein.

Nwr writes:

I can't comment on that, since I have never held a platonic view of reality. It has always seemed to me that the world (i.e. the universe) is a messy, disorderly place.

Yeah those cave shadows are just no substitute for mathematical reality.


This message is a reply to:
 Message 139 by nwr, posted 05-16-2010 10:43 AM nwr has acknowledged this reply

  
cavediver
Member (Idle past 1814 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 146 of 172 (560706)
05-17-2010 6:02 AM
Reply to: Message 139 by nwr
05-16-2010 10:43 AM


Re: Mathematical Elegancecccccccc
Straggler writes:

As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant.

nwr writes:

If physicists believe that, then they are mistaken.

Given the success that approach brought to 20th century physics, I think I'll stick to being "mistaken"

One of the things Dirac did, was to use a notion of generalized functions.

That's like pointing out Einstein's contribution to refridgeration as a counterexample to the elegance of his work in physics - the delta-function is not exactly amongst Dirac's highest achievements...

Likewise, I suspect that many mathematicians would consider Einstein's treatment of GR as somewhat inelegant.

Again, I think you are missing the point - it is not the treatment that is elegant but the mathematics that lies behind.

I am inclined to say that is wrong.

It's actually correct. And is precisely how Hilbert beat Einstein to the Field Equations, by jotting down the only possibly action one morning over breakfast.

I look at it as finding a way to modify Newtonian mechanics to incorporate the new assumptions.

No, nothing like this at all. Newton plays the role of the desired end-point - as in an r-2 law in the weak field limit - which determines the coupling to the stress-energy tensor. But that is all. For vacuum space-times, Newton is not used at all.

It has always seemed to me that the world (i.e. the universe) is a messy, disorderly place.

Then you need to check out QCD, Electro-Weak, and Gravitation more. And remember that today's world is sat at the bottom of a hierarchy of symmetry breaking. You need to get out of the trees to see the real nature of the wood.

Edited by cavediver, : No reason given.


This message is a reply to:
 Message 139 by nwr, posted 05-16-2010 10:43 AM nwr has acknowledged this reply

  
cavediver
Member (Idle past 1814 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 147 of 172 (560715)
05-17-2010 7:50 AM
Reply to: Message 136 by Straggler
05-16-2010 9:41 AM


Re: Mathematical Elegance
As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant.

As Son Goku mentioned, you have to be clear what is meant here. Actual solutions (things that look like our world) can be exceptionally messy - the elegance is in the top level theory.

Einstein and Dirac spring to mind as two obvious examples of those who have achieved an immense amount with this abstract and highly non-empirical approach.

Yes, though the real use of this approach was later with the application of group theory to particle hierarchies, and most successfully (as SG mentioned) with the SU(3) Yang-Mills theory of Quantum Chromodyanamics (QCD).

Is that right?

Almost, though Einstein used the requirement that the end theory must reduce to ewton in the weak field limit to produce the correct coupling to the stress-energy tensor. However, that correct coupling is also the most trivial coupling when viewed from the action principle, so even the connection with Newton is not exactly required.

And that is where this more platonic view of reality is derived from.

Is that how you see it?

Not quite - it certainly speaks to that view, but far more interesting to me is the nature of our fundemental particles and how they are pure group representations.


This message is a reply to:
 Message 136 by Straggler, posted 05-16-2010 9:41 AM Straggler has not yet responded

  
Straggler
Member
Posts: 10285
From: London England
Joined: 09-30-2006


Message 148 of 172 (560747)
05-17-2010 10:53 AM
Reply to: Message 143 by Son Goku
05-16-2010 3:26 PM


Re: Simplicity
I know this is addressed to cavediver, but I'll give it a go.

Please do.

The best way to describe it would be that we would like to derive physics as the consequence of simple but powerful ideas. Ideas that are quite short to write down mathematically, but contain a wealth of information about the physical world.

I get that. E=mc^2 is the most famous example I guess.

The whole of nuclear physics from three principles and one experimental constraint. That's what we want.

Cool. Much like the whole of gravitation from a couple of postulates and the equivalence principle. "Simple but powerful ideas" as you put it previously.

"Yang-Mills field theory". All of particle physics is based on this.

So we still seeking one equation that incorporates a quantum theory of all the fundamental forces. How's that going?


This message is a reply to:
 Message 143 by Son Goku, posted 05-16-2010 3:26 PM Son Goku has not yet responded

  
Peepul
Member (Idle past 3188 days)
Posts: 206
Joined: 03-13-2009


Message 149 of 172 (560903)
05-18-2010 4:23 AM
Reply to: Message 50 by Stile
05-09-2010 7:39 PM


Re: Objective Math
quote:
All things that are collectively agreed to exist within objective reality (as defined above in this post) are testable and verifiable through the scientific method.

I think putting 'collectively agreed' in your statement makes it meaningless. Who is to do the agreeing here?

If everyone on earth collectively agreed that God exists, then your statement would imply that God would be testable and verifiable through the scientific method. This is not true.

Suppose there are some genuine solipsists out there. In that case, there is nothing that is collectively agreed to exist within objective reality.

Leaving aside the collectively agreed piece, I agree with Cavediver that there is some kind of objective reality to mathematical concepts. If two different species invented the concepts of integer and prime number, then the same integers would be prime numbers for both of them. I can see no way in which that could not be true.

Many properties of mathematical objects are NOT verifiable by the scientific method. For example, the existence of an inifinity of prime numbers can be proved but not observed.


This message is a reply to:
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Phage0070
Inactive Member


Message 150 of 172 (560905)
05-18-2010 4:46 AM
Reply to: Message 136 by Straggler
05-16-2010 9:41 AM


Re: Mathematical Elegance
Straggler writes:

Now I am frankly too mathematically ignorant to even really know what is meant exactly by "mathematical elegance". Also "elegance" by it's very nature would seem to be a highly subjective quality. But this approach does seem to have borne much fruit.

I am certainly no expert either, but this is the way I look at it:

The roots of mathematics lie in what I would equate to almost logical rules born of observation; 1 + 1 = 2 would not only be mathematically valid, but also a tautology. More advanced mathematics are in essence based on remaining internally consistent with those underpinnings, so that while entire sections may have no manifestation (irrational numbers for instance) the field itself is firmly rooted in reality.

Now what happens when we are wrong with a theory, where we have an incorrect formula? Usually we require weird constants and gyrations in order to fit our curve or answer to observations. These formula are accurate only within certain ranges, outside of which they are unreliable. A formula that is correct is correct in all cases, and usually fits nicely with other known formula.

What I am getting at is that the concept of "elegance" is talking about internal consistency. Mathematics is based on being internally consistent with itself, and being based on reality the assumption becomes that reality is internally consistent as well. This appears to have born out to this point in time, and the confidence in this trend continuing is the expectation of "elegance" in formula for natural laws.


This message is a reply to:
 Message 136 by Straggler, posted 05-16-2010 9:41 AM Straggler has responded

Replies to this message:
 Message 152 by Straggler, posted 05-18-2010 8:57 AM Phage0070 has responded

  
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