Register | Sign In


Understanding through Discussion


EvC Forum active members: 65 (9162 total)
4 online now:
Newest Member: popoi
Post Volume: Total: 915,817 Year: 3,074/9,624 Month: 919/1,588 Week: 102/223 Day: 13/17 Hour: 0/1


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Author Topic:   Mathematics and Nature
RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 31 of 90 (269425)
12-14-2005 8:21 PM
Reply to: Message 28 by cavediver
12-14-2005 7:28 PM


Re: Why mathematics is so useful in the sciences
Just out of interest, why? Always is a very strong word.
Because math is a purely - and idealized - intellectual construction that does not exist outside the mind.
Take the counting of objects as an example: no two objects are really completely, purely 100% identical, so there is only 1 of anything. We "fuzzy" the definition of "object" to include a set of extremely similar objects - idealize them - to apply the intellectual concept.
We could argue about the concept of a plane as a surface, but let's cut to the quick and take {the still simple yet one level more complex concept of} the mobius strip: no such thing exists in reality.
You know my answers to the other questions - they have been extensively covered elsewhere, so we do not need to take this ot - lets keep this one about just the maths eh?

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
by our ability to understand
RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

This message is a reply to:
 Message 28 by cavediver, posted 12-14-2005 7:28 PM cavediver has replied

Replies to this message:
 Message 32 by Brad McFall, posted 12-14-2005 8:24 PM RAZD has replied
 Message 34 by Ben!, posted 12-14-2005 8:31 PM RAZD has replied
 Message 37 by cavediver, posted 12-14-2005 8:44 PM RAZD has replied
 Message 39 by nwr, posted 12-14-2005 9:01 PM RAZD has not replied

  
Brad McFall
Member (Idle past 5032 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 32 of 90 (269427)
12-14-2005 8:24 PM
Reply to: Message 31 by RAZD
12-14-2005 8:21 PM


Re: Why mathematics is so useful in the sciences
You sound like "Frege" to me. Sorry I have no more time tonite!!

This message is a reply to:
 Message 31 by RAZD, posted 12-14-2005 8:21 PM RAZD has replied

Replies to this message:
 Message 35 by RAZD, posted 12-14-2005 8:32 PM Brad McFall has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 33 of 90 (269432)
12-14-2005 8:28 PM
Reply to: Message 29 by nwr
12-14-2005 8:13 PM


Re: Why mathematics is so useful in the sciences
I see it a lot in discussions of cognitive science/artificial intelligence
Interesting. I wasn't aware of this, but it is easy to see how this can happen.
There is perhaps an appearance of this sort of problem in cosmology, but I suspect that most physicists and cosmologists well understand the need to involve reality.
Most excellently stated. And I certainly agree that there is an "appearance" to the outsider...

This message is a reply to:
 Message 29 by nwr, posted 12-14-2005 8:13 PM nwr has not replied

  
Ben!
Member (Idle past 1398 days)
Posts: 1161
From: Hayward, CA
Joined: 10-14-2004


Message 34 of 90 (269437)
12-14-2005 8:31 PM
Reply to: Message 31 by RAZD
12-14-2005 8:21 PM


Re: Why mathematics is so useful in the sciences
Take the counting of objects as an example: no two objects are really completely, purely 100% identical, so there is only 1 of anything. We "fuzzy" the definition of "object" to include a set of extremely similar objects - idealize them - to apply the intellectual concept.
I'm not so sure this is a valid objection. After all, if you're going to talk about "reality", then you have to also say that there's actually not any "1" thing at all; "objects" change all the time, whether it's their molecular motion or some atoms getting scrubbed off, etc.
And if you really want to talk "reality" and abstraction... then talk about how "objects" are "identified" and "persist", even though the input signals we get from the world basically show us CHANGE. "Objectness" itself is an abstraction, an abstraction of the human mind. It fits right in with all other types of categorization.
So I would say that, exactly in the same way that math is an abstraction of some "reality", so is our consciousness. We live an abstraction.
And in the same way, I would say, don't mistake the abstraction for the "reality".
Don't mean to push this off topic, just to point out that ... if you're going to go the philosophical route you are going, I think it's proper to "complete" the route.
Ben

This message is a reply to:
 Message 31 by RAZD, posted 12-14-2005 8:21 PM RAZD has replied

Replies to this message:
 Message 36 by RAZD, posted 12-14-2005 8:38 PM Ben! has not replied

  
RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 35 of 90 (269438)
12-14-2005 8:32 PM
Reply to: Message 32 by Brad McFall
12-14-2005 8:24 PM


Re: Why mathematics is so useful in the sciences
Gottlob Frege
Frege's Advances in Logic:
Frege virtually founded the modern discipline of mathematical logic. He developed a system of conceptual notation (inspired by Leibniz's conception of a rational calculus), and though we no longer use his notation, his system constituted the first predicate calculus. Frege's second-order predicate calculus was based on the `function-argument' analysis of propositions and it freed logicians from the limitations of the `subject-predicate' analysis of Aristotelian logic. Frege's formal system made it possible for logicians to develop a strict definition of a proof. Unfortunately, Frege employed a principle (Basic Law V) in his later system (Grundgesetze) which turned out to be inconsistent. Despite the fact that a contradiction invalidated his system, Frege validly derived the Peano Axioms governing the natural numbers from a powerful and consistent principle now known as Hume's Principle (some philosophers have proposed that the derivation of the Peano Axioms from Hume's Principle should be called `Frege's Theorem'). Frege is most well-known among philosophers, however, for suggesting that the expressions of language have both a sense and a denotation (i.e., that at least two semantic relations are required to explain the significance of linguistic expressions). This seminal idea in the philosophy of language has inspired research in the field for over a century.
Interesting. Thanks.

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
by our ability to understand
RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

This message is a reply to:
 Message 32 by Brad McFall, posted 12-14-2005 8:24 PM Brad McFall has not replied

  
RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 36 of 90 (269449)
12-14-2005 8:38 PM
Reply to: Message 34 by Ben!
12-14-2005 8:31 PM


Re: Why mathematics is so useful in the sciences
After all, if you're going to talk about "reality", then you have to also say that there's actually not any "1" thing at all; "objects" change all the time, whether it's their molecular motion or some atoms getting scrubbed off, etc.
Or the subatomic level where particles change from one to another, yes, true enough, and that just makes the idealized concept of a set of objects just that much more fuzzy at any substantiative closer level of inspection.
the mathematical concept of integers doesn't.
I would say, don't mistake the abstraction for the "reality".
map.

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
by our ability to understand
RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

This message is a reply to:
 Message 34 by Ben!, posted 12-14-2005 8:31 PM Ben! has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 37 of 90 (269458)
12-14-2005 8:44 PM
Reply to: Message 31 by RAZD
12-14-2005 8:21 PM


Re: Why mathematics is so useful in the sciences
Because math is a purely - and idealized - intellectual construction that does not exist outside the mind.
This is a statement of one's philosophy of course; a philosophy with which many mathematicians would not agree.
Take the counting of objects as an example: no two objects are really completely, purely 100% identical, so there is only 1 of anything.
At your length scale, you are approximately correct. But you are made up of fermions and bosons. These are identical... completely identical. This is why we have the Pauli exclusion principle, which is a good thing because we couln't exist without it!
We could argue about the concept of a plane as a surface, but let's cut to the quick and take {the still simple yet one level more complex concept of} the mobius strip: no such thing exists in reality.
I'm not sure what you mean here. I have made hundreds of mobius strips.
A mathematical space can be realised by far more than just a surface. Rotations of objects are better realisations, and rotations of fermions and bosons are even better. And these spaces are far far more bizarre than the good old mobius band.
Mathematics is certainly idealised at the length scales with which you are familiar... I have no problem with that. But I am not referring to those length scales.

This message is a reply to:
 Message 31 by RAZD, posted 12-14-2005 8:21 PM RAZD has replied

Replies to this message:
 Message 38 by RAZD, posted 12-14-2005 8:53 PM cavediver has replied

  
RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 38 of 90 (269463)
12-14-2005 8:53 PM
Reply to: Message 37 by cavediver
12-14-2005 8:44 PM


Re: Why mathematics is so useful in the sciences
I'm not sure what you mean here. I have made hundreds of mobius strips.
With edges, joints, and thickness. you might as well make a donut and call it a mobius strip.
made up of fermions and bosons.
always the same ones?

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
by our ability to understand
RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

This message is a reply to:
 Message 37 by cavediver, posted 12-14-2005 8:44 PM cavediver has replied

Replies to this message:
 Message 41 by cavediver, posted 12-14-2005 9:08 PM RAZD has replied

  
nwr
Member
Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 39 of 90 (269465)
12-14-2005 9:01 PM
Reply to: Message 31 by RAZD
12-14-2005 8:21 PM


Re: Why mathematics is so useful in the sciences
Because math is a purely - and idealized - intellectual construction that does not exist outside the mind.
Take the counting of objects as an example: no two objects are really completely, purely 100% identical, ...
That's a strange thing to say. After all, our concept of "object" is an idealized intellectual construction that does not exist outside the mind.

This message is a reply to:
 Message 31 by RAZD, posted 12-14-2005 8:21 PM RAZD has not replied

Replies to this message:
 Message 40 by Ben!, posted 12-14-2005 9:06 PM nwr has not replied

  
Ben!
Member (Idle past 1398 days)
Posts: 1161
From: Hayward, CA
Joined: 10-14-2004


Message 40 of 90 (269472)
12-14-2005 9:06 PM
Reply to: Message 39 by nwr
12-14-2005 9:01 PM


Re: Why mathematics is so useful in the sciences
Gee nwr, thanks for saying what I said in 4 paragraphs, in 2 lines.
Back to the drawing board One of these days, I'll figure out this whole communication thing.

This message is a reply to:
 Message 39 by nwr, posted 12-14-2005 9:01 PM nwr has not replied

Replies to this message:
 Message 44 by RAZD, posted 12-14-2005 10:58 PM Ben! has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 41 of 90 (269473)
12-14-2005 9:08 PM
Reply to: Message 38 by RAZD
12-14-2005 8:53 PM


Re: Why mathematics is so useful in the sciences
With edges, joints, and thickness
You are confused in your concept of mathematical space. A mobius band is a statement about the topology of a space. My cellotaped piece of paper has the correct topology and is hence a mobius band. The thickness is immaterial. The point is that a mobius band need have no thickness to be a mobius band, in the same way that a 2-sphere has no interior. The surface of the earth is a 2-sphere, despite the earth having an interior.
always the same ones?
How would I tell? They are identical. This is a pivotal point of quantum/particle physics. It is not an idealisation. The quantum theory of electrons falls apart if there is the slightest hint of even a theoretical possibility of being able to distinguish two electrons.

This message is a reply to:
 Message 38 by RAZD, posted 12-14-2005 8:53 PM RAZD has replied

Replies to this message:
 Message 43 by cavediver, posted 12-14-2005 9:30 PM cavediver has not replied
 Message 45 by RAZD, posted 12-14-2005 11:10 PM cavediver has replied

  
robinrohan
Inactive Member


Message 42 of 90 (269481)
12-14-2005 9:18 PM
Reply to: Message 12 by Dr Jack
12-13-2005 9:04 AM


Elegance
Maths is an entirely human construct
I don't see this. When math conflicts with common sense, math always wins. Quantum philosophy.
The universe is formal.
Elegant.

"And from water we made all living things."-- The Quran

This message is a reply to:
 Message 12 by Dr Jack, posted 12-13-2005 9:04 AM Dr Jack has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 43 of 90 (269486)
12-14-2005 9:30 PM
Reply to: Message 41 by cavediver
12-14-2005 9:08 PM


Quick probability quiz
Following on from my discussion with RAZD...
You have two electrons. Shake them up so they are equally likely to be spin up or spin down.
What is the prob they are both spin up?
What is the prob they are both spin down?
What is the prob one is spin up and the other spin down?

This message is a reply to:
 Message 41 by cavediver, posted 12-14-2005 9:08 PM cavediver has not replied

  
RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 44 of 90 (269517)
12-14-2005 10:58 PM
Reply to: Message 40 by Ben!
12-14-2005 9:06 PM


Re: Why mathematics is so useful in the sciences
It all comes down to perceptions of reality eh?

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
by our ability to understand
RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

This message is a reply to:
 Message 40 by Ben!, posted 12-14-2005 9:06 PM Ben! has not replied

  
RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 45 of 90 (269520)
12-14-2005 11:10 PM
Reply to: Message 41 by cavediver
12-14-2005 9:08 PM


Re: Why mathematics is so useful in the sciences
My cellotaped piece of paper ...
... models the mathematical concept close enough to convey the idea, but it is not the concept. Topologically or otherwise.
The quantum theory of electrons falls apart if there is the slightest hint of even a theoretical possibility of being able to distinguish two electrons.
And yet, when you look inside the subatomic particles are forever dancing and changing partners ... based on QT eh?
And you seem to be confusing "theoretical" with "actual" possiblity of distinguishing, are you claiming that theory is more important? Isn't that just exactly the point here? If it WAS measured and DID invalidate QT what would happen to reality?

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
by our ability to understand
RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

This message is a reply to:
 Message 41 by cavediver, posted 12-14-2005 9:08 PM cavediver has replied

Replies to this message:
 Message 46 by cavediver, posted 12-15-2005 4:26 AM RAZD has replied

  
Newer Topic | Older Topic
Jump to:


Copyright 2001-2023 by EvC Forum, All Rights Reserved

™ Version 4.2
Innovative software from Qwixotic © 2024