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Author Topic:   Physics contradicts maths - how is this possible?
PurpleYouko
Member
Posts: 714
From: Columbia Missouri
Joined: 11-11-2004


Message 31 of 69 (442542)
12-21-2007 3:53 PM
Reply to: Message 1 by Agobot
12-20-2007 5:24 PM


I much prefer the proof that a fly can stop a moving train.
imagine a fly heading north at a few miles per hour collides directly with a train heading south at 100 miles per hour.
There has to be an instant in time at which the fly's velocity passes through zero as it reverses direction. If the fly is in physical contact with the train (i.e. splattered all over it like a coat of paint) at that instant when its velocity is zero then it stands to reason that the train must also be stationary at that instant.
trouble is that this only works if you think of the collision as an inelastic contact like that between two pool balls (yeah I know that is elastic too but what the heck)
In reality, the molecules of the train and the fly actually deform or even slightly pass through each other so while the fly is stationary it is somewhat inside the fast moving train.
Kind of make my head spin thinking about it

This message is a reply to:
 Message 1 by Agobot, posted 12-20-2007 5:24 PM Agobot has not replied

Replies to this message:
 Message 33 by sinequanon, posted 12-21-2007 4:16 PM PurpleYouko has replied

  
sinequanon
Member (Idle past 2865 days)
Posts: 331
Joined: 12-17-2007


Message 32 of 69 (442543)
12-21-2007 3:55 PM
Reply to: Message 30 by Modulous
12-21-2007 3:40 PM


If it's not a real number, then it doesn't matter does it?
Yes it does. It could mean the sequence diverges.
Yes I can see that. I'm not sure how one could argue that 9/10 + 9/100 +9/1000... diverges.
Proving it doesn't is mathematics.
'Not being sure how one could argue otherwise' is not mathematics.

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 Message 30 by Modulous, posted 12-21-2007 3:40 PM Modulous has replied

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 Message 37 by Modulous, posted 12-21-2007 6:15 PM sinequanon has replied

  
sinequanon
Member (Idle past 2865 days)
Posts: 331
Joined: 12-17-2007


Message 33 of 69 (442547)
12-21-2007 4:16 PM
Reply to: Message 31 by PurpleYouko
12-21-2007 3:53 PM


If the fly is in physical contact with the train (i.e. splattered all over it like a coat of paint) at that instant when its velocity is zero
Physical contact does not necessarily imply travelling at the same speed. Physical contact means significant intermolecular interaction at molecular scales. The molecules of the fly are decelerated to zero by intermolecular forces as they approach the molecules of the train. The fly molecules go through zero velocity while the train is still approaching them, because intermolecular forces act at a finite distance (albeit small). They are then accelerated (still approaching the train from a tiny but finite distance) until the speeds match.
Edited by sinequanon, : No reason given.

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 Message 31 by PurpleYouko, posted 12-21-2007 3:53 PM PurpleYouko has replied

Replies to this message:
 Message 34 by PurpleYouko, posted 12-21-2007 4:24 PM sinequanon has replied

  
PurpleYouko
Member
Posts: 714
From: Columbia Missouri
Joined: 11-11-2004


Message 34 of 69 (442550)
12-21-2007 4:24 PM
Reply to: Message 33 by sinequanon
12-21-2007 4:16 PM


ummmm didn't I just say that?

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 Message 33 by sinequanon, posted 12-21-2007 4:16 PM sinequanon has replied

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 Message 35 by sinequanon, posted 12-21-2007 4:27 PM PurpleYouko has replied

  
sinequanon
Member (Idle past 2865 days)
Posts: 331
Joined: 12-17-2007


Message 35 of 69 (442552)
12-21-2007 4:27 PM
Reply to: Message 34 by PurpleYouko
12-21-2007 4:24 PM


Perhaps. But the way I put it doesn't make the head spin.

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 Message 34 by PurpleYouko, posted 12-21-2007 4:24 PM PurpleYouko has replied

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 Message 36 by PurpleYouko, posted 12-21-2007 4:42 PM sinequanon has not replied

  
PurpleYouko
Member
Posts: 714
From: Columbia Missouri
Joined: 11-11-2004


Message 36 of 69 (442556)
12-21-2007 4:42 PM
Reply to: Message 35 by sinequanon
12-21-2007 4:27 PM


Hmmm. that's not a bad point.
Your way just makes it seem so .... reasonable. hehe.

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Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 37 of 69 (442595)
12-21-2007 6:15 PM
Reply to: Message 32 by sinequanon
12-21-2007 3:55 PM


Yes it does. It could mean the sequence diverges.
Of course it matters for the proof. It doesn't really matter in context unless Agobot is of the opinion that it does diverge. I don't see that is the case, and it seems implied that Agobot does not think they diverge.
'Not being sure how one could argue otherwise' is not mathematics.
An obvious statement. Did you think that I thought it was mathematics that you needed to correct me?

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 Message 32 by sinequanon, posted 12-21-2007 3:55 PM sinequanon has replied

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 Message 38 by sinequanon, posted 12-22-2007 5:46 AM Modulous has replied

  
sinequanon
Member (Idle past 2865 days)
Posts: 331
Joined: 12-17-2007


Message 38 of 69 (442641)
12-22-2007 5:46 AM
Reply to: Message 37 by Modulous
12-21-2007 6:15 PM


Of course it matters for the proof. It doesn't really matter in context unless Agobot is of the opinion that it does diverge. I don't see that is the case, and it seems implied that Agobot does not think they diverge.
I could give you another series where it 'seems implied that I do not think it diverges', and for which your logic would fail.
I suppose what you are saying is that it is 'obvious' to you that this one converges, so you didn't bother to prove it?

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 Message 37 by Modulous, posted 12-21-2007 6:15 PM Modulous has replied

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 Message 39 by Modulous, posted 12-22-2007 7:26 AM sinequanon has replied

  
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 39 of 69 (442655)
12-22-2007 7:26 AM
Reply to: Message 38 by sinequanon
12-22-2007 5:46 AM


I suppose what you are saying is that it is 'obvious' to you that this one converges, so you didn't bother to prove it?
We are on a debate forum, not a pure mathematics exam. I only bother to debate points that are under contention. As I said, it is possible to fill every answer with pages of axioms - but why bother if everyone already accepts them? How would that advance the debate?
Further - a more complete proof had already been given, I gave an admittedly much simpler one which was obviously less complete that might help Agobot understand the point, serving a springboard to further discussion.
Now, had Agobot turned around and said "But, you are assuming that the series converges", then we'd could move from there to demonstrating that it does. Baby steps, in debate, often prove more valuable than taking great leaps.

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 Message 38 by sinequanon, posted 12-22-2007 5:46 AM sinequanon has replied

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Son Goku
Inactive Member


Message 40 of 69 (442667)
12-22-2007 9:08 AM
Reply to: Message 26 by Chiroptera
12-21-2007 1:20 PM


Population of the Reals.
Here's another cool fact. At least I find fascinating.
Take the real numbers. Obviously within this set of real numbers are the set of integers (whole numbers). Now another set within in the real numbers is the set of rationals (fractions). The set of rationals contains the integers since any whole number like 3 is also a fraction when written as 3/1.
Now the next set we have is the algebraics. The algebraics are any number which is the solution to a "high-school algebra" equation like: X^3 + X^2 + 3X = 4. Basically anything that is a root of a polynomial, for people who know what that is. This set includes numbers like the square root of 2(solution of x^2 = 2) which aren't fractions. However it also includes fractions. So it's an even larger set of numbers than the rationals. However it doesn't include things like Pi.
Now an even bigger set is the computables. These are any numbers for which there exists (even in theory) an algorithm which can compute their digits one by one. This includes all of the algebraics, but it also includes numbers like Pi and e, since we can compute their digits one by one.
Basically the computables contain every single numbers you've ever heard of and all numbers that can theoretically be found with a computer if you had infinite time to find them.
Now what about the Real numbers that are left over, the so called uncomputables. It turns out they're most of the real numbers.
This means for instance that between 3 and 4, every fraction, every algebraic and every computable number forms just a vanishing amount of the numbers between 3 and 4.
Most of the numbers between 3 and 4 are numbers which can never be found or described, even in theory given an infinite amount of time.

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 Message 26 by Chiroptera, posted 12-21-2007 1:20 PM Chiroptera has replied

Replies to this message:
 Message 41 by Chiroptera, posted 12-22-2007 9:11 AM Son Goku has replied

  
Chiroptera
Inactive Member


Message 41 of 69 (442669)
12-22-2007 9:11 AM
Reply to: Message 40 by Son Goku
12-22-2007 9:08 AM


Re: Population of the Reals.
Now what about the Real numbers that are left over, the so called uncomputables. It turns out they're most of the real numbers.
That I did not know.

It has become fashionable on the left and in Western Europe to compare the Bush administration to the Nazis. The comparison is not without some superficial merit. In both cases the government is run by a small gang of snickering, stupid thugs whose vision of paradise is full of explosions and beautifully designed prisons. -- Matt Taibbi

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 Message 40 by Son Goku, posted 12-22-2007 9:08 AM Son Goku has replied

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 Message 54 by Son Goku, posted 12-22-2007 5:17 PM Chiroptera has replied

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


Message 42 of 69 (442678)
12-22-2007 10:04 AM
Reply to: Message 1 by Agobot
12-20-2007 5:24 PM


Math models reality with abstract constructions
Welcome to the fray Agobot,
I'm going to answer in a different vein than the others:
Physics contradicts maths - how is this possible?
Because the math can be perfect and still wrong.
Contention - maths proves that in theory moving objects should never touch each other, physics shows the opposite.
Because the math can be perfect and still wrong.
How is this possible?
Because the math can be perfect and still wrong.
Math is based entirely on assumption, it is an intellectual abstract construction, and not part of the objective world, ie - "1" does not exist in the objective world, only in the abstract world.
As such there is no real tie between any mathematical computation and any object of the world of objective reality. Math can be used to model reality, but the model is only as good as the assumptions used in the maths, and thus whenever math and reality contradict one another it is the math that is wrong.
Bees fly. An engineer calculated that it couldn't, but it was the assumptions that the aerodynamics of man-made plane wings to the flight with bee wings that was in error.
Finding these contradiction improves our understanding of reality and our ability to model it, with theory and math.
Enjoy.
ps - some tips just in case: type [qs]quotes are easy[/qs] and it becomes:
quotes are easy
or type [quote]quotes are easy[/quote] and it becomes:
quote:
quotes are easy
also check out (help) links on any formating questions when in the reply window.

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This message is a reply to:
 Message 1 by Agobot, posted 12-20-2007 5:24 PM Agobot has not replied

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sinequanon
Member (Idle past 2865 days)
Posts: 331
Joined: 12-17-2007


Message 43 of 69 (442685)
12-22-2007 10:17 AM
Reply to: Message 39 by Modulous
12-22-2007 7:26 AM


I gave an admittedly much simpler one which was obviously less complete
It wasn't just incomplete, it was a wrong method. Convergence would normally be proved by showing the series tends to one. In this case assuming convergence would be assuming the thing you are trying to prove.

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 Message 39 by Modulous, posted 12-22-2007 7:26 AM Modulous has replied

Replies to this message:
 Message 44 by Modulous, posted 12-22-2007 12:10 PM sinequanon has replied
 Message 47 by Chiroptera, posted 12-22-2007 3:45 PM sinequanon has replied

  
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 44 of 69 (442709)
12-22-2007 12:10 PM
Reply to: Message 43 by sinequanon
12-22-2007 10:17 AM


It wasn't just incomplete, it was a wrong method. Convergence would normally be proved by showing the series tends to one. In this case assuming convergence would be assuming the thing you are trying to prove.
Perhaps you are yet again misunderstanding my purpose; it was to serve as a point of advancing discussion rather than piling on with mathematics that Agobot might have been ignorant of. If Agobot was able to follow kongstad's proof, then that is fine. However, it might have been over his head so I thought I'd start with something else. In some circumstances I have found it useful for springboarding discussion onto more advanced and correct matters. I find that a good way to learn is to try and argue against a certain position - but it helps if you understand the position.
As wiki usefully summarises:
quote:
The validity of the digit manipulations in the above two proofs does not have to be taken on faith or as an axiom; it can be proven by investigating the fundamental relationship between decimals and the numbers they represent. For finite decimals, this process relies only on the arithmetic of real numbers. To prove that the manipulations also work for infinite decimals, one needs the methods of real analysis.
I guess something akin to springboarding did occur, which is good, but the original poster hasn't chimed in since the question was asked and things are devolving into needless pedantry. I don't dispute your points from a pure mathematics point of view - I just dispute the wisdom of requiring ironclad proofs for all statements in a debate setting. I eagerly await Agobot's return to see what they make of the subsequent discussion.

This message is a reply to:
 Message 43 by sinequanon, posted 12-22-2007 10:17 AM sinequanon has replied

Replies to this message:
 Message 45 by sinequanon, posted 12-22-2007 1:05 PM Modulous has replied

  
sinequanon
Member (Idle past 2865 days)
Posts: 331
Joined: 12-17-2007


Message 45 of 69 (442722)
12-22-2007 1:05 PM
Reply to: Message 44 by Modulous
12-22-2007 12:10 PM


Agobot writes:
Distance between the wall and the fly is:
S=0.99999999999999999999999999999...metres
v=0.99999999999999999999999999999... m/sec
t=S/v
How much is infinity/infinity? Again infinity
Take Agobot's post#13. He has implied the series diverges.
Your implicit use of the convergence of the series doesn't actually pinpoint the error.

This message is a reply to:
 Message 44 by Modulous, posted 12-22-2007 12:10 PM Modulous has replied

Replies to this message:
 Message 46 by Modulous, posted 12-22-2007 1:15 PM sinequanon has not replied

  
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