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Author Topic:   Physics contradicts maths - how is this possible?
Agobot
Member (Idle past 3607 days)
Posts: 786
Joined: 12-16-2007

 Message 1 of 69 (442277) 12-20-2007 5:24 PM

Contention - maths proves that in theory moving objects should never touch each other, physics shows the opposite. Simple example - 1 stationary object(eg. - a wall) and a fly flying toward it. Say the fly is 1 metre away from the wall. In 0.5 sec she is 0.5 metres from the wall. In 0.9 sec she is 0.1 meters from the wall, in 0.999 sec she is 1 mm from the wall, in 0.9999999999sec she is 0.000000009mm from the wall. In 0.9999999999999999999999999999 sec she'd be 0.0000000000000000000000000009mm from the wall and so on. Obviously, the distance between the fly and wall cannot and will never ever become zero. Yet practice shows that the fly lands on the wall and makes that distance zero. How is this possible?

Edited by Agobot, : No reason given.

Edited by Agobot, : No reason given.

 Replies to this message: Message 3 by Rrhain, posted 12-21-2007 12:22 AM Agobot has not yet responded Message 4 by anglagard, posted 12-21-2007 12:35 AM Agobot has not yet responded Message 5 by Taz, posted 12-21-2007 12:37 AM Agobot has not yet responded Message 10 by kongstad, posted 12-21-2007 5:04 AM Agobot has not yet responded Message 14 by cavediver, posted 12-21-2007 7:20 AM Agobot has not yet responded Message 16 by RickJB, posted 12-21-2007 7:56 AM Agobot has not yet responded Message 17 by Son Goku, posted 12-21-2007 7:56 AM Agobot has not yet responded Message 31 by PurpleYouko, posted 12-21-2007 3:53 PM Agobot has not yet responded Message 42 by RAZD, posted 12-22-2007 10:04 AM Agobot has not yet responded

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 Message 2 of 69 (442385) 12-20-2007 11:40 PM

Thread moved here from the Proposed New Topics forum.
Rrhain
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Posts: 6349
From: San Diego, CA, USA
Joined: 05-03-2003

 Message 3 of 69 (442390) 12-21-2007 12:22 AM Reply to: Message 1 by Agobot12-20-2007 5:24 PM

Agobot writes:

quote:
How is this possible?

It's called a "limit."

As the time goes to 1 s, the distance goes to 1 m.

It is because of the mathematical process of limits that we have modern physics. This idea that physics contradicts math is silly.

Physics is nothing more than applied math.

Rrhain

Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
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anglagard
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From: Socorro, New Mexico USA
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 Message 4 of 69 (442391) 12-21-2007 12:35 AM Reply to: Message 1 by Agobot12-20-2007 5:24 PM

Zeno of Elea
Nothing new here, it's one of Zeno's paradoxes

See the article (or perceive reality) for proposed solutions.

Read not to contradict and confute, not to believe and take for granted, not to find talk and discourse, but to weigh and consider - Francis Bacon

The more we understand particular things, the more we understand God - Spinoza

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Taz
Member (Idle past 1368 days)
Posts: 5069
From: Zerus
Joined: 07-18-2006

 Message 5 of 69 (442392) 12-21-2007 12:37 AM Reply to: Message 1 by Agobot12-20-2007 5:24 PM

 Agobot writes:maths proves that in theory moving objects should never touch each other, physics shows the opposite.

What on Earth are you talking about?

 Simple example - 1 stationary object(eg. - a wall) and a fly flying toward it. Say the fly is 1 metre away from the wall. In 0.5 sec she is 0.5 metres from the wall. In 0.9 sec she is 0.9 meters from the wall, in 0.999 sec she is 1 mm from the wall, in 0.9999999999sec she is 0.000000009mm from the wall. In 0.9999999999999999999999999999 sec she'd be 0.0000000000000000000000000009mm from the wall and so on. Obviously, the distance between the fly and wall cannot and will never ever become zero. Yet practice shows that the fly lands on the wall and makes that distance zero. How is this possible?

It's called a limit.

If I remember correctly, the ancient Greek mathematicians were the first to notice this so-called contradition between mathematics and the real world. That's because they didn't have the concept of a limit yet. But, as you may have noticed, it's been several thousand years since then and I'd like to think that we have made at least some progress in this area.

Owing to the deficiency of the English language, I have occasionally used the academic jargon generator to produce phrases that even I don't fully understand. The jargons are not meant to offend anyone or to insult anyone's intelligence!
 This message is a reply to: Message 1 by Agobot, posted 12-20-2007 5:24 PM Agobot has not yet responded

Taz
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Posts: 5069
From: Zerus
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 Message 6 of 69 (442393) 12-21-2007 12:41 AM Reply to: Message 3 by Rrhain12-21-2007 12:22 AM

 Rrhain writes:Physics is nothing more than applied math.

Haha. I'd like to think of it the other way around, that math is nothing more than physics without the meat.

Owing to the deficiency of the English language, I have occasionally used the academic jargon generator to produce phrases that even I don't fully understand. The jargons are not meant to offend anyone or to insult anyone's intelligence!
 This message is a reply to: Message 3 by Rrhain, posted 12-21-2007 12:22 AM Rrhain has responded

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sidelined
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 Message 7 of 69 (442403) 12-21-2007 2:08 AM Reply to: Message 6 by Taz12-21-2007 12:41 AM

Taz

"Physics is to math what sex is to masturbation" R.F.

 This message is a reply to: Message 6 by Taz, posted 12-21-2007 12:41 AM Taz has not yet responded

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dwise1
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 Message 8 of 69 (442406) 12-21-2007 2:42 AM Reply to: Message 7 by sidelined12-21-2007 2:08 AM

Aye. Physics describes how the universe works. And mathematics is the language of physics.

Eg, specifically to the OP, Newton had created the calculus to describe his view of the universe (proper nods to Leipniz, natÃ¼rlich).

BTW, mathematics can describe something completely nonsensical. Physics can only describe our models of what is. Ie, yeah, some nonsense might happen, but precious little.

{When you search for God, y}ou can't go to the people who believe already. They've made up their minds and want to convince you of their own personal heresy.
("The Jehovah Contract", AKA "Der Jehova-Vertrag", by Viktor Koman, 1984)

Humans wrote the Bible; God wrote the world.
(from filk song "Word of God" by Dr. Catherine Faber, http://www.echoschildren.org/CDlyrics/WORDGOD.HTML)

Of course, if Dr. Mortimer's surmise should be correct and we are dealing with forces outside the ordinary laws of Nature, there is an end of our investigation. But we are bound to exhaust all other hypotheses before falling back upon this one.
(Sherlock Holmes in The Hound of the Baskervilles)

Gentry's case depends upon his halos remaining a mystery. Once a naturalistic explanation is discovered, his claim of a supernatural origin is washed up. So he will not give aid or support to suggestions that might resolve the mystery. Science works toward an increase in knowledge; creationism depends upon a lack of it. Science promotes the open-ended search; creationism supports giving up and looking no further. It is clear which method Gentry advocates.
("Gentry's Tiny Mystery -- Unsupported by Geology" by J. Richard Wakefield, Creation/Evolution Issue XXII, Winter 1987-1988, pp 31-32)

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Rrhain
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Posts: 6349
From: San Diego, CA, USA
Joined: 05-03-2003

 Message 9 of 69 (442408) 12-21-2007 3:32 AM Reply to: Message 6 by Taz12-21-2007 12:41 AM

Taz responds to me:

quote:
quote:
Physics is nothing more than applied math.

Haha. I'd like to think of it the other way around, that math is nothing more than physics without the meat.

Well, as my physics prof said on the first day, biology is applied chemistry. Chemistry is applied physics. And physics is applied math.

As the other joke goes (and I know I've told it here before):

Biologists think they're biochemists.
Biochemists think they're chemists.
Chemists think they're physical chemists.
Physical chemists think they're physicists.
Physicists think they're god.
And god? Well, god thinks he's a mathematician.

Rrhain

Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
 This message is a reply to: Message 6 by Taz, posted 12-21-2007 12:41 AM Taz has not yet responded

 Replies to this message: Message 11 by cavediver, posted 12-21-2007 6:54 AM Rrhain has not yet responded

Member (Idle past 947 days)
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From: Copenhagen, Denmark
Joined: 02-24-2004

 Message 10 of 69 (442415) 12-21-2007 5:04 AM Reply to: Message 1 by Agobot12-20-2007 5:24 PM

Like others have said, the problem is just one of representation. You are just picking out certain points on the timeline of the experiment, and it is your method of selection that - apparently gives the contradiction. You can solve the problem without resorting to limits by changing the description of the problem, for instance -

the fly flies with a speed of 1m/s, the distance is 1m, so the fly reaches the wall in 1m / (1m/s) = 1s.

Your choice of description gives the same result. After 1/2 sec the fly has moved 1/2m, after another 1/4 sec it has move further 1/4 m etc, so to see how far it moves in 1 sec you have the statement

1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2^n + ...

Luckuly you can solve this, and the result is .. 1!

If that freaks you out the please consider another little joke

IT is true that 0.9<1 , 0.99<1, 0.9999999 < 1
But it is also true that
0.99999... = 1 !

That is, the infinite decimal fraction 0.999999... equals 1

/Soren

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cavediver
Member (Idle past 1720 days)
Posts: 4129
From: UK
Joined: 06-16-2005

 Message 11 of 69 (442417) 12-21-2007 6:54 AM Reply to: Message 9 by Rrhain12-21-2007 3:32 AM

 As the other joke goes (and I know I've told it here before):Biologists think they're biochemists.Biochemists think they're chemists.Chemists think they're physical chemists.Physical chemists think they're physicists.Physicists think they're god.And god? Well, god thinks he's a mathematician.

Joke? Simple statement of fact, surely?

And god is either not a mathematician, or she's simply capricious/sadistic - how else do you explain five digits... base 10 ffs, ranking slightly above base 17 in usefulness.

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cavediver
Member (Idle past 1720 days)
Posts: 4129
From: UK
Joined: 06-16-2005

 Message 12 of 69 (442418) 12-21-2007 6:58 AM Reply to: Message 7 by sidelined12-21-2007 2:08 AM

 "Physics is to math what sex is to masturbation" R.F.

And when you get to Dick's level at both, you're allowed to make statements like this...

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Agobot
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 Message 13 of 69 (442419) 12-21-2007 7:05 AM

Will somebody care to explain how "0.99999999..." is "1" in the real world and under what circumstances? The explanation about there being a limit is mute as there is no observable limit between "0.99999999999999..." and "1". Also, in the real world there is never a speed of 1m/sec. If you have to be precise, and in this case we must be, there can be 0.999999...m/sec or 1.0000... m/sec but not 1m/sec. We use 1m/sec as a rounded value for simplicity, but that does not mean that such an exact value exists. When you apply the real speed, which will always be different than the rounded value 1m/sec., you'll see that the fly will never touch the wall. Example:

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

Edited by Agobot, : No reason given.

Edited by Agobot, : No reason given.

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cavediver
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Posts: 4129
From: UK
Joined: 06-16-2005

 Message 14 of 69 (442422) 12-21-2007 7:20 AM Reply to: Message 1 by Agobot12-20-2007 5:24 PM

Enough replies have already dealt with the mathematics (and the simple fact that an infinite sum can converge to a definite value.)

What about the physics? You are talking about distance between two objects, a fly and a wall in this case. The notion of there being an unabiguous distance only works at sufficiently large length-scales. As you start to approach the molecular length-scale, you will notice that you no longer have well-defined edges demarking the extent of your objects. Objcts that are naively touching (end of leg on wall) is a massively complicated picture, involving many levels electromagnetic interaction. A poor analogy that perhaps gets the complication across is imagine holding two small bushes, and pushing them against each other. At what point are they together? When the first twigs touch? When you can feel real resistance? When you can't push them any further together?

As is often the case, the physical picture changes long before issues with the mathematics become apparent.

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

PaulK
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 Message 15 of 69 (442424) 12-21-2007 7:33 AM Reply to: Message 13 by Agobot12-21-2007 7:05 AM

quote:

Will somebody care to explain how "0.99999999..." is "1" in the real world and under what circumstances?

Always. They're different representations of the same number.

quote:

The explanation about there being a limit is mute as there is no observable limit between "0.99999999999999..." and "1".

You don't understand the use of 'limit' here. (Or that it's "moot", not "mute"). The limit of 0.99999... as you add on more '9's is 1. Of course there isn't anything between 0.999999.... and 1 because they're the same number.

quote:

If you have to be precise, and in this case we must be, there can be 0.999999...m/sec or 1.0000... m/sec but not 1m/sec.

Because 0.99999... is an infinite decimal, it has the same infinite precision as 1.0. Even if they weren't the same number they'd be equally "impossible".

 This message is a reply to: Message 13 by Agobot, posted 12-21-2007 7:05 AM Agobot has not yet responded

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