Physics contradicts maths - how is this possible?

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.

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Agobot writes:

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How is this possible?

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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.

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Rrhain

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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.

Nothing new here, it's one of Zeno's paradoxes See the article (or perceive reality) for proposed solutions.

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

What on Earth are you talking about? 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.

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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!

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

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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!

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

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, natrlich).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.

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{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, No webpage found at provided URL: 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)

Taz responds to me:

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Physics is nothing more than applied math.

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

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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.

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Rrhain

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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.

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 statement1/2 + 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 jokeIT 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

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.

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

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/sect=S/vHow much is infinity/infinity? Again infinityEdited by Agobot, : No reason given.Edited by Agobot, : No reason given.

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.

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

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

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

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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.

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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.

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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".