Will you ever hit the wall?

kgun · #1 (**permalink**) 02-26-2008, 01:46 AM

"The Greek philosopher Zeno wrestled with this concept in a slightly different context. In Zeno's dichotomy paradox, you run toward a wall. As you run, you halve the distance to the wall, then halve it again, and so on. But if you continue to subdivide space forever, how can you ever actually reach the wall? (The answer is that you can't: Once you're within a few nanometers, atomic repulsion forces become too strong for you to get any closer)."

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Tubby · #2 (**permalink**) 02-26-2008, 04:43 AM

That's just one of those silly things that demonstrate that thinking too much is silly.

There is always a point where the change over between what is real and what is conceptual. .
You can blur that point without a great deal of trouble. . (especially for mathematicians)

creatures with high IQ's can often 'see' things that do not exist. (and often actually believe what they see to be real)

kgun · #3 (**permalink**) 02-26-2008, 04:55 AM

Tubby, but I would not rely on that paradox in a real situations

Again we have to introduce infinity, your "favourite" term:

lim (n --> infinity) (1/2)^n = 0 (You hit the wall)

What happened to my key board??

Had to cut and paste from Word to write the end of the above equation. Sometimes this editor goes mad.

Tubby · #4 (**permalink**) 02-26-2008, 06:22 AM

Kgun said
"Again we have to introduce infinity, your "favourite" term:"

You know my thoughts mate. . To my mind Kgun the concept of Infinity is almost evil. It is useful as a tool. . but when people start believing it confusion reigns.

You probably confused your keyboard by messing about thinking of infinity.

Alan-Hart · #5 (**permalink**) 02-26-2008, 06:28 AM

is that a similar theory to... when a fly hits the windshield of a speeding train it stops the train for a very small amount of time? (for that split second of impact neither the train nor the fly are moving in either direction)

kgun · #6 (**permalink**) 02-26-2008, 02:50 PM

According to Zeno's paradox about infinity (Tubby, our friend once more) and the movement of an arrow, motion is nothing but an illusion.

So your example should be part of the same illusion (theory).

My personal explanation of infinity and the wall.

Imagine you:

Stand 1 meter from the wall.
Then you move your foot 1/2 meter from the wall. The continuation is
1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024, 1/2048, .... meter from the wall and so on.

When your foot hit the wall, you have "multiplied 1/2 with 1/2 an infinite number of times".

Was that movement?

Ask Decartes if you moved your foot fast enough.

It hurts ==> I exist

and motion is no illusion.

And the conclusion is

bj · #7 (**permalink**) 02-26-2008, 06:04 PM

I tell you what, Kgun. If you believe this stuff then you should have no problem with me shooting a gun at you since the bullet will never reach you.

cw1865 · #8 (**permalink**) 02-26-2008, 06:20 PM

Kgun likes his math

I think in English the word is asymptotes (the Norwegian word is probably different). In math the function will constantly approach the x or y axis and of course never get there. When I was in high school at first I wasn't really that interested in calculus (thought it was boring), but, and I forget the function now, when evaluating the area underneath a curve using integrals between 1 and infinity, the infinity dropped out because 1/infinity by definition is zero hence the area under the curve was 1, but obviously the surface area was infinite....saw that and it piqued my interest! (for the life of me I can't remember the function, it was simple, 1/x square or something like that)

Tubby · #9 (**permalink**) 02-26-2008, 06:40 PM

Kgun said. re infinity and the wall.
if you moved your foot fast enough. It hurts therefore you exist
I like that Kgun. that's funny. (and true)

That pretty well sums it up. It never hurts when you do it on a calculator.

I am content with the conclusion

if you moved your foot fast enough. It hurts, therefore you exist

BJ said.
"I tell you what, Kgun. If you believe this stuff then you should have no problem with me shooting a gun at you since the bullet will never reach you. "

Now this is an example of why I find the concept of infinity evil. If in BJs example the person holding the gun believes it - someone is dead.

Many people do accept the concept of infinity as a reality. Many people believe in infinity. In a time of stress a persons thinking can come to some 'crazy' conclusions if they do not have some solid building blocks to construct the answer to their problems.

the concept of infinity is the most widly used false building block used in human thought

This message should be posted in every school. It is merely a concept. .

Tubby · #10 (**permalink**) 02-26-2008, 06:57 PM

Kgun

here is two books you can write.

The argument against infinity and the sequel Emotion; the recognition factor

The word needs them. somebody will write them one day, it will not be me..

craigmn3 · #11 (**permalink**) 02-26-2008, 07:09 PM

When Dealing with a finite space, infinity doesn't apply. If the wall is ten feet away, it will be reached by a certainty of acceleration. If the speed is 1 ft per second and the acceleration constant the wall will be reached in ten seconds. You can spilt your nanoseconds all you please but impact will occur in the related time space. Having stated that, we must accept the fact that there is no real infinity, atleast between 1 and zero. There is a number reached at somepoint when impact happens. and it is finite. Perhaps as we are splitting those nano seconds we reach a warp that finaly closes the gap.

bj · #12 (**permalink**) 02-26-2008, 07:12 PM

Maybe instead of "Will you ever hit the wall?" the question should instead be Will you ever close a door?

kgun · #13 (**permalink**) 02-26-2008, 07:42 PM

Quote:

Originally Posted by bj

I tell you what, Kgun. If you believe this stuff then you should have no problem with me shooting a gun at you since the bullet will never reach you.

An American Woman, with a gun shooting kgun.

Have you seen the movie "The matrix"?

bj · #14 (**permalink**) 02-26-2008, 07:52 PM

LOL!

Nope, I don't watch movies. If I can't interact with the screen it puts me to sleep.

Don't worry, I've never shot a gun, so in reality the bullet would probably hit the broad side of the barn. Or not.

kgun · #15 (**permalink**) 02-26-2008, 07:57 PM

Quote:

Originally Posted by cw1865

Kgun likes his math

I think in English the word is asymptotes (the Norwegian word is probably different). In math the function will constantly approach the x or y axis and of course never get there. When I was in high school at first I wasn't really that interested in calculus (thought it was boring), but, and I forget the function now, when evaluating the area underneath a curve using integrals between 1 and infinity, the infinity dropped out because 1/infinity by definition is zero hence the area under the curve was 1, but obviously the surface area was infinite....saw that and it piqued my interest! (for the life of me I can't remember the function, it was simple, 1/x square or something like that)

Look at this function f(n) = (2n)/(1/n) That is a triangle with area (integral): [(2n)*(1/n)]/2 = 1.

Then let n --> infinity. In the limit it collapses to a Dirac puls with infinite height and zero base. But the integral (area) is constant, 1. A traditional Rieman integral over a point = 0. But this function is so infinite that it has all its mass in the origin. If you understodd this, you have understood mathematics on the graduate level.
Norway's coast line is often used as an example of a fractal with infinite length. But the area of Norway is definitely final. Inscribe Norway in a big enough circle with finite ara.

kgun · #16 (**permalink**) 02-26-2008, 08:18 PM

Quote:

Originally Posted by Tubby

Kgun

here is two books you can write.

The argument against infinity and the sequel Emotion; the recognition factor

The word needs them. somebody will write them one day, it will not be me..

Tubby, do you know that a Norwegian mathematician Abel, Niels Henrik (1802-1829) -- from Eric Weisstein's World of Scientific Biography (that died 27 years old and wrote his PHD Thesis 6 pages long that was approved), showed so sloppy precision in mathematics, especally regarding the concept of infinity, that it has been said that he gave work to mathematicians for a least 100 year.

Infinity is fundamental and beautiful.

Divergence and convergence, too. It is very important in finance where you may value an bond with infinite life. I has a finite present value, because of convergence. Look at my example above again, where I claimed that by moving your foot to the wall, you have "multiplied 1/2 with 1/2 an infinite number of times"

1/2 x 1/2 x ...... x 1/2 infinite times = 0. (Your foot hit the wall)

You feel that "foot calculator" on your toe if you kick hard enough. If you understand that, you have understood infinity in this setting.

I have a friend working for a Norwegian Tv station that says:

"I love deadlines."

I love infinity.

Without divergence, you could not have produced many of these beautiful fractals.

kgun · #17 (**permalink**) 02-26-2008, 08:26 PM

Quote:

Originally Posted by craigmn3

When Dealing with a finite space, infinity doesn't apply

Take a look at this simple fractal (The Cantor set) that is constructed within the unit interval [0,1]

The number of elements is not countable:

1,2,3,4,5,6,7,.....

There are an over countable number of elements, but the length = 0.

So "in as sense" there are "more than an infinite number of elements".

This is math.

Have to go to bed.

Tubby · #18 (**permalink**) 02-27-2008, 12:04 AM

Kgun said
"Infinity is fundamental and beautiful."

I have never denied its beauty Kgun. . . I simply deny its existence. I can see it, it is beautiful. . but alas it is a concept. It works in maths because that also is a concept. Math is beautiful. and if ever you come across one you can feed it for me. or pick it up and toss it into the sea, or climb it . . If you can, but you cannot, it is merely a concept, and the basis for many false presumptions.

If you say the average woman has 2.83 children. . That's a conceptual calculation, it is merely a tool used for calculation - there are no .83 persons. every living person is whole - even if they lost two legs and have just had a haircut. if you count the guests at an amputees convention . . you still record "120 guests"

You can award maths scientist as much as you like. . Infinity is still merely a concept. Believing in it is no more than schitzoprenic.

thehappysmoker · #19 (**permalink**) 02-27-2008, 03:49 AM

Quote:

Originally Posted by Tubby

That's just one of those silly things that demonstrate that thinking too much is silly.

There is always a point where the change over between what is real and what is conceptual. .
You can blur that point without a great deal of trouble. . (especially for mathematicians)

Mathematicians seem to believe that maths is a science, when, in reality (if there is such a thing), it is an art. If it was a science, every question would have a possible answer, but every schoolchild knows about the square root of minus one, and the absolute value of pi. As for the Cartesian theory, an unconscious person doesn't think, therefore he is not, and anyway, the pain of kicking the wall doesn't prove that it's you who feels it, just that you're pretty stupid to go around kicking walls. The frog will never get out of the pond. Pass me the gun, BJ. Let's put his theories to the test.