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James Dunn
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WNTFBS2
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 Posted: Thu Apr 21, 2005 12:00 am Post subject: Re: OT: The mathematics of movement |
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| Quote: | Anyhow, here's the proof:
"In order for one to move, you must transition >>from one point to
another
point. We'll call the first point 'Point A' >>and the second point
'Point
B'. You agree that, in order for movement to >>occur, we must move
from
'Point A' to 'Point B'?"
here is where you nod
"So, using the principle of endpoints and >>midpoints that exist in any
line, one could argue that in order to move >>from 'Point A' to 'Point
B',
you must first cross 'Mid-point C'. That's >>simple geometry; it is
impossible to cross from one point on a line >>to another without
crossing a
middle point"
this is where you nod some more and pretend >>to be interested as you
get
sleepy
"So now we are faced with the issue of moving >>from 'Point A' to
'Mid-Point
C' before moving to 'Point B', on the other side >>of the line. Well,
to
move further with this process, it is apparent >>that in order to move
from
'Point A' to 'Mid-Point C', we have to cross a >>mid-point between this
two
new points, which we will call 'Mid-Point D'."
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Does the concept of convergence or continuity ring a bell MysteriAce ?
Lets normalize the distance between A and B to 1.
So what you are saying is that to go from A to B you will have to travel
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ....
That sum is nothing more than a geometrical series with an infinite number
of terms and quotient 1/2 (to get one term you have to multiply the former
by 1/2)
Because all terms are positive, and there are infinitely many terms, you
might be inclined to think that the sum might be infinitely large.
Guess what, ITS NOT. That series is a convergent series, which means
although it has an infinite number of terms it has a FINITE SUM (as
puzzling as that might sound when you hear it for the first time)
The sum of a geometrical series with an infinite number of terms is given
by the formula: First term / (1- quotient) if Abs(quotient)<1
In the present case that sum is (1/2)/(1-1/2)=(1/2)/(1/2)=1
The sum of that infinite number of terms is a finite number (1)
So although you are right that to go from A to B you will have to cover an
infinite number of small distances, it is possible to do it because the
sum of that infinite number of small distances is a finite distance and
therefore you can you do it in a finite time. |
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Stephen Jacobs
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| Posted: Thu Apr 21, 2005 1:00 am Post subject: Re: The mathematics of movement |
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"andreas kinell" <[email protected]> wrote in message
news:[email protected]...
| Quote: |
"Stephen Jacobs" <[email protected]> schrieb im Newsbeitrag
news:[email protected]...
"MysteriAce" <[email protected]> wrote in message
news:[email protected]...
On Apr 20 2005 2:37 PM, andreas kinell wrote:
Prove me wrong MATHEMATICALLY, not with your empirical evidence and
conjecture.
:)
I could do it, but it's doubtful that you'd understand what I said.
Developing the right concepts from everyday ideas would take several
pages.
or it takes like 8 lines.
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I'm afraid you don't have a clue what mathematical rigor really is. I could
just about justify integer arithmetic in 8 lines to someone who wanted to be
convinced. We have to show here that the limit of a non-changing sequence
is equal to the value of the members of the sequence. The definitions of
sequence and limit would be a page to start with, maybe more. And yes, it
is necessary to be that pedantic or the truth can escape. |
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Rich Shipley
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| Posted: Thu Apr 21, 2005 2:01 am Post subject: Re: OT: The mathematics of movement |
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MysteriAce wrote:
| Quote: | On Apr 20 2005 1:03 PM, OrangeSFO wrote:
you can demonstrate that there are infinite mid-points to cross, but
you haven't shown why it's not possible to traverse them.
You cannot traverse them because, before you can move to any midpoint, you
must cross the one before it. And there are an infinite number of
midpoints. Therefore, for every midpoint you attempt to traverse, you
must first traverse the one before that.
For example, to move 1 foot, you must first move 1/2 foot, but before that
move 1/4 foot, 1/8 foot, 1/16th, 1/32nd, 1/64th....
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You have not demonstrated that one can't pass an infinite number of
arbitrary points in finite time.
Rich |
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Guest
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| Posted: Thu Apr 21, 2005 4:00 am Post subject: Re: OT: The mathematics of movement |
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Empirical results support my hypothesis that higher math gives me a
headache - although I do wish I understood it better. :-)
On Wed, 20 Apr 2005 21:33:10 -0400, Rich Shipley <[email protected]>
wrote:
| Quote: | MysteriAce wrote:
On Apr 20 2005 1:03 PM, OrangeSFO wrote:
you can demonstrate that there are infinite mid-points to cross, but
you haven't shown why it's not possible to traverse them.
You cannot traverse them because, before you can move to any midpoint, you
must cross the one before it. And there are an infinite number of
midpoints. Therefore, for every midpoint you attempt to traverse, you
must first traverse the one before that.
For example, to move 1 foot, you must first move 1/2 foot, but before that
move 1/4 foot, 1/8 foot, 1/16th, 1/32nd, 1/64th....
You have not demonstrated that one can't pass an infinite number of
arbitrary points in finite time.
Rich |
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Peter Lizak
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| Posted: Thu Apr 21, 2005 7:00 am Post subject: Re: OT: The mathematics of movement |
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who says you can only travel through a finite number of points in a finite
time?
P.
Don't mess, B.Math, M.Math
On Wed, 20 Apr 2005, MysteriAce wrote:
| Quote: | Since we're on the 'post non-poker-related' gibberish today, I have one
that has always been my favorite.
The argument is that movement is an illusion, since it is mathematically
impossible for us to move. Therefore, one could argue that this state of
existance is purely an illusion, which opens the door to all sorts of
possibilities...
Anyhow, here's the proof:
"In order for one to move, you must transition from one point to another
point. We'll call the first point 'Point A' and the second point 'Point
B'. You agree that, in order for movement to occur, we must move from
'Point A' to 'Point B'?"
here is where you nod
"So, using the principle of endpoints and midpoints that exist in any
line, one could argue that in order to move from 'Point A' to 'Point B',
you must first cross 'Mid-point C'. That's simple geometry; it is
impossible to cross from one point on a line to another without crossing a
middle point"
this is where you nod some more and pretend to be interested as you get
sleepy
"So now we are faced with the issue of moving from 'Point A' to 'Mid-Point
C' before moving to 'Point B', on the other side of the line. Well, to
move further with this process, it is apparent that in order to move from
'Point A' to 'Mid-Point C', we have to cross a mid-point between this two
new points, which we will call 'Mid-Point D'."
"Of course, you cannot move from 'Point A' to 'Mid-Point D' without
crossing 'Mid-Point E', and so forth. Using the mathematical principle
behind halving numbers, you will find that there are an infinite number of
'Mid-Points' between any two given points, since the distance that you are
halving approaches - but never reaches - zero."
"Therefore, movement is impossible, and strictly an illusion, since you
cannot move from one point to another without having to cross an infinite
number of midpoints in between."
So how did I type this?
~ MysteriAce
"I'm a lot like Jesus, but not in a sacrilegious way"
----
* kill-files, watch-lists, favorites, and more.. www.recgroups.com
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Peter Lizak
[email protected]
Scientific Computing Lab, University of Waterloo |
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Peter Lizak
Guest
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| Posted: Thu Apr 21, 2005 8:00 am Post subject: Re: The mathematics of movement |
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On Wed, 20 Apr 2005, Stephen Jacobs wrote:
| Quote: |
"MysteriAce" <[email protected]> wrote in message
news:[email protected]...
On Apr 20 2005 2:37 PM, andreas kinell wrote:
well, you typed far to much.
Obviously, there is an infinite amount of mid-points,
and obviously, you can cross several midpoints in one step.
so the whole argument falls.
Prove me wrong MATHEMATICALLY, not with your empirical evidence and
conjecture.
:)
I could do it, but it's doubtful that you'd understand what I said.
Developing the right concepts from everyday ideas would take several pages.
But here's some more hand waving with a tiny bit more rigor: We may as well
say that to go from point A to point B, you first have to get to the
half-way point. It takes half the nominal time of the trip to get from A to
the halfway point, and it takes half the nominal time of the trip to get
from the halfway point to B. No problem. But now you tell me that I have
to get to the quarter-way point before I can get to the halfway point. It
takes me a quarter of the nominal time for the whole trip to get to the
quarter-way point, and another quarter to get to the halfway point, total,
half the nominal total. Again, no problem. As the division continues to
get finer, the total time doesn't change at any stage, so in the limit
there's still no problem.
Here's one that ought to drive you batty. God decides to play a card game.
He has an infinite number of cards, with the integers on them. Every second
(count the seconds as 'n'), He puts the cards numbered 2n and 2n+1 in a hat,
but removes the card numbered n. At the end of infinite time, even though
one card a second has been going into the hat, the hat is empty---for any
number you choose, that card is not in the hat because I can tell you when
it was removed from the hat.
Georg Cantor, who worked out most of the mathematics of infinities, spent a
large part of his life in insane asylums.
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yay number theory, now on to poker.
P
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Peter Lizak
[email protected]
Scientific Computing Lab, University of Waterloo |
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andreas kinell
Guest
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| Posted: Thu Apr 21, 2005 10:00 am Post subject: Re: The mathematics of movement |
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"Stephen Jacobs" <[email protected]> schrieb im Newsbeitrag
news:[email protected]...
| Quote: |
"andreas kinell" <[email protected]> wrote in message
news:[email protected]...
"Stephen Jacobs" <[email protected]> schrieb im Newsbeitrag
news:[email protected]...
"MysteriAce" <[email protected]> wrote in message
news:[email protected]...
On Apr 20 2005 2:37 PM, andreas kinell wrote:
Prove me wrong MATHEMATICALLY, not with your empirical evidence and
conjecture.
:)
I could do it, but it's doubtful that you'd understand what I said.
Developing the right concepts from everyday ideas would take several
pages.
or it takes like 8 lines.
I'm afraid you don't have a clue what mathematical rigor really is. I
could just about justify integer arithmetic in 8 lines to someone who
wanted to be convinced. We have to show here that the limit of a
non-changing sequence is equal to the value of the members of the
sequence. The definitions of sequence and limit would be a page to start
with, maybe more. And yes, it is necessary to be that pedantic or the
truth can escape.
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anything wrong with my two proofs?
andreas |
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Stephen Jacobs
Guest
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| Posted: Thu Apr 21, 2005 3:00 pm Post subject: Re: The mathematics of movement |
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"andreas kinell" <[email protected]> wrote in message
news:[email protected]...
| Quote: |
anything wrong with my two proofs?
andreas
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As far as rigor, everything. But don't sweat it. When a guy says something
about cutting the hand-waving and giving him math, I am inclined to give him
the real thing. In person, the offer to do so is often interpreted as a
threat (you need to see the gleam in my eyes as I begin to develop the exact
mathematical representation of the everyday concept of going from "here" to
"there"). |
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Arthur Samuels
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| Posted: Thu Apr 21, 2005 6:01 pm Post subject: Re: OT: The mathematics of movement |
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A mathematical 'point' is a mathematical abstraction. It has no real
existence. Points exist in theoretical math - not in physics.
The closest you can get to your analysis in physics is a limit
approach. As time approaches zero, distance traversed also does so.
However, the concept of 'zero time' is meaningless in physics.
This same conundrum can be stated as 'instants of time'. "The bullet
travels zero distance in one instant, therefore it never moves". The
term "instant" has no scientific definition. Would a thousand instants
be a kiloinstant? Would a thousandth of an instant be a milliinstant? |
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