Half, and half again...

[nameless]

It is true that it would be impossible to sit down and add up an infinite series of numbers. However, it is possible to calculate what the result would be if you were to do so.

The point is that Xeno was right.
Please feel free to referrence the following;

Physicists Who Know That Nothing Can Move in Spacetime

First, discontinuity (quanta) vs. continuity. Quantum mechanics seems to contradict everyday common sense and classical mechanics because it presents the reality as discrete or segmented into discontinuities rather than as a continuous transition such as we expect from everyday experience and classical mechanics.

CHAPTER 2: ARISTOTLE'S ZENO AND THE PARADOXES OF MOTION

Zeno and Naagaarjuna on motion

Space, Time and Einstein
J. B. Kennedy
An enlightening introduction to the philosophy of time and space... such topics as Einstein's special and general relativity, how to build an atom bomb, the four-dimensional universe, the possibility of time travel, the impossibility of motion, whether space curves, the big bang, black holes, and the idea of inflationary and accelerating universes.

Please see the following for a plethora of related sites:
"impossibility of motion"

 

[Communist Hamster]

I contradict that. I move. Do you?

 

[cato]

rather than exclaiming that we are wrong, why don't you walk us through how the universe really works? explain how the universe works while nothing moves.

 

[Nasor]

The point is that Xeno was right.
Please feel free to referrence the following;

No, the point is that Xeno mistakenly assumed that the sum of an infinite series must be infinite. I don't really know how you can argue that an infinite series must give an infinite result, because it's pretty easy to demonstrate. Consider the series 1/2 + 1/4 + 1/8 + 1/16 + 1/32... This series goes on forever, but if you were to sum it out to infinity it would exactly equal 1. Similarly, there are an infinite number of points that must be passed through to move any distance - but it takes a finite amount of time to do it. If you sum the time necesary to pass through each of the infinite points, it converges to a finite value just as the above series converges to 1 as you sum its infinite components.

 

[Spectrum]

According to my computer:

x=0
y=1

[y]
y=y/2
x=x+y

print x:

Output:...0.99999999
1.0

goto [y]

 

[Communist Hamster]

Indeed, And what if you add 1/2 and 1/2? It equals 1

 

[nameless]

I contradict that. I move. Do you?

No. You only appear to move.
What actual 'real' things 'move' in a night dream? Dream that you are in a car hurtling down the road. You feel wind, speed, mass, etc.. What, who is 'actually' moving in that dream? What, when you stomp across the floor in your dream proclaiming that you actually move, is actually moving? Where's the mass? Where the 'space'? Your 'naive' refutation was witnessed by Xeno also, from an acquaintance, as a refutation. His refutation has been thoroughly refuted. Read the links.
That you 'BELIEVE' the 'monitor images' in your mind to be some sort of 'actual representation of reality'... indicates to me that you haven't 'dug very deeply', yet, in your quest for 'Truth' (or perhaps have not yet had the time), and that you harbor (insidious) 'beliefs'. You are interested in Truth, not 'appearances', yes? Perhaps you'd be interested to read the links that I have generously provided to help you understand where I am coming from. I am not asking you to believe anything or change your mind, I'm asking y'all to be a 'free-thinker' willing to attempt to understand another perspective without feeling pressured or the need to adopt it. That is 'free-thought'.

Freethinkers are those who are willing to use their minds without prejudice and without fearing to understand things that clash with their own customs, privileges, or beliefs. This state of mind is not common, but it is essential for right thinking; where it is absent, discussion is apt to become worse than useless.
-Leo Tolstoy (On Life and Essays on Religion)

rather than exclaiming that we are wrong, why don't you walk us through how the universe really works? explain how the universe works while nothing moves.

No where have I exclaimed that you (we? do you represent a group of some sort?) were 'wrong'. I was offering a 'perspective', for your pleasure. It won't hurt you, go ahead, take a bite. You aren't required to change your diet, operators are NOT standing by, just taste (understand) and THEN decide... For starters, how about re-reading my 'movie' metaphor. Apply thought, meditation, doodle, understand the implications. That should get you started, if you really are interested. Try reading some of those links. I can't spoon feed it to you.

The human mind treats a new idea the way the body treats a strange protein; it rejects it.
-Biologist P.B. Medawar

(Unless, of course, the 'new idea' happens to be yours.)

..it converges to a finite value..

More correctly, 'converges toward', a never actually reached, finite value. Is this what y'all have been waving like a flag? You 'fudge'? Round off? .999... = 1?!? What kind of sloppt fundamentalist thinking is that? Yeah, the tangent 'converges' ad infinitum, upon the forever-out-of-reach axes. Shall we just 'round off/fudge' to make the math 'fit' our prejudices?
Sorry, that doesn't make sense to me. I am interested in raw, terrifying, transformational Truth, not comfortable notions and edible concepts.

"if you were to sum it out to infinity it would exactly equal 1.


Show me. Do it.

And Spectrum, that little 'jump' from 0.99999.... to 1.0? That was a jump from the Truth Zone to the Comfort Zone. The 'comfort zone' (of beliefs and assumptions) is wide and well travelled and many there are who 'dwell' there!

Indeed, And what if you add 1/2 and 1/2? It equals 1

Isn't it amazing what can be taught to a hamster these days?
But, you are adding apples and oranges.
I suspect that you are still attempting to validate the illusion of motion by your formula. Perhaps you might study Einsteins formulae showing the impossibility of motion. Neils Bohr's. Those other links that I provided.

You are still attempting to validate the notion of the sun going around the earth.
Hell, your own eyes can validate that, no? Certainly don't need a pencil to figure that one out, eh?
*__-

Doubt everything;

Ubi dubium ibi libertas:
Where there is doubt, there is freedom

 

[Communist Hamster]

One of your links has "crackpots" in the title. It says a great deal about the plausibility of the theory that movement is impossible.

I'm no physiscist, but how is adding a half and a half "apples and oranges"?

 

[cato]

Show me. Do it.

he already did. the "..." implies that he did it forever. its much more efficient that actually writing out an infinite amount of numbers, don't you agree?

 

[cato]

No where have I exclaimed that you (we? do you represent a group of some sort?) were 'wrong'. I was offering a 'perspective',

we (we=the other posters and myself) say that movement is possible, and you say it is not, how do you claim that you are not calling us wrong?

your different perspective is simply existentialism as it applies to math. however, the math speaks for itself. zeno didn't have the tools to prove his argument was wrong. it took Newton and calculus to do that. you are still thinking of math before calculus where you physically had to add everything. calculus can add a series of number, that converge to a finite number, out to infinity. thus you actually reach the number that you converge towards. if you try to stop the summation at any time (even with the largest numbers imaginable) you will find it not quite at the value it approaches. however, if you let the summation go to infinity, it is said number.

 

[Spectrum]

And Spectrum, that little 'jump' from 0.99999.... to 1.0? That was a jump from the Truth Zone to the Comfort Zone. The 'comfort zone' (of beliefs and assumptions) is wide and well travelled and many there are who 'dwell' there!

Hey man it's not me, it's a computer that calculated it.

Another solution, for all you modern computer users, is:

#include <iostream>
using namespace std;

main ()
{
float a=0;
float b=1;
while (a!=1)
{
b=(b/2);
a=(a+b);
cout << a << "\n";
}
return 0;
}

Output:

0.5
0.75
0.875
0.9375
0.96875
0.984375
0.992188
0.996094
0.998047
0.999023
0.999512
0.999756
0.999878
0.999939
0.999969
0.999985
0.999992
0.999996
0.999998
0.999999
1

 

[Nasor]

More correctly, 'converges toward', a never actually reached, finite value. Is this what y'all have been waving like a flag? You 'fudge'? Round off? .999... = 1?!? What kind of sloppt fundamentalist thinking is that?

0.999... exactly equals 1.

Let us suppose that X=0.999...

10X=9.999...

10X - X = 9

9X = 9

X = 1

Or, if you prefer:

1/3 = 0.333...

0.333... * 3 = 0.999...

1/3 * 3 = 1

 

[Spectrum]

On a side issue isn't it annoying when you have something floating on the far side of your drink and you try to turn the container around to retrieve it, but the liquid remains stationary as the container turns around the fluid. The object can rarely be retrieved.

 

[nameless]

True, if we conveniently ignore the implications of '...' we can make everything fit nicely. Still looks to me like convenient 'rounding'. The bitty that has been conveniently ignored might be of great value, might change everything. Couldnt have that. Gallileo has just recently been 're-communicated'! Old memes die hard in the massas and the individual. Much is invested.

"we (we=the other posters and myself) say that movement is possible, and you say it is not, how do you claim that you are not calling us wrong?"

Perhaps there is a language problem. From what I have discerned from my studies, in my world, from my perspective, from my experience, this is what I have found to best describe 'existence'. This perspective is also shared by other celebrity (I know how y'all love to refer to 'celebrities' for validation) thinkers throughout history. This VIEW can also be logically and quantumly and experientially supported. So can other views. Believe what you like. I find this to tentatively be the best description. I could have referrenced links in support of naive realism also. Having tasted both dishes, I have determined for myself the most probable scenario. Perhapa you have done the same. The term and concept of 'wrong' has not been brought up but by you. Is it your ego that demands to be not only 'right', but 'right' for everyone else also? Meaning that a differing perspective is automatically 'wrong' if it differs from yours?
And, hey, everyone, does cato really speak for you? Everyone? Makes no difference to me, but seems to be another example of the 'assumptions' that I hear all over.

Hey man it's not me, it's a computer that calculated it.

Are you denying ultimate responsibility for the computer's programming, o human?

One of your links has "crackpots" in the title. It says a great deal about the plausibility of the theory that movement is impossible.

Actually, it says that you haven't read past the title. The term 'crackpot' is often the term used by the 'cement-headed 'believing' rabble' in referrence to the genii who have the ability to creatively think out of the box. Free thinkers. Just look at history! I don't understand why you would rather argue before you examine the 'evidence' presented. That seems to evidence an 'emotional attachment' to your 'beliefs'. Fundamentalists of all stripe do the same 'twisting and redefining' of science to support their preconceived beliefs.

Bye the bye, if I had the same sophistic math (artificial construct that it fundamentally is) to argue with my math teachers to show that .999... was the same as 1, or 3, or 5.339... I could have aced the courses. Check quantum and other branches. Motion is a paradox for those who insist on its actuality, and is impossible for those who are willing to believe the evidence of their equations. Just like 'time'. And without time, motion is again, impossible. The numbers are all over the net for those free thinkers who are interested in Truth, not merely supporting their dearly held beliefs.

And as far as I am concerned, logically and rationally;
0.999... = 0.999...
and;
1=1
You cant piss down my neck and convince me that it is raining.
Maybe it is just me...

 

[Nasor]

And as far as I am concerned, logically and rationally;
0.999... = 0.999...
and;
1=1
You cant piss down my neck and convince me that it is raining.
Maybe it is just me...

Wait a minute now. You are apparently ready to believe the (seemingly unlikely) idea that motion is impossible because of logic, but when I show you two perfectly logical, rational proofs that 0.999... and 1 are two different ways of expressing exactly the same value, you just blow it off because it seems counterintuitive to you?

You keep saying that just because motion seems apparent doesn’t make it a reality. Well, just because 0.999… does not seem to equal one to you does not make your view of the value of 0.999… a reality. Do you base your beliefs on logic, or not? Because I’ve just given you two perfectly logical proofs that 0.999… exactly equals 1.

 

[nameless]

"You are apparently ready to believe the (seemingly unlikely) idea that motion is impossible"

No I 'believe' nothing. I find it to be the currently most probable description of existence. Tentatively..
That is not 'exactly equal' to 'belief', no matter the gyrations involved.
*__-

Bye the way, logic in and of itself is also incapable of completely defining reality.

So why is my son not learning that .999... + .999... = 2 in school? I have seen nothing here to indicate that .999... = exactly 1. I hear it 'approaches'.. I hear 'rounds off to'...
And, even if, in someone's world, .999.. actually is synonymous with '1', there can still be no motion.

I will ask some local college profs if .999... exactly equals '1'. If they respond in the positive (which I doubt, but..) I'll have them explain it to me so that I can understand their reasoning. Once I can understand their reasoning (if, of course, they answered in the affirmative) than I can use their reasoning and findings as data and determine the 'validity' of their reasoning (as accurate descriptors of 'reality') against ALL THE OTHER DATA on the subject, from all branches of knowledge, throughout history, and my own critical and creative thoughts.
Till then, we are still (comfortably) choking on the seeds (of this lightweight math 'problem') and ignoring the real MEAT of the 'impossibility of motion' and the 'world shaking' implications thereof.
("If it doesn't fit - it must be shit!" - Johnny Cochran *__-)

Perhaps I am not ready to accept your hypothesis that 0.999... 'exactly' equals 1 so quickly because it violates all my experience and all previous data. It seems like a 'flyer'. Like statistics, math can lie also.

Put it to the test! Next time in the store and your change is $100., just accept the $99.99 each time! After all, if .999... can equal 1 if the ever repetition dots are ignored, it can also = .999 by ignoring the same 'dots' (and perhaps a few '9's), no?

I guess I'll go see what the profs say. I'll let you know. Makes no sense repeating ourselves here. Maybe I'll learn something new and important! I doubt it, but hops and spring water is eternal!

Have YOU read the links that I offered, or is this another argumentum ad ignorantum?

And the whole idea of 'eternity' and 'infinity' is just another mathematical absurdity. Aint no such thing in existence or reality. My ex-neighbor Richard Feynman explained that he removed those pesky infinites (treated them as bugs) from his equations and they (equations) then made sense without losing meaning. This isn't just more nonsense from nameless... Never was.

 

[nameless]

Another quick point, words are not the 'items', 'concepts', 'things' that they are trying to convey, hence, words are to be taken as metaphor. Is math not a 'language'? Are the 'symbols' one and the same as what they are trying to convey? If not, then they are also metaphor, requiring intelligent and creative interpertation to be understood at all.

 

[nameless]

OK, I just called Dr. Harry Lyons of the California University system and he mentioned that there was a 'set theory' that is where you are comming from, but he agrees with me. He mentioned parabola, tangent, Greek geometry and a bit more.. but agreed, that .999... is NOT exactly equal to 1 (in his opinion, of course) nor does the tangent ever reach the axes. I guess that it is another case of deciding what works for you. You cannot have a tangent and eat it too!
Enough.
The point was about the 'impossibility of motion'. I said 'paradox' to him, he used the term 'impossibility'.
peace

 

[Nasor]

Do you have some problem with either of my proofs? If so, please explain it. If not, I believe I have demsonstrated that 0.999...exactly equals 1 twice.

Do you believe that 1/3 = 0.333...?
Do you believe that 3 * 1/3 = 1?

 

[nameless]

Do you believe that 1/3 = 0.333...?
Do you believe that 3 * 1/3 = 1?

Actually, I 'believe' nothing.
That being said, I find that 1/3 = 0.333... is a sometimes convenient working approximation; close, but an 'assumption', an 'approximation' for convenience. And, yes, I have found 3(1/3) = 1 to be an exact and reliable hypothesis when dealing with most things and abstract numeric entities. Now, I'm guessing that you'd like to be entertained with an instance where that doesn't hold true? Ok, how about this; Would the overall quantity of grief that you would feel be diminished by 1/3 if only one of your children were killed, contrasted to the quantity of grief you'd feel if all three were killed? That illustration would hold, I guess, to invalidate the statement that 1+1=2 exactly, forever and always.

I read again your;

0.999... exactly equals 1.
Let us suppose that X=0.999...
10X=9.999...

again. I am not a mathematician, perhaps that is why your tricky number game cannot fool me. I have encountered enough sophistry before to recognise the stink.

Actually, there would be an infinite number of sets of infinities for motion to be plausible. Between the first point and the second point to 'traverse' there are an infinite amount of points. Between the second point and the third point there are another infinite amount of points to traverse, and on... If you are going to use that same bit of mathematical sophistry to claim that an infinite number of sets of infinities is exactly equal to some 'number' you can come up with, save yourself the trouble.
I've heard it before.
If you really believe what you are 'pushing' (and I tend to think that you are being ingenuous, and not simply fukking with me), and it doesn't cause problems in other areas of your life, Dog bless you and peace. But I would guess that some 'authoritarian figure' somewhere down the line taught you this BS, probably because HE 'believed' it (which is how memes are born), and you sucked it right down because, after all, HE was the mathematician, the 'authority'! Perhaps you should have gotten a second opinion.
This sort of thing makes the brain writhe. Please, enough. Let us agree to disagree and let it go between us here. Besides, I am disinterested in mathematical disemination, my point is that time/motion is impossible in any 'real' way, and this half and half stuff was just another bit of 'folk doggerel' in support of that reality. Could it be that your 'belief' helps keep you from the mind stretching work of incorporating this 'reality' into a functional world-view? Many manage, once one is willing to discard emotionally held prejudices for 'Truth'.

Did I hear someone mention a Planck distance? Like a Planck moment? Theres motion for you! Hahahahha... It would take a Planck moment to cover a Planck distance! No time to cover no space.
All 'still' on the western front!
Motionless, silent, timeless, dark...