## Zeno's Parafusion

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### Zeno's Parafusion

Is there really any difference between the word "confusion" and "parafusion"? Every paradox is merely a confusion.

For those unfamiliar, Zeno of Elea (ca. 490–430 BC) proposed a few mind puzzles very many years ago involving the basic logic of simple motion, generally referred to as "Zeno's Paradoxes" (or so history is written). Perhaps the most famous of these paradoxes (all of which are similar) is called the "Dichotomy Paradox".

The Dichotomy Paradox is presented thusly:

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.– as recounted by Aristotle, Physics VI:9, 239b10

Suppose Homer wishes to walk to the end of a path. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion. An alternative conclusion, proposed by Henri Bergson, is that motion (time and distance) is not actually divisible.

Aristotle answered these paradoxes by revealing that both time and distance are involved in motion and when the distance is cut in half, so is the time required to travel it. Thus no matter how infinitely one divides the distance required to travel, the time is divided as well yielding a constant speed. Simple solution. Motion flows on.

===============

But besides the issue of speed and motion, there is a confusing issue of the division of any distance. If one can infinitely divide a distance and one must add each divided segment together in order to complete the whole distance, how can the whole ever be assembled? If there are an infinity of numbers between 0 and 1, how can a number line between them exit at all? How could the number line ever get to 1?

Think about it for a moment. In order to get from 0 to 1, an infinity of fractions must be appended. But in reality, to get to any one of those fractions, an infinity of additional fractions must be appended. And, to make it even worse, to get to any of those additional fractions, an infinity of double-additional fractions must be appended. And that scenario has no end .. aka "is endless", aka "is infinite". In short, you can't get to 1 from 0. So what gives?

If you are like me and don't really like to read all that much, let me cut to the essential:
The universe is not made of location points (numbers), but rather is made of the space between them.
What that means is that between any two numbers one can arbitrarily assign in infinity of new numbers. So what? Numbers, when it comes to physical distance, are merely location points. They have no physical existence at all. They take up absolutely no space on the number line. One can add an infinity of location points together and still have absolutely zero distance. So how does a number line exist?

The one thing that philosophers can contribute to (and would seriously improve) the world is to require physicists and mathematicians to take a course in ontology construction.

When constructing an understanding of the world/universe (an ontology), there are options (females tend to innately understand this for whatever reason you might like to believe -- males .. not so much). For sake of cognitive understanding and dealing with the world, a person can choose to allow a division between 0 and 1 meter (for example) up to a limit of 1000 (one millimeter segments). Perhaps that is fine for their need. 10,000 years ago, can you even imagine a need to be more accurate? And with that chosen limit, one can construct a "quantized" version of all physical reality. Later in human development, much greater precision was required. The point is that it is arbitrary as to what limit one chooses as the standard for their ontological construction.

People keep realizing that any distance can be divided, so no matter what standard is chosen, a more precise standard is conceived. Quantum Physicists have tried (once again) to declare that distance cannot be divided more than a particular chosen (too small to measure) amount (about 10^-38m), called "Plank's Constant". It's just another effort to get around the truth of the matter.

The distance 1 (of whatever) can be divided into 2 segments, or 4, or 10, or 1,000,000 or any number chosen. The thing to keep in mind is that it is a distance that was divided, not a number. And as long as one multiplies by the same number of segments, the original distance is reestablished. The distance can be divided infinitely, but as long as the infinitesimal segments are multiplied by the same degree of infinity (yes, infinity comes in degrees), the original distance is reestablished. And that resolves the issue of Zeno's paradox.

One must traverse half of every half of any distance in order to gain any distance. But all that is saying is that one must be accomplishing motion - the changing from one segment to the next. Any size segment may be used in the understanding. But every segment takes up space, else it isn't a segment nor a division of a distance, but merely a location point. And if something is proposed to take up absolutely zero space, then it doesn't physically exist (to exist is to have affect from one point to another - the affect between the points is the existence). You are made of the space between what isn't you on one side and what isn't you on the other (as is everything else). And if you are moving, every segment and affect within you is relocating to the next segment of space. What size you choose those segments to be is completely up to you and your ontology.

==================

This whole issue then relates to the recent debate concerning whether the value expressed as "0.999..." is really exactly equal to the value expressed as "1.0".

Carleas raised the question of how one could get from 0 to 1 if taking a 90% step and 90% of each remaining amount (aka "0.999...") did not add up to exactly 1.0. I contended that if you are required to only take 90% of each remaining amount with each step, then by definition, you could not ever get to 1.0.

So how does the real number line ever get to 1.0?

The answer, as explained above, is simple. The real number "line" is made of line segments, not of location points. Any and every segment may be divided infinitely. As George Cantor pointed out long ago, the number of potential numbers between 0 and 1 (or actually between any two numbers) are uncountably infinite. The real number line can have an infinity of numbers between any pair of numbers and another infinity of numbers between each of those, and so on infinitely. But the number LINE doesn't care, because any and every "line" is made of segments, not numbers.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Zeno's Parafusion

Interesting.

If one can infinitely divide a distance and one must add each divided segment together in order to complete the whole distance, how can the whole ever be assembled? If there are an infinity of numbers between 0 and 1, how can a number line between them exit at all? How could the number line ever get to 1?

The world cannot construct the perspective/observational space mathematically. That is why it doesn't do it with math and maths is only representative. Spatial locations are denoted by the relative positions of observers, and that's how the universe is built. Movement is thus between relative positions and not >exact< points in space.

The smallest integer or iteration of that, would be between a particle in superposition and one e.g. a photon, in existent form. I can only imagine that the number [if it goes by numbers et al] range would be between 0 and infinity? ...and yet the relative distance between manifest existences are finite and do have a mathematical value. So it goes from extremely vague to having some measure and dimensionality [size shape ets], then on into the micros and then macroscopic, getting more aggregate as it takes shape. Thereafter numbers represent objects, and a step is like an object. It doesn't mean the world is built like that though.

_
The truth is naked,
Once it is written it is lost.
Genius is the result of the entire product of man.
The cosmic insignificance of humanity, shows the cosmic insignificance of a universe without humanity.
the fully painted picture, reveals an empty canvas

Amorphos
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Location: infinity

### Re: Zeno's Parafusion

Amorphos wrote:The smallest integer or iteration of that, would be between a particle in superposition and one e.g. a photon, in existent form.

I'm afraid that isn't how superposition works.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Zeno's Parafusion

Example: "Achilleus" - Zenon's fallacy.

The error is the confusion and permutation of (a) the thought of the succession of time with (b) the thought of the succession of space. One could also say: It is a misjudgement of the fact that the merely mathematically infinite divisibility of a stretch or a time length says nothing aginst its real finiteness.

Arminius
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### Re: Zeno's Parafusion

James S Saint wrote:Is there really any difference between the word "confusion" and "parafusion"? Every paradox is merely a confusion.

For those unfamiliar, Zeno of Elea (ca. 490–430 BC) p
roposed a few mind puzzles very many years ago involving the basic logic of simple motion, generally referred to as "[
Zeno's Paradoxes[/url]" (or so history is written). Perhaps the most famous of these paradoxes (all of which are similar) is called the "Dichotomy Paradox".

The Dichotomy Paradox is presented thusly:

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.– as
recounted by Aristotle, Physics VI:9, 239b10

Suppose Homer wishes to walk to the end of a path. Before he can get there, he must get halfway there.
Before
he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and
so on.

The paradoxical conclusion then would be that [
b]travel over any finite distance can neither be
completed nor begun[/b], and so all motion must be an illusion. An alternative conclusion, proposed by Henri Bergson, is that motion (time and distance) is
not actually divisible.

Aristotle answered these paradoxes by revealing that
both time and distance are involved in motion and when the distance is cut in half, so is the time required to travel it. Thus no matter how infinitely
one divides the distance required to travel, the time
is divided as well yielding a constant speed. Simple solution. Motion flows on.

=
==============

But besides the issue of speed and motion, there is a
confusing issue of the division of any distance. If one
can infinitely divide a distance and one must add each divided segment together in order to complete the whole distance, how can the whole ever be
assembled? If there are an infinity of numbers
between 0 and 1, how can a number line between them exit at all? How could the number line ever get to 1?

Think about it for a moment. In order to get from 0 to 1, an infinity of fractions must be appended. But in
reality, to get to any one of those fractions, an infinity
of additional fractions must be appended. And, to make it even worse, to get to any of those additional fractions, an infinity of double-additional fractions
must be appended. And that scenario has no end .. aka
"is endless", aka "is infinite". In short, you can't get to 1 from 0. So what gives?

If you are like me and don't really like to read all that much, let me cut to the essential:
The universe is not made of location
points (numbers), but rather is made of the space between them.
What that means is that between any two numbers
one can arbitrarily assign in infinity of new numbers.
So what? Numbers, when it comes to physical distance, are merely location points. They have no physical existence at all. They take up absolutely no
space on the number line. One can add an infinity of location
points together and still have absolutely zero distance. So how does a number line exist?

[
color=#FF0000]The one thing that philosophers can contribute to (and would seriously improve) the world is to require physicists and mathematicians to take
a course in ontology construction.
[/color]

When constructing an understanding of the
world/universe (an ontology), there are options
(females tend to innately understand this for whatever reason you might like to believe -- males .. not so much). For sake of cognitive understanding
and dealing with the world, a person can choose to
allow a division between 0 and 1 meter (for example) up to a limit of 1000 (one millimeter segments). Perhaps that is fine for their need. 10,000 years ago,
can you even imagine a need to be more accurate?
And with that chosen limit, one can construct a "quantized" version of all physical reality. Later in human development, much greater precision was
required. The point is that it is arbitrary as to what limit
one chooses as the standard for their ontological construction.

People
keep realizing that any distance can be divided, so no matter what standard is chosen, a more precise standard is conceived. Quantum Physicists have tried (
once again) to declare that distance cannot be divided more than a particular chosen (too small to measure) amount (about 10^-38m), called "Plank's
Constant". It's just another effort to get around the truth
of the matter.

The distance 1 (of whatever) can be divided into 2

segments, or 4, or 10, or 1,000,000 or any number chosen. The thing to keep in mind is that it is a distance that was divided, not a number.
And as long as one multiplies by the same number
of segments, the original distance is reestablished. The distance can be divided infinitely, but as long as the infinitesimal segments are
multiplied by the same degree of infinity (yes, infinity
comes in degrees), the original distance is reestablished. And that resolves the issue of Zeno's paradox.

One must traverse half of every half of any distance in order to gain any distance. But all that is saying is that
one must be accomplishing motion - the changing from one segment to the next. Any size segment may be used in the understanding. But every segment takes
up space, else it isn't a segment nor a division of a distance, but merely a location point. And if something is proposed to take up absolutely zero space
, then it doesn't physically exist (to exist is to have affect from one point to another - the affect between the points is the existence). You are made of the space
between what isn't you on one side and what isn't you on the other (as is everything else). And if you are moving, every segment and affect within
you is relocating to the next segment of space. What size
you choose those segments to be is completely up to you and your ontology.

=
=================

This whole issue then relates to the recent debate
concerning whether the value expressed as "0.999..." is
really exactly equal to the value expressed as "1.0".

Carleas raised the question of how one could get from
0 to 1 if taking a 90% step and 90% of each remaining amount (aka "0.999...") did not add up to exactly 1.0. I contended that if you are required to only
take 90% of each remaining amount with each step, then by definition, you could not ever get to 1.0.

[
list]So how does the real number line ever get to 1.0?[/list]

The answer, as explained above, is simple. The real number "line" is made of line segments, not of location points. Any and every segment may be
divided infinitely. As George Cantor pointed out long
ago, the number of potential numbers between 0 and 1 (or actually between any two numbers) are uncountably infinite. The real
number line can have an infinity of numbers between
any pair of numbers and another infinity of numbers between each of those, and so on infinitely. But the number LINE doesn't care, because any and every
"line" is made of segments, not numbers.
[
/quote]

The problem here as I can see it, is that every segment can be divided into sub segments, and if that is carried to infinity-1 reps, the conceivable point is needed to uphold this reduction. The Russell paradox of the absolute ad absurdum reduction of sense data proves relevant here, because, segments have to be reducible ad infinitum, to enable the absolute positing of the point. If you disallow this, then the necessary idea of the point is raised. Then there are no points from which a minimum segment can arise, albeit, there not be possible to construct a segment interposed between two points. This is a spatial connection which can not be solved, except by saying, that at the very minimal extension of a segment, there is an absolutely small segment which somehow contraverts the definition of a segment constructed between two points, real or hyper real.
If so, segments may not represent any a difference within the definition of it's integral function, other than, one where, it could be said of the number of angels dancing on the head of a pin. Here no spatial differentiation can be made upon the integral sum of all possible subsets.

Unbounded sets will, accordingly, suffer the same spatial-numerical collapse, since the differentiation between them dissolve.

The reduction of real into virtual systems, may not yet be clearly defined, as Cantor seemed to. Rather, again, it is the logical precedence, which has an intuitive basis, can solve it.
Meno_
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### Re: Zeno's Parafusion

But this analysis may have faults of their own, and although some references I can dig up, it may very well turn into a vacuous argument.

Following an intuitionism route, given the equally abstract nature of both lines, consisting
of points, I see the probability favoring the argument.
Meno_
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### Re: Zeno's Parafusion

Arminius wrote:Example: "Achilleus" - Zenon's fallacy.

The error is the confusion and permutation of (a) the thought of the succession of time with (b) the thought of the succession of space. One could also say: It is a misjudgement of the fact that the merely mathematically infinite divisibility of a stretch or a time length says nothing aginst its real finiteness.

If reality was (it is not) merely mathematical, then Achilleus could not reach the turtle, thus the mathematical solution (see: a) would be right in any case (because: reality = ideality); but our reality is also resp. mainly physical (see: b), and we have senses and brains for experiencing (observating, perceiving) this reality, so that we can know that Achilleus can reach the turtle. All this (see: a nd b) means that we can solve the "Achilleus" problem exactly, thus mathematically.

The merely mathematically infinite divisibility of a stretch or a time length does not contradict its real finiteness.

Arminius
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### Re: Zeno's Parafusion

Arminius wrote:The merely mathematically infinite divisibility of a stretch or a time length does not contradict its real finiteness.

Precisely.

It is always and forever merely up to what standard of minimal measure one chooses - what degree of infinitesimal is going to represent "1". If none is chosen, then a physical ontology cannot be formed because every infinitesimal distance could be infinitely divided such as to have no means to sum up any distance at all.

Ontology is a Choice. One must choose how many infinitesimals are going to exist between 0 and 1.

And a necessary choice if any understanding is to be formed or maintained. Ontological understanding is not reality itself, which has no limits for infinity. Thus the limits for infinity and infinitesimal must be set by choosing a standard independent of the fact that reality has no limit. It really isn't any different than choosing the length of a meter. Reality has no such thing as a meter, so someone must choose a length, else length measurements are impossible to logically handle.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Zeno's Parafusion

I already told you folks the solution...

Apparently you're all deaf...

For any y/x, multiply x times y for distance and you can cover it!!!

Am I that confusing !?!?!?

If it's 1/2, double it to 2... And you'll always reach the point!!!
Ecmandu
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### Re: Zeno's Parafusion

It is not necessary to invoke every other number between any two integers to get from one to the other. So for example if one is referencing the infinite
set of primes one does not include non primes as well. This set would be 2 3 5 7 11 ... and anything else which was not a member of it would effectively
not exist in this particular case. And so the fact that there is an infinity of numbers between each prime is completely irrelevant and of no consequence

It is important not to confuse physical infinity and mathematical infinity as they are not the same. If I walk a mile it can be mathematically represented
as going from 0 to 1 and they can have an infinity of other numbers between them but it would not take me an infinite amount to walk it as it is a finite
distance. The infinite number of places between any two numbers only exists as an abstraction so is not real as such. If it was real it would literally take
forever to travel any distance regardless of how infinitesimal it may be
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious57
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### Re: Zeno's Parafusion

*sigh*

The problem is a problem of infinities surreptitious, no matter how you categorize it to this degree, doesn't solve the problem.

The problem is simple:

If for every spatial part, you always divide it, how can you ever reach a whole destination???

The solution is to multiply the divisions!!!

If you can only travel half the space, then double the space and half will be 1!!!!

It's really simple!!!

And, I actually solved the real numbers on a single list!!!

Look at my inferential proof!!!

Clay doesn't even offer a prize for this because they consider it impossible ... I should get twice the money for solving it then!!!
Ecmandu
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### Re: Zeno's Parafusion

If it is really simple why is it regarded as being impossible to solve
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious57
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### Re: Zeno's Parafusion

surreptitious57 wrote:
If it is really simple why is it regarded as being impossible to solve

I solved it !!!

Just like counting the reals was considered impossible to solve and I solved it.
Ecmandu
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### Re: Zeno's Parafusion

surreptitious57 wrote:
If it is really simple why is it regarded as being impossible to solve

Because very many intelligent people do not catch the trick (much like the rest of society).

An ontology begins with segments of distance in 3 dimensions, not location points. The segments physically exist. The location points do not. So what you have to do is decide on the size of segments for your ontology. No matter how infinitesimal that is, the inverse gets you back to exactly 1.

If you choose to not have a limit for infinity ("absolute infinity"), then the inverse is as close to zero as you can get. Thus absolute infinity times 1/(absolute infinity) still accomplishes 1.

The confusion is that the universe has an absolute zero distance, which it doesn't. People presume to be able to get to absolute zero, but not to absolute infinity.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Zeno's Parafusion

You have convinced me to change my mind. I now think that 0.999 ... does not equal 1. I only accepted the alternative
since it is generally regarded as being true. However I can no longer accept this since it makes zero logical sense to me
As I cannot accept something as being objectively true [ even if it is ] if I do not understand why it is supposed to be so
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious57
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### Re: Zeno's Parafusion

Posted that in the wrong thread so I will re post it in the other one
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious57
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Joined: Sun Oct 11, 2015 2:05 am

### Re: Zeno's Parafusion

James S Saint wrote:
Arminius wrote:The merely mathematically infinite divisibility of a stretch or a time length does not contradict its real finiteness.

Precisely.

It is always and forever merely up to what standard of minimal measure one chooses - what degree of infinitesimal is going to represent "1". If none is chosen, then a physical ontology cannot be formed because every infinitesimal distance could be infinitely divided such as to have no means to sum up any distance at all.

Ontology is a Choice. One must choose how many infinitesimals are going to exist between 0 and 1.

And a necessary choice if any understanding is to be formed or maintained. Ontological understanding is not reality itself, which has no limits for infinity. Thus the limits for infinity and infinitesimal must be set by choosing a standard independent of the fact that reality has no limit. It really isn't any different than choosing the length of a meter. Reality has no such thing as a meter, so someone must choose a length, else length measurements are impossible to logically handle.

Yes.

We have to distinguish between (1.) the realm(s) of ratiocination / logic / mathematics and (2.) the realm(s) of physics / chemnistry / biology. So if one logical / mathematical task does not only contain a mathematical subtask but also a physical subtask (like the „Achilleus“ task does), then we have to consider that two subtasks.

Arminius
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