Dividing Infinity

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Dividing Infinity
If I took infinity, traced my finger half way out on it, and cut it equally in half, and added that quantity of 'one' to one of the two sides, would the two sides be equal in size, or would the one with 'one' added be bigger?
If a Babylonian lacking the concept of Zero did the same, would both my halves be bigger than his if my two parts had a zero at the start? Or would he be first because he had a head start?
If a Babylonian lacking the concept of Zero did the same, would both my halves be bigger than his if my two parts had a zero at the start? Or would he be first because he had a head start?
Re: Dividing Infinity
Both sides would still be the same. As an example, think of the real number line that goes from negative infinity on the left, to positive infinity on the right. You could divide it at 0, and both sides would still be the same. Or you could divide it at 1, and both sides would still be the same. There's no "middle" of infinity.EchoesOfTheHorizon wrote: ↑Sat Oct 28, 2017 1:15 amIf I took infinity, traced my finger half way out on it, and cut it equally in half, and added that quantity of 'one' to one of the two sides, would the two sides be equal in size, or would the one with 'one' added be bigger?
On the other hand we could do the same experiment with the counting numbers 1, 2, 3, 4, 5, ...
In that case, wherever you put your finger, the part to the left would be finite and the part to the right would be infinite. So the halves would NEVER be the same!
I don't think the ancients had sufficiently well developed ideas about infinity to have ever contemplated such a thought experiment. It's not just 0, though. They didn't have negative numbers. In fact the concept of "number" was a lot different for them than it is for us. It's really kind of a meaningless question. Though we can imagine that some Babylonian might have had the thought but not the vocabulary to express it.EchoesOfTheHorizon wrote: ↑Sat Oct 28, 2017 1:15 amIf a Babylonian lacking the concept of Zero did the same, would both my halves be bigger than his if my two parts had a zero at the start? Or would he be first because he had a head start?

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Re: Dividing Infinity
Not necessarily, I envisioned this concept of infinity from the perspective of Omar Khayyam's Moving Finger.
Both sides would still be the same. As an example, think of the real number line that goes from negative infinity on the left, to positive infinity on the right. You could divide it at 0, and both sides would still be the same. Or you could divide it at 1, and both sides would still be the same. There's no "middle" of infinity.
On the other hand we could do the same experiment with the counting numbers 1, 2, 3, 4, 5, ...
In that case, wherever you put your finger, the part to the left would be finite and the part to the right would be infinite. So the halves would NEVER be the same!
https://www.amazon.com/MovingFingerOm ... ar+khayyam
He envisioned a finger able to trace over history outside of time, as if time was causally recorded time and effect into the patterns of sand, every particle observed from a viewpoint of god, a absolute vision of time and space.
If we take this viewpoint, this moving finger, then we should be able at any point in time to put our finger right upon the center of time and cut it in half, as entropy would be no bar to the vision of God to see particles even after they've essentially stopped behaving relativistically at the end of the universe. Everything is seen, just like how in the book Flatland people from another dimension could see inside of beings in lower dimensions.
It then isn't a matter of sequentiality, of 1, 2, 3, 4, 5 etc being counted, as Etc represents a formulaic expectation, one not accounted for in Khayyam's position. It would be something imposed, only what is should be counted if we are counting, correct? Does Etc. have a sequential spot in number theory, as solid number like Zero gained? Remember, Zero used to be a mere place holder, then some clever person decided it was a number. Is Etc also? If infinity?
If I split the universe in half and added one, what does this mean? In pure abstract math, 1 isn't necessarily a number.... mathematicians have debated this for thousands of years.... but if I add one, does it change the causality of it all? If I take away the zero, does it change it, because our number theory has changed? Or are numbers only valid when actually related to a object, or set of objects, some sort of grouping? What do numbers presume about the user? Are numbers inherently cartographical tools? Do they in a sense manufacture the map of the mind, lay the foundations for information to be used for our modes of navigation, when we mentally think of a map? Can numbers exist independently of this?
Can numbers exist in space independent of time, or are just of time and no space, or space and no time? Are numbers a force in the universe, independent of a user, or are they dependent upon a observer and user, and therefore can be used mistakenly telologically, and therefore in once set of circumstances be right, and in another set wrong?
Can a infinite number stretch pass the ability of a God view to observe it? Can infinity be bigger than God, especially in the case of a self contained, Ex Nihilo universe observed in full by a omnipresent observer, but not of that created, finite in relation to him? What would infinity mean if it was presumed it could be more than the sum of the universe and God? Would that make infinity a false concept? Something fundamentally flawed? Note that Archimedes in the Sand Reckoner only climbed up to a number that was Myriad Myriad... it was the highest number he was willing to go. He could of gone higher with his method, but didn't. Why should one mathematician be so conservative and not just let loose with presumptions, when he was trying to measure the size of everything, much akin to what Khayyam was trying? Why do we presume differently today? Is it rational and reasonable to continue on with our number theory as it is, knowing it is fundamentally flawed, and is there a better way?
Re: Dividing Infinity
I am addressing a similiar subject on another thread.
Infinity cannot be divided (an any of arithmatic function) without resulting in "absence of definition" (according to the mathmaticians) or infinity (according to nonmathematicians such as physicists, etc.)
The problem is that infinity implies division as an elements of itself and in this respect must be proportional to 1 (and therefore all number). The reason for this is that all proportions, as ratios, imply division.
1) The problem is "infinity" implies existence as number exists if and only if they manifest unto infinity. 1n cannot exist unless their are infinitely further numbers to quantify it as 1n.
2) "1" implies existence as number exists if and only if they are structural extensions of 1.
3) 1 and quantitative infinity seem to cycle between eachother as neither can exist without the other as all rational numbers are merely reflections of "1" unto infinity. 1 exists if and only if their is quantitative infinity. Quantitative Infinity exists if and only if their is one. In this respect they can be observed as dualistic: ⟨1∞⟩.
4) Infinity must contain "1" as an element otherwise it would not exist. 1 must contain infinity as an element otherwise it would not exist.
5) All number contains as an element "1" and "1" exists through selfreflection if and only if there is infinity as it must reflect itself through infinite number to infinitely exist. If One does not contain as an element "infinity" is is not "stable" as it is "finite". If Infinity does not contain 1 as an element neither is it stable as it does not contain "all".
6) Because 1 as a unit or "unity" must both contain as an element and be an element of infinity as: 1 ∋ ∞ and 1 ∈ ∞ which would be similiar but not equal to ∞/1 and 1/∞ as "fractions". This is considering if x contains as an element y, the element y can be observed as a degree of x.
∞/1 and 1/∞ can be observed as "proportional to eachother" as fractions even though these fractions in themselves cannot equate to anything other than themselves.
so ∞/1 ∝ 1/∞
The problem occurs as "lack of definition" is proportional to "lack of definition" cannot exist as thier is no definition to be proportional too.
7) In this respect ∞/1 ∝ 1/∞ cannot exist except as 1nx/1ny and 1ny/1nx as both contains as elements and are elements of 1nx and 1ny. 1nx/1ny and 1ny/1nx are striclty observation of "division" in one respect and "ratios" in another for a ratio exists if an only if their is division and vice versa.
In this respect 1 and ∞ contain as an element and are an element of "proportionality/ratios" and "division". In this respect, and possiblity this respect only, 1 is proportional to infinity as they both contain as an element and are an element of 1nx and 1ny.
or (1 ∝ ∞) ↔ ∃(∞/1 ∝ 1/∞) ↔ {(1,∞) ∈∋ (1nx,1ny) ∧ (1nx/1ny ∝ 1ny/1nx)}
Assuming the equation is correct, and that is where I need an opinion, One is proportional to infinity maybe only in this respect.
Infinity cannot be divided (an any of arithmatic function) without resulting in "absence of definition" (according to the mathmaticians) or infinity (according to nonmathematicians such as physicists, etc.)
The problem is that infinity implies division as an elements of itself and in this respect must be proportional to 1 (and therefore all number). The reason for this is that all proportions, as ratios, imply division.
1) The problem is "infinity" implies existence as number exists if and only if they manifest unto infinity. 1n cannot exist unless their are infinitely further numbers to quantify it as 1n.
2) "1" implies existence as number exists if and only if they are structural extensions of 1.
3) 1 and quantitative infinity seem to cycle between eachother as neither can exist without the other as all rational numbers are merely reflections of "1" unto infinity. 1 exists if and only if their is quantitative infinity. Quantitative Infinity exists if and only if their is one. In this respect they can be observed as dualistic: ⟨1∞⟩.
4) Infinity must contain "1" as an element otherwise it would not exist. 1 must contain infinity as an element otherwise it would not exist.
5) All number contains as an element "1" and "1" exists through selfreflection if and only if there is infinity as it must reflect itself through infinite number to infinitely exist. If One does not contain as an element "infinity" is is not "stable" as it is "finite". If Infinity does not contain 1 as an element neither is it stable as it does not contain "all".
6) Because 1 as a unit or "unity" must both contain as an element and be an element of infinity as: 1 ∋ ∞ and 1 ∈ ∞ which would be similiar but not equal to ∞/1 and 1/∞ as "fractions". This is considering if x contains as an element y, the element y can be observed as a degree of x.
∞/1 and 1/∞ can be observed as "proportional to eachother" as fractions even though these fractions in themselves cannot equate to anything other than themselves.
so ∞/1 ∝ 1/∞
The problem occurs as "lack of definition" is proportional to "lack of definition" cannot exist as thier is no definition to be proportional too.
7) In this respect ∞/1 ∝ 1/∞ cannot exist except as 1nx/1ny and 1ny/1nx as both contains as elements and are elements of 1nx and 1ny. 1nx/1ny and 1ny/1nx are striclty observation of "division" in one respect and "ratios" in another for a ratio exists if an only if their is division and vice versa.
In this respect 1 and ∞ contain as an element and are an element of "proportionality/ratios" and "division". In this respect, and possiblity this respect only, 1 is proportional to infinity as they both contain as an element and are an element of 1nx and 1ny.
or (1 ∝ ∞) ↔ ∃(∞/1 ∝ 1/∞) ↔ {(1,∞) ∈∋ (1nx,1ny) ∧ (1nx/1ny ∝ 1ny/1nx)}
Assuming the equation is correct, and that is where I need an opinion, One is proportional to infinity maybe only in this respect.
Re: Dividing Infinity
You mean:EchoesOfTheHorizon wrote: ↑Sat Oct 28, 2017 4:06 am
Not necessarily, I envisioned this concept of infinity from the perspective of Omar Khayyam's Moving Finger.
“The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.”
Clearly old Omar never saw an Edit button.

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Re: Dividing Infinity
dividing infinity is why motion is impossible (at least according to Zeno)
Imp
Imp

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Re: Dividing Infinity
I haven't look at it in the Greek, but don't think it was dividing infinity, but the infinite metric not based on physical reality but a abstract scale that always presumed another half point existed between points.
But so much of Zeno is lost it might very well be the case he did that too. I'm suspicious of any scale that doesn't know When it is too big or too small to apply. It is a aspect of the Banach Tardski paradox (hardly the full reason), if you split a thing up (under certain maths) and can be reassembled at any size.
If you can see colored waves when you close your eyes (only a few here will be able to on average), such as blue and greens and blacks, try to measure the distance. Notice you can? Your having a low level hypnagogic hallucination, and can apply measurement. A aspect of the Pythagorean table of Opposites is already at play at this incredibly low level of vision.
http://lizzfonacier.com/artwork/2677296 ... rk_II.html
https://en.m.wikipedia.org/wiki/Table_of_Opposites
You can apply some of the Opposites from the table upon this void, but not others. Zeno' paradox of space seems to apply here, but wouldn't apply in 3D space, such as when we see, or lucid dream. You make it to where you are going in such a case, because it has form, and not just relative contrast. Our dreamscapes are merely higher stages of hypnagogic sight. Our wzking vision far stronger.
So where does infinity sit in this? The sands of time has a resemblence to this grade of hallucination, does it not, as it advances, turns into waves, elementary forms.
But so much of Zeno is lost it might very well be the case he did that too. I'm suspicious of any scale that doesn't know When it is too big or too small to apply. It is a aspect of the Banach Tardski paradox (hardly the full reason), if you split a thing up (under certain maths) and can be reassembled at any size.
If you can see colored waves when you close your eyes (only a few here will be able to on average), such as blue and greens and blacks, try to measure the distance. Notice you can? Your having a low level hypnagogic hallucination, and can apply measurement. A aspect of the Pythagorean table of Opposites is already at play at this incredibly low level of vision.
http://lizzfonacier.com/artwork/2677296 ... rk_II.html
https://en.m.wikipedia.org/wiki/Table_of_Opposites
You can apply some of the Opposites from the table upon this void, but not others. Zeno' paradox of space seems to apply here, but wouldn't apply in 3D space, such as when we see, or lucid dream. You make it to where you are going in such a case, because it has form, and not just relative contrast. Our dreamscapes are merely higher stages of hypnagogic sight. Our wzking vision far stronger.
So where does infinity sit in this? The sands of time has a resemblence to this grade of hallucination, does it not, as it advances, turns into waves, elementary forms.
Re: Dividing Infinity
He might be right. Perhaps we live in a block universe. Time is an illusion. All the points of spacetime exist "at the same time" in a 4D rectangle whose points are specified by three spatial and one temporal dimension. The past, present, and future all exist at once. The universe is a frozen, static collection of points of spacetime. My understanding is that one could adopt that point of view without affecting the equations of physics in the least.Impenitent wrote: ↑Sun Oct 29, 2017 2:18 amdividing infinity is why motion is impossible (at least according to Zeno)
That's right. BanachTarski is a theorem of set theory applied to Euclidean 3space.EchoesOfTheHorizon wrote: ↑Sun Oct 29, 2017 4:26 amBut so much of Zeno is lost it might very well be the case he did that too. I'm suspicious of any scale that doesn't know When it is too big or too small to apply. It is a aspect of the Banach Tardski paradox (hardly the full reason), if you split a thing up (under certain maths) and can be reassembled at any size.
That shows that physics and math are not the same. Nobody believes the theorem is valid in the world. The idea of being able to take arbitrary subsets of continuous space is a mathematical concept, not a physical one. Ub fact the reason the theorem works is because we assume a sphere is made of infinitely many points. There's no reason that's true of the world. And a lot of evidence that it's false.
I'm not sure from reading your posts if you are perhaps confusing or conflating mathematical space with physical space.
 Arising_uk
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Re: Dividing Infinity
How would you be able to tell 'half way out'?EchoesOfTheHorizon wrote:If I took infinity, traced my finger half way out on it, ...
Re: Dividing Infinity
Infinity doesn't exist beyond being an idea or a symbol.EchoesOfTheHorizon wrote: ↑Sat Oct 28, 2017 1:15 amIf I took infinity, traced my finger half way out on it, and cut it equally in half, and added that quantity of 'one' to one of the two sides, would the two sides be equal in size, or would the one with 'one' added be bigger?
If a Babylonian lacking the concept of Zero did the same, would both my halves be bigger than his if my two parts had a zero at the start? Or would he be first because he had a head start?
If you divide an idea in half you get nothing. Similarly if you divide a symbol in half.
Re: Dividing Infinity
Infinity must contain division by its very nature. To counterbalance this "division" "multiplication" exists and an equilibrium which maintains infinity for what it is.
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