The Paradox of Multiplication and Division
The Paradox of Multiplication and Division
1. All numbers exist as points in space. All points are the same; hence all points exist as one point.
2. If I take 1 point and halve it, I get 2 of the same points, not half of a point.
3. If I take these 2 points, which exist as 1 point, and halve it I get 8 points.
The reason is because the two points exist as 1 point while each point is one in itself. To halve anyone of them is to halve the same point.
So
A)2 is halved to 4 either as 1 group (equivalent to a point) or individually.
B) These 4 points in turn are halved to eight in accords with point 3a.
C) Multiplication and Division are duals happening simultaneously through Pointspace.
2. If I take 1 point and halve it, I get 2 of the same points, not half of a point.
3. If I take these 2 points, which exist as 1 point, and halve it I get 8 points.
The reason is because the two points exist as 1 point while each point is one in itself. To halve anyone of them is to halve the same point.
So
A)2 is halved to 4 either as 1 group (equivalent to a point) or individually.
B) These 4 points in turn are halved to eight in accords with point 3a.
C) Multiplication and Division are duals happening simultaneously through Pointspace.

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Re: The Paradox of Multiplication and Division
motion is impossible as distance is infinitely divisible, where zeno parks his boats
Imp
Imp
Re: The Paradox of Multiplication and Division
Zenos paradoxes require motion of measurment.Impenitent wrote: ↑Mon Jan 07, 2019 11:24 pm motion is impossible as distance is infinitely divisible, where zeno parks his boats
Imp
Re: The Paradox of Multiplication and Division
Points are meant to be indivisible. They have no mass, no volume, no dimensions or any quantifiable properties whatsoever. Points are only conceptual.
Every time you allow yourself to divide the indivisible or expand the unexpandable you will end up with a paradox. Because you are ignoring your own, implicit axioms.
We are bounded rationalists. Such are the limits of our minds.
For if you have individuated them as "two things" then at the very least least their spacetime coordinates are different.
Every time you allow yourself to divide the indivisible or expand the unexpandable you will end up with a paradox. Because you are ignoring your own, implicit axioms.
We are bounded rationalists. Such are the limits of our minds.
Your argument is semantic and is play on the process of individuation. What do you mean by "same" ? Can two individual things ever be "the same" ?
For if you have individuated them as "two things" then at the very least least their spacetime coordinates are different.
Re: The Paradox of Multiplication and Division
The division of points results in the basic axioms of the line and circle. Points can be divided.Logik wrote: ↑Tue Jan 08, 2019 9:25 am Points are meant to be indivisible. They have no mass, no volume, no dimensions or any quantifiable properties whatsoever. Points are only conceptual.
Every time you allow yourself to divide the indivisible or expand the unexpandable you will end up with a paradox. Because you are ignoring your own, implicit axioms.
We are bounded rationalists. Such are the limits of our minds.
Your argument is semantic and is play on the process of individuation. What do you mean by "same" ? Can two individual things ever be "the same" ?
For if you have individuated them as "two things" then at the very least least their spacetime coordinates are different.
All limits end in a paradox, might as well be rational and start with one.
1. Methamatics is dependent upon the frameworks expanding from the axioms justifying the axioms and the axioms being justified by the frameworks. Math is sophistry and subject to the fallacy of circularity if circularity is considering a fallacy.
I do not believe circularity is a fallacy because there is proof is can result in expanding answers.
Second because the fallacy of circularity is subject to the other fallacies, thus necessitating a truth statement. Circularity is a holistic self referencing proof.
2. A point is always a point, so yes a point is always the same. Quantum entanglement gives some proof to similarity. Second if no two things are the same, we are left with infinite variations of 1, and the principle of identity is violated according to it's own laws. Now I argue elsewhere this is no problem, but this does not change that modern maths (not all "if" memory serves, but that is a big "if") are still dependent on it. If 1 equals 1 then a point will always be a point.
3. There are many matches, potentially infinite maths because of the axioms can always be added. As such individuation can be a foundation without contradiction tonother maths.
4. This approach contradicts the "maths is meaningless thread", by nullifying the paradoxes of math with another paradox.
5. Yes the space/time coordinate are different, I am glad you brought that up. I wanted to cover it, but people get pissed if I have an argument for everything, or they would be too lazy too read.
The point individuating into another point results into time/space, where each point isnan approximation of the 1 point. I will probably have to go more in depth on point 5, but the post is already long as is.
Re: The Paradox of Multiplication and Division
Hmm?
Points the fundamental building blocks of Euclidian geometry. Lines and circles are constructed from points.
A line junction of two points.
A circle is all the points which are distance r (radius) from a point called the centre.
Re: The Paradox of Multiplication and Division
https://math.stackexchange.com/question ... nesegment
1) All lines between two points have a center point.
2) The line with a center point, in turn is composed of 2 lines with each line in turn composed of center point.
3) The process continues, where the line is composed of infinite lines through infinite points.
4) inverting points 1 and 2, all 2 points have a line between them which connect them.
5) In accords with point 4, the line existing between two points is the line as the individuation of the point.
6) All points, as the same point, are connected through the line.
Re: The Paradox of Multiplication and Division
I don't see how any of that ends up division of points?Eodnhoj7 wrote: ↑Tue Jan 08, 2019 7:38 pmhttps://math.stackexchange.com/question ... nesegment
1) All lines between two points have a center point.
2) The line with a center point, in turn is composed of 2 lines with each line in turn composed of center point.
3) The process continues, where the line is composed of infinite lines through infinite points.
4) inverting points 1 and 2, all 2 points have a line between them which connect them.
5) In accords with point 4, the line existing between two points is the line as the individuation of the point.
6) All points, as the same point, are connected through the line.
You end up with infinitely many segments and infinitely many points  sure.
Re: The Paradox of Multiplication and Division
The foundational measurement of phenomena, the basic line, is premised in the individuation of points. The point inverting from one point to many.Logik wrote: ↑Tue Jan 08, 2019 10:29 pmI don't see how any of that ends up division of points?Eodnhoj7 wrote: ↑Tue Jan 08, 2019 7:38 pmhttps://math.stackexchange.com/question ... nesegment
1) All lines between two points have a center point.
2) The line with a center point, in turn is composed of 2 lines with each line in turn composed of center point.
3) The process continues, where the line is composed of infinite lines through infinite points.
4) inverting points 1 and 2, all 2 points have a line between them which connect them.
5) In accords with point 4, the line existing between two points is the line as the individuation of the point.
6) All points, as the same point, are connected through the line.
You end up with infinitely many segments and infinitely many points  sure.
Re: The Paradox of Multiplication and Division
Sounds like you are describing a mathematical field.Eodnhoj7 wrote: ↑Tue Jan 08, 2019 11:01 pmThe foundational measurement of phenomena, the basic line, is premised in the individuation of points. The point inverting from one point to many.Logik wrote: ↑Tue Jan 08, 2019 10:29 pmI don't see how any of that ends up division of points?Eodnhoj7 wrote: ↑Tue Jan 08, 2019 7:38 pm
https://math.stackexchange.com/question ... nesegment
1) All lines between two points have a center point.
2) The line with a center point, in turn is composed of 2 lines with each line in turn composed of center point.
3) The process continues, where the line is composed of infinite lines through infinite points.
4) inverting points 1 and 2, all 2 points have a line between them which connect them.
5) In accords with point 4, the line existing between two points is the line as the individuation of the point.
6) All points, as the same point, are connected through the line.
You end up with infinitely many segments and infinitely many points  sure.
 Arising_uk
 Posts: 12313
 Joined: Wed Oct 17, 2007 2:31 am
Re: The Paradox of Multiplication and Division
Not really it was premised on having a yardstick, the abstraction of points appeared later.Eodnhoj7 wrote:The foundational measurement of phenomena, the basic line, is premised in the individuation of points. The point inverting from one point to many.
Re: The Paradox of Multiplication and Division
Infinities are a sideeffect of our conceptualisation of a point as zerodimensional.
By dividing a linesegment into points you are effectively dividing by zero  that's why you keep falling into the vortex.
If you recognise recursion as meaning then you are in the same frame of mind as digital physicists or a computer scientist (because another name for 'recursion theory' is 'Computability theory').
In a computational universe you must account for the halting problem. An algorithm that does not halt is an infinite loop.
You cannot divide a finitelength line into infinitely many parts. The moment your line is less than 2*ℓ P (Planck length) dividing it would violate the laws of physics. So if you adhere to the laws of physics, you cannot divide a line infinitely. You can only divide a line log(length) > 2*ℓ P
Logic is symbol manipulation. Symbol manipulation is computation. Reason.
Symbols are merely representations of other things, not the things themselves.
The representation of nothing is 0. So the representation of nothing is something? That is a paradox.
You can't solve this paradox without giving up your use of the symbol 0. The same goes with ∞.
This leaves you with a conceptual (metaphysical?) dilemma. Do you keep 0 and ∞ in your vocabulary or do you abandon them?
You can't deny that they are useful concepts, but Mathematics becomes very hard very quickly without them. Try it.
Quantim physicists absolutely HATE infinities. https://en.wikipedia.org/wiki/Renormalization
Last edited by Logik on Wed Jan 09, 2019 12:08 pm, edited 6 times in total.
Re: The Paradox of Multiplication and Division
Yardsticks are the symbol of relativism.Arising_uk wrote: ↑Wed Jan 09, 2019 11:06 amNot really it was premised on having a yardstick, the abstraction of points appeared later.Eodnhoj7 wrote:The foundational measurement of phenomena, the basic line, is premised in the individuation of points. The point inverting from one point to many.
I fact. I think I shall add a ruler to my family crest.
 Arising_uk
 Posts: 12313
 Joined: Wed Oct 17, 2007 2:31 am
Re: The Paradox of Multiplication and Division
What's relative to the 'yardstick' of Light?Logik wrote:Yardsticks are the symbol of relativism. ...
Funny play of words.I fact. I think I shall add a ruler to my family crest.
Re: The Paradox of Multiplication and Division
Actually a 1d point is entirely logical in the dichotomy of "being" and "nonbeing", which is a foundation in mathematics.Logik wrote: ↑Wed Jan 09, 2019 11:33 amInfinities are a sideeffect of our conceptualisation of a point as zerodimensional.
By dividing a linesegment into points you are effectively dividing by zero  that's why you keep falling into the vortex.
If you recognise recursion as meaning then you are in the same frame of mind as digital physicists or a computer scientist (because another name for 'recursion theory' is 'Computability theory').
In a computational universe you must account for the halting problem. An algorithm that does not halt is an infinite loop.
You cannot divide a finitelength line into infinitely many parts. The moment your line is less than 2*ℓ P (Planck length) dividing it would violate the laws of physics. So if you adhere to the laws of physics, you cannot divide a line infinitely. You can only divide a line log(length) > 2*ℓ P
Logic is symbol manipulation. Symbol manipulation is computation. Reason.
Symbols are merely representations of other things, not the things themselves.
The representation of nothing is 0. So the representation of nothing is something? That is a paradox.
You can't solve this paradox without giving up your use of the symbol 0. The same goes with ∞.
This leaves you with a conceptual (metaphysical?) dilemma. Do you keep 0 and ∞ in your vocabulary or do you abandon them?
You can't deny that they are useful concepts, but Mathematics becomes very hard very quickly without them. Try it.
Quantim physicists absolutely HATE infinities. https://en.wikipedia.org/wiki/Renormalization
0 canceling itself results in 1. 0 is an observation of relation between multiple entities, it is not a thing in itself as well...there is nothing to be observed. The line is a result
Dually if the point is 1 dimensional, directed through itself as itself, the resulting line is a connector absent of the same directional nature of the 1d line and effectively negative dimensional.
1. The plank law is the boundary of division before quantum entanglement comes into effect and we are left with a random state of determining movements. A fraction of a Planck unit effectively results in entangled particles and the cycle continues as the quantum entanglement sets the foundation for the phenomenon being measured.
Infinite division results in quantum entanglement.
2. All phenomenon are composed of and composing further phenomenon, and as such are equivalent to medial points synonymous by definition to symbols.
3. 0 can only be observed relative to existing numbers. The number line observes it as a center point where positive numbers are inverted to negative numbers. It is less an thing itself but a foundation for multiplicity.