The Paradox of Multiplication and Division

What is the basis for reason? And mathematics?

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Logik
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Re: The Paradox of Multiplication and Division

Post by Logik » Thu Jan 10, 2019 6:05 am

Arising_uk wrote:
Thu Jan 10, 2019 1:34 am
What's relative to the 'yardstick' of Light?
It's relative to the medium in which its speed is measured. It's only constant in a vacuum.

A constant with a fineprint is not a constant. The speed of light is an upper bound. A limit.

https://www.sciencenews.org/article/spe ... -after-all
Last edited by Logik on Thu Jan 10, 2019 7:03 am, edited 4 times in total.

Logik
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Re: The Paradox of Multiplication and Division

Post by Logik » Thu Jan 10, 2019 6:20 am

Eodnhoj7 wrote:
Thu Jan 10, 2019 3:54 am
Actually a 1d point is entirely logical in the dichotomy of "being" and "nonbeing", which is a foundation in mathematics.
Yes, but mathematics is just a conceptual/theoretical man-made tool. To allow yourself to forget that the laws of physics don't apply to imagination is to allow yourself to remain strictly in the theoretical realm. It's a closed system without a feedback loop from external reality.

There are no such things as "error in imagination" so anything goes. Ramanujan proved that 1+2+3+4+... = -1/12

But in the physical realm you have to worry about negative consequences as there are such things as errors and limits as to what is possible.

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Re: The Paradox of Multiplication and Division

Post by surreptitious57 » Thu Jan 10, 2019 10:40 am

Eodnhoj wrote:
All numbers exist as points in space . All points are the same

If I take I point and halve it I get 2 of the same points

If I take these 2 points which exist as I point and halve it I get 8 points
The number line does not exist in space because it is entirely abstract so therefore requires no space at all
And because it is abstract it does not require points either even if you define a point as having zero volume
Even though both the number lines [ standard / complex ] extend to infinity and there are multiple infinites

Every number on the number line occupies a unique fixed place so in that respect it cannot be altered in any way
A number can therefore only be halved for example when it exists as a separate entity not part of the number line

So you can say halve 6 to get 3 when 6 exists by itself in total isolation but when it is on the number line it cannot be altered in any way
And even though 2 X 3 = 6 there is also only one 3 on the number line not two because there is only one space for each individual number

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Re: The Paradox of Multiplication and Division

Post by Eodnhoj7 » Thu Jan 10, 2019 4:50 pm

Logik wrote:
Thu Jan 10, 2019 6:20 am
Eodnhoj7 wrote:
Thu Jan 10, 2019 3:54 am
Actually a 1d point is entirely logical in the dichotomy of "being" and "nonbeing", which is a foundation in mathematics.
Yes, but mathematics is just a conceptual/theoretical man-made tool. To allow yourself to forget that the laws of physics don't apply to imagination is to allow yourself to remain strictly in the theoretical realm. It's a closed system without a feedback loop from external reality.

There are no such things as "error in imagination" so anything goes. Ramanujan proved that 1+2+3+4+... = -1/12

But in the physical realm you have to worry about negative consequences as there are such things as errors and limits as to what is possible.
It may be a man made tool, but men use tools to form them and effectively it acts as a form of adaptation.

The laws of physics are obscure...just like math for that matter. Math forms the frameworks of physics, physics forms the framework of math. Failed theory is merely an abstract framework not aligning with an empirical one.

There is no such thing as an error in "physics" either considering physics is strictly a localization of empirical movements...nothing more. The "laws as localizations" thread in the "metaphysics?" section covers this.

Negative consequences are entirely theoretical if the physical universe realigns to any potential warp in it.


Link for ramanujan's proof?

I have argued all progressive whole number lines are simultaneously directed to point 0. It is logically possible for what he argues.

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Re: The Paradox of Multiplication and Division

Post by Eodnhoj7 » Fri Jan 11, 2019 1:26 am

surreptitious57 wrote:
Thu Jan 10, 2019 10:40 am
Eodnhoj wrote:
All numbers exist as points in space . All points are the same

If I take I point and halve it I get 2 of the same points

If I take these 2 points which exist as I point and halve it I get 8 points
The number line does not exist in space because it is entirely abstract so therefore requires no space at all
And because it is abstract it does not require points either even if you define a point as having zero volume
Even though both the number lines [ standard / complex ] extend to infinity and there are multiple infinites

Every number on the number line occupies a unique fixed place so in that respect it cannot be altered in any way
A number can therefore only be halved for example when it exists as a separate entity not part of the number line

So you can say halve 6 to get 3 when 6 exists by itself in total isolation but when it is on the number line it cannot be altered in any way
And even though 2 X 3 = 6 there is also only one 3 on the number line not two because there is only one space for each individual number
Abstraction is the closest thing to "empty space" we understand...or rather "space" but "empty" can be applied for some as well.

The progressive nature of numbers, as having a linear nature of the actual number line and the "form/function" of logic which produces them, is inseparable from a spatial entity.

The number line is composed of halving, it's inherent nature is contradiction by dualistic opposition:

1 → 2 = 1 → 1/2

a. Where each 1/2 of a point is equivalent to a doubling of the point



1 → 3 = 1 → 1/3

a. because 1 progressing to 1/2 and 2 observes 1 directed to this very same 1/2 and 2 as 1/3 and 3.
b. Because 1 always splits between 1 and Many, it is founded upon a contradictory "halving".

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Re: The Paradox of Multiplication and Division

Post by commonsense » Sun Jan 13, 2019 6:37 pm

Eodnhoj7 wrote:
Mon Jan 07, 2019 9:43 pm
1. All numbers exist as points in space. All points are the same; hence all points exist as one point.
Sorry, but no. Logically, you cannot claim much more than:

All numbers exist as points at various coordinates in space. All points are identical; therefore, all numbers exist as identical points at various coordinates in space.

Therefore the remainder of your post is unfounded.

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Re: The Paradox of Multiplication and Division

Post by Eodnhoj7 » Sun Jan 13, 2019 8:21 pm

commonsense wrote:
Sun Jan 13, 2019 6:37 pm
Eodnhoj7 wrote:
Mon Jan 07, 2019 9:43 pm
1. All numbers exist as points in space. All points are the same; hence all points exist as one point.
Sorry, but no. Logically, you cannot claim much more than:

All numbers exist as points at various coordinates in space. All points are identical; therefore, all numbers exist as identical points at various coordinates in space.

Therefore the remainder of your post is unfounded.
Actually if all points are effectively the same point, approximated through many points, then by default I can claim more than that.

The corridinate is merely a position of one point relative to another, however those positions are effectively 1 point observed approximately through many. The "field" which gives an apparent seperation of these "1" points effectively is void.

Now this breaks down to a basic yin/yang type dualism. If the coordinates are 0d points then we are left with a 1d point field. The same occurs if the coordinates are a 1d point, we are left with a 0d point field.
****See "do points act as fields" thread in the...I think it is metaphysics section.

Without these foundations you posts are illogical as we are left with corridinates, as 0d points, and the surrounding as non-zero points equivalent to a 1 dimensionality.


The number line alone necessitates the prime foundation of number as point space, both rationally and intuitively.

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Re: The Paradox of Multiplication and Division

Post by Logik » Sun Jan 13, 2019 9:33 pm

Eodnhoj7 wrote:
Sun Jan 13, 2019 8:21 pm
Actually if all points are effectively the same point
What do you mean by "same"?

Are you perhaps appealing to the law of identity where A=A?

Or perhaps a better question. Is it a statement (axiom) or an assertion/comparison?
Eodnhoj7 wrote:
Sun Jan 13, 2019 8:21 pm
The corridinate is merely a position of one point relative to another
I would argue that the coordinate defines the point. No coordinates - no point.

Definition gives birth.

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Re: The Paradox of Multiplication and Division

Post by Eodnhoj7 » Sun Jan 13, 2019 11:29 pm

Logik wrote:
Sun Jan 13, 2019 9:33 pm
Eodnhoj7 wrote:
Sun Jan 13, 2019 8:21 pm
Actually if all points are effectively the same point
What do you mean by "same"?

Are you perhaps appealing to the law of identity where A=A?

Or perhaps a better question. Is it a statement (axiom) or an assertion/comparison?
Eodnhoj7 wrote:
Sun Jan 13, 2019 8:21 pm
The corridinate is merely a position of one point relative to another
I would argue that the coordinate defines the point. No coordinates - no point.

Definition gives birth.
Circularity: corridinates are also defined by the point.

In a seperate respect a standard definition of the point, as 0d, negates definition.

It can appeal to the law of identity, however the law of identity has issues as well, I address that elsewhere (epistemology, if memory serves, "new laws of identity"/"contradiction in laws of identity")


A point is a point is a point, under standard defintion it is always 0d. Even under a theoretical 1d nature it is still the same.

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Re: The Paradox of Multiplication and Division

Post by Logik » Sun Jan 13, 2019 11:39 pm

Eodnhoj7 wrote:
Sun Jan 13, 2019 11:29 pm
Circularity: corridinates are also defined by the point.
You say circularity - I say choice.
Eodnhoj7 wrote:
Sun Jan 13, 2019 11:29 pm
In a seperate respect a standard definition of the point, as 0d, negates definition.
Since you can always divide by 2 on the number line the point doesn't exist.

infinities break everything.

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Re: The Paradox of Multiplication and Division

Post by Eodnhoj7 » Sun Jan 13, 2019 11:47 pm

Logik wrote:
Sun Jan 13, 2019 11:39 pm
Eodnhoj7 wrote:
Sun Jan 13, 2019 11:29 pm
Circularity: corridinates are also defined by the point.
You say circularity - I say choice.
Eodnhoj7 wrote:
Sun Jan 13, 2019 11:29 pm
In a seperate respect a standard definition of the point, as 0d, negates definition.
Since you can always divide by 2 on the number line the point doesn't exist.

infinities break everything.
So if it is a matter of choice the axioms can be chosen, allowing further axioms. In a separate respect the axioms are subject to bandwagon fallacy.

Actually all lines are both composed of and composing further lines/points by definition. Each line is a quantification of infinite lines. Each point is a quantification of infinite points.

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Re: The Paradox of Multiplication and Division

Post by Logik » Sun Jan 13, 2019 11:56 pm

Eodnhoj7 wrote:
Sun Jan 13, 2019 11:47 pm
So if it is a matter of choice the axioms can be chosen, allowing further axioms. In a separate respect the axioms are subject to bandwagon fallacy.
Yes. Axiomatic reasoning is an elaborate exercise in combinatorics. You tweak the axioms and see what patterns emerge. Some of those patterns are practically useful in the real world.

The first "axiom" (pre-supposition) on which logic is based is that the world has structure and is governed by rules. The fact that we are observing structure/rules could be entirely coincidental. A temporary statistical anomaly.
Eodnhoj7 wrote:
Sun Jan 13, 2019 11:47 pm
Actually all lines are both composed of and composing further lines/points by definition. Each line is a quantification of infinite lines. Each point is a quantification of infinite points.
Conceptually - yes.

In line with counter-factual reasoning you ought to assume that there is non-zero chance the first pre-supposition of logic is wrong. e.g that the universe has no structure whatsoever. In which case logic is entirely metaphysical. And predictive models work entirely by accident.

Either way - infinities. Those are abstract. Or rather - even if infinities exist, our representation of infinities is abstract/finite.

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Re: The Paradox of Multiplication and Division

Post by Eodnhoj7 » Mon Jan 14, 2019 12:06 am

Logik wrote:
Sun Jan 13, 2019 11:56 pm
Eodnhoj7 wrote:
Sun Jan 13, 2019 11:47 pm
So if it is a matter of choice the axioms can be chosen, allowing further axioms. In a separate respect the axioms are subject to bandwagon fallacy.
Yes. Axiomatic reasoning is an elaborate exercise in combinatorics. You tweak the axioms and see what patterns emerge. Some of those patterns are practically useful in the real world.

The first "axiom" (pre-supposition) on which logic is based is that the world has structure and is governed by rules. The fact that we are observing structure/rules could be entirely coincidental. A temporary statistical anomaly.
Eodnhoj7 wrote:
Sun Jan 13, 2019 11:47 pm
Actually all lines are both composed of and composing further lines/points by definition. Each line is a quantification of infinite lines. Each point is a quantification of infinite points.
Conceptually - yes.

In line with counter-factual reasoning you ought to assume that there is non-zero chance the first pre-supposition of logic is wrong. e.g that the universe has no structure whatsoever. In which case logic is entirely metaphysical. And predictive models work entirely by accident.

Either way - infinities. Those are abstract. Or rather - even if infinities exist, our representation of infinities is abstract/finite.
A temporary statistical anomaly still necessitates statistics, through fractions fundamentally as all statistics are fractions, as a constant.

Infinities are unprovable, except through pure geometric axioms, but act as the foundation of proof.

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Re: The Paradox of Multiplication and Division

Post by Logik » Mon Jan 14, 2019 12:14 am

Eodnhoj7 wrote:
Mon Jan 14, 2019 12:06 am
A temporary statistical anomaly still necessitates statistics, through fractions fundamentally as all statistics are fractions, as a constant.

Infinities are unprovable, except through pure geometric axioms, but act as the foundation of proof.
Sure. And statistics is number theory. Counting is all.

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