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
It's relative to the medium in which its speed is measured. It's only constant in a vacuum.
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.
The number line does not exist in space because it is entirely abstract so therefore requires no space at allEodnhoj 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
It may be a man made tool, but men use tools to form them and effectively it acts as a form of adaptation.Logik wrote: ↑Thu Jan 10, 2019 6:20 amYes, 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.
Abstraction is the closest thing to "empty space" we understand...or rather "space" but "empty" can be applied for some as well.surreptitious57 wrote: ↑Thu Jan 10, 2019 10:40 amThe number line does not exist in space because it is entirely abstract so therefore requires no space at allEodnhoj 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
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
Sorry, but no. Logically, you cannot claim much more than:
Actually if all points are effectively the same point, approximated through many points, then by default I can claim more than that.commonsense wrote: ↑Sun Jan 13, 2019 6:37 pmSorry, 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.
What do you mean by "same"?
I would argue that the coordinate defines the point. No coordinates - no point.
Circularity: corridinates are also defined by the point.Logik wrote: ↑Sun Jan 13, 2019 9:33 pmWhat 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?
I would argue that the coordinate defines the point. No coordinates - no point.
Definition gives birth.
You say circularity - I say choice.
Since you can always divide by 2 on the number line the point doesn't exist.
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.
Conceptually - yes.
A temporary statistical anomaly still necessitates statistics, through fractions fundamentally as all statistics are fractions, as a constant.Logik wrote: ↑Sun Jan 13, 2019 11:56 pmYes. 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.
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.
Sure. And statistics is number theory. Counting is all.
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