sordavie

Related to Tarenth's post, I've wondered for a while--but haven't spent any time looking for a definitive answer--whether it's mathematically consistent to have an infinite or transinfinite based number system. I'm inclined to think yes for the former but no for the latter.

By the way Tarenth, you can get linear motion in one dimension. Remember, a point can be represented in zero dimensions, a line in one dimension, a square in two dimensions, a cube in three dimensions, a hypercube in four, and so on. So that's why I was confused at your description of the dimensions.

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leejo

I can't see why an infinite-base system would be a problem. It would be nearly useless, but it would work.

What's "transinfinite"?

sordavie

Oops, typo. I meant 'transfinite'. I suppose what I'm wondering in particular is if there can be such a thing as an aleph-1 based number system. The transfinite numbers are cardinals which are larger than any finite number.

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ScratchMonkey

"Transinfinite" is a synonym for transfinite.

http://en.wikipedia.org/wiki/Transfinite_number
http://groups.google.com.sb/group/sc...49e48c1832e3a4

What's an "infinite base"? If you mean radix infinity, I can't see how that would have any value. It means encoding numbers using an infinite number of symbols.

http://en.wikipedia.org/wiki/Radix

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sordavie

When i said base infinity, I meant base aleph-0, the smallest transfinite number, not the upper bound of the number line.

The language of first order logic and set theory give you an infinite supply of non-logical symbols. So that wouldn't be a theoretical roadblock.

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ScratchMonkey

I'm a little slow: What's the utility of base aleph-0?

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sordavie

Probably nothing. Just theoretical curiosity. A lot of high level mathematics and set theory is like this--testing the limits of logic. It's pure mathematics rather than applied mathematics.

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leejo

Oy. Well anyway, the infinite supply of symbols is why an infinity-base system would work - that seems to be your thinking as well. The transfinite system sounds like many pages of inequalities to prove whether it would work or not, but I don't see why it wouldn't. Set theory is more your wheelhouse though. Don't we just need a well-defined ordered set of symbols?

I've never had to tackle the matter of defining what properties are necessary and sufficient to describe a working numerical system. Do you have those? Seems hard to prove whether or not an inifinity-base or transfinite-base system would "work" without first defining what "work" means.

Oh, and UFOs in Texas. Be sure to say something about that so you-know-who doesn't get snippy.

El_Gringo_Grande

What does any of this have to do with UFO's in Texas?

I have read a couple more stories about this.

The tinfoil hat people did show up. But it does seem that at least some of the eye witnesses stories do seem valid.

But I am tending to think that it was a meteor that broke up. Outside a real craft nothing else seems to fit.

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I’m not racists, I have republican friends. Radio show host.
- "The essence of tyranny is the denial of complexity". -Jacob Burkhardt
- "A foolish consistency is the hobgoblin of little minds" - Emerson
- "People should not be afraid of it's government, government should be afraid of it's People." - Line from V for Vendetta
- If software were as unreliable as economic theory, there wouldn't be a plane made of anything other than paper that could get off the ground. Jim Fawcette

leejo

Maybe nothing. Maybe....everything! Maybe Sordavie is our Keanu Reeves and Jeff Goldblum rolled into one, defeating the invading hoard with set theory. It's brilliant! A few minutes into the invasion, the aliens would start looking around, checking their watches, yawning. What's this guy saying about aleph-0? Do we eat him or worship him? I TOLD you we should have invaded the planet of hot divorcees" and so on until a fight broke out and the aliens destroyed themselves.

sordavie

http://www.cnn.com/2008/US/01/23/air...ufo/index.html

Conspiracy theorists and those who believe intelligent life from other planets are visiting earth fail at abductive reasoning.

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El_Gringo_Grande

Why?

Edit Actually, why is that important?

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I’m not racists, I have republican friends. Radio show host.
- "The essence of tyranny is the denial of complexity". -Jacob Burkhardt
- "A foolish consistency is the hobgoblin of little minds" - Emerson
- "People should not be afraid of it's government, government should be afraid of it's People." - Line from V for Vendetta
- If software were as unreliable as economic theory, there wouldn't be a plane made of anything other than paper that could get off the ground. Jim Fawcette

sordavie

I don't understand your question. Why do these people fail at abductive reasoning? Why is what important?

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El_Gringo_Grande

Why did you make that statement?

What is it about the fact that they fail at some particular form of reasoning that you find important enough to point it out?

Why does it matter that they failed at abductive reasoning?

What is it about failing at abductive reasoning you find so interesting?

In what way does failing at abductive reasoning relate to this thread?

Is failing at abductive reasoning a super secret code phrase that means something else?

Maybe even why do you think they failed at abductive reasoning?

Or just think a bit and I think you will understand what I am asking.

__________________
I’m not racists, I have republican friends. Radio show host.
- "The essence of tyranny is the denial of complexity". -Jacob Burkhardt
- "A foolish consistency is the hobgoblin of little minds" - Emerson
- "People should not be afraid of it's government, government should be afraid of it's People." - Line from V for Vendetta
- If software were as unreliable as economic theory, there wouldn't be a plane made of anything other than paper that could get off the ground. Jim Fawcette

sordavie

That they fail at abductive reasoning is the reason why they come to silly, unreasonable conclusions. That is why reasonable people regard these people as kooks.

Abductive reasoning is, in other terms, inference to the best explanation. Conspiracy theorists and such fail at this sort of reasoning because they ignore, don't recognize, or just refuse to accept what the best explanation is, and instead infer something else.

If you can't see why that's important to this discussion, I don't know what to say to you. I am pointing out the kind of mistake in reasoning that these people make--a failure of their capacities for abductive reasoning.

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