Proof Infinity is Impossible

[devans99]

Yes, I follow the thought experiment, but still find it nonsensical (nothing personal - I just find most talk involving infinity to be nonsensical in general ). It cannot have 'every number' on it, because by definition, there is no such thing as 'every number'. Terms such as 'every' and 'all' only apply sensibly to finite sets or quantities.

So it also doesn't make sense to say that the infinite ruler is longer than all natural numbers. It could be said that for any given natural number X, that the infinite ruler has a length greater than X units. In other words, for any finite ruler that you could place against the infinite one, you could see that the infinite extended further. But it could not be said that length of the ruler is greater than all numbers, because that is not sensible. (And even if it was, I still don't see how that would prove that the infinite object is impossible.)

Incidentally, I have read that Cantor did make proofs that there are different kinds of infinities and that actually some infinite sets can be shown to be larger than other infinite sets - that there are actually different kinds of infinities - but that's a level of mathematics that's a bit over my head.

If you think about an infinite ruler, you can walk along it to the right (the end that goes on forever) and find every natural number X on it - if the ruler stops at any natural number X - then its a finite ruler. So an infinite ruler must have natural number X on it.

Now the infinite ruler goes on forever - so given any natural number X, it must go on longer than that. So an infinite ruler must be longer than all natural numbers.

I do not agree with Cantor's set theory. I find it to be very illogical. I have a lot of issues with it. Just one example:

- it claims that sets with a greater than finite number of objects actually exist in reality
- but a set is a whole number of objects only
- so the size of all sets must is constrained to be a finite number
- and also sets are formed by adding 1 object at a time, so its not possible for their size ever to become non-finite
- so (contrary to set theory) sets with a greater than finite number of objects actually DO NOT exist in reality

[Terrapin Station]

Here's an example of a hydrogen bomb test video:


What do we see there? Super-heated particles (at least some of it in a plasma state), smoke-like, billowing, expanding clouds of particulates, buildings being destroyed, etc. Right?

Super-heated particles? Guess they must of been heated up by the energy released in the explosion?

Note that I'm not saying "There's no such thing as energy."

You're supposed to be supporting the claim that "There can be energy that's just energy, that's NOT matter in motion."

The way particles are heated is via energy in the form of matter in motion.

Your claim was that you can observe energy that's just energy. You're supposed to be supporting that claim.

[Sculptor1]

No. Maths has some abstract ideas, that can exist in people's heads without ANY reference to reality.
Such as the square root of minus one. Or ANY negative number. Or ANY irrational number.
It can have perfection such as circles, and straight lines. None of which can exist in reality.

I think it you read the actual definition, it clearly says 'there exists...':

https://en.wikipedia.org/wiki/Axiom_of_infinity

If then you look at the dictionary definition of 'exists' - 'have objective reality or being'.

That's pretty clear - maths says infinite objects exist in reality.

If you believe that then that is your bag.
However, the case for things existing in reality is an empirical matter, not a rational matter.

[Sculptor1]

HAHAHA

Or did you really think that there can only be one kind of "actual" infinity

There is one type of infinity. An expression used where the quantity is unknown.
There can be no case for the other use of the world which means endless in measure, as this is impossible.

[devans99]

Super-heated particles? Guess they must of been heated up by the energy released in the explosion?

Note that I'm not saying "There's no such thing as energy."

You're supposed to be supporting the claim that "There can be energy that's just energy, that's NOT matter in motion."

The way particles are heated is via energy in the form of matter in motion.

Your claim was that you can observe energy that's just energy. You're supposed to be supporting that claim.

The bomb is small yet it destroys an entire city. So it can't just be the matter in the bomb that is doing this.

Something else is released to - energy - and in the vast quantities predicted by E=mc^2.

[Sculptor1]

Our biggest 'brick' is our mind. The concept of infinity is suprarational, beyond reason, logic or images.

It is also contra-empirical, counter-rational, and otherwise impossible.
It can only exist as a mental abstraction.

[Steve3007]

Incidentally, I have read that Cantor did make proofs that there are different kinds of infinities and that actually some infinite sets can be shown to be larger than other infinite sets - that there are actually different kinds of infinities - but that's a level of mathematics that's a bit over my head.

I don't think the idea of different levels of infinity has to be conceptually difficult, once we've accepted one of the rules of the game of mathematics: that there are an infinite number of integers. (i.e. for any integer one can think of, one can always think of a bigger or smaller one.)

If we accept that rule of the game, then logically we have to accept that there are an infinite number of even numbers. We might then decide to make a rule that there are twice as many integers as there are even numbers. Or we might follow Cantor and decide to think in terms of making one-to-one matches between the numbers in each set. If we do that, then we could conclude that every number in the set of even numbers can be matched to a number in the set of integers (2>1, 4>2, 6>3, ...). In that case, we might conclude that the infinite set of even numbers is the same size as the infinite set of integers. We conclude that a bigger set would be one in which every member in the smaller set maps to an infinite number of members in the bigger set. i.e. a one-to-one match can't be made.

One thing is for sure in this game. As I said in an earlier post, if we conclude that there is only one level of infinity then the reductio ad absurdum from that is that if there is an infinite number of even numbers and an infinite number of integers, then there are no odd numbers.

But we have to remember that it's all a game, and the only requirement is logical self-consistency. If, by chance, there is some mapping from the game to reality, great. Bonus. But it's not necessary. There might be some mapping from other games (e.g. Monopoly, Chess or Buckaroo) to reality. But it's not essential.

[Steve3007]

Incidentally, there is definitely as mapping from Kerplunk to reality. A government minister said so recently on the News.

[Terrapin Station]

The bomb is small yet it destroys an entire city. So it can't just be the matter in the bomb that is doing this.

??? How in the world would you be figuring that? Even if you're positing that energy can exist sans matter, the bomb still only starts with that relatively small amount of matter. If that matter can destroy the city via being turned into energy sans matter, why wouldn't it be able to destroy the city when we're limiting our ontology to matter in relative motion?

Also, what you're writing here has nothing at all to do with what you're observing on the video. You were supposed to be arguing that we can actually observe energy sans matter.

[devans99]

The bomb is small yet it destroys an entire city. So it can't just be the matter in the bomb that is doing this.

??? How in the world would you be figuring that? Even if you're positing that energy can exist sans matter, the bomb still only starts with that relatively small amount of matter. If that matter can destroy the city via being turned into energy sans matter, why wouldn't it be able to destroy the city when we're limiting our ontology to matter in relative motion?

Also, what you're writing here has nothing at all to do with what you're observing on the video. You were supposed to be arguing that we can actually observe energy sans matter.

But plain and simply, there is not enough matter in the bomb to destroy a whole city. So the matter in the bomb must have been transmuted into a much more abundant quantity of something - IE energy - as per E=mc^2.

The matter in the bomb cannot have produced more matter - there is no process that takes 1 unit mass of matter and produces 1000000 unit mass of matter - so it is clearly a matter->energy conversion that is taking place.

[Atla]

There is one type of infinity.

And you know this how?

An expression used where the quantity is unknown.

Unkown quantity? Where did you get this one?

There can be no case for the other use of the world which means endless in measure, as this is impossible.

And you know this how?

[Terrapin Station]

??? How in the world would you be figuring that? Even if you're positing that energy can exist sans matter, the bomb still only starts with that relatively small amount of matter. If that matter can destroy the city via being turned into energy sans matter, why wouldn't it be able to destroy the city when we're limiting our ontology to matter in relative motion?

Also, what you're writing here has nothing at all to do with what you're observing on the video. You were supposed to be arguing that we can actually observe energy sans matter.

But plain and simply, there is not enough matter in the bomb to destroy a whole city. So the matter in the bomb must have been transmuted into a much more abundant quantity of something - IE energy - as per E=mc^2.

The matter in the bomb cannot have produced more matter - there is no process that takes 1 unit mass of matter and produces 1000000 unit mass of matter - so it is clearly a matter->energy conversion that is taking place.

This is the problem with typing more than one issue at a time. You ignored this part yet again:

You were supposed to be arguing that we can actually observe energy sans matter.

[devans99]

This is the problem with typing more than one issue at a time. You ignored this part yet again:

You were supposed to be arguing that we can actually observe energy sans matter.

So the sun then, its made of hydrogen which it converts to helium with nuclear fusion - matter is converted into photons and neutrinos.

Those photons arrive on earth and power photosynthesis in plants.

We can detect these photons by the difference between day and night.

Terrapin - why are we going through this?

[Ron Krumpos]

Our biggest 'brick' is our mind. The concept of infinity is suprarational, beyond reason, logic or images.

It is also contra-empirical, counter-rational, and otherwise impossible.
It can only exist as a mental abstraction.

Suprarational consciousness is is complete intuitive insight. It combines the very definition of all three words. Complete: “The entirety needed for realization; consummate.” Intuitive: “Knowing something without rational processes; the immediate cognition of it.” Insight: “Discernment of the true nature of a situation; the penetration beyond the reach of the senses.”

[Terrapin Station]

This is the problem with typing more than one issue at a time. You ignored this part yet again:

You were supposed to be arguing that we can actually observe energy sans matter.

So the sun then, its made of hydrogen which it converts to helium with nuclear fusion - matter is converted into photons and neutrinos.

Those photons arrive on earth and power photosynthesis in plants.

We can detect these photons by the difference between day and night.

Terrapin - why are we going through this?

We're going through this because you're claiming things that, although sometimes they're popular or are even conventional wisdom in their milieu, are really incoherent twaddle ontologically.

So what do you take to be observational evidence that photons are "just energy" and are not matter in motion?