Infinity

[polymath257]

Either motion is an illusion or we perform infinite tasks all the time.  You win for now, Zeno.  But this isn't over.

Cantor resolved that nicely.

The problem is that 'finite time' and 'infinite number of points in time' are not contradictory: they are discussing different things. One is the measure of an interval of time, the other is counting how many instants there are.

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How many other people think that when equations produce the answer 'infinity' that they are not deep and profound but actually are simply nonsense and point to the fact that we have no idea what's going on.

For example, the singularity which has infinite mass and density is a product of our ignorance and simply cannot exist.

Since infinity is a concept rather than a number it's pretty clear that you've done something horribly wrong with your math if that's what you're getting as an answer.

It seems to me that numbers are concepts as well, so that doesn't seem to be a relevant distinction. There are valid places where an infinite answer is both correct and reasonable (I gave one in another post). Often, that just means you need to look at the reciprocal (which in most cases will be zero).

Mathematicians deal with different aspects of infinity all the time. There are actually several different *types* of infinity (as a limit, as a cardinal, as an ordinal, etc.)
and it is quite possible, for example, to have an infinite cardinality and a finite length (or area, or volume). For some of these *types*, there are also different *sizes* of infinity. So, the infinite size of the set of counting numbers {1,2,3,...} is a smaller infinite cardinality than the infinite size of the set of decimals. There are actually infinitely many sizes of infinite cardinalities. Infinite ordinalities are related but different in specifics.

[onlinebiker]

Ya.gotta say that.


Every guy does...

She is really an angel. She is dead.

Got me.

[no one]

This guy:
Infinity, I went there once. Now I am beyond.

Sama:
I represent Ms. Beyonce in the pending copyright infringement suit she's bringing against you.

I don't follow. Does she work for apple?

[Gawdzilla Sama]

Beyond
Beyonce

[Fireball]

GR assumes that you can push to infintely smaller amounts of spacetime, all the way down to zero which produces infinities when you try to calculate density.
However if we live in a quantum universe then spacetime is granular and there is a definite point (Planck Constant) which would mean that it isn't a zero and thus singularities do not achieve infinite density. However the Theory of Everything has not yet been written so we can't square the circle.

Have you some equations to show me?

[LastPoet]

She is really an angel. She is dead.

Got me.

In Portugal we have a saying rougly translated "Mothers in law are like potatos, the best ones are buried.

[Mr Greene]

GR assumes that you can push to infintely smaller amounts of spacetime, all the way down to zero which produces infinities when you try to calculate density.
However if we live in a quantum universe then spacetime is granular and there is a definite point (Planck Constant) which would mean that it isn't a zero and thus singularities do not achieve infinite density. However the Theory of Everything has not yet been written so we can't square the circle.

Have you some equations to show me?

At this point we're in danger of wading into the debate of Quantum Loop Gravity and the various String Theories.
Slightly arcane for a biologist come accountant, but the discussion seems to be progressing, albeit without any experimental data on the horizon.

[Jehanne]

Have you some equations to show me?

At this point we're in danger of wading into the debate of Quantum Loop Gravity and the various String Theories.
Slightly arcane for a biologist come accountant, but the discussion seems to be progressing, albeit without any experimental data on the horizon.

Point is that these scientific models, even if they are inaccurate, are naturalistic explanations for reality. You can, for instance, believe that stars and planets move because there are angels or other invisible beings that are pushing them, but as such a proposition is not testable, falsifiable and leads to no predictions whatsoever, it competes with a limitless set of such hypotheticals. Like religion, such faith-based claims are themselves drawn from an infinitet set.

[onlinebiker]

Got me.

In Portugal we have a saying rougly translated "Mothers in law are like potatos, the best ones are buried.

Brain cells dedicated to this one....

[Mr Greene]

At this point we're in danger of wading into the debate of Quantum Loop Gravity and the various String Theories.
Slightly arcane for a biologist come accountant, but the discussion seems to be progressing, albeit without any experimental data on the horizon.

Point is that these scientific models, even if they are inaccurate, are naturalistic explanations for reality.  You can, for instance, believe that stars and planets move because there are angels or other invisible beings that are pushing them, but as such a proposition is not testable, falsifiable and leads to no predictions whatsoever, it competes with a limitless set of such hypotheticals.  Like religion, such faith-based claims are themselves drawn from an infinitet set.

Of course as Theoretical Physics they are purely mathmatical models with no testable hypothesis, so some question if they are scientific at all.
But as it stands we seem to have choice of granular spacetime, foamy spacetime or infinitely twisted spacetime.