Are we too free with infinity?

[Xamonas Chegwé]

Ok Xamonas, but you've replied to only part of what I wrote.
You've ignored the phrases ''If there actually was such a thing'', and ''You can't have an infinite number of numbers, and the numbers can't have a predecessor, because they don't exist.''.

So what the fuck are you arguing about, if you don't mind me asking? You just don't like the phrase "an infinite number"? It's shorthand - it saves typing out "the set of numbers is boundless" every time.

[mistermack]

So what the fuck are you arguing about, if you don't mind me asking?

Sorry, Xamonas, I can't make it any simpler.

You just don't like the phrase "an infinite number"?

No, because it's wrong and it leads to totally nonsensical consequences.
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[colubridae]

So what the fuck are you arguing about, if you don't mind me asking?

Sorry, Xamonas, I can't make it any simpler.

You just don't like the phrase "an infinite number"?

No, because it's wrong and it leads to totally nonsensical consequences.
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I think what he is trying to say is that there are no irrationals.

Since irrationals need an infinite number of digits after the decimal point, they cannot exist.
Hope I got that right mistermack. Let me know if I'm wrong.

[Twiglet]

A good example of why infinity is useful as a mathematical construct in science can be seen in the "Escape Velocity" question over in Jims questions here: http://rationalia.com/forum/viewtopic.p ... 5&start=25

Note Ipetrich's second solution to it.

When solving the integral, the second term of the equation (the bit which is subtracted) vanishes because r is assumed to be infinite. Naturally, no particle which has escaped Earths gravitational field travels an infinite distance from Earth, however, if we looked for a finite, but very large difference, say 10^9km and substituted that term instead of infinity, then the answer would be different to the calculated.

How different - I leave that for you to work out directly mistermack, but I'll give you a hint: The difference is very fucking small.

Also, technically, the question is correct in that escape velocity defines the velocity required for the particle to travel an infinite distance away, rather than an arbitrary one.

[mistermack]

I'll leave the maths to those who like it, Twiglet. But I think to travel to infinity, you would have to escape the pull of the Sun as well, and the Milky Way, and the cluster of Galaxies it is in, ( if we are in one ), and plot a course that avoided other galaxies and stars. You would also be relying on spacetime continuing to expand. It's so much easier on Star Trek!!
Infinity is a useful concept in maths, I've no problem with using it, I'm just suggesting we should always bear in mind that it's a concept, or a shortcut.
Otherwise, we slide into actually believing that there is an infinite this or that.
If you hear it said enough times, you tend not to question it.
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[Xamonas Chegwé]

I'll leave the maths to those who like it, Twiglet. But I think to travel to infinity, you would have to escape the pull of the Sun as well, and the Milky Way, and the cluster of Galaxies it is in, ( if we are in one ), and plot a course that avoided other galaxies and stars. You would also be relying on spacetime continuing to expand. It's so much easier on Star Trek!!

The calculation is a simplified mathematical model. It assumes that there is only the escaping spacecraft and the Earth in the universe - I am pretty sure that it also assumes that both are points, although I am not 100% on that. Infinity enters into things because there is no limit to the influence of the Earth's gravitational field - it literally 'goes on forever', albeit reduced to an unmeasurably small force relatively quickly (in galactic terms.)

Infinity is a useful concept in maths, I've no problem with using it, I'm just suggesting we should always bear in mind that it's a concept, or a shortcut.
Otherwise, we slide into actually believing that there is an infinite this or that.

Believing! No true scientist would ever be found believing anything!

I am still a little puzzled by your antipathy towards infinity however. In order to represent the fraction 1/9, accurately as a decimal, you would need to write an infinite number of 1s - the decimal representation of 1/9 is 0.1111111111... Of course you could never actually write them all - that is the very meaning of infinity, they never stop - but the fact is, if the 1s don't go on forever, then the decimal is NOT equal to 1/9. The dots in that expression mean that the 1s go on forever, that there are an infinite number of them.

There are many more examples of infinity in extremely simple mathematics but what about the 'real world'?

Consider the light from our sun. Photons whizz out in all directions at c. How far do they go if they don't encounter any solid matter in their way? And how long do they travel for? Will they eventually run out of puff and stop? Think about it. The universe is expanding - how much bigger will it get? Do you think there is a limit? To time? To space? Perhaps they are potentially infinite - what do you think?

If you hear it said enough times, you tend not to question it.
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I question pretty much everything. I'm just put together like that. A fucking weirdo!

[mistermack]

Infinity enters into things because there is no limit to the influence of the Earth's gravitational field - it literally 'goes on forever', albeit reduced to an unmeasurably small force relatively quickly (in galactic terms.)

For all practical purposes it 'goes on forever', but not in reality. It propagates at the speed of light, which is finite, so it would need infinite time to 'go on forever'.
You would need spactime to continue to expand for infinite time as well, which is not decided on yet.
So especially if you use the word 'literally', it's not correct.

I am still a little puzzled by your antipathy towards infinity however. In order to represent the fraction 1/9, accurately as a decimal, you would need to write an infinite number of 1s - the decimal representation of 1/9 is 0.1111111111... Of course you could never actually write them all - that is the very meaning of infinity, they never stop - but the fact is, if the 1s don't go on forever, then the decimal is NOT equal to 1/9. The dots in that expression mean that the 1s go on forever, that there are an infinite number of them.

But the truth is that you can't write 1/9 as a decimal. You can represent it as a decimal. We used to say 0.11111111 recurring, which says it fairly well. The 1s recur, but can never get there. You say there ARE an infinite number of them, I would say that you WOULD NEED an infintite number of them, and there is no such thing. That's all I'm pointing to. The difference between ''THERE ARE'' and '' YOU WOULD NEED'' sums it up.

Consider the light from our sun. Photons whizz out in all directions at c. How far do they go if they don't encounter any solid matter in their way? And how long do they travel for? Will they eventually run out of puff and stop? Think about it. The universe is expanding - how much bigger will it get? Do you think there is a limit? To time? To space? Perhaps they are potentially infinite - what do you think?

The light from the Sun and Earths gravity are in similar situations. They both propagate at a finite speed. So they would need infinite time to reach infinity, which is obviously impossible. You can never have infinite time, because time either stops at a finite number, or goes on increasing, neither of which yields 'infinity'.
If there is a limit to the expansion of 'spacetime', perhaps light would reach the limit, and would have no option than to be reflected back, like a wave in a rope, to preserve the laws of thermodynamics. You would then have a slowly accelerating imploding universe.

I question pretty much everything. I'm just put together like that. A fucking weirdo!

Pretty much my problem too. And I really don't care if the question turns out to be dumb. I say, just find out why and keep going.
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