infinitesimal probability

Teralek
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infinitesimal probability

I have read this :

"If there is a finite probability of something happening (ie. a planet forming around a star, or a galaxy forming), then in an infinite universe there will be an infinite number of that thing. So there would be an infinite number of galaxies and planets in an infinite universe. If however there is an infinitesimal probability of something happening, then in an infinite universe there would only be a finite number (for example 1) of those things."

here: http://curious.astro.cornell.edu/question.php?number=476

I find this concept very hard to grasp, is this true?!

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Beyond Saving
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Teralek wrote:I have read

Teralek wrote:

I have read this :

"If there is a finite probability of something happening (ie. a planet forming around a star, or a galaxy forming), then in an infinite universe there will be an infinite number of that thing. So there would be an infinite number of galaxies and planets in an infinite universe. If however there is an infinitesimal probability of something happening, then in an infinite universe there would only be a finite number (for example 1) of those things."

here: http://curious.astro.cornell.edu/question.php?number=476

I find this concept very hard to grasp, is this true?!

I suppose it would be true if the premises are. But assuming that there is a such thing as an infinite universe or a probability that is infinitesimal are rather large assumptions. Things often seem infinite or infinitesimal to us because we are unable to measure the size, but that is a comment on our technological abilities not the actual size. Humans once thought the oceans were infinite, now we know they are not. From our perspective, for our purposes and with the abilities we will have in our lifetimes the universe is infinite to us, but it is a mistake to assume that because it is infinite from our current perspective that the universe is in fact infinite. 

 

Similarly, it is a mistake to assume that because a probability seems infinitesimal to us now that it is in fact infinitesimal.

I just usually go with my own taste. If I like something, and it happens to be against the law, well, then I might have a problem.- Hunter S. Thompson


digitalbeachbum
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Ditto on what Beyond said...

Ditto on what Beyond said... humans think the universe is infinite, but it actually has limits.

I don't see either being any thing more than assumptions, but slightly probable. There are plenty of variables to consider.

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ax
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Mathematics supports these

Mathematics supports these assertions due to the (calculus) concept of indeterminate form. Sometimes this can be safely applied to nature and science (e.g. continuum mechanics), but as the system of variables increases macroscopically, the more impractical the original simple model becomes.

Beyond Saving mentioned a good one that I want to elaborate on a bit more. We know for a fact that the ocean is of finite depth, but if I am studying the rate of decomposition of a solvent in water, I must place finite bounds on the size of the solvent but may place infinite bounds on the depth of the ocean since irregardless of the size of the solvent, it can never be large enough to decompose so slowly that it will reach the bottom. The ratio of the size of the solvent to the depth of the ocean is so large that I can safely make a mathematical assumption to determine the rates and limits without losing accuracy and form a more simplified equation.

So the astrophysicists are correct in their math, but to apply what Beyond Saving and digitalbeachbum said to this context, you must first assume the probability of either two variables in this argument are very high or very small.

It is an impossible question to gauge because we cannot observe space beyond our hubble volume so we cannot make assumptions on anything outside of this space. Many astrophysicists will use this limitation to reduce the scope of their equations, but the macroscopic reality is that the equation will always be inaccurate unless it can account for the entire universe including unobservable space.