On 28-Jul-08 20:16, Warp wrote:
> Orchid XP v8 <voi### [at] devnull> wrote:
>> Well, the number of grains of sand on the entire English coastline is 
>> "obviously" a pretty damned big number. And the number of subatomic 
>> particles in the universe is equally obviously *very* much larger.
> 
>   The funny thing about the amount of particles in the universe is that,
> if current theories are right, there's no way of knowing how big the
> universe is and how much material there is. There's a thing called
> cosmological horizon which makes it completely impossible for us to
> observe the entire universe, no matter what the means.
> 
>   That's where the term "observable universe" comes from: It's everything
> inside the cosmological horizon, which is at least in theory possible to
> be observed.
> 
>   The real size of the universe is completely impossible to know. It
> could be just slightly larger than the observable universe, or it could
> be staggeringly larger. There's just no way of knowing.
> 
I have apparently missed a lot since my physics study. I was under the 
impression that the size of the universe is of the order of a sphere 
with a radius of the age of the universe times the speed of light. Could 
you give a pointer to those current theories that you mentioned?

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Kevin Wampler <wampler+pov### [at] uwashingtonedu> wrote:
> Mueen Nawaz wrote:
> >     Well, at least I wasn't wrong - Skewes number appeared first.

> I sort of like Skewes number as well, as it provides a useful 
> counterexample to provide to someone who thinks that checking the first 
> several billion examples of a conjecture makes it virtually certain to 
> be true.

  Hmm, I wonder if you aren't confusing it with the Polya conjecture...
(which is famous for having a rather big counter-example).

-- 
                                                          - Warp

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andrel <a_l### [at] hotmailcom> wrote:
> I have apparently missed a lot since my physics study. I was under the 
> impression that the size of the universe is of the order of a sphere 
> with a radius of the age of the universe times the speed of light. Could 
> you give a pointer to those current theories that you mentioned?

  Glad you asked.

  It is, in fact, a rather common misconception that the theory of
relativity limits the speed at which the universe can expand (even
some scientists and cosmology papers hold this misconception).

  However, the theory of relativity does not limit the speed at which
the universe can expand. The distance between two points in the universe
can grow faster than c without it breaking relativity. The reason why
people get confused is that they tend to think that if the distance
between two points increases at a rate which is larger than c, that means
that the points are *moving* away from each other faster than c, thus
breaking relativity. However, the points are not moving. The space
geometry between them is changing (in very simplistic terms, new space
appears between them). This is summarized, for example, here:

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

"The metric expansion leads naturally to recession speeds which exceed
the "speed of light" c and to distances which exceed c times the age
of the universe, which is a frequent source of confusion among
amateurs and even professional physicists.[1] The speed c has no
special significance at cosmological scales."

  No information of any type whatsoever can be transferred by any means
between two points which are recessing faster than c. This is exactly
what causes the so-called cosmological horizon (stub article at
http://en.wikipedia.org/wiki/Cosmological_horizon )

  In fact, assuming that the borders of the universe had always grown
at a constant rate of c is against observation. Moreover, it has been
conjectured that the universe suffered an exponential inflation period
at its first moments, which would explain many observed phenomena. This
is an interesting article about the subject:

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

-- 
                                                          - Warp

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"Orchid XP v8" <voi### [at] devnull> wrote in message
news:488e046e$1@news.povray.org...
> somebody wrote:
>
> > Do you really find it easy to visualize the number of subatomic
particles in
> > the visible universe? I don't see why thinking about that would be more
> > informative than, say, 1E80.
>
> Well, the number of grains of sand on the entire English coastline is
> "obviously" a pretty damned big number. And the number of subatomic
> particles in the universe is equally obviously *very* much larger.
>
> Call it a failure of the simplistic human mind, but seeing a handful of
> symbols on a page isn't very impressive. Likening it to something that
> at least "feels real" makes it slightly easier to grasp.
>
> For example, off the top of your head, how long is "10^14 seconds"?

It's 10^14 seconds.

> I mean, is that like, months? Millenia? What?

1 year is close to PI*10^7 seconds (something easy to remember), so it's
close to PI*10^7 years.

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Another interesting (and nerdier) example:

  Assume we have a 3GHz processor, and that it can increment a 32-bit
register at each clock cycle. How long does it take to go through all
the values of that register?

  Now assume that it's a 64-bit register instead. How long does it
take now?

-- 
                                                          - Warp

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Warp wrote:
>   Hmm, I wonder if you aren't confusing it with the Polya conjecture...
> (which is famous for having a rather big counter-example).


Nope, although the Polya conjecture is also an excellent example for 
such situations.  I somewhat prefer Skewe's number for such things as I 
can somehow remember the exact form of theorem from which it arises more 
easily.

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On 28-Jul-08 23:27, Warp wrote:
> andrel <a_l### [at] hotmailcom> wrote:
>> I have apparently missed a lot since my physics study. I was under the 
>> impression that the size of the universe is of the order of a sphere 
>> with a radius of the age of the universe times the speed of light. Could 
>> you give a pointer to those current theories that you mentioned?
> 
>   Glad you asked.
> 
>   It is, in fact, a rather common misconception that the theory of
> relativity limits the speed at which the universe can expand 
is it?
> (even
> some scientists and cosmology papers hold this misconception).

yup, this physicist for instance.

>   However, the theory of relativity does not limit the speed at which
> the universe can expand. The distance between two points in the universe
> can grow faster than c without it breaking relativity. 

yup, but that has no additional implication for the speed at which the 
universe can expand.

> The reason why
> people get confused is that they tend to think that if the distance
> between two points increases at a rate which is larger than c, that means
> that the points are *moving* away from each other faster than c, thus
> breaking relativity. However, the points are not moving. The space
> geometry between them is changing (in very simplistic terms, new space
> appears between them). This is summarized, for example, here:
> 
> http://en.wikipedia.org/wiki/Metric_expansion_of_space

yes, but as I said above that has no implication for the size of the 
universe.

> 
> "The metric expansion leads naturally to recession speeds which exceed
> the "speed of light" c and to distances which exceed c times the age
> of the universe, which is a frequent source of confusion among
> amateurs and even professional physicists.[1] The speed c has no
> special significance at cosmological scales."
> 
>   No information of any type whatsoever can be transferred by any means
> between two points which are recessing faster than c. This is exactly
> what causes the so-called cosmological horizon (stub article at
> http://en.wikipedia.org/wiki/Cosmological_horizon )
> 
>   In fact, assuming that the borders of the universe had always grown
> at a constant rate of c is against observation. Moreover, it has been
> conjectured that the universe suffered an exponential inflation period
> at its first moments, which would explain many observed phenomena. This
> is an interesting article about the subject:
> 
> http://en.wikipedia.org/wiki/Cosmic_inflation

And what exactly does this all prove? I haven't seen anything in those 
links that I did not know (but I admit I did not read everything) and 
nothing that even remotely supports your 'The real size of the universe 
is completely impossible to know. It could be just slightly larger than 
the observable universe, or it could be staggeringly larger. There's 
just no way of knowing.' but I might have missed it.
Unless you are in a roundabout way referring to the problem that you can 
not define the 'now' for which you are computing the size.

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On 28-Jul-08 23:33, somebody wrote:
> "Orchid XP v8" <voi### [at] devnull> wrote in message
> news:488e046e$1@news.povray.org...
>> somebody wrote:
>>
>>> Do you really find it easy to visualize the number of subatomic
> particles in
>>> the visible universe? I don't see why thinking about that would be more
>>> informative than, say, 1E80.
>> Well, the number of grains of sand on the entire English coastline is
>> "obviously" a pretty damned big number. And the number of subatomic
>> particles in the universe is equally obviously *very* much larger.
>>
>> Call it a failure of the simplistic human mind, but seeing a handful of
>> symbols on a page isn't very impressive. Likening it to something that
>> at least "feels real" makes it slightly easier to grasp.
>>
>> For example, off the top of your head, how long is "10^14 seconds"?
> 
> It's 10^14 seconds.
> 
>> I mean, is that like, months? Millenia? What?
> 
> 1 year is close to PI*10^7 seconds (something easy to remember), so it's
> close to PI*10^7 years.

<nitpick> that'll be 1/PI*10^7 or (as PI^2 is almost 10) PI*10^6 </nitpick>

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"Kevin Wampler" <wampler+pov### [at] uwashingtonedu> wrote in message 
news:488e4494$1@news.povray.org...
> Warp wrote:
>>   Hmm, I wonder if you aren't confusing it with the Polya conjecture...
>> (which is famous for having a rather big counter-example).
>
>
> Nope,

   Heh, I knew you were going to say "Nope" before I looked at your reply. 
:)

      Time for bed said Zebedee...

       ~Steve~

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St. wrote:
>    Heh, I knew you were going to say "Nope" before I looked at your reply. 
> :)

Clearly I have become far too tomato.

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