andrel <a_l### [at] hotmailcom> wrote:
> 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.

  Uh? I said that the current widely agreed consensus is that the universe
not only can expand faster than c (which you don't seem to disagree with),
but most probably has done so (because that would explain many observed
phenomena). I gave links to wikipedia pages where you could find references
to more material.

  Of course there's no absolute *proof* of this. By the very definition
of cosmological horizon it's *impossible* to have an absolute proof of
this (ie. that the universe is larger than the observable universe).
However, currently science most agrees that this is very likely.

  Your way of writing seems to imply something like "you have not given
me any proof about this, and thus I don't believe you". In other words,
you still state that the size of the universe is at most the size of
a sphere with a radius of the age of the universe itmes the speed of
light (although you don't seem to deny that the universe *can* expand
faster than c).

  Well, where's your proof? Or any serious references, for that matter.
At least I gave you *something*.

-- 
                                                          - Warp

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Invisible <voi### [at] devnull> wrote:

> Does anybody know of a list anywhere that gives examples of really large
> numbers? I'm thinking of things like the number of grains of sand in a
> cubic meter, the brain cells in a human brain, or the number of
> subatomic particles in the visible universe. I for one have no idea even
> approximately "how big" these numbers are.


I'd recommend Project Euler ( projecteuler.net ).  It's a couple hundred math
problems for the not-particularly-mathematically-inclined whose answers are all
moderately large integers, e.g. the sum of the digits in 100!.  (That's
factorial, not emphasis.)  You create an account and can't see the answer...
until you have the answer.  Most require programming, but a good share require
nothing more than brute force.  Realizing how quickly problems become
intractable with brute force though will give you a real appreciation for how
quickly numbers grow.  Fun too.

 - Ricky

P.S.  Keep your distance from #160.  I lost at least a couple evenings to that
one.  Never figured it out.

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Invisible wrote:
> the brain cells in a human brain,
> 

Human brain was thought to be about 10^11 neurons.

Hit google books search and look for "On Number Numbness" by Hofstadter, 
right up your alley I think.

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> For example, off the top of your head, how long is "10^14 seconds"? I
> mean, is that like, months? Millenia? What?

GIYF

http://www.google.com/search?q=1e14s+in+millenia

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Warp wrote:
>   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?

Ooo... 2^32 = 4 billion. 3 GHz = 3,000,000,000 incriments per second. So 
we have... a little over 1 second.

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

2^64 = (2^32)^2, so if 2^32 takes 1 second, 2^64 should take 4 billion 
seconds (which is about 136 years). So... a ****ing long time then.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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And lo on Mon, 28 Jul 2008 17:44:55 +0100, Warp <war### [at] tagpovrayorg> did  
spake, saying:

>   Another funny example, which you can use on someone: Assume you have
> a really, really large piece of cardboard which is 1 mm thick. Also  
> assume
> that you can fold it in half as many times as you want (thus doubling its
> thickness each time you fold it). How many times do you have to fold it
> before the thickness reaches the Moon?

31 times to roughly match the length of the UK. 40 times will easily reach  
the Moon and about 58 times to get very close to the Sun. Yeah I was bored.

-- 
Phil Cook

--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com

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And lo on Mon, 28 Jul 2008 23:20:44 +0100, andrel  
<a_l### [at] hotmailcom> did spake, saying:

> On 28-Jul-08 23:27, Warp wrote:
>> andrel <a_l### [at] hotmailcom> wrote:
>
> 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.

Imagine standing in a circle of light and all around you is darkness. If  
the light increases in diameter and the floor increases in size (i.e. not  
revealing new areas of floor) and the increase is such that you cannot  
reach the circumference by any means; does the floor you're standing on  
extend beyond the light?

-- 
Phil Cook

--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com

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On Mon, 28 Jul 2008 20:20:59 EDT, "triple_r" <nomail@nomail> wrote:

>moderately large integers, e.g. the sum of the digits in 100!.

Reminds me of how I was quite surprised at the number of unique sorts that can be
obtained from a deck of cards, 52!, or 8.0658175170943878571660636856404e+67.

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On 29-Jul-08 1:26, Warp wrote:
> andrel <a_l### [at] hotmailcom> wrote:
>> 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.
> 
>   Uh? I said that the current widely agreed consensus is that the universe
> not only can expand faster than c (which you don't seem to disagree with),

Oh, but I do. Two points may move from one another faster than c, making 
it impossible for one point ever to see the other one. That does not 
imply, however, that the universe itself expands faster that c. I think 
that is also the point that 
http://en.wikipedia.org/wiki/Metric_expansion_of_space is trying to make.

> but most probably has done so (because that would explain many observed
> phenomena). I gave links to wikipedia pages where you could find references
> to more material.

No you gave a website that discusses the 'observable universe' which is 
a totally different beast than the size of the universe at some moment 
in time.

>   Of course there's no absolute *proof* of this. By the very definition
> of cosmological horizon it's *impossible* to have an absolute proof of
> this (ie. that the universe is larger than the observable universe).
> However, currently science most agrees that this is very likely.

What is in the page you referred to seems to me to be a standard 
relativistic approach of the concept of what the observable universe is. 
'Currently' would then seem to mean 50+ years or so.

>   Your way of writing seems to imply something like "you have not given
> me any proof about this, and thus I don't believe you". In other words,
> you still state that the size of the universe is at most the size of
> a sphere with a radius of the age of the universe itmes the speed of
> light (although you don't seem to deny that the universe *can* expand
> faster than c).

I think that the size of the universe (at least from some time, say, a 
million years, after the big bang) is expanding with at most c. I have 
not followed cosmology really closely over the last 20 years or so, so I 
am not really familiar with any recent theories on the early years of 
the universe. Yet, the couple of hundred thousand years that span that 
era are dwarfed by the nearly 14 billion years when normal physics 
applies. What I do know is that I studied special and general relativity 
and some cosmology when I was at the university and that your claim that 
the real size of the universe may be 'staggering larger' than the 
observable universe does not seem to fit what I remember. Although I 
moved to applied physics for my masters, I have still some links with 
the physics and astrophysics community and I tend to think that I would 
have noticed a theory that would imply that.

Please also note that even if someone comes up with a new cosmological 
theory that does not mean that from now on that is the accepted theory. 
Not even when it is reported on discovery channel. Science journalists 
have a habit of suggesting that (and not only for cosmology), but 
science does not work that way.

>   Well, where's your proof? Or any serious references, for that matter.
> At least I gave you *something*.

Yes, a page that was about something else and if anything was 
contradicting your claim. ;)

BTW the concept of the universe having a size at one point in time is 
rather useless, indeed because of relativistic reasons. Observable 
universe is a more useful concept, I grant you that one.

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andrel wrote:
> No you gave a website that discusses the 'observable universe' which is 
> a totally different beast than the size of the universe at some moment 
> in time.

Two fallacies: (1) "observable universe" technically is the same as 
"universe".  (2) "moment in time" is a meaningless term, even for things 
fairly close together, let alone separated in a spacelike way.

In other words, define "universe" first. This gets you into Clinton 
areas, of trying to define what "is" is.

-- 
Darren New / San Diego, CA, USA (PST)
  Helpful housekeeping hints:
   Check your feather pillows for holes
    before putting them in the washing machine.

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