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>> 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.
Well, when people say "number of atoms in the universe", they usually
mean "number of atoms in the *observable* universe" - since, as you
point out, the true size of the *entire* universe can never be known to
mankind.
However, even this (much?) smaller number cannot really be known with
much accuracy. One has to make assumptions about Dark Matter and Dark
Energy and so on and so forth. So it's really a wildly approximate estimate.
Even so, if you do a calculation and it says that the amount of storage
required comes anywhere near to our "estimated" number of particles in
the visible universe... you *know* you aren't going to find a computer
anywhere that can run this algorithm. (!)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Kevin Wampler wrote:
> Mueen Nawaz wrote:
>> Didn't look that up, but the first Skewes number was once believed
>> to be the largest number ever used in a proof (or for anywhere useful?):
>>
>> http://en.wikipedia.org/wiki/Skewes_number
>
> I believe that Graham's number is (significantly!) larger still and
> first appeared as a bound in a proof. Hilariously, the lower bound was 6.
>
> http://en.wikipedia.org/wiki/Graham%27s_number
Wow. Mind-bogglingly wow.
Well, at least I wasn't wrong - Skewes number appeared first.
--
Fax me no questions, I'll Fax you no lies!
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawaz org<<<<<<
anl
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In case it amuses anybody, I have put together the following data from
Wikipedia:
1.000 * 10^0 sec = 1 second.
1.000 * 10^1 sec = 10 seconds.
6.000 * 10^1 sec = 1 minute.
6.000 * 10^2 sec = 10 minutes.
9.000 * 10^2 sec = 15 minutes = 0.25 hours.
1.800 * 10^3 sec = 30 minutes = 0.5 hours.
3.600 * 10^3 sec = 60 minutes = 1 hour.
2.880 * 10^4 sec = 8 hours.
4.320 * 10^4 sec = 12 hours = 0.5 days.
8.640 * 10^4 sec = 1 day.
6.048 * 10^5 sec = 7 days = 1 week.
8.640 * 10^5 sec = 10 days.
1.209 * 10^6 sec = 14 days.
2.592 * 10^6 sec = 30 days = Roughly 1 month.
8.640 * 10^6 sec = 100 days = Roughly 3-4 months.
1.577 * 10^7 sec = 0.5 years = 6 months.
2.366 * 10^7 sec = 9 months.
3.155 * 10^7 sec = 1 year.
3.155 * 10^8 sec = 10 years.
1.577 * 10^9 sec = 50 years.
3.155 * 10^9 sec = 100 years = 1 century.
4.102 * 10^9 sec = 130 years = Electric light, recorded round,
telephone, etc.
5.206 * 10^9 sec = 165 years = Orbit of Neptune.
5.806 * 10^9 sec = 184 years = Beethoven's 9th symphony.
6.910 * 10^9 sec = 219 years = French revolution.
7.321 * 10^9 sec = 232 years = USA formed.
1.243 * 10^10 sec = 394 years = Shakespear's last play.
1.625 * 10^10 sec = 515 years = Columbus finds America.
1.751 * 10^10 sec = 555 years = Oldest SURVIVING printing press.
2.161 * 10^10 sec = 685 years = The Devine Commedy.
3.155 * 10^10 sec = 1,000 years = 1 millenium.
4.831 * 10^10 sec = 1,531 years = Fall of Roman Empire.
4.891 * 10^10 sec = 1,550 years = First Anglo-Saxon invasion.
6.081 * 10^10 sec = 1,927 years = Pompeii razed by volcanoe.
6.336 * 10^10 sec = 2,008 years = Birth of Jesus Christ.
7.352 * 10^10 sec = 2,330 years = Death of Alexander the Great.
7.592 * 10^10 sec = 2,406 years = Death of Socrates.
7.889 * 10^10 sec = 2,500 years = Euclid's Elements.
8.779 * 10^10 sec = 2,782 years = Rome founded.
1.199 * 10^11 sec = 3,800 years = Alphabetic writing.
1.420 * 10^11 sec = 4,500 years = Domestic horse.
1.441 * 10^11 sec = 4,567 years = Great Pyramid, Giza.
1.704 * 10^11 sec = 5,400 years = Start Bronze Age.
1.803 * 10^11 sec = 5,715 years = Halflife carbon-14.
2.051 * 10^11 sec = 6,500 years = The wheel.
3.155 * 10^11 sec = 10,000 years = End last glacial age.
3.471 * 10^11 sec = 11,000 years = Jericho founded.
3.786 * 10^11 sec = 12,000 years = Start Neolithic.
6.626 * 10^11 sec = 21,000 years = End last Glacial Maximum.
9.151 * 10^11 sec = 29,000 years = Neanderthals died out.
3.155 * 10^12 sec = 100,000 years = Domestic dogs.
4.733 * 10^12 sec = 150,000 years = Mitochondrial Eve.
7.889 * 10^12 sec = 250,000 years = Homo sapiens.
2.492 * 10^13 sec = 790,000 years = Homo erectus first uses fire.
7.889 * 10^13 sec = 2.5 million years = Homo habilis.
1.262 * 10^14 sec = 4 million years = End last Ice Age.
1.072 * 10^15 sec = 34 million years = First cats.
2.051 * 10^15 sec = 65 million years = Start of Tertiary. End of dinosaurs.
6.153 * 10^15 sec = 195 million years = Start of Jurassic. First mammals.
7.889 * 10^15 sec = 250 million years = Galactic year. (1 revolution
around Milky Way.)
7.933 * 10^15 sec = 251.4 million years = Start of Triassic. Permian
extinction. Age of the dinosaurs.
1.072 * 10^16 sec = 340 million years = Start of Carboniferous.
1.672 * 10^16 sec = 530 million years = Cambrian explosion. First
vertabrates.
1.704 * 10^16 sec = 540 million years = Start of Cambrian.
2.220 * 10^16 sec = 703.8 million years = Halflife uranium-235.
4.029 * 10^16 sec = 1,227 million years = Halflife potassium-40.
1.293 * 10^17 sec = 4.1 billion years = Oldest life on Earth.
1.409 * 10^17 sec = 4.486 billion years = Halflife uranium-238.
1.420 * 10^17 sec = 4.5 billion years = Age of the Earth.
4 * 10^17 sec = 13 billion years = Age of the Universe.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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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.
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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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