Suppose that every atom in the known universe had a unique serial 
number. Suppose I picked a serial number at random, and then asked you 
to go find out where that particular atom is. (Let us assume that there 
is no particular correspondence between serial numbers and position in 
space.)

Well your first problem is going to be that if I pick a random serial 
number, that atom is probably many billions of light years away from 
Earth, and so even if you knew where to go, you couldn't possibly go 
there. But suppose you somehow have access to an electronic database of 
all the atoms, their serial numbers, positions, and other interesting data.

(We casually ignore for the moment the minor detail that a database 
describing the known universe would obviously be very much larger than 
the actual universe itself, and hence could not possibly exist inside it...)

Given such a database, there are two ways you could try to find this atom.

One is to simply go through the database table, one row at a time. This 
is equivilent to examining every atom in the universe, one by one, until 
you find the one you want.

Assuming that you could somehow examine several million million million 
records per second (highly implausible), to find the atom you're looking 
for would take... several tens of billions of times the current age of 
the universe. As in, after all the energy in the universe had been spent 
and the entire cosmos had died an icy death of silent stillness at zero 
entropy, your hypothetical computer would still have not made 1% 
progress yet.

Just stop and think about that for a moment. There literally isn't 
enough time in the universe to perform this search. Woah.

(But hey, you're searching all the atoms in existence! It's hardly 
surprising...)

Alternatively, you could perform an index lookup. Assuming you have an 
index on the main table that consists of a tree with 10 entries in each 
node, you could find the atom in question after examining... 100 nodes. 
(If we assume the tree is well-balanced.) Even if we type in the index 
node requests by hand, it will take well less than 10 minutes to find 
out atom.

So, one way has O(n) complexity, and would take so long that there 
simply isn't enough time or energy in the universe to complete the 
computation. The other way is O(log n), and would take less than 10 
minutes even if done partially by hand.

Wow. Just... wow.

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Invisible <voi### [at] devnull> wrote:
> Alternatively, you could perform an index lookup.

  It's enough for the values to be sorted. Then you can simply perform
a binary search. Assuming fast random access the search should take
much less than a second.

-- 
                                                          - Warp

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Invisible <voi### [at] devnull> wrote:
> (We casually ignore for the moment the minor detail that a database
> describing the known universe would obviously be very much larger than
> the actual universe itself, and hence could not possibly exist inside it...)

Asimov solved this long ago!
http://www.multivax.com/last_question.html

:)

> Assuming that you could somehow examine several million million million
> records per second (highly implausible), to find the atom you're looking
> for would take... several tens of billions of times the current age of
> the universe.

BTW, what if when you finally reach the area the atom was at originally it
already moved on to an area you had already inspected?  concurrency problems?
:)

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Warp <war### [at] tagpovrayorg> wrote:
> Invisible <voi### [at] devnull> wrote:
> > Alternatively, you could perform an index lookup.
>
>   It's enough for the values to be sorted. Then you can simply perform
> a binary search. Assuming fast random access the search should take
> much less than a second.
>
> --
>                                                           - Warp

Today, the number of atoms of the observable universe is estimated at about
10^80. (See http://en.wikipedia.org/wiki/Observable_universe).

Whish it were my bank account! But presently only the absolute value is correct
....

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Warp <war### [at] tagpovrayorg> wrote:
> Invisible <voi### [at] devnull> wrote:
> > Alternatively, you could perform an index lookup.
>
>   It's enough for the values to be sorted. Then you can simply perform
> a binary search. Assuming fast random access the search should take
> much less than a second.
>
> --
>                                                           - Warp

Today, the number of atoms of the observable universe is estimated at about
10^80. (See http://en.wikipedia.org/wiki/Observable_universe).

Whish it were my bank account! But presently only the absolute value is correct
....

Post a reply to this message

Invisible wrote:
> Suppose that every atom in the known universe had a unique serial 
> number. Suppose I picked a serial number at random, and then asked you 
> to go find out where that particular atom is. (Let us assume that there 
> is no particular correspondence between serial numbers and position in 
> space.)

I don't want to spoil your gedanken experiment, but in modern physics 
you can not distinguish one (e.g.) hydrogen atom from another. It is not 
that they are two different objects that are not marked so you can not 
distinguish them, but much more fundamental. If you exchange two protons 
nothing happens. There is no way to figure that out, because there is 
absolutely no difference. You probably better say that this one proton 
is at all these places at the same time.

Perhaps you know the interpretation that a positron is just an electron 
flying backwards in time. It has been suggested that if the universe 
ends in a big crunch (probably not) then you only need one electron 
weaving forwards and backward in time. i.e. if an electron and a 
positron annihilate, what actually happens is that the electron changes 
direction again. So probably not true, but a funny image anyway.

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andrel wrote:
> I don't want to spoil your gedanken experiment, but in modern physics 
> you can not distinguish one (e.g.) hydrogen atom from another.

You say this, but it's not actually true.  You cannot distinguish two 
hydrogen atoms as long as you ignore the stuff that lets you distinguish 
them.  Like, say, their positions.

Certainly the hydrogen atoms in my coffee are distinguishable from the 
hydrogen atoms emitting light eight minutes ago in the sun.

Basically, science has a list of "things it's safe to ignore when 
replicating an experiment."  Given that list, hydrogen atoms are 
indistinguishable. But there's still a list.

It's like saying "pennies are indistinguishable, from a spending point 
of view. I can replace one penny with any other penny."  Yet I'll still 
get arrested for putting all your pennies in my bank account.

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

Post a reply to this message

Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> Alternatively, you could perform an index lookup.
> 
>   It's enough for the values to be sorted. Then you can simply perform
> a binary search. Assuming fast random access the search should take
> much less than a second.

Indeed. A binary index lookup and a binary search are equally efficient.

However, inserting a record for a new atom becomes somewhat 
compute-intensive if we have to keep all the data in sorted order. (If 
it's a typical array-like structure, O(n) complexity again. For an 
index, it's just O(log n) - assuming any rebalancing you choose to do 
doesn't blow it up.)

Of course, whether you have an unordered table and seperate index or 
whether the index *is* the table doesn't matter too much. (Depending on 
just how much data you store per atom...)

Post a reply to this message

Actually, the real problem would be that electronic representation of the 
atomic data would require atoms for storage purposes....So you'd have to 
have the database operating outside the space/time continuum to begin 
with. :-)

Jim

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andrel wrote:
> Invisible wrote:
>> Suppose that every atom in the known universe had a unique serial 
>> number. Suppose I picked a serial number at random, and then asked you 
>> to go find out where that particular atom is. (Let us assume that 
>> there is no particular correspondence between serial numbers and 
>> position in space.)
> 
> I don't want to spoil your gedanken experiment, but in modern physics 
> you can not distinguish one (e.g.) hydrogen atom from another.

Sure. You're probably right. And anyway, how the heck would you write 
serial numbers on them, even if you could? More to the point, how would 
you catelogue them all in a giant database? And what if they move 
around? What if an atom is created or destroyed? etc.

My point is really just the staggering difference between complexity 
classes, rather than physical correctness. The same argument would apply 
to *anything* that there's 10^100 of - atoms in the universe is about 
the only [remotely] comprehensible way to describe just what a big 
number that is. ;-)

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> BTW, what if when you finally reach the area the atom was at originally it
> already moved on to an area you had already inspected?  concurrency problems?
> :)

Oh yeah.

I think your "database" would have to be at a specific point in time - 
which leads us nicely to the fact that time is not universal...

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Jim Henderson wrote:
> Actually, the real problem would be that electronic representation of the 
> atomic data would require atoms for storage purposes....So you'd have to 
> have the database operating outside the space/time continuum to begin 
> with. :-)

Yes, I believe I meantioned that one. ;-)

Other obvious problems include the clear impossibility of obtaining this 
data in the first place (uncertainty, anyone?), the subjective nature of 
both time and space, and the sheer craziness of the idea in the first 
place...

Post a reply to this message

Darren New wrote:
> andrel wrote:
>> I don't want to spoil your gedanken experiment, but in modern physics 
>> you can not distinguish one (e.g.) hydrogen atom from another.
> 
> You say this, but it's not actually true.  You cannot distinguish two 
> hydrogen atoms as long as you ignore the stuff that lets you distinguish 
> them.  Like, say, their positions.

no.

> Certainly the hydrogen atoms in my coffee are distinguishable from the 
> hydrogen atoms emitting light eight minutes ago in the sun.

nope

> Basically, science has a list of "things it's safe to ignore when 
> replicating an experiment."  Given that list, hydrogen atoms are 
> indistinguishable. But there's still a list.
Sorry, no. It may sound counterintuitive but there isn't. A proton does 
not have a position, but a peaked distribution in one place with a small 
but finite change that it is somewhere else entirely. If you have two 
protons, you have a distribution with two peaks with an amplitude large 
enough for two protons. Nothing more and individuality is a meaningless 
concept here. I am trying to find a macroscopic equivalent, but I can't, 
yet.
> 
> It's like saying "pennies are indistinguishable, from a spending point 
> of view. I can replace one penny with any other penny."  

There is a difference between the (sub)atomic and the macroscopic range. 
In the latter common sense is just that, in the former not.

> Yet I'll still 
> get arrested for putting all your pennies in my bank account.
> 
No as long as we assume that you exchanged all your pennies with mine 
simultaneously, I don't see why anyone would bother. ;)
Don't try this at home though, the number of pennies in this house will 
probably not exceed 2, mainly because we use a different currency.

Post a reply to this message

On Mon, 12 Nov 2007 19:05:34 +0000, Orchid XP v7 wrote:

> Jim Henderson wrote:
>> Actually, the real problem would be that electronic representation of
>> the atomic data would require atoms for storage purposes....So you'd
>> have to have the database operating outside the space/time continuum to
>> begin with. :-)
> 
> Yes, I believe I meantioned that one. ;-)

Ah, yes, so you did. ;-)

> Other obvious problems include the clear impossibility of obtaining this
> data in the first place (uncertainty, anyone?), the subjective nature of
> both time and space, and the sheer craziness of the idea in the first
> place...

Heisenberg would be proud. :-)

Jim

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Orchid XP v7 nous apporta ses lumieres en ce 2007/11/12 13:23:
> Warp wrote:
>> Invisible <voi### [at] devnull> wrote:
>>> Alternatively, you could perform an index lookup.
>>
>>   It's enough for the values to be sorted. Then you can simply perform
>> a binary search. Assuming fast random access the search should take
>> much less than a second.
> 
> Indeed. A binary index lookup and a binary search are equally efficient.
> 
> However, inserting a record for a new atom becomes somewhat 
> compute-intensive if we have to keep all the data in sorted order. (If 
> it's a typical array-like structure, O(n) complexity again. For an 
> index, it's just O(log n) - assuming any rebalancing you choose to do 
> doesn't blow it up.)
> 
> Of course, whether you have an unordered table and seperate index or 
> whether the index *is* the table doesn't matter too much. (Depending on 
> just how much data you store per atom...)
If you have a sorted list of serial numbers, the next item will have it's number 
set as n+1, or 1 after the current last element.
In the case of a balanced tree structure, concidering a tree with about 10^80 
elements, randomly adding a few billions elements is prety much insignifient.

-- 
Alain
-------------------------------------------------
At the feast of ego everyone leaves hungry.
	Bentley's House of Coffee and Tea, Tucson, AZ

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nemesis nous apporta ses lumieres en ce 2007/11/12 12:33:
> Invisible <voi### [at] devnull> wrote:
>> (We casually ignore for the moment the minor detail that a database
>> describing the known universe would obviously be very much larger than
>> the actual universe itself, and hence could not possibly exist inside it...)
> 
> Asimov solved this long ago!
> http://www.multivax.com/last_question.html
> 
> :)
> 
>> Assuming that you could somehow examine several million million million
>> records per second (highly implausible), to find the atom you're looking
>> for would take... several tens of billions of times the current age of
>> the universe.
> 
> BTW, what if when you finally reach the area the atom was at originally it
> already moved on to an area you had already inspected?  concurrency problems?
> :)
> 
> 
The data will, of course, include the precise speed and direction of every 
atoms, along with it's mass, magnetic momentum and spin, and how it can interact 
with other atoms and any photons. With that information, you can predict where 
it will be at any time of your choosing within a Km radius.

-- 
Alain
-------------------------------------------------
Lutheran: If shit happens, don't talk about it.

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Darren New wrote:
> You say this, but it's not actually true.  You cannot distinguish two 
> hydrogen atoms as long as you ignore the stuff that lets you distinguish 
> them.  Like, say, their positions.

	Have to agree with andrel here.

> Certainly the hydrogen atoms in my coffee are distinguishable from the 
> hydrogen atoms emitting light eight minutes ago in the sun.

	Nope. Just that the wavefunction will be such that most likely that if 
we ignore that there is another H atom near the sun, the physics near 
your coffee will barely change.


-- 
Give a man a fish and you feed him for one day. Teach him to use the Net 
and he won't bother you for weeks.


                     /\  /\               /\  /
                    /  \/  \ u e e n     /  \/  a w a z
                        >>>>>>mue### [at] nawazorg<<<<<<
                                    anl

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Alain wrote:
> The data will, of course, include the precise speed and direction of 
> every atoms, along with it's mass, magnetic momentum and spin, and how 
> it can interact with other atoms and any photons. With that information, 
> you can predict where it will be at any time of your choosing within a 
> Km radius.

You're joking, right? :-)

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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Mueen Nawaz wrote:
> Darren New wrote:
>> You say this, but it's not actually true.  You cannot distinguish two 
>> hydrogen atoms as long as you ignore the stuff that lets you 
>> distinguish them.  Like, say, their positions.
> 
>     Have to agree with andrel here.

Hmmmmm.... OK.  I can see that.  How does space-like separation affect 
that, tho?

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

Post a reply to this message

Orchid XP v7 <voi### [at] devnull> wrote:
> Jim Henderson wrote:
> > Actually, the real problem would be that electronic representation of the
> > atomic data would require atoms for storage purposes....So you'd have to
> > have the database operating outside the space/time continuum to begin
> > with. :-)
>
> Yes, I believe I meantioned that one. ;-)
>
> Other obvious problems include the clear impossibility of obtaining this
> data in the first place (uncertainty, anyone?), the subjective nature of
> both time and space, and the sheer craziness of the idea in the first
> place...

I don’t think the idea is crazy but the people that are answering you are. :)

Stephen

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Darren New wrote:
> Mueen Nawaz wrote:
>> Darren New wrote:
>>> You say this, but it's not actually true.  You cannot distinguish two 
>>> hydrogen atoms as long as you ignore the stuff that lets you 
>>> distinguish them.  Like, say, their positions.
>>
>>     Have to agree with andrel here.
> 
> Hmmmmm.... OK.  I can see that.  How does space-like separation affect 
> that, tho?
> 
space- like is from relativistic physics, the point we are discussing is 
  quantum mechanics. As you know the two are incompatible. So, being a 
formally trained physicist with a 20 year old education, I don't know. ;)

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Alain wrote:
> The data will, of course, include the precise speed and direction of
> every atoms, along with it's mass, magnetic momentum and spin, and how
> it can interact with other atoms and any photons. With that information,
> you can predict where it will be at any time of your choosing within a
> Km radius.
> 

Which leads to the question: Is our universe the real one, or the one
modeled by this giant database existing outside of our perceived space-time?

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Darren New wrote:
> Alain wrote:
>> The data will, of course, include the precise speed and direction of
>> every atoms, along with it's mass, magnetic momentum and spin, and how
>> it can interact with other atoms and any photons. With that
>> information, you can predict where it will be at any time of your
>> choosing within a Km radius.
> 
> You're joking, right? :-)
> 
Why joke? We are already considering a giant computer outside of
space-time. Why not assume it has enough processing power to model all
of the physical forces that the universe requires?

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Darren New nous apporta ses lumieres en ce 2007/11/12 23:52:
> Alain wrote:
>> The data will, of course, include the precise speed and direction of 
>> every atoms, along with it's mass, magnetic momentum and spin, and how 
>> it can interact with other atoms and any photons. With that 
>> information, you can predict where it will be at any time of your 
>> choosing within a Km radius.
> 
> You're joking, right? :-)
> 
Not at all! If you could realy have all of that information for every atoms in 
the univers, you could conceivably be able to predict when a star will apears, 
how long it will live, how it will finish, if it will have planets and how many, 
the exact description of every single one, if it will host any life, and if 
inteligent life will apears. All that for a future star for whitch most of it's 
constituant matter is still contained in several other stars. Star that will 
only start to form in a billion years.

The joke is that: You can't have all of that information, and even if you could 
have it, there is no way that you could possibly process it.

-- 
Alain
-------------------------------------------------
'I had to hit him -- he was starting to make sense.'

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Sabrina Kilian nous apporta ses lumieres en ce 2007/11/13 18:03:
> Alain wrote:
>> The data will, of course, include the precise speed and direction of
>> every atoms, along with it's mass, magnetic momentum and spin, and how
>> it can interact with other atoms and any photons. With that information,
>> you can predict where it will be at any time of your choosing within a
>> Km radius.
>>
> 
> Which leads to the question: Is our universe the real one, or the one
> modeled by this giant database existing outside of our perceived space-time?
Very good question.

-- 
Alain
-------------------------------------------------
"If you see me running, try to keep up."
       ...Back of bomb technician's shirt

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Sabrina Kilian wrote:
> Which leads to the question: Is our universe the real one, or the one
> modeled by this giant database existing outside of our perceived space-time?

Permutation City, by Greg Egan.

Buy it, read it, love it. :-)

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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andrel wrote:
> Darren New wrote:
>> Mueen Nawaz wrote:
>>> Darren New wrote:
>>>> You say this, but it's not actually true.  You cannot distinguish 
>>>> two hydrogen atoms as long as you ignore the stuff that lets you 
>>>> distinguish them.  Like, say, their positions.
>>>
>>>     Have to agree with andrel here.
>>
>> Hmmmmm.... OK.  I can see that.  How does space-like separation affect 
>> that, tho?
>>
> space- like is from relativistic physics, the point we are discussing is 
>  quantum mechanics. As you know the two are incompatible. So, being a 
> formally trained physicist with a 20 year old education, I don't know. ;)

Heh. OK, fair enough.

And thank you. I think I've had that misconception for a while. Thanks 
for clearing it up.

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

Post a reply to this message

> Not at all! If you could realy have all of that information for every 
> atoms in the univers, you could conceivably be able to predict when a star 
> will apears, how long it will live, how it will finish, if it will have 
> planets and how many, the exact description of every single one, if it 
> will host any life, and if inteligent life will apears. All that for a 
> future star for whitch most of it's constituant matter is still contained 
> in several other stars. Star that will only start to form in a billion 
> years.

Could the machine also tell you exactly what happened in the past?

The key question is if it is possible to predict the exact behaviour of 
every particle based on its current state.  Are there not some things that 
exhibit truly random behaviour?

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scott nous apporta ses lumieres en ce 2007/11/14 03:01:
>> Not at all! If you could realy have all of that information for every 
>> atoms in the univers, you could conceivably be able to predict when a 
>> star will apears, how long it will live, how it will finish, if it 
>> will have planets and how many, the exact description of every single 
>> one, if it will host any life, and if inteligent life will apears. All 
>> that for a future star for whitch most of it's constituant matter is 
>> still contained in several other stars. Star that will only start to 
>> form in a billion years.
> 
> Could the machine also tell you exactly what happened in the past?
Absolutely!
> 
> The key question is if it is possible to predict the exact behaviour of 
> every particle based on its current state.  Are there not some things 
> that exhibit truly random behaviour?
> 
> 
Quantum fluctuations, with it's probability coud, is purely random. But, the 
random range is prety tight, even if it extend almost to infinity.
Take any given electron at rest. You can know it's location within an amstrong 
radius, and you have more than a 99.999999% chance to effectively find it within 
that radius, BUT, there is a non-zero chance to find it at over 1 light-year away.

-- 
Alain
-------------------------------------------------
'Power corrupts. Absolute power is kind of neat, though.'

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