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Warning – the following contains a lot of math
“One in a googolplex”
Remember when Doc Brown said this about his future (Past) wife – Clara in back to the future 3?
This got me thinking. Is this really true? If I could come up with un upper limit of the number of possible realities, then this would define an upper limit of what can exist in reality. If this number is less than a googolplex, then Clara isn’t one in a googolplex (as it is certain to have more than one of her in a googolplex possible realities with all distinct realities represented).
The solution I came up with was that if we look at all the possible arrangements of atoms in the known universe, at least one (actually several) would contain an arrangement whereby the above scenarios occur. Brilliant I thought – then the upper limit for the probability would be one in the number of ways these atoms can be arranged.
Now I just needed to determine the number of ways the atoms in the universe could be arranged.
Here’s the method I used.
1 I took the number of atoms in the observable universe. I already knew this from reading Wikipedia to be around 10^80.
2 The space that these can be arranged in is a maximum of roughly 10^185 spots for each atom (this is the number of planck volumes in the observable universe – I don’t understand what a planck volume is but for this exercise, I assumed that you can’t position an atom outside of these planck volumes)
3 from this, I could see that the upper bound for total possible ways of placing atoms in these planck volumes would be (10^185)^(10^80). This is roughly 10^10^83
4 Great, but an atom doesn’t just have one property. If you change it’s velocity or energy level or spin for instance, it behaves differently than and so two universes with the same configuration of atoms would be different if the atoms are moving differently. I decided to give the atoms 10^1000 possible distinct attributes. I feel this is a sufficiently large number to fully describe all the properties of the atom in question.
5 Now the total configurations of one universe would be roughly 10^1000 configurations to the power of 10^80 atoms. Again, this figure comes to a total of around 10^10^83.
6 Now I have the total number of ways to arrange the atoms and the total number of atom attributes per configuration. Now to get the total possible universes, all I have to do is multiply them together: 10^10^83x10^10^83 equals roughly 10^(2x(10^83)) which I will round up to 10^10^84.
Note that the margin for error with such massive numbers is incredible. I have also not taken into account a number of things such as atoms are not the only thing in the universe and other factors could influence a given universe.
Nonetheless, even taking the margin for error and possible things I’ve missed into account, I don’t think a reality would be observably different than one of the 10^10^84 I’ve listed. I have also ignored quantum mechanics and assumed Newtonian mechanics explain the universe. This is because it is too difficult to calculate if it can even be calculated but would obviously change the outcome.
What this means – nothing really. Just a way I can now look at reality. All possible realities are bound by this number. There are no more realities (again ignoring the limits of Newtonian physics) that could exist that are not represented by this number (eg. You could take all possible realities and number them). It seems to give perspective to reality just as reality now to me gives perspective to this number. Anything you can imagine that is possible to exist would exist in one of these hypothetical realities that can be counted. I just wanted to post my thoughts and hopefully someone else finds it interesting.
It also means that Doc was wrong about Clara. She is not one in a googolplex. Indeed there is an arrangement of atoms and therefore a possible reality (possible in the sense that it could have happened not that it exists) whereby there exist hundred’s of atom configurations identical to and indistinguishable from Clara’s. They would for practical purposes be Clara’s. The number of Clara’s in these realities are (to me at least) incalculable.
I appreciate feedback. As much as I like the idea where all possible realities are bound by a googolplex, if I am wrong, I want to know about it.
As a final word, it is possible that the total number of universes exceeds my calculations and is indeed exactly 1 Googolplex. What are the odd’s of that? I don’t know but my guess is about 1 in a googolplex.
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Get Day9 on this and we will have it solved in no-time!
On topic, I know nothing about math sorry, just wanted to mention day9 in a post :3
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One could of course question the assumption that the observable universe is the whole universe, which would throw your calculations off.
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I agree. I know my calculations are based on a number of assumptions but I can't calculate on the unobservable universe - who knows what that contains (it is, afterall, unobservable). I calculated on what I can.
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Read 'Skewered!' a short story by Isaac Asimov.... Its on Skewes Number a whole series of magnitudes higher than this!
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You are vastly underestimating the number of possible realities by just looking at atom configurations. Each atom consists of protons and neutrons, which further increases the number of degrees of freedom. Granted, the vast majority of the visible matter in the known universe consists of hydrogen, which is just a single proton in its most common form. Next to the atomic nuclei there are the electrons that can be in a ton of different energy levels, orbiting the nucleus.
But atomic matter is just a small part of what is out there. The sun is estimated to emit something along the lines of 10^45 photons per second. Particles that have energy and direction. And that's just our sun, there are 3 * 10^11 stars in our galaxy (estimate) and our sun is relatively small. There are billions of galaxies in the universe.
And that's just photons. We also have neutrinos. These particles (that do not travel faster than light!) are extremely numerous as well, even though they rarely interact with matter.
And when all is said and done, it is estimated the less than 5% of the mass and energy of the universe consists of the things that we know: atoms, photons, neutrinos and the likes. The rest, the "dark matter" and "dark energy" is completely unknown so far, but it provides a significant contribution to our universe on the level of galactic superclusters.
Finally, can we assume that our physical constants are the same between different realities? Some philosophical ideas say that there may be many other realities where the physical constants (and laws of physics) are different. It's quite possible that the number of possible values for something like that Planck constant is not bounded, but rather a continuum. In which case the number of possible realites would be unbounded.
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Sorry to burst your bubble, but this gets way weirder when you bring quantum physics into the equation. Ignoring the fact that "atoms" are really just factors of amplitude distributions, you need to consider that, if we have Helium Atom X and Helium Atom Y, each in certain positions, and then you change the universe, so that the entirety of the universe is the same except Helium Atom X and Helium Atom Y have changed places, you get an identical configuration...not just something that looks identical, but a literally identical configuration, the same mathematical object, as Helium Atom X and Helium Atom Y are identical mathematical objects, so your calculations are off. (In an equation of 5 + 2 + 2 = 9, changing the twos around makes literally no difference, as the twos are identical.)
Still an interesting thought experiment, however.
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Your model is only good for any specific time t. Every time frame where an electron moves and is considered to be in a "different" spot would have to be accounted for.
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On April 10 2012 22:22 Rannasha wrote:
You are vastly underestimating the number of possible realities by just looking at atom configurations. Each atom consists of protons and neutrons, which further increases the number of degrees of freedom. Granted, the vast majority of the visible matter in the known universe consists of hydrogen, which is just a single proton in its most common form. Next to the atomic nuclei there are the electrons that can be in a ton of different energy levels, orbiting the nucleus.
But atomic matter is just a small part of what is out there. The sun is estimated to emit something along the lines of 10^45 photons per second. Particles that have energy and direction. And that's just our sun, there are 3 * 10^11 stars in our galaxy (estimate) and our sun is relatively small. There are billions of galaxies in the universe.
And that's just photons. We also have neutrinos. These particles (that do not travel faster than light!) are extremely numerous as well, even though they rarely interact with matter.
And when all is said and done, it is estimated the less than 5% of the mass and energy of the universe consists of the things that we know: atoms, photons, neutrinos and the likes. The rest, the "dark matter" and "dark energy" is completely unknown so far, but it provides a significant contribution to our universe on the level of galactic superclusters.
Finally, can we assume that our physical constants are the same between different realities? Some philosophical ideas say that there may be many other realities where the physical constants (and laws of physics) are different. It's quite possible that the number of possible values for something like that Planck constant is not bounded, but rather a continuum. In which case the number of possible realites would be unbounded.
very informative and useful post, thanks
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On April 10 2012 21:19 ssj_ds wrote:
1 I took the number of atoms in the observable universe. I already knew this from reading Wikipedia to be around 10^80.
2 The space that these can be arranged in is a maximum of roughly 10^185 spots for each atom (this is the number of planck volumes in the observable universe – I don’t understand what a planck volume is but for this exercise, I assumed that you can’t position an atom outside of these planck volumes)
3 from this, I could see that the upper bound for total possible ways of placing atoms in these planck volumes would be (10^185)^(10^80). This is roughly 10^10^83
Firstly the observable universe is just that, the bit we can see, there's no reason it isn't much much larger with more particles, that's just an estimate.
A planck length is 1.616 X 10^-35 m, now technically you should be using spheres for this not cubes as you can't have a quantum passage longer than the planck length, which would be the case if you had cubes (going across the diagonal vertex for instance), so you'd have to use spheres and some kind of packing like hcp.
Second of all 1 atom will not fit in this volume, not even close, there are many ways to define atomic volume but all of them are on the scale of pm (1x10^-12) and generally atoms range between 30-300 pm.
Im really tired so I wont do the math for you, and im going to stop there but you get the idea, you've made some assumptions to make your life easier, or just possible without seriously considering entropy, black holes etc
However making those assumptions invalidates your whole proposal.
http://www.thefoggiestnotion.com/how_many_universes.htm
This may shed some light on things for you.
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The problem with this idea is you are calculating the number of different ways the universe could be configured. But doc's statement was that Clara was one in a googloplex; meaning that out of a googolplex humans that all the things which make Clara unique such as personality and physical appearance would only occur together in that specific form once. The arrangement of the atoms within a cloud of intergalactic dust unobservable from Earth, for example, is unlikely to have any impact on Clara's life.
There is a theoretical maximum number of ways human DNA can be configured. If I recall correctly the upper limit is somewhere around 3 trillion. Meaning that, if you had over 3 trillion human beings, by definition there would be some who would have the exact same genetic makeup and DNA profile. Of course identical DNA does not imply identical individual, but depending on where one sits in the nature versus nuture debate, an argument might be made that identical DNA would result in a very similar individual with a similar personality. However this still does not account for environmental factors. Something like lead poisoning or parasites can drastically affect an individual's neural chemistry
So perhaps a more realistical approach would be calculating the total number of ways the atoms in Clara's body could be configured. For the purpose of this thought experiment, let us assume that the whole of an individual's conciousness and personality is the sole result of the configuration of their brain and neural chemistry. In which case, there is one specific configuration of atoms and molecules that would define every aspect of Clara's being--not unlike a "transporter patter" from Star Trek. However we are again limited here by the fact that many of this ways that atoms could be configured would not represent a life form, for example one possible organization which would be counted would include all the the Carbon, Oxygen, Hydrogen, etc. in her body in separate groupings. Clearly that's not a human being. Clearly the intent of doc brown's words were that Clara was 1 in a googolplex of humans so again this falls short of entirely addressing the question but would perhaps be more accurate than measuring the total number of realities; which quantum physics and quandries like black holes make impossible.
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On April 11 2012 01:26 TheToast wrote:
The problem with this idea is you are calculating the number of different ways the universe could be configured. But doc's statement was that Clara was one in a googloplex; meaning that out of a googolplex humans that all the things which make Clara unique such as personality and physical appearance would only occur together in that specific form once. The arrangement of the atoms within a cloud of intergalactic dust unobservable from Earth, for example, is unlikely to have any impact on Clara's life.
There is a theoretical maximum number of ways human DNA can be configured. If I recall correctly the upper limit is somewhere around 3 trillion. Meaning that, if you had over 3 trillion human beings, by definition there would be some who would have the exact same genetic makeup and DNA profile. Of course identical DNA does not imply identical individual, but depending on where one sits in the nature versus nuture debate, an argument might be made that identical DNA would result in a very similar individual with a similar personality. However this still does not account for environmental factors. Something like lead poisoning or parasites can drastically affect an individual's neural chemistry
So perhaps a more realistical approach would be calculating the total number of ways the atoms in Clara's body could be configured. For the purpose of this thought experiment, let us assume that the whole of an individual's conciousness and personality is the sole result of the configuration of their brain and neural chemistry. In which case, there is one specific configuration of atoms and molecules that would define every aspect of Clara's being--not unlike a "transporter patter" from Star Trek. However we are again limited here by the fact that many of this ways that atoms could be configured would not represent a life form, for example one possible organization which would be counted would include all the the Carbon, Oxygen, Hydrogen, etc. in her body in separate groupings. Clearly that's not a human being. Clearly the intent of doc brown's words were that Clara was 1 in a googolplex of humans so again this falls short of entirely addressing the question but would perhaps be more accurate than measuring the total number of realities; which quantum physics and quandries like black holes make impossible.
A person takes up about 10^10^70 quantum states, so no, not one in a googolplex (10^10^100)
That means if you took roughly 1m^3 (a person, close enough approx) and iterated through all possible quantum states that could occupy that area you would iterate through the same states after 10^10^70 iterations, meaning its possible to have a duplicate of someone after that many times.
Now if you wanted to add limits to that, to say that the quantum states had to be organized in such a fashion as to represent a 'human' you'd probably find that the number of iterations required would be significantly, and I mean significantly less.
People are forgetting that a googolplex is unfathomably large.
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On April 11 2012 01:37 adwodon wrote:Show nested quote +On April 11 2012 01:26 TheToast wrote:
The problem with this idea is you are calculating the number of different ways the universe could be configured. But doc's statement was that Clara was one in a googloplex; meaning that out of a googolplex humans that all the things which make Clara unique such as personality and physical appearance would only occur together in that specific form once. The arrangement of the atoms within a cloud of intergalactic dust unobservable from Earth, for example, is unlikely to have any impact on Clara's life.
There is a theoretical maximum number of ways human DNA can be configured. If I recall correctly the upper limit is somewhere around 3 trillion. Meaning that, if you had over 3 trillion human beings, by definition there would be some who would have the exact same genetic makeup and DNA profile. Of course identical DNA does not imply identical individual, but depending on where one sits in the nature versus nuture debate, an argument might be made that identical DNA would result in a very similar individual with a similar personality. However this still does not account for environmental factors. Something like lead poisoning or parasites can drastically affect an individual's neural chemistry
So perhaps a more realistical approach would be calculating the total number of ways the atoms in Clara's body could be configured. For the purpose of this thought experiment, let us assume that the whole of an individual's conciousness and personality is the sole result of the configuration of their brain and neural chemistry. In which case, there is one specific configuration of atoms and molecules that would define every aspect of Clara's being--not unlike a "transporter patter" from Star Trek. However we are again limited here by the fact that many of this ways that atoms could be configured would not represent a life form, for example one possible organization which would be counted would include all the the Carbon, Oxygen, Hydrogen, etc. in her body in separate groupings. Clearly that's not a human being. Clearly the intent of doc brown's words were that Clara was 1 in a googolplex of humans so again this falls short of entirely addressing the question but would perhaps be more accurate than measuring the total number of realities; which quantum physics and quandries like black holes make impossible. A person takes up about 10^10^70 quantum states, so no, not one in a googolplex (10^10^100) That means if you took roughly 1m^3 (a person, close enough approx) and iterated through all possible quantum states that could occupy that area you would iterate through the same states after 10^10^70 iterations, meaning its possible to have a duplicate of someone after that many times. Now if you wanted to add limits to that, to say that the quantum states had to be organized in such a fashion as to represent a 'human' you'd probably find that the number of iterations required would be significantly, and I mean significantly less. People are forgetting that a googolplex is unfathomably large.
Well to account for morbidly obese individuals, I would think you would need to expand that to the area of the largest person known to exist. So probably at least 4 cubic meters (then again idk, how much space does a 900lb person take up?)
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Can I just say... There are some ridiculously intelligent people on TeamLiquid.
I can't be the only one completely and totally lost here; is there any way to compress these ideas into something a little more understandable for someone that could only barely scratch through his high school algebra classes? =p
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On April 11 2012 01:48 TheToast wrote:+ Show Spoiler +On April 11 2012 01:37 adwodon wrote:Show nested quote +On April 11 2012 01:26 TheToast wrote:
The problem with this idea is you are calculating the number of different ways the universe could be configured. But doc's statement was that Clara was one in a googloplex; meaning that out of a googolplex humans that all the things which make Clara unique such as personality and physical appearance would only occur together in that specific form once. The arrangement of the atoms within a cloud of intergalactic dust unobservable from Earth, for example, is unlikely to have any impact on Clara's life.
There is a theoretical maximum number of ways human DNA can be configured. If I recall correctly the upper limit is somewhere around 3 trillion. Meaning that, if you had over 3 trillion human beings, by definition there would be some who would have the exact same genetic makeup and DNA profile. Of course identical DNA does not imply identical individual, but depending on where one sits in the nature versus nuture debate, an argument might be made that identical DNA would result in a very similar individual with a similar personality. However this still does not account for environmental factors. Something like lead poisoning or parasites can drastically affect an individual's neural chemistry
So perhaps a more realistical approach would be calculating the total number of ways the atoms in Clara's body could be configured. For the purpose of this thought experiment, let us assume that the whole of an individual's conciousness and personality is the sole result of the configuration of their brain and neural chemistry. In which case, there is one specific configuration of atoms and molecules that would define every aspect of Clara's being--not unlike a "transporter patter" from Star Trek. However we are again limited here by the fact that many of this ways that atoms could be configured would not represent a life form, for example one possible organization which would be counted would include all the the Carbon, Oxygen, Hydrogen, etc. in her body in separate groupings. Clearly that's not a human being. Clearly the intent of doc brown's words were that Clara was 1 in a googolplex of humans so again this falls short of entirely addressing the question but would perhaps be more accurate than measuring the total number of realities; which quantum physics and quandries like black holes make impossible. A person takes up about 10^10^70 quantum states, so no, not one in a googolplex (10^10^100) That means if you took roughly 1m^3 (a person, close enough approx) and iterated through all possible quantum states that could occupy that area you would iterate through the same states after 10^10^70 iterations, meaning its possible to have a duplicate of someone after that many times. Now if you wanted to add limits to that, to say that the quantum states had to be organized in such a fashion as to represent a 'human' you'd probably find that the number of iterations required would be significantly, and I mean significantly less. People are forgetting that a googolplex is unfathomably large. Well to account for morbidly obese individuals, I would think you would need to expand that to the area of the largest person known to exist. So probably at least 4 cubic meters (then again idk, how much space does a 900lb person take up?)
Times it by 16 then, doesn't make any real difference, just going off approximate orders of magnitude, do it for a person / house / mouse / whale you're still going to have about 10^10^70 (+/- 1) quantum states.
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On April 11 2012 03:36 adwodon wrote:Show nested quote +On April 11 2012 01:48 TheToast wrote:+ Show Spoiler +On April 11 2012 01:37 adwodon wrote:Show nested quote +On April 11 2012 01:26 TheToast wrote:
The problem with this idea is you are calculating the number of different ways the universe could be configured. But doc's statement was that Clara was one in a googloplex; meaning that out of a googolplex humans that all the things which make Clara unique such as personality and physical appearance would only occur together in that specific form once. The arrangement of the atoms within a cloud of intergalactic dust unobservable from Earth, for example, is unlikely to have any impact on Clara's life.
There is a theoretical maximum number of ways human DNA can be configured. If I recall correctly the upper limit is somewhere around 3 trillion. Meaning that, if you had over 3 trillion human beings, by definition there would be some who would have the exact same genetic makeup and DNA profile. Of course identical DNA does not imply identical individual, but depending on where one sits in the nature versus nuture debate, an argument might be made that identical DNA would result in a very similar individual with a similar personality. However this still does not account for environmental factors. Something like lead poisoning or parasites can drastically affect an individual's neural chemistry
So perhaps a more realistical approach would be calculating the total number of ways the atoms in Clara's body could be configured. For the purpose of this thought experiment, let us assume that the whole of an individual's conciousness and personality is the sole result of the configuration of their brain and neural chemistry. In which case, there is one specific configuration of atoms and molecules that would define every aspect of Clara's being--not unlike a "transporter patter" from Star Trek. However we are again limited here by the fact that many of this ways that atoms could be configured would not represent a life form, for example one possible organization which would be counted would include all the the Carbon, Oxygen, Hydrogen, etc. in her body in separate groupings. Clearly that's not a human being. Clearly the intent of doc brown's words were that Clara was 1 in a googolplex of humans so again this falls short of entirely addressing the question but would perhaps be more accurate than measuring the total number of realities; which quantum physics and quandries like black holes make impossible. A person takes up about 10^10^70 quantum states, so no, not one in a googolplex (10^10^100) That means if you took roughly 1m^3 (a person, close enough approx) and iterated through all possible quantum states that could occupy that area you would iterate through the same states after 10^10^70 iterations, meaning its possible to have a duplicate of someone after that many times. Now if you wanted to add limits to that, to say that the quantum states had to be organized in such a fashion as to represent a 'human' you'd probably find that the number of iterations required would be significantly, and I mean significantly less. People are forgetting that a googolplex is unfathomably large. Well to account for morbidly obese individuals, I would think you would need to expand that to the area of the largest person known to exist. So probably at least 4 cubic meters (then again idk, how much space does a 900lb person take up?) Times it by 16 then, doesn't make any real difference, just going off approximate orders of magnitude, do it for a person / house / mouse / whale you're still going to have about 10^10^70 (+/- 1) quantum states.
Interesting, so this could prove that Clara was not one in a googolplex....
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On April 11 2012 03:40 TheToast wrote:Show nested quote +On April 11 2012 03:36 adwodon wrote:On April 11 2012 01:48 TheToast wrote:+ Show Spoiler +On April 11 2012 01:37 adwodon wrote:Show nested quote +On April 11 2012 01:26 TheToast wrote:
The problem with this idea is you are calculating the number of different ways the universe could be configured. But doc's statement was that Clara was one in a googloplex; meaning that out of a googolplex humans that all the things which make Clara unique such as personality and physical appearance would only occur together in that specific form once. The arrangement of the atoms within a cloud of intergalactic dust unobservable from Earth, for example, is unlikely to have any impact on Clara's life.
There is a theoretical maximum number of ways human DNA can be configured. If I recall correctly the upper limit is somewhere around 3 trillion. Meaning that, if you had over 3 trillion human beings, by definition there would be some who would have the exact same genetic makeup and DNA profile. Of course identical DNA does not imply identical individual, but depending on where one sits in the nature versus nuture debate, an argument might be made that identical DNA would result in a very similar individual with a similar personality. However this still does not account for environmental factors. Something like lead poisoning or parasites can drastically affect an individual's neural chemistry
So perhaps a more realistical approach would be calculating the total number of ways the atoms in Clara's body could be configured. For the purpose of this thought experiment, let us assume that the whole of an individual's conciousness and personality is the sole result of the configuration of their brain and neural chemistry. In which case, there is one specific configuration of atoms and molecules that would define every aspect of Clara's being--not unlike a "transporter patter" from Star Trek. However we are again limited here by the fact that many of this ways that atoms could be configured would not represent a life form, for example one possible organization which would be counted would include all the the Carbon, Oxygen, Hydrogen, etc. in her body in separate groupings. Clearly that's not a human being. Clearly the intent of doc brown's words were that Clara was 1 in a googolplex of humans so again this falls short of entirely addressing the question but would perhaps be more accurate than measuring the total number of realities; which quantum physics and quandries like black holes make impossible. A person takes up about 10^10^70 quantum states, so no, not one in a googolplex (10^10^100) That means if you took roughly 1m^3 (a person, close enough approx) and iterated through all possible quantum states that could occupy that area you would iterate through the same states after 10^10^70 iterations, meaning its possible to have a duplicate of someone after that many times. Now if you wanted to add limits to that, to say that the quantum states had to be organized in such a fashion as to represent a 'human' you'd probably find that the number of iterations required would be significantly, and I mean significantly less. People are forgetting that a googolplex is unfathomably large. Well to account for morbidly obese individuals, I would think you would need to expand that to the area of the largest person known to exist. So probably at least 4 cubic meters (then again idk, how much space does a 900lb person take up?) Times it by 16 then, doesn't make any real difference, just going off approximate orders of magnitude, do it for a person / house / mouse / whale you're still going to have about 10^10^70 (+/- 1) quantum states. Interesting, so this could prove that Clara was not one in a googolplex....
Personally I find it disgusting they didnt do the appropriate research before writing the script.
Shameful display of ignorance.
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Thanks for the feedback everyone.
@ TOCHMY – I would love for Day9 to post in this thread
@ Fireweaver – I know there are numbers much greater than this and am fascinated by them. I am truly in awe of Graham’s number after looking it up on Wikipedia but I wasn’t looking for the biggest number.
@ Rannasha – You’re right about photons but from what I understand, neutrinos are not easily observed and as such I ignored them because 2 realities that differ only by neutrinos would appear to be the same. I didn’t include dark matter it is such an unknown itself (can’t really calculate on it). Finally, I didn’t consider other realities as I was looking at possibilities of this reality
@ Salivanth – I know what you are saying. I was, however, looking for an upper bound to the number of realities (notice how I was conservative and rounded up where possible), not the actual number (which would be way harder to calculate but obviously smaller). As long as the upper bound is less than a googolplex, I can say that the total possible realities (rather configurations of this reality) are less than a googolplex.
@ RAGEMOAR – True. However if we look at one reality that changes over time, it has to change into one of the other realities that could be numbered (and if they were, the total would be less than a googolplex). It would not change into something that is outside of what I calculated.
@ adwodon – The assumptions I made were done to make the calculations possible (for me). I think you will find that if you take away the assumptions I have made regarding black holes, the answer would not change much. Indeed, because I simplified the equation, the current one I used takes into account that several atoms can occupy the same place planck volume (as might happen in a black hole).
Atoms are much bigger than a planck volume - using a smaller figure for where atoms can occupy would only lower number of possible realities. Think of the universe divided into planck volumes and where you place an atom is in the centre of one. As there are so many more planck volumes than atoms and as the universe is mostly empty space and a planck length is the smallest possible distance (from what I understand), this gives a good estimate of the where the atoms can be placed.
Entropy - I did, in a way, take entropy into account (although I don’t know what this is exactly it is some attribute of an atom) by assuming an atom will have 10^1000 distinct attributes I think you will find that increasing this number by a factor of 10 digits (eg. 10^10000) would only increase the final exponent of possible realities by 1 (eg. from 10^10^83 to 10^10^84). I think this number is high enough that an atom that is different to another by an attribute that is less than 1 distinct attribute (eg. a minor speed increase), it would be indistinguishable from said other atom.
@ TheToast – Your way of calculating would be more accurate but also more difficult. I really just wanted to count the possible realities but in doing so answered this question along the way. My real conclusion was the number of possible realities and that anything you can imagine that is possible would be in one of these numbered realities. Our imaginations and possibilities are not boundless but there is a limit to what can be achieved, created or imagined.
@ adwodon (2nd post) – I guess you have answered what I was trying to far better (and more accurately) than my attempt (I assume you’re right as I can’t check and also will assume the quantum states of an volume the size of a person represents all possible realities that can exist in that volume but as I said, I don’t understand quantum mechanics). So to extrapolate from what you wrote then, if we multiply the possible quantum states of the volume of a person 10^10^70 but the volume of the universe over the volume of a human (not sure what this would be but would not be more than the planck volumes in the universe so say 10^185) this woud give the quantum states of the universe as 10^10^70x10^185 which roughly still equals 10^10^70.
I have to say that although this is much smaller than my upper bound of 10^10^84, I’m not too disappointed as it looks pretty close and I was right in that Clara is not one in a Googolplex.
@ MeeMeesiko –You were probably talking about adwodon but unless you state otherwise, I will assume you meant me as well – so thanks  .
@ adwodon (last post) – Agreed lol. He should have said “She is a million, one in a billion, one in 10 to the power of 10 to the power of (say) 68”. Then the casual viewer would think “that sounds smart” and the scientific viewers can do the math and think “That’s scientifically accurate”, the script writers get it right and everyone feels better about themselves.
And seriously, what girl wouldn’t love to hear that about themselves whilst thinking “So romantic”.
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EPT
