plus, another thing to point out is that these are just single quantities that just so happened to be represented by more than one digit because of our base. The number 3.465 looks like a string of digits, but if we worked in base 3.465, that number would be represented by a 1
sorry, that would be 10, not 1
anyway, getting back to the initial point (sorry to bring up this thread again, but I find the subject fascinating), I think the question of whether the overall function of the universe contains random elements, boils down to this:
if time were rewound and then played back, do you believe things would turn out the same, or differently?
If you believe things would turn out the same, then their is no randomness to the universe other than subjective perception.
A few “random” thoughts I want to share…
G: "If you believe things would turn out the same, then their is no randomness to the universe other than subjective perception."
“Believe” being the key word here.
In the various religious debates, people occasionally say things like “I know there’s an afterlife, because thats the only way things make sense.” In other words they are deciding to believe something because it makes them more comfortable. Which is as good a way as any to choose between two undecidable propositions I suppose.
Einstein disliked the apparent lack of cause and effect in quantum physics and so spent a lot of time looking for the “hidden variable” and devising thought experiments which invalidated it. He wasn’t successful, which doesn’t mean he was wrong. Or right. But his antipathy was a belief, a matter of personal preference.
** CurtC: “The current state of the very well tested quantum theory is that when an atom decays seemingly randomly, it really is random, and not just a function of our not knowing enough about its initial conditions.”**
The trouble being, there’s no way to tell the difference! In the absence of contrary evidence and having a very powerful, successful theory, we use occam’s razor and assume randomness.
G: "Radioactive decay is a great example, but it does not illustrate randomness at all. If it did, there would be no such thing as a “half-life”, ie: the rate of decay would constantly fluctuate."
The rate of decay DOES constantly fluctuate. It’s just that for large numbers of atoms, these fluctuations are too small to be seen. If you started out with 128 atoms, the half-life for the decay from 128 to 64 would be different from that for the decay from 16 to 8.
Myrr21 "You’re missing the point. THe point is that the digits are random, no matter what base we work in, or what irrational number we use. In base 12, the digits of pi are no less random than they are in base 10–just different."
Maybe I’m missing the point too, but I don’t see how PI is random. The digits are generated by an algorithm, after all. Pseudorandom maybe? If you gave someone the second million decimal places of PI, it’s possible that with a lot of time and effort they could derive the algorithm that generated them and give you the next digit. It’s very hard, which is why encryption works, but it’s theoretically possible. Whereas if I gave you a million digits generated using a truly random process, it’s impossible even in theory for someone to predict the next digit in the series.
** G: “if time were rewound and then played back, do you believe things would turn out the same, or differently?”**
I’ve no idea, and you can quote me!
We measure the particle by shining light on it, the smaller the wavelength (i think) gives more accurate position but this requires more energy and so it travels faster.
Therefore less energy gives us a more reliable speed (momrntum, whatever) but less accurate position.
The smallest amount of light energy we can shine is a quanta (wording?) and this means we can never be truly accurate until we discover a better way of measuring things.
This is off the top of my head so excuse the poor wording and incorrect use of terms, but i haven’t done this for about a year so i’m a little hazy. 
i tend to agree with G there.
Pnuk Guy, illustrates a good point, in that the unknown factors of the universe are not necessarily locked away indefinately, and we are restricted by measuring techniques that will one day be old and antiquated.
thank you for the great response matt!
I did not know the half life of a substance fluctuated, burt now that I think about, it couldn’t really be any other way. Thanks for the interesting facts
my last post about “If you believe…” was not meant to offer any logical explanation, but rather to offer a familiar context. Of course we’ll never be able to proove this, but the thing we have to think about is can we model either situation, or both, or neither? Well deterministic chaos seems to be a good model. It shows how far away we really are from total predictive powers over the universe, but at the same time it’s still cause an effect, and it makes sense. We use deterministic chaos to model the weather, the stock market, fluid dynamics… it seems to be a valid choice.
The other option is to create a model with a real element of randomness. Now I’ll point out that even a random number given by a computer is generated by some sort of algorithm, and therefore isn’t really random. I don’t claim to be an authority, but I’d be very interested to know if there are any mathematical models we use that have a true “uncertainty principle”.
Another interesting thing about the nature of deterministic chaos is that there is a great level of uncertainty when trying to trace it backwards through time. When followed chronologically, there can only be one result for each given state. When you go backwards, however, the amount of possible roots to each iteration in time is equal to the dimensions of your model (eg: a quadratic has 2 roots).
I thought about this some more, and asked “how long should an iteration be”? Well, planck time is the amount of time by which anything smaller is not worth considering, because nothing could possibly happen in the universe in such a short period. Planck time is about 10[-43] seconds. SO, if you were working with 3 spatial dimensions and you wanted to find the absolute maximum number of ways the universe could have arrived at this state, from the state it was in a second ago, the answer would be…
3 to the power of 10000000000000000000000000000000000000000000
Hmmmm… entropy is not a point, but maximum entropy is… I’m confused now. Can there be maximum entropy in an infinite universe? Maximum implies a limit. Is the universe infinite, or not? (My capacity for stubborness appears to be limitless, and – as far as I know – I live in this universe. Can something be bigger inside than out? Besides this thread?)
The temperature equilibrium of the universe was what I was equating to randomness. If all energy is unusable, and the application of energy is required to create order then order would be impossible, and if order is knowabilty while randomness is unknowability, would this not be (maximum?infinite?) randomness?
I truly don’t know. Perhaps I’m in over my head. Oh well.
the universe, while being a system to itself, is full of little subsystems. Entropy leads to disorder, but out of that, new systems of a higher level of order emerge. While the universe is heading towards total disarray, life is busy creating highly organized structures, and of course, itself growing and becoming more ordered.
A recent Great Debate kind of overlapped into this subject. If you’re interested, here it is…
http://boards.straightdope.com/sdmb/showthread.php?threadid=46958
If we stop a particle at a certain point then don’t we know it’s position and it’s momentum, or is that impossible to actually achieve?
If we were to travel to another universe that is our own except a little while in the future. (Already by entering the future universe we have created another future universe for our own universe because by just being in it we have already altered it.) Anyway then we could see what the future was like, measure things like the radioactive decay of a substance we placed in our former universe. Then return to our universe and wait for that particular substance to decay, (now remember we went to an alternate future universe because just by existing in it we changed it).
Then if the results turned out exactly how we predicted it then doesn’t this prove that radioactive decay isn’t really random, or is a function of variables? Or does this prove that it could be random but is deterministic? Because if there was no function to work out the result then maybe randomness actually does exist but so does determinism.
PerfectDark.
PS. I get Christmas before you guys because I live in Australia, hahahahaha!
The GQ answers to this question were all given back on the first page: The Universe is definitely not predictable, and it is unknown and unknowable whether it’s deterministic. Since it’s unknowable, any further discussion on the matter belongs in Great Debates, so I’m moving this thread there.
Hey thanks, thats extacted my thoughts
I just wanted to high light that no digits of an expressed value can be random. If pi’s digits were random every time I tried to figure out the circumference of a circle, I would get thousands of different mearsurements for the same circle. pi always starts with 3.14…
I just wanted to state that my thoughts are not necessarily that everything is pre-ordained. I just think it is somewhat arrogant of man to see something that looks random and that we cannot decipher, and so we call it random. I am not saying I am sure that this is true but I am asking why are we so quick to form theories of something in the least way credible. I often ask questions that require the answer to come from a god, for only then could something measure an object but not affect it in any way. This is not really a question of right or wrong(which is the basis of this forum) it is more a look at one point from many directions.
Back to the subject at hand. If quantum mechanics could be explained beyond the idea of “it’s uncertain”, doesn’t the idea of knowing a future already cancel its existance. I mean could we change it, if we knew, or is it pre-ordained as others tell me it would be.
And if quatum mechanics were actually the source of a very chaotic and random/repeating world, is there a rhythm or pattern to it? Yes random means no pattern but could all that randomitity translate into a orderly system that can be described using conventional mathmatics? And a side note, if this whole hypothetical “randomitity translate[d] into a orderly system” existed (it does as described by some chaotisist[sp?]) and you could find a pattern in the order, couldn’t you then break down the order into its random strings and find how the equilibrium comes about and how the randomness could be canceled.
Don <— :wally
The reason I put this last part is because if random things exist, then how is it possible to see any patterns at all. In reality, there are no patterns. Even things like rolling dice can be effected by outside forces. If those forces could be effected by the [QM uncertain forces] previously mentioned then we really have no basis for discussion of [whether or not randomness would effect law bound systems it is man that puts a pattern in a place that may or may not have it]. The main question at hand (sorry if this makes no sense to anyone because my my its late, wait this does not make sense, but I will post so that I can decipher what I am thinking right now).
Um, because they’re in our brain? Hardwired?
Chocobo wrote:
Pi is an irrational number. For it to have a final digit would mean it is rational. Such a contradiction would destroy the fabric of mathematics as we know it.
I think someone mentioned it. The digits of pi are pseudo-random. They are not truly random, but random enough for our purposes.
Also, regardless of what base we choose, pi would still be irrational. Unless, of course, we chose pi as the base. If that were the case, I would not like to be an accountant.
(How much is pi dollars?)
Upon second thought, I don’t think pi can be a base. Or maybe it can. Can a real mathematician step in here?
Oh yeah, there are patterns to randomness, called probability distributions (nice curves.) So there is beauty in the beast afterall.