A boundary between knowable and un-knowable?

Question

Here's a thought experiment:
1) Let us assume that the total amount of energy in the universe is finite. Or at least, the total amount of available energy.
2) And let us assume that in order to perform any sort of calculation, energy is required.
3) Let us use all the energy (and/or mass) in the universe to construct an optimally-designed computer, which could then perform calculations at the fastest possible rate.
4) Let us employ the computer to calculate a sequence of digits, say the decimal expansion of an irrational number such as pi. I think this is an example where one can prove that there is no simple algorithm to calculate the nth digit based on a simple formula, rather one needs to laboriously calculate the preceding digits first.
5) Then, let us use all the energy in the universe to calculate as many digits as possible in this sequence, and suppose we end up with "p" digits.
6) Then the (p+1)st digit is calculable in theory, but unknowable in the universe!
Yes / No ?

Answer 1

Wow, interesting theory! It reminds me of that book where these people build an amazing computer to answer any question. They ask it the meaning of life, and it takes it millions of years, but it answers '42' and they have to build a whole new computer to figure out what it meant by '42'... yeah... Well, I guess people (well, computers) are always working out the next digit of pi, so now we just need to harness all of the energy in the universe and transform it into a calculation... probably killing ourselves in the process... oh well! It's a nice idea!

Answer 2

i'm no longer a physicist, a mathematician, nor even a scientist. i'm in touch by technique of your video, and by technique of the suggestions, yet don't have any practise to appreciate them at some thing previous the most simplified element. i imagine the Universe is orderly and exceptionally knowable, yet i'm no longer positive of its being "finally" so. finally, what absolutely everyone human can understand is constrained by technique of time and area, the very issues the Universe is derived from. we may, as a species, come to some expertise. i locate it comforting that when the "ten dimensions" camp ought to no longer come to words with the maths, they further the eleventh measurement, and embraced that ingredient of the "supergravity" camp. i pick to imagine that as a set, we may be able to discard suggestions that do not artwork, even even as those suggestions are loved. those human beings staked personal reputations on the arguments they offered and the formulation they devised. it isn't any longer a lot distinct that the chants and rituals that keep one crew of human beings at odds with yet another. I bear in mind vividly a debate between the moms of a few formative years acquaintances, one a Lutheran and the different a Catholic. even as the talk became good natured, it also became vehement contained in the prevalence of one expression of religion over the different. I observed better similarities than adjustments between them, on an similar time as a baby. This video jogged my memory of that journey. the girls remained acquaintances, and each and each and every committed to her personal church. How astounding it may were in the journey that they could each and each and every have regarded at the different and admitted that there became no enormous deal right here between what kind of hat the guy at the front wore. yet human beings have litterally lengthy gone to warfare over such trivialities. i'm hoping that the Universe is finally orderly and knowable. it ought to save us distinctive heartache. regrettably, there is many who will die quite than look heavily on the (emotional) equations of yet another and say, "Oh! properly, yeah, that makes good experience. Nevermind the argument, then."

Answer 3

Sure. This is a common computer science problem. There are plenty of problems where the algorithm to find the answer is known, but there is not enough computing power or memory to actually get the answer. That is, until someone comes up with a better algorithm. Or a faster computer. :)

Answer 4

Actually, it is quite possible that assumption 4) is false. It is certainly false base 16 since there is a known algorithm for finding hex digits of pi without finding earlier ones.

Other than that, your view has some validity. So?

Answer 5

Assumption #2 is just plain wrong.

Ok, I've thought about it and see what you're getting at. But we already knew that the decimal places in Pi is infinite so of course there is a limit to what we can calculate.

Answer 6

If the quantity of paper , that is needed to write down the result of a calculation, does not fit in the universe then the number is unknown.

Answer 7

You would like the fiction SF novel "Psychohistorical Crisis". The author puts the above theory into mathematical form (the novel is about a bunch of methematicians who rule the universe).

Answer 8

in order to use truly all the energy in the universe, you would have to convert all mass in the universe to energy, since mass and energy are one in the same. therefore, theoretically, when you reach the goal, you no longer exist, nor does the computer, nor ANYTHING. of course, energy and mass can not just cease to exist as matter cna not be created or destroyed, so this means your energy used in this formula has to go somehwere. either it is transferered into light, or heat, or matter. this is impossible. i've realy confused my self, THANKS ALOT! interesting question/experiment.

like this riddle..


who shaves the barber if the barber shaves everyone who doesn't shave himself?...

kinda like that, your thinking just goes in circles..

Answer 9

Assuming the truth of your assumptions, the logic seems to hold up.

Best wishes and God bless.

Answer 10

too long to read hahaha