4 ms·
The smallest possible distance is the Plank lenght, 1,610^-35 (110^-15 is the diameter of a proton). And for that you only need around 60 digits of pi to calcul
by gmuslera 11y ago
The smallest possible distance is the Plank lenght, 1,610^-35 (110^-15 is the diameter of a proton). And for that you only need around 60 digits of pi to calculate the circumference of the universe.
Of course, that is just for the simple operation of calculate the circumference given the diameter, more complex operations with pi may require more precision.
- ghayes 11y agoNever heard it stated that way. Can you elaborate on "the smallest possible distance is Plank's length"? Is that the smallest observable distance?
- jaseemabid 11y agoIf you have some time to spare, watch this talk "The astonishing simplicity of everything" by Neil Turok. He explains all this so beautifully. https://www.youtube.com/watch?v=f1x9lgX8GaE https://www.youtube.com/watch?v=f1x9lgX8GaE
- CoryG89 11y ago> According to the generalized uncertainty principle (a concept from speculative models of quantum gravity), the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that. At least according to Wikipedia, it seems it is indeed the smallest observable distance. Although it has never been proven and follows from the theoretical generalized uncertainty principle. https://en.m.wikipedia.org/wiki/Planck_length#Theoretical_significance https://en.m.wikipedia.org/wiki/Planck_length#Theoretical_si...
- deleted 11y ago[deleted]
- lisper 11y agohttp://physics.stackexchange.com/questions/28720/how-to-get-planck-length http://physics.stackexchange.com/questions/28720/how-to-get-...
- contravariant 11y agoFrom what I understand the particles you need to probe distances on the order of the Planck length are so energetic that their own gravity would start interfering. Their Swarzschild radius would become bigger than the distance you're trying to measure.
- api 11y agoDoes that mean the rest of the digits of pi are not "real," at least according to a realist rather than a Platonic philosophical position on the meaning and nature of mathematics? Seems like you could argue that digits beyond what are needed to render measurement to within one Planck length are meaningless and therefore a kind of fiction... at least if you take that philosophical position.
- 21echoes 11y agoPi is far more than just the ratio of the diameter to the circumference, even as a constructivist: https://affinemess.quora.com/What-is-math-pi-math-and-while-were-at-it-whats-math-e-math?__snids__=1596646755&__nsrc__=2 https://affinemess.quora.com/What-is-math-pi-math-and-while-...
- venomsnake 11y agoPi has other uses. The digits are real, but they just don't matter in practical engineering. But lets assume that there really are 10 dimensions - in that case a volume of a 10 dimensional sphere will require (pi^5)*r^10. If you want to measure the volume to 1 plank 10 dimensional cube, you will need more digits.
- Al-Khwarizmi 11y agoPi appears in many more places than in ratio of circumferences to their diameter. For example, if you flip a coin n times, the probability of getting exactly n heads and n tails asymptotically tends towards 1 / sqrt(π*n). The probability that two randomly chosen integers are coprime is 6/π^2. Etc. There is a list of formulae where π appears (some related to circles, some not) here: https://en.wikipedia.org/wiki/List_of_formulae_involving_π https://en.wikipedia.org/wiki/List_of_formulae_involving_π
- ikeboy 11y agoBut how many coins can you flip before the heat death of the universe, and does using 43 digits make your expectation off by more than say 1/1000000? In other words, if you were trying to calculate pi by checking the actual probabilities, how many digits can you get?