A Sense of Scale

>>> age=14*10**9
>>> c=3*10**8
>>> proton=10**-15
>>> universe_size=age*c
>>> face_universe=universe_size**2
>>> cube_face_universe=face_universe*6
>>> cube_face_universe_in_protons=cube_face_universe/(proton**2)
>>> cube_face_universe_in_protons

The area above (around 10^68) is an upper bound on the area of a sphere the size of the universe. If we wanted to construct such a sphere from protons, and wondered how many it would take if we wanted to leave no “holes”, we would need to know pi to within 69 places. As this is the most ambitious project I can imagine that will require knowing pi to a high degree of accuracy, this is my upper limit on how much accuracy will ever be needed.

I know it to 150 places…


6 Responses to A Sense of Scale

  1. Ben Leitner says:

    Someone has too much free time on his hands.

  2. Not Impressed says:

    This is utterly ridiculous. Just a mish-mash of illogical reasoning, misunderstood science, bad arithmetic, and self-promotion (“I know pi to 150 places”…Really? Wow).

    First off, your units are incompatible. “age” is given in years, while “c” is given in meters per second, yet you multiply the two without proper factors. You’re already off by 8 orders of magnitude.

    Second, you make estimate the *surface area* of a bounding box, then divide it by the *surface area* of the proton (again leaving out factors), never really needing surface area or even pi, since you have the diameter of the proton already.
    Why not realize that since you never bothered to calculate the surface area of a sphere, you don’t need to know pi to even a single place?
    If you’re going to be lazy and and half-assed with your calculations, why not go whole hog and just list c ** c as your upper limit?

    Good God, man. You should be ashamed of yourself.

    PS Ever heard of quantum mechanics? Electrostatic force? Good luck constructing your sphere. Oops, I meant cube.

  3. Ben L. says:

    Hmmm… one more thought. What about universe volume in protons? The extra factor of r will give a higher bound, so you’d need to know pi to more places.

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