I get it now: pradius = UnitConvert[codata["ProtonRMSChargeRadius"],"PlanckLength"] = (5.206\[PlusMinus]0.012)*10^19Subscript[l, P] pvolume=(4/3) Pi pradius^3 = (5.91\[PlusMinus]0.04)*10^59Subsuperscript[l, P, 3] h2pvolume=codata["HubbleVolume"]/pvolume = (1.024\[PlusMinus]0.020)*10^123 hsurface=UnitConvert[4 Pi codata["HubbleLength"]^2,"PlanckArea"] = (8.99\[PlusMinus]0.11)*10^122Subsuperscript[l, P, 2] RelativeError[QuantityMagnitude[h2pvolume],QuantityMagnitude[hsurface]] = -0.122\[PlusMinus]0.023
As Dirac-style "Large Number Coincidences" go, a -12±2% relative error is quite remarkable since Dirac was intrigued by coincidences with orders of magnitude errors! However, get a load of this: CH4=2^(2^(2^(2^2-1)-1)-1)-1 = 170141183460469231731687303715884105727 protonAlphaG=(codata["PlanckMass"]/codata["ProtonMass"])^2 = (1.69315\[PlusMinus]0.00004)*10^38 RelativeError[protonAlphaG,CH4] = 0.004880\[PlusMinus]0.000022 0.5±0.002% relative error! Explain that. On Sun, Mar 31, 2024 at 9:45 PM Matt Mahoney <mattmahone...@gmail.com> wrote: > On Sun, Mar 31, 2024, 9:46 PM James Bowery <jabow...@gmail.com> wrote: > >> Proton radius is about 5.2e19 Plank Lengths >> > > The Hubble radius is 13.8e9 light-years = 8.09e60 Planck lengths. So > 3.77e123 protons could be packed inside this sphere with surface area > 8.22e122 Planck areas. > > The significance of the Planck area is it bounds the entropy within to A/4 > nats, or 2.95e122 bits. This makes a bit the size of 12.7 protons, or about > a carbon nucleus. https://en.wikipedia.org/wiki/Bekenstein_bound > > 12.7 is about 4 x pi. It is a remarkable coincidence to derive properties > of particles from only G, h, c, and the age of the universe. > >> >> *Artificial General Intelligence List <https://agi.topicbox.com/latest>* > / AGI / see discussions <https://agi.topicbox.com/groups/agi> + > participants <https://agi.topicbox.com/groups/agi/members> + > delivery options <https://agi.topicbox.com/groups/agi/subscription> > Permalink > <https://agi.topicbox.com/groups/agi/Teaac2c1a9c4f4ce3-Me023643f4fef1483cfab3ad6> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Teaac2c1a9c4f4ce3-M035b6d3a4509d0706e916fef Delivery options: https://agi.topicbox.com/groups/agi/subscription
