On Mon, Feb 3, 2020, 7:52 AM John Rose <johnr...@polyplexic.com> wrote:
> Talking big numbers, what is an expression of the sum of ALL edit > distances in the universe? Not just Hamming but say Levenshtein distance, > for sequences of unequal length. The distance from one sequence to ALL > other sequences, summed for all sequences. > Less than 8.7 x 10^244 bits. That's the square of the Bekenstein bound of a black hole with a Schwartzchild radius equal to the Hubble radius,13.8 billion light years. Edit distance expressed as the shortest program that inputs one string and outputs the other is equal to the size of the output for the vast majority of random string pairs. > Gotta be yuge! Something on the order of 10^(N!) or even bigger. Though it > could be reduced I suppose, deduplicated. > Not really. It's much smaller than 3^^^^3, Graham's number, or iterated Ackerman functions, which are too large to correspond to anything physically imaginable. > And then how does that change over time…. > The Bekenstein bound is 1/ln 16 times surface area in Planck units, so it grows as the universe expands. Kinda gets ya wondering. And does information have mass. Yes, I answered this in Quora. Reading and writing bits takes energy equivalent to a mass of kT ln 2/c^2, where k is Boltzmann's constant, T is the microwave background temperature (3 K), and c is the speed of light. It's a tiny number, but what you might notice is that the Bekenstein bound gives a value 10^30 times the mass of the universe. That's because most of the entropy of the universe is not accessible. You can only encode and read back 10^90 to10^92 bits using the universe's 10^80 atoms as a giant storage device. There's not enough mass/energy to read the rest. Is dark matter actually information? No, it has all the characteristics of ordinary matter in objects smaller than stars, like planets or comets, but free floating and not orbiting stars. That's what makes it dark. We don't know for sure, but to me it seems the most plausible explanation. Not to be confused with dark energy, which is what ordinary gravity looks like near a black hole. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T65747f0622d5047f-M53bb40814f3b38e950fe53fc Delivery options: https://agi.topicbox.com/groups/agi/subscription
