You can't measure anything with infinite precision because of quantum mechanics. The best you can do is an integer multiple of Planck's constant, 4.135667696 x 10^-15 electron volt seconds. You can sample voltage at a higher rate with less precision.
This applies to any measurement. We commonly measure time and distance, which are not quantized, but these are actually inferred quantities in our model of the universe. All measurements consist of counting particles, such as photons bouncing off a tape measure or clock face. We only observe particles because they are the solution to a huge, deterministic second order differential equation describing the quantum state of the universe. We can't know that state, so the particles appear to us to be random. The observable universe has finite entropy given by the Bekenstein bound of the enclosing surface of 4 nats = 5.77 bits per Planck area. For a sphere with radius 13.8 billion light years, it's 2.95 x 10^122 bits. But only about 10^90 to 10^92 bits are usable for computation or storage because the rest is heat. Lloyd estimated 10^90 by calculating how much information can be encoded in the positions and velocities of the 10^80 atoms in the universe within the uncertainties of Planck's constant. Alternatively, I estimate 10^92 as the mass energy of the universe (10^53 kg = 10^70 J) divided by Boltzmann's constant at the CMB temperature of 3 K. This is why immortality is not possible. The universe will eventually die. I estimate that the Kolmogorov complexity of a human is 10^9 bits of DNA + long term memory. This gives us at most 10^83 conceptual lifetimes before the universe ends. It also gives us a cost estimate for the software. A line of code costs on the order of $100 at 10 lines per day, and compresses to 16 bits in my tests. Thus, 60M lines of code costing $6 billion, which is negligible (0.0006%) compared to the $1Q cost of hardware and training for AGI. On Sun, Aug 20, 2023, 9:08 PM John Rose <johnr...@polyplexic.com> wrote: > On Wednesday, August 16, 2023, at 3:38 PM, Matt Mahoney wrote: > > On Tue, Aug 15, 2023, 7:44 AM John Rose <johnr...@polyplexic.com> wrote: > > I suspect human K complexity is larger than most people realize. > > > It's about 10^9 bits of long term memory (based on recall tests for words > and images) and 10^8 to 10^9 bits in our DNA. The compressed size of human > genome is 5 x 10^9 bits, but only 8% is functional and the rest is not > easily compressed because it accumulates random mutations that don't get > removed by natural selection. The coding parts are more repetitive. > Evolution can only add 1 bit of information per population doubling > generation. > > > Yes, as an estimate of K. But, for example, I can estimate the distance to > a particular star by evaluating its brightness and be off by 1000x. The > real K complexity of the distance might be quite large. If you look at an > electrical circuit and say it’s 5V that’s just a convenient average > estimate. The exact voltage could be trillions of bits as in > 4.999981347534783487… And that would have to be sampled over a period of > time since it would be changing rapidly. Also, the sampling itself effects > the value at the quantum level. The K of a sample typically isn’t the K of > a physical object it’s an estimate from a finite string representation of > the object, or a virtualized perceptual instance. The specific human's K IS > and the perception's K- estimate of the human is OUGHT. Throwing stuff away > is lossy. > > So, the real K complexity of a human being would be quite large. The size > would less than or equal to the K 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/T772759d8ceb4b92c-M5ebad4e16c1888178f030018> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T772759d8ceb4b92c-Me7e0ae170dc73a24a81fdc88 Delivery options: https://agi.topicbox.com/groups/agi/subscription
