On Wednesday, October 16, 2024, at 2:49 PM, Matt Mahoney wrote: > You first equation looks like the Bekenstein bound of a black hole with mass > M. It gives the entropy as A/4 nats (1 nat = 1/ ln 2 ≈ 1.44 bits) where A is > the area of the event horizon in Planck units. The Schwartzchild radius of a > black hole is 2GM/c^2, thus the nonlinear dependency on M^2. I calculated the > entropy of the universe at 2.95 x 10^122 bits based on a radius of 13.8 > billion light years. This is close to Lloyd's rough estimate of 10^120 qubit > operations possible by converting the mass of the universe (10^53 kg) to > 10^70 J over the age of the universe, 4 x 10^17 s, using your second equation. > > Unfortunately, most of this entropy is heat, not available for computation. > Lloyd estimated that the universe could encode 10^90 bits in the states of > 10^80 particle positions and momentums within the limits of Heisenberg's > uncertainty. I independently estimated that 10^70 J could write 10^92 bits > within the Landauer limit at the CMB temperature of 3 K. Yes, thank you for pointing out an area of improvement needed in the paper. Your assertion about entropy would be taken into account in the efficiency factor η(M), as well as other things such as relativistic effects. The inequality becomes an absolutely ideal (unobtainable) upper bound when you set η(M) equal to 1. I need to make this more clear.
On Wednesday, October 16, 2024, at 2:49 PM, Matt Mahoney wrote: > I'm interested in how you would proceed from here to build a self optimizing > AGI. Evolution would be one way. The biosphere uses 10^41 carbon atoms to > encode 10^37 bits of DNA and has performed 10^48 DNA base copy operations and > 10^50 amino acid transcription operations over the last 10^17 s to evolve > humans. That's 10^33 operations per second. The Earth receives 90,000 TW of > sunlight at the surface, of which 500 TW is converted to carbohydrates by > photosynthesis, or 10^-17 J per operation. The Landauer limit at 300K is 4 x > 10^-21 J. By comparison, a synapse operation takes 10^-15 J and a transistor > operation 10^-11 J. Global electricity production is 18 TW. I actually do not know how to build an AGI, and the paper does not address that. What the paper is about is what it would 'look' like if an AGI/ASI entity decided to maximize its computing power: what that process would 'look' like and what bounds there would be on that computing power for a given amount of 'computronium' material. In the next versions of the paper, I will add a section for the speculative concept of an AGI/ASI entity ascending into a computronium abyss in order to acquire maximum computing power. Why would an AGI/ASI do this? There could be a variety of reasons, but perhaps it would be an attempt to figure out how to avoid the heat death of the universe. Additionally, in later versions of the paper, I want to: * *Formalize the mathematics and algorithmic aspects of the dual search for more efficient computronium and more powerful predictive algorithms (and related algorithms). *For any given computing time, the abyss must determine whether to devote computing resources either towards finding more efficient computronium or more powerful predictive algorithms. Finding breakthroughs in either search category is chaotic, but perhaps there are ways to optimize determining which to focus on at any given time. I am no mathematician and so I will probably (and unashamedly) outsource the development of the algorithms/equations to optimize the dual search, as well as the verification of their accuracy. * *Formalize the mathematics and algorithmic aspects of how breakthroughs in the development of more efficient computronium (and more powerful predictive algorithms) would propagate through the abyss. *The breakthroughs would be transmitted at the speed of light as cannibalistic wavefronts (as soon as a computing unit within the abyss receives the recipe for the more efficient computronium, it reconfigures itself into the new version with the more efficient computronium). Since the breakthroughs can't be transmitted faster than the speed of light, it is possible for other parts of the abyss could discover even more efficient computronium. At that point a counter wavefront transmission is generated. In the same vein of your line of thinking, I would argue that the Earth is a highly unoptimized computronium abyss itself, both with respect to biological processes (as you point out) and man-made computing processors (our computronium variants of CPUs, GPUs, TPUs etc. so-to-speak) since both world population is growing (slowed down significantly but still growing), which means more brains and every year and more and more of Earth's physical matter and energy is converted into man-made 'computronium' variants. On Wednesday, October 16, 2024, at 2:49 PM, Matt Mahoney wrote: > You can't make transistors smaller than atoms, so further advances in Moore's > law will require nanotechnology, moving atoms instead of electrons. Assuming > this happens and global computing power doubles every 3 years, it will take > about 130 years for self replicating nanotechnology to catch up to and > displace DNA based life. Yes, perhaps the Barrow Scale https://en.wikipedia.org/wiki/John_D._Barrow could be a general guide here, and it would be interesting to look at the specific computing boundaries based on where a civilization is on that scale. On Wednesday, October 16, 2024, at 2:49 PM, Matt Mahoney wrote: > What would be your approach? I don't have an approach for directly trying to achieve AGI. I am, however, starting to work on a software project that will help determine where we are in terms of our algorithmic chops. It will be a competitive computing platform for Matching Pennies competitions and other turn based games where contestants can submit programs that run safely in a sandbox with strict resource constraints to compete in these games. It is based on the emerging technology of WASM/WASI: https://wasi.dev/. I was actually partially inspired by your competitions for data compression. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T86ee7f7b146878af-Mcf5d356db18f237b37478351 Delivery options: https://agi.topicbox.com/groups/agi/subscription
