Why does space have 3 dimensions? 3 is the minimum number of dimensions in which a graph (such as a communication network) can be fully connected without intersecting edges. It is the only number of dimensions in which knots are possible. A 1975 paper by Li and Yorke showed that any dynamic system with a cycle of length 3 must have all possible cycle lengths and also be chaotic.
So perhaps you need 3 dimensions for complex behavior. But 1 dimensional cellular automata and Turing machines can also exhibit complex behavior. Just not as efficiently. If the universe is a simulation, or part of a multiverse, then the number of dimensions we observe tells us nothing about the number of dimensions in the universe doing the simulation. -- Matt Mahoney, [email protected] On Thu, Mar 26, 2026, 2:01 AM Quan Tesla <[email protected]> wrote: > James, your intuition is correct abd also not. For starters, the SM > couldn't yet mathematically explain the dimensionality of time. That's an > arbitrary hole that needs plugging, especially with real quantum memory and > addressing concepts, such as the quantum eraser and retrocausility. > > These are critical data/information management horizons to cross for > activating dimensionless potential. > > Within the theoretical specification of the proposed entangled E8xE8, > lattice (as 248D), data storage limitations would only be arbitrarily > imposed via the constraints of 4D architectures. This is synonymous to a > supersonic jet that pilots choose to drive on the limiting road structure > from points A to B. > > However, based on reliable theory, the value of 3 is also an auto-elected > limit by nature. > > We should temper our intuiton with the certainty that both the SM and QM > model are incomplete. > > There's much work still to be done. > > On Thu, 26 Mar 2026, 01:45 James Bowery, <[email protected]> wrote: > >> There is quite a lot of work in "information physics" that indicates 3 >> dimensions aren't arbitrary. One aphorism I've run across is for a >> sufficiently large space, the maximum global dimensionality of a discrete >> and finite space with a homogeneous distance function is three. >> >> When I say "I suspect" I'm not making much of a claim let alone a >> conjecture that could be "even wrong". It's more about my intuition from >> working with some of the founders of the Alternative Natural Philosophy >> Association that the dimensionless constants of nature arise from an >> inevitable combinatorial explosion given certain very simple and plausible >> assumptions about distinguishability that were originally derived within >> the Cambridge Language Research Unit subsequent to WW II. >> >> I'll just say that the number "3" is not arbitrary from that standpoint, >> nor is its connection to language. >> >> >> >> On Mon, Mar 23, 2026 at 3:29 PM Matt Mahoney <[email protected]> >> wrote: >> >>> >>> On Mon, Mar 23, 2026, 1:54 PM James Bowery <[email protected]> wrote: >>> >>>> >>>> >>>> On Sat, Mar 21, 2026 at 12:28 PM Matt Mahoney <[email protected]> >>>> wrote: >>>> >>>>> ... >>>>> >>>>> There's something I'm not getting. Why does the brain need 10^15 >>>>> synapses to store 10^9 bits? Maybe it's a speed optimization, like how >>>>> a server farm has a million copies of Linux, or your body has 10^13 >>>>> copies of your DNA. Or is it something else? Is it the reason we >>>>> didn't solve AI in 2000? >>>>> >>>> >>>> I suspect it has to do with Bekenstein bound placing data points in >>>> such a high dimensional space that they are all on a surface where they can >>>> be treated as orthogonal. >>>> >>> >>> How is that so? I realize that random bit vectors all have an average >>> Hamming distance of n/2, which puts them all on a hypersphere surface >>> surrounding any one of them. But word vectors are not like that. Some are >>> more correlated than others. They would have to be, because otherwise text >>> would not be predictable and we wouldn't have AI. >>> >>> I realize that other parts of the brain are highly repetitive, like >>> thousands of copies of line and edge detectors in the visual cortex, or >>> thousands of motor neurons controlling the same muscle. Language evolved >>> relatively recently and there is not a lot of evolutionary pressure to >>> optimize it. It uses maybe 10% of our brain, or 2% of resting metabolism. >>> >>> The Bekenstein bound is different. Space only has 3 dimensions. It might >>> explain the size of the proton* but I don't see how it explains language. >>> We already have LLMs that are not far off the 0.3 bits per parameter stored >>> in a Hopfield net. >>> >>> * The Bekenstein bound of the Hubble radius is A/ln(16) of its surface >>> area in Planck units, or 2.95 x 10^122 bits. This is about the number of >>> protons or neutrons that would fit inside, which is a strange coincidence >>> given that the number depends only on h, G, 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/Tc9fe35df94409188-M13af39e62af60adfb5eb92e2> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Tc9fe35df94409188-M0e434bc085cabc98d07dcede Delivery options: https://agi.topicbox.com/groups/agi/subscription
