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-Mad595c3e3a8538380e77b94f> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Tc9fe35df94409188-M6d427e193a49441de744ec85 Delivery options: https://agi.topicbox.com/groups/agi/subscription
