[ExI] The physical limits of computation

[Stuart LaForge]

On 2024-01-19 12:34, Jason Resch via extropy-chat wrote:
> I thought I would share this work with the extropy list, as it covers
> topics of relevance to the future of technology and future
> civilizations.
> 
> In it, I describe the physical bounds on information storage,
> computation, computronium, black hole computers, and the limits of the
> universe as a whole:
> 
> https://drive.google.com/file/d/124q3ni51E3sf9kMC_sNKgP3ikcl8ou1t/view?usp=sharing
> 
> Any comments, or corrections would be most welcome.

Since you asked for it... ;)

On p.18 you wrote:
"The DNA molecules that compromise your genome encode
750 MB of data — and they fit in a cell nucleus just five
millionths of a meter across."

Nitpicking here but the information content a cell nucleus is twice that 
figure or 1.5 GB. This is because you have two copies, really versions, 
of every chromosome in each of your cells, one from your mother and one 
from your father. Each of your cell nuclei contains approximately 2 
meters of DNA. As an adult male you have approximately 36 trillion 
nucleated cells, so you have 72 trillion meters of DNA inside of you. 
For perspective, if you made a circle out of all the DNA inside you, the 
ring of DNA could encircle the sun out well past Jupiter's orbit and 
almost reach Saturn. So if all the DNA in your body were considered, 
your total DNA's information capacity, at 750 MB per meter, would be 108 
zettabytes.

So the Matrix got it wrong. If intelligent machines were to exploit us, 
it wouldn't be as an energy source but as data storage. ;)

On p.49 you wrote:
"Using the holographic principle to model the observable
universe as a black hole with a radius of 46.5 billion light
years, we find it contains:
2.33 * 10^123 bits
Which is the total information content of the universe."

The observable universe cannot be modelled as a black hole because it is 
defined by the particle horizon which, while it is one of the three 
cosmic horizons (Hubble horizon, event horizon, and particle horizon), 
it is NOT the event horizon in a technical sense and therefore using the 
holographic principle on it is not really physically valid. The particle 
horizon defining the observable universe is the boundary of everything 
we can currently see in our past light cone since the big bang. As you 
say, it is 46.5 billion light years away from us.

The cosmological event horizon on the other hand is the boundary 
encompassing everything that we will ever be able to affect in our 
future light cone. The cosmological event horizon is at approximately 16 
billion light-years from us. You could consider it the the largest 
distance an object could be from us which, if we could wait forever, we 
could bounce a radar signal off of and get a signal back.

The Hubble horizon, however is defined on our plane of simultaneity in 
the present as the boundary at which space is expanding away from us at 
the speed of light at this precise moment in time. As such, the Hubble 
radius is a proper distance defined in the present moment at c/H = 14.4 
billion light years from us.

My own work on causal cell theory demonstrates that the Hubble horizon 
located at the Hubble radius is the most valid event horizon to set the 
Schwarzschild radius at for modeling our causal cell as a black hole. 
This is because it the proper distance to the causal boundary of the 
space-time that we are able to causally affect by an action we do right 
now. It is also easier to work with because it depends on only the speed 
of light (c) and the Hubble constant/parameter (H). If H was constant, 
the cosmological event horizon would correspond exactly with Hubble 
horizon. Because H is getting smaller, however, that means that the 
Hubble radius is getting farther and the Hubble horizon is increasing in 
area. In any case, as can be seen in the upper right corner of this 
graph that BillK sent to the list earlier, the Hubble radius corresponds 
to the Schwarzschild radius of a black hole with a mass the same as that 
of our causal cell. It lies exactly on the line that the graph uses to 
depict black holes. The universe modelled in general relativity is 
boundless and could well be infinite so it cannot be a black hole. But 
there ARE boundaries which define our causal cell which is finite and 
therefore COULD be a black hole.

https://www.universetoday.com/163927/everything-in-the-universe-fits-in-this-one-graph-even-the-impossible-stuff/#google_vignette


It should be noted all three horizons change over time, and in the far 
future our causal cell will reach its maximum extent possible, where the 
Hubble constant will stop changing and the Hubble horizon will stop 
moving. This future state will be a black hole that is composed entirely 
of dark anergy and would be the largest black hole possible in a causal 
cell composed entirely of dark energy or the cosmological constant. In 
other words a blackhole composed entirely of the vacuum energy of empty 
space where the cosmological event horizon coincides exactly with the 
black hole event horizon. This is also called a Nariai black hole and is 
a feature of the De Sitter- Schwarzschild metric. If current estimates 
of the cosmological constant are correct, then this ultimate  black 
hole/ causal cell will have a radius of about 16 billion light years 
which coincides with the current cosmological event horizon.

I hope that I am not being overly pedantic with regards to what you were 
trying to show about limits of computation. I sort of went down this 
same track myself a few years ago and came up with answers within an 
order of magnitude or so of yours, so you are on the right track.

Stuart LaForge