From Here: "The average human brain has about 100 billion neurons (or nerve cells) and many more neuroglia (or glial cells) which serve to support and protect the neurons (although see the end of this page for more information on glial cells). Each neuron may be connected to up to 10,000 other neurons, passing signals to each other via as many as 1,000 trillion synaptic connections."

From Here: "Today's transistors are about 70 silicon atoms wide, so the possibility of making them even smaller is itself shrinking. We're getting very close to the limit of how small we can make a transistor."

I will tackle this by first considering just how much space it would take to store such a brain; without processing: a pure "download". The minimum requirement would be to store every one of these connections, so that other future (much larger) machinery could reproduce the function of a given human brain. Just like we store a computer program in bits on a hard drive, but it cannot execute there, it must be loaded into memory, have hardware and power to translate the bits into activating circuits that accomplish instructions, and so on.

A single silicon atom is approximately spherical about 0.2 nm wide; presume a binary bit (0 or 1) could plausibly be stored in a cube about 0.3 nm on a side in some crystal-like matrix (in some future technology; but we can already manipulate individual atoms; so not entirely implausible).

How many bits do we need to store

Naively; Each of 100 billion neurons $(10^{11})$ can be connected to any other neuron; so we could store 100B bits per neuron with a 1/0 to indicate connected or not.

However, the average is only 7000 connections per neuron, but we don't know which 7000, so we need to store neuron numbers instead. It takes 37 bits to store a number up to 100B, so assuming the average holds for our quick estimate, about 49000 bits per neuron to store all the connections in the brain. We need $4.9\times 10^{15}$ bits to store the brain.

How large is the Crystal

We take the cube root of that to determine the number of elements per side in our crystal cube. The result is about 170,000 atoms per side. Multiplied by 0.3nm, our cube is 0.000051 meters per side; or 0.051 millimeters. If you prefer inches: 0.0020079, about 1/498 of an inch (larger than 1/500).

For comparison; human hair varies from about 0.002 to 0.006 in width; so this is in the range of the thinnest human hair. Given two such hairs crossing each other, the size of just their intersection can contain enough atoms to store all the connections in the brain. To store 1 billion people on such cubes would require 1000 times as much space on each side: So a 2-inch per side cube per billion people.

To Execute

Now you require transistors and support circuitry and power. Here is some information on that front. In that project, they require 100 elements per neuron and 20 per synapse (connection). Since we have 7000 connections per neuron, 20x7000 = 140,000 transistors for the synapses per neuron, versus 100 for the neuron itself: Plus we need both input and output; so figure about 250,000 transistors per neuron. On top of that, actual transistors extant today are 70 silicon atoms. Perhaps 24 is plausible; but I think we push credibility to get down to molecule size. Add cooling requirements (this would be blazing hot). So our problem is for execution we must scale up to 24 x 250,000 per neuron (a factor of 6 million). To get our storage cube to 6M times the volume; it scales up to 0.365 inches per side.

Now if you want to store a billion people; you need 365 inches per side, about 28,141 cubic feet. Presuming a processor 10 feet tall, you need a footprint 54 feet on a side; this could fit in a small warehouse. Or more likely a spaceship. Chances are you need a nuclear power plant to supply power, and need to run it cooled by empty space to about 3K, or -270C, shaded from the sun and well away from Earth (a heat source).

But those are engineering details!

posted almost 7 years ago

Amadeus‭

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