# How physically small can human intelligence get?

A common trope in science fiction is the idea that a human's consciousness and intelligence can be downloaded onto a computer. I recently had the idea that maybe in some apocalyptic scenario, millions of people could download their brains onto computers to be stored for later. They would still be able to think and have awareness during this time and maybe even communicate with each other. So, I got to wondering: how small can that computer reasonably get? Could you have a computer storing the information of a brain be the size of, say, a flash drive, or could it be done with nanotechnology? How far down could you go?

• This question does NOT have an answer at the link, at best it is a non-answer (as small as you want). This question should be re-opened. – Amadeus Jun 11 '17 at 22:40
• My design is about a micogram for the quantum computer proper, 10× that with necessary isolation shielding. I had to really try to come up with a way to do that many operations in a small enough package, and lowball estimates of data storage. – JDługosz Jun 12 '17 at 3:17

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!

• Storage bits: you considered addressing links, but did not discuss the weights associated with them, or the current state of the cell. But your figure for addressing is too high because most connections are local, and in fact a cortical column is a standard part that can be repeated from a template. – JDługosz Jun 12 '17 at 4:12
• One very important thing that you have overlooked here is that the state of synapses &c is analog, not binary, so you need at minimum several floats to represent the state, not just a bit. For a reference, about a decade ago simulating a few cortical columns (of which there are about 10^8 in the human brain) took a BlueGene supercomputer, which occupied a few dozen refrigerator-sized cabinets. – jamesqf Jun 12 '17 at 5:03
• @jamesq: The operation is analog; whether there is a connection is not. For storage purposes I think a single bit per pair is sufficient. As for operation: Transistors are actually analog! Recall they replaced amplifiers and have a graduated response map (or ramp) from fully closed to fully open. I wouldn't assume that how IBM did it is the best way of all time to get the job done. I am just trying to compute a minimum which may not be realizable; e.g. you can't hide this in a garage: But it might fit in the space of an existing large mall or factory; you don't need a square mile. – Amadeus Jun 12 '17 at 9:26
• @Amadeus: The action potential firing by one neuron and propagating to the connected neurons is a binary event. The cumulative state that determines whether the firing will or will not take place is very much an analog process, though. I do realize you're trying to guess at a minimum: what I'm trying to say is that that minimum is probably much larger than you think. – jamesqf Jun 12 '17 at 20:53
• Definitely worth noting that 1 bit per atom on each atom in a crystal matrix would be an absolute physical laws minimum on size. This avoids the messy issue of "how the hell do you read it?" But we can scale up easily enough by multiplying the number of atoms needed by the current scale of electronics and adding some padding and bussing space. So starting at a grain of sand and adding all that in...yeah, you might end up with a crystal the size of a current flash drive. – Draco18s Jun 12 '17 at 21:10

I think this is one of those questions that ultimately boils down to "whatever size you need it to for your story", depending on how far into the future it's set. On the one hand, while we're not able to model the human mind, we've made a lot of recent advances in neural networking and artificial intelligences, and many of the cutting edge tools that have been developed can be run on a high-end desktop (just be sure to get the best graphics card you can afford). On the other hand, computer hardware is constantly both increasing in performance and shrinking in size. The smartphone in your pocket has more computing power than all of the computers that put mankind on the moon back in the 60s.

At some point in the future, we'll be able to model neural nets complex enough to replicate a human mind, and figure out a way to "upload" ourselves. None of us know exactly when we'll reach that point. It may happen in ten years, it may take a hundred, it may take a thousand. And of course, your apocalypse doesn't have to happen immediately after we've reached that point. Brain-uploading technology could be well-developed and centuries old by the time of your story.

And similarly, no one knows how small or how powerful computers will have become by then. If we've managed to get quantum or optical computing working by then, the computers capable of doing this might be desktop-sized, or even smaller. You might be able to run a human brain-model on your supersmartphone. You could even dream up some sort of "hyperspace" computer that is the size of a grain of rice and yet more powerful than the entirety of modern-day computing.

So, having said all of this, you are asking about uploading millions of people into an environment where they're all networked with one another. I would expect that would require at least some sort of significant size, if you're trying to stay within the bounds of physics as we know it. I'm picturing something data-center-sized, unless you're bringing hyper-advanced tech into play.

• I don't find «some sort of significant size» to be a useful answer. – JDługosz Jun 12 '17 at 4:07
• Which is why the next sentence specifies "something data-center-sized". :-p – Salda007 Jun 12 '17 at 7:45
• The question that needs to be asked here is whether neural nets or "artificial intelligence", however useful they may be for automating certain tasks, actually replicate the actual mind (human or animal) in any meaningful way. – jamesqf Jun 12 '17 at 20:56

Very small. We have only applied serious resources to research in neural nets and quantum computing since the 80's. Assume some hefty developments in those areas, and a building the size of a large shopping mall might house the equipment for storing a planetary population. This makes the reasonable assumption that there would be similar geometric progressions to Moore's law in those technologies. https://en.wikipedia.org/wiki/Moore%27s_law A great example of this is that discrete parts were used to emulate neurons in the 80's to wire up neural nets that had no more than a cockroaches nervous system. Today you can buy for \$4000 a credit card board that has 4096 neurons. http://www.general-vision.com/hardware/neurostack/

• Do you think you could quantify better than ”very small”? – JDługosz Jun 12 '17 at 4:08
• Sure I could. I could even post calculations to back up my statements that are wrong by two orders of magnitude and ask somebody else to check my calculations. I made a very conservative statement that a large building could hold a planetary populations consciousness and dispensed with making any calculations that would require making possibly invalid assumptions. – steverino Jun 12 '17 at 18:25

My design is about a micogram for the quantum computer proper, 10× that with necessary isolation shielding. I had to really try to come up with a convinsing way to do that many operations in a small enough package, and lowball estimates of data storage.

In this post I go over the needed resources. The smallest is of course a direct program not an emulation of our own physical layers:

you already knew how the brain worked to produce intelligence, writing that program fairly directly would require 1015 FLOPS (Blue Gene/P circa 2007) and 100 Terabytes.

The size requirement is driven by the data storage. Figure 1 atom per bit? Figure the needed volume for that.

Some other answers go over the connectivity, having more wiring than processing. But real hardware already avoids that problem: 1 core simulates many nurons, and data transfer is over network links, not point to point between every pair of cores! With a program (not a simulation) the concept is clearer — each op needs its own argument data, and as long as the store can keep up with the mill, a normal memory back attached to the processor will suffice.

In my quantum computer description from my story (in the linked post) it avoids all wiring by having waves of interference patterns play over the storage matrix. More generally, you can imagine a 3D crystal being addressed by lasers that find the crystal transparent to individual beams and non-linear where they intersect. So no wiresv the probe light passes through the storage itself without problems.

A quantum computer can perform a lot of operations. In fiction they are just ridiculously fast, and that may hold for you. In reality they can solve or search certain classes of problems using superposition as parallelism to find the right one; the program would have to be written to use that kind of operation to get that kind of exponential speedup. But even classical computation is fast if the parts are very tiny. If you do logic usingbspin states of single atoms, the speed would be limited to lightspeed getting information through it. In my fictional treatment, I try to minimise the volume used for most common calculations, to boost the speed imposed by this limit.

If you have multiple nano-sized cores, unlike my design, you can have a lot of them in what we consider a small space. So you might consider a design that's a cube of 1000 to a side or a billion nano-cores, each having simple processing capability and some local memory. Look up how many gates a CPU needs — say, 12000 for the ARM M0 — and say each gate is made from just a few atoms.

A billion × 12000 × 10 is about 1014 atoms, which is about 2 nanograms of carbon if I figured that right. Add 1014 bits of storage at about the same size for single-atom memory. If memory takes up several atoms, or is stored in multiple copies, multiply that out.

Give the whole thing an extra order of magnitude for measure, and that's 50 nanograms. At 3.5 g/cm³ that’s about 25µm cube. (Somebody check my calculations please.)