Uploading

Transferring Consciousness from Brain to Computer

Ralph C. Merkle

Xerox PARC 3333 Coyote Hill Road Palo Alto, CA 94304

Your brain is a material object. The behavior of material objects is described by the laws of physics. The laws of physics can be modeled on a computer. Therefore, the behavior of your brain can be modeled on a computer. Q.E.D.

So why haven’t we done it already?

Well, we’d need a fairly big computer. And we’d have to get a very detailed description of your brain. The only ways we know of getting that detailed a description are destructive. That means we’d have to take your brain apart. Most people most of the time object to this. Even if you don’t object, the legal system would. Destructive analysis of someone’s brain is viewed dimly by the courts. These minor objections could be circumvented by waiting until you are legally dead. At that point, the courts wouldn’t object if you didn’t object. And although brain function has usually (though not always) stopped by the time you’re declared legally dead, the information should still be there for a while (though you’d probably lose short term memory). When we power down the system we lose volatile memory, but non-volatile memory and the circuitry are still there.

Let’s assume we’ve solved the legal hassles, and we’re preparing to analyze your brain using the new, advanced Mark 7 Neural Analysis System. We’ve hooked up the Mark 7 to the Intel Pentadecium. The first question we might ask is: how much memory should we buy? How many bits does it take to describe your brain?

Your brain is made of atoms. Each atom has a location in three-space that we can represent with three coordinates: X, Y, and Z. Atoms are usually a few tenths of a nanometer apart. If we could record the position of each atom to within 0.01 nanometers, we would know its position accurately enough to know what chemi-

cals it was a part of, what bonds it had formed, and so on. The brain is roughly .1 meters across, so .01 nanometers is about 1 part in 10¹⁰; we need to know the position in each coordinate to within one part in ten billion. A number of this size can be represented with about 33 bits. There are three coordinates, X, Y, and Z, so the position of an atom can be represented in 99 bits. An additional few bits are needed to store the type of the atom (whether hydrogen, oxygen, carbon, etc.), bringing the total to slightly over 100 bits.

With about 100 bits per atom we could certainly describe your brain as precisely as we’d need. (Purists might object that this does not take into account the positions of the electrons. While this is technically true, it’s usually not hard in biological systems to infer the electronic structure if you have the coordinates of all the nuclei. We might wish to have a little more information, e.g., Na+, OH-, etc. With this additional ionization information our knowledge of the system would be essentially complete). Examining the published plots of the number of atoms required to store a bit of information as a function of the year, we find that somewhere between 2010 and 2020 we should be able to store one bit with one atom. If one atom in your brain is described by 100 bits, and each bit occupies one atom, then the memory required to hold a digital description of your brain accurate to the last atom would occupy about 100 times the size of your brain. The brain is somewhat over one liter, so it would require a computer memory with a volume of somewhat over one hundred liters to encode the location of each and every atom in the brain in a digital format. There are some-

what over 10²⁶ atoms in the brain, so our storage system needs to hold about 10²⁸ bits.

For those readers who might view the feasibility of such a memory system with some doubt, recall that DNA requires roughly 16 atoms to store a bit of information (not including the water in which it floats). Your body, with 10³⁰ bits per cell stored in DNA and 10¹⁴ cells, stores almost 10²⁴ bits of information (and it’s unlikely that you’re an optimal memory storage device). We’re assuming only a modest improvement in storage technology over DNA; and as we’ll see, we don’t actually need as much storage as we’ve computed here.

How Many Bits to Describe a Molecule

While such a feat is remarkable, it is also much more than we need. Chemists usually think of atoms in groups — called molecules. For example, water is a molecule made of three atoms: an oxygen and two hydrogens. If we describe each atom separately, we will require 100 bits per atom, or 300 bits total. If, however, we give the position of the oxygen atom and give the orientation of the molecule, we need: 99 bits for the location of the oxygen atom plus perhaps 20 bits to describe the type of molecule (“water”, in this case) and perhaps another 30 bits to give the orientation of the water molecule (10 bits for each of the three rotational axes). This means we can store the description of a water molecule in only 150 bits, instead of the 300 bits required to describe the three atoms separately. (The 20 bits used to describe the type of the molecule can describe up to 1,000,000 different molecules: more than are present in the brain).

As the molecule we are describing gets larger and larger, the savings in storage gets bigger and bigger. A whole protein molecule will still require only

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150 bits to describe, even though it is made of thousands of atoms. The canonical position of every atom in the molecule is specified once the type of the molecule (which occupies a mere 20 bits) is given. A large molecule might adopt many configurations, so it might at first seem that we’d require many more bits to describe it. However, biological macromolecules typically assume one favored configuration rather than a random configuration, and it is this favored configuration that we will describe.

Describing the brain one atom at a time is much less compact than describing it one molecule at a time.

Do We Really Need to Describe Each Molecule?

While this reduces our storage requirements quite a bit, we could go much further. Instead of describing molecules, we could describe entire sub-cellular organelles. It seems excessive to describe a mitochondrion by describing each and every molecule in it. It would be sufficient simply to note the location and perhaps the size of the mitochondrion, for all mitochondria perform the same function: they produce energy for the cell. While there are indeed minor differences from mitochondrion to mitochondrion, these differences don’t matter much and could reasonably be neglected.

If we’re concerned about the behavior of the nervous system then worrying about the location of each mitochondrion seems excessive. We could describe an entire cell with only a general description of the function it performs: this nerve cell has synaptic connections of a certain type with that other cell, it has a certain shape, and so on. If we assume there are 10¹⁵ synapses, and if we need (very roughly) 100 bits per synapse, this brings us down to 10¹⁷ bits. We could be yet more economical of storage: a group of cells in the retina might perform a ‘center surround’ computation, so the entire group (including all their synapses and fine morphology) could be summarized in one succinct functional description.

How Many Bits Do We Really Need?

This kind of logic can be continued, but where does it stop? What is the most compact description which captures all the essential information? While many minor details of neural structure are irrelevant, our memories clearly matter. If we

can’t fully describe long term memory we’ve gone too far.

How many bits does it take to hold human memory? Cherniak[6] said: “On the usual assumption that the synapse is the necessary substrate of memory, supposing very roughly that (given anatomical and physiological ‘noise’) each synapse encodes about one binary bit of information, and a thousand synapses per neuron are available for this task: 10¹⁰ cortical neurons x 10³ synapses = 10¹³ bits of arbitrary information (1.25 terabytes) that could be stored in the cerebral cortex.” A problem with hardware-based estimates is that they have to make assumptions about how the information is stored. The brain is highly redundant and not completely understood: the mere fact that a great mass of synapses exists does not imply that they are in fact contributing to the memory capacity. This makes the work of Landauer[7] very interesting for he has entirely avoided this hardware guessing game by measuring the actual functional capacity of human memory directly.

A Functional Estimate of Human Long Term Memory Capacity

Landauer works at Bell Communications Research — closely affiliated with Bell Labs where the modern study of information theory was begun by C. E. Shannon to analyze the information carrying capacity of telephone lines (a subject of great interest to a telephone company). Landauer naturally used these tools by viewing human memory as a novel “telephone line” that carries information from the past to the future. The capacity of this “telephone line” can be determined by measuring the information that goes in and the information that comes out, allowing the great power of modern information theory to be applied.

Landauer reviewed and quantitatively analyzed experiments by himself and others in which people were asked to read text; look at pictures; hear words, short passages of music, sentences and nonsense syllables. After delays ranging from minutes to days or longer the subjects were then tested to determine how much they had retained. The tests were quite sensitive (they did not merely ask “What do you remember?”) often using true/false or multiple choice questions, in which even a vague memory of the material would increase the chances of making the correct choice. Often, the differential abilities of a group that had been exposed to the material and another group that

had not been exposed to the material were used. The difference in the scores between the two groups was used to estimate the amount actually remembered (to control for the number of correct answers an intelligent human could guess without ever having seen the material). Because experiments by many different experimenters were summarized and analyzed, the results of the analysis are fairly robust; they are insensitive to fine details or specific conditions of one or another experiment. Finally, the amount remembered was divided by the time allotted to memorization to determine the number of bits remembered per second.

The remarkable result of this work was that human beings remembered very nearly two bits per second under all the experimental conditions. Visual, verbal, musical, or whatever — two bits per second. Continued over a lifetime, this rate of memorization would produce somewhat over 10⁹ bits, or some hundreds of megabytes.

While this estimate is probably only accurate to within an order of magnitude, Landauer says

We need answers at this level of accuracy to think about such questions as: What sort of storage and retrieval capacities will computers need to mimic human performance? What sort of physical unit should we expect to constitute the elements of information storage in the brain: molecular parts, synaptic junctions, whole cells, or cell-circuits? What kinds of coding and storage methods are reasonable to postulate for the neural support of human capabilities? In modeling or mimicking human intelligence, what size of memory and what efficiencies of use should we imagine we are copying? How much would a robot need to know to match a person?

Landauer’s estimate is interesting because of its small size. While Landauer doesn’t measure everything (he did not measure, for example, the bit rate in learning to ride a bicycle nor does his estimate even consider the size of “working memory”) his estimate of memory capacity suggests that the capabilities of the human brain are more approachable than we had thought.

How many bits do we need to satisfactorily describe your brain? We have quite a range: from 10²⁸ to 10⁹. If we assume we have to describe every neuron and every synapse (and every nerve impulse traveling along every neuron), we’re probably safe in estimating something like 10¹⁸ bits. Those who object to this approximation can buy the more expensive High Fidelity system which keeps

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track of each and every atom. If people will buy gold-plated Monster Speaker cables…

How Much Computing Power?

Now that we have a rough idea of the information storage we’ll need, how many operations per second will we need? How fast does the brain operate? While mips are appropriate for a PC, there are several measures we might use for the brain. We might count the number of synapses, estimate their average speed of operation, and so determine synapse operations per second. If there are roughly 10¹⁵ synapses operating at about 10 impulses/second[2], we get roughly 10¹⁶ synapse operations per second.

A second approach is to estimate the computational power of the retina, and then multiply this estimate by the ratio of brain size to retinal size. The retina is relatively well understood so we can make a reasonable estimate of its computational power. The output of the retina — carried by the optic nerve — is primarily from retinal ganglion cells that perform “center surround” computations (or related computations of roughly similar complexity). If we assume that a typical center surround computation requires about 100 analog adds and is done about 100 times per second[3], then computation of the output of each ganglion cell requires about 10,000 analog adds per second. There are about 1,000,000 axons in the optic nerve[5, p. 21], so the retina as a whole performs

If the changes that have been introduced by the uploading process are smaller than the behavioral changes introduced by (say) a beer, a night’s sleep or a cup of coffee, then it’s getting rather difficult to argue that uploading has somehow destroyed the real you and substituted a “fake” you that just seems (by all objective measures) to be you.

about 10¹⁰ analog adds per second. There are about 10⁸ nerve cells in the retina[5, p. 26], and between 10¹⁰ and 10¹² nerve cells in the brain[5, p. 7], so the brain is roughly 100 to 10,000 times larger than the retina. By this logic, the brain should be able to do about 10¹² to 10¹⁴ operations per second (in good agreement with the estimate of Moravec, who considers this approach in more detail[4, p. 57 & 163]).

A third approach is to measure the total energy used by the brain each second, and then determine the energy used for each “basic operation”. Dividing the former by the latter gives the total number of basic operations per second. We need two pieces of information: the total energy consumed by the brain each second, and the energy used by a “basic operation”.

The total energy consumption of the brain is about 25 watts[2]. Much of this is used either for “house keeping” or is wasted, perhaps 10 watts is used for “useful computation”.

The Energy of a Nerve Impulse

Nerve impulses are carried by either myelinated or un-myelinated axons. Myelinated axons are wrapped in a fatty insulating myelin sheath, interrupted at intervals of about 1 millimeter exposing the axon. These interruptions are called “nodes of Ranvier”. Propagation of a nerve impulse in a myelinated axon is from one node of Ranvier to the next — jumping over the insulated portion.

A nerve cell has a “resting potential” — the outside of the nerve cell is 0 volts (by definition), while the inside is about -60 millivolts. When a nerve impulse passes by, the internal voltage briefly rises above 0 volts because of an inrush of Na⁺ ions. The inrushing Na⁺ goes through special protein pores in the nerve cell membrane called “voltage activated sodium channels”. They are normally closed, but when

the nerve impulse comes by they open for about a millisecond and then spontaneously close again[2].

When a single voltage-activated sodium channel opens, it has a conductance of about 15 picosiemens [1]. (A siemen is the reciprocal of an ohm, and is also called a “mho”). In myelinated nerve cells there are roughly 60,000 channels at each node of Ranvier (and nowhere else). The total charge that crosses the membrane at one node in one millisecond can thus be computed: about 5.4 x 10⁻¹¹ coulombs (over 300 million ions per node). The energy dissipated is just the charge times the voltage, or 3.2 x 10⁻¹² joules. If we view this one millimeter jump as a “basic operation” then we can easily compute the maximum number of such “Ranvier ops” the brain can perform each second: 3.1 x 10¹².

Although the details differ for unmyelinated nerve cells, the energy cost of traveling one millimeter is about the same.

To translate “Ranvier ops” (1-millimeter jumps) into synapse operations we must know the average distance between synapses, which is not normally given in neuroscience texts. We can estimate it: a human can recognize an image in about 100 milliseconds, which can take at most 100 one-millisecond synapse delays. A single signal probably travels 100 millimeters in that time (from the eye to the back of the brain, and then some). If it passes 100 synapses in 100 millimeters then it passes one synapse every millimeter — which means one “synapse operation” is about one “Ranvier operation”.

If propagating a nerve impulse a distance of 1 millimeter requires about 3.2 x 10⁻¹² joules and the total energy dissipated by the brain is about 10 watts, then nerve impulses in your brain can collectively travel at most 3.1 x 10¹² millimeters per second. By estimating the distance between synapses we can in turn estimate how many synapse operations per second your brain can do. This estimate is three to four orders of magnitude smaller than an estimate based simply on counting synapses and multiplying by the aver-

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age firing rate, and similar to an estimate based on functional estimates of retinal computational power. It seems reasonable to conclude that the human brain has a “raw” computational power towards the low end of the range between 10¹² and 10¹⁶ “operations” per second.

We’ll use the upper end of this range, 10¹⁶ operations a second.

Our Model Isn’t Perfect

We have been glossing over a point: a computational model of a physical system will fail to precisely predict the behavior of that system down to the motion of the last electron for two reasons: quantum mechanics is fundamentally random in nature, and any computational model has an inherent limit to its precision. The former implies that we can at best predict the probable future course of events, not the actual future course of events. The latter is even worse — we cannot precisely predict even the probable course of future events. A good example of this second point is the weather: weather prediction more than a week or two into the future might well be inherently impossible given any error in the initial conditions or computations. Any error at all (rounding off to a mere million digits of accuracy) will eventually result in gross errors between the actual events and the events predicted by the computational model. The model predicts sunshine next Tuesday, and we get rain. This kind of error cannot be avoided.

We have been simplifying our computations even further by not bothering to compute the state of every atom, or even of every molecule. We’ve been operating at the level of synapses or higher, which introduces another sort of “noise” into the computation.

It’s safe to conclude that any computational model of your brain will almost certainly deviate from the behavior of the original — eventually in some gross and detectable fashion. If you decide that it doesn’t matter which of two courses of action to follow and allow yourself to decide on whim, then it seems plausible that some slight influence might cause a computational model of your brain to select the opposite course. But is this difference “significant?” Given that our model is highly accurate for short periods of time and that any deviations are either random or represent the accumulation of slight errors, does it matter that the behavior of the model and of the original eventually deviate in some gross and obvious fashion?

We can view this another way: your brain, as a physical system, is already subject to a variety of outside and essentially random influences caused by

(among other things): temperature fluctuations; microwaves, light, and other electromagnetic radiation; cosmic rays; last nights dinner; a beer, etc. If the errors in our computational model are smaller than these influences do we really care about the difference? Is it “significant?” The human brain can and does continue to function reasonably well in the presence of gross perturbations (the death of many neurons, for example) yet this does not detract from our consciousness or life — I don’t die even if tens of thousands of neurons do. In fact, I usually don’t even notice the loss. A model of your brain that described the behavior of every synapse and nerve impulse, and did a reasonably accurate job at that level, would seem to capture everything that is essential to being “you.”

Yet how can we tell? How will we judge the “accuracy” of our computational model? How can we say what is “significant” and what is “insignificant?” We might adopt a variation of the Turing test: if an external tester can’t tell the difference, then there is no difference. But is the opinion of an external tester enough? How about your opinion? If you “feel” a difference, wouldn’t this mean that the model was a “mere copy” and not really you?

Well, we could ask: “Hi! We’ve uploaded your brain into an Intel Pentadecium, how are you feeling?” “Absolutely top notch!” “Do you think you’re not you?” “Nope, I’m me. And this simulated body is great!” “How’s the orgy?” “Wonderful! Who worked on this software? I’d like to shake their hand, they’ve done a really great job! Uh, I hope you don’t mind, but maybe I could talk with you a bit more after the party’s over? I’m being distracted…”

The ultimate in experimental evidence: try it and see!

If everyone agrees that you’re you, including you, and if behavioral tests can’t show any difference, then is there any difference? Perhaps, but the grounds for objection are getting rather slim. If the changes that have been introduced by the uploading process are smaller than the behavioral changes introduced by (say) a beer, a night’s sleep or a cup of coffee, then it’s getting rather difficult to argue that uploading has somehow destroyed the real you and substituted a “fake” you that just seems (by all objective measures) to be you.

Summary

Roughly, uploading will need a computer with a memory of about 10¹⁸ bits, able to do around 10¹⁶ “operations” a second. A computer of this capacity should fit comfortably into a cubic centimeter in the

early 21st century.

It will also require the highly accurate analysis of your nervous system. This kind of analysis should also become feasible in the 21st century. There is already considerable interest in understanding the human brain: for example, the Brain Mapping Initiative has already been started[8]. Transmission electron microscopy has been used to do complete three-dimensional reconstructions of small volumes of neural tissue and this relatively primitive approach could be scaled up to much larger volumes[9]. The use of more advanced technology should make the complete and inexpensive analysis of the human brain feasible.

The biggest obstacle to uploading today is the primitive state of current technology and the unfortunate fact that our current hardware has an MTBF (Mean Time Between Failures) of 70 years (I’ve already used up 41, how about you?). Even worse, actual failures occur unpredictably and the failure mode is catastrophic, resulting in complete erasure of all software. Bummer.

But if you can bridge the gap (it’s only a few decades) then you’ve got it made. All you have to do is freeze your system state if a crash occurs and wait for the crash recovery technology to be developed. Fortunately, cryonic suspension services are available today which quite literally let you freeze your state: call Alcor at 800-367-2228. Which means if you can’t stay alive and healthy until the technology is developed (and approved by the FDA, don’t forget the regulatory delays!) you can be suspended until you can be uploaded.

And then you’ll get to find out exactly how good that Roman Orgy simulation package really is.

References:

1. Ionic Channels of Excitable Membranes, by Bertil Hille, Sinauer 1984.

2. Principles of Neural Science, by Eric R. Kandel, James H. Schwartz and Thomas M. Jessell, 3rd ed., Elsevier 1991.

3. Tom Binford, private communication.

4. Mind Children, by Hans Moravec, Harvard University Press, 1988.

5. From Neuron to Brain, second edition (1984) by Stephen W. Kuffler, John G. Nichols, and A. Robert Martin, Sinauer.

6. “The Bounded Brain: Toward Quantitative Neuroanatomy,” by Christopher Cherniak, Journal of Cognitive Neuroscience, Volume 2, No. 1, pages 58-68.

7. “How Much Do People Remember? Some Estimates of the Quantity of Learned Information in Long-term Memory,” by Thomas K. Landauer, in Cognitive Science 10, 477-493, 1986

8. Mapping the Brain and its Functions, edited by Constance Pechura and Joseph Martin, National Academy Press 1991.

9. “Large Scale Analysis of Neural Structures” by Ralph C. Merkle, Xerox PARC Technical Report CSL-89-10, November 1989.

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