Ontological Warfare

The Measure of Mind

2011-12-29T21:12:58-08:00

A human brain is a collection of cells that are massively interconnected. Assuming we knew how to build and program one, how much data would we need to recreate any particular human? That is, what is the best estimates for the total size (in bytes) needed to store a Homo sapiens mindstate? In the following I'm going to try to work out an upper-bound estimate.

Connectivity Information Content

There are about a 100 billion neurons in the human brain. Each one makes, on average, 10,000 connections as inputs. How much information is stored in the connectivity graph of the neural net? How many ways can a single neuron make 10,000 connections? Just

where is the number of neurons and the number of connections. Given that each neuron is approximately independent, we then have for the entire brain a total number of states:

The information content in bits is then

Now the neural system is sparsely connected that is the number of connections, 10,000, is far less than the number of neurons, 100 billion, so . This allows the simplifying assumption

For the human brain: bits - That's 3 petabytes! (about 2,000 modern hard drives).

Now, actually the brain is compartmentalized and any given neuron can't make a connection to any of the other 100 billion neurons. Instead, it can only connect to an average subset of neurons. Let's say only a million potential partners are available for any given neuron. The change is:

1 petabyte, not much of a change, since the sheer number of synapses involved sets the petabyte figure.

Synaptic Weight Information Content

The above calculation naively assumes that each connection is binary, just like a junction. In reality, each connection is a synapse that acts like a complex biochemical amplifier of electronic signals that holds lots of state variables. If we assume each synapse has on average σ state variables with r bits of resolution, then we have the additional information source of .

An oversimplified assumption is that there are only two variables: the receptor number and the size of the synapse, each varying within a 6-bit range (a 64-fold range). This leads to the estimate of 10¹⁵ 2 6 = 12 petabits = 1.5 petabytes to store the synaptic strengths in addition to the connectivity diagram.

There are certainly more synaptic state variables than this. We can set an upper limit of perhaps 100 6-bit variables arising from variable local synaptic protein levels and modification states (phosphorylation, ubiquitinylation, etc.). This implies a much larger storage size of

There is ambiguity at how well such raw data compresses, but it's probably safe to assume a information density of 1-100 petabytes to store a human mindstate.

Note that there are many other variables, such as global protein expression levels and of course the transient electrical state of neurons but these variables tend to scale per-neuron, not per-synapse, and so contribute a much smaller amount of information that we can neglect for an order of magnitude analysis. (i.e. We have less than a gigabyte of genomically coded "human nature".) ²

This implies that static immortality amounts to several million dollars of storage space, if only we knew how to tease the ghost from the skein and rehaunt another.

A loose, general definition of "information" is the number of yes/no questions needed to fully specify an individual member of a given set of possibilities. "Twenty questions" can, in theory, specify the member of a set of 2²⁰ = 1 million possibilities. In general, if your set of possibilities has N possibilities: log₂ N_{possibilities} = N_bits
It's more complicated than that, as the true definition of information includes the probabilities of any member of the set occurring. ↩
Limiting Information Density of Matter Given the huge value of Avogadro's number (6.022 10²³), the information density of ordered matter is potentially immense. Let us assume that there's some means of encoding 1 bit per 1000 atoms (for metals a cube roughly 3nm on side). How much information can we hold in our hand? (0.1 m / 3nm)³ = .3 10²³ bits, about 5 million petabytes, Enough to store 50,000-5 million mindstates. ↩

Who Would Survey the Library of Babel?

2011-12-29T14:52:35-08:00

The Library of Babel was conceived by the inimitable Jorge Luis Borges and stands as one of the greatest metaphors for combinatorial potential ever penned.

A brief excerpt from the unnamed narrator, a native of the library:

The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest...

...there are five shelves for each of the hexagon's walls; each shelf contains thirty-five books of uniform format; each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters which are black in color.

Based on this description, it is possible to calculate the size of the Library of Babel, presuming that it is a finite universe containing every possible book.

410 pages/book x 40 lines/page x 80 letters/line = 1312000 letters per book

There are 25 different letters.

This means that there are:

25^1312000 = 10^1834097 possible books.

4 walls/room x 5 shelves/wall x 35 books/shelf = 700 books/room

Implying that there are 10^1834094 hexagonal rooms in the Library. If we assume each room to measure some 80 cubic meters, then one expects the approximate linear extent of the universe to be:

(80 x 10^1834094)^1/3 = 10⁶¹¹³⁶⁵ meters

Compare it to the size of the known, visible universe: a mere 10²⁷ meters.

10^1834014 of our visible universes could fit into the Library of Babel.

This is the nature of our Reality. It is but a tiny mote couched inside a sea of potentiality of mathematical vastness.

Jorge Luis Borges
*4 August 1899
†14 June 1986

"Life itself is a quotation."

"One concept corrupts and confuses the others. I am not speaking of the Evil whose limited sphere is ethics; I am speaking of the infinite."

"To fall in love is to create a religion that has a fallible god." ↩

Quantum Brain Hypothesis is Bunk

2011-12-29T14:52:35-08:00

The underlying assertion of most goofy new-age claims about quantum mechanics and the brain is that consciousness is a quantum process. Of course, in a trivial sense it is quantum insofar that every process in the physical world seems to obey quantum mechanics. The exact claim is that something "essentially quantum" is behind the phenomenon of consciousness, that the computations of the brain actually exploit uninuitive quantum behaviours that cannot be explained by a classical physics picture -- the claim is that our brains are quantum computers.

You build a quantum computer by exploiting the fact that a simple, perfectly isolated physical entity does not act like a tiny billiard, but rather as a complex-valued wave that isn't in any particular place at a given time, it's spread out. We say that small systems can be in "superpositions" of multiple states. Now when the system interacts with the environment, by hitting a photon from our lasers, say, it will "collapse" ¹ into one state, we will see the photon bouncing off as though the particle had been at one particular place.

Quantum computers exploit superpositions by encoding data into the states of small particles and allowing them to interact and evolve with each other isolated from the environment in such a way as to perform a simple calculation without collapsing until the very end when you measure (read out) the answer. The advantage comes from the fact that every possible history of the simple computation is performed in such a way that certain parallel algorithms can try all the combinatorial possibilities at once before being summoned to give an answer when they're collapsed. A quantum computer with N bits is like classical computer with 2^N bits.

The key requirement is that the quantum computer not interact with the environment (stray light, cosmic rays, etc.) during the duration of the calculation. The more complex the computer, the larger the number of particles needed to encode the data, the more exquisitely sensitive the computation becomes to outside noise:

It is so difficult to get more than a few particles isolated long enough to perform calculations that after about 10 years of effort, the biggest quantum computer has about 8 qubits. The quantum brain hypothesis ² says that there is some remarkable way that the proteins of our neurons could form an isolated network of qubits such that the brain could perform quantum calculations, and that the mysterious nature of consciousness could be chalked up to the weirdness of its quantum underpinnings.

There are two major reasons for why this quantum brain hypothesis is extremely doubtful:

Any time a stray particle hits a quantum computer it collapses back into a world-entangled state, ruining the computation before it's finished. The brain is a hot, disordered, massively chaotic place with countless particles bouncing into everything a billion times a second. The longest biological quantum superposition known happens in chlorophyll, and that lasts about a trillionth of a second.

A general, conservative calculation about the survival times of quantum states in the brain was done by Max Tegmark ³, suggesting a trillionth of a second as the limit. Now, biology certainly does exploit quantum effects at the timescales at which they happen in cells. i.e. quantum effects influence photosynthesis ⁴ and the electron transport chain of respiration. Natural selection cannot select for life that uses extremely short-lived physical processes to perform long-lived tasks.

Mental phenomena seem to be explicable solely in terms of the electrical spikes neurons use to signal with each other. i.e. In animal experiments, we can see that the external information of sight and sound is encoded in the frequency and pattern of these spikes in populations of neurons. Controlling these electrical signals artificially seems to influence animal behaviour in a predictable fashion.

We are still very much in ignorance of the brain's operation, but not so much at the level of its biophysics. More so in the level of detail about how these signals work across the hundred billion or so neurons of the brain, and how individual neurons alter their connections and sensitivities over time to other neurons. The fastest of these processes happen at the millisecond timescale, meaning that any quantum process is much too fleeting to influence the phenomenon we know to be directly involved in neural computation, by a factor of at least 10⁹!

The consensus scientific opinion is that the brain acts as a massively parallel, stochastic, ⁵ and classical computer. Whatever the "secret" to consciousness is, it's not quantum superposition.

It should be noted that "collapse" is not a real a-priori physical process, but only an apparent phenomenon. The modern understanding is that collapse happens when system of few degrees of freedom interacts with one of very many (the environment) causing the two to become "entangled" and forcing any given history of the environment to "see" only one well defined state of the small system through a process called "decoherence". ↩
This hypothesis was first proposed by Roger Penrose in his book "The Emperor's New Mind" and has since captured a generation of imaginative theorists who never bothered to learn anything about the brain. ↩
quant-ph/9907009, Phys. Rev. E, 61, 4194-4206 ↩
Gregory S. Engel, et. al. "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems" Nature 446, 782-786 (12 April 2007) ↩
The one thing quantum mechanics does provide is a kind of guarantee of absolute, true "randomness" at the level of the particles that make up the brain. This in turn provides a kind of basic guarantee of non-predictability for human actions. ↩