# How many possible states does a brain have?

Suppose I have a box, inside of which is a light which can be either on or off: it has exactly two states.
Suppose I wanted to take some "snapshot" of the state of this device, and store all the information about it, so that if I at some point had another device with sufficiently identical hardware + environment and a way of writing all the state to that device, I could recreate the state of that box. There are n=two possible states (so it would require log2(n) = 1 bits to store the state).

Now suppose my box is a brain. To the nearest order of magnitude, how many possible states does the brain have?

Assuming it's an adult human brain might make for the most useful answer to this question, but if you have more solid answers for brains of other animals while we wait on an answer for humans, feel free to post an answer stating that assumption.

• I imagine that how you define a brain state depends on your level of analysis (molecular, chemical, single cell, cell population, oscillations, regions, networks, etc.). – mrt Oct 20 '15 at 22:56
• @mrt defining that level is part of the challenge of the question. It's definitely more than a single cell, though. – WBT Oct 20 '15 at 23:00
• Well, I'm not sure we can really reduce the brain to a specific level, so you'd probably need to consider all of them (each having different information). But even then, it's not really clear what a "state" is or if the idea of "brain states" is theoretically coherent at all. But I don't know enough math or theory to say anything with confidence. ;) – mrt Oct 20 '15 at 23:28
• – WBT Jul 12 '16 at 18:26

# 2 2,752,000,000,000,000,000,000 states

Disclaimer: This is obviously a very crude and imprecise estimation (in fact, it is ignoring some obvious parameters for the sake of simplicity). As Scott E. Page puts it: Even models that are far from accurate can teach us something.

If one considers the design of future artificial brain, you can make these rough assumptions:

• A 32 bit floating point representation should suffice to capture synapse elasticity.
• There are about 86 billion neurons in the brain. The connectivity of which can be represented by a square matrix of size 86 * 1018 (86 * 109 to the power of 2). Each connection is weighted, 32-bit float.

Resulting in 86 * 1018 * 32 bits =

2752000000000000000000 bits (2.75 sextillion).

These many bits result in these many states:

2 2752000000000000000000

or: This obviously a very rough estimation - you don't account, for example, to membrane potential, although you can argue that discarding membrane potential while maintaining neural connectivity and synaptic strength should suffice to 'reignite' a frozen brain.

Perhaps more importantly, a network structure can be represented by a matrix, but more often is represented by a sparse matrix - no neuron is connected to all other neurons, I believe 1000 is the average and some sources state that there are about 1,000 trillion synaptic connections.

• Pardon my ignorance (about information theory, computational neuroscience), but is a state equivalent to a bit? – mrt Oct 21 '15 at 1:30
• @mrt I'm not sure I understand the question. Surely in the representation of state the bit has its place? – Izhaki Oct 21 '15 at 1:36
• Hmmm, clearly I'm out of my depth here lol. Is the logic that if there is X number of bits, and each bit can take on the value 0 or 1, then there are $2^X$ states? Oh wait…never mind. I'm missing the whole connectivity calculation, too. – mrt Oct 21 '15 at 1:47
• @mrt, the possible amount of possible values in any numbering system is the (amount of possible digit values) ^ (amount of digits). Two decimal (base 10) digits can represent 100 values (00..99); Three Binary digits (base 2) can represent 8 values (0..7). The amount of possible values also represents the amount of unique digit combinations. – Izhaki Oct 21 '15 at 12:53
• To me, connectivity seems much more a potential energy landscape than a state. A state is inherently about the current position on that landscape, so e.g. membrane potentials would clearly be important. That's gonna add a few orders of magnitude. – jona Oct 24 '15 at 16:34