Tuesday, September 08, 2009

You Brain Is Like A Lump of Coal

School has started again and I find that I need to fill my Human Social Science requirements. So I am taking Psychology; yes I know psychology. The professor is a bit of an eccentric, also makes rather large statements as if they where facts. The one statement that I have decided to nitpick is a fun one, he stated that the brain is incredibly amazing (a fact that I will not debate), however felt it necessary to add one more thing to how amazing the brain is. He informed the class that the brain has more connections in it then there are atoms in the universe. Of course this immediately range alarm bells in the scientist part of me. Looking at this from the most basic logical standpoint, the fact that your brain is enclosed in the universe means that it can't possibly have more things in it than the universe. However, for the sake of argument lets work it out. The human brain weighs around 3 pounds or 1400 grams assuming that all of the material in your brain is carbon (ignoring that it is mostly water weight) every 12 grams of carbon would be one mole of atoms or Avogadros number (6.02*10^23) atoms per 12 grams. So lets divide the 1400 by 12 then multiply this by 4 which is the number of bonds carbon is capable of making. Now lets multiply this by Avogadros number and we find that at most the brain can have about 2.81*10^26 connections in it. Another way to look at this, which is really the whole point is that what the professor was saying is that your brain is about as amazing as a lump of wet coal, of course mabey his is.


  1. you are apparently not the first to notice this obvious misunderstanding of the basic concepts of the universe and logic which some phsychologists make.
    It should be noted though that if they consider not the number of connections but the number of 'possible' connections then this claim is somewhat reasonable. A single Purkinje cell can regularly have 200,000 connections and so combinatorially there are quite a few possibilities. But as Bascule stated: "That's not a very useful definition of 'connection'. By that logic my sewage is connected to your drinking water."

  2. Aryeh, there is no reason why the number of connections between objects cannot exceed the number of objects. In fact, it is usually the case that they do.

    Take five widgets numbered 1-5. To go from Widget 1 to Widget 5, I can go 1 5, 1 2 5, 1 3 5, 1 4 5, 1 2 3 5, 1 3 2 5, 1 3 4 5, 1 4 3 5, 1 4 2 5, 1 2 4 5, 1 2 3 4 5, 1 3 2 4 5, 1 3 4 2 5, 1 3 2 4 5, 1 4 3 2 5, 1 4 2 3 5, which is 17 possible pathways. Your count is only a calculation of direct linkages.

    Between all the cells in the brain, there will invariably be many more. However, you have to ask do all of these matter in any way, and the answer is probably not.

  3. To formalize what notElon pointed out, for N objects there are N(N-1)/2 possible connections between them, if we allow them to be fully interconnected. See Triangle number. For a large N, this is approximately N^2/2.
    So, for your carbon example, where N~7x10^25, the number of possible connections is around 2.5x10^51. However, the number of atoms in the universe is at least 10^80, so we're still way fewer than that.
    And, of course, considering the brain to be a lump of carbon is completely silly. The better bet would be to consider it water, approximate its volume, and divide by size of average neuron. Or, to be generous, the smallest neuron's diameter are around 4um (source), so call it 1um. Then, you get around 10^15 neurons, or 5x10^29 possible connections.

    An unrelated point: Your (or should I say "You") spelling and grammar -- quite entertaining.

  4. That could explain lumpy :)

  5. I don't know how this impacts y'all's math (and don't feel like calculating how), but two neurons can be connected with two or more connections - Neuron A can have multiple synapses with Neuron B.

  6. Eli's approximation assumes one direct connection from each neuron to each other neuron, no matter how far apart those two are in the brain. And he was off by a factor of 10^50.

    Adding a scaling factor at the front of that won't come near making the statement true.