And every time a neuron connects with that neuron it’s like it’s connecting with all the other neurons it’s ever connected to. So always use a synaptic sheath!
I did a bit of googling and the highest estimate I could find for the number of neurons in the brain on an edu website (without phrasal variations) is 10e14 (note that Google recognizes 10e14 is a nunber and does the translations)
[ul]
[li]site:edu “10e10…10e15 neurons”[/li][/ul]
Interestingly that’s also the largest number of synapses cited
[ul]
[li]site:edu “10e14…10e99 synapses|connections”[/li][/ul]
This Stanford powerpoint verifies what I said above about the average number of synapses being between 1000 and 10000, but raises the maximum bar to 150,000.
So, in your best case scenario, 10e14 * 150,000 = 1.5x10^20 = 1,500,000,000,000,000,000,000 < that long ass number Carnac posted. (but for all intents and purposes, c’mon, that is a damn lot of connections)
There is something called the shannon number which states there are more moves on a chessboard than there are atoms in the universe.
If the brain has 10 billion neurons and is connected to every other neuron that still may not reach over 10^79 but I don’t know how to do the calculation to figure out what it’d look like if every neuron was connected to every neuron both as an axon and as a dendrite.
Didn’t see it. 
For a fully connected set of N nodes (a.k.a. a complete graph), there will be N x (N-1) / 2 connections. For large N, you might as well call that N[sup]2[/sup] / 2.
A hypothetical fully-connected human brain with 10[sup]11[/sup] neurons would therefore have about 5 x 10[sup]21[/sup] synapses. Still far short of the number of atoms in the observable universe — as we’d expect from arguments already given here.
You are all WAY WAY WAY off.
Let’s assume for the moment that there are 10^11 neurons, and each one can be connected to 10,000 other Neurons. Then the possible connections for each of those Neurons is not 10^11 multiplied by 10,000. Rather, it’s in the neighborhood of 10^11 raised to the power of 10,000. Now, obviously there are physical limitations as to what neurons can plug into what neurons, but still, it’s got to be a truly preposterously huge number.
Exponentiation gets nuts. In another thread recently we were discussing the number of possible DVDs. The number of bits on a DVD is (I think) around 32 billion, a very very very very large, but basically comprehensible number. The number of possible DVDs, 2^(32 billion), is so ludicrously large that you basically can’t come up with any way to understand it.
Correct me if i’m wrong (although, you surely wouldn’t hesitate =)
If each neuron has 10,000 synapses, then for every item in the set of 10^x you add 10,000. That’s 10,000 10^x times. That’s 10,000 * 10^x.
If it were 10^x^10,000, that would be 10^x times itself 10,000 times. But it’s not true that every neuron gets to connect to every other neuron 10,000 times. It’s only true that each neuron itself has 10,000 connections.
I swear I thought someone bumped that old thread…damn that was good!
Three-ways aren’t my thing, thanks all the same. 
I can’t agree. If there are N neurons, and each neuron has S connections, then there are (N x S)/2 connections total. (You have to divide by 2 to compensate for counting each connection twice, in each direction, with just the product N x S.)
It is truly huge, but it cannot be any larger than N x (N-1) / 2. N[sup]S[/sup] is way (way way way) off.
That’s the correct result for a string of 32 billion bits, but it’s also a different math problem altogether.
You’re talking theoretical connectivity, of course. I’ve never heard a neuroscientist postulate the interconnectivity of every neuron. But if the theoretical is our benchmark, some cosmologists theorize our universe is but one of an infinite number of universes, thus possibly redefining our notion of “universe.”
There are 11 billion neurons. Each can be connected to 10,000 other neurons. So, how many possible configurations of this neuron are there?
Well, if there was only one connection, there would be 11 billion (minus one) possibilities.
For two neurons, there are 11 billion (minus one) possibilities for the first, and 11 billion (minus two) possibiltiies for the second (assuming we disallow duplicate connections), and 11 billion (minus three) for the third, and so forth. So the total number of ways that the neuron can be attached is basically the number of non-repeating ordered sequences of length 10000 with an 11-billion-digit alphabet, which is fairly close to 11 billion raised to the power of 10000.
I highly recommend Roger Penrose’s book “The Emporer’s New Mind” to those wishing to investigate this topic in depth.
There are more potential connections in the brain than atoms in the universe, IIRC. Fortunately, we only use a small number of those connections.
I think you’re answering a different question than the one raised in the OP. The question was how many “connections” (which some of us have taken to mean synapses) there are in the human brain, and then secondly, how does that number compare with the total number of atoms in the universe. Or the observable universe anyway, the portion we have an estimate for.
I’m not sure what you mean by “configuration” in your post, but you seem to mean states, maybe, which hasn’t been brought up yet. Certainly, if there are N components in your brain — neurons or synapses, I don’t care which — and each component has K possible states (firing, resting, dead, etc.), and every component is independent of all the others, then your brain has K[sup]N[/sup] possible states in toto. That number would indeed be very large (for K = 2 and N = 10[sup]11[/sup]), much larger than the number of atoms in the universe.
Or perhaps you mean how many ways a given brain could have been wired up, theoretically. In that case, yes, there is a combinatorial explosion like you describe, and a huge number of possible configurations for the whole brain — but again, that’s not the OP’s question. For any particular mature brain, the neuron connections are settled and hardly change. (Maybe they can, very slowly, over the years. But they’re not flipping around from second to second and thought to thought.)
So, I’m sticking by my post.
Right, the purely theoretical maximum number of connections — a gross overestimate for the real brain, but which, large as it is, is still puny compared to the total number of atoms in the universe. It’s just another way of seeing why the claim in the French film can’t be right.
(Your earlier reasoning is really sufficient though, and more elegant.)
Might be some pretty brainy creatures out there then — “brain the size of a planet” maybe.
If we have three nodes, and count the possible connections, it isn’t (3 * 2) / 2 = 3.
A B C (none connected)
A-B C (A and B connected)
A B-C
<-A B C-> (A and C connected)
A-B-C
<-A-B C->
<-A B-C->
<-A-B-C->
Giving us 8 possibles.
And might I refer you to post 18
All right, Marvin - just go sweep up.
Can I just chime in to say that 2[sup]32,000,000,000[/sup] ain’t that asskickingly big of a number? Why, you can represent it with exponents - and only one level of exponents at that.
Yes, that’s how many possible networks you can form with 3 nodes. That’s not the maximum number of connections available for connecting 3 nodes.
In other words, connect up all your N nodes, all possible pairs with each other, then count how many lines you’ve drawn. You will have N x (N-1) / 2 of them. If you want to try removing various subsets of those connections, to see what sorts of networks you get, then there will be 2[sup]N x (N-1) / 2[/sup] possible networks you can make.
But that’s not how the brain works. Your brain, on a moment to moment basis, does not freely add and remove synapses, constantly forming new networks. As an adult your neural network — the topology of it anyway, if not the neural responses — changes very slowly, if at all.
I think it’s basically bigger than it’s ever possible to get via real life questions without going into “possible combinations of…”.
For instance, if you basically try to max out a question, something like “if you go all the way back to the beginning of the universe, and for every single elementary particle that has ever existed (proton, neutron, electron, photon, etc.), you record it’s precise position and spin and charge and so forth at every point in time from then to now, using as your time interval the amount of time it takes something travelling at the speed of light to travel the width of an electron, how many bytes of data would you generate”, which is kind of like the UR-question, as you’re going to end up generating data which will answer every possible question about the universe, you’re still going to be drastically short of 2[sup]32,000,000,000[/sup].