# Number of Connections in the Brain

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Probably the statement giver could have thought that every cell in the brain is connected with every other cell. In this way the number of connections would be equal to the square of the number of cells present in the brain. I have heard that there are about 2 billion cells in the brain so the total number of connections would be (2000000000 x 2000000000). I don't think this value is greater than the number of atoms in the brain.

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This is a pure combinatorial question:

To take it into the real world let's discuss Buckminsterfullerene:

http://en.wikipedia.org/wiki/Buckminsterfullerene

http://en.wikipedia.org/wiki/Truncated_icosahedron

See that:

Buckminsterfullerene has 60 atoms and 90 edges, edges are equivalent to connections, yes?

Now add 1 atom in the middle, there is a line or 'connection from each of the 60 atoms to this new atom:

Now we have, 61 atoms and 150 connections, see?

Combinatorially, brain connections is a massively huge number, easily more than atoms in the universe.

Let's say the maximum number of connections n atoms can have is X, as a function, we can represent this as f(n)=X

This new atom can connect to maximally n other atoms so:

f(n+1) = X + n

but

f(n)=X therefore

f(n+1)= f(n) + n

but then, f(n) = f(n-1) + (n-1)

so we have

f(n+1)= f(n)+n = [ f(n-1) + n-1 ] + n = f(n-1) + 2n -1

now

f(1)=0 - dot

f(2)=1 - line

f(3)=3 - triangle

f(4)=6 - cross hatched square or tetrahedron

Dimensionality also has an effect.

In 2d you will see that f(n)= Summation (Binomial n,k) for k=1 to k=n-1.

binomial tree:

1

11

121

1331

14641

f(4) = 6 =

f(5)=1+3+3+1=8 - cross hatched pentagon

however 5 points in 3 dimensions, what happens,

.......work it out, it will take you a few hours

OR

type in

maximum number of edges and vertices in 3 dimensions

Thanks,

D

f()

f()

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mathsgiup,

I read the first page of this thread, and the last. Don't know what came up in between, but in addition to the very large numbers that one can come up with for possible brain states, I would like to add the thought, that we are not probably dealing so much with a binary situation, as we are with an analog one. Hence the large numbers are only proof that our brains have the capacity to reflect, or "model", or "remember" the analog universe, we find ourselves in. Each of us aware of "here" and "now", and our relationship to the rest, in terms of space (that which we are in, and that which is within), and in terms of time (that which has led up to now, and that which we predict will happen next.)

If it is the case that our "brain state" contains a certain amount of "information", I would argue that that information can not be helpfully considered as a "number" of bits. As an early poster in this thread pointed out, it is the "relationship" between the bits that counts.

And that relationship counts a mighty lot. Especially if you consider the amount of information contained in a sunset, or in your mate's embrace, or in your muse as you gaze into a starry sky.

Regards, TAR2

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mathsgiup nailed it.. The statement is meant in the combinatorial sense.

As to what Chris L said, you are absolutely correct about the astrophysical aspects of the "size" of the universe, (except for the expansion part, because the expansion of the universe, as it is currently understood and as it was first suggested, means the increase in the spacetime separation of faraway galaxys from the center of the universe where the Big Bang is supposed to have occured, it does NOT mean that the amount of matter/energy in the universe is changing...).

However, had the initial statement been formulated more accurately, meaning: "The number of POSSIBLE connections in the brain is higher than the upper bound of the number of atoms of CONVENTIONAL MATTER (i.e. in the form of one of the currently known elements) in the KNOWN universe, as of 07/31/2012". With "KNOWN universe" being the key words here, in addition to the combinatorial calculations which clearly yield much higher numbers than 10^88 or 10^100 or even 10^1000, the statement, when stated in the manner above, becomes absolutely CORRECT!!!!

BAM! the answer to end all speculation. You're welcome.

One more thing I forgot to add:

What lead me to believe the statement is meant in the combinatorial sense are the two key words "POSSIBLE CONNECTIONS"

mathsgiup nailed it.. The statement is meant in the combinatorial sense.

As to what Chris L said, you are absolutely correct about the astrophysical aspects of the "size" of the universe, (except for the expansion part, because the expansion of the universe, as it is currently understood and as it was first suggested, means the increase in the spacetime separation of faraway galaxys from the center of the universe where the Big Bang is supposed to have occured, it does NOT mean that the amount of matter/energy in the universe is changing...).

However, had the initial statement been formulated more accurately, meaning: "The number of POSSIBLE connections in the brain is higher than the upper bound of the number of atoms of CONVENTIONAL MATTER (i.e. in the form of one of the currently known elements) in the KNOWN universe, as of 07/31/2012". With "KNOWN universe" being the key words here, in addition to the combinatorial calculations which clearly yield much higher numbers than 10^88 or 10^100 or even 10^1000, the statement, when stated in the manner above, becomes absolutely CORRECT!!!!

BAM! the answer to end all speculation. You're welcome.

One more thing I forgot to add:

What lead me to believe the statement is meant in the combinatorial sense are the two key words "POSSIBLE CONNECTIONS"

One more thing, great answer shelby, only you are answering the wrong question. "Possible connections" are different from "physical connections" as synapses can detach and reattach to different synapses, hence the word "possible". So, yes at any one time, the max number of synapse connections is in the range you have stated. However, if you check the same brain again, while the number of synapse connections will not exceed the range you mentioned, synapses will be connected differently. Hence, the number of combinations which CAN happen (i.e. are possible) are much higher than the number you stated, and are obtained through combinational calculations.

Hmmm. After reading jdah4's reply, while the statement remains abstractly correct, it is logically flawed since it compares possibilities to actualities...

So I guess it all depends on each person's definition of correctness.

To me, I find that many axioms of science (especially the natural sciences) can be easily deconstructed to seem "logically" wrong. However, most modern scientists care much more about the abstract correctness of a statement than it's logical value... They care more about the actual consequences of a statement than if it makes logical sense...

Therefore, I still believe the statement should be deemed correct...

I have replied so many times, only because I care for accuracy.

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Oooh lovely I couldn't but help to jump in here. I wonder if the start of the thread was inspired by me (?! just a thought) - because I speak on neuroscience in behavioural business contexts. And I use that quote. But also note:

- I state that the brain has 100 billion neurons (most people including all the most respected neuroscientists quote this figure - recent research has shown it to be closer to 85 billion)

- I state that the brain is estimated to have 100 trillion synapses (as many have noted above, neurons can have up to 10'000 synapses). Again as commonly used estimation.

- I state that the "more connections in the brain than atoms in the universe" refers to the number of way the synapses can potentially connect

- I state that I don't know whether it's true or if the calculation is correct (but thank you for the mathematics above)

- I state that is is almost not biologically true in the actual brain because the brains wires in certain ways and not everything is connected to everything and not forgetting that neurons only have one axon and certain neurons are only stimulated by certain neurotrasnmitters, etc.

- I state that I use this figure for representative reasons to illustrate the vast complexity and also magical beauty of the brain and to comprehend what sits in our skulls

So to draw a close to the fascinating discussion I think we can agree

- the brain has 85 billion neurons (for the sake of accuracy 85 not 100)

- the brain has an estimated 100 trillion synapses (will that be revised to 85 trillion in light of the research into numbers of neurons?)

- the brain has in theory more possible connections than atoms (of conventional matter) in the (known) universe

- the brain in reality does not have more possible connections than atoms in the universe much less in fact (but it is a mind-boggingly large number)

Oh and I didn't mention that there are another 85 billion glial cells in the brain which have supportive functions - some research has indicated that these can also transmit information...

All clear now?

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*cough, cough*, my Friends, no sense to discuss the number of possible connections between neurons because mostly they're (possible networks) fully unstable. here runs the simple Law: the more complexity of system the lesser percent of stable states out there

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The original statement was by V.S. Ramachandran where he stated there are 100 billion neurons and anywhere between 1000 to 10000 POSSIBLE connections from each neuron. This refers to the plasticity of the human brain where new connections are formed and old connections are sloughed on to be reformed again at a different site later again.

There is an estimated 10^85 atoms in the known universe from classic matter (not dark matter, antimatter, nor even photons)

I believe the the proper equation for this problem would be nCr where n = total sample size and r = number of items to be selected from the sample. You would use the combinatorial function because it is all possible outcomes in any given order. Therefore:

n= number of neurons = 100,000,000,000

r = number of possible connections (assuming any neuron can connect to any other neuron) = 10000

However, the website I am using can only do:

n= 100 billion

r = 10 but...

nCr = 2.75573e+103 (http://www.calctool.org/CALC/math/probability/combinations)

2.75573e+103 is greater than 10^85

This is flawed though because the human brain does not in fact connect at every point and cannot send connections everywhere. It is a mass of order and chaos that lies somewhere in the middle . There are many scientists working out the human connectome as we speak as well as connectomes for mouse, rat, cat, monkey, dog, etc. The full connectome of C. elegans has in fact been sorted out and is easier to find on google.

Another flaw with the statement is that glial cells are not accounted for at all in the estimate which is unfortunate because they outnumber neurons 10 to 1. Astrocytes are capable of forming gap junctions with their neighbors as well as storing, synthesizing, and releasing glutamate, GABA, and ions within the extracellular space. There are even recently discovered glial cells within the white matter tracts that send and receive signals through a traditional synapse.

Lastly, any prediction as to the size of the universe and the atoms contained with it relies on what we can observe of the universe. Much of our knowledge about the universe comes from distant star systems many thousands and millions of lightyears away. The light is just reaching our tiny planet now after millions of years and there could potentially be new star systems, new galaxies, collapsed systems, black holes that eat up all the atoms (such as that at the center of the milky way) or new particles forming on the edge of a black hole. We cannot be certain of the extent of the universe nor do we know how the human brain fully connects yet. Although, all else being said its a fun mind exercise to grapple the enormity of both the universe and the mind. I have also read that the number of snow flakes that fall in one year on earth outnumber the stars in the milky way galaxy (10^23 stars).

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