You're using combination again. If there are 7000 connections per neuron, and 10^14 neurons, then there are 10^18 connections, not 10^8432.

We don't need to model a synapse "completely" to mimick it's function. We don't need to know what every atom in an asteroid belt is doing to simulate it's formation. I'm sure a simpler mathematical stand-in can serve. As far as the intelligence of the macroscopic brain is concerned, a neuron is just a complicated switch/routing device.

__________________
http://amssolarempire.blogspot.com

Yup. Speculation is great, but this is another subject where our information is limited. The fact that we don't understand the details means we certainly can't do it yet, but because of that we can't make sweeping statements about hardware requirements.

__________________
I say there is an invisible elf in my backyard. How do you prove that I am wrong?

Disclaimer: Avatar is not an official NASA image and does not imply any specific interplanetary or interstellar capability.

The Leif Ericson Cruiser

Combinations is correct, since each possible combination forms a unique neural pathway. Each pathway constitutes (conservatively) a memory bit. Once activated the brain "remembers" each pathway. We'll conservatively assume 100 billion neurons with 3,000 synapses each.

The formula is very simple:

connection possibilites (unique pathways) = n! / m! * (n - m)!, where
n = number of neurons
m = average # of connections between neurons

= 10^11! / 3000! * (10^11 - 3000)!

It takes a special program to calculate such large factorials, but the result is 10^8432. It's been published and checked:

Discovering the Capacity of Human Memory, Wang, et al, 2003, Brain and Mind, vol 4, no 2, p. 189-198.

You don't need to know what every atom in the brain is doing, but without correctly modeling the synapse (which we can't do since we don't yet fully understand it), you can't model the brain or even a subset. The neuron is absolutely NOT just a switch. That's a popular-level simplification. Here's a quote from a neurological research paper:

"What does the [neuron] cell control? Fluid and precise movements, fine hand movements and balance as of a ballet dancer, illustrating how wrong it is, how far off one must be to consider this complex executive merely as an "on' or "off" state at a given moment in mathematical representations."

http://www.pneuro.com/publications/i.../01_part3.html

There are 6.02*10^26 atoms/kg-mol. (6.02E23 atoms/mol) The brain weighs about 1.5 kg.

Considering that there must be fewer than 9E26 atoms in the brain, and that each atom probably has 6 degrees of freedom, building a model of the brain that is accurate to the atomic level would not take any more than 5.5E27 variables.
Our brains must have fewer than 10^27 connections in them, because they don't have the atoms to form them.

In fact, we don't need to simulate every atom. I'm sure to emulate intelligence, a model with more than a few orders of magnitude of simplicity over that one can be used.

(I doubt there are 10^8000 atoms in our galaxy! When you start getting numbers of that magnitude, you know you aren't talking about physical quantities, and rather about the number of ways to arrange it, which can have far larger degrees of scale over the quantity involved. )

If every possible path that a signal can take really does constitute a memory bit, we still only need to model the paths, not the bits directly.

__________________
http://amssolarempire.blogspot.com

That's a good point about this vs memory capacity. Let me think about this a bit...

Just a follow up: now discussing this on http://www.scienceforums.net.

To summarize the issue:

The authors of the Wang paper reason that any synapse can connect to any other synapse via a unique neural pathway, often transiting through other intervening neurons and synapses.

IOW it's not just the neuron-to-neuron direct connections, but the unique PATH between any two synapses. It could be many thousands of neurons long. Each synapse could participate in many different memory "bits", as each is usually part of many different unique neural paths. The authors of the Wang paper posit that it's the RELATIONSHIP between any two synapses, anywhere in the brain, that stores a memory "bit", not a physical bit "container" in a specific brain location.

I think there's some basis for that, based on current limited understanding of neural electrical activity. However as you implied, it requires each unique path to be "remembered". IOW once activated SOME biological mechanism, SOMEWHERE in that path must be changed. Otherwise a subsequent trigger of that path would engender no different response than the first.

Even if only one atom changed, you only have so many atoms in the brain. Therefore although 10^8432 path possibilities mathematically exist, it seems impossible they could all simultaneously be available for storage. Ultimately something, somewhere must store each equivalent "bit", and even if that's on a discrete atomic level, as you said there's not enough atoms to exceed roughly 10^27 bits.

Therefore I agree with you -- upon reflection, I don't understand statements about the brain having "more storage bits than there are atoms in the universe" (often repeated, don't know original reference), or 10^8432 bits (above Wang paper).

Still thinking about this...

After watching Star Trek:First Contact the Borg collective started making appearrances. I wouldn't call them nightmares because I usually deffeated them.

__________________
There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.
-Douglas Adams
Aim high (but don't blow yourself up)!- Homer Hickam

In Soviet Russia, UFO report you!- Phil Plait

Clear skies Maksutov.

linky

http://www.spacedaily.com/news/Living_Forever.html


"This moment that Kurzweil sees coming 20 years hence is when our intelligence becomes non-biological and trillions of times more powerful than unaided human intelligence. What this will mean f! or humanity is that aging can be reversed, pollution eradicated, hunger solved and our bodies and the environment transformed by nanotechnology that will also overcome the limitations of biology - and death."