Preface: I'm not particularly well schooled in either neuroscience or in the mechanics of microprocessors.
However, I'm very close to certain that your post is basically a lot of hand-waving that is ultimately not only poorly reasoned but also actually incorrect.
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The question we're trying to answer is basically, "What's the computational capacity of the brain?"
But that's not really a good question to work with, because "computational capacity" isn't well-defined. [Actually, I'm not sure about that. I know that either it's not well-defined, or its definition is something that's clearly not what we want in this situation.]
So let's ask something that we can actually reason about, like, "Assuming infinite memory, roughly how many floating point operations per second would a computer need to be able to execute in order to direct a human body in a way that's indistinguishable from what a real person does -- in real time?"
And, okay, we really only want the brain's conscious thought and maybe some of its unconscious thought, but it's hard to make a well-defined question involving just those things, and I doubt that the answer to our question will be more than a few orders of magnitude off of what we're really after.
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Anyway, your post does a really, really bad job of answering that question (or anything like it). Your worst offense:
> "So the human brain has about 10^11 neurons and about 10^4 synapses per neuron. Naively representing the state of each synapse with one byte requires 10^15 bytes that's about 500,000 PCs."
Come on. Did the fact that you had to use the word "byte" not tip you off? YOU'RE DISCUSSING MEMORY. Nobody cares about memory, because the amount of memory needed to store the brain's state is vastly less than the number of operations needed to simulate its function in real time.
I seriously am not able to articulate how frustrated I am that at least 12 people felt justified in upvoting you without taking the time to process the first two sentences of your post.
Before I go, another treat:
> "Electronics are potentially a factor of 10^8 faster."
No. Electronics are a factor of 10^8 "faster", when "faster" is taken to mean "more rapid in executing a cycle." Which is an absolutely pointless irrelevent piece of shit statistic.
What the fuck.
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Anyway, let me wrap up this post by actually answering the above question as best we can, given the current state of scientific understanding (or, more precisely, my understanding of that state of understanding):
There are on the order of 10^10 neurons and on the order of 10^11 glial cells in the adult human brain. These cells are directed by untold numbers of chemoattractants. We have no good theoretical model for the behavior of these cells in huge numbers of situations.
Therefore, WE HAVE ABSOLUTELY NO FUCKING IDEA how much processing power it would take to simulate the brain's macro function. We can put an upper bound on it: we know that if we could simulate every atom in the brain to a reasonable degree of accuracy, we'd get human behavior. Obviously the number of FLOPS it would take to do such a thing is unreachable. And beyond that, I don't think it's fair to say we know anything at all.
Oy man, I'm not used to people getting this fired up over a back of the envelope calculation! I'm sorry if my post sounded arrogant - I'm just trying to have some fun here.
I don't think I can really comprehend what any of your objections are, but I can certainly think of some major flaws in the toy argument I gave, and maybe these are what you were getting at even if you couldn't really articulate them.
first, just saying the state of a brain is the state of each synapse assumes a fixed topology of the brain. This is obviously false - there is a lot of evidence that the topology of the brain is changed by experience e.g. the occular dominance columns. Okay, so how much extra space would we need to deal with this - not that much actually: how much space do we need to store an arbitrary weighted directed graph with 10^11 nodes and 10^15 edges? Well for each edge we need to know the two vertices and the weight. Give each neuron a unique id and this requires about 10-12 bytes per synapse instead of 1. This is only one order of magnitude difference between a fixed and arbitrary topology! And this is probably a gross overestimate of the storage space required because the topology of the nervous system is far from arbitrary - after all the thing is generated by a genetic code of very modest size. See my posts on why the large search space doesn't kill attempts to solve protein folding.
Obviously I ignore the functioning of the glia - I know for a fact that these are very important for the growth and development of the brain but I'm not sure they are the critical part of its computational function. If you know otherwise please point me to some references, I would love to know!
The reason that I mentioned the speed difference of electronics and neurons is that this is what makes it possible to update the state of those 10^15 synapses in real time. Of course it would be wasteful to use the standard PC architechture for this process, but still.
However, I'm very close to certain that your post is basically a lot of hand-waving that is ultimately not only poorly reasoned but also actually incorrect.
- - -
The question we're trying to answer is basically, "What's the computational capacity of the brain?"
But that's not really a good question to work with, because "computational capacity" isn't well-defined. [Actually, I'm not sure about that. I know that either it's not well-defined, or its definition is something that's clearly not what we want in this situation.]
So let's ask something that we can actually reason about, like, "Assuming infinite memory, roughly how many floating point operations per second would a computer need to be able to execute in order to direct a human body in a way that's indistinguishable from what a real person does -- in real time?"
And, okay, we really only want the brain's conscious thought and maybe some of its unconscious thought, but it's hard to make a well-defined question involving just those things, and I doubt that the answer to our question will be more than a few orders of magnitude off of what we're really after.
- - -
Anyway, your post does a really, really bad job of answering that question (or anything like it). Your worst offense: > "So the human brain has about 10^11 neurons and about 10^4 synapses per neuron. Naively representing the state of each synapse with one byte requires 10^15 bytes that's about 500,000 PCs."
Come on. Did the fact that you had to use the word "byte" not tip you off? YOU'RE DISCUSSING MEMORY. Nobody cares about memory, because the amount of memory needed to store the brain's state is vastly less than the number of operations needed to simulate its function in real time.
I seriously am not able to articulate how frustrated I am that at least 12 people felt justified in upvoting you without taking the time to process the first two sentences of your post.
Before I go, another treat: > "Electronics are potentially a factor of 10^8 faster."
No. Electronics are a factor of 10^8 "faster", when "faster" is taken to mean "more rapid in executing a cycle." Which is an absolutely pointless irrelevent piece of shit statistic.
What the fuck.
- - -
Anyway, let me wrap up this post by actually answering the above question as best we can, given the current state of scientific understanding (or, more precisely, my understanding of that state of understanding):
There are on the order of 10^10 neurons and on the order of 10^11 glial cells in the adult human brain. These cells are directed by untold numbers of chemoattractants. We have no good theoretical model for the behavior of these cells in huge numbers of situations.
Therefore, WE HAVE ABSOLUTELY NO FUCKING IDEA how much processing power it would take to simulate the brain's macro function. We can put an upper bound on it: we know that if we could simulate every atom in the brain to a reasonable degree of accuracy, we'd get human behavior. Obviously the number of FLOPS it would take to do such a thing is unreachable. And beyond that, I don't think it's fair to say we know anything at all.