A mind is like a parachute
It might save your life,
but you have to know how to use it first.

Saturday, June 30, 2012

How do you count soup?

If I handed you a pot of soup and asked you to count out 27 for me, you might ask me, "27 what, spoonfuls?"

"No," I'd answer, "27 soup."

"27 SOUP?"

"Yes, please."

"I can't do that," you'd say.  "It makes no sense."

"Okay, I see. Then give me 27 flavor units."

And at this point, you'd probably shove the pot of soup back at me and storm out. You're so easily annoyed.

But do you see the problem here?  I have a huge pot of soup. I know it is soup because I can see and taste it.  It is held in a pot, but the pot is not the soup.  It is just the vessel for the soup.  The good stuff is the soup sloshing around inside.  And I know it is there, and I know that it has flavor.  It has lots of different flavors all mixed together, actually.  And I want to count the soup flavor.

So now let's look at another problem I have.  I want to calculate how many thoughts my brain can hold and how many thoughts it can have in a second.  I know that there is such a thing as thought.  It is here in my brain.  It comes in many flavors.  They are all sloshing together and I want to count them.

Well clearly that's just going to be a dead end.  You can't count thought any more than you can count soup.  You could put some arbitrary measurement in place and count spoonfuls of soup or completed thought tasks (like pronouncing the word that appears on a screen), but you can't simply separate thought into its component parts any more than you can assign a soup a "flavor unit".

Here's an interesting problem.  Try not to think of the number 4.  Take a minute and focus on not thinking of the number 4.  I'm not saying think of something besides the number 4, I mean specifically instruct yourself to stop thinking of the number 4.  Every time the number comes into your mind, bat it away and focus on how you're not supposed to be thinking about it.

If you're anything like me, this rather confusing process starts out a little slow but gets faster.  You may be surprised by how few times you actually get to dismiss the number in a span of a few seconds.  Maybe you could do it once or twice a second or even three to four times a second it you're really into the flow.  But time ticks by amazingly fast as you focus on not thinking of the number 4.  This suggests some interesting things.

In the first place it suggests that there is a huge disconnect between conscious puzzle solving thought and the speed of synaptic firing in the brain.   Neural synapses are widely reported to be capable of 100 times a second though in practice the figure seems closer to 30 times a second.  And we know from dreaming and being scared and exercising and lots of other activities that our minds are capable of making decisions and adjustments at incredible speeds under certain circumstances.  But for good ole run of the mill puzzle level concentration, thought does not come close to approximating 100 times a second.

To get a sense of the maximum horsepower of the brain we could calculate the theoretical maximum number of synapses that could occur in a second.  Sources vary on a number of metrics, such as how many neurons we have, how many synaptic connections these cells have, and how fast exactly a neuron can fire, but one estimate I read was 100 billion neurons each with 7000 connections on average.  The number of neurons seems pretty uncontroversial, but I've seen as few as 1000 connections per neuron.  On the other hand I've seen suggestions that the fire rate of a synapse could be 200 per second.

So let's just pick a number on the low side and come up with some number that tells us at least in some small way something about the raw firepower of the brain.  A common convention seems to be to assume 100 trillion (100 million million) synaptic connections in the brain.  At a fire rate of 30 times a second, you could produce 3000 million million or 3 billion million synapses a second if your brain were ever in the unlikely state of "firing on all cylinders".   To put this impossibly large number into context we could try a couple images.

Here's a fun one.  Imagine that every person on the planet who is not already completely bald shaved his or her head and then took each hair and cut it into four pieces.  Each person places that hair into a shoe box which they hold in front of them.  Then one day at the stroke of midnight GMT, every person on the planet throws the entire contents of the box into the air, in that one instant, each piece of hair floating in the air all over the globe would represent one synaptic firing in the maxed out brain we calculated above.  400,000 pieces of hair for each of over 7 billion people.

Another one...  There are about 500 billion grains of sand on a beach volleyball court --- 8 meters wide and 16 meters long and half a meter deep.

If each grain of sand represented a synapse from our above calculation, it would take 6,000 volleyball courts worth of sand to reach the number of synapses in one second in the brain.

So we get that it's a big number.  But it is also a meaningless number in a lot of ways.  It gives us a sense of just how many synapses the brain is capable of, but it vastly overstates how many times synapses in a normal brain will fire under normal circumstances.  It is a little like seeing the speedometer labelled all the way up to 200.  It is not ever going to get there.

And of course another important consideration for our purposes is that the vast majority of synaptic firings in the brain are not devoted to the kind of thinking we are focused on.  We are not so much concerned with the "total wealth" of the brain as we are its "disposable income".  In other words, all the activity in the brain that pays the rent and keeps the lights on (keeps the heart beating and the lungs breathing, and monitors and controls all the basic body functions including response to sudden danger), is activity that is not really available for conceptual organization of data.

But for fun we can assign some tiny percentage of total brain power and assume a very low load (slow firing rate) just to see how many synapses we may associate with a thought puzzle.  Now this is all completely bogus in any literal sense, but it can be instructive nevertheless.  We have no set description of how many synapses might be required to make one symbol or token or thought, much less how many discreet thoughts it may take to solve a puzzle.  We simply don't even know how the electrochemical process in the brain translates into conceptual understanding.  But we know that it does.  This pot has soup in it, even if we don't know how it's made.

For the sake of argument, lets just assume the "4 puzzle" takes .001% of our brain's total neurons (1 in 1 million) and that the firing rate is a leisurely 10 per second. Furthermore of the 1000 possible connections each neuron can make, we will use just 10%.  We established before that it takes us maybe half a second to "not think about 4".  That would imply 50,000,000 synaptic firings.  50 million synapses to perform the puzzle.

What's the point of making blind guesses to put numbers to something that we don't even understand the underlying mechanism of?  Because it shows us just how vast the brain's capacity is.  Even using scaled down assumptions about how much brain power would be required to focus our thought for a half a second, we end up with a very large number.  We could obviously be off by several orders of magnitude.  But if our estimate is too low, that's not a problem, since what we're trying to do is get a sense for just how complex the synaptic process may be.  On the other hand, it is possible we guessed too high.  But even if we were off in two factors by a power of ten (for example only 1 in 10 million neurons is involved and they only make 1% of possible connections), we still end up with 500,000 synapses to get the single puzzle completed one time.  It makes no difference how well we have guessed at something that doesn't happen as literally as we are assuming it does anyway.  What we have shown is that no matter what the mysterious process actually is, the brain is capable of generating a great many synapses for each task.

This concept will be more meaningful when we pull it over to the hive-mind analogy and compare our results for the brain with our results for the planet if each human were a little neuron.

And that's where we're going next as we finally get to tie some of these concepts together.

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