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

Sunday, May 26, 2013

On a Scale of 1 to 10, Do You Like Bananas?

What kind of question is that, you may wonder.  Either you like bananas or you don't.  If the question is how much you like bananas on a scale of one to ten, that makes some sense, but a yes or no question can't be answered on a scale (unless it is a scale of zero to one).  You either don't or you do.  A scale of one to ten does not measure "yes or no" matters, it measures how much.  So what is the point of this exercise?

The point is that there are two ways at looking at information such as your fondness for bananas.  The first is to simply determine whether you like them or not and the second is to rank them on a scale.  Each method has its own shortcomings and they will, unsurprisingly, both figure in to our discussion of perception and thought.

Let's begin with the scale of one to ten.  We all know it and have used it before.  But what does it really mean?  "How much do you like bananas on a scale of 1 to 10?"  We all accept that 1 means the least amount of love we could feel for bananas and ten the most, but what would it mean to love bananas so much you rank them a 10.  Does it mean you really enjoy bananas?  Does it mean it is among your favorite foods (holding the same rank as all your other "love to the power of ten" foods)?   Could it mean you are obsessed with bananas?    I mean, it stands to reason that no one could like bananas to the power of 11 -- the scale does not go that high.  So if you say you like bananas to the power of 10 and someone else likes bananas more than you, how much does he like bananas?  Would someone who ranked bananas a perfect 10 want to make toys out of them or build their home out of bananas or think of a way to get to work on banana power?  I mean, after all, ten is supposed to be the most you can love bananas, so what does it mean?  Are we talking about just the flavor or are we considering everything that it means to enjoy bananas.  Is the price of the fruit, its availability, its shelf life, its nutritional value, and its cache as a food you could order in a restaurant all figured into the concept of what we mean when we rank how much we "like" bananas?  We'll come back to this.

But let's consider the equally hard question, "Do you like bananas?"  It demands a yes or no answer.  Presumably I either like them or I dislike them.  It is an easy thing to answer if I hate bananas or I love them.  But what if I am kind of indifferent to them?   I mean, let's say I generally like fruit but they are not my favorite fruit.   Let's assume that at a buffet of many options they would not be my first choice but they would not be my last.  What if they fall somewhere in the middle?  Can I say I like them?   And we don't know anything about how hungry I am.  If I am sitting down to Thanksgiving dinner, I may not be craving a banana.  But if I am a castaway on an island with some smart guy, a farm girl, a movie star, a billionaire and his wife, I may be perfectly psyched to have a banana to eat.  Do I like bananas?  That can be a complicated question.

Besides the problematic nature of these banana questions, there is another feature we will want to examine.  That is precisely that the yes or no option is what we can characterize as "digital data" while the other is best characterized as "analog".   Digital data breaks down everything into yes or no questions that can be answered by a single switch (or scale of zero to one).  The switch is either "off" (I don't like bananas) or "on" (I do).  Analog answers everything on a scale.

But to be clear, it is best not to think of analog as a scale of integers from one to ten, but rather a smooth continuum.   Instead of a scale of 1-10 it is more like you have a glass that is nine inches tall and can pour water into it.  (We use 0-9 instead of 1-10 because the glass may in fact contain no water.)  The water we pour in may be 3 inches high, or eight, or it can be just ever so slightly more than 6 and three quarters, something that if we measured to precision might be 6.768349 inches of water.  It can, in the end, be zero or nine or an infinite number of values in between.  In fact the best example of analog would have been to not provide a scale of numbers at all and simply ask someone to "describe how much you like bananas".

The capacity of analog for subtlety is its strength.  It is also its weakness.

Things in nature tend to be analog.  The breeze does not blow in finite increments but along a continuum of movement.  This is fine in that it allows natural forces to combine in an infinite variety of ways, but it is more troublesome if we are trying to measure something.  When we want to get around to assigning numbers to a thing so we can size it up, we end up drawing arbitrary lines that say more about how we number things than it does what we are trying to measure.

Electronic circuits can handle analog values pretty well, because current is intrinsically analog in nature.  We measure current in amperes, but that does not stop real current from flowing in whatever amount it chooses.  Amperes are the "inch marks" we assign, but like water in the glass, the actual current may be flowing in any value between two amps that it chooses.

On the other hand, logic circuits -- like the ones that do the thinking for computers -- require digital precision.  Since they are made up of a series of switches (or relays), these switches are in only one of two states at any time -- on or off.  There is no room for equivocation in a logic circuit.  Either you like bananas or you don't.

I Robot

It is often said that computers are digital and our brains are analog.  But that is really an oversimplification.  To begin with, computers run on electrical current and we have already established that current is analog.  True, this current is used to drive logical circuitry that makes all of its decisions and stores all of its data using 1's and 0's (on and off switches).  But the current that drives the device starts off as analog and must be coerced into behaving digitally.

In the same way, it is true that our brains seem to be able to manage a full spectrum of subtlety between the yes and no of a question.  But our actual neurons fire digitally.  That is, they either fire or they do not.  Yes the electrochemical process in the brain, like the current in computer, is an analog process.  But there can only be two states for a given synapse.  It either fires or it doesn't.

This mixture of digital and analog in computers and our brains will be worth coming back to when we look at how we make decisions and how our mind communicates with our body.

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