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

Friday, June 28, 2013

Chapter 6, Wherein Aristotle Gets Hooked on Real Housewives of New Jersey

This is the only civil caption I could think of.
A mind needs concepts like a body needs enzymes.

As mentioned earlier, without the right enzymes we can not digest food.  Similarly, without the right mental enzymes (concepts) we can not digest information.

Take the example of an ancient greek watching an episode of "The Real Housewives of New Jersey" on a TV screen you have brought back in time.  (Assume the TV is hooked up to a DVR and that power is being provided by a generator – in other words, you loaded down your time machine with all the technology it takes to make a self contained video machine).  The greek can not comprehend what is happening, not because he is stupid, but because his mind lacks the enzymes needed to digest the information.

Some of the information will be clear to him.  He will see that the images on the screen are moving.   He will see the little images of people and will recognize them as such.  He might find the fashion confusing (or given the picture above, maybe not as confusing as we might think).  He wouldn't understand anything that was being said, of course, unless it was in Greek.  Maybe The Real Housewives of Athens would be a better program to introduce him to.  Of course, even then the modern Greek would be substantially different from ancient Greek.

In any case it is not clear what he would make of the moving people images.  Would he think they are very tiny people in some sort of window or would he think it was some kind of moving mosaic?  Perhaps he would think it was a vision, a prophecy, or a collection of spirits.   Whatever sense he did make out of what he saw would be determined by the concepts he was used to or was working from.   The information would be digested, even if imperfectly, but it would only be broken into whatever pieces those concepts could process.

There is a well known quote which is actually Arthur C. Clarke's "3rd Law":
Any sufficiently advanced technology is indistinguishable from magic.
Arthur C Clarke 1917-2008
There are several implications of this assertion, but one of them is surely that our minds can not comprehend what we are not conditioned to accept.  To the ancient Greek, watching a television show -- even a mind-rottingly bad television show like Real Housewives -- would be a transcendental experience.

Could we ever hope to explain to the ancient citizen what was "really happening"?  For that matter, how many of us actually have a firm grasp on exactly what it is that is happening with our little machine.  From the endothermic reaction of burning hydrocarbon in the generator and the digital storage of video and sound on the hard drive of the DVR, to the use of lighting and lenses and editing to convey the dramatic storyline, there are a lot of details many of us modern folk may be a bit fuzzy on.  Would we be able to adequately explain our video machine even if the Greek listener was willing and able to learn?  It is an interesting feature of concepts that they can function on a high level without needing to understand every single detail which constructs the lower levels of a process.  We can use a microwave without knowing how to build one, or even how it works.  And we can watch TV without needing to understand all that goes into making, transmitting, and storing a television show.

But if this is true it is because we were taught to accept these concepts.  In all the discussion so far on thinking and context forming, we haven't yet touched on TEACHING.  But that will have to wait for now.

What is Smarts?

Intelligence takes many forms -- another topic of discussion that is long overdue -- but I'd like to focus on learning and analytical intelligence for the time being.  I will call it "intelligence" even though we know that word is slippery.  We'll get more precise later.

One mark of intelligence is mental flexibility.  This is in large part the ability to adapt existing concepts or create new ones on the fly in order to process new information.  A "smart" person learns easily because she can move around the legos of her mind to build sensible shelves for storing new data and ideas.  As context means "woven with", an intelligent learner joins strands from existing mental fabric into the threads of new information quickly and securely.

But if the blocks of new learning fall easily into place, it is largely because existing mental enzymes catalyze this process.  Concepts can hold new ideas in place like vice grips while the work to join them with other information is being performed.  Picture a person trying to nail two boards together without any surface to place them on or any tool to hold anything in place.  A great deal of effort would be expended before even the most tenuous connection is made.  This is because every hammer blow meant to drive the nail into the boards simply pushes the boards away from each other.  And this is a little like trying to absorb information with no context to set upon and no concepts to hold them in position.

Another look at mental enzymes we call concepts

If I gave you three pencils, how would you know how many pencils you had just received?  You could count them.  But now what if I gave you three more pencils.  How many would you have now?  You know the answer is six.  And you could derive this by the same method as before (counting them all) or you could simply add 3+3 and come up with 6.  In this case the concept of “addition” is the mental enzyme that simplifies the work (or lowers the reaction energy) of counting and gives you a result very quickly.  You could still use the "manual method" of counting.  You will certainly not get the wrong answer, but counting is a slower (if more natural) reaction pathway and takes more time and effort.

To drive the point home, what if I gave you 94 pencils and then 93 more?  We already know you have to count them all to begin with.  I give you 94 pencils and you count them.  I give you 93 pencils and you count them.  But now how many pencils do you have.  If you count them you will reliably come up with 187.  Or you could simply do the math.

3+2 = 5
Once we have formed the concept of addition in our minds, we have catalyzed all future number problems of the same type.  Instead of counting one number on top of another, we simply “add them together”.  This saves us time and effort.  Of course the concepts of subtraction, multiplication and division function much the same way.  And each concept builds on the others that precede it.   It is almost as if the enzyme we call multiplication is made up of addition enzymes joined with some new material.  The fact that we know that multiplying something by four is the same as adding it to together four times  (2*4 = 2+2+2+2 and 19*4 = 19+19+19+19) helps us build the mental enzyme we call multiplication.   But each new concept which builds on the previous ones contains its own new powers.  So for example we learn (to our initial surprise) that 19*4 is not only 19+19+19+19 but also equal to 4*19 which is also 4 added together 19 times (4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4).  We could confirm this by counting, but once we have mastered the concept, we do not need to. We are sure the catalyzed reaction gives us same product as the more basic one, only much faster.

Basic math is a great example to use in explaining the principle of concepts as mental enzymes, partly because we all share that knowledge and can verify its outcome.  And the beauty of numbers is that they are discreet.  The number 2 always means the same thing whether it is in a recipe for chocolate cake or a formula for determining the escape velocity on the moon.

If we want to be technical (and the jury is out on whether we actually do want to be technical or not) we would have to admit that we glossed over some other concepts in our rush to extol the virtues of the mathematical concepts above.  For even the notion of counting or heck even numbers themselves are concepts.  It is easy to say “Here’s three pencils.  You can count them and see.”  But the reality is that “numbers” and “counting” are both concepts.   And they are pretty abstract concepts at that.

George Gamow, in his book One Two Three... Infinity, says that many Hottentot tribes in Africa have no specific words for numbers larger than three.  Anything requiring an answer larger than three is simply "many".  So we may take counting for granted, but we would do well to remember that it is a mental concept to assess the number of objects in a group in an unambiguous way.

This will not end well.
So even for our addition example, we needed to rely on the concept of counting to set the stage.  It becomes clear that as we try to explain even very basic concepts we are stuck using still other more basic concepts in the process.  This paradox is both common and problematic.  It is a bit like trying to use language to describe language or indeed using our minds to think about how our minds think.  “Thinking about thinking” is a nice playful phrase, but it is also a kind of paradox.  "I think therefore I am" could really be described as "I think I think, therefore I think I am."  For we can't know what thinking is without thinking about it.  As such it is a mental Uroboros, a thought snake eating its own tail.

Douglas Hofstadter examines some of the mental paradox of thinking about thinking and using our sense of identity to discover our own identity in his book I am a Strange Loop.   We will leave recursive systems and strange loops for another day so as to stick with the concept of concepts for the time being (pun unintended but unavoidable -- as so many recursive systems are).

For now it is sufficient to say that although there is something oddly delightful about seeing something perform its function on itself (a child will marvel at the site of a tow truck being towed by another tow truck and I still enjoy pointing a mirror at another mirror) there is nothing intrinsically illegitimate about a recursive process.  We may think about thinking all we want. The result may simply not be what we expect.

Another feature of enzymes and concepts

If you'll recall, when we touched upon the definition of an enzyme, or any catalyst really, we mentioned that it was not consumed in the reaction that took place.  It can be ALTERED, but not CONSUMED.  So too it is with concepts.

No matter how many times we add numbers together, we do not destroy or consume the concept of addition.  Addition is not the fuel that powers this energy saving device.  Rather it is the mental mold that we fit numbers into in order to produce the sum.   The mold is re-usable.  No matter how many numbers we add, we can "dump them out" and add new ones as many times as we want to.

Birthdays were once exciting and delightful
A catalyst can be affected by the reaction it catalyses, however.  In the chemical world there are many catalysts which become less efficient over time due to minor changes in the catalyst (such as coking referred to earlier).  Concepts can similarly be affected by the information they help process.  So while the concept is never "used up", we can form additional insight or flexibility (find more cases where a concept applies for instance), or we can even find that certain concepts we rely upon don't age well and become less useful.  What was once a concept that produced a perfectly acceptable result may over time yield information which is less useful or accurate for our evolving purposes.  To cite a crudely complex example, our notion of "happiness" changes over time as we grow from early childhood into adulthood.  The kinds of mental states we craved as children become less meaningful or fulfilling as we age.  Our knowledge of this change can even lead to melancholy as we long for a time when "life was simpler".  But what has happened is that the concepts we used to measure, evaluate -- and even seek out -- happiness changed over the years we used them.  And interestingly they were changed by the very experiences brought about in our quest for happiness.  So in other words, the information process that was catalyzed by the concept in turn altered the concept.

As we proceed in the coming months to examine what kinds of concepts we build and how they relate to the contexts we form, we will investigate these points further.  Specifically we will look at how concepts help us build new concepts, how concepts evolve through use, and what happens when people are confronted with information when they lack the conceptual basis for breaking down the data and forming any kind of understanding.

Before we do that, though, we'll take some detours into self-similarity, recursive systems, strange loops, and that troubling news Godel forced us to confront with his Incompleteness Theorem.  As we'll see, these will all illuminate something about how we form conceptual understanding.  Ultimately we will need all of these tools to properly think about thinking.

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