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Calculus for Hamsters

November 18, 2013

One of the perennial problems I face talking to anyone about my faith is that I hold what are generally thought to be two opposites very dear: a critical, thoughtful reading of Scripture and mysticism.  There are some bad reasons these are considered to be opposites (including the fact that any idiot who mutters nonsense can call themselves a mystic and not get called out for it) but there are also some very good reasons that these seem to be opposites.  One of the most compelling reasons is that careful reading is based on establishing what we do know whereas mysticism is more interested in establishing that whatever we know it isn’t much.  It is hard to say, “Even these small details matter,” and also, “No one really knows much of anything.”  However, I find myself doing both quite a lot.

One of the reasons I do this is because I am a scientist.  There’s an idea out there that science is about having grand ideas that explain parts of nature.  That’s not actually true – science is about testing those ideas and throwing them out when they don’t work1.  All sorts of people have grand unifying ideas and science recognizes scientists for truly great grand unifying ideas but what separates science from other methods of inquiry is testing.  This means that sometimes in my religious life I find that two things are true and cannot explain how this can be.  Instead of insisting that my grand theory must be correct I take the evidence (that both things are true) and ask how to string together a theory that does not reject one of the two truths.  What follows is my best attempt at such a theory to explain why one should read the Bible very carefully and thoughtfully, why it matters when people read it loosely and sloppily2, and yet no one really knows much of anything about God because Who He is fundamentally beyond human comprehension3.

Imagine teaching a hamster calculus.  It won’t work.  Even the brightest hamster will never learn calculus.  There are basic mental prerequisites (including the ability to handle the language necessary to describe calculus) that a hamster lacks.  However, since you have imagined yourself to be sufficiently motivated you will start on this task anyway.  The first part of the larger (impossible) task is to get a hamster to comprehend numbers and attach these numbers to their symbolic representations.  This is probably doable for smaller numbers.  I doubt that hamsters can understand the number 20,000 but they can probably manage the number 2 just fine4.

This may be where the teaching ends.  The hamsters will spend the rest of their short lives working on larger numbers with maybe the very bright ones working on simple addition and subtraction5.  At this point the mystic can step in and make his or her point: the hamsters will never get close enough to calculus to so much as smell it.  They will never touch their paw to algebra, trigonometry, or even long division.  When you draw an integral symbol on the board, a very bright hamster will assume that you meant to write 2 but got it backwards and sort of flattened out.

However, the careful reader can also make a point here.  Numbers are fundamental to calculus.  If a hamster throws in the towel and gives up on that important distinction between the flavor of “many” known as 5 and the flavor of “many” known as 6, then calculus will actually retreat further out of view.  The fact that numbers are not calculus or even close to calculus, does not mean that we can play fast and loose with numbers because they don’t matter.  If some other trainer came in and trained one of these numerically-adept hamsters that 2 is really the same as 8 then you would not shrug and say, “Sure, in the grand scheme of things these differences are minor,” you’d be very irritated.  Just because understanding that 2 is not 8 will not vault you to calculus (or even calculus’s nearer neighbors) does not mean that regarding 2 and 8 as the same is not a major problem.

The union of the mystic and the careful reader comes here: careful reading of the Bible is not going to bring all mysteries and all knowledge bursting in on one’s hermetically-sealed mental world6.  However, it will allow one to lay the groundwork for the larger structure.  If the groundwork is laid wrong everything else will be wrong too.  This is where the bad mystic gets it all wrong – foundations don’t matter because we think they are houses and haven’t yet realized that there’s more to a house than that; foundations matter because houses sit on them.  You can’t say, “Yes, but that’s not the whole thing or even much of it,” and then ignore it.  If the mystic strives to see the workings of a machine too complex to fathom it is exactly the wrong attitude to say that it doesn’t matter what an individual gear looks like.  Instead because the machine is so complex there are more things resting on the shape of each gear than there would be if the machine were simple.

To understand the big picture one must also understand the small.  You will never understand a forest if you spend your whole life studying one tree but it is equally true that if you think trees are a sort of small elephant that forestry will never make much sense.  It is simultaneously necessary to have a large view that places the smaller objects correctly and an understanding of what those small objects are.  A view that gets fuzzy at either end of the spectrum is in some ways fuzzy at both ends since both ends inform each other.  To know that true reality is unknowable without knowing anything else is just giving up.  To be unaware that there is more to know is just sad.

[1] The opposite of science is politics, having an idea and throwing out reality when the idea doesn’t work.

[2] I actually won’t go into as much detail here as I could but the evidence is everywhere.  When people read the Bible funny they do things that are bad to other people – endorse slavery, start crusades, start heartless churches and stare blankly at you when you try to explain why a church that can’t send anyone to talk to the mother who has just lost a child has gone around an important bend without so much as shuddering when it plowed through the safety rails.

[3] Not fundamentally incomprehensible, which would mean that He works in ways that are completely alien to us.  He is fundamentally beyond us – the small fragments of His methods make sense to us (we understand dimly justice and love and truth and so on) but we are incapable of hooking all the pieces together without our brains exploding.  (Which they generally don’t.  Instead they just drop pieces of the puzzle in reflexive self-protection.)

[4] Most humans don’t really understand very large numbers either except by understanding how much work it would be to whittle them down to numbers small enough to understand.

[5] I may be short-changing hamsters here.  Mathematical ability seems to be wider-spread in the animal kingdom than one would guess from the average freshman math class.

[6] And if it did people would ban the Bible in self-protection.


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