What a strange question: How big is a thought? Can have sizes?
We know that a blue whale is larger than the krill on which it feeds. Does that mean that the blue whale thought must be larger, by 100s of thousands of times, than the krill thought? What about the thought of a star and the thought of a quark? Is the thought of the universe the biggest thought of all? If so, is it contained in that sentence, by mere inclusion of the phrase, “thought of the universe”, for that sentence is a small thing, is it not?
I suppose one might as well ask: How many thoughts can you put on the head of a pin, nicely arranged, by category? Now, if one asked that of books, the answer is simple: None, books are each one alone, typically, much larger than a pin head. Now, if we could miniaturize the books—I’m thinking of Nelson Shrinkafeller (scan down the page), an occasional character from the old Li’l Abner cartoon strip . . . .
The size of a book depends on many things, kind and weight of paper, page size, how the type is set, and so forth. But it depends mostly on the number of words. Words represent thoughts, no? Do lots of words imply a big thought, perhaps standing behind them, like the sun rising through the trees, spreading streams of glory through the forest? But what of a telephone book? Lots of words, but nary a thought among them.
If all those questions are born of category mistakes, you say, then how is it that we talk of big ideas? There’s a website called Big Think, presenting “Blogs, Articles and Videos from the World's Top Thinkers and Leaders.” What is it about those thoughts that makes them big? I suppose its their implications. Perhaps a BIG THOUGHT has implications for many other thoughts, brings a new order to them, whereas small and medium-sized thoughts are not so richly linked to other thoughts.
Perhaps we can represent thoughts by networks, like maps. Each atomic thought is a place on the map. These thoughts are connected to one another across the surface of the map. We could then say that thoughts with more connections, with a larger network, are BIGGER than thoughts with few connections.
Here’s a paragraph that’s influenced me a great deal. It’s from the introduction to Constructing Social Theories, by Arthur Stinchcombe, one of my undergraduate teachers.
In my first year of graduate-school, I turned in a paper to Reinhard Bendix called “Rhetorical Opportunities in Some Theories of Social Change.” After some discussion of the substance of the paper, he made a comment that has shaped my attitude toward “theory.” He said, “you know, a little bit of theory goes a long way.” He went on to say I ought to decide what phenomenon I wanted to explain.
If a little bit of it goes a long way, then perhaps theory consists of big thoughts. Yet, if you know anything about the conversations between teachers and students, you know that there’s a bit of kindly irony in that statement. Too much theory chasing too few observations leads to a mess.
But it was the next paragraph that floored me. I would even say it had a considerable impact on the way I conduct my intellectual life, though not in a BIG THINK kind of way.
A second graduate-school conversation, with Philip Selznick, shaped my attitude toward what theory is for. He remarked that one felt satisfied that he understood something when he could summarize in a sentence the guts of a phenomenon. He gave the illustration that he felt satisfied when he realized that the achievement of the Bolshevik parties was “to turn a voluntary association into an administrative apparatus.” To use, as a criterion of judgment, the guts of a phenomenon—what is going on—is better than to use any logical or formal criterion.
There you have it, a single sentences, but the guts of a phenomenon. The blue whale, a single sentence. The krill, a single sentence. A star, a quark, the universe, single sentences all.
But who can write those sentences? Would each expert, whether scientist or poet, write the same sentence? And who to understand them?
Can you do that? A single sentence. Try it.
Take something you understand well, and express that understanding in a single sentence. It need not be a particularly short or pithy one, but it shouldn’t ramble through a dozen clauses netted over 100 words either. If you can’t get there in one swoop, try expressing your understanding in a single paragraph, even a long one of 400 or 500 words. Then distill the paragraph into that one sentence that grabs the guts of the phenomenon.
Now, I ask you: How big is a thought?
Of course everyone would write a different sentence. More importantly, the metaphoric "guts" of an idea will vary widely because people are so idiosyncratic. I find the Russian Revolution example quite ungutty, not even intestinal, for instance; rather, I find it makes so many abstract theoretical presuppositions that it's as useless for understanding as psychoanalysis or universal grammar.
ReplyDelete"Idea" is as metaphorical as "guts", and the strangeness of the question echoes the strangeness of the question about whether language influences thought. Language IS thought, or a part of thought, and a different part for each person. So how about if the question were:
Do ideas influence thought? Now there's a strange sentence.
...I find it makes so many abstract theoretical presuppositions that it's as useless for understanding as psychoanalysis or universal grammar.
ReplyDeleteWell, sure, one-liners are going to be like that. I've got no idea whether or not that particular one line adequately abstracts the Bolschvik achievement because I've never seriously thought about it. But coming up with a one-liner that I like, on something I've thought about, that's tough.
I put myself through grad school by writing abstracts of the technical literature in computational linguistics. The idea was to state the 'guts' of a piece in 250 words or less (which is, of course, considerably more than a single sentence). Assume, in a given case, that 1) you trusted the author of a piece and/or you trusted the journal, and 2) you didn't need technical details. The abstract should tell you all you need to know about the article. Writing abstracts like that was tough & not all the many articles came with such abstracts already written.
I imagine you know must OTSOG, Bill – any given thought of real stature stands on the shoulders of more than one earlier thought (Koestler on creative ideas springing from the unexpected juxtaposition of two thought complexes, cf Coleridge's "hooks and eyes of memory") -- so there's a sort of pyramid of thoughts, like acrobats on acrobats on ranks of acrobats… Hesse in the Glass Bead Game says his players are building "the hundred-gated cathedral of mind".
ReplyDeleteIf that's the case, then the "scope" of a thought would be figured in terms of the "arch" that's formed as one idea builds on two or more previous thoughts. Maxwell's electromagnetism thus has very large scope, as does the Wiles proof of Fermat's theorem
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Wiles builds an arch between "modular forms" and "elliptic equations" – the possibility had been suggested in the "Taniyama-Shimura conjecture" which Barry Mazur describes thus:
It was a wonderful conjecture -- the surmise that every elliptic equation is associated with a modular form -- but to begin with it was ignored because was so ahead of its time. When it was first proposed it was not taken up because it was so astounding. On the one hand you have the elliptic world, and on the other you have the modular world. Both these branches of mathematics have been studied intensively but separately. Mathematicians studying elliptic equations might not be well versed in things modular, and conversely. Then along comes the Taniyama-Shimura conjecture which is the grand surmise that there's a bridge between these two completely different worlds. Mathematicians love to build bridges. [Simon Singh, Fermat's Last Theorem, pp. 211-12]
But the Wiles proof does more than suggest or even confirm such a linkage – it builds the arch with intricate, detailed mathematical masonry, as Sing tells us (or me at least, I'm no mathematician):
During Wiles's eight-year ordeal he had brought together virtually all the breakthroughs in twentieth-century number theory and incorporated them into one almighty proof. He had created completely new mathematical techniques and combined them with traditional ones in ways that had never been considered possible. In doing so he had opened up new lines of attack on a whole host of other problems. According to Ken Ribet the proof is a perfect synthesis of modern mathematics and an inspiration for the future: 'I think that if you were on a desert island and you had only this manuscript then you would have a lot of food for thought. You would see all of the current ideas of number theory. You turn to a page and there's a brief appearance of some fundamental theorem by Deligne and then you turn to another page and in some incidental way there's a theorem by Hellegouarch -- all of these things are just called into play and used for a moment before going on to the next idea. [Singh, p. 304]
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I don't think we can get granular enough to see the "elementary ideas" -- what do you think?
And I'm pretty sure we can't get enough altitude to see the topmost pinnacle of the cathedral… It seems to me that the top, if there's a top, would be where two become one, Jung's coincidentia oppositorum, which I think Pico or someone gives as a definition of God – effectively, "cloud hidden, whereabouts unknown" as Alan Watts puts it, or like the peak of Mount Analog, which Rene Daumal does not live to write…
And as in Hesse's game, surely these arches can have aural, visual, and numerical components as well as verbal ones, and are built of emotion as well as intellect…
Otsoggery rulz!
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