Those solutions make the greatest
appeal to the mind which depend upon ideas rather than upon calculations. It is
sometimes amazing to see what can be produced from a simple idea, and what
great consequences may flow from it.
It seems almost incredible
that so much can come from
so little.
-- Louis J. Mordell, Reflections
of a Mathematician (1959), p. 40
An essay in this morning’s NYTimes, on the dwindling public status of Big Ideas, prompted me to fret upon the fact that I’ve been sitting on an exploration of the subject for several years, adding a paragraph every few months or so, until (in the fullness of infinite time) it might be ripe (“Pauca, sed matura” -- the motto of Gauss): thus virtually daring the Reaper not to take me just yet, ere the work be finished. But the Reaper might have other plans. And so, as earlier with the subject of Causality, I here publish some preliminary notes.
The essay in question, by the author of a study on such wide-ranging deep thinkers as John von Neumann and Arthur Koestler -- oh no wait, actually his magnum opus is about Walt Disney, nevermind -- is the lead article on the front page of the section I always go to first: what used to be known as “The Week in Review”, but which, in a bold rebranding, aimed no doubt at recuperating those twentysomethings and panda-handlers and whatever other demographic has been abandoning the print media, has been re-baptized… wait for it…. [But! We! Can’t! Wait for it! We’re the InstantGratificationGeneration !!!] …. ‘Sunday Review”. But on the Times website, it is deeply buried, so we link to it here:
It, itself, dives to no particular depths, seeming more like the musings of someone who is bored with what has recently been on TV (hey man, it’s summer, hold out till the fall schedule). But it is very, very refreshing, even to see a sort of placeholder of an article on the subject of ideas, rather than the latest vaporings of Michelle Bachmann, or a conspectus of Celebrity Tattoos.
And even at that, in the timid middlebrow venue of the New York Times, as a primary representative of the "Elusive Big Idea", we are offered (along with the inevitable Einstein) ... George Washington Carver.
(True, true, I’m being snarky again. The Times article in turn used its lead paragraph to be snarky about the Atlantic -- apparently an eyebrow’s-breadth lower on the nation's Middle Brow. -- Meanwhile somewhere there’s a blog that is snarky about me. Unfortunately, it is written in Klingon.)
And so, I herewith offer, the beginning of a selection of observations, to be continued if I am spared -- as yet but halfway baked, but which else would have been mere scraps in the Nachlass, while I lay cold upon the slab.
~ ~ ~
ANY IDEAS? (incipit)
Basic ideas, like idealized geometric figures, are few.
--S.J. Gould
Locke, we learn, innovated, in his use of the term idea:
The term ‘idea’ as coined by Locke and used by Berkeley does not have its normal sense – a fact much remarked upon by Locke’s contemporaries. … Locke.. defined an idea as ‘whatever is the object of the understanding..’
[H. Robinson, intro to Berkeley, p. xii]
We too shall do so, though not with philosophical intent, but only expository convenience. We shall use the term roughly in the sense of a ‘leading idea’ (French: idée-force), one which really does lead your thought and behavior, as opposed to, say, ‘bright idea’, a balloon that goes poof when it bumps up against the cactus of reality; or idea in the sense of ‘general impression’ (“Any idea how…?”); or ‘proposal’ (“I have an idea! Let’s go out for tacos.”) . Idea, in our shorthand sense, denotes battle-scarred propositions that have repeatedly won laurels on the open field. We shall crown them with a capital: Ideas.
Our concern is not at all with the (perhaps hopelessly) abstract, and properly philosophical, question of what ideas ARE, simpliciter. Rather, given an initial intuitive notion of leading ideas, what are some examples? The answers will differ from epoch to epoch, and nation to nation, and person to person – and to that extent, the question is of scant general interest. (You might want to stop reading right here.) I am simply attempting an inventory of the various struts and strengths of my own ideation, and more broadly that of the scientific/intellectual community with which I am conversant.
First, a sketch of what we shall not be considering under this head. We mean only such ideas as we come to learn, and may explicitly reflect upon, and cite evidence for: thus excluding capabilities or notions that we are more or less born with. Otherwise many or most lower species might be said to possess Ideas. In some sense they may, but it is not our sense here.
Nor do we consider Life’s Lessons Learned. As a result, the roster below may seem skewed towards the brainy and the bloodless, but there is a reason for the exclusion. I have the sense (and this itself might almost qualify as an Idea) that such life-lessons tend to be, and perhaps always are, merely relative to a time and a culture, and even to be largely conditioned by one’s individual psychology. The Ideas we consider must be of general validity, so far as we know (things like the Existence of Other Minds, or Induction; rather than, say: “Women – you can’t live with them, and you can’t live without them” – true enough for most of us, but a dictum which singularly fails to obtain on the Isle of Hnork).
So, to our roster, in no particular order.
(1) The Isomorphism of Other Minds
Consider any member of a species of born solipsists. As time goes on, he would notice a large number of regularities; and, if of a logical cast of mind, would soon hit upon the Idea that his conspecifics are mentally quite comparable to himself – that solipsism is in fact false: in a sense, radically so. Human beings, apart perhaps from autists, are not born solipsists, so this insight does not arrive as an Idea: we innately assume the existence of like minds; it does not strike us as a revelation. We have to be taught in philosophy class even to entertain the solipsistic hypothesis as logically possible.
[In like fashion: After reading a great many attacks on the notion of free will, both empirical and philosophical, I have nevertheless concluded that some core thereof is epistemologically as irreducible as the Cogito. But this does not qualify as an Idea, since it merely preserves the naïve assumption.]
So: Thus far we have an organizing principle, a basic assumption, but it is not an Idea, because we are born with it; we share it equally with Mike the Milkman.
There may, however, be a further appreciation of Other Minds which does qualify as an Idea in our sense. Namely, that successful communication often depends upon a wealth of shared tendencies and attributes among communicants; failing these, attemps at communication, even elaborate attempts, seemingly inexplicably go awry. This (quite disturbing) result contravenes the straightforward assumption that communication succeeds by virtue of its content and presentation. The model of human communication becomes not so much the Dialogue concerning Two New Sciences, as rather the antennae-canoodling of ants -- very effective, but whose content is nowise propositional, but lies wholly in chemistry..
Much could be said on this score, but it is not our concern here to prove or even motivate this. It is a conclusion I have gradually come to, and it qualifies as an Idea. It may of course just possibly be false, and would indeed be so if even the weaker hypothesis of the Existence of Other Minds (connected to our own) were false – the old brain-in-a-vat scenario. For that matter, all of mathematics may somehow be a mistake, the physical world an illusion, etc. etc. We won’t worry about that. In light of our best intuitions, tutored by reason and guided by experience, it is well-founded, and is an Idea.
(2) There is a Universe
Which is to say: There are more things in heaven and earth, than are dreamt of in the nursery.
Here the genetic development is straightforward, and well-known. Initially there is just the Breast, and (in its tragic absence) one’s Blankie. Then there is the House to be explored, and the Neighborhood, and School; and foreign lands, and even planets; et cetera, et amazingly cetera.
It grows to an Idea, in that it eventually reflects back on items initially not conceived as so situated. The cup of coffee on one’s desk is no longer just an object, surmounted by a curl of steam, but the proverbial Universal Cup of Coffee, embedded in a nexus of economic-social-technical relations. Eventually, every single thing you meet you may assess in terms of its being an instantiation of a universal.
http://worldofdrjustice.blogspot.com/2013/06/ideas-case-of-induction.html ]
I am surprised to find no plethora of commentary. I can feel an idea formulating. Let me ruminate about it. I shall read on.
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