Wednesday, April 20, 2005

Why My Old Post Is Wrong

On March 30 of this year I wrote On the Uselessness of Intuition; An Untestable Hypothesis to Explain Creationism.  In it, I posited my own definition of intuition: Intuition may be defined as the practice of drawing conclusions based upon untestable propositions.  Of course that is not really wrong.  Because of the fact that it is my own definition, it is correct, by definition.  But I have to admit that it is not the definition that everyone else uses.

Now consider what someone (Jeff Everist) wrote on a where-to-go-hiking website:

[...] That's really not enough sentences to do justice to the complex geologic processes involved, but it gives a rough idea of where the dunes come from and how they travel. The result of those processes is a somewhat weird and surrealistic landscape, but it is a place full of natural beauty, too. There is an outer-worldly feel to this Earthly realm.

That's why White Sands is at its best on full moon nights. Then magic and mystery, science and sorcery, the heavens and the Earth all mingle in the moonlight. Plants and animals, every living thing, and there are more than you might imagine, all react to the light. Some flowers are tricked into blooming, and a few extremely nocturnal creatures stay holed up until the moon goes down. [...]

click: someone else will sell you this pictureNew Mexico has a number of virtues.  Las Cruces, for example, is the true Pecan Capitol of the World.  And if you ever watch the sun go down, over the Organ Mountains, while putting your mind at ease, at White Sands, you will understand why the place attracts a lot of artists and persons interested in alternative spirituality.  Others have noticed this: if you google "sunset White Sands Organ Mountains," you get over seventy-two thousand hits.  I looked at a lot of the pictures that people have taken, in order to illustrate an aspect of intuition, but it is a pointless exercise because you really have to be there. 

I'm not really a Las Crucian, having spent only about two years there, but Cyndy, of Mousemusings fame, did spend a lot of time there.  Therefore, she is much more intuitive than I.  Her response to my rhetorical dismissal of intuition is contained in a single sentence:
"It is by logic that we prove, but by intuition that we discover."
Really.  That statement is attributed to a guy named Jules Henri Poincaré.  Here is the link to a bio at the Internet Encyclopedia of Philosophy.
[...] Poincaré studied mining engineering, mathematics and physics in Paris. Beginning in 1881, he taught at the University of Paris. There he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.

At the beginning of his scientific career, in his doctoral dissertation of1879, Poincaré devised a new way of studying the properties of functions defined by differential equations. [...]

Poincaré sketched a preliminary version of the special theory of relativity and stated that the velocity of light is a limit velocity and that mass depends on speed. [...]
A serious man, Poincaré.  (His essays probably do not contain spurious references to pecans or corned beef sandwiches.)  If you follow the link to his biography, and scroll down, you find a discussion of his thoughts about intuition and logic. 
For Poincaré, the principle of complete induction, which is not provable via analytical inferences, is a genuine synthetic a priori judgment. Hence arithmetic cannot be reduced to logic; the latter is analytic, while arithmetic is synthetic. [...]

In other words, every elementary inference in a proof is easily verifiable through formal logic, but the invention of a proof requires the understanding -- grasped by intuition -- of the general scheme, which directs mathematician's efforts towards the final goal.
In other words, in the realm of logic, it is possible to really prove things.  But once you make the leap from logic to arithmetic, you have to make at least one assumption.  You can prove that things are true by definition, for example; but beyond that, you are relying -- to some extent -- on guesswork. 

Now, if you consider the phylogeny of knowledge...

logic --> arithmetic --> mathematics --> physics -->
chemistry --> biology --> psychology --> perception

...it becomes apparent that our understanding of the world we live in -- the world we perceive -- is constructed upon a lot of guesses, and guesses upon guesses.  Thus, intuition is far from useless.  In fact, intuition is necessary for us to to have any understanding of the world. 

Therefore, I will revise my definition of intuition: Intuition refers to two similar but distinct processes: the practice of drawing conclusions based upon untestable propositions; and the practice of generating hypotheses based upon untestable propositions.  The former application is problematical; the latter is necessary just to get out of bed in the morning. 

Before you get out of bed, you first must assume that you are really awake, and not merely dreaming that you are awake.

(Note: The Rest of the Story/Corpus Callosum has moved. Visit the new site here.)
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Read "Blink" by Malcolm Gladwell.
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