DOES INTUITION…
Stage 15 / Monday 11 May / From Saint-Alban-sur-Limagnole to Malbouzon / 29 km
I now find myself in the department of Lozère, after walking in the Isère, the Drôme, the Ardèche and the Haute-Loire departments. There’s no doubt, the bays of my cathedral are beginning to take shape, even if it’s only the beginning of the nave! I line up my stages the way one aligns columns, and the one today will take me into a wild region of magical charm: Aubrac. There we find rustic honey-colored cows, with lyre-shaped horns, and eyes to fall in love with at first sight…
I notice on this chilly morning that the cows tend to all be aligned in the same North-South direction while they graze or ruminate (chew their cuds) in the pastures still dew-covered. The theory has been advanced that these useful mammals are gifted with “magneto-reception:” they arrange themselves so as to diminish the prickling of magnetic currents which pass through them! Intuitively, that seems reasonable, but is it reasonably proven?
As for ourselves, humans, what currents pass through us? What currents of thought? There are those based on intuitive thinking and those grounded in methodical reasoning. Intuition for some, reasoning for others, which current is closest to the truth? To be deeply convincing, is story telling more valuable than a scientific treatise?
The proverb “He that will steal a penny, will steal a pound”, in its pleasant brevity is typical of a popular wisdom that stands the test of time. This saying is at the same time intuitive and empirical. It can be neither demonstrated nor proven. But better than a treaty of civil code, a course in civic morals, the vigilance of a busload of policemen, or the severity of a judge assigning penalties, this saying transmits a message on the importance of honesty. In the same way, intuitive formulas “One swallow does not make a spring,” or “The best is the enemy of the good” resume in a nutshell what the science of meteorology or a treaty on efficiency take pages and pages to establish.
Does the conviction of “what is” come only by a recurrent and inductive reasoning, as it does in mathematics? Is correct reasoning sufficient? We know how great the step is between the privileged and coherent universe of pure mathematical reasoning and its application to natural sciences, physics and chemistry in particular. Mathematics leads us to better understand the notion of infinity, even to classify a hierarchy of infinities more and more immense. But the complexity of natural phenomena, and the infinity of variables which affect them, quickly force the physicist or cosmologist to formulate simplifying hypotheses to “frame” the validity of the laws they seek to establish.
Thus did the grave Newton succeed in establishing the theories of the celestial mechanism based on the law of universal gravitation. The latter was supported by the hypothesis that space and time were realities independent of each other. The more burlesque Einstein made the more preposterous hypothesis, but which turned out to be right, to see a connection between space and time. For him, the presence of matter provokes a curvature in space and affects, in due time, the course of all other objects moving by. Gravity becomes therefore a perturbation in space wherever it is not empty! This curvature of space-time is more and more pronounced if much matter is condensed in a very heavy body of small size.
Deformation of space near a massive body, the curving of |
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Near a massive body like the sun, space-time is “hollowed out”, and other bodies no long move in a straight line: their trajectories curve inward! Even the trajectory of light can thus be deviated. This was discovered during an eclipse in observing the stars which appeared just beside the sun and noticing that they were stars that should have been spatially hidden behind the sun! Yet, Einstein’s equations could take into account this phenomenon of “gravitational magnifying”, but Newton’s laws are incapable of explaining it. His formulae are powerless to calculate it. In introducing the influence of a new entity, time, and accepting that space can be bent, Einstein has invented a new magnification tool. What intuition!
However, neither these deviations in space-time, nor inductive reasoning permit resolving the well-known chicken and the egg dilemma. “Which one appeared first?” If you say “the egg” then the question is “Who laid it?” And if you say “the chicken”, the reply is “But didn’t the chicken come from an egg?” And we fall into an infinite series of questions and answers; a circle which once entered can never be exited. A circle has neither beginning nor end. Thus, two undeniable truths, one just as inductive as the other, become incapable of resolving a questioning which is of a superior metaphysical order. We see that reason cannot do without intuition, for induction may lead to the generalization, but one cannot escape an inadequate generalization except by a thesis of a superior order.
Unlike the straight line, which in geometry never stops prolonging into infinity, the circumference of a circle is of a finite length. But one has to escape this circle to realize it! Let’s imagine a circle of radius R inhabited by a single person named Vincent. Leaving in one direction, he will be able to find in a given time the handkerchief he dropped at the start! For example, let’s say this takes one minute. If Vincent doesn’t pick up the handkerchief but decides to go back in the opposite direction, it will take him exactly one minute to find the handkerchief again, walking at the same speed around the circumference in the other direction.
Imagine a neighbor of Mr. Vincent, Emil, who loses his handkerchief on a circle twice as big, with a radius of 2R. Emil will never be able to explain to Vincent why he himself needs twice as much time to find his own handkerchief. This assumes of course that Emil moves at the same speed as Vincent. Starting at the same time, Emil will see Vincent moving away, then coming toward him, then passing him to move away again before coming toward him a second time. And finally, when Emil finds his handkerchief after two minutes, Vincent will tell him he found his own twice!
Seen from a helicopter high above, the story of the Thompsons’ jerrycan [cf. Tintin stories by Hergé] and the concentric tracks of their jeep in the desert in Land of Black Gold are easy to understand. Elevation gives understanding of what stupefies them. But who then can provoke the intuition giving the key to this passage at a higher level? Who would uplift Vincent and Emil to envisage two concentric circles, one twice as big as the other?
Thus I realize the necessity of an intuitive power to help the human confront an otherwise inaccessible notion. Facetiously I add a pretty neighbor near Vincent and Emil. I call her Perpetua. She also loses her handkerchief at the start. But unfortunately Perpetua lives on a straight line, not a circle! Watch with me as Perpetua moves away following her departure, at the same speed as Vincent and Emil. We’ll never see Perpetua finding her handkerchief. Vincent and Emil will wonder forever why they have never seen her again! Hello infinite shapes!
Although similar in nature (circles), the dimension of their worlds were different for Vincent and Emil…But Perpetua’s world in which she evolved (a straight line) was of a different nature than her neighbors … The formulation of different hypotheses (different worlds) completely modifies the conclusion reached by the same processes (the walks, at the same speed). Oh intuitive power, what is your source? Can I call you God? Are you the revealing God of the Bible? The Bible, which is said to be divinely inspired… “The proof? It’s written in the Bible!” Aye-aye-aye! Here I go again, caught in the circle of an auto-referential affirmation! Intuition, please help me!
