Blaise Pascal on the Intuitive vs. the Logical Mind and How We Come to Know Truth

“The heart has its reasons, which reason does not know…”

“Your intuition and your intellect should be working together… making love,” Madeleine L’Engle asserted in contemplating how creativity works. Ray Bradbury believed that intuition and emotion should guide creative work, the intellect coming in only to revise after the act of creation, and Susan Sontag admonished against buying into this polarity in the first place: “The kind of thinking that makes a distinction between thought and feeling is just one of those forms of demagogy that causes lots of trouble for people.” But it’s hard to deny that in most minds there exists a combination of the two and in very few a perfect balance.

The duality of these two faculties and their interplay is what the great French physicist, philosopher, inventor, and mathematician Blaise Pascal (June 19, 1623–August 19, 1662) explores in Pensées (free ebook | public library) — the same masterwork of fragmentary reflections that gave us Pascal on the art of changing minds.

In a passage outlining the difference between the intuitive and the mathematical mind — “mathematical” meaning “logical” or “rational” — he writes:

In the intuitive mind the principles are found in common use, and are before the eyes of everybody. One has only to look, and no effort is necessary; it is only a question of good eyesight, but it must be good, for the principles are so subtle and so numerous, that it is almost impossible but that some escape notice. Now the omission of one principle leads to error; thus one must have very clear sight to see all the principles, and in the next place an accurate mind not to draw false deductions from known principles.

All mathematicians would then be intuitive if they had clear sight, for they do not reason incorrectly from principles known to them; and intuitive minds would be mathematical if they could turn their eyes to the principles of mathematics to which they are unused.

Suggesting that it is a greater failure to be unintuitive than to be unanalytical, Pascal adds:

The reason, therefore, that some intuitive minds are not mathematical is that they cannot at all turn their attention to the principles of mathematics. But the reason that mathematicians are not intuitive is that they do not see what is before them, and that, accustomed to the exact and plain principles of mathematics, and not reasoning till they have well inspected and arranged their principles, they are lost in matters of intuition where the principles do not allow of such arrangement. They are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics; because the principles are not known to us in the same way, and because it would be an endless matter to undertake it… Mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous.

Art from 'The Boy Who Loved Math,' a children's book about the life of legendary mathematician Paul Erdos. Click image for more.

But this mathematical (or logical) mind is only a subset of the intellect that stands opposite intuition:

There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.

Pascal argues that our failure to understand the principles of reality is due to both our impatience and a certain lack of moral imagination:

Those who are accustomed to judge by feeling do not understand the process of reasoning, for they would understand at first sight, and are not used to seek for principles. And others, on the contrary, who are accustomed to reason from principles, do not at all understand matters of feeling, seeking principles, and being unable to see at a glance.

He considers what mediates the relationship between our intellect and our intuition:

The understanding and the feelings are moulded by intercourse; the understanding and feelings are corrupted by intercourse. Thus good or bad society improves or corrupts them. It is, then, all-important to know how to choose in order to improve and not to corrupt them; and we cannot make this choice, if they be not already improved and not corrupted. Thus a circle is formed, and those are fortunate who escape it.

Pascal makes a peculiar and rather poignant aside — doubly so in our divisive age of harsh snap-judgments directed at others via soundbites and status updates — suggesting that our inability to appreciate the singular gifts of other people is essentially a failure of our own intelligence, for the prerequisite for appreciation is comprehension:

The greater intellect one has, the more originality one finds in men. Ordinary persons find no difference between men.

One of Antoine de Saint-Exupéry's original watercolors for 'The Little Prince.' Click image for more.

Three centuries before the most beloved line from the most beloved children’s book — “It is only with the heart that one can see rightly,” wrote Antoine de Saint-Exupéry. “What is essential is invisible to the eye.” — Pascal observes:

The heart has its reasons, which reason does not know… We know truth, not only by the reason, but also by the heart.

Nearly four centuries later, Pensées remains a revelatory read, full of timeless wisdom on everything from navigating uncertainty to the key to eloquence. Complement this particular portion with a fascinating read on the role of intuition in scientific discovery, Carl Sagan on the necessary balance between skepticism and openness, and Hannah Arendt on the crucial difference between truth and meaning.

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Gorgeous 19th-Century Illustrations of Owls and Ospreys

The science of the familiar “owl-face” and the art of its varied permutations.

In his glorious meditation on science and spirituality, Alan Lightman writes beautifully of finding transcendent experiences in our quotidian existence — experiences like his life-altering half-second encounter with two baby ospreys. Indeed, birds of prey like ospreys, owls, hawks, eagles, and falcons have long possessed the human imagination. A fixture of fables and fairy tales — in other words, a symbolic centerpiece of our civilizational proclivity for thinking with animals — they have continued to enchant storytellers and scientists alike.

Nowhere does the transcendent magnificence of this avian family come more fully alive than in the fourth volume the the six-volume masterwork The Royal Natural History (public library | public domain) by English naturalist, geologist, and writer Richard Lydekker, originally published in 1893.

The fifth chapter of the volume explores owls and ospreys, with engravings at once scientifically scrupulous and wonderfully expressive, emanating a warm celebration of the splendid biodiversity of our world.

Barn-owls

Snowy owl and Lapp owl

Ural owl

The beautiful art, of course, is but a complement to the scintillating science:

[The] characteristic “owl-face” is due, firstly, to the forward direction of the eyes; and, secondly, to a circular disc of radiating feathers, more or less distinctly developed round each eye, and which may be bounded by a ruff of closely-set feathers. In common with many diurnal birds of prey, the owls have a short, stout beak, of which the upper ridge is strongly curved, and the tip deflected in a perpendicular direction ; at its base is a cere, usually covered with stiff bristles concealing the nostrils. The feet are furnished with strong, curved, and sharp claws, and have the fourth toe reversible.

Short-eared owl

Scops owl and long-eared owl

Little owl

Hawk-owl

Tengmalm's owl and pigmy owl

Tawny owl

Eagle-owl

Indian fish-owl

Burrowing owl

Osprey and young

Complement Lydekker’s The Royal Natural History with this showcase of some of the rarest and most beautiful natural history illustrations of the past 500 years.

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Emerson on Small Mercies, the True Measure of Wisdom, and How to Live with Maximum Aliveness

“To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom.”

In contemplating the shortness of life, Seneca considered what it takes to live wide rather than long. Over the two millennia between his age and ours — one in which, caught in the cult of productivity, we continually forget that “how we spend our days is … how we spend our lives” — we’ve continued to tussle with the eternal question of how to fill life with more aliveness. And in a world awash with information but increasingly vacant of wisdom, navigating the maze of the human experience in the hope of arriving at happiness is proving more and more disorienting.

How to orient ourselves toward buoyant aliveness is what Ralph Waldo Emerson (May 25, 1803–April 27, 1882) examines in a beautiful essay titled “Experience,” found in his Essays and Lectures (public library; free download) — that bible of timeless wisdom that gave us Emerson on the two pillars of friendship and the key to personal growth.

Emerson writes:

We live amid surfaces, and the true art of life is to skate well on them… To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom. It is not the part of men, but of fanatics … to say that the shortness of life considered, it is not worth caring whether for so short a duration we were sprawling in want or sitting high. Since our office is with moments, let us husband them. Five minutes of today are worth as much to me as five minutes in the next millennium. Let us be poised, and wise, and our own, today. Let us treat the men and women well; treat them as if they were real; perhaps they are… Without any shadow of doubt, amidst this vertigo of shows and politics, I settle myself ever the firmer in the creed that we should not postpone and refer and wish, but do broad justice where we are, by whomsoever we deal with, accepting our actual companions and circumstances, however humble or odious as the mystic officials to whom the universe has delegated its whole pleasure for us. If these are mean and malignant, their contentment, which is the last victory of justice, is a more satisfying echo to the heart than the voice of poets and the casual sympathy of admirable persons.

Indeed, Emerson highlights the practice of kindness as a centerpiece of the full life, suggesting that our cynicism about the character and potential of others — much like our broader cynicism about the world — reflects not the true measure of their merit but the failure of our own imagination in appreciating their singular gifts:

I think that however a thoughtful man may suffer from the defects and absurdities of his company, he cannot without affectation deny to any set of men and women a sensibility to extraordinary merit. The coarse and frivolous have an instinct of superiority, if they have not a sympathy, and honor it in their blind capricious way with sincere homage.

An equally toxic counterpart to such self-righteousness, Emerson argues, is our propensity for entitlement, which he contrasts with the disposition of humility and gratefulness:

I am thankful for small mercies. I compared notes with one of my friends who expects everything of the universe and is disappointed when anything is less than the best, and I found that I begin at the other extreme, expecting nothing, and am always full of thanks for moderate goods.

Illustration by Julia Rothman from 'Nature Anatomy.' Click image for more.

In a sentiment almost Buddhist in its attitude of accepting life exactly as it unfolds, and one that calls to mind his friend and Concord neighbor Thoreau’s superb definition of success, Emerson bows before the spiritual rewards of this disposition of gratefulness unburdened by fixation:

In the morning I awake and find the old world, wife, babes, and mother, Concord and Boston, the dear old spiritual world and even the dear old devil not far off. If we will take the good we find, asking no questions, we shall have heaping measures. The great gifts are not got by analysis. Everything good is on the highway. The middle region of our being is the temperate zone. We may climb into the thin and cold realm of pure geometry and lifeless science, or sink into that of sensation. Between these extremes is the equator of life, of thought, of spirit, of poetry, — a narrow belt.

Only by surrendering to life’s uncontrollable and unknowable unfolding graces — or what Thoreau extolled as the gift of “useful ignorance” — can we begin to blossom into our true potentiality:

The art of life has a pudency, and will not be exposed. Every man is an impossibility until he is born; every thing impossible until we see a success.

Or, as a modern-day wise woman admonished in one of the greatest commencement addresses of all time, it pays not to “determine what [is] impossible before it [is] possible.”

A century and a half before Harvard psychologist Daniel Gilbert illuminated how our present illusions hinder the happiness of our future selves, Emerson adds:

The results of life are uncalculated and uncalculable. The years teach much which the days never know… The individual is always mistaken. It turns out somewhat new and very unlike what he promised himself.

Emerson’s Essays and Lectures is indispensable in its totality. Complement it with his kindred spirit Thoreau on what it really means to be awake and the true measure of meaningful work.

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Body, Soul, and the Elusive Seedbed of Our Identity: Lewis Carroll on the Material and Immaterial Forces of Life, in a Letter to a Little Girl

The perplexity of why your identity endures even if all the cells in your body are wholly replaced every seven years.

“I am not one of those who neglect the body in order to make of it a sacrificial offering for the soul,” Rilke wrote in a beautiful 1921 letter, “since my soul would thoroughly dislike being served in such a fashion.” The relationship between the material and immaterial forces of life has occupied poets and physicists like for as long as we humans have been aware of our mortality and able to articulate that awareness. More recently, it has prompted philosophers to pose such fascinating questions as how we know who we are if our present selves are unrecognizably different from past ones.

That immutable inquiry is what mathematician and writer Charles Dodgson, better-known as Lewis Carroll (January 27, 1832–January 14, 1898), explores in one of the many witty and wise missives collected in The Life and Letters of Lewis Carroll (public library; free download) — the indispensable volume that also gave us Carroll on how to alleviate our discomfort with change and his three tips for overcoming creative block.

In the fall of 1885, one of Carroll’s “child-friends” — he had many largely epistolary friendships with children throughout his life, including the real-life little girl who inspired his Wonderland — wrote to him after reading Thomas Carlyle’s 1836 philosophical novel Sartor Resartus and finding herself particularly captivated by Carlyle’s treatment of the relationship between the body and the soul. The subject — perhaps unsurprisingly, given the profound transcendentalist undertones of Alice in Wonderland, published two decades earlier — was also of deep interest to Carroll, who wrote to his young friend:

My dear Edith, —

One subject you touch on — “the Resurrection of the Body” — is very interesting to me, and I have given it much thought (I mean long ago). My conclusion was to give up the literal meaning of the material body altogether. Identity, in some mysterious way, there evidently is; but there is no resisting the scientific fact that the actual material usable for physical bodies has been used over and over again — so that each atom would have several owners. The mere solitary fact of the existence of cannibalism is to my mind a sufficient reductio ad absurdum of the theory that the particular set of atoms I shall happen to own at death (changed every seven years, they say) will be mine in the next life — and all the other insuperable difficulties (such as people born with bodily defects) are swept away at once if we accept S. Paul’s “spiritual body ,” and his simile of the grain of corn. I have read very little of “Sartor Resartus,” and don’t know the passage you quote: but I accept the idea of the material body being the “dress” of the spiritual — a dress needed for material life.

Complement The Life and Letters of Lewis Carroll, which is nothing short of addictive in its totality, with Carroll on how to feed the mind, his four rules for digesting information, and his tips for making email more civil, then revisit Carl Sagan’s timeless treatise on science and spirituality and Rebecca Goldstein on the perplexity of why you and your childhood self are the same person despite a lifetime of material changes.

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