Midweek pick-me-up: Mathematician Lillian Lieber on infinity, creativity, the meaning of freedom, and how to be a finite but complete human being

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If my labor of love enriches your life in any way, please consider supporting it with a [donation]( – all these years, I have spent tens of thousands of hours, made many personal sacrifices, and invested tremendous resources in Brain Pickings, which remains free and ad-free and alive thanks to reader patronage. If you already donate: THANK YOU. [FROM THE ARCHIVE | Mathematician Lillian Lieber on Infinity, Art, Science, the Meaning of Freedom, and What It Takes to Be a Finite But Complete Human Being]( [infinity_lieber.jpg?fit=320%2C483]( “We’re all intrinsically of the same substance,” astrophysicist Janna Levin wrote in her [exquisite inquiry into whether the universe is infinite or finite](. “The fabric of the universe is just a coherent weave from the same threads that make our bodies. How much more absurd it becomes to believe that the universe, space and time could possibly be infinite when all of us are finite.” How, then, do we set aside this instinctual absurdity in order to grapple with the concept of infinity, which pushes our creaturely powers of comprehension past their limit so violently? That’s what the mathematician and writer Lillian R. Lieber (July 26, 1886–July 11, 1986) set out to explore more than half a century earlier in the unusual and wonderful 1953 gem [Infinity: Beyond the Beyond the Beyond]( ([public library]( — one of seventeen marvelous books she published in her hundred years, inviting the common reader into science with uncommon ingenuity and irresistible warmth. Emanating from Lieber’s discussion of infinity is a larger message about what it means, and what it takes, to be a finite but complete and balanced human being. [lillianrlieber.jpg?resize=585%2C841] Lillian R. Lieber Lieber belongs to [the “enchanter” category of great writers]( and was among the first generation of women mathematicians to hold academic positions in her role chairing the Department of Mathematics at Long Island University. She had a peculiar style resembling poetry, though she insisted it was not free verse but, rather, a deliberate way of breaking lines in order to speed up reading and intensify comprehension. (Curiously, I find her style to have precisely the opposite effect, which is why I’ve enjoyed it so tremendously — it does what poetry does, which is slow down the spinning world and dilate the pupil of attention so that the infinite becomes comprehensible.) Populating her books is the character of T.C. Mits, “the Celebrated Man-in-the-Street,” and his mate, Wits, “the Woman-in-the-Street.” Accompanying Lieber’s writing are original line drawings by her own mate, the illustrator Hugh Gray Lieber. [lieber1.jpg?resize=680%2C647]( Lieber’s work was so influential in elevating the popular science genre that even Albert Einstein himself heartily praised [her book on relativity]( yet many of her books have fallen out of print — no doubt because the depth, complexity, and visionary insurgency of her style don’t conform to the morass of formulaic mediocrity passing for popular science writing today. Lieber frames the premise of [Infinity]( in the charming opening verse — or, as she insisted, decidedly not-verse — of the second chapter: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]Of course you know that the Infinite is a subject which has always been of the deepest interest to all people — to the religious, to poets, to philosophers, to mathematicians, as well as to T.C. Mits (The Celebrated Man-in-the-Street) and to his mate, Wits (the Woman-in-the-Street). And it probably interests you, or you would not be reading this book. But it is in the first chapter, titled “Our Good Friend, Sam,” that Lieber’s genius for science, metaphor, and wordplay shines most brilliantly as she takes on everything from the symbiotic relationship between art and science to free will to the vital difference between common sense and truth to the evils of antisemitism and all exclusionary ideologies. (It is self-evident to point out that Lieber, a Jewish woman writing shortly after WWII in a climate of acute antisemitism and sexism, was, like any artist, bringing all of herself to her art.) Lieber writes: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]For those who have not met SAM before, I wish to summarize VERY BRIEFLY what his old acquaintances may already know, and then to tell to all of you MORE about him. In the first place, the name “SAM” was first derived from Science, Art, Mathematics; but I now find the following interpretation much more helpful: the “S” stands for OUR CONTACT WITH THE OUTSIDE WORLD; please note that I do NOT say that “S” represents “facts” or “reality”, for the only knowledge we can have of the outside world is through our own senses or “extended” senses — like microscopes and telescopes et al which help us to see better, or radios, etc., which help us to hear sounds which we would otherwise not be aware of at all, and so on and so on. But of course there may be many, many more things in the world which we do not yet perceive either directly through our senses or with the aid of our wonderful inventions. And so it would be Quite arrogant to speak as if we knew what the outside world “really” is. That is why I wish to give to “S” the more modest interpretation and emphasize that it represents merely that PART of the OUTSIDE world which we are able to contact, — and therefore even “S” has a “human” element in it. Next: the “A” in SAM represents our INTUITION, our emotions, — loves, hates, fears, etc. — and of course is also a “human” element. And the “M” represents our ability to draw inferences, and hence includes mathematics, logic, “common sense”, and other ways in which we mentally derive the “consequences” before they hit us. So the “M” too is a “human” element. Thus SAM is entirely human though not an individual human being. Furthermore, a Scientist utilizes the SAM within him, for he must make “observations” (“S”), he must use his “intuition” (“A”) to help him formulate a good set of basic postUlates, from which his “reasoning powers” (“M”) will then help him to derive conclusions which in turn must again be “tested” (“S” again!) to see if they are “correct”. Perhaps you are thinking that SAM and the Scientist are really one and the same, and that all I am doing is to recommend that we all become Scientists! But you will soon see that this is not the case at all. For, in the first place, it too often happens, — alas and alack! — that when a Scientist is not actually engaged in doing his scientific work, he may “slip” and not use his “S”, his “A”, and his “M”, so carefully, will bear watching, like the rest of us. In a sentiment which physicist and poet Alan Lightman would come to echo decades later in his beautiful meditation on [the creative sympathies of art and science]( Lieber adds: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]So, you see, being a SAMite and being a Scientist are NOT one and the same. Besides, a SAMite may not be a Scientist at all, but an Artist! For an Artist, too, must use his “S” in order to “observe” the world, his “A” (“intuition”) to sense some basic ways to translate his “observations”, and his “M” to derive his “results” in the form of drawings, music, and so on. Thus an Artist, too, WHEN AT HIS BEST, is a SAMite. [lieber2.jpg?resize=680%2C692]( Perhaps Lieber’s most interesting, layered, and timelessly relevant discussion is of the concept of freedom, its misconceptions and mutations, and its implication for our private, public, and political lives: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]Now consider a person who is SOMETIMES or OFTEN like this: SaM. He is evidently relying very heavily on his “intuition”, his “hunches”, his “emotions”, hardly checking to see whether the “observations” of the outside world (“S”) and his own reasoning powers (“M”) show his “hunch” to be correct or not! And so, precious as our “intuition” may be, it can go terribly “haywire” if not checked and double-checked by “S” and “M”. Thus, a person who habitually behaves like this is allowing his “S” and “M” to become practically atrophied, and is the wild, “over-emotional” type, who is not only a nuisance to have around, but is hurting himself and not allowing himself to become adjusted to the world he lives in. Such a person, with an exaggerated “A”, and atrophied “S” and “M”, has a feeling of “freedom”, of not being held down by “S” and “M” (“facts” and “reason”) ; but, as you can easily see this makes for Anarchy, for a lack of “self-control” — and can lead to fatty degeneration from feeling “free” to eat all he wants; to the D.T.’s from feeling “free” to drink all he wants; to accidents because he feels “free” to drive as fast as he wants and to “hog” the road; to a sadistic lack of consideration for others by feeling “free” to kick them in the teeth for “nuttin'”; to antisocial “black market” practices from a similar feeling of “freedom”, giving “free” reign to the “A” without the necessary consideration of “facts” (“S”) and “reason” (“M”). Needless to say this is a PATHOLOGICAL FREEDOM as against a NORMAL, HEALTHY FREEDOM of the well-balanced SAM which is so necessary in society in which EACH individual must be guided by the SAM within himself in order to avoid conflict with the SAM in someone else. This is something that a bully does not understand — that if he acts like a pathological sAm, he induces sAmite-ism in others, as in mob violence; this is indeed a horrible “ism” that can destroy a society as well as individuals in it. Lieber proceeds to build on this taxonomy of psychological imbalances, reminiscent of neuroscience founding father Santiago Ramón y Cajal ‘s [taxonomy of the “diseases of the will.”]( She turns to the next imbalance — the person blinded by isolated facts, unable to integrate them into an understanding of the big picture: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]Similarly, there is the Sam type: he may be called the “tourist” type — running around seeing this and that but without the “imagination” (“A”) or the reasoning power (“M”) to put his observations together with either heart (“A”) or mind (“M”), but is concerned only with ISOLATED BITS OF INFORMATION: he is like the man who, seeing a crowd had gathered, wanted to know what happened. and, when someone told him “Ein Mann hat sich dem Kopf zerbrochen” (It happened to be in Germany), corrected the speaker’s grammar and said “DEN Kopf!” He knew his bit of grammar, but what an inadequate reaction under the circumstances. don’t you think? Next comes the flawed rationalizer, who misuses the tools of logic against reason: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]And there is also the saM type — one who can reason (“M”) but starts with perhaps some postulate (“A”) favoring murder. Such a man would make a wonderfully “rational” homicidal maniac or crook who could plan you a murder calmly and rationally enough to surprise any who are not familiar with this sAM type of pathological case. [lieber4.jpg?resize=680%2C626]( Lieber returns to the core purpose of her SAM metaphor and its relationship to the central question of the book: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]Thus SAM gives us a way of examining our own behavior and that of others, taking into account the “facts” (“S”), and using imagination and sympathy (“A”) in a rational way (“M”). Are you perhaps thinking, “Well, this may be interesting, but why all this talk about SAM, when you are writing a book about Infinity?” To which the answer is: The yearning for Infinity, for Immortality, is an “intuitive” yearning (“A”): we look for support for it in the physical world (“S”), we try to reason about it (“M”), — but only when we turn the full light of SAM upon it are we able to make genuine progress in considering Infinity. [lieber3.jpg?resize=680%2C706]( In a brilliant and necessary caveat reminiscent of mathematician Kurt Gödel’s [world-changing incompleteness theorems]( which unsettled some of our most elemental assumptions by demonstrating the limits of logic turned unto itself, Lieber adds: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]There is only one more point I must make here: Namely, that even being a well-balanced SAMite — and not a pathological anti-SAMite like SAM, etc. etc. — is NECESSARY but NOT SUFFICIENT. You will probably agree that it is further necessary to have our SAM up-to-date. For he is a GROWING boy, and what was good enough for him in 1800 is utterly inadequate in 1953; and unless the “S” is up-to-date and the postulates (“A”) and reasoning (“M”) are appropriately MODERN, we cannot make proper ADJUSTMENT in the world TODAY. And ADJUSTMENT is what we must have. For adjustment means SURVIVAL, and that is a MINIMUM demand — for, without survival we need not bother to study anything we just won’t be here to tell the tale. In a passage of piercing pertinence today, as we watch various oppressive ideologies and tyrannical regimes engulf the globe, Lieber concludes by returning to the subject of freedom, its malformations, and its redemptions: [2e292385-dc1c-4cfe-b95e-845f6f98c2ec.png]And so let me summarize by saying that the ANTI-SAMITES hurt not only themselves, by getting “ulcers”, nervous breakdowns, drinking excessively, etc. etc., but hurt others also, for from their ranks are recruited those who advocate war and destruction, the homicidal maniacs, the greedy crooks, the gamblers, the drunken drivers, the liars, et al. […] Just a word more about FREEDOM — you have seen above the pathological idea of freedom, but when you consider this important concept from SAM’s WEll-BALANCED viewpoint, you will see that, from this point of view, the “feeling” of freedom (“A”), being supported on one side by “S” (the “facts” of the outside world), and on the other by “M” (“sweet reasonableness”) — is definitely NOT the ANARCHICAL freedom of SAM, but is a sort of CONTROLLED FREEDOM — controlled by facts and reason and is therefore SELF-controlled (by the SAM within us) and hence implies VOLUNTARY COOPERATION rather than FORCE. Thus anyone who demands “freedom unlimited” as his right, is a pathological SAM, a destructive creature; whereas, in mathematics you will find the CONTROLLED FREEDOM of SAM and you will feel refreshed to see how genuine progress can be made with this kind of freedom. [Infinity: Beyond the Beyond the Beyond]( is a thoroughly magnificent read in its totality. Pair it with the lovely children’s book [Infinity and Me]( then complement this particular fragment with Simone de Beauvoir, writing shortly before Lieber, on [art, science, and freedom]( and James {NAME}, writing shortly thereafter, on [freedom and how we imprison ourselves](. [Forward to a friend]( Online]( [Like on Facebook]( donating=loving Each month, I spend hundreds of hours and thousands of dollars keeping Brain Pickings going. For a decade and a half, it has remained free and ad-free and alive thanks to patronage from readers. I have no staff, no interns, not even an assistant — a thoroughly one-woman labor of love that is also my life and my livelihood. If this labor makes your life more livable in any way, please consider aiding its sustenance with a donation. 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You can beam some bit-love my way: 197usDS6AsL9wDKxtGM6xaWjmR5ejgqem7 KINDRED READINGS: [pi.jpg]( [An Ode to the Number Pi by Nobel-Winning Polish Poet Wisława Szymborska]( * * * [mandelbrotset.jpg]( [The Pattern Inside the Pattern: Fractals, the Hidden Order Beneath Chaos, and the Story of the Refugee Who Revolutionized the Mathematics of Reality]( * * * [zero.jpg]( [The Invention of Zero: How Ancient Mesopotamia Created the Mathematical Concept of Nought and Ancient India Gave It Symbolic Form]( * * * ALSO, I WROTE A CHILDREN’S BOOK: [The Snail with the Right Heart: A True Story]( [thesnailwiththerightheart_0000.jpg]( [---] You're receiving this email because you subscribed on Brain Pickings. This weekly newsletter comes out each Wednesday and offers a highlight from the Brain Pickings archives for a midweek pick-me-up. 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