Book Review: LOGICOMIX
We are living in an age of, amongst other things, excellent graphic novels. One shining example, which I have just finished reading, is LOGICOMIX, a graphic novel biography of mathematician and philosopher Bertrand Russell. (Side note: can a biography still be called a graphic novel? Our terminology may need an update.)
Seeking an escape from his authoritarian religious upbringing, young Bertrand turned to mathematics as the one source of absolute certainty in his life. But the more he studied mathematics, the more he realized that underlying all the sophisticated theories of the time were arguments based more on intuition than full rigor. Driven by his quest for absolute truth, Russell embarked on a project to rebuild mathematics from the foundations up, and thereby establish its status as absolute truth.
Unfortunately, his project ran into major difficulties of the mathematical/philosophical variety (to say nothing of his equally great personal difficulties) including the famous paradox of Russell’s own invention, the arguments of his student Wittigstein that logic was merely a tool for generating tautologies, and finally, Godel’s proof that even in the self-consistent world of mathematics, there must always be true statements that cannot be proven.
In the end, though Russell and his contemporaries eventually succeeded in placing mathematics on a rigorous footing, the dream of a logically grounded “universal truth” had to be abandoned. Mathematics is only as true as the assumptions it rests on, and cannot even prove all that is true in its domain.
While the mathematical and philosophical ideas are well-illustrated for a lay audience, the heart of LOGICOMIX is Russell’s personal struggle, first to find the universal truths in mathematics and then to accept their nonexistence. Like others engaged in this project, Russell’s struggle with logic occasionally veered into a struggle with sanity. Through a meta-narrative of the book’s creation, the authors debate the “logic and madness” theme, and ask whether some amount of detachment from reality a prerequisite for one who spends his or her life searching for its foundations.
This narrative of Russell’s quest had personal resonance for me: I went through my own late-high-school/early-college phase of viewing mathematics as a bastion of truth in an illogical world. I wonder if many of my mathematical colleagues’ careers had their genesis in the same yearning for certainty. I imagine we all eventually come to the same realization as Russell: that mathematics is a powerful tool for clear thinking, but the only “truth” it contains is ultimately tautological.
Disillusioned by his self-described “failure” but ultimately freed from his need for unblemished truth, Russell turns to more worldly concerns, including pacifist activism and the founding of a school with no rules (spoiler: it doesn’t go well). The book ends on a bittersweet note as Russell encourages students to accept their lives in an uncertain world.
I had great pleasure following Russell’s journey, and the many ideas and people encountered along the way. If anyone is interested in what really drives mathematicians, this book is heartily recommended.
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5 Responses to “Book Review: LOGICOMIX”
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Biographic Novel? :) The books sounds very interesting.
I’m not quite sure I understand why tautological truth is a shortcoming. I can see the disappointment due to the natural limit of the quantity of tautologies that can be discovered, but not in the quality/soundness of the discovery. What about universal constants? Where would we be without pi? Of course much of the world depends on the scientific process – tautology’s mentally challenged cousin. I wouldn’t want to live in a world where one is limited to tautologies. Even science isn’t enough because it makes an assumption of cooperating honest humans. So game theory is a requirement to fully simulate reality. Trying to discover something in a fully tautological environment however is maddening and sounds like a great premise for a book.
I was on a math path early in college as well, but two things got me out:
1. I just reached a limit of my abilities somewhere between differential equations and probability and didn’t feel like i could be successful personally or financially (yes i sold out and went into finance – a very distant mentally challenged cousin of hard sciences)
2. The world is a nasty place and a balance between theory and reality is needed.
Of course mathematics is both beautiful and powerful. I am continually amazed by just how many surprises there are in the world of pure mathematics–how simple, plausible axioms can have nontrivial and often counterinutitive consequences.
The problem is when people like Russell (and perhaps myself for a time) viewed mathematics as not just true, but as the Truth. Mathematics can’t tell you anything beyond the scope of the assumptions on which it is based.
Amen to your point #2. I would add that all theory is based on assumptions, and that many people, in attempting to apply theory to reality, neglect to consider the assumptions on which the theory is based.
Ben, thanks for the review/recommendation, I have been recently introduced to Russell’s later turn towards what I consider to be a CAS or holism mindset, having only really learned of his work on the reductionist program in school (imagine that!) I’m looking forward to reading Logicomix.
Alex, I think there’s an Universal Intellectual Peter Principle at play here. That is, at some point all academic/theoretical pursuit leads us to our personal limits of competence, be you Einstein or someone less “brilliant”. Ultimately we have to experience to gain further insight, as your point #2 suggests. But rather than view this as selling out (your point #1), I view the unwillingness to get out of the ivory tower as the height of irrationality (and the surest path to insanity).
Quite so. There is only so much you can learn from your own head.
Or rather, there must be a balance between experiencing the “real world” and reflecting on that experience to develop new insights.
Which makes me wonder why APPLIED Ethics isn’t a more common course. Arguing whether a pig enjoys not being killed more than Abraham Lincoln enjoys not killing it is a philosophical exercise to tune those tautological verbal skills, but we’re missing an opportunity to learn something real about how we ought to conduct ourselves in the REAL world ( with legal, political, tragedy of the commons constraints). Maybe our collective peter principle is at work here!