Book review: The Outer Limits of Reason

I love this book. I’m fascinated by physics and mathematics, even though my poor education confines me to their pop culture derivations. Noson Yanofsky organizes his work around the limits on what can scientifically be known, and tells it clear and easy, to me. He presents a series of mathematical wonders, while announcing many unknowns beyond the reach of science. He’s well aware, this is an invitation to pursue my own fantasies. My attraction is really about what I hope to find – not what the actual science would present if I could learn it. Yanofsky writes with encouraging clarity, and I want to believe he knows what he’s talking about.

This topic is everywhere appropriate: what is reason and what sorts of questions can it be used to answer?

Mathematics is a wonderful way of thinking. From the first human efforts to organize our notions into sensibility, math has shown itself to be universally repeatable and reliable. It can be elaborated in one place and culture, put down and forgotten for centuries, recovered and reapplied and, behold, it works exactly as before. Like no other language, and no other way of thinking, it appears to accurately and unerringly describe physical reality itself. We can almost imagine it exists without us. Some of us do.

What is reason? To Yanofsky: the methods and processes which do not lead to contradictions or falsehoods. There are some surprising things which simply can’t be known. We can’t know the shortest route between a hundred cities. We can’t know the exact amount of time it takes the moon to orbit the earth. These things aren’t mathematically calculable. Yanofsky insists: if our assumptions don’t logically produce truths, or results can appear either true or false – then we simply cannot know. We’re beyond reason.

He Intersperses his romp along the boundaries of the reasonably knowable with tales from the history of mathematics. By coupling logic with a willingness to abandon contradictions and falsehoods – as soon as they’re discovered – science (and science alone) has learned to describe what is actually true.

Yanofsky’s interested in physical truth. Mostly, of course, I am not. If I were, I, too, would have become a mathematician or physicist. What I want to learn, and I habitually hope to prop up with claims from science, is whether my own irrational beliefs are correct.

Yanofsky cheerfully elucidates a bunch of truly arcane stuff. It’s fun for it’s own sake. He uses page after page to suggest and imply, without finally just saying so, that we – us, you and I, the conscious ones in the universe – are contradictions to what is reasonable. He often observes we’re capable of contradictions, but my intuition wants to leap: in its conclusions, reason appears to show we are the contradiction itself. Read the book, and you will know why reason dictates my intuition is wrong, but you will also find yourself this side of what (I think) everybody wants to know: where’s the proof we are what we’re supposed to be?

It’s not an accident such books are popular. Yanofsky knows why. He simply declares that, uniquely among human endeavors, science and technology build upon themselves, and so make progress. Nothing else progresses. Nothing. Not art. Not literature. Not culture or morality. Art by its definition wants to be different from what went before. How can literature have built upon itself if the greatest authors lived centuries ago? He quickly moves on.

This is a tremendous, though possibly unreasonable, idea. It has all that intuitive good feeling to it: we are what we have always been, playing with different toys. While today’s politicians and poets are indistinguishable from their neolithic counterparts, scientists have invented the computer. Science appears to be true.

This is why ‘scientific reason’ so easily becomes the religion Yanofsky himself is selling: there’s nothing inevitable about human beings. We’re unreasonable and we’ll believe anything. Only science can unerringly discern what is. What Yanofsky carefully reveals is: science doesn’t know the truth, either.

One way to show this is to talk about infinities. I was boggled by infinities as a child – how there are mathematically twice as many positive integers as positive even integers, but there are the same number of either in infinity. Yanofsky presents unsolvable problems, like the fact no computer program can predict if it will ever halt, and shows there’s a relation between problems which can be solved and those which cannot. Since a relationship exists, it’s a fact there are an uncountably infinite number of unsolvable problems.

Even he succumbs to himself, though: “world hunger will not be solved using feelings of love and warmth. Rather, genetically modified crops and ammonium nitrate fertilizers will help feed the world.”

Drink the elixer, and the same contradictions which tricked us into worshiping a Great Spirit will compel you to believe in a Multiverse – and your faith will be no less incomprehensible. The truth, however it’s approached, is extremely hard to find. For nearly all of us, believing is about being persuaded by someone else’s story. Science worshipers today self-consciously await imminent publication of the formal equations describing the human sensation of God. Why even have a sensation of God?

Yanofsy is clear: human progress results from the application of reason. Civilizations which adhere to reason advance. Those which do not, decline. He pulls us into his analysis of reason, and suggests our success depends on applying it. This has a familiar, religious, tone. He claims the universe is physically perfect, describable by perfectly consistent laws. Imperfect ideas contain contradictions. Discarding these ideas permits clarity and growth.

It is, however, very hard to understand what Yanofsky is saying. It takes diligence, and a lifetime of practice, really, to reflect fluidly and comfortably inside the pure language of science. So, too, with other methods of self-perfection: discarding the pretentious, artificial, or distracting, to settle simply on what remains within the permitted extent of awareness.

In all of these, what are so commonly ‘human’ inclinations – conflict, inhibition, desire, intuition – are methodically examined and set aside toward achieving a perfection of consciousness and a liberation from, well, being ‘human.’ Yanofsky asserts only the human mind, itself, is capable of the contradictions which disrupt the perfection of the universe. Outside the human mind, what does the universe matter?

Yanofsky’s is value laden science, and it’s very powerful religion indeed. Science is also the language of atheism. Today’s common cultural practice of non-scientific believers is to sit peaceably at table, quietly acknowledging each other’s mythologies and refraining from vocal dissent. But these mythologies are foundational truths for what I believe about all of reality. Consenting to share the table is formal acknowledgement that, in fact, I do not know what to believe. Otherwise, it would be silly (even indecent) not to correct my friends in their intellectual errors. Underlying my ‘not knowing’ is the assumption something else is the truth.

The (less and less frequently) unspoken something else is ‘scientific reason.’ I should take it seriously. If I have a contrary belief I want to preserve, I should not, in fact, be sitting respectfully at table. I should be yelling my head off.

There are those who believe in ‘reality.’ There are those who do not; who believe, instead, only in the descriptions of things – the ‘stories’ – told in human minds. Yanofsky makes clear discovering the difference may well be beyond the limits of reason.

All of this is enormously attractive to me, and it’s given urgency because of death. When I’m drawn toward ideas which pretend to eliminate contradictions and explore perfection, I’m interested because these hint at understanding being dead. Absent death, for me, there’s rarely reason to be urgently interested in anything at all.

There is no sorrow like that of watching a loved one recede.


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