Ambiguous Certainty

So, uhm. Let my situation while writing this book review be describe. I am sitting alone on the beach side while the tide’s low and chains of city lights glow in the distant shores. I’m 72 minutes away from the deadline and yet I don’t mind spending with the unusual and contradicting coldness and party music in the air around me. Tonight I’m entering a contemplation I’m not sure I can express well in this review, but I’ll do my best.

I introduced you Ravi. For all that I have read, he was the promising protagonist. And frankly, I thought the author would start with a low note on mathematics. Instead, he started fast with infinity. Gaaah. Infinite sets, in particular, were discussed earlier in the book. Relate The Story of Maths Part 4 here and you’d be sure to understand all the points this book is trying to portray.

What amused me are the conversations between Vijay Sahni and Judge Taylor. Throughout the book, these exchange of views and criticisms were what made this book an essential read when learning complicated complexities between science and faith. Or rather, mathematics and faith. ;)

‘Medieval mathematicians saw infinity as an awe-inspiring and sometimes a fear-inspiring idea. ‘Only God is infinite’ was their conclusion; everything else is limited. An Italian thinker, Giordano Bruno, was tortured for nine years in part because he refused to retract his idea that the universe was infinite and extended forever. Bruno believed that reason and philosophy are superior to faith, and to knowledge founded on faith. He refused to accept the finiteness of the universe merely because the Church decreed that only God could be truly infinite. At his trial, which ended in 1600, he was as defiant as ever. Upon hearing his death sentence, he responded, ‘Perhaps your fear in passing judgment on me is greater than mine in receiving it.’

Personally, I’m open to such views but it disheartens me to know some people forget their faith in God when it comes to explaining both the natural and unnatural phenomena around them. There’s even Galileo’s insight about realizing that you cannot apply the laws of finite mathematics to infinite sets. How would you ever make sense of such statements? Sure, it opens up new and definitely bright ideas. But what do you make of that? There is a statement said by Vijay Sahni.

‘There is no democracy in the realm of ideas. Just because so many people believe something or live in a certain manner is not reason enough for me to concede they are right. And your own laws allegedly give me the freedom to speak about such matters without fear of reprisal or arrest. My confinement violates some of the most basic principles of your constitution.’

What do you make of that? Suppose we debate on math and religion. Isn’t that debating also logic and reason against faith and God Himself? I’m on the latter side always, and truthfully speaking, this book may have hurt me for real but actually, I’m enlightened to the fact that not everyone would see both sides and I guess I’m privileged enough to see the contradicting points pointed out in this book. Math relies on reason, not mysticism. The book offers more than just arguments. It took me to new places, sure, but I'm sticking with my faith.

It comprehensively discusses Pythagorean Theorem, Georg Cantor’s Continuum Hypothesis, Euclid’s geometry and postulates in The Elements, Einstein Theory and David Hilbert. Also, I’m amazed to find out that Descartes is a devout Christian. Sighs.

Euclid’s fifth postulate and the Continuum Hypothesis are concrete examples of important, interesting questions that were shown to be undecidable in the context of their respective axiom schemes. Gödel provides a measure of finality to the conclusions we came to from the specific instances of geometry and set theory. No matter what the axiom system, truth will outrun proof.

Throughout the talks of JT and VS, I noticed one thing, though. I know, JT was trying to question VS on his stand and most of it talks strength in VS’s views. It would have been more entertaining and more pleasing if JT also voiced out more significant discussions on his side. Anyway, they ended well after 5 sessions of listening mostly to VS’s deductions and explanations of some traditional mathematics. It continues to test what we already knew and discover things we never knew.

Like the party music, sometimes we get distracted to what we should do or focused on. Our beliefs and principles, the very essence of our faith, would always be questioned with things very different from the rhythm we’re used to.  Like the faint little lights across the dark horizon, once in a while we glimpsed into the reality that when a greater light comes to eat all the darkness, they would be turned off to make way for a new truth we embraced. Laws and axioms and lists of standards and bases will be revised over time. Like the passing ships swimming through the liquid glass, mankind would be always willing to wander through known and unknown, through certainties and uncertainties alike, challenging themselves. But like the tides of the sea, it would exposed now and then every hope that once in a while, the truths we needed are nearer than we thought they’d be. It only matters how high or low our views amongst such things. I think mathematics already questioned faith way before numbers are presented as unknown quantities. Like they said, people change, hearts move on. But never can a heart change if people do not move on. So forward is all the direction we needed to continue understanding all we need to know and explain. We needed the brain and sadly, the heart was left to accept the rest.

It’s hard saying what this book is all about. But one thing’s for sure. Ravi became successful in his career. He was molded through thick and thin with mathematics as his passion and foundation. And true enough, a calculator makes you pass the test. Cheating is strictly discouraged. Long live book review! And one more thing. Read it when you're not in a hurry. And not on evenings near the beach with party music in the cold air. ;)