Shameless Plug

Here's a brief description of my (mathematical) novel that will be out in the next 12-18 months (2 of you sent mail asking for it and I don't need much more incentive than that!):

The human heart yearns for absolute truth and certainty. But can we be truly certain about anything—or is everything we believe accidental and meaningless, shaped by the happenstance of genetic and social inheritance? Perhaps mathematics alone, with its uncompromising rigor, can lead us to certainty. In our 90,000 word novel, we examine where mathematics can and cannot take us in the quest for certainty.

Our book will show the reader the following: First, that mathematics can be deeply beautiful—in this regard it is not unlike music or painting; second, that mathematics has profound things to say about whether absolute truth is obtainable; and lastly, that a novel is the best medium through which to convey the excitement and meaning of doing mathematics

Our protagonist, Vijay Sahni, an Indian mathematician, has glimpsed the certainty that mathematics can provide and does not see why its methods cannot be extended to all branches of human knowledge, including religion. Arriving to pursue his academic career in a small New Jersey town in 1919, his outspoken views land him in jail, charged under a little-known Blasphemy law (on the state statute books to this day). His beliefs are challenged by Judge John Taylor, who does not believe that mathematical deduction can be applied to matters of faith. In their discussions the two men discover the power—and the fallibility—of Euclid's axiomatic treatment of geometry, long considered the gold standard in human certainty. In the end both Vijay and Judge Taylor come to understand that doubt must always accompany knowledge.

Big News!

As some of you know, I've authored a novel that examines whether absolute certainty is achievable through Mathematics. I'm thrilled to report that it has been accepted for publication. More details coming...

Numbers and Biology

Watching Vir, my 2 year old, attempt to count I realize that numbers may appear more natural to us (human adults) than they really are. Vir makes 3 kinds of mistakes in his counting:
1) He will count an object more than once before moving on to the next one
2) He ignores some items in front of him completely, or
3) He’ll continue counting even though he has accounted for every item on the list. So unless I stop him he often ends up at nineteen (the largest number he knows) even when I have asked him to count the 3 apples in the fruit basket.

To be sure, he’s got the sequence down. He understands that 1 is followed by 2 is followed by 3 etc. He even understands that counting somehow refers to the number of objects. And he understands the idea of ‘many’. “So many cars,” he’ll observe on the freeway.

But that’s it. He hasn’t grasped yet that counting a set means ticking off each element exactly once. Which if you think about it, is quite an advanced idea. We’re so familiar with the idea, however, that we tend to forget that numbers are merely shorthand notations for the cardinality of sets, and are ultimately the creations of our intelligence. In this they are exactly like groups or rings or transfinite cardinals.

And in a few months as Vir understands the rules governing numbers, he too will think that theyare woven in the fabric of the universe…and are not products of human biology.

Wait I hear you say—won’t any intelligence, at the very least, have to be able to count? I’m not so sure any more. Not sure at all.