Book Signing @ Kepler's in Menlo Park

I'll be speaking and signing books at Kepler's in Menlo Park on Thursday Sept 26th, at 7.30pm.

http://www.artsopolis.com/event/detail/24097


Meanwhile the book is selling well and getting a lot of good press. Here's the amazon link:

http://www.amazon.com/Certain-Ambiguity-Mathematical-Novel/dp/0691127093/ref=pd_bbs_sr_1/104-9722234-0627160?ie=UTF8&s=books&qid=1190471905&sr=8-1

The book is available for pre-order

A Certain Ambiguity is available for pre-order.

You may go to Princeton University Press or to Amazon to pre-order it.

Thankfully, the reviews have been very good:

Martin Gardner : A Certain Ambiguity is an amazing narrative that glows with a vivid sense of the beauty and wonder of mathematics. The narrator is deeply troubled by the ancient question of whether the objects and theorems of mathematics have a reality independent of human minds. Mixing fiction with nonfiction, A Certain Ambiguity is a veritable history of mathematics disguised as a novel. Starting with the Pythagorean theorem, it moves through number theory and geometry to Cantor's alephs, non-Euclidean geometry, Gödel, and even relativity.

Eli Maor, author of "e: the Story of a Number" and "The Pythagorean Theorem: A 4,000-Year History" : This is a truly captivating thriller that will take you on a whirlwind tour to infinity--and beyond. But be warned: once you start reading, you won't be able to put it aside until finished! A masterly-told story that weaves together criminal law, ancient and modern history, a young man's quest to know his deceased grandfather-and some highly intriguing mathematics.

Keith Devlin, Stanford University, author of "The Math Gene" : This rich and engaging novel follows the path that leads one young person to become a professional mathematician. By deftly blending the young man's story with mathematical ideas and historical developments in the subject, the authors succeed brilliantly in taking the reader on a tour of some of the major highlights in the philosophy of mathematics. If that were not enough, the book also examines, through the minds of its characters, the natures of faith (religious and other) and truth. I am strongly thinking of building a university non-majors math course around this novel.

Joan Richards, Brown University : A Certain Ambiguity is a remarkably good effort to work through some fundamental issues in the philosophy of mathematics in the context of a novel. Crucial to the success of such a venture is creating characters and a plot that are strong enough to hold a reader's interest. Suri and Bal succeed particularly well in the story of Vijay Sahni and Judge Taylor. This well-written book will, I believe, find readers not only among mathematicians, but in a wider audience that is intrigued by mathematical meaning.

Alexander Paseau, University of Oxford : Suri and Bal convey the beauty and elegance--as well as the fascination--of basic mathematical concepts.

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.

Numbers and Experience

It is often argued that while geometry is unable to adequately describe the world around us, numbers are more reliable, more certain. 2 cows plus 2 cows, always equal 4 cows. Unlike non euclidean geometries, there are no non standard arithmetics. Gauss, for a time at least, believed that ‘truth resides in number.’ In a similar vein Jacobi said “God ever arithmetizes” (as opposed to eternally geometrizing).
However, as Kline observes in Mathematics, The Loss of Certainty, the sharpest attack on the truth of arithmetic came from Hermann von Helmoholtz, a superb physicist and mathematician. In his Counting and Measuring he observed that the problem in arithmetic lay in the automatic application of arithmetic to physical phenomena. Some kinds of experiences suggest whole numbers and fractions, while others don’t: one raindrop added to another does not make two raindrops. Two pools of water, one at 40◦ another pool of water at 50◦ when mixed together do not make a pool of water at 90◦. Lebesgue facetiously pointed out that if one puts a lion and a rabbit in a cage, one will not find two animals an hour later! Helmoholtz gives many (more serious) examples but his overarching point is that only experience can tell us where to apply, and not apply, standard arithmetic.

Like Euclidean Geometry, arithmetic is not absolutely applicable to the physical world.

Evolutionary Mathematics

Chaitin, as he often does, has got me thinking. He writes:

Von Neumann also said that we ought to have a general mathematical theory of the evolution of life... But we want it to be a very general theory, we don't want to get involved in low-level questions like biochemistry or geology... He insisted that we should do things in a more general way, because von Neumann believed, and I guess I do too, that if Darwin is right, then it's probably a very general thing.
For example, there is the idea of genetic programming, that's a computer version of this. Instead of writing a program to do something, you sort of evolve it by trial and error. And it seems to work remarkably well, but can you prove that this has got to be the case? Or take a look at Tom Ray's Tierra... Some of these computer models of biology almost seem to work too well---the problem is that there's no theoretical understanding why they work so well. If you run Ray's model on the computer you get these parasites and hyperparasites, you get a whole ecology. That's just terrific, but as a pure mathematician I'm looking for theoretical understanding, I'm looking for a general theory that starts by defining what an organism is and how you measure its complexity, and that proves that organisms have to evolve and increase in complexity. That's what I want, wouldn't that be nice?

And if you could do that, it might shed some light on how general the phenomenon of evolution is, and whether there's likely to be life elsewhere in the universe. Of course, even if mathematicians never come up with such a theory, we'll probably find out by visiting other places and seeing if there's life there... But anyway, von Neumann had proposed this as an interesting question, and at one point in my deluded youth I thought that maybe program-size complexity had something to do with evolution... But I don't think so anymore, because I was never able to get anywhere with this idea...

Tons of interesting stuff to chew on, but I'll limit myself to this: Imagine a simulation where you have two entities: organisms and resources. The organisms are just data structures which reproduce when they have been getting enough resources. The resources are re-generable and are of various types.

Now let's add on a few complexities: Assume that an organism 'eats' only certain types of resources. So Organism 42 can only live on Resource 118 for example. Further assume that the quantity of Resources stays relatively stable...with exceptions of rare time units of plenty and others (also rare) of drought. Also assume that there can be more than one type of Organism that consumes a certain type of Resource, and also that there are Resources that are not consumed by any organism when the simulation starts.

An Organism will then have the following data elements: Its type [corresponds to the species it belongs to]; its number [i.e. its name]; the Resource number(s) it consumes; its wellness number - a measure of how well fed the organism is - if the wellness number goes over a limit the organism will reproduce; an organism competitive index which will measure how well the individual competes within his species; and a species competitive number that measures how well the species competes with other species vying for the same resource. Reproduction passes on the competitive indices to the progeny. When the wellness index falls below a certain level, the organism dies.

Now also imagine that you have random mutations. A random mutation could change the type of resources an individual consumes and/or its competitive indices (either up or down).

These are only the barest details...but I hope you believe that it is possible to capture the main points of Darwin theory in a reasonable simulation.

Hit start and run the simulation: You will probably see organisms dying and being born; species will be created by the right mutations - they will also thrive or struggle - but eventually all will die out. The world itself may reach some kind of stable equilibrium, but more likely than not...at some point we'd hit zero organisms or zero resources.

All this is worth doing in its own right (in fact I'd be shocked if someone hasn't already done it), but now, just for fun, imagine one last externality: Say that organisms of a certain complexity level can perceive a proportional complexity of mathematical truths. So for example an organism of complexity index 1088 could really 'get' that there can be no largest prime (but other, more difficult theorems are beyond it), and an organism of complexity index 4063 could 'get' the prime number theorem ('get' = a deep understandig that does not allow for the result not be true. Similar, but not equal to proof).

It seems to me then that there will always be mathematical statements that we humans couldn't get, no matter what.

This is far from air tight, but there may be something to chew on here.

--Gaurav Suri