## How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics | Category Theory

For those who are intimidated by the thought of higher mathematics, but are still considering joining our Category Theory Summer Study Group, I’ve just come across a lovely new book by Eugenia Cheng entitled How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics.

It just came out in the U.S. market on May 5, 2015, so it’s very new in the market. My guess is that even those who aren’t intimidated will get a lot out of it as well. A brief description of the book follows:

“What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard. Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.

At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.”

Dr. Cheng recently appeared on NPR’s Science Friday with Ira Flatow to discuss her book.  You can listen to the interview below. Most of the interview is about her new book. Specific discussion of category theory begins about 14 minutes into the conversation.

Dr. Eugenia Cheng can be followed on Twitter @DrEugeniaCheng. References to her new book as well as some of her syllabi and writings on category theory have been added to our Category Theory resources pages for download/reading.

## Why Information Grows: The Evolution of Order, from Atoms to Economies

I just ordered a copy of Why Information Grows: The Evolution of Order, from Atoms to Economies by Cesar Hidalgo. Although it seems more focused on economics, the base theory seems to fit right into some similar thoughts I’ve long held about biology.

From the book description:

“What is economic growth? And why, historically, has it occurred in only a few places? Previous efforts to answer these questions have focused on institutions, geography, finances, and psychology. But according to MIT’s antidisciplinarian César Hidalgo, understanding the nature of economic growth demands transcending the social sciences and including the natural sciences of information, networks, and complexity. To understand the growth of economies, Hidalgo argues, we first need to understand the growth of order.

At first glance, the universe seems hostile to order. Thermodynamics dictates that over time, order–or information–will disappear. Whispers vanish in the wind just like the beauty of swirling cigarette smoke collapses into disorderly clouds. But thermodynamics also has loopholes that promote the growth of information in pockets. Our cities are pockets where information grows, but they are not all the same. For every Silicon Valley, Tokyo, and Paris, there are dozens of places with economies that accomplish little more than pulling rocks off the ground. So, why does the US economy outstrip Brazil’s, and Brazil’s that of Chad? Why did the technology corridor along Boston’s Route 128 languish while Silicon Valley blossomed? In each case, the key is how people, firms, and the networks they form make use of information.

Seen from Hidalgo’s vantage, economies become distributed computers, made of networks of people, and the problem of economic development becomes the problem of making these computers more powerful. By uncovering the mechanisms that enable the growth of information in nature and society, Why Information Grows lays bear the origins of physical order and economic growth. Situated at the nexus of information theory, physics, sociology, and economics, this book propounds a new theory of how economies can do, not just more, but more interesting things.”

## A world of languages – and how many speak them (Infographic)

An infographic from the South China Morning Post has some interesting statistics about which many modern people don’t know (or remember). It’s very interesting to see the distribution of languages and where they’re spoken. Of particular note that most will miss, even from this infographic, is that 839 languages are spoken in Papua New Guinea (11.8% of all known languages on Earth). Given the effects of history and modernity, imagine how many languages there might have been without them.

## Molecular Programming Project

Bookmarked Molecular Programming Project (Molecular Programming Project)

“The Molecular Programming Project aims to develop computer science principles for programming information-bearing molecules like DNA and RNA to create artificial biomolecular programs of similar complexity. Our long-term vision is to establish molecular programming as a subdiscipline of computer science — one that will enable a yet-to-be imagined array of applications from chemical circuitry for interacting with biological molecules to nanoscale computing and molecular robotics.”

Source: MPP: Home

## Collective learning has potentially been growing at the expense of a shrinking body of diverse language

Yesterday, I saw an interesting linguistic exercise:

I have to imagine that once the conceptualization of language and some basic grammar existed, word generation was a much more common thing than it is now. It’s only been since the time of Noah Webster that humans have been actively standardizing things like spelling. If we can use Papua New Guinea as a model of pre-agrarian society and consider that almost 12% of extant languages on the Earth are spoken in an area about the size of Texas (and with about 1/5th the population of Texas too), then modern societies are actually severely limiting language (creation, growth, diversity, creativity, etc.) [cross reference: A World of Languages – and How Many Speak Them (Infographic)]

Consider that the current extinction of languages is about one every 14 weeks, which puts us on a course to loose about half of the 7,100 languages on the planet right now before the end of the century. Collective learning has potentially been growing at the expense of a shrinking body of diverse language! In the paper “Global distribution and drivers of language extinction risk” the authors indicate that of all the variables tested, economic growth was most strongly linked to language loss.

To help put this exercise into perspective, we can look at the corpus of extant written Latin (a technically dead language):

These numbers become even smaller when considering ancient Greek texts.

Another interesting measurement is the vocabulary of a modern 2 year old who typically has a 50-75 word vocabulary while a 4 year old has 250-500 words, which is about the level of the exercise.

As a contrast, consider the message in this TED Youth Talk from last year by Erin McKean, which students should be able to relate to:

[ted id=2158]

And of course, there’s the dog Chaser, which 60 minutes recently reported has a vocabulary of over 1,000 words. (Are we now destroying variants of “dog language” for English too?!)

Hopefully the evolutionary value of the loss of the multiple languages will be more than balanced out by the power of collective learning in the long run.