John C. Baez's Blog, page 35

Language Complexity (Part 2)

David A. Tanzer

Decision problems, decision procedures and complexity

In Part 1, we introduced the formal idea of a language, as being just a set of sentences. Now let’s approach the topic of language complexity.

For any given language, there is an associated decision problem: given a candidate string of characters, determine whether or not it belongs to the language. A decision procedure, or decider, is a program that solves the decision problem: it returns True or False to indicat...

Language Complexity (Part 1)

David A. Tanzer

A simple view of languages

How complex is the English language? The question has many dimensions and nuances. What does complexity mean, and how could it be measured? This a tough nut to crack, so in this post we’ll make a retrenchment to reconsider the question in a more formal setting — computer science.

In this setting, a language gets identified with its extension — the collection of all its sentences. So English gets modeled as just a large repository of sentenc...

Language Complexity, Part 1

David A. Tanzer, 12 February, 2021

A simple view of languages

How complex is the English language? The question has many dimensions and nuances. What does complexity mean, and how could it be measured? This a tough nut to crack, so in this post we’ll make a retrenchment to reconsider the question in a more formal setting — computer science.

In this setting, a language gets identified with its extension — the collection of all its sentences. So English gets modeled as just a large ...

The Signal Beat – A Related Blog

David Arthur Tanzer, 12 February, 2021

Greetings Azimuth readers! This is a note to introduce myself and a new math blog that I am starting. I’ve been involved with Azimuth for a long time now, having written some blog articles years back, and have been helping to keep things organized on the forum. I have a PhD in CS and an undergraduate degree in math, and have continued to study math in the context of Azimuth and the applied category theory community. Professionally I am experienced ...

Geoengineering – The Tipping Point

Back in 2013 I wrote about how we are approaching a tipping point, where public opinion on geoengineering suddenly starts to shift:

Many express the fear that merely researching geoengineering schemes will automatically legitimate them, however hare-brained they are. There’s some merit to that fear. But I suspect that public opinion on geoengineering will suddenly tip from “unthinkable!” to “let’s do it now!” as soon as global warming becomes perceived as a real and present threat. This ...

Neutrinos and Neutrettos

The Wikipedia article on the muon neutrino says:

The muon neutrino is a lepton, an elementary subatomic particle which has the symbol νμ and no net electric charge. Together with the muon it forms the second generation of leptons, hence the name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by Leon Lederman, Melvin Schwartz and Jack Steinberger.

But it doesn’t say who hypothesized it. So I got curious: who predicted the existence ...

The Hoyle State

Nuclear physics is complicated compared to atomic physics, because the strong force is complicated compared to the electromagnetic force, and nucleons—protons and neutrons—are bag-like groupings of quarks and gluons held together by the strong force, elastic bags which attract each other and jostle each other closely in the nucleus… all governed by the rules of quantum mechanics.

To begin to understand such a complex thing as a nucleus, people started with approximate models. In 1930 George Gam...

Nitrogen-14

Having an even number of neutrons and/or an even number of protons tends to make a nucleus more stable against radioactive decay:

• Wikipedia, Even and odd nuclei.

I just learned there are only 5 stable nuclei with an odd number of neutrons and an odd number of protons:

• deuterium (hydrogen-2), with 1 proton and 1 neutron.

• lithium-6, with 3 protons and 3 neutrons.

• boron-10, with 5 protons and 5 neutrons.

• nitrogen-14, with 7 protons and 7 neutrons.

• tantalum-180, with 73 proto...

Structured vs Decorated Cospans

Some of us just finished a paper clarifying the connection between two approaches to describing open systems—that is, systems that can interact with their environment, and can be composed to form larger open systems:

• John Baez, Kenny Courser and Christina Vasilakopolou, Structured versus decorated cospans.

And, next week I’m giving a talk about it at YAMCaTS! This is not a conference for felines who like sweet potatoes: it’s the Yorkshire and Midlands Category Seminar, organized by Simona Pa...

General Motors to Stop Selling Petroleum-Powered Cars

General Motors announced today that it would stop selling petroleum-powered cars by 2035:

• Fred Krup, Why GM’s clean cars announcement is a really big deal, EDF Voices Blog, 28 January 2021.

Fred Krup is president of the Environmental Defense Fund, a famous environmental organization. He writes:

Today I was pleased to lend my support to GM’s dramatic announcement that it is working to eliminate tailpipe emissions from all of its new light-duty vehicles by 2035, and to be carbon neutral in it...