John C. Baez's Blog, page 40

Roger Penrose’s Nobel Prize

Roger Penrose just won Nobel Prize in Physics “for the discovery that black hole formation is a robust prediction of the general theory of relativity.” He shared it with Reinhard Genzel and Andrea Ghez, who won it “for the discovery of a supermassive compact object at the centre of our galaxy.”

This is great news! It’s a pity that Stephen Hawking is no longer alive, because if he were he would surely have shared in this prize. Hawking’s most impressive piece of work—his prediction of blac...

Fisher’s Fundamental Theorem (Part 3)

Last time we stated and proved a simple version of Fisher’s fundamental theorem of natural selection, which says that under some conditions, the rate of increase of the mean fitness equals the variance of the fitness. But the conditions we gave were very restrictive: namely, that the fitness of each species of replicator is constant, not depending on how many of these replicators there are, or any other replicators.

To broaden the scope of Fisher’s fundamental theorem we need to do one of two ...

Network Models

Good news: my student Joe Moeller will be taking a job at NIST, the National Institute of Standards and Technology! He’ll be working with Spencer Breiner and Eswaran Subrahmanian on categories in engineering and system design.

Joe Moeller will be talking about his work on ‘network models’ at the online category theory seminar at UNAM on Wednesday October 14th at 18:00 UTC (11 am Pacific Time):

Network Models

Abstract. Networks can be combined in various ways, such as overlaying one on top of...

Markov Decision Processes

The National Institute of Mathematical and Biological Sciences is having an online seminar on ‘adaptive management’. It should be fun for people who want to understand Markov decision processes—like me!

• NIMBioS Adaptive Management Webinar Series, 2020 October 26-29 (Monday-Thursday).

Adaptive management seeks to determine sound management strategies in the face of uncertainty concerning the behavior of the system being managed. Specifically, it attempts to find strategies for managing dynami...

Compositional Game Theory and Climate Microeconomics

guest post by Jules Hedges

Hi all

This is a post I’ve been putting off for a long time until I was sure I was ready. I am the “lead developer” of a thing called compositional game theory (CGT). It’s an approach to game theory based on category theory, but we are now at the point where you don’t need to know that anymore: it’s an approach to game theory that has certain specific benefits over the traditional approach.

I would like to start a conversation about “using my powers for good”. I am hop...

Stretched Water

The physics of water is endlessly fascinating. The phase diagram of water at positive temperature and pressure is already remarkably complex, as shown in this diagram by Martin Chaplin:

Click for a larger version. And read this post of mine for more:

• Ice.

But it turns out there’s more: water is also interesting at negative pressure.

I don’t know why I never wondered about this! But people study stretched water, essentially putting a piston of water under tension and measuring its propertie...

Fock Space Techniques for Stochastic Physics

I’ve been fascinated for a long time about the relation between classical probability theory and quantum mechanics. This story took a strange new turn when people discovered that stochastic Petri nets, good for describing classical probabilistic models of interacting entities, can also be described using ideas from the quantum field theory!

I’ll be talking about this at the online category theory seminar at UNAM, the National Autonomous University of Mexico, on Wednesday October 7th at 18:00 UT...

Reframing Superintelligence

Eric Drexler has a document calling for a view of superintelligent systems where instead of focusing on agents or minds we should focus on intelligent services. This is, of course, the approach taken by industrial AI so far. But the idea of a superintelligent agent with its own personality, desires and motivations still has a strong grip on our fantasies of the future.

• Eric Drexler, Reframing Superintelligence: Comprehensive AI Services as General Intelligence, Technical Report #2019-1, Futu...

Fisher’s Fundamental Theorem (Part 2)

Here’s how Fisher stated his fundamental theorem:

The rate of increase of fitness of any species is equal to the genetic variance in fitness.

But clearly this is only going to be true under some conditions!

A lot of early criticism of Fisher’s fundamental theorem centered on the fact that the fitness of a species can vary due to changing external conditions. For example: suppose the Sun goes supernova. The fitness of all organisms on Earth will suddenly drop. So the conclusions of Fisher’s ...

Fisher’s Fundamental Theorem (Part 1)

There are various ‘fundamental theorems’ in mathematics. The fundamental theorem of arithmetic, the fundamental theorem of algebra, and the fundamental theorem of calculus are three of the most famous. These are gems of mathematics.

The statistician, biologist and eugenicist Ronald Fisher had his own fundamental theorem: the ‘fundamental theorem of natural selection’. But this one is different—it’s a mess! It was unclearly stated, the first few proofs were packed with mistakes, and people d...