David Aldous: Essays and musings
In general, I'm not a fan of blogs. What you're thinking today,
or your reactions to current events, or debating with commentators,
should be as transient as a conversation; what you write for a permanent
public record should be
better thought out.
As it happens there seem to be no individual blogs on the kind of ``probability in the mathematical
sciences" or ``probability in the real world" topics that interest me.
Perhaps closest (and excellent food for thought) are
the more statistical
These brief writings of mine are instead intended as permanent "food for thought",
on topics such as the mathematics research profession in general, and uses of
probability in particular.
The overall style is similar to
J. Michael Steele's Semi-Random Rants.
The ones on this page are not published anywhere but here, except as noted.
Because it's not a blog, you can't leave comments, but if you know of (or write
where the same idea is expressed better,
or where an opposing idea is argued, please do email me the links.
Published on medium.com
Some of the topics are related to topics in the
Probability in the Real World project, but
should not be regarded as representative of that whole project.
David's Musings, published in Bernoulli News
Data Science for everyone, and probability models meet player ratings.
Vol 22, Number 1 (May 2015).
- On The Good Judgment Project, and on being the 365,625th
most famous person in history.
Vol 21, Number 1 (May 2014).
Using resources wisely, and the
breadth of the mathematical sciences Vol 20, Number 2 (November 2013).
- Cooper versus Greene, Peters versus Mercator, and Silver
versus Big Data Vol 20, Number 1 (May 2013).
- On suspiciously precise answers to intrinsically imprecise questions
Vol 19, Number 2 (November 2012).
- On password security, Republican candidates and
predictability of economic crises.
Vol 19, Number 1 (May 2012).
- What should our
college students know (aside from what we teach them)?
Vol 18, Number 2 (November 2011).
- In search of a missing word: entropy and ????.
Vol 18, Number 1 (May 2011).
David Stirzaker pointed out a
related discussion by David Ellerman who calls 1-S
logical entropy, that I.J. Good has called it the quadratic diversity index,
and an application to block codes is given in
Ahlswede and Cai (2006).
What are the Limits to "Rules Plus Dice" Modeling?
Vol 17, Number 2 (November 2010).
Popular books on Chance, and Teaching
Non-Technical Probability Vol 17, Number 1 (May 2010).
Brief thoughts regarding mathematics
These are a collection of thoughts that have occured to me over a career in mathematics.
They are intended to be somewhere on the spectrum from serious to the opposite of serious
(= humorous or frivolous or wry or quixotic?)
and the reader can decide where to place them on such a spectrum.
I attempt to phrase each thought in a crisp sentence or two, and then add a commentary.
Thoughts like these undoubtedly occur to every mathematician, so no particular
originality is claimed. Where I consciously borrow from another source I quote it,
and what I perceive as ``commonplace" is labeled as such.
Blog-like comments on current events
Three recent book reviews:
The "contagion" book is highly recommended.
Five recent book reviews:
The Right Way to Think About the Future:
scenario planning and probabilistic forecasting.
I remain enthusiastic about Tetlock's emphasis on probabilistic forecasting; the link is to a current
article of his from Foreign Affairs.
serious contender principle
worked pretty well
2020 Democratic presidential nomination: maximum Predictit prices were
Recall that the principle says that (on average) there should be
2 candidates whose maximimum price exceeds 50
3 candidates whose maximimum price exceeds 33
4 candidates whose maximimum price exceeds 25
5 candidates whose maximimum price exceeds 20
so the fluctuations in perceived winning probabilities are close to typical.
Another 2 minute speech, this time from Persi Diaconis's 75 birthday celebration.
I remain available at low rates .....
Because of my interest in
probability assessments for the medium-long term future
I always look at the annual
Global Risks Report.
Here is the
and here is the
key graphic I discuss in class and
Looking at predictions from 5 or 10 or 15 years ago gives some sense of how accurate
such consensus predictions have been.
Unfortunately neither the likelihoods nor the economic impacts are honestly quantitative;
they just ask participants to assess "on a scale of 1 to 5" with only
verbal descriptions of those numerical meanings.
Note that the risks assessed as most serious are climate change related.
I have written both a longer PDF review and a
shorter amazon.com review
of Ian Stewart's Do Dice Play God: The Mathematics of Uncertainty.
Analogous to Wikipedia's nice "zooming in"
of Brownian scaling,
Yucheng Wang has made
this MP4 demonstration
of the emergence of scale-invariance
when we grow a network in the plane by adding random points and using a scale-invariant rule for linking them
to the existing network.
See this page for explanation.
A coincidence question.
Almost all probability-related questions on Quora
are elementary or inane, but I noted a recent one (ironically, soon deleted) that was more interesting to me.
What are the odds that at least 2 players of a 128 players tournament face each other 2 consecutive years?
Here is my brief analysis.
- (1/19) The most thorough book-length discussion of the Fermi Paradox has been given by
Milan M. Cirkovic: see my review here.
I was asked to give a 2-minute talk at the dedication ceremony for the new
David Blackwell Hall. Several people kindly said they enjoyed the talk,
so here it is.
- (8/18) My review of an excellent book
The Money Formula: Dodgy Finance, Pseudo Science, and How Mathematicians Took Over the Markets.
(6/18) Were there unusually many upsets in the 2018 World Cup?
Here is a little statistical analysis from the "round of 16" and
Of these 16 matches, 9 were won by the favorite and 7 by the underdog.
This sounds like around 2 more underdog wins than expected,
but this is too little data to say anything more precise.
A more sophisticated analysis [see details of what follows]
exploits the probabilities for each match winner.
This allows us to attach more weight to "major upsets".
We use a formula that represents the overall "extent of upsets" on a scale of 0 to 100,
where 0 means "every match won by the favorite"
and 100 means "every match won by the underdog".
The formula is designed so that,
before the tournament starts, each number between 0 and 100 would be equally likely.
The bottom line is 90. That is, in only 10% of tournaments would one expect
more than this level of upsets.
The single main upset, as most would agree, was Russia's win over Spain.
FYI A BBC article on other aspects of the World Cup
This page shows an unexpected literary appearance of my old
Poisson Clumping Heuristic book
(in Helen DeWitt's Some Trick).
Presumably some real mathematician had this particular eclectic selection of books -- who could that be?
$200,000 prize money is being offered in the current
IARPA Geopolitical Forecasting Challenge,
but there is a curious Prediction Tournament Paradox which says that the winners
are not so likely (as you might imagine) to be the best forecasters.
So maybe my performance in the 2017 HFC Challenge pre-season was just luck.
- (8/17) Here's one of the more sensible non-technical blog posts re
Elon Musk, AI and AGI.
- (2/17) Was the NE Patriots comeback in the Superbowl
(and Barcelona's in the Champions League) incredibly unlikely?
There's a simple, but surprisingly little known, relevant bit of math.
- (1/17) Review of Aaron Brown Financial Risk Management for Dummies and his response.
Interesting short discussion article
Science in the age of selfies by Geman and Geman.
And from the "how others see us" department,
Taleb's The Intellectual Yet Idiot.
- (3/14) Warren Buffett's billion dollar gamble.
(7/10) Has the teaching of introductory probability changed over the last 40 years?
Looking at the tables of contents of
book 2, can you guess
which was published in 1970 and which in 2007?