Making Connections Between Paradoxes

Connecting Berry's Paradox to Gödel's Incompleteness Theorem:

https://thatsmaths.com/2020/07/30/berrys-paradox-and-gdels-incompleteness-theorem/

Taleb On the Pandemic

Nassim Taleb recently on the pandemic, risk, fat tails, etc. (hour+ podcast), with an odd digression to geronticide toward the end:

https://www.listennotes.com/podcasts/econtalk/nassim-nicholas-taleb-on-the-i3JgS0nsF6W/

Summary/review of the podcast here:

https://podcastnotes.org/econtalk/nassim-nicholas-taleb-on-econtalk/

"The system is broken"... and an "Amen" to Andrew Gelman

Gelman reflecting on bad research (...which has been known to exist ;)

https://statmodeling.stat.columbia.edu/2020/07/28/bad-research-scientism-the-importance-of-description-and-the-challenge-of-negativity/

Meta-Meta...

The always-interesting Liv Boeree going meta:




Sean Carroll had physicist, poker-player, thinker, tinkerer, Boeree on his Mindscape podcast almost exactly 2 years ago here:

https://www.preposterousuniverse.com/podcast/2018/07/23/episode-6-liv-boeree-on-poker-aliens-and-thinking-in-probabilities/

Matt Parker Messes With Your Mind

Just a little puzzle from insidious Matt Parker today regarding David and Anton (...in case you have no better way to while away the afternoon):

http://www.think-maths.co.uk/agepuzzle

(...despite my understanding that corporal punishment has been banned in Britain for a few decades, anyone available has my permission to spank Matt mercilessly)

"Carpe diem..."

It was Robin Williams' birthday today... I can't let that pass unrecognized....

So Much Winning....?

Mehhh, just a few numbers on the TrumpVirus:

New Covid-19 cases in the last week: Mainland China: 172 Norway: 50 Greece: 186 Japan: 3516 France: 4377 Australia: 1831 Italy: 1394 United Kingdom: 5239 South Korea: 259 Canada: 2969 United States: 465,027

Presidential 'task force'(LOL) pr(opaganda)ess conference on tap for later today. ~5pm.

Friday ASMR

Yet another horrible week for the worldwide laughingstock that the USA and its joke leadership has become... maybe a good time to end with some ASMR... once again courtesy of a shoeshiner:

Wolchover on Gödel

Natalie Wolchover has a new piece on Gödel’s Incompleteness Theorem at Quanta Magazine:

https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/

As usual Natalie does a great job. I’m too lazy right now to look it up, but my favorite explanation of Gödel is probably Raymond Smullyan’s that he gives in one or more of his volumes. Rudy Rucker also does a good job for the layperson in at least one of his volumes, and Ms. Wolchover mentions the Ernest Nagel/James Newman short older volume “Gödel’s Proof” as another good source.

Lastly, I’ll re-post a quote/tribute I’ve used before from Freeman Dyson in "The Scientist As Rebel":

"Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.

"It is a curious paradox that several of the greatest and most creative spirits in science, after achieving important discoveries by following their unfettered imaginations, were in their later years obsessed with reductionist philosophy and as a result became sterile. Hilbert was a prime example of this paradox. Einstein was another…

"Science in its everyday practice is much closer to art than to philosophy. When I look at Gödel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as Chartres Cathedral… The proof is a great work of art. It is a construction, not a reduction. It destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas. Gödel proved that in mathematics the whole is always greater than the sum of the parts. Every formalization of mathematics raises questions that reach beyond the limits of the formalization into unexplored territory."

Ramsey Done Wright....

Nice introduction to Ramsey Theory from Colin Wright:

https://www.solipsys.co.uk/new/InfiniteRamseyTheorem.html?tg12tw

Shearer Delight....

                        
Most readers here likely already know of Catriona Shearer's incredible geometry problems regularly presented on Twitter (though they travel around the Web elsewhere), but if you don't, time to get started with this recent fun one:

https://twitter.com/prdoyle/status/1281905636914204682

Ahhh Yes, the Research Literature…. ;))

Cleaning out some old files I stumbled across this vintage piece from sometime in my 1970s academic career (I believe at the time I adapted this from some other original source?). Am sure most of you have seen such parodies before. I do find it noteworthy that several of the issues taken quite seriously in statistics and research methodology currently were already being hinted at and joked about by we grad students 40+ years ago….:

**************************************

A Guide to the Reading and Understanding of Research Literature

Phrase:                                                                    

"it has long been known that…."                                                    

Really means:

I haven’t bothered to look up the original references

Phrase:

"…of great theoretical and practical interest"

Means:

interesting to me

Phrase:

"the … reagent was chosen as especially suitable for the experimental procedure"

Means:

the fellow in the next lab over already had some made up

Phrase:

"subjects for the study were randomly chosen"

Means:

students in Psych. 101 were asked to participate as a prerequisite for passing the course

Phrase:

"three of the samples were selected for detailed study"

Means:

the results on the others didn’t make any sense

Phrase:

"accidentally strained during mounting"

Means:

dropped on the floor

Phrase:

"handled with extreme care throughout the experiment"

Means:

not dropped on floor

Phrase:

"typical results are shown…"

Means:

the best results are shown

Phrase:

"the data revealed a linear correlation"

Means:

we took a ruler and drew a line

"agreement with the predicted curve is:"

excellent  (means fair)

good  (means poor)

satisfactory  (means doubtful)

fair  (means imaginary)

Phrase:

"the values are correct at least within an order of magnitude"

Means:

the values are wrong

Phrase:

"statistically significant"

Means:

possibly plausible

Phrase:

"it is suggested that…”

Means:

I believe

Phrase:

"it may be that…”

Means:

I think

Phrase:

"It is generally believed that….”

Means:

a couple of other guys think so too

Phrase:

"it is clear that much additional work will be required before a complete understanding…”

Means:

I don’t understand it

Phrase:

"unfortunately, a quantitative theory to account for these results has not been formulated”

Means:

neither does anyone else understand it

Phrase:

"while it has not been possible to provide definite answers to these questions…”

Means:

the experiment didn’t work, but I figured I could at least get a publication out of it

Phrase:

"further work in this area is warranted…”

Means:

I intend to get a second publication out of this data

Phrase:

"special thanks are due to R. Stoodle for technical assistance and to J. Goober for valuable discussions”

Means:

R. Stoodle did the work and J. Goober explained what it all meant

**************************************

In His Prime....

“[Andrew] Granville, who is writing a book on analytic number theory, complained that Maynard has greatly slowed his progress. 'I’ve had to add about 150 extra pages because of him,' Granville said.”

Erica Klarreich with another lovely profile of an outstanding mathematician, in this instance number theorist James Maynard:

https://www.quantamagazine.org/james-maynard-solves-the-hardest-easy-math-problems-20200701/