ocfnash

For anyone interested, there's a really excellent book on the history of the problem as well as the AH proof, going into quite a lot of detail. Very highly recommend.

"Four Colors Suffice: How the Map Problem Was Solved" by Robin Wilson.

https://www.goodreads.com/book/show/450635.Four_Colors_Suffi...

Thanks for the kind remarks :-)

Ah yes, but it is the generalisation to _fractional_ ideals that is required to obtain the ideal class group.

A rather obvious but often overlooked piece of advice is to "read the masters".

IMHO it is very easy to waste tonnes of time reading papers / books that are OK but still vastly inferior to an account of a master.

Want to learn index theory: read Atiyah and Singer's original papers.

Interested in the classification of quadratic forms: read Serre's course in arithmetic.

Need to learn about the recent breakthroughs on prime tuples: read Tao!

Find time to read Weil, insist on reading Poincare, come up with an excuse to read Scholze etc.

Top mathematics literature is often spectacularly well written.

See also: https://mathoverflow.net/questions/28268/do-you-read-the-mas...

I think that disc-ish object is the light source, which I suppose is rendered to make it clear why one side of a polygon is dark while the other is bright etc.

Have you tried writing down the Parsons Code [1] for the melody and searching against a large corpus? E.g., https://www.musipedia.org/melodic_contour.html

1. https://en.wikipedia.org/wiki/Parsons_code

The phrase "Simon robot" reminds me of the following _Simon-playing_ robot, way too cool not to mention in this context: http://redfrontdoor.org/blog/?p=702

This reminds me, of Edith Einstein, niece of Albert. She was also a talented physicist overshadowed by her extremely famous (male) relative.

Her academic path even crossed with that of her uncle: she wrote a paper analysing the physics of radiometers, after which Albert did too.

[Her paper argued in favour of the radiometric force being proportional to the surface area of the veins, Albert argued (more convincingly) in favour of a model in which the force in proportional to the perimeter.]

Possibly a good time to plug moissanite again: http://diamondssuck.com

Indeed. Reading my own words, I sound rather more worked up than I am :)

I do think this article is a bit sneaky dressing itself up as entertainment since it is published by a business that profits from people deciding to invest.

It does provide a means to illustrate the agency problem though.

If I had perfect knowledge of the future and had to buy and hold a given set of positions for myself for some fixed period, I would simply choose those that maximised my return at the end. HOWEVER if instead I had to invest on behalf of others (in return for some fee) and was subject to being fired, I would be tempted to choose a different (thus suboptimal) set of positions such as those with smallest drawdown / maximised minimum rolling quarterly Sharpe / ...

I think this article is attempting to make a different point.

It essentially argues (unconvincingly IMHO) that it is difficult to _distinguish_ a (very contrived type of) "perfect" active investor from a "bad" investor whereas Buffet argues that it is difficult to _be_ a good active investor.

These are not necessarily inconsistent but they do have opposite impacts on investment decisions.

To my mind this is dishonest marketing "research" whereas Buffet is making an important point.

Can the figures for "Real Residential Housing Price Index for Canada" be correct? The quoted index values are:

2010: 36.3

2016: 413.9

I simply cannot believe there was an 11-fold price increase on this index over this period.

Googling I cannot match either of these figures to various Canadian real estate indexes reported on the web.

Thanks for these helpful words of clarification!

As I commented above, I was rather sloppily using the words "explosion", "detonation" to mean flash and boom.

On the two occasions on which I witnessed this event, it was stunningly powerful but I now believe most likely just a deflagration.

I am sure of nothing except that there was a sudden big flash and boom :)

From the clarifying comments below it seems likely it was a deflagration but I confess I've been using the words "explosion", "detonation" rather sloppily to mean "flash and boom" till now.

Thanks again for a marvelous article.

Very interesting, thanks!

I carried out two rounds of thermite "experiments", both times using oxides of iron, manganese, and copper. I witnessed two "explosions" (I now presume deflagrations) and they occurred with the copper oxide. I've occasionally wondered if that was a coincidence that it was the same metal that "exploded" both times. Mystery solved: apparently not!

This is a good piece but I have one nit: it is incorrect to say "thermite [...] will not detonate."

I was shocked to discover this first hand some years ago: http://olivernash.org/2009/11/12/fun-with-thermite/index.htm...

I can still recall the echoing boom of that (copper) thermite.

I don't know; no doubt we could debate the point at length.

Nevertheless I stand by my original remark. IMHO the conflation of "Chinese" with "cheap crap" is:

  * Not relevant

  * Debatable / Subjective 

  * Divisive

and thus distracts attention from the actual point being made.

I think this comment would be improved by removal of the word "Chinese".

There are famously-many other axioms that can be added to ZF, and which turn out to be equivalent to Choice.

Of the following three equivalent extensions to ZF:

  * Axiom of Choice

  * Zorn's Lemma

  * Well-ordering Principle

Jerry Bona quipped:

"The Axiom of Choice is obviously true, the Well-ordering Principle obviously false, and who can tell about Zorn's Lemma?"

And it's not just any old radioactive source, it's a positron emission!

I believe the way it works is that the injected source emits positrons as it decays (having swiped them from the vacuum), shortly thereafter, these annihilate with the electrons of your body, and the scanner looks for the signature pair of gamma rays thus created, using the relative time of arrival to determine their common origin in 3-space. That reduces the problem of scanning to arranging for the decaying source to accumulate in the place we wish to scan which apparently can be done.

That we scan ourselves by annihilating antimatter with our bodies in targeted ways just seems so awesome to me.

Yes indeed, quite right!

0xA000 is the memory _segment_ and so the linear address is 0xA0000

I think I would have got this right first time ~20 years ago: ftp://ftp.scene.org/mirrors/hornet/code/3d/systems/gsescher.zip :)

Surely this is the point, though?

We rearrange the approximation: h = 6.626069934 x 10−34 kg∙m2/s to solve for kg and thus have our definition in terms of h?

0xA000 is also the address of the memory location that holds the contents of the display in so-called "mode 13h" in the old IBM VGA displays.

Mode 13h was an extremely popular graphics mode, used by many PC games in the early 90s (probably also late 80s). It gave a resolution of 320x200 pixels with 8-bit colour palette.

After entering mode 13h, the way to plot a pixel is to poke the corresponding 8-bit memory address, where the 0th pixel (display top left) is 0xA000.

I am the other commenter!

The special icosahedron functions can be expressed in many ways but perhaps the most elementary _explicit_ representation is as particular Gaussian hypergeometric functions. See this repo for example: https://github.com/ocfnash/icosahedral_quintic The special functions are used here: https://github.com/ocfnash/icosahedral_quintic/blob/master/q...

Geometrically these functions locally invert the (branched) covering represented by the diagram at the top of this page: http://olivernash.org/2012/02/05/on-kleins-icosahedral-solut...

Another lovely aspect to this problem is that the quintic _is_ solvable if you allow yourself to use certain special functions naturally associated to the icosahedron.

The genesis of the relationship is that the group of rotations of the icosahedron is the same group, A_5.

I work at Susquehanna and I believe you may have incorrectly understood this to imply there is a pressure to stay at one's desk over lunch. In my experience, this is not at all the case and I head out over lunch fairly frequently.

Or she!

Unfortunately Wakefield's paper that essentially kicked off the "MMR vaccine controversy" was published by the Lancet. They eventually retracted but enormous damage was done (including deaths apparently).

Great example.

It also seems to have been the case that when he became Abbot of his monastery in 1867 he ceased research.

If we knew that there would only ever be £45m worth in existence then perhaps not but one would expect that this figure is growing.