Disqus - Latest Comments for briantung

Re: How Galois Groups Used Polynomial Symmetries to Reshape Math | Quanta Magazine

briantung — Tue, 10 Feb 2026 13:34:49 -0000

I know this is an old thread, but: It is indeed straightforward to calculate the Galois groups for second and third degree polynomials, but I think there's some pedagogical mileage to be gotten out of the cubics in particular. (This article is a bit on the thin side in that regard, though.) The quadratics are probably not very illuminating, though.

Re: How Galois Groups Used Polynomial Symmetries to Reshape Math | Quanta Magazine

briantung — Tue, 10 Feb 2026 13:31:11 -0000

This example needs just a bit more exposition. Without it, the reader could be left thinking that the 7 in (t – s)(t – r)(s – r) = 7 comes from the constant term in the polynomial. The obvious question is then, why doesn't f (x) have a corresponding constraint? The answer to that is that the 7 doesn't come from the constant term; it's (the square root of) the determinant.

For the depressed monic cubic (no quadratic term) x³ + px + q, the discriminant is –4p³ – 27q². For f (x), this yields 697, whose square root is irrational; for g(x), it produces 49, whose square root, 7, is rational and therefore the source of the extra constraint.

Re: The Null Hypodermic: Constructions with Compass, Straightedge, and Flatiron

briantung — Tue, 30 May 2017 17:29:44 -0000

A lot of comments seem to have disappeared at some point. I'm not sure why or how to get them back.

ETA: Ooh, OK, I found an archive of them. How would you like to resolve this? Should I just e-mail you your old comments?

Re: The Null Hypodermic: Rating the Droughts

briantung — Wed, 30 Nov 2016 02:18:20 -0000

Now that you've posted the same comment both here and on Facebook, I've got to respond in both places. Curse you! :-)

You make good points, all of which I might have ventured into, but didn't, if you can believe that. One reason is sheer laziness; I only meant to give a measure of how long a franchise and its fans have waited for a championship title, not how unlikely the wait is, statistically speaking. But another reason is that in order to say something more than vaguely qualitative, one needs a model of championship contention.

*If* seasons were independent and identically distributed (i.i.d.) trials with a uniform distribution over all teams for the pennant (also not a given, since the divisions have not always been balanced, but let's ignore that), and then between the two pennant-winners for the World Series, then the statistics you've calculated should hold (I'm going to trust you provisionally on those calculations).

But of course, as you've noted, there's probably some "stickiness" in those
probabilities. A lot of the reason why the Cubs waited so long is that for many of the years, they simply weren't very good. A prolonged stretch of mediocrity that lowers a team's chances from 1/16, let's say, to 1/32 is going to elevate considerably their probability of going an extended number of years without a title.

Unfortunately, this is something where we simply don't have the ability, at present, to formulate a reliable model of how good or bad a team is, and/or how that goodness varies over a period of years. So I thank you for using the simplest model to give what amounts to a bound on how unlikely such a wait is, and giving me an opportunity to point out that it is, after all, only a bound. :-)

Re: Girls With Slingshots - GWS Chaser #384

briantung — Fri, 26 Aug 2016 12:54:22 -0000

"I'm gonna start GWS back up in three years." OK, I'm good with that.

Re: Girls With Slingshots - GWS Chaser #343

briantung — Thu, 30 Jun 2016 13:57:46 -0000

It's interesting (to me) the various differences people see between friendships and romantic relationships. For some people, the difference is sex, but for others, it's (possibly non-sexual) intimacy and most importantly, reciprocation. (Not to imply those are the only two alternatives.)

But back to the point at hand: I think (without much insight into a fictional character's approach to dating) Jim may possibly be focusing too much on pleasing his date. By that I do *not* mean that he shouldn't be pleasing his date; we should all strive to do that. But in terms of finding someone who complements him, there first has to be someone to complement.

And Jim strikes me as something of a cipher in that regard. People want someone interesting to date. (They want interesting people as friends, too, of course.) One has to strike a balance, of course—no one likes to date someone who only talks about themselves. But although it might be enjoyable at first, someone who continually asks what you want so they can cater to you must surely be exhausting to be around, eventually. People generally want to date someone they can fun *with*, as opposed to someone who wants to provide Fun as a Service (FaaS™).

Re: Girls With Slingshots - GWS Chaser #323

briantung — Thu, 02 Jun 2016 11:29:51 -0000

Well, Hazel doesn't--oops, hold on:

Hazel doesn't die at the barricades.

Re: Girls With Slingshots - GWS Chaser #323

briantung — Thu, 02 Jun 2016 11:28:00 -0000

He did, after all, say that he wanted a girl who could be his friend *first*.

Re: The Null Hypodermic: Stages of Prejudice

briantung — Thu, 30 Oct 2014 20:11:17 -0000

Hi Brian.

I agree that it's not enough, by itself, to eliminate social prejudice. That seems to me, however, to be an unrealistically high bar to pass. Why does it have to eliminate prejudice in order to be worth doing? Isn't it enough that it simply reduce it, both in extent and severity? And I think it has every promise to do that. Even if it doesn't (and I find that to be rather implausible), I think it's still worth it for people to be aware that they have biases that are not conscious yet need to be accounted for.

The thing that I hope to avoid is the feeling that this is too big a problem for any one measure to tackle (which it probably is) and therefore not to take any of those measures (which I don't agree with).

Re: The Null Hypodermic: Stages of Prejudice

briantung — Thu, 25 Sep 2014 20:06:09 -0000

@Brian: I realize this comment is getting musty, but why should I let that stop me? :-)

I don't think that's the only reason. There is also the culture in science that bias is to be expected, that it is normal for even scientists who are aware of bias to be biased, and that it makes sense therefore to confront them, and correct for them explicitly, rather than try to avoid them altogether (which is considered an exercise in futility).

What we could use in other circles is the same mentality. Not to try to avoid biases, but to assume they will exist within us, and to compensate accordingly. The problem is not, in my opinion, that such compensations are intractably arduous, but that no one who is not a scientist generally wants to think of themselves as occasionally irrationally biased (and probably many scientists don't want to think that way, either). The motivation to correct ourselves for a flaw we don't wish to have is simply lacking.

Nonetheless, I would urge people to try. Even a partial success in this arena is worth something.

Re: Are cruise ships floating petri dishes?

briantung — Wed, 29 Jan 2014 17:14:02 -0000

Hunh, that's weird what Disqus did with my mock-html tag.

Re: Are cruise ships floating petri dishes?

briantung — Wed, 29 Jan 2014 17:12:59 -0000

<arithmetic_alert>

"In 2013, the CDC's Vessel Sanitation Program logged nine gastroenteritis outbreaks aboard ships, seven of which had a confirmed cause of norovirus. About 1,200 cruise passengers were affected by those norovirus cases. To put those figures in perspective, the industry's Cruise Lines International Association says more than 10 million passengers embarked on CLIA member cruise ships from a U.S. port in 2012, and norovirus sickens an estimated 21 million people in the United States every year, according to the CDC."

Technically, that's almost enough to put things into perspective, but seems to me there's a fair bit to draw between the lines here. Wouldn't it be necessary to convert the 10 million passengers into person-years first? If those 10 million people spent an average of, let's say, 5 days on a cruise, that's about the same as 140,000 person-years. The U.S. has a population of about 320 million, nearly all of which is in the U.S. at any particular time, natch.

So, on board, 1,200 people got sick, out of 140,000 person-years, or less than one case per 100 person-years. On land, we've got 21 million who got sick, out of 315 million person-years, or about one case per 15 person-years. On a per-person, per-unit-time basis, then, you're only about one-seventh, maybe one-eighth as likely to get that specific illness on board, as you are in the U.S. at large.

Maybe people don't stop being gross once they step off onto dry land.

Re: Senate to start votes on gun bill

briantung — Wed, 17 Apr 2013 19:32:17 -0000

*sigh* Americans actually have a memory that is practically mayfly-short. People wring their hands over things their favorite candidates do, yet if it happens more than about a month before the election, it can be almost guaranteed that it will be a non-issue by the time votes are cast.

Re: 'Top Dog': How to raise a winner

briantung — Wed, 20 Mar 2013 17:32:52 -0000

I think that's a pretty facile response. By the same token, we could reject medicine by saying "You mean like Mengele?" and acting by saying "You mean like John Wilkes Booth?" The alternative to bad competitors isn't shying away from competition; it's smarter and fairer competition. Competition and good moral character aren't mutually exclusive; in fact, the point the authors are proposing (open to debate, but not ridicule, I think) is that competition is one avenue to building good moral character.

Re: Small World: NASA Kepler Mission Finds Smallest Exoplanet Yet

briantung — Wed, 20 Feb 2013 16:52:11 -0000

Maybe it should be called a dwarf planet.

Re: Spielberg’s Lincoln Indirectly Leads to Mississippi Finally Ratifying 13th Amendment

briantung — Tue, 19 Feb 2013 15:41:36 -0000

Delaware. Not Deleware. Thought it was a typo, but you put it that way twice...

Re: Right in Our Wheelhouse: New British Citizenship Test Demands Knowledge of Monty Python

briantung — Mon, 28 Jan 2013 18:45:46 -0000

"...where your water meter is..." Sorry, pet peeve.

Re: A baseball game nobody wins

briantung — Thu, 10 Jan 2013 21:14:06 -0000

A minor technicality: Bonds was never convicted on any of the perjury charges, because the jury was deadlocked. He was convicted on an obstruction of justice charge, for giving an evasive answer to a question under oath. To be sure, that case is still under appeal. One may, of course, decide nevertheless that the evidence is overwhelming that Bonds took steroids (albeit mostly during the time when it was not technically cheating in baseball, "merely" illegal without a prescription). I don't think that's an unreasonable stand to take. But what we saw in the vote was not a referendum on these players, nor even the morality of these players; it was the first volley in a skirmish over how to address both the impact of steroids, as well as the uncertainty over who used them. I wouldn't be surprised to see the voting change substantially over the years. (I'd also be curious to see the age distribution on those who voted yea vs nay, but we obviously won't get that.)

Re: Researchers Find Biological Indicator of Being a Rude Loudmouth

briantung — Wed, 09 Jan 2013 21:37:24 -0000

Some of them probably have a very high 3D:4D ratio...

Re: A different kind of parenting resolution

briantung — Wed, 02 Jan 2013 16:25:50 -0000

Being rich isn't automatically bad, or unimportant, any more than having children is automatically good, or important. Bydand's point, presumably, is that (as with anything of the sort), there's a trade-off involved. If one isn't committed to being a parent, then not having children is probably wise; so long as one isn't a jerk about it, one could do a lot worse than becoming rich.

Re: 5 Things You Should Never Say While Negotiating

briantung — Sat, 23 Jul 2011 12:46:40 -0000

If you're upset by the language here, I suggest you take a look at Glengarry Glen Ross. It's a much more seemly examination of negotiation tactics.

Re: In Berkeley, a venerable grocery market comes under fire

briantung — Tue, 17 May 2011 05:17:40 -0000

I said nothing about sinister; I am not attempting to read motive, or to impose a value judgment. I intend to point out only that 20 percent > 10 percent, so that the customer is ultimately harmed by the loss of the smaller business, if the larger business does indeed plan to overcharge. Replace 10 by 30 and 20 by 50, then. (Perhaps these figures are unrealistic for that area; that would be a matter of fact, not of logic.)

As I said, of course I don't know what Monterey is going to do; all I am doing is challenging the *presumption* that they are going about everything fair and aboveboard, and that the illegal collusion by its competitors, if it is indeed illegal (IANAL), is morally reprehensible.

In other words, to answer your question: No, it is not hard to imagine that they might be competing fairly, but it is also not hard to imagine that they might not.

Re: In Berkeley, a venerable grocery market comes under fire

briantung — Tue, 17 May 2011 02:42:25 -0000

That's certainly possible, but it's far from clear.

Suppose I run a store that only sells Product Z. I buy it for $10, and sell it for $11. It's enough to keep me in business, but it certainly doesn't gouge my customers.

Then another store, with a far larger bottom line, comes in. They sell Products A through J for a 10 percent profit--same as I do. Then they also sell Z; they buy it for $10, but they sell it for $7. They can afford to do this, because they make enough money from A through J to afford the loss on Z.

Now, it's *possible* that Z is just a loss leader to get people into the store, in the hopes that they'll also buy A through J for the larger store's profit--but then, why couldn't they just choose any of Products K through Y? Why pick the one product I sell, and use *that* as the loss leader? Aren't I justified in thinking that they're not just trying to compete, but to put me out of business? Isn't it possible that once I'm out of business, the larger store will charge $12 for Z?

The larger store has the right to do that. I have the right to complain about it. Most importantly, the consumer has the right to see on the whole what is going on, and to make their own choice about whether they'd prefer to have at least the threat of competition? Keep in mind that any agreement (legal or not) would be handshake at most, and if the stores decide to take too much advantage, by gouging the customer, retaliation would be swift and decisive.

Obviously, I don't *know* that that's what Monterey is doing, but are you sure you know what the other businesses are doing?

Re: On Steve Francis and 20-6-6

briantung — Tue, 13 Apr 2010 12:55:57 -0000

I think you've drawn a few too many conclusions from as bare a statistical line as 20-6-6. Six assists per game does not necessarily mean he's a bad passer (or a good one, for that matter). He may be selective. The offense may not be conducive to him getting double-digit assists. Without other statistics like turnover rate (per usage) or some measure of shooting accuracy, it's practically pointless to characterize his playmaking ability using "six assists" as a milestone.

But for the sake of argument, let's say that 20-6-6 means what we think it means, and that there are no unusual factors hiding in there. I still say that this milestone, however arbitrary, is easy to give short shrift, because it's a conjunction. For instance, suppose a team ranks, oh, fifth in team defense, measured in terms of points per possession. Without knowing anything about how well they play offense, you might guess that they're a pretty good team, probably top ten or so. The same would follow if they were fifth in team offense, but you knew nothing about how well they played defense. The reason is that although there's some correlation between team offense and team defense, there's not enough to say firmly where they fall in an overall ranking--say, in point differential per possession.

But now suppose you knew that they ranked fifth in both team offense AND team defense. You'd be virtually guaranteed they'd be one of the top two or three teams in the league, and for the same reason: The correlation between the two is small enough that very few teams--possibly no others--will be simultaneously that good in both.

In the same way, even if individually the numbers in 20-6-6 meant what you attribute to them, collectively they are a more impressive achievement. Because if 30 percent of starting guards score better than he does, and 65 percent of them make plays better, and 15 percent of them rebound better, there's probably in the neighborhood of 5 percent who do all three better than he does, and let's guess 10 to 15 percent who have a better PER (or pick your favorite, or least unfavorite, arbitrary stat combiner) than he does. That's nothing to sneeze at.

On the other hand, let's not make more of this stat than there really is: Stevie Franchise's superstardom was born of his flashy playing style. The stats were just used in an attempt to substantiate that. Players become superstars because they are memorable, over and over again, not because their stats are impressive; impressive statistics merely bolster a case and make it more defensible, but they're not the reason the player became a superstar in the first place.

Re: Rungeek.com - Bernie's Blog

briantung — Mon, 02 Nov 2009 18:07:25 -0000

Not any more!