{celebrating a decade of learning to write in front of an audience}

Archive for the 'math' Category

… because it was a fair coin, you see

Wed, 23 Jun 2010 22:07:00 +0000

Information Theorist One:  “I heard something completely surprising today.”

Information Theorist Two:  “What?  Tell me!”

Information Theorist One:  “‘Heads’”

Facebook humor FAILs

Fri, 07 May 2010 02:51:16 +0000

The frequency of people failing to get my jokes on Facebook suggests to me that I’m either far less clever than I think I am or far more clever.

Or maybe both?  I asked two logicians if this could be possible.  The first replied, “It seems paradoxical that you could be more clever than you think and not more clever than you think because we’re used to a formal logic system that prohibits the simultaneous truth of a postulate and its negation.”  The second logician then said to the first, “You know what else seems logically impossible?  Your MOM!  ‘Cause she’s so FAT!  Oh, SNAP!”  The latter then explained that his assessment of the obesity of the former’s mother might be amended if he were to “exclude her middle”.

Oh, and we had this conversation immediately after walking into a bar.

There’s a whole generation in there

Fri, 01 Jan 2010 21:10:32 +0000

So, I turned 31 a few weeks ago — but it wasn’t today until a site reminded me of the (n/2)+7 dating-age-eligibility calculation.  It’s — 22 to 48 now.

That means that there are plenty of college grad women out there, each one of whom I could date — or date her mom.  And mom could comfortably have had a Master’s degree when daughter was born.

I think … either the law breaks down somewhere, or I’m going to have to come to terms with the creepiness of that.

“So that’s, like, compressed into history, right?”

Sat, 14 Nov 2009 20:36:00 +0000

I’ve been tutoring a high schooler in mathematics.  It’s pretty rewarding (watching his test scores jump from 65% to 93% has been pretty cool, for instance.)  His mother insists, over and over, that I give him “real world” applications of the math he’s learning.  I happen to believe that the math itself is cool and beautiful enough on its own, but, whatever, I can swing with that.

So he was being introduced to exponential decay (“So why is a power of e?”  “No good reason, actually, but it fits the points best.  Since decays aren’t time-sequenced in discrete jumps, it is modeled best as a continuous function.”)  So, aha, applications!  Chernobyl!

1986 … Ukraine … how a power reactor works … how criticality works … how operators try to plunge and remove cores so that they don’t get oscillations, which are modeled like this … criticality … radioactive chain reactions … decay byproducts … Strontium 90 … Calcium … incorporated into bone matricies … people with Strontium irradiation are having children now … geopolitics … Soviet Union … government secrecy and inter-state intervention … shit, I’m outside of the scope of math teaching, get back quick.

I think it helped.  So I do the couple-minute review at the end which concluded, poking fun at myself, “And now, if you see Chernobyl in your history book, you’ll know something about it.”

And he says, “Well, maybe.  1986: that’s, like, Nixon, right?”

I try to maintain a poker face while tutoring, but I said, “God, man!  Nixon was before I was born!”

“Well then …?”

Reagan!

“Oh.”

“What year were you born?!”

“1993.”

And I’m reminded that Niall will construct sentences that begin with phrases like “Back when Daddy and Nonna were little …”  And then I feel really, really, really old.

2 + 2 = cute

Wed, 28 Oct 2009 07:50:28 +0000

I have a shirt that I love from ThinkGeek.  It reads:


2 + 2 = 5
(for extremely large values of 2)

This is through-and-through a math joke, to the point that I think few people who see it really get how funny it is.  Niall doesn’t get it, either, but at least he’s super-gracious about it:

“Daddy, I know you really like that shirt, but I don’t want you to store two-plus-two-equals-five in your brain, because two-plus-two-equals-four.  OK?”

Maximizing charitable donations

Tue, 08 Sep 2009 18:10:02 +0000

I had a rewarding email exchange with my brother about six months ago about charitable donations.  I quoted Benjamin Franklin, I cited specific numbers, I did other could-be-humble-but-could-be-self-aggrandizing things that I’m comfortable doing in private conversation with Dave.  He is, after all, both the most reflective person I know and the person most similar in thought to me (I believe the latter does not shade the former, although that may be hopelessly optimistic.)

So, parable about woman giving her farthings or whatever, I’m skipping the numbers and the hyperbole.  Basically — how do I divide my contributions?

Steven E. Landsburg wrote an article in Slate on this topic, wherein he argues that splitting your contribution is inherently flawed.  To his credit, he actually presents the calculus, and by “calculus” I don’t just mean “calculations”, I literally mean multivariate calculusHere is a link to the math page.  Go check it out.

That is one of the most ridiculous arguments I have ever read, but the reason why it’s ridiculous is (to be charitable to Landsburg) a bit subtle.  For his approximation to be valid, one has to imagine “good” to be a scalar; that is, everything else stripped away, a single number that can be compared to other single numbers.  But that’s not how charity works.  Charities define an n-space — a multidimensional mathematical world with very many dimensions — and we’re not trying to optimize a number, we’re trying to optimize a containing volume.  Follow?  If you think you glork from context, you probably do, regardless of the lingo.

So, that’s out the window.  And here enters the most frustrating thing about this argument, for me: this is a perfect AskMeFi question, and is precisely the single question I cannot ask there.  Google “metafilter givewell” and prepare to spend an arbitrarily large amount of time on the inner clockwork of a community you probably don’t care about.  It might be worth it, though, to add two useful terms to your vocabulary: astroturfing and sockpuppetry.

Dave provided CharityNavigator, which I know from the MeFi clusterfrak, and it is extremely useful for making fine-grained distinctions.  But I am interested — very, very interested, and I mean you — by your theories for optimal charitable giving.  Do you give it all to one charity?  One meta-charity?  Several charities?  Do you pay back all of the readers of your blog who’ve lent you money (another large number), and only worry about charity when you reach a zero balance (we’ll take that one as a given)?  I don’t care about your list (maybe I’ll do another post for that) — what I care about is your criteria and, generally, your theory.  If you’ve thought about it, I want to read about it.  And how do you donate?  My method of choice is an anonymous money order made out to the charity in an envelope with no return address.  I don’t want them to incur Visa charges; I don’t want them to send me free return address labels; in fact, I don’t want to waste a single penny — or a single sheet of paper — on an acknowledgment letter, no matter how nice it is or how much they mean it.  That’s the case even if they wouldn’t sell my address for other kinda-like-minded charities to use for mass mailings of expensive glossy press kits, and their likelihood of doing that, to their great shame, is essentially 100%.

Please comment.  I want this to be ultra-useful to people, especially if AskMeFi cannot.

Amazon Associates Central: Fail

Tue, 04 Aug 2009 12:05:04 +0000

For some reason — I’m going with sheer spite — more than a billion people retroactively removed themselves from ever having ordered something from me through Amazon.com.

Either that, or some naive programmer was working directly with a signed 32-bit number and forgot what signed number representation was being used, which in turns leads me to believe that the back end of Amazon is (and this is surprising to me) c or c++.

Tracking ID Summary for mcgeesorg-20

Glossary

April 1, 2009 to June 30, 2009

Tracking ID
Clicks
Items Ordered
Items Shipped
New Customers
Shipped Items Revenue
Referral Fees
mcgeesorg-20 232 15 15 0 $28.05 $1.98
TOTALS 232 15 15 -1075784408 $28.05 $1.98

(If your primary response is “You make less than $2 per fiscal quarter through your Amazon Associates ID?!”, the answer is, “Yes, and that was a good quarter.”)

Risk-reward

Mon, 03 Aug 2009 16:48:49 +0000

Friend:  … which is why they say the lottery is a tax on people who are bad at math.

Joshua:  But that’s not quite true.  The expected return is less than 50%, yes, but the distribution is extremely skewed.  In terms of risk-reward, most people can spend a dollar without thinking much about it — and the possible return is enormous.

Friend:  But the people who buy lottery tickets usually aren’t spending a dollar.  They are spending twenty or forty dollars, and usually they are the people who can least afford it.

Joshua:  I agree, that’s irresponsible.  But for $1, people could take it out of their entertainment budget, not their investment budget.  Some people really enjoy the rush of waiting for the numbers to be called.

Friend: [huge 'gotcha' grin]  Do you play the lottery?

Joshua:  No, of course not.  That would be ridiculous.

Auto-generating attractive geometries

Sat, 27 Jun 2009 01:31:20 +0000

I have an “Old Glory Problem” (just coined that phrase.)  I have n icons (stars in the case of the flag, Favicons in the case of this site) and I need to arrange them in a visually-appealing way.

It regards the “Presence” feature I developed (look to your right on The Real Site.)  I keep thinking of sites I can add.  My first crop was fifteen, and I used a 5×3 grid.  When it got to sixteen, a pleasant 4×4 grid.  Then it was seventeen.

The cutest I could come up with is:















This would be roughly bounded by an astroid whatever a convex astroid would be — actually, among simple shapes, a parallelogram might be the optimal bounding box.

It seems the ideal arrangement for the eye to find it pretty is — what? — symmetry?  Preferably along two axes?  I suspect that this rule of thumb could be programmed and a set of “pretty” solutions would be spat out (1/2/3/5/3/2/1 in this case.)

Anyone want to take a stab at either telling me what the real name of this problem is, or writing a bit of code?  Maybe at some time other than 02h30 I can do it myself.

CSI: Bizarro World

Sat, 09 Feb 2008 02:13:09 +0000

Or, to aficionados, CSI: New York.

I’ve discussed the show before, after the standalone (non-crossover) Pilot.  I remarked after that episode, “I’m not sure if they’re taking liberties with the medicine on the show or not, but they are taking extreme liberties with the trigonometry, so I wouldn’t necessarily expect rigorous stuff from the show.”

And how.

The best of the Pilot, the Gothic Horror feel, evaporated after the first episode.  I rapidly lost interest.  It’s essentially a science fiction show now.  Or comic book show.  The frequency of I’mSorryWhat?! moments in the show defy belief.

I tried watching last week’s episodes.  They have frakking tricorders: they pointed a laser scanner at a fragment of material, and the readout said “Silica”.  They concluded it must be ceramic.  Um…

Hold on, same episode.  Their mass spec isolated various points in a chemical mixture, one of which was biodiesel.  Um…

Hold on, though.  The episode has a sub-plot about the sport of street luge.  In Manhattan.  We’re back to trigonometry.  The way-too-fancy visuals on their software (into which, by the way, they entered speed in miles per hour, weight in pounds, and acceleration in meters per second to get their answer) determined that for the street luger to reach the speed at which he was estimated, he had to have descended a 35% grade (for an unspecified time or distance).  The investigators looked for one.  In Manhattan.  They found one a quarter mile away.

OK, forget the fact that a 35% grade, anywhere, followed by flat road for a quarter mile, would not yield a street luger going 80 miles per hour at the terminus.  Let’s talk about a 35% grade for a moment.  The infamous Lombard Street in San Francisco has a native 27% grade, which was considered completely impassible.  They put in extensive switchbacks, taking it down to a 16% grade.  You ever driven down that street?  You ever see anything more than a quarter again as steep as Lombard Street in Manhattan?  To be specific, on 45th between Fourth and Sixth?  Other than, say, the 10 cm drop-off from sidewalk to street?

These writers are insane.  It’s not even fun to watch the show.  It’s less plausible than The X-Files, where at least they’d give Mulder a few hand-wave lines.  There’s no way to figure out a mystery, because the answer might as easily be “mutated chipmunks did it”, in what is supposed to be a procedural melodrama.

There is exactly one compelling thing about this show.  That’s in the next post.  Look up, look down, or click right, depending on how you’re reading this post.

Could be Goldkit.com does not pay you very much…

Sat, 29 Dec 2007 18:15:22 +0000

“We’ve paid out millions of dollars to hundreds of thousands of satisfied customers”

Assuming “millions of dollars” means “greater than or equal to $2,000,000 and less than $1,000,000,000″, and that “hundreds of thousands of satisfied customers” means “greater than or equal to 200,000 satisfied customers and less than 1,000,000 satisfied customers”, they could pay the average recipient just over $2 for his gold and still be speaking the truth.  But maybe the people who got $2 were the “satisfied customers”.  Maybe they have millions more customers who received less than $1 for their gold, and who were not satisfied customers, and therefore not counted in the statistics.

Methinks the ad could use more clarity.  Something like “Our average payout is $300, and we’ve paid over 300,000 people. Want to join them?”  Exact same number of characters.

109,263 errors. Five grand a pop. Let’s do the math…

Sun, 25 Nov 2007 23:50:42 +0000

Reviewers found 109,263 errors when reviewing Houghton Mifflin’s math textbooks that were submitted to the state of Texas.  Seriously.  That’s with real math, not Houghton Mifflin math.  Texas imposes a $5,000 fine on each mistake.  The state’s letting them off on a technicality, so the textbook publisher will not have to pony up half a billion dollars to pay the education department.

Ah, Texas textbooks.  Ring a bell?  Go read that link if you haven’t.  It tells about Texas’s textbook standards, which, I swear I’m not making this up, must glorify “free enterprise”, “patriotism”, and the “values” of the state’s heritage (of Texas.  Uh-oh.  Then again, not to worry.  “Lying” is clearly one of their values, so when they deceive students, they’re actually teaching them an important lesson about the values of the state.  See?  Neat, huh?)

Go read.  At the time of that post, the chairperson of the Board of Education co-owned a petroleum company, and explained that “The oil and gas industry should be consulted” when it comes to textbooks, because they “always get a raw deal.”

Canadians get a math test?

Wed, 07 Jun 2006 17:31:35 +0000

eBay Pack Your Bags & Win It Contest Rules: “All random drawings will be conducted on or about 12:00 pm, P.T. by Strobe Promotions, Inc., the independent judging organization, in Hicksville, NY … As a condition for receiving any prize, winners who are residents of Canada will be required to correctly answer (unaided) a time-limited mathematical skill-test question.”

What?

Enter the contest.

The Wolfram Integrator

Mon, 05 Jun 2006 19:39:12 +0000

integrals.wolfram.com.  Powered by Mathematica.