Archive for the ‘Math in the News’ Category

Counting Chickens

April 13, 2009

chickWatch out — those cute little chicks will know if you’ve eaten one of their chocolate eggs.

At least, that’s the word according to the folk in Italy at the Universities of Padova and Trento.  They did experiments and found that newly hatched chicks can tell More versus Less:

In tests the chicks were shown a set of objects, in this case identical small balls, in groups of either two or three.

In one of the experiments the chicks choose consistently to walk towards a group of three balls rather than a group of two.

You can sort of see a video here, although the video doesn’t seem to show actual experiments:

The one aspect that bothers me a little is this:

When the ball were hidden behind a screen, but one of the balls could be seen being passed from the larger group to the smaller one, the chicks were still able to identify which group now contained three objects.

It wasn’t clear from my source (The Telegraph) if they ever moved one from a group of, say, 4 to a group of 1 so that the group that received the ball was still the smaller group.  In other words, maybe the chicks just were following the action.  (But it seems possible according to the BBC news article that the researchers took that into account — I can only access the journal Proceedings of the Royal Society. B where this was published for articles that are at least a year old, so I can’t verify it.)

There’s no word yet on whether the Easter Bunny has these same addition skills.

Chick photo by Fir0002 [cropped and flipped], published under GNU-FDL.

FutureGen

March 24, 2009

us-deptofenergy-sealIt’s hard to estimate how much it will cost to start/change a company, especially because it’s reasonable to expect that $1 today is worth less than $1 in the future.  Do you use today’s prices, or take inflation into account?  On the other hand, if what you’re doing is comparing costs, it doesn’t really matter which method you use as long as you’re consistent.

A mistake with that last bit ended up possibly costing FutureGen its future.

Here’s some background.  According to the US Department of Energy, “FutureGen is an initiative to equip multiple new clean coal power plants with advanced carbon capture and storage (CCS) technology.”  This was announced in 2003, but a year ago the top folk in the Department of Energy decided that it was going to be too expensive to build.

Certainly it would have been expensive:  over a billion dollars (about 8% of which would have been paid for by China and India as research into cleaner energy that they might be able to use).  But not quite as expensive as they thought.  According to Scientific American,

the Department of Energy (DOE) had essentially forgotten to account for inflation when estimating FutureGen’s projected costs. Specifically, the department had said in 2004 that it would cost $950 million to build, a sum that it last year said had ballooned to $1.8 billion when projected through 2017. In fact, the GAO says, the actual cost considering inflation would be closer to $1.3 billion….

These new figures were released in a 54-page report by the Government Accountability Office (GAO) on March 11, 2009, which you can read here.  In particular, one of the problems was that the Department of Energy was making comparisons of FutureGen as originally planned versus replacing/restructuring, but in one case they were taking inflation into account (that $1 spent in 5 years is worth less than $1 today) and in another case they weren’t, so the numbers weren’t comparable.  In The New York Times, Representative Bart Gordon (a Democrat from Illinois) said,

I am astonished to learn that the top leadership of the Department of Energy in the last administration made critical decisions about our nation’s energy future and capacity to combat global warming based on fundamental budget math errors…This is math illiteracy on a grand scale and with global consequences.

(In the interests of full disclosure, Illinois is the state where FutureGen would be located, so the consequences may have hit closer to home, so to speak.)

With this disclosure and a new administration, FutureGen might be back on the table.  Or maybe not — presumably the price has increased even since those figures were taken into account, and so other comparisons would have to be made before a decison would be made.  Hopefully this time using comparable data.

Two is Older than One

March 19, 2009

1And so are three and five, but not four.   I’m Spring Cleaning my Inbox, and I ran across this BBC news article from Feb 26 about the Reading Evolutionary Biology Group (consisting of Dr. Mark Pagel and possibly other people) and how they’re analyzing the change of certain words in English and other Indo-European languages.  According to The Telegraph:

Dr Pagel’s work has shown that the pace at which words evolved depends on how they are used. Numerals are the slowest to change, followed by pronouns, probably because they are used extremely often and have a very precise and important meaning. Nouns evolve more slowly than verbs, and verbs evolve more slowly than adjectives. Words that are used less frequently evolve more quickly than those that are common.

The number One is a pretty old word (although apparently it used to be pronounced with a hard o, like only, and only started sounding like “won” about 600 years ago).  Two ,Three, Five, I, and Who are even older, though not much much [and by “old” they’re talking about thousands, if not tens of thousands, of years].  The number word Four, however, evolved much more recently.  I find that last fact rather intriguing, but my searching skills are failing me in learning more about that; perhaps it has something to do with the fact that four doesn’t sound anything like the Latin quattuor or the Greek tessares.

This research also suggests which words will eventually disappear from English.  One leading contender is “dirty”, because there are a lot of unrelated words across the Ind0-European languages that mean the same thing.   Not surprisingly, no numbers were slated for disappearance.

Pick 3 Coincidences

January 23, 2009

196Nebraska has a lottery.  One of the games is “Pick 3”, where each player selects 3 one-digit numbers, and once a day a computer selects a winning sequence.  The player wins if they have the same three numbers in the same order.

Monday (Jan 19, 2009), the winning numbers were 1-9-6.  One lucky Nebraskan had bet the same combination, winning the top prize of $600.

Tuesday (Jan 20, 2009), the winning numbers were ALSO 1-9-6.   This time, three people had the winning combination.  (No, the person who won on Monday didn’t play the same combination on Tuesday.)

The news accounts of this event say that the two drawings were done on different computers (preempting the unspoken suspicion that there was some systematic error in the process).

According to the Associated Press, the probability of this happening are one in a million.  And indeed, there are 1,000,000 possible combinations of winning numbers over two consecutive nights, since if you just concatenate the digits you get all the strings from 000000 to 999999.

But to say the probability is one in one million means you’re measuring the probability of having 1-9-6 come up a winner in both drawings.  Most readers of the news story probably aren’t struck by that specific combination, but merely from the fact that the two numbers agree.  That sort of coincidence is far more likely to occur, with a probability of 1 in 1000 (since there are 1000 possible draws on Tuesday, and only 1 of them will match Monday’s combination).

The probability that two consecutive draws do not match is 999/1000.  But the probability that after n+1 drawings, no consecutive pair will match, is (0.999)^n.   For n=366, we find that the probability of no matching pairs to be roughly 70%, which means that over the course of one year of Pick 3 drawings, there’s a 30% chance of having the same numbers win two nights in a row at least once that year.

In two years of Pick 3 drawings, there is a more than 50% likelihood that the winning numbers will match on some pair of consecutive evenings.

As one of my Philosophy professors used to say, “Some surprises are not unexpected.”

5 – 1 = 4, unless it equals 5

November 30, 2008

olympic_pictogram_modern_pentathlonThe Union Internationale de Pentathlon Moderne held their 2008 Congress in Guatemala in November, and the main headline from the Congress was the decision to combine two of the five Modern Pentathlon events into a single competition.

From its introduction at the 1912 Olympics until the end of 2008, the five events of the Modern Pentathlon have included running, fencing, swimming, show jumping, and shooting. (The phrase Modern Pentathlon is meant to distinguish this competition from the Pentathlon, an ancient Olympic event involving competitions in javelin, shot put, wrestling, discus, and running.)

The recent change has involved combining the running and shooting events into a combined event:

Athletes will begin … with a short run to the shooting range, here they take 5 shots before a 1km run. They repeat this 2 further times, in total 15 shots and 3km run. [link]

Unlike the winter biathlon, athletes will not carry their sidearms while running.

The Yahoo News article on this describes it as changing the Pentathlon from five to four events, which raises some obvious doubts as to nomenclature. (Quadrathlon, perhaps?) The UIPM insists, though, that the Pentathlon is not being reduced to four events, since “All five disciplines are still equally represented and competed”.

I anticipate a fantastic Final Jeopardy question: “The combined number of events in the Decathlon, the Heptathlon, and the Modern Pentathlon.”

Math Confusion in the News: percent

November 12, 2008

dollarLast week Governor Arnold Schwarzenegger proposed a temporary (3-year) sales tax increase in California to help close the budget deficit. Some newspapers, however, are mixing up the amount of the increase in an effort to get the news out.

Error #1: “Governor Proposes 1.5 Percent Sales Tax Hike” from MyFox Los Angeles

The proposed increase isn’t actually 1.5 percent (which wouldn’t be all that much). It’s 1.5 percentage points, which makes it about a 20% increase from the current 7.25% state sales tax. I suspect that most people understand what the headline intends, however, because using “percent” instead of “percentage point” is fairly common. (Kudos to the LA Times for being precise in their story!)

Error #2: “Schwarzenegger proposes 1.5-cent sales tax increase to close budget gap” from the San Jose Mercury News

This headline is just wrong. A 1.5¢ tax? And it’s not just in the title, but in the body of the story. Several other newspapers made the same mistake, either running the Mercury News story without correction or writing their own story about the 1.5-cent increase (I’m looking at you, Sacramento Bee). Indeed, these 1.5-cent increase stories were common enough that I actually double checked that it wasn’t some new terminology for “percentage points”.

Incidentally, the word “per cent” is only 440 years old, and “per centage” only 222 years old. Tidbits from the OED!

A Hard Day’s Night: Math finds a missing piano

November 3, 2008

What do you think when you hear the opening chord of “Hard Day’s Night” by the Beatles?

Is it, “I wonder if that opening chord is G, D, F, C, D, G like many web sites suggest or if it is G, D, G, C, D, G (George Harrison’s 12-string), plus D, G, C, G (John Lennon), and D on bass (Paul McCartney), as given in the official Beatles’ score?” And if you don’t know (you don’t know, do you?), do you think, “I wonder if Fourier Transforms could help me figure it out.”

If that’s what you’ve been thinking, you’ll be delighted to learn that the answer is YES! Fourier Transforms are those integrals that allow you to take a function like f(x) and turn it into another function by calculating
\int_{-\infty}^{\infty} f(k) e^{2 \pi i k x} dk
and then playing around with it there. As explained in this article on Science Daily,

The process allowed him to decompose the sound into its original frequencies using computer software and parse out which notes were on the record.

The “him” is Dr. Jason Brown, a professor in the Mathematics and Computer Science Department at Dalhousie University in Halifax, Nova Scotia. He looked at the notes, and discovered that neither of the chords mentioned above actually works. What he found, instead, was that there had to be a piano. In particular,

Some music scholars and authors have previously suggested that a piano was included in the sonic layer, and Harrison allegedly offered differing versions of the guitar voicings himself in various interviews. But, how can we be sure that rock and roll’s most famous guitar chord is part piano, and what the most likely guitar voicings were? With a bit more deductive work, I found the presence of the piano did indeed solve the frequency problem, and the voicings I deduced (along with likely positioning on the guitars) are shown in the diagram. The important point is that the piano is there because the math says it is. (From this article on Guitar Player, which is also where the notes on the two chords above came from.)

This story is apparently a few years old, but was recently picked up and is making the rounds. There are more details on Dr. Brown’s web site [with more musical information], plus he has a program he wrote that lets you explore more about math and music. And that’s totally cool.

Elephants can also do math!

November 2, 2008

It turns out that bees and fish aren’t the only ones who count. Naoko Irie tested the elephant Ashiya at the Ueno Zoo in Tokyo, Japan. According to this article in The Times from September:

In [Irie’s] tests, three apples were dropped into one bucket and five into a second one next to it. Two more apples were added to each bucket, leaving the first with five and the second with seven apples. Unable to see inside the buckets or probe them with her trunk, 30-year old Ashiya selected the bucket with the more apples having, apparently, counted the contents of each as it was being loaded-up with fruit.

What makes this noteworthy is that the numbers are above five and fairly close together. The bees and fish mentioned above were able to keep track of numbers, but only through four — that appears to be a common threshold for animals. These elephants had little trouble with the larger numbers, although not perfect: Ashiya only scored 87% on the test, but that’s still above the 50% predicted if it were random guessing. And, umm, higher than I was scoring on the Dots Test.

Bzzz Bzzz Bzzz: Bees can Count

October 27, 2008

It turns out that bees can count. Not very high (four is about as well as they can do), but still…they can COUNT!

My first question upon hearing this was, “How did they figure that out?” because I couldn’t really see an examiner sitting down with a bee to ask them to list a few numbers. It turns out (according to The Australian, found via the story on Yahoo! News) that Professor Mandyam Srinivasan placed landmarks in tunnels. If the bees were trained to go to the first landmark (where “trained” means that they discovered that nectar was always placed there), then they went to the first landmark to look for more nectar. If bees were trained to go to the second landmark, then that’s where they went to look for the treats. Same thing when the bees were trained to go to the third or fourth landmark.

But four was it: they couldn’t be trained to go to a fifth landmark. If there were more than four landmarks, they looked at all of them equally in their quest for sweet sweet nectar. (Note: it’s not clear to me if they were able to go to the first landmark if there were more than five, or if having more than five landmarks just completely confused them.)

Incidentally, a different news story in The Telegraph earlier this year announced that North American mosquito fish can also count to four. The fish could also distinguish between groups of very different sizes (16 versus 8, but not 16 versus 12). No word on how bees would do at the dots test.

Predicting Avalanches and Tsunamis

October 25, 2008

Equations, exciting and new
Oh Tsunamis, they’re expecting you
And Math, life’s sweetest reward
Let it float, it floats back to you

Savage-Hutter
soon will be making another run
With Coulomb
promises something for everyone
In the course of a landslide
On Alborón can still be romance

Because Tsunamis won’t hurt anymore
There are open smiles on these friendly shores
It’s Math
Welcome aboard it’s math
Welcome aboard it’s math

Thank you, thank you, we’ll be here all week. Today’s news story was brought to you by Science Direct, and concerns a paper written by E.D. Fernández-Nieto, F. Bouchut, D. Bresch, M.J. Castro Díaz, and A. Mangeney. They took the Savage-Hutter equations, which have already been used for rock avalanches, added some information about the Coulomb friction term (which is related to the fact that when a liquid spills it spreads evenly all over the floor, but when something more solid like sand spills it forms a pile), and used it to examine landslides from the Spanish island of Alborón (Almería). It might even be possible to predict tsunamis, although not necessarily to prevent them.

And if you can’t concentrate on any of that because you have the theme song for The Love Boat stuck in your head, here’s a little something TwoPi and I found when we did a guest post for Our Best Friend Craig on Puntabulous when he was on a cruise:

Math Mistake costs several hundred jobs

October 20, 2008

CNN reported on Friday (and JD2718 mentioned on Saturday) that the Dallas school system had to lay off some employees after realizing that its budget was just a tad short, where “just a tad” stands for $84,000,000 [more even than the $64 million first reported]. Whoops! According to the CNN news article:

The district laid off 375 teachers and 40 counselors and assistant principals Thursday, and transferred 460 teachers to other schools within the district.

The deficit was caused by a massive miscalculation in the budget, CNN affiliate WFAA-TV reported.

So that got me wondering what possible miscalculation could have led to that kind of error. It turns out that a large part of it was due to underestimating the average salary of the teachers (which runs on the order of $50,000 for elementary school teachers, according to this site). In this September 23 video, Dr. Michael Hinojosa (superintendent of the Dallas Independent School District) stated:

When you take, you underestimate your average teacher’s salary by $3900 and you multiply that over 11,000 teachers, then that creates a huge budget error.

Yes. Yes it does. About 43 million dollars. The rest of the error was apparently due to not following a formula for how many administrative positions to have at each of the 225 DISD campuses, resulting in 1-2 “extra” people at each campus, for a total of 338 extra positions.

Moral: Being close is not always good enough.

Mail Goggles: Using math to save you from yourself

October 9, 2008

Earlier this week, one of the Official Gmail Engineers (Jon Perlow) announced the launch of a new lab: Mail Goggles. This is an optional feature that requires you to solve math problems before you can send out email.

Here’s how it works: you preset certain days and times (e.g. weekend nights, the default) when you think you might be prone to sending out emails that you’ll later regret. You also select the difficulty of the math problems, on a scale of 1 to 5. If you try to send an email during a designated time, a window pops up with five math problems, which you have to solve in under a minute in order for your message to actually be sent.

Here’s a sample of the problem in Level 1, with the big red numbers counting down from 60 in order to let you know just how much (or little) time you have left to prove you’re thinking clearly:

Too easy to dissuade you when you really need stopping? Try Level 3.

And finally, here’s an example from Level 5 (which doesn’t seem so different from Level 3, and occasionally appears to be easier):

If you take too long to answer, you get the note, “Oops, looks like your reflexes are a little slow. Try again.” with five new problems. If you get any answers wrong, the program suggests water and bed. And if you do still manage to compose and deliver some news that you wish you hadn’t? At least you can say you really are too smart for your own good.

I initially learned about this from ars technica.

The Smarts of Slime Mold

October 8, 2008

When looking up the Ig Nobel prizes for Monday’s post, I was intrigued by the mention that slime molds can solve puzzles. As near as I can tell, here’s what was going on:

The Cast of Characters: Your everyday Physarum polycephalum, otherwise known as slime mold. Normally this mold likes to hand out in dark places, like under logs, but according to sites like this it can be useful to scientists because the cells are huge and easy to see. (“Cell” might be the wrong word; apparently lots of cells fuse together into one giant creeping amoeba-like thing.)

The Temptation: Slime mold gets hungry and wants to eat. Normally it eats things like rotten plants, but for illustrative purposes we’ll use a carrot and a cupcake.

The Problem: What if the slime mold is in a maze, and there are two pieces of food? If it were just one, then the mold would check out the entire maze and head over to the nutrients. With two different pieces of food, however, it runs into a problem: it can’t be in two places at once, and it’s not patient enough to eat one item and then move to the other.

The solution: It stretches between the two nutrients using the shortest path. It was for this recognition − that the slime mold was finding the shortest path − that Toshiyuki Nakagaki, Hiroyasu Yamadam, and Ágota Tóth won the Ig Nobel prize in Cognitive Science (for their September 2000 article “Intelligence: Maze-Solving by an Amoeboid Organism,” in Nature magazine). The article requires a subscription, but even without one you can look at a series of photos here. [From the photos, it looks to me like the slime is actually checking out a few different paths, but among them is the shortest.]

The follow-up: Almost three years later, the first two authors (Toshiyuki Nakagaki and Hiroyasu Yamadac) and a third (Masahiko Hara) pointed out that when the mold was trying to get to food in several different locations, it did the same trick of trying to be at each food source at once. Furthermore, “These findings indicate that the plasmodium can achieve a better solution to the problem of network configuration than is provided by the shortest connection of Steiner’s minimum tree.” (from the abstract to “Smart network solutions in an amoeboid organism,” which appeared in the magazine Biophysical Chemistry in January 2004).

But wait, there’s more! Klaus-Peter Zaune created a six-legged robot that was powered by this same kind of mold. Slime mold generally avoids the light; circuits underneath the slime could sense the stuff shying away, and that caused the robot to move away as well. The robot made its appearance at the Second International Workshop on Biologically Inspired Approaches to Advanced Information Technology in January 2006, according to New Scientist.

Finally, a January 2008 article back in Nature (“Cellular memory hints at the origins of intelligence” by Philip Ball) states that Slime Mold remembers the things it’s done:

When the amoeba Physarum polycephalum is subjected to a series of shocks at regular intervals, it learns the pattern and changes its behaviour in anticipation of the next one to come.

Poor slime mold, getting those shocks. I’m sure it would prefer the carrot.

The Ig Nobels

October 6, 2008

The 2008 Ig Nobel prizes have been awarded!!! In the words of the official site:

The Ig Nobel Prizes honor achievements that first make people laugh, and then make them think. The prizes are intended to celebrate the unusual, honor the imaginative — and spur people’s interest in science, medicine, and technology.

So who were the winners this year? The complete list (including linked references) is here, but as a quick summary they are:

  • NUTRITION PRIZE. Massimiliano Zampini of the University of Trento, Italy and Charles Spence of Oxford University, UK, for electronically modifying the sound of a potato chip to make the person chewing the chip believe it to be crisper and fresher than it really is.
  • PEACE PRIZE. The Swiss Federal Ethics Committee on Non-Human Biotechnology (ECNH) and the citizens of Switzerland for adopting the legal principle that plants have dignity.
  • ARCHAEOLOGY PRIZE. Astolfo G. Mello Araujo and José Carlos Marcelino of Universidade de São Paulo, Brazil, for measuring how the course of history, or at least the contents of an archaeological dig site, can be scrambled by the actions of a live armadillo.
  • BIOLOGY PRIZE. Marie-Christine Cadiergues, Christel Joubert, and Michel Franc of Ecole Nationale Veterinaire de Toulouse, France for discovering that the fleas that live on a dog can jump higher than the fleas that live on a cat.
  • MEDICINE PRIZE. Dan Ariely of Duke University (USA), Rebecca L. Waber of MIT (USA), Baba Shiv of Stanford University (USA), and Ziv Carmon of INSEAD (Singapore) for demonstrating that high-priced fake medicine is more effective than low-priced fake medicine.
  • COGNITIVE SCIENCE PRIZE. Toshiyuki Nakagaki of Hokkaido University, Japan, Hiroyasu Yamada of Nagoya, Japan, Ryo Kobayashi of Hiroshima University, Atsushi Tero of Presto JST, Akio Ishiguro of Tohoku University, and Ágotá Tóth of the University of Szeged, Hungary, for discovering that slime molds can solve puzzles. [This may warrant its very own post in the near future!]
  • ECONOMICS PRIZE. Geoffrey Miller, Joshua Tybur and Brent Jordan of the University of New Mexico, USA, for discovering that a professional lap dancer’s ovulatory cycle affects her tip earnings.
  • PHYSICS PRIZE. Dorian Raymer of the Ocean Observatories Initiative at Scripps Institution of Oceanography, USA, and Douglas Smith of the University of California, San Diego, USA, for proving mathematically that heaps of string or hair or almost anything else will inevitably tangle themselves up in knots. [But of course you already read about that here last December!]
  • CHEMISTRY PRIZE. Sharee A. Umpierre of the University of Puerto Rico, Joseph A. Hill of The Fertility Centers of New England (USA), Deborah J. Anderson of Boston University School of Medicine and Harvard Medical School (USA), for discovering that Coca-Cola is an effective spermicide, and to Chuang-Ye Hong of Taipei Medical University (Taiwan), C.C. Shieh, P. Wu, and B.N. Chiang (all of Taiwan) for discovering that it is not.
  • LITERATURE PRIZE. David Sims of Cass Business School. London, UK, for his lovingly written study “You Bastard: A Narrative Exploration of the Experience of Indignation within Organizations.”

Equally amusing is the online program from this past Saturday’s ceremony, which includes the 24/7 Lectures (three experts each speak for 24 seconds on their subject, then summarize it in 7 words), the Win-a-Date-With-a-Nobel-Laureate Contest (reported by The Boston Globe to be Benoît Mandelbrot himself!), and previous winners, including the creator of the pink plastic flamingo.

Fancy Fields

October 2, 2008

Michael, over at God Plays Dice, posted a neat article yesterday about the geometry in Baseball fields and the history of mowing the grass in interesting patterns (like these stripes at Petco Park):

There’s a lot more detail in the New York Times article, “Groundskeepers Display Artistry on the Diamond”.

I was immediately reminded of Crop Circles. There’s a bunch of geometry there, too, though it’s more about circles than stripes. Like this one:

Or this one:

Or this little guy (by Perfectblue97) which looks simpler but might have been just as hard to make:

There are some more designs at CoolMath4Kids, and more about how to physically make the circles on WikiHow. But if what you want is a step by step description of particular designs, your best bet is to head over to Zef Damen’s page, which has lots and lots of designs (updated frequently, too!). I think I’m totally going to assign this as a creative assignment in Geometry when we’re using a straightedge and compass.

All of which is to say that groundskeepers aren’t the only ones who get to make neat designs.