## Archive for the ‘Math Mistakes’ Category

### Fox News Fail

December 12, 2009

It really wan’t my intent to post three math fails in a row — indeed, the only intent was to post something, since the last month semester six months have been rather sparce, post-wise.  But then I saw an article on the Huffington Post which they got from Media Matters (which includes a great graphic and a video) and, well, another fail it is!

Here’s the scoop:  Rasmussen Reports posted the results of a poll about climate change that included the following question and answers:

3* In order to support their own theories and beliefs about global warming, how likely is it that some scientists have falsified research data?

35% Very likely
24% Somewhat likely
21% Not very likely
5% Not at all likely
15% Not sure

If you were going to summarize this, how would you do it?  Maybe combining categories, like this:

59%  Very or somewhat likely
26%  Not very or not at all likely
15%  Not sure

But that’s a little awkward, isn’t it?  So maybe you’d change the wording to emphasize the likely and not likely, and drop the people who are sure.  that leaves:

59%  Likely
26%  Not very likely

Hmmmm.  This is accurate enough, but to make it sound better, you might add back in the “Very likely” as a parallel to “Not very likely” [OK, you probably wouldn’t do that.  But let’s pretend you would.].  That would give

59%  Likely
35% Very likely
26%  Not very likely

And that, my friends, is how Fox News you do a poll.

As a follow up, Producer Lauren Patterson claimed, “We were just talking about three interesting pieces of information from Rasmussen….We didn’t put on the screen that it added up to 100 percent.”    Yeah, sure, that makes it all OK.

### Ahhh, those holiday deals!

December 10, 2009

Isn’t it great how many places are giving such big discounts?  It’s not quite two for the price of three, but still…

see more Epic Fails

And to think, it’s still good for another month!

### A Couple Food-Related Fails

October 11, 2009

I’m a sucker for a gimmick, particularly food gimmicks.  I’ve tried just about every flavor of Mountain Dew, as well as every variety of Reese’s peanut butter whatevers.  So when Starbucks released their new VIA instant coffee, I lined up with everyone else to take the taste test.  (It’s not bad, if you like Starbucks coffee.)

As a reward for tasting the coffee, I got a coupon for $1.00 off any VIA purchase. I then heard the barista explaining to another customer that with the coupon, the 3-pack was only$2 (actually $1.95), but the 12-pack was a better deal. So I looked at the price of the 12-pack:$9.95, or $8.95 with the coupon. And then I did a quick calculation in my head, and discovered that no, the 12-pack isn’t a better deal after all. With the coupon. Of course, it is a better deal without the coupon, and I’m sure that’s what she meant, so maybe this isn’t a FAIL, but it’s still a fail. Next up, however, is definitely a FAIL. The following was spotted at my local Target store, where Halloween candy is on sale right next to the Christmas decorations: Can anyone figure out where this number came from? The box weighs something like 38 ounces (so it’s about$4.21 per pound).  If it really were $159.84 per pound, a Butterfinger (2 oz) would cost$20.  I think I’d frame it instead of eating it.

### Amazon isn’t Transitive

September 2, 2009

You know on Amazon.com how, when you’re looking at an item, at the bottom it will sometimes suggest combinations?  Usually I just see one suggestion, but sometimes there are two:

Really?  These are frequently bought together?  I can believe that bed pillows and lap desks are often bought together (at least, more often than other combinations) but even if the tan pillow is often bought with a lap desk, and a lap desk is often bought with the pink shag pillow, it doesn’t follow that customers often buy tan and muppet-pink bed pillows together, in the same shipment, even for the Super Saver discount.  It’s an odd combination, though surpassed by a similar triple that I found but didn’t think to save and couldn’t recreate:  a home theater system that is “Frequently Bought Together” with HDMI cords and another complete home theater system.  Perhaps to encourage you to have a backup at the ready in case you don’t like the first.

The photo in the upper left is actually another strange combination, but not about transitivity:  one brand of lap desk is purportedly frequently bought with a different brand of lap desk.  I guess this demonstrates that the Frequently Boughts, while not reflexive, is also not anti-reflexive.

### Silly pricing

August 20, 2009

It seems to be the month for odd pricing schemes.  First, Michael at God Plays Dice questioned why two items sometimes cost more than twice the cost of one:  there were lots of examples in the comments, but one of my favorites is Chicken McNuggets at McDonalds, where a 4-pack costs 99 cents but a 10-pack typically costs over $3. Then JD2718 shared a story of how he went to buy a bottle of water, only to discover that one bottle cost$1.09 but you could get two bottles for a total of only $1. I followed up in the comments of JD’s post with a similar experience from earlier this week. We have a cheapo movie theater in town, which is really quite a bargain: big plush seats, second run movies, and only$2 per person for matinees.  Except on Mondays, when groups of 3 or more can get in for 50 cents each.

That means that two of us had to pay $4 to escape the heat for a few hours, but if we’d though to bring along Godzilla and buy him his very own seat, it would have cost a grand total of$1.50.

Guess who’se coming to the theater with us next time?

The photo above isn’t our theater, it’s one in Victoria, Australia that Fernando de Sousa took (CC license).  But our cheapo theater is pretty similar, except I think the seats are purple.

August 10, 2009

I  am, right the second, baking chocolate chip cookies for a bunch of teachers who are at a workshop this week.  And since me and cookies are pretty much Best Buds I’m not actually confused by the following instructions (which I’m only loosely following anyway), but still, how many ounces of chocolate chips would you add if  you were following the recipe below:

(butter, sugar, all that good stuff, then):
1/2 pkg (24 oz) Wegmans Semi-Sweet Chocolate Morsels

[Incidentally, when did Chocolate Chips become Chocolate Morsels?]

Chocolate chip photo published under CC by Editor at Large.

### Failure and Bottled Water

June 2, 2009

It’s no secret that we love Fail Blog (G-rated version here), because they have posts like this:

And this:

(Although this sign really makes me love New Cuyama.  Who else puts random addition on their City Sign?    New Cuyama is about 40 miles due north of Santa Barbara, and I totally want to visit there now.)

Fail Blog also posts signs like this:

This last post actually made me pause for a while.  Yes, the 167 bottles was clearly wrong, but working backwards suggests that this sign intended to say that Americans drank 50 billion bottles of water in 2006, that 32% (16 billion) were recycled, and the remaining 68% (34 billion) ended up in the landfill.  And that just seemed wrong.  There are about 300 million people in the United States [assuming that Americans refers to the single country and not all of North or South America], so that would means that in 2006 there were over 160 bottles of water sold per person.  And that couldn’t be right, could it?

Actually, it could.  According to the Beverage Marketing Company, there were over 8.7 billion gallons of bottled water sold in the US in 2007.   If there are 16 oz. of water per bottle, then each gallon would give 8 bottles, leading to well over 60 billion bottles of water sold in 2007, which is in the same ballpark as above.  Who knew?

(This reminds me of Chris Jordan’s photographs.  And lo, it turns out he has one of bottles, partway down the page.)

### Math Teachers at Play #7 plus a video

May 15, 2009

Math Teachers at Play #7 is living this week at Homeschool Bytes, with lots of neat posts (like this one about Math and Language Reversals).

Incidentally, if you haven’t seen it yet, on April 30 The Daily Show had a great piece [not quite safe for work in places] about the Large Hadron Collider (currently due to start up again in the fall).   Pay careful attention to the calculation that the world had a 50% chance of being destroyed; Walter probably checks this site regularly.  (There’s a lot more discussion at Good Math, Bad Math.)

[Hmmm, the embedding isn’t working.  Bummer.  You’ll have to go here.]

### Sunscreen confusion

May 14, 2009

An article in the New York Times describes consumer confusion over the ever-rising SPF numbers (used to rate the efficacy of sunscreen lotions), and their interpretation.

Unfortunately, the NYT adds to the confusion with the following:

The difference in UVB protection between an SPF 100 and SPF 50 is marginal. Far from offering double the blockage, SPF 100 blocks 99 percent of UVB rays, while SPF 50 blocks 98 percent. (SPF 30, that old-timer, holds its own, deflecting 96.7 percent).

Technically they’re right:  doubling the blockage is not the same as halving your radiation exposure.  But in terms of safety, the issue isn’t how much UV exposure you’ve avoided, but rather how much UV actually gets to your skin cells (which would then be a 2% versus 1% comparison).

According to the article, SPF measures how much longer a person wearing sunscreen can be exposed to sunlight before getting a burn, when compared to someone wearing no sunscreen.  Someone wearing SPF 50 can remain in the sun 50 times longer than someone with no sunscreen, and so SPF 100 sunscreen provides the wearer with twice the protection (in terms of time) as SPF 50 sunscreen.

It turns out there is a sense in which SPF100 is not twice as effective as SPF50 in protecting your skin, but it has nothing to do with the 99%/98% comparison.

According to the NY Times, “a multiyear randomized study of about 1,600 residents of Queensland, Australia” found that most users applied at most half of the recommended amount of sunscreen.

“If people are putting on about half, they are receiving half the protection,” said Yohini Appa, the senior director of scientific affairs at Johnson & Johnson, of which Neutrogena is a subsidiary.

But in fact they are receiving far less than half the protection:   a 2007  British Journal of Dermatology study noted that cutting the amount of sunscreen in half did not reduce the effective SPF in half, but rather reduced it geometrically to its square root.

If a person uses half of the recommended amount of an SPF50 sunscreen, they’ll get the protection of an SPF7 (since 7.1 is roughly √50), while similarly underapplying SPF100 sunscreen gets the protection of SPF10.

Apparently, if you’re looking for the protection of an SPF30 product, but like most people tend to under-apply sunscreen, you should be shopping for sunscreen rated as SPF 900.   No word yet on when such products will hit the marketplace.

(One wonders: does this work the other way ’round?  If I apply TWICE the recommended amount of a cheaper SPF8 sunscreen, do I end up with the protection of SPF64 sunscreen?)

### Counting Trouble

May 12, 2009

There have been posts here before about how bees and elephants can count small numbers.  Sometimes it’s a little difficult for us humans, however.

see more pwn and owned pictures

### Unit Comparison

May 7, 2009

Here’s the price of Flax Oil at our local Wegmans:

Is that too hard to read?  The bottle on the far left is 16 fluid ounces for $15.49, and the bottle next to it is 8 fluid ounces for$8.49.  As it happens, even though the bottles are different sizes it’s pretty easy to compare the prices for this particular example:  the large bottle is just under $1/ounce and the small bottle just over, so the prices are similar but the large bottle is the better deal. In general, though, it can be difficult to compare different sizes of the same product so the store provides a unit comparison to the left of the price. In theory this gives the price per ounce/pound/quart or whatever makes sense. The most important part of this is that you use the same unit for the different brands/sizes — that’s what makes for the comparison. Yet if you look at this picture [which is a little grainy, because Wegmans doesn’t like people taking photos so this was done on the sly with a cell phone] you can see that the small bottle is$33.96 per quart, while the larger bottle is only \$15.49 per… pint.    Every other bottle on that shelf has the price per quart except for that bottle of Flax Oil, which happens to be the Store’s Name Brand.

What makes it worse is that when TwoPi first noticed this a couple weeks earlier, Wegmans Flax Oil was more expensive and so the large bottle was not the better deal.  That make the sneaky “per pint” price even worse, because it hid the truth.

Wegmans, we love your store but in this particular regard, you blew it.

### Math in the Movies

May 6, 2009

A recently ran across a great resource page of  “Math in the Movies” from MathBits.  This page lists clips of movies (with links if they’re available online) and worksheets that can be used in the classroom.

Two of the examples relate to Star Trek, which as you all know (right?) will be in theaters starting this weekend.  In Episode 20 (“Court Martial”) of The Original Series, James T. Kirk is accused of murdering Benjamin Finney, the Records Officer.  At one point late into the episode, Kirk uses the computer to hear the heartbeats of everyone on The Enterprise.  As he explains:

Gentlemen, this computer has an auditory sensor.  It can, in effect, hear sounds.  By installing a booster we can increase that capability on the order of one to the fourth power.  The computer should be able to bring us every sound occurring on the ship.

One to the fourth power?  Not so impressive (and was I the only one thinking that you’d hear a lot more than heartbeats if every sound was magnified?  Wouldn’t breathing and moving be really LOUD?  But I’d better be careful with my critiques, because I’m a big fan of The Next Generation and a recent viewing revealed that it isn’t immune to problems either.)

The MathBits worksheet to accompany the scene is here.  They don’t link to a video clip, but you can see it on YouTube.  Actually, you can see the entire episode on YouTube:  the mistake starts at 38:10.

(Edit 5/9:  the embedding no longer works, but you can see the episode at this link.)

### Faulty Unit Conversion

April 16, 2009

Language Log has a post up (via HeadsUp the blog) about a Fox News story that had some metric issues:

The tests involved head-on crashes between the fortwo and a 2009 Mercedes C Class, the Fit and a 2009 Honda Accord and the Yaris and the 2009 Toyota Camry. The tests were conducted at 40 miles per hour (17 kilometers per liter), representing a severe crash.

On a personal note, I have a 1999 Camry that does 23.4 km/l highway, 12.8 km/l city.

### We sleep HOW MUCH?

March 31, 2009

I’m an alum of UW-Madison, and have many fond memories of the place (indeed, TwoPi and I met in grad school there).   As a bonus, they have a good alumni magazine.  But even the best magazines make mistakes from time to time, and  the Spring 2009 issue of On Wisconsin includes a graph that is simply wrong.

The graph, illustrating how much time we sleep compared to other activities, appeared in the article “Bedtime Story” (description “Why do we snooze?  UW researchers are pursuing an unconventional theory — that our brains downsize while we sleep, getting us ready to face another day.”)  Here’s what the graph looks like:

Take a look at the two biggest circles:  we spend 36% of our life sleeping, and 19% on other [unlisted] activities.  But that gray circle is pretty small — you could fit 3 or 4 of them into the Sleeping circle.  I grabbed a ruler and, sure enough, its the diameters, not the areas, that have the 36:19 ratio.  The distinction is even more striking when you look at the tiny circles:  we spend 36 times as much of our time sleeping as we do on telephone calls, mail, and email and that’s a LOT, but it’s not a ratio of 1296 (as the areas would suggest).

So I created a graph in which the areas are in correct proportion:

There’s still a clear difference in how much time we spend doing different things, but it no longer looks like 61% of our lives are spent in bed.

### Tidal force, or The Moon and the Mosquito revisited

March 30, 2009

As Ξ noted in an earlier post, the claim that the gravitational pull of a mosquito is stronger than the gravitational pull of the moon is off by a fair bit … roughly five orders of magnitude.

The original author of the claim, George Abell, was an astronomer.  Aren’t astronomers supposed to be good at working with large numbers?  Wondering if he had been misquoted in Scientific American, I set out to find out what I could about this claim.

A google search turned up a fair number of sources that describe Abell’s claims; most of their accounts are similar to that of Lilienfeld and Arkowitz.  One of the more widely read accounts appears in The Skeptics Dictionary (by Robert T. Carroll):

Astronomer George O. Abell claims that a mosquito would exert more gravitational pull on your arm than the moon would (Abell 1979).

The secondary literature is pretty much in agreement: Abell claimed that the mosquito exerts a stronger gravitational pull than the moon.  (And clearly that claim is false.)

A quick stop at the library of a nearby college turned up Abell’s original article.  He had written a piece for the Skeptical Inquirer, a review of a book on the putative effects of the moon on human behavior.  The book’s author had suggested a plausible mechanism for such influence:  the body is largely made up of water, and we all know the moon is a primary cause of tides on the Earth.

Abell’s discussion notes the source of the Moon’s influence on terrestrial tides:  not the gravitational pull of the moon, but rather the difference in that force between the nearest and farthest points on the Earth.  Because of that difference, the Earth is (very slightly) distorted, with its fluid surface in motion attempting to achieve equilibrium.

Abell notes that while the Sun’s gravitational pull on the Earth is more than 100 times stronger than the Moon’s, its tidal force — the difference in the Sun’s pull over the diameter of the Earth — is less than half that of the tidal force of the Moon.

If the Moon’s influence on human behavior were tidal (acting on the fluids in the body), then that tidal effect would  be due to differences in the Moon’s gravitational pull on the fluid in different parts of your body — differences due to the fact that (for a 6 foot tall person) part of their body could be six feet closer to the center of mass of the Moon than other parts of their body.   Abell quotes this difference as being “about one part in $3 \times 10^{13}$ (or 30 trillion) of the weight of that fluid”, and states that the copy of a magazine in the reader’s hand is tens of thousands of times more significant in producing tidal forces.

If we take the weight of the magazine to be roughly 1/2 lb [based on weighing a stack of AMS Notices], or 2.2 Newtons, leading to a mass of 0.2 kg, then the tidal force due to the magazine (over distances ranging from .2 m to .5 m — assuming I hold the book about 20 cm from my torso, and my torso is roughly 30 cm deep) will be

$\frac{G\cdot M \cdot (0.2)}{.2^2} - \frac{G \cdot M \cdot (0.2)}{.5^2 }$

(where G is the gravitational constant, and M is the mass of the fluids in your body), which works out to approximately $2.8 \times 10^{-10} \cdot M$ newtons.  A similar calculation for the lunar tidal force acting on my body when I am standing (taking my height to be 2 meters):

$\frac{G\cdot M \cdot (7.3483 \times 10^{22})}{(3.844\times 10^8 - 2)^2} - \frac{G\cdot M \cdot (7.3483 \times 10^{22})}{(3.844\times 10^8)^2}$

which is roughly $3.5 \times 10^{-13} \cdot M$ newtons.

So indeed, as Abell claimed, it is reasonable to conclude that a small book or magazine in your hand exerts a tidal force on the order of thousands of times stronger than the moon on your body.

But wait!  Where are the mosquitoes?

Abell described a second potential source of lunar influence on the human body.  He writes:

What might matter is the difference between your weight in the presence of the moon’s gravitational effect and what it would be if there were no moon.  At the most, that difference amounts to only 0.01 gram, or about 0.0003 ounces, less than the effect of a mosquito on your shoulder.

In the paragraph leading up to that passage, Abell noted that this isn’t the same as the gravitational pull of the Moon on your body, since the Moon is also pulling on the Earth (so you have a slightly larger acceleration toward the Moon than the center of the Earth does — in effect, this is the tidal force calculation in a different guise).

It isn’t quite clear what Abell means by “the effect of a mosquito on your shoulder”:  is he referring to a gravitational (tidal) effect due to the mosquito, or is he just referring to the weight of the mosquito — the amount by which it increases your weight when it lands?

I’ll leave the analysis of these two interpretations as exercises for our readers.  But the conclusions I found:  if we compute the tidal force of the mosquito on your body, it is far greater than the tidal force of the moon on your body (because of its proximity versus the great distance to the Moon).  If instead we believe that Abell is claiming that the weight (mass) of the mosquito is greater than the 0.01 g that he had computed, then he is wrong:   Ξ had generously estimated the mass of a mosquito at 5 mg; Abell’s estimate of the Moon’s influence on a person’s weight is about twice that.

Abell’s review of Arnold Leiber’s The Lunar Effect: Biological Tides and Human Emotions (1st ed, 1978) appeared in the Skeptical Inquirer 3 (1979) pp 68 – 73.