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The columnist Ann Landers printed the following letter from a reader:
    "Dear Ann. If you were to count a trillion one-dollar bills, one per second, 24 hours a day, it would take 32 years."
and then she commented:
    "It is a real eye-opener."

Physicist's comments: In fact, it would take about 32 thousand years to do so, while it would take about 32 years to count a billion one-dollar bills.

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In the article "How To Do Business With Government", a reporter for the Carbondale Times wrote about the efforts of the John A. Logan College Procurement Technical Center in helping secure government business contracts for local businesses

"Director of JALC's Procurement Center (PTAC) has been instrumental in helping southern Illinois businesses obtain almost $600 billion in government contracts. PTAC, part of the Illinois Small Business Development Center Network, specializes in assistance to firms in the government contracting process."

Physicist's comments: PTAC is doing a fantastic job in helping local businesses, but the number above just does not make any sense. The population of Southern Illinois is below 1 million people, and $600 billion would mean about $600,000 per person going into a local economy. That would have been nice!

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"Since Gov. George Ryan took office three years ago, lawmakers have amassed $1.5 billion in the special fund. Just so you can grasp that number, it has nine zeroes and looks like this: $15,000,000,000."

Physicist's comments:  Evidently a typo, but quite embarassing in a political editorial piece...

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"What's for lunch, dinner, even breakfast? Pizza. Americans eat it in all shapes, sizes and flavors. Proof of that claim? We eat about 100 acres of pie each year."

Physicist's comments: The truth is, we eat about that much each day. Here is how it works. There are some 270 million Americans. Let's assume conservatively that an average person eats pizza once a month, so one in 30 will have a pizza on any given day. This gives us 9 million pizza eaters a day. Now, suppose that on average a person will consume 2 slices, or about 0.5 sq. ft. That gives 9 million x 0.5 sq.ft. = 4.5 million sq. ft. daily. Now, one acre is 43,560 sq. ft. so one gets about 100 acres daily.

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"HYDERABAD, India - Asthma patient Sarah Ahmed looked uneasily at the 1-inch sardine swimming in a plastic bag. A robed man grabbed the fish, placed a bead of yellow paste in its mouth, and deftly popped the wriggling remedy down the woman's throat.

On Sunday, Ahmed and some half a million other asthma sufferers received the unconventional treatment they believe is a miracle cure. Every June, on a date chosen by astrologers, patients from all over India get the free treatment at a house in the southern city of Hyderabad.

"I don't know how it works. Perhaps its God's blessing", said Harinath Goud, one of the five brothers who knows the formula. The Gouds refuse to give anyone the formula - not even medical researchers - for fear it will be used for profit. (...) Family members refuse any payment."

Physicist's comments: Let's do some quick estimates. One has to grab a live fish with one hand, grab a bead of paste with a second hand, put the paste in fish mouth and then push the wriggling fish down the throat of the patient. Let's say you work real fast so all it takes is 10 seconds. If so, you treat 6 people a minute, 360 people per hour, and if you work 10 hours without as much as a rest room break, you treated 3600 people. There are 5 brothers, so together they could treat 18,000 people, maybe 20,000 people, but no way they could have treated 500,000 people in one day. And it appears that they do not use assistants, as the accompanying picture shows Harinath Gould giving a patient fish-and-herb medicine, with a huge line in the background.

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"Las Vegas, Nev. On Nov. 16, 1973, hotels shut off their outside signs to comply with Nixon's request for voluntary cutbacks in energy use. That's when the Las Vegas Hilton recruited an aging workhorse to shuffle in a circle three or four hours a night, pumping 5,500 watts of power from the generator, keeping the marquee aglow while much of the city was dark."

Physicist's comments: What a super horse! As there are 746 watts to one horsepower (hp), it appears that this aging horse generated 7.4 hp of electric power output, and hence its mechanical power input must have been even higher. Yet an average horse in a good shape is capable of generating about 1/2 hp only, so this poor horse allegedly did work that would require twenty healthy workhorses.

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Clarence Ditlow, the executive director of the Washigton-based Center for Auto Safety, published an article entitled "Dumping 55 limit was deadly decision", where he argued:

"A vehicle traveling 55 mph covers 807 feet in one second, almost three football fields. At 70 mph, a vehicle covers 220 feet more or 1027 feet in one second."

Physicist's comments: Let's see. There are 5280 ft to a mile, and 3600 second to an hour, hence 55 mph = 55 x 5280 ft / 3600s = 81 ft/s. So in one second the vehicle at 55 mph travels 81 ft. Likewise a vehicle at 70 mph travels 103 ft.

What really bothers me is not that the Washington lobbyist made an embarrassing decimal point error, but that it never occurred to him that the results make no sense. Anyone who drives a car simply knows that the car does not cover 3 football fields in one second!

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"How long does it take your brain to translate the desire to move your index finger into an action? About 900 milliseconds. While it sounds speedy, it isn't. According to studies by Danish researchers, the move-your-finger thought begins in one section of the brain, then travels to another section about 2 ¹/₂ inches away before the action takes place. Given that distance, say researchers, the brain is actually sending impulses at a speed of less than one-fifth of a mile per hour. So much for quick thinking."

Physicist's comments: Let's see. There are 5280 ft to a mile, 12 inches to a foot, and 3600 seconds to a hour. So the speed is 2.5 in/0.9 s = (2.5 /5280/12) mile / (0.9/3600 h) = 0. 16 mph, so it's not only less than one fifth of a mph, but in fact less than one sixth of a mph.

Visitor's comments: After the above has been posted for a while, Toby D. Jones, a visitor to this website, pointed out to me that I overlooked a much more serious problem. He wrote: "I don't know the actual time taken (900 micro- or nano-seconds perhaps?), but (...) it does not take 0.9 s - nearly a whole second - for me to manage to move a finger." Indeed, an average reaction time for an adult is about 0.1 - 0.2 second!

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In the section Food, we found recipe for several quick casseroles. They all have same problem, so I just quote one, for
"Baked Orzo with Seafood and Pasta". It goes as follows:

"3/4 cup orzo pasta
1 pound halibut, fillet or steak
1 teaspoon olive oil
1 cup finely chopped yellow onion
2 medium cloves garlic, peeled and minced
1 can (28 ounces) chef's cut tomatoes
1 cup reduced-sodium chicken broth
1 teaspoon sugar
3/4 teaspoon dried Italian herbs, crushed
1 1/4 to 1/2 teaspoon slat
1/4 teaspoon ground black pepper
1/2 pound cooked baby shrimp
2 tablespoons chopped parsley
4 ounces crumbled feta cheese seasoned with basil and dried tomatoes

Preheat oven (...) Makes 4-6 servings. Per serving: 271 calories, 28.73 g proteins, 5.38 g fat, 25.90 g carbo., 591 mg sodium, 99.03 mg cholesterol."

Physicist's comments: These per-serving data are meaningless, for several reasons. First, we do not know whether the whole casserole has been divided into 4 or 6 servings. Further, assuming that the author had in mind the 6 serving case, the implied accuracy of the data does not make any sense whatsoever. The author measures ingredients in teaspoons and cups, and we all know how imprecise that is, and then he or she claims to know a protein content up to 4 significant figures, i.e. with an accuracy of 1 or 2 parts in 10,000. This simply can't be. The paragraph should read:

Per serving: Approximately 270 Calories, 30 g proteins, 5 g fat, 26 g carbo., 600 mg sodium, 100 mg cholesterol. Note also that I wrote Calories, not calories, since Calorie (Cal) used to describe energy content of foods is actually a kilocalorie, 1 Calorie = 1 kcal = 1000 calories.

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In the section Mind & Body, the article "Go for the Goal. Learn to make an Olympic workout of your common chores" was illustrated by the following table and caption:

"How many calories does the average person burn doing everyday activities? The number of calories burned is different for everyone and depends primarily on weight and metabolism."
 

Physicist's comments: For starters, there are some quite obvious errors here:

• The caption should have refered to Calories, not calories. 1 Calorie (Cal) used to describe energy content of foods is actually a kilocalorie, i.e. 1 Cal = 1 kcal = 1000 cal, where 1 calorie (cal) is the unit known from physics!
• The entries were meant to represent rates, i.e. the amount of Calories burned per one hour of activity.
• Data for Racquetball are evidently in error, and appear to be a repetition of Jogging data.

The source of this error could be easily spotted, when you inspect the "125 lb." column: All but the first entry there are expressed as multiples of ten, i.e. are given with an accuracy of +/- 10 Cal/hr. The author of the article probably recalculated these entries for other weights, but forgot to round off her results to a nearest ten.

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In a little note "From trees to houses" we read:
"The average single family home, and we are calling average 2,000 square feet, can have 15,824 board feet of lumber."

Physicist's comments: There is no justification to write a number as precise as 15,824. We do not know how precise is the quoted value of 2000 square feet, but it is reasonable to assume that it implies the average area of 2000 square feet rather than 1900 square feet or 2100 square feet, i.e. that the number 2000 square feet has estimated uncertainty of +/- 100 square feet, or +/- 5%. In other words, the number 2000 has two significant figures. Hence the amount of lumber should be given also with two significant figures as 16,000 board feet.

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"Bill Elliott struck a blow for the older drivers, nipping rookie Ryan Newman for the pole in qualifying Friday for the MBNA America 500 at Atlanta Motor Speedway. Elliott was the 42nd of 45 drivers to make his two-lap run and turned the 1.54 mile oval at 191.542 mph, narrowly beating Newman's speed of 191.463 mph."

Physicist's comments: How can one determine the speed with such an amazing accuracy? The simple answer is one can't.  These speed numbers are meaningless. Here is why.

Note that the length of the oval is reported as 1.54 mile, i.e. has three significant figures. This means that the actual length could be as short as 1.53 miles or as long as 1.55 miles. Therefore, each speed should have been reported with three significant figures as well, i.e. 192 mph for Elliott and 191 mph for Newman. But the race was much closer than these two numbers would imply. So what should have been done to convey the drama of a very close race and yet avoid the mathematical pitfall?

Let us work backwards and calculate the time needed to complete a two-lap run. For Elliott, we get 3.08 miles/191.542 mph = 57.8880872082 seconds, and for Newman we get 3.08 miles/191.463 mph = 57.9119725483 seconds. Now, time at the Atlanta Motor Speedway is measured with the precision of 0.001 second or 1 millisecond, so apparently Elliott was clocked at 57.888 seconds, and Newman at 57.912 seconds, i.e. Elliott won by 24 milliseconds. This is what was measured and what should have been reported. Instead, they calculated Elliott's speed as 3.08 mile/57.888 seconds = 191.542 mph and Newman's speed as 3.08 mile/57.912 seconds = 191.463 mph, but these results are meaningless, since the length of the run is known as 3.08 miles, not as 3.08000 miles (that would require knowing the length of the track with the precision of 0.00001 mile, i.e. 0.06 inch.)

However, it is still correct to say that Elliott's speed was by 0.079 mph greater than Newman's. Check for yourself and repeat calculations using above quoted run times, while changing the length of the oval to 1.53 mile and 1.55 mile. You always get the same speed difference. So to convey the closeness of the race they should have reported that Elliott was by 0.079 mph faster than Newman.

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"Snowfall increases avalanche risk. DAVOS, Switzerland - The Federal Institute for Snow and Avalanche Research said there was a general risk of snow slides above 4620 feet."

Physicist's comments: So at 4610 ft there will be no risk? Switzerland uses a metric system, so the original warning likely quoted the altitude as 1400 meters, meaning two significant figures, i.e. 1400 +/- 100 meters, i.e. 1400 meters rather than 1300 meters or 1500 meters. The AP reporter mechanically converted this to US units, and simply wrote down the number displayed by his/her pocket calculator. The AP wire should have said 4600 ft, meaning 4600 ft +/- 300 ft or so. Giving the number as 4620 ft is unreasonable. (Since 1 ft = 0.305 meter, the reporter should have gotten 4590 ft, but most likely he/she made a typo entering 1 ft = 0.303 meter.)

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A headline in a local paper:
"Randolph County. Twister caused severe damage. 24 buildings were hit along 70-yard path."

Physicist's comments: How is it possible to squeeze 24 buildings into a 70 yard path?

Visitor's comments: Dr. Charles Sadler, a retired professor of orthosurgery (I'm so glad that not only physics types visit this site) pointed out to me that the paper probably meant a tornado path 70 yards wide and several buildings long. After all, "approximating common experiences quantitatively, "one building" does not seem like an unreasonable (if approximate) unit of length" wrote Dr. Sadler.

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A student columnist contemplating ways to prevent cold fast food wrote:

"The question is how to heat fries so they remain hot in transit from the counter to your seat in restaurant. Good way to combat the heat loss of fries would involve embracing physics. Any scholar can tell you that the classic fry design of four sides (ignoring the negligible heat loss of the ends) lends itself well to a heat loss. A kinder, gentler fry with three sides would have less surface are, which therefore would lose less heat in the long journey from the Styrofoam container to the mouth."

Physicist's comments: Let us consider a cross section of a fry. The problem at hand reduces to the question what shape has the smallest perimeter assuming the cross-sectional area stays constant. The answer is a circle, of course, so the best design would be to have a cylindrical fry, looking like a cigarette. As to a three sided fry, it would have even larger surface area than the classical four sided fry, making matters worse.

It would also help to make bigger fries, as a smaller fry cools faster than a larger one of the same shape.

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Question to Marilyn: "Say I have a box of Ping-Pong balls and arrange them so they form a four-sided pyramid, square on the bottom and with equilateral triangles as the four sides. What is the smallest number of balls I'll need to build such a pyramid?"

Marilyn's answer: "I hope your box is large - you're going to need 4900 balls. Surprisingly, this is the only number (not just the smallest) that will work."

Physicist's comments: Huh? 5 balls work just fine - 4 as a base, and 1 on the top.

Visitor's comments: Upon reading my comments, Dr. Virgil Stubblefield observed: I began to wonder what motivated her answer. It occured to me that if the original box of balls was square, so that the number of balls were a perfect square, that might explain her answer... A pyramid 24 layers high and containing 4900 balls was the only one I could quickly find such that the total number of balls was a perfect square. Later I found confirmation (Grenade Stacking, in the book Wonders of Numbers by Clifford A. Pickover, Oxford Press, page 207). Bottom line: if the original question were slightly modified to start "Say I have a square array of Ping-Pong balls..." then it seems to me that Marilyn's answer becomes correct. I wonder if an editor changed those words?

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Days are getting longer.
(APS News, August/September 2005)

Even the APS News, which is an on-membership publication of the American Physical Society, goofs occasionally, as evidenced by the following quote in the column Members in the Media:

"By changing we're talking about a millionth of a second per day. But long term slowing is due to the moon. It's about 1.5/1000^th of a second slower per century. The day is longer today than it was in 1905" - Tom O'Brien, NIST, on the leap-second to be added at the end of 2005, LiveScience.com, July 5, 2005.

Physicist's comments: Indeed, the day is longer today than it was hundred years ago by about 1.5 millisecond. But this increase in length amounts to only 1.5 millisecond/(100 years * 365 days/year) = 41 nanoseconds/day, not a millionth of a second per day. (Days are getting longer primarily due to a braking action of tides on the rotation of the Earth - c.f. the review "Myths about Gravity and Tides" for more details). To calculate the accumulated time lag, note that in each year the last day is longer by about 41 ns * 365 = 15 microseconds than the first day, i.e. the average day of a year is 15 μs/2 = 7.5 μs longer than the first day. Thus after one year the accumulated time lag is 7.5 μs * 365 = 0.0055 s. After 2 years the accumulated lag is 2² = 4 times more, after 3 years 3² = 9 times more etc., so after some 13.5 years the accumulated lag reaches 1 second and NIST has to add the leap second to the time kept by atomic clock.

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