Stories tagged math


No more negativity: Take a good look, this is the last you'll ever see of negative numbers.
No more negativity: Take a good look, this is the last you'll ever see of negative numbers.Courtesy SMM
In a sudden change of direction, international math scholars have announced today a whole new concept for numerals with a value below zero.

“We literally are taking the negativity out of math,” explained Gordon von Himpter, president of the International Alliance for Math Education. “It’s not secret that many people don’t like math. Through our evaluation and focus group testing, we’ve found out that negative numbers are big contributors to this negative image of math.”

So beginning today, numerals with a value less than zero will be lose their little minus sign and be referred to in a new way. Click here to see the full results of the study.

“When you count backwards, it will sound like this now,” said von Himpter, “Un one, un two, un three and so forth. The prefix ‘un’ will take the place of the old minus sign.”

The same applies to the actual numerals. New denotation for those numbers will look like this: u1, u2, u3, etc.

“We’re not phasing this in. We think a quick, clean change is the best way to try to rebuild math’s reputation,” continued von Himpter. “And we’re expecting that people will be quick to embrace this exciting change.”

The move has already been embraced in the world of meteorology.

“The most common complaints we get are in the dead of winter when the temperatures go so far below zero,” said National Weather Service spokeswoman Leslie Noting. “Now, when we say the temperature is un10 degrees, we’re pretty sure people won’t feel it’s so cold.”

Click here to get your free outdoor thermometer with the new “un” notation.

The only field that seems to be resisting this mathematical change is the world of banking.

“When our customers’ accounts go below zero, we want them to feel it is truly a negative experience,” said Henry T. Potter IV, CEO of the United Group of Banking Top Honchos. “And banks are such traditional outfits. We just don’t change.”

And Potters reminded anyone reading this report who has not clicked on the links to remember the date that this blog post is being made: April 1, 2015.

“Yes, we bankers can pull April Fools Day pranks, too,” he said.

All together now

by Anonymous on May. 15th, 2013

What happens if you start 32 metronomes at different times on a stable surface? Not much. They'll tick-tock out of sync until the cows come home. But what happens when you start the same 32 metronomes on an unfixed surface? You get to witness a nifty (and mesmerizing) example of coupled oscillations. Watch and learn.

Pick a number: The PIN you punch in at an ATM can have a higher or lower level of security based on the order of the numbers you pick.
Pick a number: The PIN you punch in at an ATM can have a higher or lower level of security based on the order of the numbers you pick.Courtesy Victor van Werkhooven
What are the most popular PIN numbers people use? What are the least? How can you best ensure that your PIN is something crooks would have a lesser chance of figuring out? This is a pretty neat report that talks about what works, and what doesn't, when selecting a personal identification number to use with some financial or electronic devices. You'd be surprised how often people commonly make mistakes that lead to easy uncovering of their PINs.


It's a big drawer: But I'm a grown man. This could be close...
It's a big drawer: But I'm a grown man. This could be close...Courtesy JGordon
The human body is more or less the density of water: 1000 kg per cubic meter. (I tend to sink, so I'm probably a little denser, but I think we're close enough here.)

I weigh about 150 pounds, or 68 kg (2.2 pounds per kilogram).
1000kg / 1m^3 = 68kg / ?m^3
? = .068
So the volume of my body is about 0.068 cubic meters.

Each cubic meter equals about 35.3146667 cubic feet.
.068 x 35.315 = 2.401
So the volume of my body is about 2.401 cubic feet

My file drawer is 1 foot wide by 9 inches high (or .75 feet) by 2 feet and 2 inches deep (or 2.167 feet)
1 x .75 x 2.167 = 1.62525
So the volume of my desk drawer is 1.62525 cubic feet

1.62525 < 2.401
So the answer is NO. If you were to blend me up in a giant food processor, and then pour me into my file drawer, I would literally be overflowing.

That's sort of a relief.

Then again, it depends on how much denser I am than water. Maybe I would fit.

101010: 101010 = 42.
101010: 101010 = 42.Courtesy jimmowatt
"101010 (base two (binary)) equals 42 (base ten). Oddly enough, this is evenly divisible by the number of days in a week (7 (lucky)); and equally oddly, is also evenly divisible by the number 6 (which is generally designated as being unlucky). Both a Ying and Yang situation seem to be incorporated into this date."

10 (base ten) = 1010 (base two)

(base ten): 10 x 10 = 100

(base two): 10 x 10 = 100

42 is the answer to everything

In Hitchhiker's Guide to the Galaxy, the
"Answer to Life, the Universe, and Everything" was 42.


One man, one vote.: But how those votes are counted can lead to some surprisingly complex mathematics.
One man, one vote.: But how those votes are counted can lead to some surprisingly complex mathematics.Courtesy Theresa Thompson

Winston Churchill once quipped, "democracy is the worst form of government, except for all the others." Though said tongue-in-cheek, a recent article in New Scientist shows that, mathematically at least, Winnie was on to something.

Every election has winners and losers. Different countries have different systems for determining the winners, and dealing with the losers. And, it turns out, each of those systems has mathematical quirks which prevent the results from perfectly matching the will of the people.

  • The "winner-take-all" system used in America is certainly very simple and straight-forward. The problem is, the thousands--or even millions--of people who voted for the losing candidate end up with no elected official representing their views. (In the recent British elections, the Liberal Democratic party won 23% of all individual votes cast, but ended up with less than 9% of the seats in Parliament.) And in a race with three or more candidates, you can get a winner who carries less than 50% of the vote.
  • Some countries get around this by using "proportional representation:" they count votes cast for each political party, rather than for individual candidates, and divvy up the legislature that way. The voters' voice is fairly represented. But if one party controls more than half the seats, it can effectively shut the minor parties out. And if no party has a majority, they end up sharing power in ways that do not reflect their numbers. (Again, the British elections are a good example. The leading Conservative Party won 37% of the vote and 47% of the seats--not quite enough for a majority. They may form an alliance with the Liberal Democrats. The two parties would share power 50%-50%--quite a boon for the LibDems, who control only 9% of the seats!)
  • A few countries have tried "ordered voting," in which voters rank all candidates in order of preference, and then conducting run-offs until someone gets 50% of the vote. But this can lead to a strange situation where nobody wins!
  • And dividing the electorate into districts can shift power in unexpected ways. (We had a Buzz exhibit last year explaining how the Electoral College redistributes power.)

In 1963, American economist Kenneth Arrow considered all these quirks and tried to describe the perfect voting system. He then proved that it was mathematically impossible. (Of course, this assumes the system he described really is perfect--I'm not so sure.)

It seems to me, though, that the problem isn't with democracy, but rather with representative democracy. The people of Minnesota elect only one governor, only one senator (at a time). And there's no way one person is going to perfectly reflect public opinion--be 53% in favor of issue A and 61% opposed to issue B. And even if they were, they still have to make a series of yes-or-no decisions, and be either 100% for 100% against any given bill.

The only way to have a perfect democracy is to have everybody vote on every issue, a system that would be far too cumbersome to work. Churchill was right: democracy is messy, but it's the best thing we've got.

Two girls tackle their math together: Are they inadvertently taught to fear it?
Two girls tackle their math together: Are they inadvertently taught to fear it?Courtesy gr8matt
Researchers at the University fo Chicago have published a new report in PNAS that shows math anxiety in elementary school teachers (which are predominantly female) is passed on to the young girls in their classes. The research is reported on the Smithsonian's Surprising Science blog site.

New record for pi?

by Anonymous on Jan. 06th, 2010

Pi are squared; cake are round: Photo courtesy LeJyBy at Flickr Creative Commons
Pi are squared; cake are round: Photo courtesy LeJyBy at Flickr Creative Commons
Using a desktop computer, a scientist says he's calculated pi to almost 2.7 trillion digits! That's enough information to fill more than a thousand gigabytes (one terrabyte) of hard drive space, and would take more than 49,000 years of around-the-clock counting to count at one number per second. Could this mean more slices for everyone? Let's hope so.

BBC report


GOCE Satellite: The Gravity field and steady-state Ocean Circulation Explorer
GOCE Satellite: The Gravity field and steady-state Ocean Circulation ExplorerCourtesy ESA
Can it be true? Yes, for a mere $5,544 dollars round-trip airfare to Greenland! In March 2009, the European Space Agency launched the Gravity field and steady-state Ocean Circulation Explorer (GOCE) into orbit around our planet, which is now transmitting detailed data about the Earth’s gravity. The GOCE satellite uses a gradiometer to map tiny variations in the Earth’s gravity caused by the planet’s rotation, mountains, ocean trenches, and interior density. New maps illustrating gravity gradients on the Earth are being produced from the information beamed back from GOCE. Preliminary data suggests that there is a negative shift in gravity in the northeastern region of Greenland where the Earth’s tug is a little less, which means you might weigh a fraction of a pound lighter there (a very small fraction, so it may not be worth the plane fare)!

In America, NASA and Stanford University are also working on the gravity issue. Gravity Probe B (GP-B) is a satellite orbiting 642 km (400 miles) above the Earth and uses four gyroscopes and a telescope to measure two physical effects of Einstein’s Theory of General Relativity on the Earth: the Geodetic Effect, which is the amount the earth warps its spacetime, and the Frame-Dragging Effect, the amount of spacetime the earth drags with it as it rotates. (Spacetime is the combination of the three dimensions of space with the one dimension of time into a mathematical model.)

Quick overview time. The Theory of General Relativity is simply defined as: matter telling spacetime how to curve, and curved spacetime telling matter how to move. Imagine that the Earth (matter) is a bowling ball and spacetime is a trampoline. If you place the bowling ball in the center of the trampoline it stretches the trampoline down. Matter (the bowling ball) curves or distorts the spacetime (trampoline). Now toss a smaller ball, like a marble, onto the trampoline. Naturally, it will roll towards the bowling ball, but the bowling ball isn’t ‘attracting’ the marble, the path or movement of the marble towards the center is affected by the deformed shape of the trampoline. The spacetime (trampoline) is telling the matter (marble) how to move. This is different than Newton’s theory of gravity, which implies that the earth is attracting or pulling objects towards it in a straight line. Of course, this is just a simplified explanation; the real physics can be more complicated because of other factors like acceleration.

Albert Einstein
Albert EinsteinCourtesy none
So what is the point of all this high-tech gravity testing? First of all, our current understanding of the structure of the universe and the motion of matter is based on Albert Einstein’s Theory of General Relativity; elaborate concepts and mathematical equations conceived by a genius long before we had the technology to directly test them for accuracy. The Theory of General Relativity is the cornerstone of modern physics, used to describe the universe and everything in it, and yet it is the least tested of Einstein’s amazing theories. Testing the Frame-Dragging Effect is particularly exciting for physicists because they can use the data about the Earth’s influence on spacetime to measure the properties of black holes and quasars.

Second, the data from the GOCE satellite will help accurately measure the real acceleration due to gravity on the earth, which can vary from 9.78 to 9.83 meters per second squared around the planet. This will help scientists analyze ocean circulation and sea level changes, which are influenced by our climate and climate change. The information that the GOCE beams back will also assist researchers studying geological processes such as earthquakes and volcanoes.

So, as I gobble down another mouthful of leftover turkey and mashed potatoes, I can feel confident that my holiday weight gain and the structure of the universe are of grave importance to the physicists of the world!