Daylight Saving Time is Mathematically Illogical

I’ve always found daylight saving time confusing, and now I know why:  mathematically, it doesn’t make sense.

As summer turns to winter and our part of the Earth spends less time in the sun, the length of the day contracts.  This kind of transformation is known as a dilation–a shrinking or stretching of something.

The yellow part of the graph represents the amount of sunlight per day.  This part dilates, while the times-of-day on the clock stay fixed.

In order to increase the amount of productive daylight, we translate the times-of-day.  Naturally, this doesn’t change the amount of available sunlight; it simply shifts the clock-times so that more of that sunlight occurs during preferred times-of-day .

Thus, the new day looks like this.

Essentially, daylight saving time tries to counteract a dilation with a translation.  But mathematically, the way to truly counteract a dilation is with another dilation!  Thus, the mathematical logic of daylight saving time is faulty.

Now that I fully understand the source of my confusion, I can rest easier.  And for an extra hour!

By patrick honner, ago

Geometry Photography Competition

geometry photoThe New Scientist magazine has a monthly photo contest, and the theme this month is Geometry!

I’m thinking of submitting my picture of Parabolas in Nature, but probably not my picture of my imperfect division of a squash.

The contest ends November 30th, at midnight.  The winner and select runners-up will be posted on the New Scientist website.  All the details can be found here:

http://www.newscientist.com/article/dn19684-photo-competition-geometry.html

So keep your eyes open and your camera at hand–there’s a lot of Geometry out there!

By patrick honner, ago

Shocking Mathematical Results

 

Welectroshock therapyhen it comes out that I’m a math person, the most common response from people I meet is “I was never very good at math“.  After a lifetime of struggling to find the appropriate response, I finally have something positive and proactive to say:  go get yourself some electroshock therapy.

According to a recent study, running a mild electric current through the brain seems to temporarily increase mathematical ability.   Apparently the study involved teaching the subjects a new numeration system (could it have been octomatics?) and testing their ability to organize those symbols before and after electrical stimulation of the parietal lobe.

In addition to slightly increasing mathematical ability and potentially treating dyscalculia, there is hope that such electrical stimulation could improve other brain function, as well.

Now, how can I bring this revolutionary technique into my classroom?

By patrick honner, ago

Twirling Tori

This is a mind-blowing animation of arms circulating around a torus, created by Emilio Gomariz.  I definitely became entranced for a bit, trying to follow a single hand all the way around the donut.  (Click the image or this link if you can’t see the animation).

emiliogomariz

Apart from being visually amaazing, this puts me in mind of a result about fluid flows on surfaces.  This animation demonstrates that a liquid, for example, can flow over the surface of a torus in such a way that every point moves:  nothing appears stationary here, and everything is moving in a smooth (i.e., continuous) fashion.

The remarkable result is that this same can not be done on the surface of a sphere!  There will always (at least) one point on the surface of the sphere that doesn’t move.  A popular interpretation of this result is that however windy it might be outside, there is always at least one point on the Earth that is perfectly calm.

By patrick honner, ago

Facebook Formulas

peak breakup timesThis graph on the right represents break ups per day, as determined by an analysis of Facebook status changes.  The data suggests that break-ups seem to occur most frequently in mid-February and late November.

Drawing conclusions from data is always dicey, and there are probably a lot of holes to poke in the methodology here, but it certainly is fun trying to attach meaning to these numbers!

This graph was featured in a TED Talk given by David McCandless, who runs the wonderful website www.informationisbeautiful.net.

The whole talk can be found here; this chart comes up at around the 6:50 mark.

The amount of data available through social networking sites is mindblowing, and it can’t be long before it will be used in some significant way.  Indeed, a group of MIT students has already devised a system, cleverly titled Project Gaydar, that, with some accuracy, identifies the sexual orientation of a Facebook user based on friends, likes, and other connections.

What will they compute about us next?

By patrick honner, ago
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