MPG or GPM ?

Several years ago, I discovered that the French talk about mileage in liters/kilometer which seemed pretty much upside down to me at the time. Now, upon reading a blurb in a recent Ideas section of the Boston Globe, I realize that I made two errors at the time: (1) assuming what was more natural to me was more “correct” and (2) not spending the time to think about the alternative enough to realize that the French had it right!

Certainly the higher the MPG (miles/gallon), the better your fuel economy - just as a lower GPM (gallons/mile) would. The problem is this: miles/gallon is not intuitive. I drive 10,000 miles a year because of my commute regardless of the gallons of gas this takes. I do not fill my tank and then decide how far I can drive.

MPG makes sense from a manufacturer’s viewpoint: MPG is a way to standardized cruising range (how far a care can go on a full tank of gas) from car to car. But GPM make more sense from a consumer point of view: how many gallons of gas it takes to get to work. I leave it to you to read into this discussion any implications of the US being corporate driven and France being consumer driven…

Going from 10 MPG to 12 MPG is a much greater savings than going from 40 to 42 MPG.

10,000 miles x (1 gallon/10 miles) = 1000 gallons	10,000 miles x (1 gallon/40 miles) = 250 gallons
10,000 miles x (1 gallon/12 miles) = 833 gallons	10,000 miles x (1 gallon/42 miles) = 238 gallons
saving 167 gallons	saving 12 gallons

However, going down from .42 to .40 GPM is that same benefit as going from .12 to .10!

10,000 miles x (.42 gallon/ miles) = 4200 gallons	10,000 miles x (.12 gallon/ miles) = 1200 gallons
10,000 miles x (.40 gallon/miles) = 4000 gallons	10,000 miles x (.10 gallon/ miles) = 1000 gallons
saving 200 gallons	saving 200 gallons

(image from Science Magazine)

By "intuitive" what I really mean is linear. Once a process is nonlinear, we pretty much are at a loss without using math explicitly. MPG is pretty much upside down and my apologies to the French.

Weekdays, Planets, and Gods

Ancient man looked up in the sky and saw 7 wanderers (planetoi in greek) against the backdrop of stable star constellations.

(1 & 2) The Sun and the Moon; hard to miss.
(3,4, & 5) The Earth's closest neighbors: Mars, Venus, & Mercury
(6 & 7) the Solar System's largest planets: Saturn & Jupiter

(the other wanderers in the Solar System we know of today are not visible to the naked eye.)

From this we get our seven days of the week. The romance languages have a relatively direct correspondance from planet to day. For the English, you have to go through some northern European gods that were correlates to the original greek and roman ones. Apparently, as the roman empire brought the seven day week northwards in europe, the northern peoples adopted the 7 day concept but substituted some of their own gods for certain days.

English	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
	Moon	Mars	Mercury	Jupiter	Venus	Saturn	Sun
French	Lundi	Mardi	Mercredi	Jeudi	Vendredi	Samedi	Dimanche
	La Lune	Mars	Mercure	Jupiter	Venus	Saturne	Soleil
god	Luna (Roman)	Mars/Tyr (Roman/ Norse)	Mercury/ Woden (Roman/ anglo-saxon)	Jupiter/ Thor (Roman/ Norse)	Venus/ Fria (Roman/ Norse)	Saturn (Roman)	Sol/ Dominica (Roman/ Latin)

Dimanche in French doesn't correspond well until you realize that the Holy Roman Empire did not want to be Sun-Worshipers any longer but rather have a "Day of God" or "Lord's Day". Also interesting is the movement of sunday to the front of the week (even now some calendars have it as the first day of the week and some as the last) and the movement of the Sabbath from Saturday to Sunday for early Christians.

http://www.flickr.com/photos/alele/ / CC BY-ND 2.0

Books I will never write (but should) Part One

In my travels I find the grocery stores/markets to be an underestimated proxy for culture. The book I will never write (but should) is "What your country's grocery store reveals about its people":
An entire aisle for soda in the USA!?
An open air market with laundry baskets full of mangoes in Taiwan?
As much room for cheese as for meats in the deli in France?
You get the idea I think...

360 degrees, opposable thumbs, and unit discrimination

With those cool thumbs of ours, we find ways to count to 12 (or 16) with one hand. Just move the thumb from fingertip to fingertip and then from joint to joint and most of us can keep track of numbers 1-12 (or 1-16) without having any math skills. Hence numbers that revolve around 12 and 16: a dozen numbers before we get into the teens (or 16 (a pint of?) numbers for the french before they start adding tens: "dix sept (10 7), dix huit(10 8)" etc).

Most interesting to me is the Babylonian base 60 number system (from whom the Greeks got many mathematical ideas). I think if you are counting 12's on one hand, a natural extension may be to count five sets of 12's on your other hand - giving you 60 as a natural break point (seventy in french is soixante-dix (60 10)).

From this we get 60 seconds in a minute, 60 minutes in an hour and (most interestingly) 60 degrees in an equilateral triangle angle (6 of these inscribed in a circle gives you the 360 degrees in a circle!)

Now we come to the point I have in mind in class when my students start complaining about radians. They complain about radians being unnatural and degrees being simpler. But I take the opposite tack and say we should abolish the historical baggage of the base 60 system and convert completely to the beauty of the radian.

The radian is a geometric ratio of two lengths: the arclength of a circle divided by its radius gives us the angle in radians. Much confusion reigns because degrees and radians are seen as non-units and as interchangeable to boot. Not so! Throw away the degree and adopt the radian as a true unit I say! Angles need units too! Rotation is as important as translation! Fight the power!

Header Picture

The pic at the top was taken years ago (during the self-styled "D'Artagnon" winery days) while I was lying on the beach. Someone was walking behind me and snapped this after calling my name. I like to show this picture to my students for they do not believe it to be me.

Students think of their teachers (all adults?) as static in time. I like to think that by showing them this picture, their assumptions about adulthood are to be questioned and that life can be a very dynamic ride. In so reminding them, I remind myself.

Whys and Whats

Some thoughts rattle around in your head for years, begging to be written down.

I have put some musings to paper through the years and feel guilty about not organizing them.

Finally, I occasionally have an inspiration but, with no venue for it, it dies a quick death.

So, hopefully, this will evolve into a journal of observations, rants, and asides from the past, present, and future.

The name comes courtesy of a students of mine (that's you Zack!) from 2008-2009.