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Archive for December 31st, 2010

When I was a child my father owned a National Geographic book about… well, I don’t exactly remember. However, I do remember the inside cover painting, one similar to the one below, though linear. It also based its unit of measure on the height of man, a markedly humanistic approach which at least has merit because it compares all else to something we know.  Notice that the exponents range from a mere -15 to 25 and yet this nearly emcompasses the entire known range of size in the universe (the universe is above 10^25 and elementary particles or strings (Do they have dimensions?) are below 10^-15).

Source: http://www.astrobio.nau.edu/~koerner/ast180/lectures/pic/cdrom/art_low-res/es01/figure-I-03.jpg

I loved numbers and making connections so this painting was the source of contemplation and imagination for many hours. I liked the idea of numbers and size relationships so much that one time while carrying English ivy that my father was trimming along the driveway, I asked him what the largest number was.  He replied that it was similar to an eight turned on its side. I didn’t figure out for years that this was the infinity symbol (∞). Sometime near the end of elementary school I decided to write my numbers as high as possible. Was I trying to write to infinity, or some highest number, or just a very big number? I have no idea, but frequently the young are too idealist to notice the possible failure rate of poorly laid plans. I also know that author John Piper says he believes we are drawn to bigness in its various forms because we are made in God’s image with an ability and afinity for seeing the beauty of God which we cannot clearly see at the moment. At any rate (or perhaps a specified rate within limits of one factor of ten) I had one of the old large rule writing tablets with dotted lines for teaching beginners to write their letters. I would write each number interval of 100 on a page. I don’t now know where I stopped but I do remember it was over 10,000.  Obviously these antedotes mean that I was (am?) silly, but they also partially introduce why I think “order of magnitude” thinking is important and partly explain how I know it is largely missing in education. When students crunch numbers on calculators they mindlessly accept what number it spits out not considering that perhaps they put in inappropriate numbers or incorrect key strokes. You may not immediately know what 1,549,000 times 361 equals but you should be able to know that 55,918,900,000 is not the answer by inspection because it is two orders of magnitude (100x) too large. You may not know a comparison between miles per hour and meters per second but if I tell you that a person walks at 1.5 meters per second you should be able to tell that any normal car is not likely to be traveling at 150 meters per second (unless transported to a war zone in a C-5A perhaps). If this rambling of childhood memories in any way spurs you on to consider at all or again powers of ten or orders of magnitude I have included a fun link that is useful for imparting the concept as well as firing the imagination. Enjoy it and share it with some young person who needs an introduction to magnitude so that their future answers might at least be in the ballpark.

 http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/     (As I understand it I may not link this site for copyright reasons but you may go to the site by copying and pasting it into your address line. Enjoy!)

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