Dividing the Spoils

Well, ya know--at first I thought I was going to have to recuse myself from this case, since I done figgered out the tire thang.

But the longer I watched, the more I decided that the way he did it has something to do with "kibbles" and "bits".:)
I liked it. But the thing I find about math enthusiasts is that they tend to invent imaginary problems to fit the imaginary math... not the ones from Oki though I'm sure.

So lets not overlook the detail that no matter whether redneck or not, dividing any mass by 7 without a scale is difficult. Has anyone ever tried to divide a pie into 7 equal pieces? Good luck. So why in the example would anyone want to do it twice on two different amounts? Even with a redneck's non-digital farm scale, dividing 100 lbs by 7 is not easy (14.28571)... it gets no easier dividing 500 lbs. Dividing into 7 1 sack, 5 sacks, or N sacks are each the same difficulty.

So, divide by distance. Lay the sacks together side by side and then divide the total by 7 once. Maybe lay a tarp and do it on the ground, laying out any rectangle with equal corners. Then mark off the sides into 7'ths using a ruler, and use a straight edge (broom handle) to cut the portions. Or, just lay the sacks end to end in a line on the ground, and then take a ruler to divide the total length by 7.

If a tape ruler is not available, or if the length is wrong for easy division, dividiing a length is easy with this procedure: Lay ANYTHING on the ground end to end 7 times to mark off 7 equal divisions parallel to the length to be divided. Using twine (string) find the point that forms a triangle from the ends of the length to be divided, and the ends of the length already divided. Keeping that point, move the string to scale the divisions from the one to the other.

Dividing mass or energy is harder, but a large redneck balance can roughly do the job. Nail a board to the barn and place all the bags on one side, and then place ANYTHING that can be easily divided by into 7 equal parts on the other side... like 7 jugs of milk, bags of fertilizer... whatever. Then move and find the fulcrum until it balances out. Keeping the fulcrum, with one amount on one side measure out a portion on the other side.

Fractional math can be fun in the imagination... I can solve differential equations, play with tensors, gradients, and find eigenvectors... but there are no fractional particles in the world. The Big integer math is fun too... but there are no two measurable particles or molecules in this world that are ever the same. Nope... none. They are each numbered and are always unique. :D
Actually the Egytians DID know how to divide continuous quantities like grain, and they may have even done the nuts and bolts of it in the manner you described. Thank you for your insight.

The purpose of this little vignette, as I am sure you realize, was to introduce the reader/viewer to the historical context. Our students have had the advantage of standing on the shoulders of giants, but not many of them realize it.