Over the past few years I have been making glass pieces which are based upon a mathematical concept known as “Partition Trees”. People have been asking what they are, but it takes some time to explain it fully.
If you are interested, try the following little puzzle exercise:
Take ten identical objects, say playing cards, and divide them into any number of smaller groups, with any number of cards in each group. Put the groups in order of size, largest on the left. Now take one card from each group and make another group. If any original group contained only one object, that group is eliminated. Put the remaining groups in order of size, largest on the left. Now repeat the process again, and then again. After each re-formation, see whether that particular set of numbers has occurred before. What would you expect to happen eventually? Would you expect the process to go on for ever, or would you expect to reach some final state which cannot be altered? What would you expect to happen if you tried a different starting position? What if you try a different number to start with, say eight or nine?
Try it and see! If there is any demand, I will explain some more. I can also put up some pictures of the things I’ve made.
1 comment:
Being mathematically challenged, and choosing marbles that roll everywhere for my identical objects, this was a bit hard from the start!
But I persevered, and found that, starting with any combination of grouped numbers eventually comes around to an unchanging 1, 2, 3, 4...
Starting with nine marbles there is also a pattern - I ended up with 2, 3, 4, then back there again after a couple of group changes...
Now I need some more explanation before I lie down with a cold compress over my brow.
Yes to putting photos of your work up - that would be great.
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