Numbered daze: shift-shuffling by 4 or 9 to stay caput or to bend towards the sun Our days here are numbered. Not that we know what that number is or where we're going next, but j officially resigned from her job last week so there's nothing keeping us "caput," as the saying goes .... which in this case is If you stop to think about it, everyone's days everywhere are numbered. I used to like positing this riddle:
... not because i thought the answer was interesting (the guy jumped from a plane & his parachute wouldn't open) but i just like the idea of a man headed towards a field knowing he will die. I am not sure where this blog post will end up. I haven't written a blogject for a few weeks ... since our Balkan trip. Since then we've been laying low mostly, enduring the heat of Rome, taking small little weekend trips to nearby places that we've been meaning to go, like Pompeii. And other places that end in i, like Tivoli, Chianti & Capri (where these photos were taken). And reading books by the likes of Bergson, Cixous, Delillo, Vladislaviċ, Gass & Gleick. Books & places i may or may not get around to talking about here. Since our days are numbered & we don't know that number is or where we are going next, we might just disappear for a spell & resurface elsewhere. But for now we are here in Rome, with a UK IP address, watching the olympics. The other day Christian Peet wrote a post about Before i was into words, i was into numbers. Not that i'd say it was my "first love," but they came easy for me. And i could never resist trying to solve things or figuring out patterns in numbers. When i had to pick a major (at UC Santa Cruz) as an undergraduate, i picked math just because i'd already taken enough math classes to fulfill the requirement (even in high school i was taking AP & college level classes at the local community college in the foothills, just for the hell of it). All i had to do was a thesis, which i did on Fibonacci numbers & phyllotaxis (the spiraling patterns of plants). What intrigued me most was not that plants exhibited whorling patterns in sequential Fibonacci numbers (that most everyone is probably familiar with, if not, google it or count for yourself the number of spirals in either direction on a pineapple, artichoke, pinecone or sunflower), or that the ratio of these successive Fibonacci numbers approaches the so-called Golden Ratio as you get higher in the sequence, but Optimizing sunlight ... that's the reason in a nutshell, whether the plants know it or not. I go into more here, in relation to MS 408, Roman artichokes & Ark Codex. But back to the sequence of numbers Xtian derailed/prompted me with (a 9-fold pattern which he credits to Ted Berrigan & Reuben Hersh). To satisfy my own curiosity, i wrote out the next 2 using this shuffle-shift. This is what happens with 10 (using 0 as the 10th number). 1 2 3 4 5 6 7 8 9 0 ... at which point, after 6 iterations, the sequence cycles back to the beginning. Interesting to note though, is what happens in the last row, with all the even numbers on the left & odd numbers to the right, increasing towards the middle. Also interesting is that although all the other numbers shuffle around, there is always a 7 in the 7th column (& similarly for the 5th column when you have 7 lines/topics). If you look carefully you'll start to notice other odd patterns, like look at the 3rd & 9th columns in the above, and how otherwise besides the 3rd & 9th columns there is a linear down-shifting going on between the other columns. You could probably follow any of these sub-patterns to some sort of insight. And here it's worked out for the number 11 (for which i will use an E): 1 2 3 4 5 6 7 8 9 0 E ... so it repeats after 11 iterations. (You can also use sequences of letters to do this if you don't like numbers, for example for the 9-lettered ARTICHOKE, you'd get these 9 iterations before it repeats: A R T I C H O K E So, in summary, the sequence of numbers this shuffling operation generates is: 1, 2, 3, 3, 5, 6, 4, 4, 9, 6, 11, ... If you are good at math, you wouldn't need to write out the sequences this far, if at all. Just by virtue of the operation (shifting one & then shuffling alternating from the beginning & end of the last stack) you should be able to generalize the pattern with an equation. You'd expect modular arithmetic to be at play here (a sort of arithmetic for whole integers where remainders are what counts, rather than the decimal, or as wikipedia puts it, for sequences of numbers (like the 12-hour clock) that 'wrap around'). And you'd also expect the number 2 (or
where What's interesting is that if you had a deck of 50 cards, you'd have to shuffle 50 times before it gets back to the original state, and for 51 cards you'd have to shuffle 51 times, and for 53 cards you'd have to shuffle 53 times, so there's something special about the number 52 that perhaps early developers of cards games figured out. Also interesting is that there are 26 letters in the English alphabet, or 52 if you consider miniscule & majuscule forms. Or why in my last post it bothered me to list my 50 literary pillars, and i felt inclined to list 52. Though there i said it had to do with my recent obsession with the number 4. Most of my life until now i haven't show much love for the number 4 .... i've always liked 3 or 13, but never thought about 4 much. But lately i've been mulling over the number 4, specifically in regards to the narrative structure of the text i'm working on, which for now i'm calling 'The Raft Manifest,' but likely i will call something else as i'm almost finished with the first book & they (a mixed litter of feral children & dogs) haven't even gotten around to building this raft (just like how in the That's about all i have to say about the Raft Manifest for now, or anything for that matter. As usual I set out to write a post about Tivoli & Chianti & Pompeii & Bergson & Delillo & Gass, etc. & ended up blogging about something else entirely. Go figure. |