If you just gaze into the math all you'll see is math. If you learn to recognize the kind of things in your environment the math suggests could develop and then go look, then you might get to better see what to really do about them.
For example, the ABM idea is that lots of things are individually interacting, right? If you play with that in the computer, those behaviors can enrich your imagination for how interactions among independent agents might work in physical systems. If those insights then help you discover how individual real world agents (systems) are actually interacting with each other, it will then inform you on the gaps in your thinking in designing your computer model, but more importantly, let you see the real consequences of the real world interactions, coming right at you. It lets you directly respond to the consequences approaching you in a more informed way. Yes, it's no more, at first, than a 'seeing eye dog' kind of assist, some waving stick in the dark that bumps into things with no names. That is not much of an assist, granted. But when our survival is threatened and we're stumbling around hurriedly, maybe it would keep us from falling in some great big hole. Phil From: Ken Lloyd [mailto:[EMAIL PROTECTED] Sent: Friday, August 22, 2008 10:53 AM To: [EMAIL PROTECTED]; 'The Friday Morning Applied Complexity Coffee Group' Subject: RE: [FRIAM] GridPaths, Knuth's nifty book & a Question And eventually you will re-invent back propagation through feed forward neural networks - assuming non-recurrence. The solutions to the "problem" are ensembles of paths. Ken _____ From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Phil Henshaw Sent: Friday, August 22, 2008 8:19 AM To: 'The Friday Morning Applied Complexity Coffee Group' Subject: Re: [FRIAM] GridPaths, Knuth's nifty book & a Question That sounds like you're saying that having an ability to predict an outcome with certainty, a 'final cause' in that sense, means that discovering the path the system will take in getting there is not relevant? I think that reversing that logic is the thing to do, that knowing the end gives you great tools for discovering the path. It's not whether a system that uses up resources ever faster will run out, after all. That's a simple "no-brainer" that you can answer with certainty. The question is, knowing the answer is implied, how can you be the first on the block to identify when it's happening, the path it's taking and what the choices along that path might be. Phil From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Robert Holmes Sent: Thursday, August 21, 2008 8:59 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] GridPaths, Knuth's nifty book & a Question Not quite: I'm saying that you don't need to calculate the probability of ANY of the paths because the constraints of your problem mean that the probabilities (whatever they are are) of all the paths (however many of them there are) MUST sum to one (because in your problem definition the path finally does have to get to the point (10,10)) Here's another (famous) problem that can be answered using a top-down technique rather than a bottom-up: if you have a regular 8x8 chess board and you remove the bottom left and top right squares, how many ways can you cover the remaining 62-squares completely using non-overlapping 2x1 rectangles? Robert On Thu, Aug 21, 2008 at 4:15 PM, Owen Densmore <[EMAIL PROTECTED]> wrote: On Aug 19, 2008, at 9:47 PM, Robert Holmes wrote: > I'll take a top-down approach instead of Roger's bottom-up approach... > > I'm guessing that the problem has a bunch of constraints that you've > not > specified in your email (can't double-back, path can't crossover) > and--most > importantly--you have to start at (0,0) and end at (10,10), so > stopping > somewhere in the middle or getting trapped Tron-like by your own > wall is not > a solution. So if the probability of getting to (10,10) is 1 then > the sum of > the probabilities of all the legitimate routes has to sum to 1 (and > if it > doesn't, you've missed some). Unless I misunderstand, you'd like us to fine the N possible paths, along with their probabilities (using the product of the inverse of choices for each of their moves within the paths). That's certainly a Good Thing, but the difficulty is counting all these paths, and establishing their probabilities. I see no easy way to do this. I don't even see a way to count all the paths. Thus roger's argument avoids this issue by considering the incremental probability of the paths, and showing the increment does not increase the total probability sum, and shows the initial probability sum is .5 + .5 = 1 as desired. Note the other question I asked is whether or not creating these restricted paths (no crossings, have to make it from lower left to top right) can be done without resorting to floodfills at each step. I.e. is there some local knowledge solution that would let a wanderer create a path without a global floodfill to mark "legal" moves. -- Owen ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
