Wednesday, August 23, 2017

Langton’s Ant

    
If you knew everything in the present, exactly, and you also knew the “laws of nature” could you predict the future?  We live in a dynamic system that we can measure, and we know all of the rules we can measure, so like predicting the eclipse of the sun, can’t we predict more complicated things as well?    
A conventional dynamic system (CDS) is defined as a system where all the parts (every part) are described precisely as to position, and motion, (and by implication; the rules that govern their interaction - what they can do).  The rules are that we don’t make up outside influences; they are all defined in our complete and precisely defined system.

The Rule takes the system one step from its current state to the next (possible, ergo defined state) step.  If we’ve done everything right, this will be predicable.
If we work with a planetary solar system, (this means all the planets, their sizes and densities, distances, velocities, moons, gravitational constant, etc), it’s pretty complicated.  But we can, and do, predict eclipses and the position of our planets and moons millions of years into the future with excellent accuracy.  Even the Mayans did this 1,400 years ago for eclipses, (hold that thought*).  So this means we can predict at least some parts of the future; we live among predetermined systems, right?
Consider a far simpler CDS, it has only four or five defined parts and only three rules.  The parts are a graph paper like grid (two parts?) and a locator of the  starting point, the initial state.  The rules are:

   Rule 1). Each step in this CDS takes the locator one square forward.
  Rule 2). At a white square, turn 90° right, flip the color of the square, move forward one unit
 Rule 3). At a black square, turn 90° left, flip the color of the square, move forward one unit

This called “Langton’s Ant*.  The ant is the locator that moves one step at a time, following the “rules”.  This can be run on a very simple computer program (OK, the computer is complicated but it is doing a very simple step by step process).
This is much simpler than planets, moons, velocities, orbits, distances and all their interactions as they whizz around our sun.
So when you run it, it should be very predictable, right?  Info in, info out; always the same result…  Nope.  Try, unpredictable for the first few hundred moves then a strange locked in pattern to infinity. 
This simple CDA leads to complex behavior. Three distinct modes of behavior are apparent.
Simplicity.  During the first few hundred moves it creates very simple patterns which are often symmetric.
Chaos.  After a few hundred moves, a big, irregular pattern of black and white squares appears. The ant traces a pseudo-random path until around 10,000 steps.
Emergent order.  Finally the ant starts building a recurrent "highway" pattern of 104 steps that repeats indefinitely.

All finite initial configurations tested eventually converge to the same repetitive pattern.  No one has been able to prove why this is true for all such initial configurations. It is only known that the ant's trajectory is always unbounded regardless of the initial configuration.
Here is a super simple CDS that results in a pattern that no one could predict, and even now that we know what happens, we can’t explain why, we had to run it to see it happen.
 So the debate about the future being determinable from the present is over.  Now do a CDS with 200,000 atoms in three dimensional space…. You know, like a virus.

          *The Mayans could predict the eclipses with great accuracy (at the same time that most Europeans believed the earth to be flat and the center of the Universe).  But before you get too laudatory of the Mayans’ scientific abilities, at the same time that they could do this, they still had religious mythology about jaguars eating the sun.  Their CDS still had outside influences, Gods.


If you’d like to see this in action, go to:  https://en.wikipedia.org/wiki/Langton%27s_ant

Wednesday, August 9, 2017

GRATEFUL DEADHEADING: A GARDENER'S REVELATION Guest post By Chris Bolgiano



Pinch. Snip. Snap. Severed, spent flowers drop into the compost bucket like guillotined heads into a basket. I pretend they are my bad habits, bad temper, bad hair. If only it was so easy.
In the dusk of my life, I’ve arrived at a garden plan that puts my cutting herbs on my deck. Parsley, sage, rosemary and thyme, basil, tarragon and oregano, plus a scattering of spring onions, live in four large planters on coasters and one stationary, soil-filled horse watering trough. Mixed through all the pots are flowers. First come the early season, self-seeding volunteer annuals like violas and little native poppies, then later the verbenas, petunias, calendulas, marigolds and other hummingbird and insect-attracting annuals available every spring from the local greenhouse.
In the twilight of a summer’s day, I go out on my deck to groom the herb garden. I’ve already put in some cool morning hours working the four long beds in the vegetable garden that supplies most of our meals, either fresh, from the root cellar, in the jars I can or the bags I freeze. Growing your own food was basic to the “Back to the Land” movement in the counterculture of the early 1970s, and the husband I were basic back to the landers.
A life lived close to nature offered the only real promise of inner peace in a war-centered world. So we moved from suburbia to the backwoods of rural America. Our generation was going to change the world through flower power and eating low on the food chain -- low as in on your knees cultivating vegetables and those powerful flowers.
Forty-some years later, going “Back to the Land” has taken on a darker meaning. The flower power that once seemed so gentle has revealed itself as the relentless force pushing up daisies in Nature’s perennial garden. For years I’ve called myself an aging hippie, but what looks back at me in the mirror is an aged hippie with liver spots. It’s the “hippie” part that matters, I tell myself: peace, love, and folk rock and roll.
Growing old happens to everyone who lives long enough, although I did think it would take a lot longer than it actually has. No one ever seems quite ready for it, despite its universality. It’s while I’m deadheading on the deck at dusk, in our tiny clearing in the midst of forest, that I muse over old ideals and measure how far I still have to go.
Sometimes it’s hard to tell a flower that’s done from a young unopened bud, and I end up plucking off promises for the future. Sometimes when I go away, the flowers go to seed and even clipping every deadhead doesn’t bring back any blooms.
No matter. I pour time like water onto the plants, moving my fingers tenderly through them, giving and drawing nurture. Every decision I’ve made, every path I’ve chosen, has led me here, to these plants on this deck on this dwindling summer day. Light slowly fades and cool air flows down the mountain. Everything around me is beautiful, perfect, even the dead leaves and withered flowers I pick off the plants, because they are a part of the endless, sacred cycle.
Deadheading has become a ritual of mindful mindlessness. Here is where I realize what I already knew, what I’ve learned from all these decades but could not find through conscious searching. Here is where I contemplate, not just what a long, strange trip it’s been, but how grateful I am to have arrived, even with a bad hip.