the swinging bag and the leg

Earlier this week, I was walking home from a particularly late night in the office.

I carry my lunch box in a reusable fabric bag of some sort (unfortunately I cannot be more particular because it lacks labels and my ability to identify fabrics is in its infancy at the very least, if it even nascent).

It was an almost chilly night, the epitome of an Autumn night.ⁱ As such I had my hands in my pockets, with my right wrist through the baggage handles. Gravity being what it is,ⁱⁱ the bag lay against my leg.

It is a 20-25 minute walk from campus to my house. It gives a man time to think. Time to notice things. On this occasion, what I first noticed and then thought on was how the lunch box in the bag bounced and pendulummed about my swinging leg.

Starting from closeⁱⁱⁱ to the same point- I paused in my walk to confirm this- the bag had two distinct periodic motions.

1. The centre of a long side of the box bag touched my advancing shin and the box-bag system was rotated clockwise and swung back to catch the shin as it was going back, so that it could be pushed out once more clockwise and repeat the motion.
2. A point near the front end of a long side of the box touched my shin imparting more angular velocity clockwise than observed in 1, such that the bag swung greater than 90 degrees in the time it took for my swinging leg to repeat its cycle. The rear most narrow face of the box-bag system touched my shin and was pushed outwards again, continuing the pattern.

I found that for any set of mode 1 or 2, it repeated anywhere from 1-30 times before switching to the other motion. Every now and again, the very corner of the box would catch instead of either side.^iv If that is included, then we have a scenario where three reasonably stable periods are possible. [I'll pause for those amongst my ones and ones of readers that has/have read books on Chaos theory, and are aware that period three means that any period is possible and the system can tend to unpredictable behaviour.]

I decided to see what happened when I walked faster. I kept to walked as a change in motion to trot, canter or gallop- heh! I can use the terminology, we all move the same [read section 2.2]- would have changed the basic dynamic of the system.

Of course the box-bag went nuts. For a finish, I had to unwind it.

I mused whether or not my mathematics was up to modelling the system, but the level of interplay between above the knee and below the ankle for locomotion distracted me.^v

My wonder at the chaotic nature of a bag and my leg was shortlived.^vi I recalled that technicians, scientists, engineers, farmers, and people across the world battle to make things predictable and regular- Buses, clocks, electricity supply, wireless data transmission, the pressure in a pocket filter [it took far too long to get sorted], our nap times, car engines, lunchtimes, meetings, women, crops and the stockmarket. Chaotic behaviour is the norm.

In the course of a stroll:

• I marvelled at a scientific principle (from similar initial conditions can come manifold different results), like unto Gary Oldman's Rosencrantz
• I suffered ennui for seeing the thing as trivial, akin Tim Roth's Rosencrantz.^vii

Now. It is well passed my bed time, I was close to nodding off for a while, but I powered through the get these thoughts out to my devoted reader(s) (called Martians).

ⁱUsually Ireland is too busy going from bad to worse to honour the seasons but as I always say: "Even a stopped clock is right twice a day."¹

ⁱⁱMuch like the world existed only in grayscale before the advent of colour photography, we bobbed blithely along minding our own business until a certain I. Newto- that is too obvious... Let's call him Isaac N. invented gravity so that he could steal apples from Farmer Maggot's field with Frodo and Samwise without getting twigs in his eyes or leaves in his hair.

ⁱⁱⁱClose only counts in horseshoes and handgrenades

^ivSimilar to, but far more likely than a coin landing on its edge instead of heads or tails.

^vSome interesting links about walking: in a qualitative sense; why we walk and run as we do; Bishop et al talk of prowling Felis Catus; Usain Bolt's Froude Number has to be over 5; This guy really seems to know his stuff when it comes to 100m sprints

^viawwwwww :'(

^viiOr was it Guildenstern...<sup>2

1</sup>I hoped to link to a previous post where I said it for the first time, it seems I have not said it before. I am disappointed in my past self and am relieved for his and my sakes that there is an unfordable temporal gulf between us [shakes his fist in the direction of the past]

²I like to seem intelligent, well read and cultured, there's no telling who is watching; That is one thing Sir Digby Chicken Ceaser has taught me.