I had a dream about a year ago. At the time, I was wholly enamored of the block-and-tackle; a system of pulleys which affords us an ease of lifting directly proportional to the amount of excess rope you are willing to pull. In other words, it allows you to lift a 10 pound weight 1 foot by attaching a 5 pound weight at the other end which will be lowered 2 feet. We attribute its invention to Archimedes. I and others like to think of him as the father of engineering.
In my dream, I was pulling myself up a rock face. My rigging, naturally, employed a block-and-tackle. In addition, I had a spotter at the top who, on my command, would add another pulley to the system lessening my strain. Of course, for every ounce of exertion I conserved, I had to exhaust an equally large length of rope to get me to the top. Physics is so amusing. Energy is always conserved. There is no free lunch. I don’t remember how many pulleys were involved in my ascent by the time I woke up but I know for sure I hadn’t yet reached the summit. I had arrived however, at a conclusion that still makes me smile.
Phycisists, it seems, are fond of ignoring certain variables for the sake of exposing and isolating others. In the case of the block-and-tackle, one would want to ignore the effects of the friction on the axle of the pulley. In reality, it would take a little more than 5 lbs to lift the 10 lb weight because some energy would be lost to friction. Or to put it another way, the 10 lb weight would rise a little less than 1 foot and the 5 lb weight would drop a little less than 2.
But I can still dream as the phycisist can pretend temporarily that friction doesn’t exist. And so, upon waking, I imagined what it would mean to hoist yourself up with infinite, frictionless pulleys arranged as necessary. Ha. So your muscles would feel absolutely no fatigue but pulling an infinite length of rope would get you absolutely nowhere. Slack forever. So that’s how infinity and zero know eachother.
Now back to reality. Time to get up and start the morning ritual. Make some coffee before considering anything else. Mmmmmm. Tasty. Now consider infinite pulleys subject to friction as per reality. Ha. So you could pull infinitely hard but wouldn’t be able to budge the rope a hair? The opposite of slack. That’s hysterical to me.
To sum up. you cannot pull yourself up by your bootstraps. Even with a frictionless pulley, you’re still responsible for some energy if you intend to get anywhere.
Last night I opened yet another transcendental Pandora’s box not realizing the irony of the fact that, being 2 o’clock in the morning it was officially Pi day. I have this rather unpractical habit you see of trying to resolve ancient mathematical paradoxes in a single evening. It’s ambitious, while largely unproductive yet educational and entertaining all the same.
While driving home I thought it quite unsatisfactory that the year has a fractional number of days in it and so resolved to look at the numbers and see if anything could be done about dismissing leap years, normalizing the length of the months and things of this nature . My apologies to Kepler, Galileo and the mathematical community in general for assuming this would be within my capabilities.
Half an hour after I got home I found myself entering data in the excel spreadsheet I’d created to compile all the many categories of numbers I found. Our understanding of our position in the universe, of course, is a relative one and so even the question ‘How long is a year’ is a subjective one. Furthermore, none of the lunar months or astronomical years I looked at were divisible by an integer number of days (or even seconds in many cases) and so I found myself once again in transcendental quicksand, with no foreseeable end to the quantity of significant digits that would suffice in pulling me out.
This afternoon I am patting myself on the head thinking ‘nice try killer’. I will have to rank this excursion with the time I tried to calibrate integers such that Pi and Euler’s constant would be whole numbers or the time I tried to reinvent music by splitting the difference between Pythagorean tuning and Equal Temperament. I concede for now. 1 is 1 and Pi is Pi. Regarding musical temperament however, I’ll get back to you.
This performance, as it should, could not be more haunting.
Rumors that Jimi Hendrix and Miles Davis were planning to record together when Jimi passed away in 1970 are not easy to stop thinking about once you consider the idea. Yesterday I was listening to ‘Live Evil’ and thought (ironically), if there were a God, and he were a kind one, he would have let us hear Jimi and Miles play together. Were he a vengeful one I still think he would have chosen to make this one small concession. Today I am thinking, if there is a God, let him show me a sign. Let some recording of these two surface after 40 years. (I’m just kidding. Please don’t let this heresy offend you.)
Can you imagine what Jimi would have done in this group for example?