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.