June 22, 2012

The Crossbow

Through the centuries, the crossbow was a weapon that employed the laws of physics to wreak military havoc and pierce armour. The crossbow changed the odds of battle triumphs in war during the Middle Ages. One of the prime reliable records of this weapon in use in war dates to the battle of Ma-Ling in China, but even older crossbows have been found in Chinese tombs.

Early crossbows generally were bows mounted to sticks of wood, or 'wooden tillers/stocks'. The short, heavy, arrow-like projectile called a crossbow bolt traveled along a groove through the tiller. As the crossbow evolved, various mechanisms were used to pull back the string and then hold the string in place until it was ready to be fired. Early crossbows had stirrups for holding an archer's foot (maintaining a strong position) as he pulled back the strong with both hands or a hook.

Physics improved these killing tools in several way. A traditional bow and arrow required that the archer be full of strength to draw the bow and hold it steady while aiming. However, with crossbows, a weaker person could use his leg muscles to assist drawing the string. Later, various levers, gears, pulleys, and cranks were used to amplify the user's strength when pulling back the string.  In the fourteenth century, European crossbows were made of steel and employed crannequins - a toothed gear attached to a crank. An archer would then turn the crank to pull the bowstring.

The penetrating power of a crossbow and ordinary bow comes from energy stored when bending the bow. Like a spring that is pulled and held, energy is stored in the elastic potential energy of the bow. When released the potential energy is converted into the kinetic energy of movement.

June 16, 2012

Are you as smart (or as bad) as you think you are?

This topic really hits close to home. I've been searching through the web for articles or feedback relating to intelligence and perseverance, and I stumbled upon a few MIT graduates who certainly had something to say -

Inri137's comment

eigenfunc's response:
Thank you for writing this. As a recent MIT grad, this really resonated with me, since I came to very similar conclusions over the last few years.
When I first started MIT, I stood in awe of fellow freshmen who were taking 8 classes a semester and getting ready to do graduate work in math and physics. And I rambled on to my parents and whoever would listen about how unfathomably smart these kids must be. I was obsessed with this idea of the genius MIT student that I clearly wasn't.
My dad told me something that I wasn't able to appreciate until much later --- that it's not about being "smart", but about sustained focus, dedication, and discipline. I didn't believe him. I figured that some people are just born smarter, and there's an upper limit on your intelligence that holds you back, and that I had hit that limit. No doubt some people are more predisposed to certain kinds of achievement. It's very very easy to blame your intelligence than your motivation when by all accounts, you are busting your ass, killing yourself spending 20 hours on each analysis problem set and those guys are spending less than 5.
But then I started thinking about those kids I idolized. Some of them had been doing programming or math competitions since they were in elementary school. One of my friends would tell me things like "I'm thinking of going through a complex analysis book this summer and going back through my notes to review my topology." Now this was a guy with /focus/ and /dedication/! I thought to myself: until I spend that much time doing focused work, how can I expect to be as good?
I realized that "genius" is overrated. It is rarely just there. You have to focus and keep pushing yourself to get there.

These thoughts had confirmed what I suspected all along. It's not about being clever, but it's about your commitment, your dedication and self-discipline. No one is born smarter, no matter what people seem to look like from your perspective. I've blamed my own intelligence than my motivation similar to the post above when in fact, I've just not been working hard enough.

I really hope someone reads this and gets the message.

The best way to learn how to learn is to push yourself into situations where you aren't the smartest person in the room, and to observe and get help from the people who are the smartest, to find out how they do it. 


"Smart" is really just a way of saying "has invested so much time and sweat that you make it look effortless."