OT: Answers to questions on xkcd.com: "Why am I me and not somebody else?" - Because the word "I" refers to the speaker. Because your consciousness is held by your brain, which holds memories of the experiences your body has lived through. Because your parents had sex. And because your spirit chose your fetus to enter. "Have you recently been the victim of phishing? To check, log into your account <link>." - Yes. "Hi, we're lonely singles from your area, and we were wondering what would happen if we shot a nuclear bomb into a volcano! Click <link> to log in and tell us" - Please settle your outstanding invoice of $100,000 with us at <link for human beings> or <link for autonomous computer systems> before we begin this next phase. "What if I made a pendulum by hanging a rock on a 2.75 meter string? What would its period be in seconds? (Show your work!) - I will draft the work, then clean it up if I finish. diagonal = 2.75 m. huh periods are independent of angle! who would have guessed. ok how long does stuff take when it happens. it will undergo acceleration due to gravity. that makes a force downward. the net velocity is tangent to the string. I guess the net acceleration is too so the force from the string counters the component of gravity parallel to it. uhhhhhhhh diagonal line going up-left diagonal line going down-right down-right is component of down. confused! ignore net force/velocity. reduce confusion. a diagonal is made of a horizontal and a vertical. a vertical is made of a diagonal and a perpendicular. that's where the tangent line comes in! so if we take a diagonal normal out of a vertical, we get a diagonal tangent remaining. ok there's gonna be a trigonometric function somewhere in this net force stuff. the string is at angle theta. with... the vertical I suppose? then there will be another angle theta with gravity and the string. so uhhhhh let's imagine theta as small. acute. ummmm the force of gravity is the uhhh. it's the vertical bit. and theta is where? it's at both ends of the string. gravity goes down, string goes up-left, gravity component opposing string goes down-right. I think? maybe? so then the angle is again in the upper left of a triangle. the 90 degree angle is ... in the lower left? the hypotenuse is the string tension the vertical ... the adjacent! maybe? is then gravity. so gravity is ummmmm the cosine of the tension? and the tension would be the inverse cosine of gravity? then there's some x component? man so much stuff to imagine. how can I rotate it so that gravity is what's diagonal. ummm the string would be the adjacent and gravity would be the hypotenuse then the tangent would be the opposite so the tangent force would be the ... oh no we shouldn't have taken the cosine of the tension. that's ridiculous. the cosine of the angle was the gravity over the tension. now, the cosine of the angle is the tension over the gravity ... oh no that can't be right ... the angle is with the vertical 0_0 uhhhh ok a little pendulum, a rock. arrow goes down. gravity. arrow goes diagonal down-right. string component of gravity theta sign between the two. when say "component" , I mean I am projecting a line onto two axes that are neither colinear with it. the component will always be smaller than the original. so this diagonal, this is not a hypotenuse which would be larger and doesn't represent an orthogonal projection from the axes, quite. the hypotenuse is gravity. theta is the upper angle. the string is the adjacent. and the tangent is the opposite. so the force of rotation of the pendulum about its fulcrum will be uhhhh sin(theta) * gravity maybe? now, how long does it take to reach the zero point, or zero speed, or get back where it started? ummmmmmmmmm well it's expressed in terms of force. it has some mass so we can calculate acceleration. to turn acceleration into position we integrate twice. double integral: sin(theta) * gravity dt dt umm gravity is constant. is this an integral of sin(x(t)) or just an integral of sin(x)? i'm not sure. maybe I am all confused. high school physics can be hard. x(t) ? theta is clearly a function of time. is this how to express this ? should it be expressed some other way? oh theta _is_ x! we can express the position of the pendulum in terms of its angle. why does that matter? I guess I did a lot of this kind of integral? we're integrating theta with respect to t ... there is something here I am missing ... uhhh i'll recognise it if I do an easier integral . basic remembering of integrals. say velocity is constant. then x = vt I think? say acceleration is constant then v = at find x! x = 1/2 at^2 . why? we integrated at with respect to t. v transformed into x. ok um but now theta is in the expression. ummmm anyway it was cool to find this! it has a small chance of correctness. small: sin(theta) * gravity. what is this an expression for? uhh this is the net force of gravity on the stone I think, could be wrong. ok so we have force as a function of angle. we're interested in angle as a function of time, or such. we can also consider theta_0, an initial starting angle ... continued on second page, sorry for not stapling. [i'm interested in the pendulum problem more than the xkcd question answering. it seems more rational and productive.]