How to drive part 2: Car turning ramp radius

I used to think that when going around one of those curvy ramps I should stay on the outside. My reasoning was that the turn would be less sharp, and there would be less centrifugal force so I could still go fast without flipping over. However, I always wondered why turns felt smoother and better whenever I made really tight turns instead of wide turns.

After quick physics reasoning and a recall of a high school formula it becomes obvious that when turning one should stay on the INSIDE.

Centripetal force = (v^2) / r

Circle circumference = pi*2*r

velocity = distance / time

We are judging the viability of bigger vs smaller radius given that we complete a ramp/turn in the same amount of time. For example, if I go around the ramp choosing a wide turn in 20 seconds, vs going around the ramp choosing a tight turn in 20 seconds, which one puts less force on my car?

The tight turn has a smaller r, but also a smaller v. We know that as the r decreases, the v will decrease in a way linearly proportional to r because circumference is linearly proportional to radius, and velocity is linearly proportional to distance (given the same amount of time). But now as you can see from the top equation the v is SQUAREDLY proportional to my centripetal force whereas the r is only linearly proprtional to my centripetal force. Therefore even though the v and the r will decrease at the same rate as the circle gets tighter, that also means that the overall centripetal force is DECREASING as the circle gets tighter (because the v decreasing has a greater effect on the force's value than the r decreasing).

Therefore if you want to get somewhere quickly without flipping over your car the best way is to make a tight turn. Even though you can't go as fast on the turn, the smaller distance you have to cover more than makes up for it. If you take the same amount of time in boths situations, a tighter circle will put less force on your car. Similarly, if you keep constant the amount of force you put on your car in both situations, a tighter turn will be completed sooner.

If this proof is not well-written or needs clarification please let me know.

Dementor raped by Whomping Willow (literally!)

In the following dream a dementor is literally raped by a Whomping Willow tree.

I'm at some sort of LAN party and people are playing a free-for-all first-person shooter. So I get on my computer and connect into the game.

Suddenly I am walking through some dark scenery, with building rubble and leafless trees around me. It is more like real life than a game. A guy sprays a volley of bullets at me from out of nowhere, so I retreat through the opening a large half-destroyed stone building, while throwing 3-4 grenades in my wake to discouage pursuit.

As I walk over the rubble/rocks of this half-destroyed building I realize there are dementors flying around, circling the building. I realize that this end of the "map" is highly dangerous and that's why everyone is actually choosing to fight on the other side of the map, where there are Whomping Willows (it turns out that dementors are afraid of Whomping Willows). Since I'd rather die in a gunfight than I my life sucked out by a dementor, I start making my way back to where I came from while detonating some "dementor grenades" on myself along the way (they only affect dementors). The dementors are trying to get to me, but they are repelled each time I detonate a dementor grenade.

Finally I make it back to safety and stand under a protective Whomping Willow. Alas, they are not designed to last forever, and after being pulled by a dementor, the tree begins to drift off into the air as if in a zero-gravity environment! Fortunately there is another, bigger Whomping Willow nearby. So I go stand under that one. One ambitious dementor tries to dislodge this tree as well, but fails miserably. The tree secures its branches around the dementor and reels it in.

All of a sudden the dementor has inexplicably transformed into an orange dinosaur/giraffe and the Whomping Willow was raping it doggy style. This comforted me because it meant the dementor would be unable to attack us. Then I woke up.

The end. Please feel free to add your own Freudian analyses.

Extremely important potentially world-changing idea: Judo/BJJ Machine Learning

Anyone who has followed MMA or Brazilian Jiu-Jitsu now knows that often the best combat techniques are not readily apparent -- in fact some are downright ridiculous looking and counterintuitive. A good example that comes to mind is "inverted guard". It involves raising your legs over your head as if you were trying to suck your own dick and somehow using that to your advantage against your opponent. I had it done to me at a gym recently and it completely boggled my mind how easy it was for him to put me in the rear naked choke from that initially awkward position.

Then for some reason my mind wandered to computers and their abilities in human games. We know that Brazilian Jiu-Jitsu is a special martial art in that it is extremely analagous to chess (no really, I'm not trying to sound flowery; this is a well-documented and true analogy, as people who do both BJJ and chess will understand). We also know that COMPUTERS CAN BEAT HUMANS AT CHESS.

So I was wondering "maybe we can invent a robot with same weight and strength and test its intellect against the BJJ champion". But that's too difficult b/c of the material required. So then I thought, "what are the uses for keeping it all software, no hardware?" A simulation, of course!

Now the question is: How much more "weird shit" is there to discover? Maybe martial arts and MMA have evolved long enough for humans to basically discovered most of the best techniques to use -- triangle, kimura, armbar, etc. Then again, maybe not (inverted guard is probably rather recent)! So in order to discover these new techniques, should we just roll around and discover them ourselves? Should we let the masters discover it and have it trickle down to us? OR, the third option: by MACHING LEARNING.

This is what I propose:

1. Program in the physics, kinematics, rules of the game, and the human body as accurately as possible, down to joints at least as small as the wrist. This is probably the hardest part, and we will have to tweak it until it looks like real humanoid BJJ/Judo.

2. Create a "starting" artificial intelligence agent. This agent should have a lot of pre-programmed techniques (all known techniques) and should preferrably already be as good as a black belt in BJJ/Judo.

3. The game is basically the agents running "minimax" algorithm on each other to see what is the most likely way to "finish/checkmate" (submit) the opponent.

4. Run a ton of games, 1on1, with varying weights, reaches, and reaction times, and use GENETIC ALGORITHMS to select only the most intelligent players

5. Run it for a very long time, tweaking if necessary

6. Observe the playing style of the finished product and see if it is different from regular human black belt players!