That won't trace a circular path, though.
At any point on a circular orbit, your acceleration is a constant value. If you're constantly changing both dimensions of that acceleration by the same linear rate, it's going to be taking on different values (because, if you think about it, the net acceleration would trace out a line not a circular arc).
Kill or make extinct some unlikely monsters, like djinns, skeletons, player roles.
http://www.steelypips.org/nethack/extinctionist-faq.html
The method listed for killing as many mail daemons as possible is especially ingenious. Could it be improved through manipulation of monsters?
Bring an item to a ridiculous positive or negative enchantment level.
Solve sokoban in a ridiculously rule-breaking way. Maybe arrange the boulders into letters/smiley faces then cheat your way through?
Can you get engulfed by an air elemental and have it bring you places at high speeds? Would it ever be useful to get an extra movement around?
Ring/amulet devouring fest?
Get some ludicrous number of useful pets, flood a level with them?
Get so much AC that it rolls over and becomes negative?
Get surrounded by (insert big nasties here) and not die?
It's a pity the aim is as fast as possible, else you could have fun with taming/removing the corpses of the riders for good.
Grappling hook! All the cool kids on the block have one. Also magical instruments and royal jelly.
Let's see.
ddF_x starts at 1 and becomes 3, 5, 7 and so on. These are the differences between consecutive squares - e.g. 4 - 1 = 3, 9 - 4 = 5, 16 - 9 = 7...
f is the residual, the amount of un-sqrted distance that is left over. Every time x is incremented by one, it's updated by the new amount of un-sqrted x distance that it has. Similarly, every time y is decremented the amount of un-sqrted distance lost is added to f.
The only thing I can't figure out is why f is set to 1 - radius in particular, but I get the principle.
120 wishes should be plenty, though, especially since you can wish for the maximum possible quantity and enchantment every time and manipulate it to work, plus guaranteed quest artifacts.
Since every game is different, and games are normally considered in terms of psychological impact upon those playing it (or watching it get beaten), I'd try to not find a general solution and instead analyze on a case by case basis.
Do you have any games in mind which are ambiguous?
Pudding farm for death drops and mass polymorph? Or does anything from the 'Summon Nasties' spell have death drops? If you want to be hardcore about it. ;)
Maybe buff the six cardinal stats?
Question: If Bombman can be completely skipped and afterwards reduces some amounts of lag (as you say in the description of gutsman's level), wouldn't it make sense to do it whenever you like, in particular before the level that would benefit most from this effect?
Edit: I watched, I laughed. :D
Chip's Challenge is good - most of the records have been done in real time, but there are a few that require ridiculous levels of luck manipulation that could only be achieved in a TAS.
http://chipschallenge.wikia.com/wiki/Bold_time - fastest achieved time on windows version
http://chipschallenge.wikia.com/wiki/Melinda_time - fastest possible time on windows version
http://chipschallenge.wikia.com/wiki/Lynx - take note of this if you TAS the lynx version! The windows version has many differences in its rules compared to Lynx and thus not all windows solutions will work the same. You can use Tile World to mess around with the lynx and windows versions and get a feel for how they differ.
Also, this is awesome, but only possible on Windows again: http://chipschallenge.wikia.com/wiki/The_most_insane_level_ever! Check out the video solution. :D
nfq should watch one of those science documentaries that goes over the formation of the solar system.
When a human moves on its own will, it's actually because of a particular pattern of neural activity in its brain, which sends the signals to its muscles to move, which tense up through electrochemical reactions, and all these systems exist because of the air and nutrients it takes in and the growth and repairs it does to itself, etc etc. Nothing a human does is uncaused, because its environment 'caused' the human first, and anything it decides to do is a result of a particular pattern of its neural activity, which is a result of what it's experienced, how it's brain grew and formed, etc etc etc. Or would you also say that microscopic organisms responding to their environment are uncaused movers?
An argument over 'what was the first mover' is interesting, but not really scientifically relevant - it's more a question of philosophy. You can scientifically examine the properties of a bar of soap you found in your hotel room without knowing where soap is made from; what caused soap. Similarly, we can figure out how things in our universe work without knowing what makes a universe.
EDIT: Oops, lots of posts while I was waiting.
Also, this thread reminded me about things I learned in high school physics, like how you can determine escape velocity by solving for the velocity that results in a kinetic energy exactly equal to gravitational potential energy (the version with 0 at infinity). Neat!
Good point, but if you can't accept such perfection, how come planets are a perfect distance away from the sun in this gravity based solar system model? If the speed was slightly more, the planets would be thrown out from the solar system and if they were slightly closer they would spiral/fall into the sun (like in your example about the ball).
This actually isn't true. If you take an object in an orbit with no friction and activate its thrusters momentarily it will enter the orbit that passes through the point it thrusted at and is slightly wider/narrower. However, if the thrusting is TOO strong in the outward direction it will become a parabolic or hyperbolic orbit, as it is moving away faster than the thusly weakening gravity will ever be able to grab hold of it. However, before that point, there are many many kinds of elliptical paths an orbiting object can and will orbit.
The only reason why an object that gets too close to a planet crashes is because friction in the atmosphere makes it lose speed, fall more and more vertically and then it hits the planet. If the planet had no atmosphere and no radius, then tightening its orbit would just make it a tighter ellipse - gravity + no acceleration + no friction = a path that follows a conic, which is one of: circle, ellipse, parabola, hyperbola.
