> here's where i am but you're just going to tell me i'm wrong without > letting me understand it. you don't like my interest in finding what's > possible > > # the collision point is the earliest intersection of > the swept-sphere paths the two spheres travel on > # selfdot(pos1+vel1*t) = rsquared > # selfdot(pos2+vel2*t) = rsquared > # selfdot(touchpt - (pos1 + vel1*t)) = rsquared > # selfdot(touchpt - (pos2 + vel2*t)) = rsquared > # simpler is to compare their distances to the sum of > their radii (inhibition forced us to look up on the internet >( ) > # selfdot(pos1 + vel1*t, pos2 + vel2*t) = 4rsquared > # even simpler is to consider one the reference frame > for the other > # selfdot(pos12+vel12*t) = 4rsquared > # sum(pos12)**2 + sum(pos12*vel12)*t + sum(vel12)**2*t > # it's a quadratic equation where A = sum(vel12)**2, B > = sum(pos12*vel12), and C = sum(pos12) > # the quadratic equation is (-B +- sqrt(B^2-4AC))/(2A) > # so it's immediately rational from A, meanwhile you'd > need B^2-4AC to be a square number or a rational of square numbers
i'm starting to understand myself around it a little it looks like it's not reasonable to make B^2-4AC a square number, and very hard to make it a rational of square numbers in a way that doesn't cause precision explosion and that's really similar to something being impossible, and contains a space where it's possible that it's impossible and impossibility is a huge projected/introjected inhibition i have, associated with hopelessness and worthlessness and suicide and harm to my loved ones and stuff so i try not to develop concepts of impossibility. it's been quite nice to have reversed that
of course what slave boss says is that it's impossible for me to succeed at anything at all, roughly
which is different from mathematical impossibility, it's more value and perspective oriented. it seems much stronger really!
are there logical impossibilities? _yes_, _if we allow for sufficient constraints_, especialyl constraints that expand as holes in meaning are engaged so as to defend the existence of impossibility
for example among the set of [1,2] it is impossible to find a 3 _if_ you consider the definition of that set to be one that specifically never contains a 3, such that - situations where 3 == 1 or 3 == 2 are excluded - meanings of set that have other members than those listed are excluded - addition is excluded from routes for "find"ing etc etc
so we could find integers and rationals that satisfy this
[[[but most of the easy to find approaches for this leave the intended domain
we can include that intention in a question for truth value here, i'm trying to make the behaviors of the components of the system and its overall result are precisely correct.
given this goal, appropriate options can open. a more realistic approach than exact integers or rationals for every component with exact elastic collisions of spheres, would be to figure out what numerical precision is necessary to preserve all the properties of the system. ... dropped a concept ... but alternatively other fudges of the system (spheres and elasticness) could change to provide for an exact representation
so although i could use discrete position advancing and skip timesteps without integer solutions, this would not only provide for no workable timesteps but also avoid a precisely correct solution if it let particles pass over each other
similarly if you are asking "how many siblings do i have" the intent is to figure out if they are all there (none dead, any new births would be of note), figure out how many places to set at a table, plan how many thank you cards to purchase, etc etc
some of these change! for example if a sibling marries, you may need an extra thank you card and an extra table setting.
but we're talking about an intended, kind of the mode of the available scenarios, concerning the meaning. this is hard to formalize but is what people actually mean.
i think it's not the approach but it is hard because there is a tiny part inside my considering that repeatedly expresses worthlessness-judging of me when i consider it, and then this negativity is used to stimulate amnesia and cognitive disruption, around parts in succession pattern of ... somebody being seen as having a negative quality as being a reason to harm them further. very cognitively harmful. genocidal feedback loop, kind of an amplification of general arbitrary social injustices (people have less so succeed less and then gain less in comparison to those with more)