[8:37 AM] omni: are her pistols hitscan?
[8:38 AM] omni: if not you have to consider whether or not the projectile travels fast enough to catch up to his acceleration
[8:39 AM] omni: if sonic travels at 1118 m/s and tracer has an average 0.25 second reaction time, sonic would have traveled 279.5 meters before she even pulls the trigger
[8:40 AM] omni: plus that means for a 100m dash sonic would win before tracer can even shoot him
[11:23 AM] Torb Gay: they are hitscan yes
[12:49 PM] Custard Gas: does sonic ever move that fast in-game though
[12:49 PM] Custard Gas: seems like it would be a sort of unfair comparison otherwise
[12:50 PM] Custard Gas: also doesn't tracer cover a lot more area in a short amount of time in the comic
[12:52 PM] omni: it doesn't matter how fast she is if she has normal human reaction time
[12:52 PM] omni: sonic's max speed is like 2-3x faster than it needs to be in order for him to finish the race before tracer could even fire
[12:53 PM] omni: if she has to unholster and then aim first (presumably that's only fair) then she's even more screwed
[12:54 PM] Custard Gas: it's a hologram
[12:54 PM] omni: I think it's fair to say that hitscan weaponry travels at the speed of light rather than being literally instant but we don't need to take that into account unless the numbers get really close
[12:55 PM] omni: the missing factor here is really sonic's acceleration
[12:55 PM] omni: how quickly does he accelerate to his top speed?
[12:56 PM] omni: if he accelerates too slowly that's the only thing that could really bring him down here
[12:57 PM] omni: the internet seems to say he can accelerate to at least the speed of sound "instantly"
[12:57 PM] omni: if that's the case then he definitely wins before tracer can even react to the start of the race
[12:58 PM] omni: I guess sonic must have a reaction time too though
[12:58 PM] omni: there probably isn't any data on sonic's reaction time online though
[12:59 PM] omni: luckily, I was actually able to find data on the reaction time of a live hedgehog online
[1:00 PM] omni: it's faster than human reaction time by a wide enough margin that he still wins
[1:03 PM] omni: overall I'm going to say in a 100m dash sonic absolutely wins every time
[1:03 PM] omni: if you increase the distance then eventually tracer will have enough time to fire and her projectile will catch up because it's moving at light speed
[1:04 PM] nolodi: i would also consider her accuracy in that situation
[1:04 PM] omni: I think at like 400m she has a chance to start winning at least
[1:04 PM] nolodi: say it takes her 2 seconds to aim and fire, the fastest version of sonic is almost a mile out
[1:04 PM] omni: alright I guess I need to make a graph now
[1:05 PM] omni: I never thought I would be making a graph titled "probability of sonic beating tracer for race distance"
[1:05 PM] nolodi: do we wanna assume that tracer has infinite accuracy or should that be a factor
[1:05 PM] omni: yeah but that factors into the probability specifically rather than whether she can win at all
[1:05 PM] nolodi: tru
[1:05 PM] omni: unless we want to choose a p-value that designates sucess
[1:06 PM] nolodi: yeah that's what im curious about
[1:06 PM] omni: I could make the graph 3D I guess and include accuracy
[1:06 PM] nolodi: cause i feel like that graph would start really low, peak at some distance where tracer has time to react, and then it tails off where sonic gets further and further away over time
[1:06 PM] nolodi: pun not intended
[1:07 PM] omni: actually I think it's going to rapidly increase for tracer as he gets further
[1:07 PM] omni: her projectile is like 200,000 times faster than sonic is
[1:07 PM] omni: so a longer race just gives her more time to aim
[1:07 PM] nolodi: mm
[1:07 PM] omni: although the aim point gets smaller
[1:08 PM] nolodi: im just thinking that at a certain distance a 1 degree difference makes or breaks the shot
[1:08 PM] omni: much less than one degree
[1:08 PM] nolodi: sure
[1:08 PM] omni: actual humans can shoot below 1 MOA with good rifles
[1:08 PM] omni: that would be pretty insane with a pistol though
[1:08 PM] nolodi: im sure there's graphs out there on pistol accuracy vs. distance
[1:09 PM] omni: then again it's a lightspeed laser pistol so it's kind of unique
[1:09 PM] omni: there's no bullet drop or wind
[1:09 PM] omni: don't even need to worry about barrel quality or anything
[1:09 PM] nolodi: yeah
[1:10 PM] omni: if you pretend the gun is perfectly collimated and she has a scope I don't think shooting anything you can see would be a problem
[1:10 PM] omni: if the pistol has any spread she's just screwed though
[1:10 PM] nolodi: yeah
[1:10 PM] nolodi: im just thinking like
[1:10 PM] nolodi: assuming max speed sonic, he's going a mile every 3 seconds
[1:11 PM] Torb Gay: Her pistols don't fire the bullets
[1:11 PM] nolodi: i guess at some point the distance is negligible because she's had enough time to aim?
[1:11 PM] omni: if there's no spread and she has magnification yes
[1:11 PM] omni: I know snipers have successfully killed people from miles away with conventional rifles
[1:11 PM] nolodi: what i mean is like
[1:13 PM] nolodi: there's a point where she's had enough time to aim that sonic is most likely dead
[1:13 PM] nolodi: anything before that, and sonic wins cause she hasnt had enough time to aim
[1:13 PM] nolodi: anything after that doesnt matter cause he's already been shot
[1:14 PM] nolodi: i think that was well established already and im rambling
[1:14 PM] omni: the problem is figuring out how the shot difficulty changes with time and distance
[1:14 PM] nolodi: time and distance can be the same i think
[1:14 PM] nolodi: so it'd be a 2d graph
[1:14 PM] Torb Gay: You're not really factoring in all of the variables though
[1:14 PM] omni: if we assume she has no spread (pretty much required) then we end up having to deal with some unusual aiming problems
[1:14 PM] omni: like the size of the reticle
[1:15 PM] omni: once someone is a certain distance away you would need a reticle thinner than a human hair to aim at them
[1:15 PM] omni: (fun fact the US govt during WWII used human hairs for airplane bombing reticles, they're really strong and thin)
[1:15 PM] omni: she definitely needs a scope since he's going to be miles away when she starts aiming
[1:15 PM] Torb Gay: Tracer can manipulate time so she doesn't really need "time to aim" because she can basically do that instantly
[1:15 PM] nolodi: accuracy would be a factor of two things: how fast is sonic moving relative to the vector from tracer to sonic, and what is the acceptable error in angle to hit sonic from the distance
[1:15 PM] omni: that's not the problem colossal
[1:16 PM] omni: tracer can't do anything until the race starts
[1:16 PM] omni: so she can't stop time until she can react to the start signal
[1:16 PM] Torb Gay: Also her guns don't shoot boolets, so it's unlikely they'd behave like modern guns at all
[1:16 PM] omni: we're already modelling them as firing lightspeed pulses of energy
[1:17 PM] nolodi: modelling for error in angle seems relatively easy but i have no idea how to account for the movement speed
[1:17 PM] omni: well assuming she can aim at the dead center of his position wrt the perspective vanishing point, you could ignore his movement
[1:17 PM] omni: because it would hit him at any distance
[1:17 PM] nolodi: mm
[1:18 PM] nolodi: yeah i was wondering how far apart they are
[1:18 PM] nolodi: or if they're both on the same line
[1:18 PM] omni: if they're on an infinite flat plane and he runs in a straight line his movement can be ignored completely
[1:18 PM] Torb Gay: You're forgetting that Tracer is also a lesbian
[1:19 PM] nolodi: well i mean if they're running on two parallel lines that are some distance apart, or if they're on the same line
[1:19 PM] nolodi: (and if tracer can move over to his line)
[1:19 PM] omni: oh right, they wouldn't be behind each other
[1:20 PM] nolodi: assuming they're on the same line does make this much easier but that's a less fun graph
[1:20 PM] omni: I don't see why she can't move over to his line but yeah if they're parallel it's a harder shot
[1:20 PM] Torb Gay: She could just run alongside him and shoot him
[1:20 PM] omni: no
[1:20 PM] nolodi: eek
[1:20 PM] Torb Gay: Why not
[1:20 PM] omni: by the time she can react at all he's like a mile away
[1:20 PM] nolodi: if we allow her to move then we have to factor in what direction she runs
[1:21 PM] Torb Gay: Forward, I assume
[1:21 PM] nolodi: running towards his line makes the shot easier to line up
[1:21 PM] nolodi: so do you run straight forward to minimize distance, do you run straight sideways to minimize possible error in the shot, or do you run in some vector between?
[1:21 PM] omni: presumably she wants to run directly towards sonic's current position + an offset of the distance light would travel in the time it would take her to catch up to his current position
[1:22 PM] nolodi: theres a way to model this
[1:22 PM] nolodi: some curve
[1:22 PM] omni: that is, she's running towards where the gun would need to be aimed to intersect with his path if she were to shoot right now
[1:22 PM] nolodi: i watched a vsauce video about it
[1:22 PM] omni: kind of like the one ghost in pacman
[1:22 PM] omni: that always heads for the tile in front of you
[1:23 PM] nolodi: https://en.wikipedia.org/wiki/Brachistochrone_curve
[1:23 PM] Torb Gay: What if Sonic turns into Super Sonic
[1:23 PM] omni: also if she contintually heads towards him then her velocity vector will asymptotically apprach the same line he's on
[1:23 PM] Torb Gay: he'd be able to go faster than light, then could dodge Tracer's gunfire
[1:24 PM] omni: no sonic doesn't go faster than light
[1:24 PM] Torb Gay: He does as Super Sonic
[1:24 PM] omni: no
[1:24 PM] omni: no ftl travel
[1:24 PM] Torb Gay: Why not?
[1:24 PM] Torb Gay: Is it not realistic?
[1:24 PM] nolodi: if thats the case then i think the model would just say "if sonic goes super then he wins"
[1:24 PM] omni: yes it's not realistic
[1:24 PM] Torb Gay: Because I don't think a time ghost lesbian racing and murdering a blue hedgehog is very realistic either
[1:25 PM] omni: a fast hedgehog racing a lesbian with a laser gun is still within the realm of physical possibility
[1:25 PM] Torb Gay: two laser guns*
[1:26 PM] Torb Gay: Make sure the duality of her firearms factors into your model
[1:26 PM] omni: I think at the distances she would be firing, she would want to use a telecentric lens for her scope
[1:26 PM] omni: I'm not aware of anything actually using a telecentric lens for a sniper rifle but it seems perfect for this
[1:26 PM] omni: no matter how far away he goes he would still appear the same size
[1:27 PM] Torb Gay: Tracer could also use her ult to kill the sonic
[1:27 PM] omni: he would be too far away before she could
[1:28 PM] Torb Gay: She could catch up
[1:28 PM] omni: no
[1:28 PM] Torb Gay: she can literally send herself forward in time
[1:28 PM] nolodi: here's something we didnt consider: what if sonic doesnt run in a straight line
[1:28 PM] omni: not far enough
[1:28 PM] Torb Gay: In theory she has unlimited speed
[1:28 PM] Torb Gay: what if there are loops in sonic's lane?
[1:28 PM] omni: it wouldn't matter
[1:29 PM] omni: if sonic doesn't run in a straight line he would lose time though
[1:29 PM] Torb Gay: have we considered the direction of the race + planet's rotation?
[1:30 PM] omni: if tracer has a telecentric lens and her gun has no spread, then the instant she can user her time power she'll be able to fire the fatal shot
[1:30 PM] omni: no colossal we already decided this is on an infinite flat plane
[1:30 PM] Torb Gay: if the plane is infinite, where is the finish line?
[1:30 PM] Torb Gay: why would they be racing infinitely?
[1:30 PM] omni: they're not
[1:30 PM] omni: there's a finish line but it's not like the edge of the world
[1:30 PM] omni: although to be fair we have to take the gravitational pull of the plane on the light beam
[1:31 PM] omni: at some distance that would start to matter
[1:34 PM] nolodi: http://i.imgur.com/Fin6Ih6.png i like how the other chatroom i introduced this to is going in a much less scientific direction
[1:34 PM] omni: ugh let's just pretend sonic has zero rings
[1:34 PM] Torb Gay: no that's a good thing to bring up
[1:34 PM] nolodi: is sonic allowed to attack tracer
[1:35 PM] Torb Gay: he could just jump and dash at her
[1:35 PM] omni: I don't see why not but that's harder to quantify
[1:35 PM] Torb Gay: the other discord I introduced it to just said "Tracer" and now they're talking about Superman vs. Goku
[1:45 PM] omni: alright so right now my model is that tracer and sonic stand with the centers of their bodies D feet apart, on two parallel race tracks R feet long, on an infinite massless plane with no air resistance; sonic has an acceleration function A_s(t) defining his acceleration wrt time which can be integrated to obtain his position travelling in a straight line; tracer has reaction time R_t and sonic has reaction time R_s; tracer has acceleration function A_t(t) and follows a path that continually approaches the point ahead of the center of sonic such that a ray travelling at the speed of light towards that point such that the ray and the center of sonic would intersect the point at the same instant; tracer has a spread S in minutes of arc and a repeating fire rate F measured in pulses per second and is assumed to have infinitely precise eyesight aiming with an infinitely thin reticle; the goal is to calculate the probability of success for tracer given these variables, specifically by first finding a function defining her probability of success at a time t and then integrating the timewise success function Q(t) to obtain the overall probability of success Q
[1:46 PM] omni: that's obviously too many variables to put in a 2D graph but most of them like reaction time should be held constant anyway
[1:47 PM] omni: track length and tracer's spread are probably the best two to graph, and then adding time makes it 3D
[1:51 PM] omni: conclusion: tracer forfeits the race and then receives a nobel prize for discovering the world's first infinite massless plane
