Is pool actually just mathematics?
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- Опубликовано: 20 июн 2024
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Huge thanks to Rollie and Jenn. Check out their videos on the diamond system.
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CORRECTIONS
- None yet, let me know if you spot anything!
Filming by Alex Genn-Bash
Editing by Gus Melton
Written and performed by Matt Parker
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
Playing darts in the background out of focus: Bec Hill
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b... Развлечения
remember, these are mathematicians, not physicists.
Correction. They're mathmematicians. See 1:23 and look closely.
correct
@@Anvilshock🙄 Shush, Hock of Anvils.
They should have gotten a physicist for the team
So should they assume perfectly spherical balls still 😂
2 mathematicians enter a bar with a measuring tape...
"Let's use inches!" Says one of them...
@@dj_laundry_list The other stabbed him with a bar stool
I can't believe they measured in inches then scaled in millimeters
@@russellbeaubien7430 And decimal inches while we're at it.
This is more fun than i thought
"The math doesn't make a difference if you don't know how to hit the cue ball."
Genius.
Facile.
He said at one point 80% skill 20% math. That's probably pretty accurate. Math is there but it's a shadow in comparison to the physics.
Yeah, but it's a stochastic process, so you can still use statistics...
As a maths guy who likes to play billard from time to time, that was my first thought.
You can have the perfect idea, but playinga perfectly straight shot is hard af, and the slightest spin will make any plans about bouncing off the walls useless :D
@@asdads3948 absolutely. In ideal conditions with no air, drag, friction or spin, simple geometry might work but in reality, the math involved is very complex.
"There's more air in the room than I assumed." 😆🤣😆
the pre-game banter was A-tier!
Matt's understated but incredible comedy chops really show in this one.
Best line ever
In more ways than one lol
I am 100% going to use this joke mid conversation
As a physicist, if my shot doesn't miss the pocket by 10 pocket lengths, it is pretty accurate and should thus count as a perfect hit.
As an astrophysicist, if the shot keeps the ball in the pub, it's good.
one of the funniest things about physics is that depending on the field, the inaccuracy panic threshold of "either our study or the entire theory needs to go in the bin" could be anywhere from the tenth significant figure to several orders of magnitude
As a cardiologist, If the shot misses by 10 pocket lengths the cue ball is in cardiac arrest and needs immediate response.
@@WestOfEarth the ball remains within orbit of the sun, i see this as a win
As a statistician, so long as half the balls miss to the left and half miss to the right, you're golden 👌
I think you need a bit more janky Python code for this one.
By the time the Python code has given him the position and angle, the place is closing up 💀
@@vlc-cosplayer Do it in Julia, you'll get the result sooner.
Oooo I got you covered! Wrote an incredibly mediocre billiards physics program in college. It's a bit more accurate than their math, but not by much lol.
@@DaTimmeh i'd love to take a look
what about some terrible, terrible python code?
"The table is 100 inches long, so when you divide into 80 segments, each segment is 1 inch."
New unit unlocked: the Parker Inch.
Time stamp or it didn't happen
@16:18, but he said "so that's the number of inches" a bit vaguely about it 100 is the number of inches (which it is) or if the 80 system is the number of inches.
And then Grant says 'hmm' but his expression changes 2 seconds later as he realizes the mistake. 🤣
🤣🤣🤣🤣🤣🤣🤣🤣🤣
Alternative title - "Mathematicians discover how engineers feel when handed drawing plans from architects
My brother's entire career in beam steering systems was converting physicists' abstract theoretical designs through the black art of making it actually work.😊
This required a kind of intuitive, empathic understanding of real-world electrons, photons, and materials. The pool table is probably a pretty good analogy.
Counter - "Engineers discover how Builders laugh when handed plans from an Architect"
@FatGringo Boy, is that the truth. My dad was a builder. Outside of a few, he had little respect for architects. At that time, architects were not required to take any structural engineering classes. And most didn't. A few schools, such as Cal Poly in San Luis Obispo California, did require structural engineering, and graduation requirements included actually building a small building.
One example - a home my dad was building had a cantilever deck. But the architect forgot that a cantilever requires so.ething to hold down the other end. Well on the way to building the house, they had to stop construction, wait for new plans, tear out significant work, and rebuild.
Pool Players: “They’ll never get it because they’re measuring based on the walls and not the diamonds.”
Mathematicians: “Jokes on you, we’re pretending that we’re playing in a hall of mirrors!”
Jokes on you, we just constructed a ghost universe
As one of those novel individuals that's good at both pool and math, I've long known the diamonds just made no sense at all, and to me, are nearly useless. I do use them as I can, but only as a vague guide or reference to compare to other points of reference, they don't help in determining how to actually shoot the shot. Even as stated in the video, the add-to-80 rule is only a rough guide, so it really does just all come down to practice and feel.
@@kindlinthe real question now is: can we come up with a better system for guiding marks than those diamonds?
@@engywuck85 I think the better question is: do we need to? Snooker tables don't have diamonds. If anything, we should be making things harder for the players.
Jokes on the mathematicians in this case, because they still can't play well at all and no amount of inventing theoretical universes and nonsense will change that. Pool is pure feel and tactile skill.
the scene of a pair of mathematicians breaking out the notes and measuring tape in the middle of a pool game is something straight out of a comedic skit
So many spherical, weightless cows in a vacuum.
Just a minor rounding error
I was going to say that they should probably assume a spherical pool table.
I was waiting for someone to bring up the spherical cows
@Sandeepan They have to be frictionless too. And with no momentum.
Cows.
Such wonderful physical ideals.
@@VarksterableAnd on a frictionless field!
"there's more air in the room then I assumed" Matt Parker, 2024
than*
possibly *error, not air, too.
nope it's "air"
Sorry guys, not my native language
@@nikitafilippetti7504 may or may not be my native language either, so …
3:18 i love how Grant expected that exact reaction from Matt to the use of inches that he had is face ready for the comeback
and with how he just nods when the reaction actually comes, you can basically hear him thinking "mmh yes all according to plan"
My guy preloaded his face 😂
Grant's clearly watched Matt's video on imperial units.
"You're such an imperialist", said the man using imperial units.
@@HanabiraKage He's a mathematician. He knows how impractical imperial units are.
"These guys have been failing up for their whole lives, I don't want that to happen at this table'' -- Man who affixes all mics with blue tape
"My brain REFUSES to look at the inches"
My brain refuses to accept the existence of- uhh... What were we talking about?
Weeping Angels are in the chat.
Don't tell anyone 🤫
...but modern US inches are defined using the metric system.
As soon as Grant started measuring in inches I immediately switched allegiances to the pros, a travesty of practical calculation.
Lmao same here, also the Pros use a zero based index system for counting diamonds, pretty sure Matt felt out mathematiciaed there for a second
Yeah, you should clearly measure in table-lengths.
As an American, you really should use centimeters for any physics calculations
@@Asiago9There's only one country in the whole of America who doesn't.
@@rmsgrey good idea! We could even do centitable lengths! ;)
obviously math can account for every possible thing... friction, humidity, air drag, etc etc... it's just a matter of building all these factors into the simulation
I would LOVE a part two where you over-engineer a simulation program running on a laptop and try to beat them using THAT !!!!!!!!!!
Well a laptop is probably too small to fit the balls on
They might need someone like Mark Rober in on that
stuff made here breathing intensely
That reminds me of the Stuff Made Here channel. He built an automatic pool stick that accounts to all that, you just aim and let it do the magic.
Just mathing it out is not enough, as the software telling you to hit a 23.5 degrees at 34.33N giving it a spin of 14.2RPM clockwise will hardly translate into you actually hitting the ball with those parameters... You need a robot.
@@Kleyguerth You need a robot? There are only three parameters involved in executing the shot. Angle, position of the cue striking the ball, and force applied. The last one is a bit tricky, but with practice you could use perceived effort and muscle memory.
What a great way to show the difference between theory and application. Jenn was super patient and cool about everything, she's a great communicator. Rollie was there too!
Clearly the model wasn't accurate enough.
If your model is bad, even a perfect calculation won't get you to the goal.
A good model delivering only an approximate solution is often more desirable because you at least get what you calculated
Glorious. "Jenn was cool and good at teaching. Also, there was Rollie."
Rollie is there for the lols, drinking his coffee in a bar
the guy was so annoying
@@emperortgp2424 He made one decent joke ("the table is way larger than 10cm"). For the rest of the video he was just kind of there.
Matt: "is there friction?"
Me: "You leave physics out of my maths, mister!"
Friction from the cloth is such a huge variable in billiards, like it makes an enormous difference in table playability lol
@@0Caracalla stop justifying a mathematician thinking about physics!!!
😛
friction is maths but you want to be proud of your ignorance it seems.
Reminds me of the time in high school where I proclaimed, "I CAN SEE GEOMETRY," and proceeded to totally whiff my pool shot. My friend was dying with laughter 😂
@12:00 you completely misunderstood what Jenn was telling you. In the animation the spin you gave the ball is reverse spin, it's working against the natural way the ball wants to spin off the rail. Jenn tells you to give running spin (in this case left spin). Recall that in your first attempt the ball went to the right of the 8 ball (from the POV of the balls movement). This is because you hit too far to the left on the second rail. Using reverse spin makes the cue ball rebound at a greater angle than incident which makes it move even further left before it hits the rail, missing by an even larger margin. Instead, you should have used running/left spin so that it rebounds at a lesser angle, rebounding to the second rail further to the right, and putting you more on track to the 8 ball.
Yeah I also noticed the wrong spin haha
Exactly. It was almost the opposite.
"100.4 inches"
Wow, you upset both metric AND imperial users in one phrase. That's next level!
Yeah, was that really a tape measure with markings in tenths of an inch? Or was Grant approximating to 100⅜" in his head?
I was wondering why Matt didn't ask whether it is 100 4/8 or actually 100.4, instead of talking about metric vs imperial.
OK WHEN DID GRANT GET MUSCLES 3blue1built
This comment actually made me laugh out loud! also his arm veins!?!?
3buff1built
😂
Annimation at 12:08 is incorrect. The cue should be applying left (running) spin on the ball so that the bounce off of the first cushion has a smaller angle of reflection, which then means the impact on the second cushion is closer to the left side of the screen and then the ball, again, has a smaller angle of reflection than incidence and goes towards the pocket. (backed up by viewing the ball at 22:20 and Jenns explantion of "opening the angle" i.e opening the angle between the incident and reflected line)
Huh. This is very interesting because I think it should work both ways. I was confused at 22:20 because I expected what the animation shows, but your explanation makes sense.
On the other hand, if you spin the ball the other way (like in the animation) the ball should stop spinning when it bounces for the first time and wouldn't open the angle on the second bounce, which I think should also work.
@@moonshine7753 if you were to apply the displayed spin, you would actually need to aim further down the screen as it would steepen the angle of reflection, however the spin of the ball would still be reversed after the impact due to friction on the cushion meaning the angle would still open up on the second bounce. But yes, still playable
It will only work with left hand spin, right hand spin will affect the angle of the first bounce making it come longer down the table for the second bounce and it will likely still have spin from the first bounce, the original comment is correct and the only way to make the correction apart from aiming differently.
yes, well said.
Yeh it was wrong. He showed the animation and Jen explained it, the two didn't match up 😅
The first bounce would have come off at a different angle, which was the compensation, not the spin/lack of spin on the second bounce.
"Is there friction?", "I assume not" LMAO🤣
Hi Matt, the animation at 12:08 is wrong. Jen uses running spin, which in this case is left spin - the left spin widens the angle after hitting the first rail, making the ball hit the second rail higher. This compensates for the induced spin, and the cue ball will reach the ideal target point.
Clockwise seen from the top, I presumed. Makes sense.
I was thinking that the ball should ideally contact the cushion rotating as it would if it was "rolling" along it, i.e. no slip condition with the cushion. Then it need not transfer angular momentum into momentum or v.v.
Yeah, the phone footage at 22:03 shows Jenn applying clockwise spin, as opposed to the anti-clockwise spin in the animation.
23:38 - Matt invents raytracing.
as a math student who's obsessed with pool, this crossover makes me so happy :')
Same. They should have included Dr. Dave for a mixed perspective.
It's too bad math hardly helps for actual pool shots, it would be nice if it did. It's also a pet peeve of mine that your average bar denizen will happily tell you otherwise.
Yeah a lot of people think I'm good at pool because I studied math. Couldn't be further from the truth 😂
If you were doing this on a snooker table you’d have to factor in the Higgins Boss particle
I don't get this, but I imagine it's an incredibly clever joke
@@apmcx Alex Higgins was a world champion snooker player back in the day
Now I want to name a boson the Boss Boson
@@snafu2350 Ah, I didn't even notice he spelt Higgs and Boson as Higgins and Boss, I think I literally just read the letters I expected to see and was confused about the joke without ever actually having noticed the joke.
@@apmcxIt's a play on the "Higgs boson" particle and Alex Higgins, the "boss" of snooker.
Should've chosen air hockey, not pool.
can't believe this is how I learn Rollie has a channel about pool
First thought: Can professional pool players do math better by playing pool than math professionals? 😂
We need a chess-boxing like event with maths and pool to really figure it out.
I'm sure some high level pool players possess better geometric and trigonometric intuitions in certain situations. Heck, maybe some calculus intuition too. Having such an inbuilt model of this kind of game would be interesting. Like chess players and certain kinds of pattern recognition.
@@kruksog I think they mostly just hit a million balls and get a sense for it...
I don't think anyone thinks pool is just geometry (any more than basketball), but some people believe it's just geometry and execution (ie hitting the ball straight in the computed direction). And it kind of is, but the way pool players compute the direction is different than you would expect, and the strength and spin matter a lot on every shot that hits two banks. Not everyone knows that.
@@DomenG33KThat's how the overwhelming majority of calculations are done... Train those handy neural networks to produce good enough approximate solutions ;)
12:04 is incorrect. Running side is the opposite. It opens the angle, and therefore will arrive at the same point on the third rail, but coming from a different line of the second rail. Jennifer explained it correct at 13:17
I'm sorry, the concept of doing maths in inches just makes my brain break. If I have to measure anything in inches I just think "meh... that's close enough"
Paused to comment, JENNIFER BARRETTA on your channel?!?!?!
Played pool against a friend (an aeronautical engineer) half a lifetime ago, I was already okay at pool but the maths data dump he put on me regarding angles changed my pool game.
This video excites me and I've not watched it yet, pool, Jennifer Barretta and another maths data dump... triple combo of the finest kind in the early hours no less. Life is good.
“Donald in Mathmagic Land” is when I first learned about math and billiards.
Yes! I loved watching it in school!
Me too, but I never understood what was the "key position". Sadly, after this video I still don't understand that concept too clearly (I have a PhD in mathematics now)
Thank you for mentioning this memory from Elementary School… maybe during a rainy-day recess in the mid-1970s?
As a Math teacher, I still show this at least once a year 😁
Darn, I was going to mention that too.
ruclips.net/video/yuntK56wL7A/видео.html
5:43 genuinely had no idea that air conditioning makes a difference in how pool is played
Felt is very water-absorbent and almost sponge-like in its ability to draw in fluids from its surroundings; if the humidity is high enough (like say in a very wet tropical climate) the density and surface friction of the felt will be different because of the greater water content in the felt itself. This will also have an effect on the compression and rebound of the felt and cushion along the table rail and so alter the way the ball bounces off the rail and how much spin it gains / loses in the bounce. Every pool table has its own feel that an experienced player can pick up on, any two tables in the same environment my be very marginally different, but the same table in two very different environments will also behave differently. Similar to the "run" in golf, how much friction that species of grass has against the ball and how slick the surface is from dew or rain, and so forth, or to the surface quality of an ice sheet in hockey affecting how far and fast the puck travels from the same input.
@@TehFrenchy29 I get that thinking about all these factors matter in pool and in golf, and I know the ice surface matters in hockey but I am not so sure that thinking about this happens as much in hockey. Both pool players and golfers have several seconds to think about these factors, hockey shots are taken in milliseconds. Also, I am not an expert on either pool or golf, but I am pretty sure that body checking is not allowed in these games.
@@DonkeyYotepretty sure both golf and pool would have MUCH higher broadcast ratings if body checking were allowed!
@@DonkeyYote This kind of thing definitely doesn't get considered nearly as much in hockey by the players while they're playing the game, but it is definitely something they do give a small amount of thought to. But the ice in a hockey game is also wholly resurfaced multiple times per game, in a climate-controlled arena, so it will pretty much always be within the same set of parameters and the extremes aren't that far apart. In pool just what time of year you're playing at that table can alter how the table plays, in a game where even very minimal differences can enormously alter how the balls behave on the felt.
@@TehFrenchy29 Thank you for the explanation!
As much as I love Rollie, he really didn't need to be here for this video haha, he just stands in the back silently the whole video
He is very much playing the "mutual friend" role here, being the link that connects the chain from Matt to Jen
Did you miss the scale burn?
@@OhJustSomeRandomGuy Have to admit the scale burn was pretty good. Otherwise he was just kind of there.
I love that it's implied that rollie doesn't have a specific editing style, random eagle and explosion effects just kinda show up in whatever video he's in
I wouldn’t have been shocked if the punchline was that Grant is a pro-level pool player. Because Grant.
As an excellent mathematician and pretty good pool player, my money is on the pool players. Every time.
As a mathematician, I love the collaboration between Matt and Grant.
As a pool player, I love having the pool players here to teach them a lesson.
I it's more interesting that they were both engaging with each other. Jenn teaching them about the tricks they use but still open and curious about how Matt and Grant were thinking and trying it their way
Matt! You got the explanation at 12:05 wrong! They don't add 'check side' (as you've animated - side spin to narrow the angle of reflection) to counteract the imparted spin. They add 'running side' (the opposite), so the angle off the first cushion is widened, causing an earlier second-cushion bounce (i.e., further to the left as we look at your diagram) such that, during this second bounce, the angle of reflection widening due to the running side actually brings the cue ball back on to a line that leads to the target!
When I was a kid, I used to watch this Disney VHS all the time called “Donald in Mathemagic land” (or something very similar), and there was a whole segment about using math for making shots in pool.
Using Let's Play: Bar Billiards as my other data point, see you in 10 years.
Wow I remember that video
extrapolation hasn't let me down so far.
"There's more air in the room than I'd assumed" that actually broke me
I remember watching Rollie's pool videos years ago, then finding his climate town channel and other colab with Matt.
Very sweet to see him playing pool again
Just read the corresponding chapter in "Love Triangles" and am excited that it's actually documented on video! Great stuff!
Grant’s animations are just always out of this world.
It was simply a fantastic video. Significantly better than ever before. When I’ve been in my studies, the very best and most inspiring sessions have been when we’ve had guidance, and several of us have stood by a board discussing and collaborating to solve questions or explore a topic. Where there has still been an adult to steer the conversation or provide help. Somehow, you capture exactly that feeling in your video - a sense of being in that room. Congratulations. Really impressive.
23:30 Oh. I just realized that if you have to bounce off two walls, it's basically a retro-reflector (in 2d) and so that singular point should work for anywhere along that side of the table...
In the vacuum maybe, in a pool table, where balls roll and there are frictions, not even close. For example, the shot angle that they are showing, would be completely different if the cue ball was on the same line, but closer to the rail. If you shoot from a short distance from the rail, the cue ball has not started rolling yet, and it's still flying (not touching the table), so the reaction with the rail is completely different. Math or geometry don't explain that, physics kind of does, years of practice absolutely do.
Can't get enough of Rollie on this channel. Keep the partnership up, two of the best people on youtube!
This is the Math vs Physics pool battle i didn't know always wanted to see. Thanks.
I liked the visual comparison between the add-to-80 method and the radial fan at the end. I wonder if the amount of english that a pro pool player would intuitively know to use would reduce the error between the add-to-80 lines and the purely mathematical ones.
The angle you come into the cushion at will change how much spin the cushion imparts, which changes what the correction from the mathematical approximation needs to be.
I am fairly good at putting the cue ball where I want it to go, but not so good at calculating where that should be. I have a friend who is the opposite. We made a killer team the few times we played.
This was so fascinating! Loved this video! Would love to see more pool maths videos :D
the collab I never expect but very glad to watch.
Should have invited Steve Mould; he has experience with balls picking up spin as they bounce.
"The ball's gonna pick up some spin
Steve Mould: "Hold my Perspex box"
"You're such an imperialist"
said the one using the IMPERIAL system 😂
Inches are the Imperial system. The Americans carried it over from their British background. Long afterwards, the metric system was devised. Most countries adopted it, but the USA still uses the old Imperial system for most measurements. As an aside, the metric system is the informal name for the International System of Units, also named SI units (from its French origins).
Yes. That's why 3B1B calling Matt an imperialist for mocking inches was so funny to me.
I really enjoyed this, thank you to all of you!
Watching two of my favorite math guys working together and seeing their minds bounce off each other is just a joyous sight to see.
This is why elliptical pool tables were invented.
Inches?!?!
love this! unexpected as ever and still amazing
such a pleasure to watch these interactions, I love these moments in life.
There’s an old Disney cartoon, _Donald Duck in Mathmagic Land,_ that has a segment explaining how to use the diamonds on a pool table.
bingo!!
I knew someone was going to make this comment.
I saw it when I was a child and this video also brought it to my mind.
Is that the one where he met Plato and learnt how harmonic scale works?
@@Laurabeck329 Pythagoras, not Plato.
5:18 did he.. fake drinking the coffee?
Yes 😂 Maybe he did it in the "original" shot and liked the aesthetics of it, but something different was off about that shot (like he had a lapse of memory when delivering the story), so they re-did the shot but now his coffee was empty so he faked it. Or he wanted to take a sip out of habit and had forgotten it's already empty. 😁
The edit on this was INCREDIBLE!!!
This was a super fun and interesting video, thanks!
Ahh, mathematically simple function approximations to save time calculating, neat.
Need to add a third group, and bring in stuff made here for the engineers
As a big fan of his channel, seeing multiple comments mentioning stuff made here makes me so happy
This was a really good video for showing the limitations of models. Great work
love Matt and Grant hanging out videos!
"inches" 😭
In a way, the problem you had was that you were assuming an inelastic collision, where the ball just immediately bounces off the surface.
But because the edge compresses a bit and the ball rolls while pressing it, the "elastic" nature of the edge makes the collision act as if the contact point is further back
That effect is small though, millimeter work (or 1/16ths of inches perhaps).
The bigger "problem" is that the contact with the cushion is long enough for friction to impose a no slip condition, whereby angular momentum and momentum are exchanged, resulting in a different angle of reflection.
I really love the Matt and Grant duo! Please more collab videos in the future.
glad to see rollie still playing pool. Missed the updates on the road to the US open!
If you haven't already seen it, you should watch "Automatic pool stick vs. strangers" by Stuff Made Here
I thought of that video when watching this too! Would've been nice to have the path projected on the table like in his video
What next, you two go to Las Vegas?
In Las Vegas, a mathematician would only play Blackjack. For everything else, the math says they'll lose.
@@LaughingOrange I mean yeah they have no way to influence something random
Steven Bridges crossover episode???
@@LaughingOrange if you play long enough, then yes, you'll definitely lose. But you may also get lucky on your first few turns, so it's reasonable to try at least once. Is there a model to calculate the ideal amount of tries to minimize losses, while maximizing your chances of winning?
@@vlc-cosplayer "Is there a model.....maximizing your chances of winning?" Yeah, minimum number of bets. Each bet 'pays' some to the house so multiple bets compounds the house payment. If you're gonna go to a casino with, say, $100, then just put all $100 on something. If you lose, you were gonna eventually lose anyway because of house advantage. If you win, take it and leave the casino.
The trouble with that strategy is your very short time in the casino. Nobody wants to walk out after only 5 minutes and 1 bet. So nobody does it that way and the casino owners get richer.
That's really interesting! Great video!
This is such a good idea for a video
1:23 Nice typo, mister mathmematician.
I mean, are they not math-meme-aticians?
Who said it is a typo?
🎶MathMem, MathMem, MathMem Mem Mem.
@@jonathanrichards593 "Ohhhh, it's a python"
Aiming through the diamonds compensates for the cushion, is what I have always been told.
It probably just happens to be (or was designed to be) accurate enough for people who are starting, and then you learn to compensate anyway.
The diamond is a different distance from the table depending on the angle. The shortest distance being 90 degrees to the wall, and the greatest distance being along the wall. This variable change is what makes the difference when aiming because you are adjusting your aim according to the angle.
Rollie, Grant, and Matt in one video is the summer solstice present I didn't know I needed.
This was a very insightful video!
the calculations required to predict the ball's motion must surely be a solved problem, via some complex system of equations, lest computer simulated pool games wouldn't be possible.
They do, but there's three issues. One is that there is no exact analytic solution is known for the general equations of motion, so physics simulations use numerical methods instead, which introduces error. In addition, any real computer can only calculate to a finite degree of precision. Finally, physical systems are often extremely sensitive to their initial conditions, so getting one measurement even a tiny bit off can have an enormous "butterfly effect". These combined sources of error mean that if you set up a physical experiment and run an equivalent physics simulation, they'll only stay in sync for a few seconds at best before the accumulated error causes them to drift wildly apart. The upshot of this is that while it's possible to simulate physics well enough to get useful insight into how a system behaves, it's next to impossible to make predictions about how a specific, real system will evolve. This is especially true if you were making the calculations by hand, as you would have to toss out even more precision just to get an answer in a reasonable amount of time.
You would need to model the elastic deformation of the cushion, plus the friction forces associated with it. That sounds like a PhD's worth. If the effect of humidity needs to be accounted for even, a whole tenure. There sure will be approximations derived from empirical observations, but I would not call it "solved" then.
"Well approximated"?
@@landsgevaer not really PhD's worth. All I need is some coffee, my batchmates, a few months and motivation and I probably can come up with some model that *MIGHT* end up working. I hold a bachelors in Mechanical Engineering.
@@RealJackBolt Engineers don't solve. They approximate. 😋
I would bet that a fair amount of simulated pool games just treat the ball as a point so they don't have to even worry about spin.
More complex ones might take more into account, but they're almost certainly using approximations.
Inches????😂😂😂
Cool video. Real insight in how to play pool. Fun, looks like you all had some ~.
I love this, Jenn has such deep knowledge of the game, it's very interesting to hear these things explained by a pro
11:46 - for a moment there I was genuinely expecting you to complement "angle of incidence" with "angle of outcidence"...
Since you didn't, I'm now officially disappointed.
In the diagram at 24:00, I notice that the phantom tables are all lined up based on the positions of the *cushions*.
What happens if you instead use slightly larger tables that are the size of the region within the *diamonds* , and align them so that the positions of the *diamonds* match? How does that affect the convergence of the lines on that target pocket?
That changes the point where we would expect the diamond-lines to converge (if they were a perfect approximation), but not the fact that they are not really converging at all. Look at the mirror-mirror-pocket top-left and notice that with the slightly larger table it would be just a bit further outwards, with the yellow lines unchanged.
Also, assuming that the scale in that diagram is roughly correct, we can see that the error of different table sizes is not too big compared to the diamon-approximation itself (and small compared to the non-ideal bounce and spin anyways).
great collab, cool maths, nice vibes, 10/10
Amazing episode! Thanks
matt has a real parker square of a team ;p
funny
@6:12 "Your such an Imperialist!"
Surely "Your such a metricist!"
(And don't call me Shirley!!)
Surely, "you're".
Surely, empiricist
@@Anvilshock Yep.
@@timbeaton5045 Wow, you already edited your OP and you still got it wrong, and twice no less … do you want to look like the perfect representative of your educational system that desperately?
@@Anvilshock personally i couldn't care less. i am a terrible typist, and fix typos when i can be bothered. Sorry to have caused so much upset for you, but there you go. i guess I must be a terrible person.
This is awesome! Thanks
12:09 actually, they give it the opposite spin in this case! Running spin is spin in the direction that the ball is hitting the rail, and check spin is opposite the direction the ball is hitting the rail (which is what the animation shows in this case)
Essentially any time a ball hits the rail with spin, it’s going to change the angle that the ball comes off the rail. Running spin will make the angle slightly larger than a perfect reflection, and check spin would make the angle slightly smaller than a perfect reflection
In the animation shown, the friction between the ball with check spin and the cushion would actually change that first angle to be slightly smaller, meaning it would land even further down that second rail and miss the ball by even more!
What Jen suggests in this case is actually to use running spin, so the angle off the first rail will be larger and therefore hit higher up on the second rail. There’s a little more physics that goes into how spin wears off over time, but generally running spin will last longer than check spin because not as much energy is transferred for each bounce. So in this case there would still be some spin when the cue ball hits the second rail, increasing the angle again and taking the cue ball on line to hit the 8 ball :)
Here he comes, the crush of all youtube math, Grant himself
AYYYYYYYY
Always fun to watch theory and application collide.
Enjoyed it, thank you.