The Problem Newton Got Wrong
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- Опубликовано: 25 май 2020
- Isaac Newton was right about everything from gravity to the calculus, but he didn’t quite get it right on dice and probability.
The Newton-Pepys Problem represents Isaac Newton’s only documented foray into probability. Samuel Pepys sent him a letter asking whether it would be more likely to roll one six in 6 dice, two sixes in 12 dice, or three sixes in 18 dice. In terms of computing the answer, we’ve got it pretty easy in the 21st century, whether we do it the long way, whether we apply binomial distribution, or just run a Monte Carlo simulation. To us, it’s a relatively basic problem in probability.
But Newton had to work it all out himself, and as he did that, he missed a few things. He just… didn’t get it totally right even though his numbers were accurate. The real Newton-Pepys Problem is deciding how much that even matters, and the answer gives us insight into the complex relationship between math, numbers, and the realities of human thought.
** SOURCES **
“Diary and Correspondence of Samuel Pepys,” pg. 367: www.google.com/books/edition/...
“Isaac Newton as a Probabilist,” Stephen Stigler, Statistical Science 2006, Vol. 21, No. 3, 400-403: projecteuclid.org/euclid.ss/1...
“John Smith’s Problem,” T. W. Chaundy and J. E. Bullard, The Mathematical Gazette Vol. 44, No. 350 (Dec., 1960), pp. 253-260: www.jstor.org/stable/pdf/3614...
“Newton and Pepys,” Nick Berry / DataGenetics: datagenetics.com/blog/february...
“The Gentle Art of Mathematics,” by Dan Pedoe, pg. 43: www.google.com/books/edition/...
“Probability and Random Processes,” by Venkatarama Krishnan and Kavitha Chandrapg, pg. 33: www.google.com/books/edition/...
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#education #vsauce2 #science
GRAVTY
FALLS
Vsauce2 raycon
IT HAPPENS
Do you believe in gravity?-Enrico Pucci
Can you read this vsauce2?
Newton’s been real quiet since this came out 👀
LMAO
Hmmmm SUSPICIOUS. What’s going on Newton?!
He can’t handle the gravity of this situation.
Bruh
Wait until he drops his diss track
Get it, 'drops'? Alright ill shut up
Did You Know Kevin’s favorite word is “Right”
WRONG!
Just take my freakin’ upvote
Just take my freaking upvote
@Egg YESSIR MAKE ZE TREND
just take my freakin' upvote
Just take my freakin upvote
Kevin: "those are the only 2 outcomes. It happens or it doesnt"
Schrödinger: "I'm about to end this man's whole career"
Schrödinger: It lands on the edge
@@user-zr7su5qi5d It is heads AND tails at the same time until it isn't.
if it isn't the result of what you want, just quote futurama: "They cheated by measuring the result!"
It's land on head tail and edge at the same time
@@user-zr7su5qi5d no game no life?
I still believe I’m right, young sir. An apple fell on my head.
bruh
i dont think you understand the gravity of this
@@merchdraws oh god, the apocalypse is here
Guy ℵ
Wassup newton
The 3 most common words in this video:
-Six
-Dice
-Ye
Why does he use "Ye"? Is this something from old English like "thou" as the informal "you"?
@@photelegy yes
Right?
Wrong!
-The-
@@zuckening885 missed opportunity on saying ye
Michael: Newton is right, or is he?
Kevin: Newton is right, right? *WRONG!*
Very Very Very TRUE !!!
😂😂😂🤣🤣🤣🤣🤣🤣🤣🤣🤣😹😹😹😹😹😹😹😹😹😹😹😹h
Left
@@revellations7741 omg newton politics!!!1!1!1!!1!!!1
more like duck duck goose
well, according to my simulatios (10m sessions)
atleast:
Wins: (6 dices) 66.51808%
Wins: (12 dices) 61.86901%
Wins: (18 dices) 59.72854%
exactly:
Wins: (6 dices) 40.18139%
Wins: (12 dices) 29.60475%
Wins: (18 dices) 24.51239%
That's what I get, too. Here is my Python:
import numpy as np
seed = 0
dice_count = 6
repeat = 100*1000
random_state = np.random.RandomState(seed)
score = np.zeros((3,2))
for i in range(repeat):
six_count = np.zeros((3))
for abc in range(3):
for dice_index in range(dice_count):
if random_state.randint(1,7)==6:
for who in range(abc,3):
six_count[who] += 1
#print("6COUNT",i,six_count)
for who in range(3):
if six_count[who]>=who+1:
score[who,1]+=1
if six_count[who]==who+1:
score[who,0]+=1
print("score",i,score/(i+1))
Hey, you, thank you for investing your time in running these simulations. Was going to do the same here if no one had. Kudus :)
Bore off haha
Exactly n sixes or at least n sixes?
REALLY?
Kevin: “He may’ve been right about gravity...”
Einstein: “Am I a joke to you?”
Nope. It’s gravty, not gravity
@@kyanleong8014 funny?
I was bout to comment same
😆
I mean, you can be right that 2+2 is 4 despite not knowing that addition is a property of a vector space. Newton was right about the force relationships that gravity creates; he just didn't know any of the deeper spacetime processes going on in the creation of that force or how those might create complications at extreme distances or speeds.
I just clicked for my weekly dose of "Right?... WRONG !"
LMAO 😂😂😂😂😂😂😂😂😂
Or did you?
WRONG!
*Hello everyone, this is YOUR daily dose of....*
*Right? WRONG!*
Ha!
Michael can go crazy
Jake can disappear
But only Kevin is here
Yeah what are the other guys up to?
They passed away from the virus
@@myrmatta1 not funny didn't laugh
bottom text
@@underscoredfrisk ok
Kevin: "those are the only 2 outcomes. It happens or it doesnt"
Thats why i have a 50/50 chance of winning the lottery.
And why you only need to tickets to have a 100% chance of winning
For God's sake are you serious? The possible outcomes are, it happens, or it doesn't, it doesn't mean that both cases have the same probability :/
@@srjoker8896 Well he didn't say which lottery
@@srjoker8896 lmao whoooosh
@@srjoker8896 woooooooooooooooooosh
At 6:15 when you say "12 over 1" and write that as a fraction, that's actually not how the formula works. It's actually the combination function, "12 choose 1", or how many ways you can choose 1 object out of twelve, which just happens to also equal 12. It actually has nothing to do with fractions at all, it's just notation to write the numbers on top of each other like that.
Disagreed
If 12 choose 2 = (12! / 10!)/2! = 12*11/2
I think that it makes sense to write 12 choose 1 as 12/1
Still, it's horrible to write is in a vulgarisation video, as it's extremly missleading
@@shadourow-bathory6965 yeah, I think writing the fraction without an explanation can be misleading
confused Unga Bunga
I have no idea what u guys are talking about but im getting close to it in math im omost able to understand u guys
This sounds like a ye problem
The heck is this?
ruclips.net/video/SVWvkZbhgAc/видео.html. No not Ye but thee
Dude this is the first video I am watching from that guy and im fuming. This "ye" and the way he pronounces it pisses me of so hard.
@@xgford94 but why would he say thee tho? He's talking to multiple people so you should be used
I really can't tell if he's going a bit or if he's actually trying to revive the word "ye" this aggressively
Me: *Gets everything except for the answer wrong*
Isaac: “Happens to everyone”
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"Peeps problem isnt hard to figure out until it is"
-Gravty guy
Gave you a like because I read this as he said it
"He seems to have been right about gravity."
Einstein has joined the chat.
Well, he *was* right about gravity.
He just wasn't right about time or space, which happen to make gravity *appear* to behave differently when high speeds are involved.
I might be wrong, but I think that's it.
@@alansmithee419 Newtonian gravity is an okay approximation for the orbits of planets and for things falling on them, but yes, when near-light speeds are involved, things go wacky, which is what Einstein realised.
@@apalsnerg @alan smithee .... Eeeemmm.... Not really. Things REALLY behave different in relativistic gravity than in classical gravity, and in reality they move like in relativistic gravity. The shift of the perihelion of Mercury cannot be explained by classical gravity but it is fully accounted for when you add the relativistic effect of being under a strong gravitational field. Even in a much lower and mundane gravity field, the atomic clocks in GPS satellites (in low Earth orbit) need to be corrected due to them being under a slightly weaker gravitational field compared to their counterparts in Earth.
close enough for architecture and ballistics
Well, Newton's approximations are right up to 7 decimal places from the Roman Empire all the way to Newton's own time. It's not until people did experiments involving fast stuff that Newton's approximations are different than Einstein's equations. The other way to find a large difference is to go near something much heavier than Earth.
"Here's what Newton couldn't quite handle"
... * dies *
@@hashtagnoname3931 ye thy make joke
"If he's so smart, how come he's dead?" Homer Simpson
When you cheat on the test and have to have to put in a random explanation
These are the results I obtained using Pascal's Triangle:
Getting at least:
- One 6 with 6 dice..............66.51020233%
- Two 6s with 12 dice.........61.86673737%
- Three 6s with 18 dice.......59.73456859%
Getting exactly:
- One 6 with 6 dice..............40.1877572%
- Two 6s with 12 dice.........29.60935686%
- Three 6s with 18 dice.......24.5198448%
This matches up nicely with the simulations ran by EnderCrypt (a few comments above you) ;)
Very smart man.
But me no understand maths, 2+2 very hard
I've got the same results using combination, very nice
Isn't probability of getting exactly one 6 in 6 flings supposed to be 0.6651
But it makes the sense the more dices you throw the more chance you have for 6...
Cmon now, he ain't here to defend himself
RandomU5erName ah your profile picture reminds me of the good ol XrpmX13 days
try and fly then
or is he
Every time Kevin says "ye" I like to imagine him and Kanye hanging out solving mathematical puzzles
Yo Newton, I'm really happy for you and Imma let you finish, but Leibniz is the best mathematician of all time.
I’m the only one who noticed that he got 5 “6” after throwing 18 dices? 0.o
Uhh, Timestamp Plz?
...but have you ever played Yahtzee?
@@dragonslayerslayerdragon5077 What does that have to do with it lol?
Must've tried it a lot of times until he succeeded.
@@halfcookedramen 9:00
The real problem is that there was too much ambiguity in the initial problem.
Isn't it because of people forgetting to use the choose function when calculating binomial probability
the only ambiguous part is whether it has to match the amount, or can be above. if it has to match, because of the exponential increase in the amount of cases, b and especially c will have really low probability.
I calculated it both ways, A still has the best chance of accomplishing their goal whether the goal is to roll at least one 6 or exactly 1 six.
I hope if someone has more than 1 six, their answer to "Do you have 1 six?" is "Yes".
So, 1 six means 1 or more sixes. Can't find ambiguity.
Who would have thought my man Newton would be wrong about 'GRAVTY'
YE!!!
flat earthers, but seriously how are they this damn stupid and paranoid?
I mean he kinda was. Newtonian physics don't work with special relativity
@@greengreen110 i think its purely a running joke at this point its gotta be
boyo Sorry to disappoint you but no, they’re serious asf and I ain’t lying
Fun drinking game: every time he says "ye" drink
Oh no.....
No thanks, I chose life.
Especially since it ought to be "thou"...
@@brendaneichler5244 Or thee, depending on case. Well, in modern spelling, at least. Back in ye olde days (actually, before "y"e old days, really), it was spelled with the letter thorn (which only survives today in the Icelandic alphabet). In handwriting, that eventually was written badly enough to come close to the Y form; however, more importantly, it didn't exist in print types imported from the continent, so in various works, it was replaced with the relatively unused Y type (which did exist in German and Dutch alphabets). It also was being replaced by the now common "th", so the Y thing didn't last. Finally, English discarded the singular second person pronoun, replacing it with the (already used in that way) deferential plural form (a differentiation we still keep over here in German, but now using the third instead of second person plural - to be deferential but not quite as deferential - it's complicated, like anything German). The old singular started to fade from active use/common knowledge (even to the point that people start making up new plurals) and archaic spelling/typesetting took on its own life. In this use, however, Y never was a (modern English spelling) "y" type of sound.
For the people curious regarding Newton's explanation and why it was wrong: "Although Newton correctly calculated the odds of each bet, he provided a separate intuitive explanation to Pepys. He imagined that B and C toss their dice in groups of six, and said that A was most favorable because it required a 6 in only one toss, while B and C required a 6 in each of their tosses. This explanation assumes that a group does not produce more than one 6, so it does not actually correspond to the original problem." (from Wikipedia).
I was hoping the video here would go into more detail about why Newton's intuitive explination was wrong. That is go into more of a mathematical explination of the error rather than a verbal error.
Other people: you eat
Me, an intellectual: *YeeT*
m.ruclips.net/video/q6EoRBvdVPQ/видео.html
@@napolpettone 🤣
@@napolpettone *yee....*
Ye’et
Other people: Let's go eat.
Me: Squeet.
Nicely explained. The natural follow-on is *the Birthday Problem* : "How many people should be in a room before there is a 50% chance of them sharing the same birthday?". This amounts to throwing a large handful of 365 sided dice (ignoring leap days and the challenge of constructing such dice). The answer is surprisingly low: 23.
I love how he was explaining how much more difficult it would be for c to roll 3 sixes out of 18 at 6:00 and winds up rolling 4 6’s on camera 😂
the whole video is like;
*"well yes, but no."*
Well yes, but actually no, right? WRONG!
well ye but no
I love how you explain the science and math of it, but then also open up a philosophical question in all your videos...
Why is it that Isaac Newton got the right answer with math, but wrongly explained the rationale with his words?
I've noticed this pattern in other videos you have and it's great
Kevin: probability of finding my marker A 100%!
Michael: or is it?
Actually he said marker😅. But I get the joke.
Did he really find the marker? Is the marker right there in his palm? And what do that mean? Does it have to exist between the confines of his grasp for him to be sure that he found it? What if the marker is a reflection of the real one so our eyes tricked us to think that he really does have it? Well you might argue that he senses its presence its touch but we don't know that. He may have been just pretending to have it while some kind of cgi special effects that edited the marker in there. He may have /found/ the marker but did it really happen? Only because it was video taped then it must be true right? Than I would bet that Thanos is as real as Uranus is a gas mess. And furthermore, did the past really happen? Where does the past exist?
George Orwell in his immortal classic "1984" called that exact same question into trial setting place in the dystopian future of 1949 (the year the book have been released). He argued that the past exists in two places and two places only, human memory and records made by humans. A fascist government can easily alter the former, but surely they can't alter human memory? Well, human memory is as mortal as the ones who wields, and such a weakness can easily be spoiled to wipe it out. As it had been shown to us by our total obleviance about the daily routine and religious life of our early ancestors. Maybe it can't be altered but it can be easily wiped and refilled. Furtunatly our future was far from what George foretold, at least as far as we can tell. And a large part of our history as we tell at subjectively correct.
@@xXDarQXx I came for the memes, I ended up with an existential crisis
Don't you mean kevin?
@@kyllianvanleeuwen8835 Yes, thanks for the catch. I wrote without thinking.
Newton: * gets one problem wrong *
Some guy on the internet some hundred years later: it's free real estate
After hearing lots of “ye”
He: “am I joke to you?”
Are you a memenade viewer
@@lewisho8114 The hell is that? XD
Am I a joke to ye?
Yee
Ye is the (y is þ)
SO TAKE UR HISTORY CLASSES BOI
This comment has eight words in it, right?
WRONG
Or does it?
*Ferociously slams his desk with some random object*
That depends, are we talking about AT LEAST eight words or EXACTLY eight words?
9 because it says wrong
Yes, it Does have 8 words in it technically. (Don’t whoosh me)
"And like Newton said, C is even worse"
Kevin, 7:27 2020
C is a decent programming langauge
Z You mean Csharp?
Or is it?
I actually did the math, and even if you were looking for exactly one 6, for the first set, that's about a 40.19% chance, while exactly 2 with 12 dice is about 26.61%, and exactly 3 sixes with 18 dice, is about a 24.52% chance. My math also matched that of Vsauce2's for the first idea of at least that amount of sixes.
As you yourself showed in the episode about vitamin c and scurvy, I believe it does in fact matter to know how and why something works the way it does... at least sometimes. Who knows if or when the maths behind this problem could be useful?
Nevertheless, everyone's contribution to science is more than welcome and can be the ground for further discussion. So... thanks for letting us watch!
"Probability of finding my marker *100%"*
Whenever I try to find something, that I lost, I usually have a 0% chance of finding it unless I stop looking for it.
Just like my will to live
You again
Ahh yes...The Heisenberg Lost Property Property.
He's here, he's there, he's everywhere! Who you gonna call? Physic Friend "Just Some Guy without a Mustache".
probability of me typing this: 100%
Newton: *gets correct answer but wrong explanation*
The whole world: It's ok we don't mind
Me: *gets correct answer but wrong explanation*
Teacher: You know nothing
/this :(
Love your videos man. Can you do a video on the Unexpected Hanging Paradox sometime soon?
That ending speech resonated hard with me as a game maker xD
Cool video, thanks :)
Love your videos man! Keep it up! Your enthusiasm and easy explanation keeps me coming back
9:40 has worst odds, gets at least 4 on first fling XD
They're all still above 50% chance of happening
"The important thing is someone needs to get complicated about getting simple to prevent seemingly simple things from getting suddenly complicated. Which makes things simpler for us so that we can move on to things that are more complicated" Is such a profound quote. It applies to the process of science, maths, and broader fields such as engineering or even just the modern society and division of labour.
This reminds me of a physics test I held in university. There was one question to determine what distance will an object travel after some seconds, or something like that.
I used the x = x0 + v0t + a(t^2)/2 formula and got something like 34 m. But the test didn't have 34 as an answer, it had 34.2, so that's what I picked. And later on I was trying to find my mistake. Then I used the m(v^2)/2 + mgh = const and I did get 34.2m. It's been several years since that happened, so it may have been the other way around. But I did get the correct answer, using the 'wrong' method. Granted it would've been wrong, if it was an open answer, rather than an a/b/c/d option.
I once was in physics class, we were doing extra points problems. We had a trick question about speed. So long story short the correct process was using twice the distance. I used half the time. That gave me the correct answer through the wrong method. In the end the teacher decided to give me the points because even if it wasn’t her reasoning, my reasoning was valid.
I appreciate all the effort you put into your vids. Keep it up!
(I'm paused at 2:07)
An easy way to calculate the chance of something happening with a certain amount of attempts is to raise the chance of it _not_ happening to the power of the number of attempts, so for box A you could type (5/6)^6 into a calculator and see that you have a roughly 33.5% chance of _not_ getting a single 6 within 6 dice rolls, and the chance of getting a 6 in 6 dice rolls in 100% minus that chance, or 1-(5/6)^6 which is roughly 66.5%
If you were to simply do the same for boxes B and C you would only have the chance of rolling a 6 from 12 or 18 dice. However, we need to also factor in the chances of not getting 2 or 3 6es so that's not enough.
Let's say you're guaranteed to roll a 6 on one of the 12 dice in box B. The chance of you _not_ getting another 6 with the remaining dice would be (5/6)^11. If you then multiply the chance of getting a 6 once (1-(5/6)^12) by the chance of getting a second 6 (1-(5/6)^11) you'd get about 76.8%
If you follow this process of box C your calculation would look like this (1-(5/6)^18)(1-(5/6)^17)(1-(5/6)^16) which equals approximately 86.9%
More precise chances:
A 0.665102023
B 0.768350298
C 0.869348767
So as you can see, you're much more likely to roll 3 6es from 18 dice than 1 6 from 6 dice
6:12 For some reason in Newton's calculation, he multiplies the chance of getting a second 6 in box B by 10 (12*5/6 = 60/6 = 10) and *subtracts* that from the chance of getting a single 6, making the chance of box B rolling 2 6es lower than A rolling 1, yet there's no explanation as to why he added that term and I'm extremely confused by it
The first term is the chance of rolling at least one 6. But the challenge is to roll two 6s. So, if you roll a single 6, you fail. The first term includes the possibility of rolling a single 6, so you have to subtract all those possible outcomes in order to get the probability of rolling at least two 6s.
Kevin: "It happens, or it doesnt"
so, does that mean i have a 50/50 chance of winning the lottery, because it will either happen or not happen?
Thats what i call the the 50/50 law its how i live life
No, it just means there are only two outcomes, but they don’t need to have the same probability
Chance, yes. Probability, no. Those are two different things. As stated, you have two possible outcomes, but a huge "more likely" of one over the other.
Well millions of people are in the lottery so that means it will be millions of times less than a 50/50 chance relative to if the lottery only had 1 dice with an equal amount of only 1s and 2s on it's sides and only 2 people played that year so only then can it be a 50/50 chance,other than that it is phisically imposible to have a 50/50 chance,your welcome😀.
YOU HURT MY BRAIN
Newton also did alchemy, so he got more than just this wrong.
He also thought he was the second coming of Christ and that the Bible was coded with secret messages to him. Even with the standards at the time he was a bit wacky and also a math thief
@@user-ox3ov2qt5o It's not impossible. Stars do it all the time.
@@pilotwhaleproductions5880 I have never seen the claim that Newton thought he was God. The usual claim is that he was an Arian (an early church "heresy") because he rejected the Trinity. Others claim his views resembled the Sozzinis', a 16th century Italian family of nontrinitarians. It is certainly true that he held some strange theological views, but arguably, from an objective standpoint, they were no stranger than the orthodox views of the time.
@@user-ox3ov2qt5o Transmutation (making precious metals like gold and silver from base metals like lead and mercury) was an ultimate goal of alchemy, related to other ultimate goals like creating the philosopher's stone (an object capable of transmutation to gold or silver on contact), the alkahest (a "universal solvent" capable of dissolving all substances, or at least all substances not elementally pure), and the panacaea (a cure for all ailments). But there was more to alchemy than just those end goals. Chemistry as a discipline did not exist in the 17th century, so all progress in the field had been made (and was being made) by alchemists, like Paracelsus, Robert Boyle, and Johann Joachim Becher
.
Newton's ideas in the field were somewhat influential due to the status of his name but not useful or correct, which is why they are not remembered. So he was still wrong about that stuff. But the problem isn't that alchemy itself was pseudoscience. It was _based_ in false, unscientific ideas, but then again, so was Newton's physics. The actual experiments alchemists conducted and laws they formulated were pretty scientific for the time; indeed, more so than Newton's law of gravity (which could only be mathematically confirmed to any precision for celestial bodies, as objects on Earth experience too much drag from air, and timepieces at the time were not sufficiently accurate anyway).
@@user-ox3ov2qt5o Alchemy was not just about making stuff into gold lol it was just one of the goals of all alchemists to be able to do it, Alchemy is literally just 'chemistry' before chemistry existed.
0:10 - I guess as it applies to everyone, we could say there's no I in gravty.
Nice catch!
There’s also no “me” in gravty, unlike team, which is impossible without me.
And as always... thanks for listening because these math videos are more like podcasts to me, played in the background while I work
I figured this out before I even watched this...
There is more open space on the 6th side because there are 6 dots so it is more likely for you to land on 6 because the heaviest side would most likely be down (the heaviest side is 1, which is on the opposite side of 6)
what if the dice had stickers on it that showed 1 to 6 ?
Kevin: It's less probable to get three sixes in 18 dice that to get one six in 6 dice.
Also Kevin at 9:40 : Throws 18 dice and gets at least five sixes and throws 6 dice getting just one six
Probability is weird like that. It's why game developers will sometimes bias the odds in a player's favor in higher percents, because people feel weird when their action with a 90% success rate gets that 10% fail rate.
Plot twist : it was done atleast 10 times and got more than 3 everytime, so he gave up and kept the 5 6s
Probability: Yeah bitches, it's me! Back to mess with your mind once again!
I feel like the trait that they “look nice” is probably not the first thing that I would care about with earbuds...
But What about my ear eyes. you have those, right?
Not true for everyone tho
I'm far from an audiophile but I've never been very concerned with how my sound devices look as long as they don't sound like dollar store trash.
Hey when will you be releasing the next mind blow video? Still waiting for the series to come back. Thanks!
Amazing how you misuse Occam's razor but still get the right conclusion. It isn't about how simpler works more often but about not adding (multiplying) problems without a good reason.
"Some of ye" is correct, but when you switch from object to subject in the next line, you should've switched from "ye" to "you".
Ye actually means the, not you, I believe.
@@jetison333 Ye is an English pronoun. The was written þe when printing presses were first imported to Britain. They didn't have the letter þ and they typed y instead of þ because it was the most similar letter.
@@matj12 en.wikipedia.org/wiki/Ye_(pronoun)
The other way around. Ye is usually a subject pronoun.
Thine thinks thee has too much tyme on thoust's hands.
I really, REALLY, want to say Thank You. Jake is MIA and Michael only seems interested in "pay to view" productions, and then there's our boy Kevin. You still bringing thoughtful, well explained, humorous, and sublime knowledge out on a regular basis and I cant Thank You enough. I really like these cognitive or math bias videos as it helps to really learn how to look at a situation, stop and think, think about how you thought, find the logic errors and fix them so things are done to true benefit. These really help to see where pitfalls are and why to avoid them. understanding these pitfalls makes you a better person. I want to shake your hand, buy you a beer, and hope you understand you are doin good fuckin job!
He was simplifying the explaination for the benefit of his friend. I'm not convinced that Newton himself was confused.
I believe you because I thought so too when you showed us the three options. I did some calculations in my notebook too cause we are learning about probability and chance.
Vsauce2: coin only lands on heads or tails.
Me: knowing that coins can land on their side. UNLIMITED POWER
Join Mr Smith in Washington.
In edited this comment and now you can't see why it was upvoted!
Haha same
me too , right?
Wrong!!!
ikr.
Wrong
@@hitgove2968 ikrw.
It's this channel's version of "Or is it?"
Nice touch with the all twos dice at the end used for the Vsauce(2) logo.
The background music is just amazing. Possible for you to share?
john smith has to be the most generic name ever
Ikr
@@extraterrestrialcontent WRONG
@@M_Chen333 elaborate
Actually that would be Mohammed or some of the kind
john jackson and jack johnson
It sometimes feels like Kevin doesn't have half a clue about what he is saying, as if he just remembered the text and actions needed to accompany the whole smartness
lol he doesn't have a clue, his videos breed internet fake news, but as long as you don't believe a word he says they are quite fun to watch
@@paulatkins9675 Mind pointing out which fake news his videos breed?
@Kanashimi he is akin to a magician, manipulating you into thinking something is true when in fact it is a total fabrication - he would make a good car salesman, if that isn't his full time job already - he's just a new age conman - he could probably convince you the earth was flat if you listened to him long enough - some people are easily manipulated
@@paulatkins9675 I'm curious then, could you give some examples?
Simplest answer I can come up with:
The chance of rolling NOT EXACTLY the number of dice that you expect increases when you roll more dice.
This means that on average dice will be higher and lower more frequently compared to the exact amount needed, meaning that there will be less equal to or higher then expected, since the amount of 'equal' shrinks twice as fast as the amount of 'higher' grows. In order to get this distribution, I visualised a p distribution and placed the chances of each happening within that distribution. Then I found out that some of the negative probability got mixed into the "equal" bracket.
0:10 Gravity was misspelled, it says "GRAVTY" on the screen.
Underrated
@@TheLetterJ10 wtf
Math teachers be like:
"Yes, you have the right anserw, but you didn't use a certain formula, so you are wrong"
Not "you", ye !
Issac newton: *did one mistake *
EVERYONE: IT'S THE IMPOSSIBLE TEST
Where did you buy your dice ? they looks cool
Newton was also wrong in calculating the speed of sound by assuming air to be isothermal then Laplace corrected him by taking it to be adiabatic and obtained the correct value of speed of sound as obtained experimentally
the floor is made out of the floor
@@Aurora-Palace The floor is lava!
"What are we doing with ye dice?"
Sending them to fight Dice Vader
How complicated was the work you went through making that philosophical ending before it was simple enough for you to say in few enough words so we could hear in simple enough terms your explanation of your complicated concept?
Holy crap, the dice in the thumbnail are all stacked properly. Thank you.
Actually he invented gravity, he didn’t discover it
He did neither of thosething he did model gravity which his model of gravity replaced by Einstein's model of gravity later
Red De Cipher You don’t sound smart dawg
@@AliceTheSpider what an awkward sentence
He didnt invent it, he just was aware of its and told our dumbasss about it
Haha.
I didn't find a clear explanation between all the "YE"s, where the difference in probability stems from.
The 2 equations given seem not to have a relationship between them to show the difference.
Here is, how I view it:
PrB = PrA * PrA + 2 * (1-p)^6 * [1 - (1-p)^6 - (6/1)p*(1-p)^5]
= PrA^2 + 2 * (5/6)^6 * [1-(5/6)^6-(5/6)^5]
= (0.6651...)^2 + 2 * 0.08815...
= 0.44236... + 0.1763...
= 0.6187... or actually 0.6186...
Or in words:
The B-Case (getting at least two 6s from 12 dice) is like winning Case A two times in a row (which is less probable overall), but has the advantage (extra winning cases), that you can win by having more than one 6 in one CaseA (expression in [ ]), while having none in the other ( (1-6)^6 ; overall times 2, because the order of these A-Cases can be switched ).
So these cases are added and are special to the case with 12 dice.
It's still a number game, but I think it is easier to derive and understand this way, where the difference stems from.
Math
I think ye nailed it.
it's basically an issue of whether the number of 6's required reduces the probability more or the number of dice available increases the probability more. simply put Newton was lucky even though he overlooked that there's another factor at play that buffers the effect of the number of 6's required.
That's what I thought too, it makes more sense to me that way
I think that ye are a nerd (I mean that as a compliment).
What's the music that plays at 12:48 ? I've been looking around but can't find what it's called
Kevin in any video:
Uses object to explain some complex mathematical concept
Also Kevin:
Throws it into the black abyss five seconds later
So was it Smith or was it John?
Newton: It was John, but he was also called Smith
Kevin: It was Smith but he was also called John.
Me: -_-
Vsause2 is so mathematically cool, no-one even thinks about saying "First"
Also because his viewers arent 8 years old
You are the "First" person saying such a thing
@@greenpixel716 Thou is truest thee.
So you did it for them.
@@eegzaregood9563 I'm 8 and I dont ack like my counterparts at elementary educational institutions
In my middle/elementary school 8th graders had to make a game of probability. The lower grades got to play. But honestly this video goes over probability really well!
This kind of makes me want to adapt my die roller to be able to accept arbitrary questions about the die it's rolling, possibly by incorporating the calculator I wrote to as a way to phase the questions.
My intuition was to break each problem into groups of 6 and then realize that while all 6 groups from the 3 trials had a 1/6 chance, the probability of more than one group failing to land their 6 at the same time as another, was a value greater than zero. This lowered the probability from the initial 1/6 to a lesser value as more rows of 6 are added.
But at the same time each group have also a chance to land more than needed 1 six and can borrow it to "failed" ones.
Really strange for me that you say "yee" instead of "you" 😂
6:57 Just for fun wrote a program to do it with brute force simulation. Run it for 10K, 100K, One million, Ten million times.... Always getting closer to that number.
I interpret this question to being exactly 1 2 or 3 [6] and more variables leaves more "mistakes" to be made. I agree with newton
I guess Newton lost some braincells when the apple hit his head.
Except an apple never fell on his head...
@@brycesabin4787 I am aware of this fact and was only making a joke on the behalf of the myth. but thanks for your irrelevant input.
I once asked my math teacher the probability of her not giving us homework for the rest of the year.
And then COVID-19 came.
All work given would be homework though, unless school already ended for you
I don't think Isaac Newton mistook another problem for the original one, and confused the outcome of "groups of six" tosses with the original "number of sixes in 12 or 18 tosses". The difference between both cases is obvious and Newton, having spent so much time on a careful analysis of this puzzle and on calculations, would not make such an obvious error.
I have read the "Isaac Newton as a Probabilist" paper by Stephen M. Stigler (available on arXiv) and the Wikipedia description of the Newton-Pepys problem. I think Newton wanted to provide another similar example to Pepys, as if he was saying "In answering your original question, it may be helpful to imagine a situation where B and C toss their dice in groups of six.". What may be incorrect is to draw a conclusion from that other hypothetical situation and use it directly for the original problem, but who knows what Newton had in his mind and imagination when he provided this other example. I don't think he considered both the original question and his alternative example as equivalent. As I understand, the issue brought up today is whether his alternative example was helpful at all in considering and analyzing the original problem.
PLEASE BRING BACK MIND BLOW SERIES 🥺
Drink a shot whenever he says ye. Sounds like a Fun game XD.
0:10 : *GRAVTY*
I took a class with Stigler. He was a pretty chill professor. He is best known for Stigler’s Law of Eponymy which states “No scientific discovery is named for its original discoverer, including Stigler’s Law of Eponymy.”
Wow I wanna learn how to use those tables!!
Man its crazy that math is something us humans invented and can actually be applied to real life solutions
@Hedgehog we found it correctly, but the reasons why were wrong.
That’s like saying humans invented oxygen, or gravity. Man didn’t invent math anymore than foxes did.
3:47 that moment when you realise this is more tricky than you first thought