Those graphs remind me of the graphs in my microeconomics textbook describing two different factors of production producing a specified amount produced, so there are an infinite number of combinations producing a specified amount of production, and infinitely many production amounts. I'm mentioning it cuz it just points to the way math describes the world and I find it very interesting.
One point this video missed (and hopefully the "very soon" video will cover the issue) is that many coins are not weighted evenly, and this _can_ give them a bias towards a certain side. For example, I believe the American penny has a bias towards the tails side.
oh boy. if you just count in the rotation / speed its biased. if you start with other factors like weight, weight distribution, aero dynamic, inertia, inital energy input (like if you know how to flip a coint at a certain speed, you could more or less get what you wanted). you can go forever that its not random. but thb, i think they should stay at "is it random" and "can you flip it in a way, that favors your decision". ;)
David Aceituno it turns out that they explain this is the second video. See the description for a link. The article I linked didn't make it clear (and hence I misinterpreted it), but it was talking about spinning the coin like a spinning top, rather than tossing a coin.
I've always wondered if the 51/49 odds were due to the different types of coin available, or if it was all done off a standardised piece - be it a perfectly balanced metal circle or a US quarter, or if it was due to mechanics.
When talking about the difference introduced by attaching dental floss to the coin, he said 'we hope it's a third-order effect'. What does that mean? What is a third-order effect? From context I assume it means that the influence is small? Given that we're specifically talking about a system which has chaotic behavior (sensitive dependence on initial conditions), I would think knowing the influence is small would be useless. Even tiny differences would result in it being entirely different.
there are some outlying setups that make it very non random. when I do the coin flip, tossing with the thumb as shown in the video, catching in my hand and placing on the back of my other hand (a common way to display results of a toss where i grew up) with an Australian 20 cent coin it is almost certain (~50 tosses in a row, no counter examples) to be the opposite way up to the starting orientation. i don't get the same level of consistency with other coins.
When I was a teenager I decided I was going to master the coin toss to get the result I wanted, and I did. I can safely say that 99.9% of the times I got the result I wanted setting up specific initial conditions (not in a mathematical fashion, but in a trial an error one): initial side, initial position, force applied, point of impact of the thumb on the coin, point of interception of the hand and the coin in the air. I can't tell how long it took me to master it, because I can't remember. I can now think many other parameters that one could take into consideration, but those were the ones that I thought about by that time.
It is not soo dificult to learn to flip a medium size coin and catch then in some way you can "force" 80-90% of the results. It is not about predicting the moviment, it is most like a sport. Your brain can automatically do it for you with some training, like throwing a ball in a basket or thowing a knife. (I'm sorry about my English, it is not my language). Regards!
Nice, I love investigating these simple questions. For you bicycle riders out there with O-locks on your bikes: Have you guys noticed how frequent your lock hit the spokes when trying to lock your bike? The high rate of occurrence caught my attention so much that I calculated the probability for the O-lock to hit the spokes and found P(36) ~ 0.23 for an ordinary bike having tire diameter of .6m and 36 spokes. That's almost 1 in 4 :-O
Love videos about randomness! More! We tend to call something is "random" just because it is too complicated for us to predict, but its not random at all.
I wonder if their calculations took into account the fact that the coin-flipper often doesn't catch the coin at the same point where it was flipped. So the speed of the coin isn't really a determining factor, since the coin isn't simply moving up and down the same distance.
Find it humorous people say they down-voting for use of Imperial units even though it has very little to do with the video. I am sure their mommies would love to hear about how much they were offended.
Benobot99 Different headphones/monitors have different impedance. The smaller the impedance the louder he'd sound (a kindof simplified explanation). OP might need an amplifier.
I always get heads. Or almost anytime. I think an experiment from when I was child showed a 90% chance of heads no matter how the coin initially started. But didn't check if the probability of tail was bigger if tail was upwards at initiation.
does the amount of metal (or the picture) on each side of the coin not count for any irregularity? I've always heard that a coin toss is effected by how the coin is printed or forged or whatever the process is that distributes the mass of the coin across the 2 faces For instance some of the state coins in the US have very little 3D metal on the state side which would make the head side hold more of the mass for the coin
Out of 100 starting at heads: average 51, but out of 100 starting at tails: average 51. I was the only in my class who had the reasoning. They thought I was some genius.
I can get a coin flip to land the way I want it to with 80%+ accuracy (as long as the choice is made before the throw, and I can choose which side is up before the throw), so the short answer is: not very.
This completely changes the game of "Two-up" played here in Australia, which is illegal on all days other than April 25 (Australia Day). The rules of two-up state that two coins are placed tails-up on a flat board and then flipped, with bets being made on how they fall. If flipping with a paddle exhibits the same kind of bias that flipping by hand does, then it would result in the most catastrophic undermining of Australian culture since Crocodile Dundee.
when you look at a coin that is being flipped in the air, the side that the light reflects off of is the side that will be up when it lands. same goes with spinning it.
The randomness comes from the assumption no two flips have the same initial conditions, especially the energy being put into the coin by an imperfect human doing the flipping.
Shouldn't you also take into account the design of each face? Because one side of the coin must be slightly heavier than the other side. Does that have any significant effect?
Next would be what about a magician ? Someone with nimble hands, how predictable can he become ? (Requires some parameters : a player would reject a coin toss that looks too flat or small)
Use a machine to flip a coin inside a box. While the coin is unobserved inside, it is *both heads and tails*. When you open the box, it appears either heads or tails.
A while back I used some old parts out of an R/C plan I built and ended up crashing, to make a coin flipping machine. At one point I was able to get a 70% chance of landing heads. That is, after repeated attempts, and flipping 1 coin 100 times, It averaged 70 heads, and 30 tails. I'm sure someone who is much more skilled in mathematics could do better, but I was pretty happy with that!
Both yes and no a perfect example of a reversed Schrödinger's cat. Its such a splendid question. Though i'm not going to type any more because it would be too long so i'm going to leave this up to the minds of ones reading this comment.
The beauty of SI units is that it can be easily derived from base units like meter, secs, and kg. 1 Watt = 1 Watt, no matter where the power is coming from, electrical, mechanical or thermal. The time of horses being the source of power is over. Plus, the base units are easily extended by factors of 10: meters, mm, km. No complicated conversion factors between inch, feet and mile needed. And, despite english is a good language for communication round the world, this doesnt mean we all need to like fish eaten with a newspaper wrap and a soak of vinegar.
The system you use doesn't matter, as long as you always write down and pay attention the units. Once a mars -lander- probe crashed into mars, because they used different units without noticing it. Edit: not a lander. Or at least, it wasn't supposed to.
Quarters are not 50-50 if I recall correctly and I prefer a computer for my randomness because it works a little better. Every time I flip a coin it tends to just switch sides.
To try to explain the bias towards landing on the side on which it started: If you could tally the side facing up after every "flip" during its time in the air, the starting side would either be one ahead, or equal to the side initially facing down. This would lead to that 51% chance mentioned in the video. Does that make sense?
Hey Brady for a long time I've been wondering how mathematicians work in other dimensions and even fathom things with 12 dimensions could you make a video talking about this please
Are coins usually equally heavy on both sides (sliced so discs would be created) and if not how much could a reasonable weight difference change the outcome of the coin toss?
I really liked the use of the half dollar in the video. It's a seldom used but great coin. I'm assuming you used it because it's easier to see on camera? Does the size of the coin make any difference at all in this experiment?
I wonder if the professor's analysis takes the possibility of a projectile trajectory into account, because I doubt I could ever throw a coin as vertically as it is demonstrated in this video. Most of the times it will drop some 20 cm away from the finger that threw it.
i was a kid i did a similar experience with coin tosses. I remember hypothesising that no matter how high or how fast you flip the coin the outcome will be the same from the starting side, But only if the coin's displacement was more or less 0. I never knew if i was correct or not, but i came to a conclusion to always pick the side that is up from the start. At least now i know that my hypothesis is completely crap but my conclusion is more or less on par.
so your hypothesis was that, but what did the experiment itself end up showing? because the hypothesis is what you think will happen before the actual experiment, so if you did it right, you were more likely to be correct
it kept showing that the top side that it started with, whenever it landed. I can't remember how many trials i did or the exact percentage but almost always landed top side. I won a fair bit of coin toss with that idea, with slight variation if they do a catch and flip at the end.
Is this Richard Feynman's son? He sounds and looks so much like Feynman it is quite funny. And I am pretty sure Feynman would also be interested in something like this.
I find it hard to believe that this bias is the same for all people, I am sure there is a variance. If you hardly give it any rotation the bias will be more, I would guess. But moreover he didn't include a 3rd typical variable: height! Do you drop it on the ground, or catch it in the air, and if you catch it, at a higher height, or lower, or does it depend how far away from your body you need to catch it.
Reminds me of the scene in the last episode of No Game No Life when Sora tossed a coin and Miko used her Blood Destruction to calculate how the coin would land.
recently I was bored at work and I started to flip an American quarter and catch it in my palm and then flip it over. after only about 3 flips I got tails 8 times in a row. i was pretty surprised.
Instead of flipping it, start on the floor and flick it under your finger, then how do you determine the probability of heads / tails when the starting state isn't one of the faces ?
Nuberphile videos are extremely quiet for some reason, i always have to turn up the sound only on them when im watvhing youtube, Brady, render them three times louder and we all are fine :)
Is this not more Physics related than maths? And therefore better suited to Sixty Symbols? Is it because this particular interview was not with Uni of Nottingham?
It feels more physicsy, but I don't know if it would really fall under a physics department umbrella. All of the principles are known and understood, the mechanics that are used are that of Lagrangians, and drag arguments. I would call this a statistics problem, that exists in a real situation, and so requires a grounding in the physical characteristics of the applied system. The problem could probably be tacked by anyone with a strong maths background.
0:53
Feet per second : American
Révolutions per second : French
Crazy people per second: Florida
@@michaelg8841 never have a read anything more true in my life
Tea per second: Britain
nuclear per second: north korea
Water crisis per second: Nigeria
thank you hector salamanca
he is tortuga.
jesse we have to cook
Ding Ding
literally came here to say this
Ring that Bell!
3:17 I like how his thumbnail is literally bruised from flipping coins so much. Now that's dedication!
Videos on this channel are always worth a thumb!
Bundi Derp thanks!
Numberphile A thumb down though ;)
fred col noh. a fum uhp
And it's comments ^^
??.
I love this stuff
and we love you
Never expected to see CustomGrow comment on a math video. Awesome.
Those graphs remind me of the graphs in my microeconomics textbook describing two different factors of production producing a specified amount produced, so there are an infinite number of combinations producing a specified amount of production, and infinitely many production amounts. I'm mentioning it cuz it just points to the way math describes the world and I find it very interesting.
One point this video missed (and hopefully the "very soon" video will cover the issue) is that many coins are not weighted evenly, and this _can_ give them a bias towards a certain side. For example, I believe the American penny has a bias towards the tails side.
wrong, it doesnt matter when flipping. Loaded coins have still 50 50 chance.
RobosergTV - прохождение и летсплей игр How so? :)
oh boy. if you just count in the rotation / speed its biased. if you start with other factors like weight, weight distribution, aero dynamic, inertia, inital energy input (like if you know how to flip a coint at a certain speed, you could more or less get what you wanted). you can go forever that its not random. but thb, i think they should stay at "is it random" and "can you flip it in a way, that favors your decision". ;)
David Aceituno it turns out that they explain this is the second video. See the description for a link.
The article I linked didn't make it clear (and hence I misinterpreted it), but it was talking about spinning the coin like a spinning top, rather than tossing a coin.
David Aceituno ua-cam.com/video/9RKKoXw7wJw/v-deo.html
There is a recent study published on that. They used volunteers and made 350k coin tosses with different coins. It was 50.8 to 49.2
I've always wondered if the 51/49 odds were due to the different types of coin available, or if it was all done off a standardised piece - be it a perfectly balanced metal circle or a US quarter, or if it was due to mechanics.
"I don't care how hard you flip it, you could flip it to the moon!" Just the way he says it makes me laugh.
That's a mathematical way of talking.
@@animal_shorts1 i'm going to flip it horizontal so that it's centrifugal force keeps it spinning like an alien space ship.
When talking about the difference introduced by attaching dental floss to the coin, he said 'we hope it's a third-order effect'. What does that mean? What is a third-order effect? From context I assume it means that the influence is small? Given that we're specifically talking about a system which has chaotic behavior (sensitive dependence on initial conditions), I would think knowing the influence is small would be useless. Even tiny differences would result in it being entirely different.
there are some outlying setups that make it very non random.
when I do the coin flip, tossing with the thumb as shown in the video, catching in my hand and placing on the back of my other hand (a common way to display results of a toss where i grew up) with an Australian 20 cent coin it is almost certain (~50 tosses in a row, no counter examples) to be the opposite way up to the starting orientation.
i don't get the same level of consistency with other coins.
When I was a teenager I decided I was going to master the coin toss to get the result I wanted, and I did. I can safely say that 99.9% of the times I got the result I wanted setting up specific initial conditions (not in a mathematical fashion, but in a trial an error one): initial side, initial position, force applied, point of impact of the thumb on the coin, point of interception of the hand and the coin in the air. I can't tell how long it took me to master it, because I can't remember. I can now think many other parameters that one could take into consideration, but those were the ones that I thought about by that time.
so what......
What do you do if you want to resolve something randomly?
It is not soo dificult to learn to flip a medium size coin and catch then in some way you can "force" 80-90% of the results. It is not about predicting the moviment, it is most like a sport.
Your brain can automatically do it for you with some training, like throwing a ball in a basket or thowing a knife.
(I'm sorry about my English, it is not my language). Regards!
Edgy
Nice, I love investigating these simple questions. For you bicycle riders out there with O-locks on your bikes: Have you guys noticed how frequent your lock hit the spokes when trying to lock your bike? The high rate of occurrence caught my attention so much that I calculated the probability for the O-lock to hit the spokes and found P(36) ~ 0.23 for an ordinary bike having tire diameter of .6m and 36 spokes. That's almost 1 in 4 :-O
The dental floss idea was a very clever way of measuring the number of spins.
Love videos about randomness! More!
We tend to call something is "random" just because it is too complicated for us to predict, but its not random at all.
"We did the analysis in the 12 dimensional space"
Something you should not here in a video regarding coin tosses.
I wonder if their calculations took into account the fact that the coin-flipper often doesn't catch the coin at the same point where it was flipped. So the speed of the coin isn't really a determining factor, since the coin isn't simply moving up and down the same distance.
Find it humorous people say they down-voting for use of Imperial units even though it has very little to do with the video. I am sure their mommies would love to hear about how much they were offended.
When I heard him say "miles per hour" I instantly knew there were going to be comments about it below...!
I had to turn my volume all the way up to 100 just to be able to hear what he's saying
Same
Mine was on 32 out of 100 and I heard him fine.
Are you deaf?
Benobot99 Different headphones/monitors have different impedance. The smaller the impedance the louder he'd sound (a kindof simplified explanation). OP might need an amplifier.
You're not alone.
I wonder how many of these views were Bill Belichick?
😂😂 but just one....he recorded it.
These videos are awesome!
This is one of my favorites for a long time!
I always get heads. Or almost anytime. I think an experiment from when I was child showed a 90% chance of heads no matter how the coin initially started. But didn't check if the probability of tail was bigger if tail was upwards at initiation.
Actually a pretty interesting topic. I like his explanations!
does the amount of metal (or the picture) on each side of the coin not count for any irregularity? I've always heard that a coin toss is effected by how the coin is printed or forged or whatever the process is that distributes the mass of the coin across the 2 faces
For instance some of the state coins in the US have very little 3D metal on the state side which would make the head side hold more of the mass for the coin
Right in the middle of watching this i asked myself... Why do i watch this video... Why do i wanna know this...
I was recommended this for a class. It blows my mind that even 212 people could dislike this video
The dental floss method was brilliant!
Out of 100 starting at heads: average 51, but out of 100 starting at tails: average 51. I was the only in my class who had the reasoning. They thought I was some genius.
The scariest thumb ever videoed.
I can get a coin flip to land the way I want it to with 80%+ accuracy (as long as the choice is made before the throw, and I can choose which side is up before the throw), so the short answer is: not very.
skevoid yeah, but if it hits the ground all bets are off
For deciding on a restaurant, when even asking for all the Oks didn't come up with the answer, it’s close enough ;)
dots and boxes, rock paper scissors, coin flipping? I assume the next one is about how to properly throw a stone for hopscotch.
Catching the coin makes it more random, therefore it is more fair.
This completely changes the game of "Two-up" played here in Australia, which is illegal on all days other than April 25 (Australia Day). The rules of two-up state that two coins are placed tails-up on a flat board and then flipped, with bets being made on how they fall. If flipping with a paddle exhibits the same kind of bias that flipping by hand does, then it would result in the most catastrophic undermining of Australian culture since Crocodile Dundee.
when you look at a coin that is being flipped in the air, the side that the light reflects off of is the side that will be up when it lands. same goes with spinning it.
No Country For Old Men.... That Coin toss scene
Don't forget that, with practice, people can flip coins really consistently and catch the coin as they've called it nearly all of the time.
I could listen to his voice all day long.. Dont know why..
My volume was over 9000 and I still had trouble hearing this
good thing Brady address the catching of the coin at the end I was starting to worry.
This is an unbelievable coincidence! I was thinking the exactly same thing this morning in the subway....
If you flip it to the moon, it would be 0.49 leaving you with the same side you started with! :D
The randomness comes from the assumption no two flips have the same initial conditions, especially the energy being put into the coin by an imperfect human doing the flipping.
He looks like a good italian chef.
Nothing is Random - No probability without uncertain mechanism - therefore YOU HAVE NO FREE WILL.
Please increase microphone level. Can hardly hear u on ipad at full volume
This channel is awesome
Brady can you get a slow motion video of Prof. Diconis doing false deals? He is an "Expert On the Card Table".
I heard the coin toss in the previous 48 Super Bowls has come up 50-50.
This also made me wonder what kind of calculable bias dice of varying "sizes" have.
This guy is awesome!
Shouldn't you also take into account the design of each face? Because one side of the coin must be slightly heavier than the other side. Does that have any significant effect?
Next would be what about a magician ? Someone with nimble hands, how predictable can he become ? (Requires some parameters : a player would reject a coin toss that looks too flat or small)
Use a machine to flip a coin inside a box.
While the coin is unobserved inside, it is *both heads and tails*.
When you open the box, it appears either heads or tails.
"Schrödingers coin" :D
First of all, that thumb.
Secondly, I can influence coin flips by changing the height of which I catch the coin. That or I'm bat shit crazy
A while back I used some old parts out of an R/C plan I built and ended up crashing, to make a coin flipping machine. At one point I was able to get a 70% chance of landing heads. That is, after repeated attempts, and flipping 1 coin 100 times, It averaged 70 heads, and 30 tails. I'm sure someone who is much more skilled in mathematics could do better, but I was pretty happy with that!
Those graphs look like microeconomics indifference curves
Brady, can you please get one of your professors to walk through Bayes theorem, and its implications in applied mathematics?
You can also practice to make it more likely to get the result you want. I did this as a kid for my dad
Both yes and no a perfect example of a reversed Schrödinger's cat.
Its such a splendid question.
Though i'm not going to type any more because it would be too long so i'm going to leave this up to the minds of ones reading this comment.
The beauty of SI units is that it can be easily derived from base units like meter, secs, and kg. 1 Watt = 1 Watt, no matter where the power is coming from, electrical, mechanical or thermal. The time of horses being the source of power is over.
Plus, the base units are easily extended by factors of 10: meters, mm, km. No complicated conversion factors between inch, feet and mile needed.
And, despite english is a good language for communication round the world, this doesnt mean we all need to like fish eaten with a newspaper wrap and a soak of vinegar.
He looks so pissed.
The real question is what's the most you've ever lost on a coin toss.
Interesting!
But you´re doing science, so please use the metric system
I was going to say the same thing!
*pulls out ten-sided coin
The system you use doesn't matter, as long as you always write down and pay attention the units.
Once a mars -lander- probe crashed into mars, because they used different units without noticing it.
Edit: not a lander. Or at least, it wasn't supposed to.
For once I agree with you, Patrick.
Hey! Even if I use metric system, he has the right to use non-metric systems whenever he wants to!
Great mathematics from Richard Feynman's son here!
Quarters are not 50-50 if I recall correctly and I prefer a computer for my randomness because it works a little better. Every time I flip a coin it tends to just switch sides.
I follow your instructions and flipped it to the moon. You owe me a quarter
proferrors voice - accent, rhythm, pace, manner - many things - strongly are reminiscent of feynmans. to me.
To try to explain the bias towards landing on the side on which it started: If you could tally the side facing up after every "flip" during its time in the air, the starting side would either be one ahead, or equal to the side initially facing down. This would lead to that 51% chance mentioned in the video. Does that make sense?
Hey Brady for a long time I've been wondering how mathematicians work in other dimensions and even fathom things with 12 dimensions could you make a video talking about this please
Are coins usually equally heavy on both sides (sliced so discs would be created) and if not how much could a reasonable weight difference change the outcome of the coin toss?
I was just thinking about this the other day
I really liked the use of the half dollar in the video. It's a seldom used but great coin. I'm assuming you used it because it's easier to see on camera? Does the size of the coin make any difference at all in this experiment?
I wonder if the professor's analysis takes the possibility of a projectile trajectory into account, because I doubt I could ever throw a coin as vertically as it is demonstrated in this video. Most of the times it will drop some 20 cm away from the finger that threw it.
i was a kid i did a similar experience with coin tosses. I remember hypothesising that no matter how high or how fast you flip the coin the outcome will be the same from the starting side, But only if the coin's displacement was more or less 0. I never knew if i was correct or not, but i came to a conclusion to always pick the side that is up from the start. At least now i know that my hypothesis is completely crap but my conclusion is more or less on par.
so your hypothesis was that, but what did the experiment itself end up showing?
because the hypothesis is what you think will happen before the actual experiment, so if you did it right, you were more likely to be correct
it kept showing that the top side that it started with, whenever it landed. I can't remember how many trials i did or the exact percentage but almost always landed top side. I won a fair bit of coin toss with that idea, with slight variation if they do a catch and flip at the end.
Ich you actually manage to flip the coin to the moon, it's propably not coming back :P and if it came back, you wouldnt want to catch it :D
Well, there's always the off-axis spin trick you can use to rig a coin toss...
I'd love to back to school and tell my Maths teacher a coin flip is 51/49. That would rustle his Jimmy's so bad.
Is this Richard Feynman's son? He sounds and looks so much like Feynman it is quite funny. And I am pretty sure Feynman would also be interested in something like this.
So always guess the face that starts heads up? Sweet
How did they throw the coin with no revolutions ? That was amazing.
There was an NFL game where the coin did not turn over, so they repeated the toss
NUMBERPHILE VIDEOS!!! 😄
Speaking of coins, can you do a video that explains which parts of a coin are visible when you spin it?
My teacher made me watch this, LOL 😂
When I was practiced, I could flip a quarter with tails facing up and get it to land heads about 90% if the time
i can always control what side it lands on by lowering my hand and not spinning the coin to fast.
I find it hard to believe that this bias is the same for all people, I am sure there is a variance. If you hardly give it any rotation the bias will be more, I would guess.
But moreover he didn't include a 3rd typical variable: height!
Do you drop it on the ground, or catch it in the air, and if you catch it, at a higher height, or lower, or does it depend how far away from your body you need to catch it.
Reminds me of the scene in the last episode of No Game No Life when Sora tossed a coin and Miko used her Blood Destruction to calculate how the coin would land.
How come he didn't take the probability of the coin landing on its side?
I could totally see what this guy was saying. I believe it.
real anwser:
1 % for you and 99 % for the other guy.
recently I was bored at work and I started to flip an American quarter and catch it in my palm and then flip it over. after only about 3 flips I got tails 8 times in a row. i was pretty surprised.
Wouldn't the variations of carvings or engravings on the coin also affect how the coin flips, just based on a non-uniform distribution of mass?
A lot of what we call random, is merely a lack of information and / or an inability to process the information in the given amount of time.
Instead of flipping it, start on the floor and flick it under your finger, then how do you determine the probability of heads / tails when the starting state isn't one of the faces ?
Nuberphile videos are extremely quiet for some reason, i always have to turn up the sound only on them when im watvhing youtube, Brady, render them three times louder and we all are fine :)
Is this not more Physics related than maths? And therefore better suited to Sixty Symbols? Is it because this particular interview was not with Uni of Nottingham?
It feels more physicsy, but I don't know if it would really fall under a physics department umbrella. All of the principles are known and understood, the mechanics that are used are that of Lagrangians, and drag arguments. I would call this a statistics problem, that exists in a real situation, and so requires a grounding in the physical characteristics of the applied system. The problem could probably be tacked by anyone with a strong maths background.