Brady is a gift to humanity. Been watching your other channels like periodic videos, sixty symbols etc. Thank you so much for spreading science to the masses, to people like me.
+James Oldfield I'd like to assume that, like a decent and logical person, you reserved judgement on the usefulness of Brady's videos until you had watched at least a majority of the videos on at least a few of his channels. But I get the feeling that you're just trying to undermine +Foo Fui's praise for no particular reason by questioning the utility of this specific video.
NoriMori I wouldn't watch this if it was useful because that would make it boring. This is very much recreational maths with no use whatsoever outside recreational maths.
Maths Joke: A reciprocal and an integer are having an argument about which is best. Neither side is winning - it's an argument of attrition. However, eventually, the reciprocal thinks he's got the deciding point; he says 'I've got, I know why I'm better!' 'Why?', Says the integer 'Because whatever you are, I'll always be one over you'
He's a not a _real_ magician, so his delivery isn't all that great. From that perspective it makes total sense that he'd "check for fingerprints" as a mathemagician. :P
Here is the proof, for the true numberphiles: This might look like a lot, but everything should be very easy to follow. Define the function F by stating F(0)=1, F(1)=2 and F(n+2)=F(n+1)+F(n). Define S(n) for natural numbers n, to be the set containing all values for F(k) with natural numbers k, such that 0≤k≤n. Define the statement P(n) for natural numbers n, to mean 'There are no two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(n), such that x1+x2=y1+y2.' To proof: The statement P(n) holds for all natural numbers n. Proof: I will prove this by method of induction. Base case: In the sets S(0), S(1) and S(2) there are less than 4 values each. Therefore there are no two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(0), S(1) or S(2). So P(0), P(1) and P(2) all hold. Inductive step: Because F(0) and F(1) are positive, and every next term is the sum of positive numbers, we can conclude that F(m)>0 holds for all natural numbers m. This also means that F(m+2)=F(m+1)+F(m)≥F(m+1), so F(m+1)≥F(m) also holds for all natural numbers m. Say P(k) holds for some natural number k≥3. So there are no two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(k), such that x1+x2=y1+y2. Because k≥3, we can conclude that k+1≥4. So we can take two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(k+1). Because all four values are distinct values in S(k+1), and F(k+1) is an element of S(k+1), either one of the four chosen numbers is F(k+1), or none of them are. If none of them are, then all four numbers are contained inside S(k). Using the induction hypothesis, we can conclude that x1+x2=y1+y2 does not hold. If one of the four numbers is F(k+1), without loss of generality, we can say x1=F(k+1)=F(k)+F(k-1). Because F(m)>0 holds for all natural numbers m, we can conclude that x2>0 and therefore x1+x2>F(k)+F(k-1). Because F(m+1)≥F(m) holds for all natural numbers m, we can conclude that the largest sum possible for y1+y2 is F(k)+F(k-1). Therefore x1+x2>y1+y2 holds, and therefore x1+x2=y1+y2 does not hold. We can conclude that P(k+1) holds. Via the principle of mathematical induction, we can now conclude that P(n) holds for all natural numbers n. Do note: The function F is chosen rather arbitrary. The only property of F that was used in the proof was the fact that: F(m+2)≥F(m+1)+F(m) and F(m)>0 hold for all natural numbers m. Therefore we can generalize this proof to work on any function F such that F(m+2)≥F(m+1)+F(m) and F(m)>0 hold for all natural numbers m.
+Ian Anderson Proof by induction is just the name of a mathematical concept. It's one of the most popular proving methods out there and definately worth learning. Say you have to prove a certain statement holds for all positive integers. This is often done with a proof by induction. This requires two steps: 1) Base case: Prove that the statement holds for the number 1. 2) Inductive step: Prove that when the statement holds for a number k, the statement must also hold for the number k+1. For step 2 what you do is you assume the statement holds for the number k. This assumption is called the induction hypothesis. Then you reason how, from this assumption, you can conclude the statement must also hold for the number k+1.
Ian Anderson There are a couple of axioms which define the natural numbers, and one of them literally is called the induction axiom and it basically states that the method of induction works on natural numbers.
Great video as always. Reminds me of Dr. Grimes video with the cards and the number guessing. Same principle. It's wonderful the way humans have used these principles or bumped into them out of necessity.
I did notice that he wasn't shuffling properly, but I assumed he was just doing a math trick and wasn't practiced at shuffling. I really need to learn to stop assuming.
As soon as he put the 8 down in his explanation I started excited yelling "oh! oh! Shit, what is it called... oh! Fibonacci!" This channel has successfully made a math nerd out of me.
That's true for every trick though. Don't show the same trick multiple times. The first time they see it they're amazed, the second time they start analyzing
meeeh, you've covered a much better card trick including Brown's Criterion (?). The one with base 3. No cheat-shuffling, just sorting in a sophisticated manner!
+VDX Switching bases wouldn't really do anything - you'd just write "10" instead of "2", "101" instead of "5", "1000" instead of "8", and so on. It's just a different representation, nothing about the math itself changes.
Oh I know it's not such a great hand, but it's my lucky hand, it's just like that. I draw this hand insanely often (well, let's say like 15 times in my life) and I won them all... Or most. You know, like a tennis player can have a lucky shirt because he seems to win every time he wears it even though it's not the best shirt and that it doesn't make sense, this is my lucky hand. Kind of a superstition I guess.
Can anybody give me the math behind this? I've known this trick since I was a kid but don't know why it's true. 1. 21 cards dealt out into 3 columns of 7, and have them memorize any card without telling you. 2. Have them tell you which column it is in, you pick up the columns, placing the one with their card in the middle of the other 2. 3. Deal out the 21 cards, one to each column, until each has 7 again. 4. Repeat step 2. 5. Repeat step 3. 6. Repeat step 2. 7. Repeat step 3. 8. Repeat step 2 one last time, then with all 21 cards in a pile in your hand again, instead of dealing them out to the columns just deal down 10 cards, their card will be the 11th.
the camera turns away from the cards and there were cuts in the video, why don't you just do it in one cut without moving the camera from his hands so it seems more realistic? not that i doubt your integrity but it is kind of like a pet peeve of mine lol
yes! but card numbers only go up to 13, so we would have just four cards to choose from (1, 2, 4 and 8). though with powers of two, _every_ sum is unique, unlike fibonacci numbers (1+2+8 = 3+8). so the mathemagician, their eyes closed, could let you pick any number of cards from those four cards, and they could still tell which you chose just from the sum.
Question for you guys! If you had a deck of cards. On every card there is a different number. Since there are infinite Number there are infinite cards. So, what is the chance that you pic the number 5(for example)?
+Tsuyara I don't the exact anserw either but I thing its the first number after 0. because thats the first number in the numberline (+) and its impossible to write it down just like the last number :D
Could you guys explain why if I had a bag of counters(9 red 1blue) and I pulled one out and put it back then obviously I'm more likely to get red, however if I were to do this lets say 1,000,000 times and I happen to get red every time then technically that is more likely (because there's a 9/10 chance each turn) to happen but at the same time not likely to happen because eventually you'd expect to pull out a blue one (I'm confused because the probability every turn never changes but over the course of 1,000,000 turns does it get more and more likely that I would pull out a blue counter?)
The apparent contradiction comes from the fact that you are mistaking two different probabilities to be the same probability. The probability that you draw a red counter given any number of previous red counter draws stays constant - 90%. This probability never changes because every draw is independent of all the others. However, the probability of drawing red a certain number of times in a row is different. Since multiple draws directly impact the result, the 90% probability of any one draw coming up red gets multiplied by itself for every draw we want to see happen in a row, so for n red draws in a row, the probability would be (0.9)^n. TL;DR: The two probabilities you stated in the question are actually two different probabilities: P(Red counter given n previous red counter draws) = 0.9 P(n red counter draws in a row) = (0.9)^n
No, after 10 there is Jack(11), Queen(12) and King(13) (And Ace can be 1 or 14 depending on your game). If you where right there is only Jack left but still need 2 card for 11 and 12...
Brady is a gift to humanity. Been watching your other channels like periodic videos, sixty symbols etc. Thank you so much for spreading science to the masses, to people like me.
Like any of this is useful...
+James Oldfield I'd like to assume that, like a decent and logical person, you reserved judgement on the usefulness of Brady's videos until you had watched at least a majority of the videos on at least a few of his channels. But I get the feeling that you're just trying to undermine +Foo Fui's praise for no particular reason by questioning the utility of this specific video.
NoriMori I wouldn't watch this if it was useful because that would make it boring. This is very much recreational maths with no use whatsoever outside recreational maths.
James Oldfield You didn't address my point.
James Oldfield I never said you shouldn't have that freedom, or even that recreational math videos are bad. And you still didn't address my point.
I get really excited when I see a new numberphile video on my subscription's box ^^
Maths Joke:
A reciprocal and an integer are having an argument about which is best. Neither side is winning - it's an argument of attrition. However, eventually, the reciprocal thinks he's got the deciding point; he says 'I've got, I know why I'm better!'
'Why?', Says the integer
'Because whatever you are, I'll always be one over you'
leave.
Says 0 to 8:
»Nice belt!«
Eli Reid pizza
Eli Reid S=t(sub 1)/1-r
S=2, so 2 is the limit.
Eli Reid i dont know this one. Why?
I might refer to lies from now on as Fibonaccis.
"Stop telling Fibonaccis!"
"He's/ she's a compulsive Fibonacci."
"Fibonaccis! Damned Fibonaccis!"
This story doesn't add up. It's a Fibonacci!
The cake is a Fibonacci!
Fibonaccis don't travel far.
+Gismo 359 Thanks for making me laugh at 3 in the morning. XD
The problem is, you start off telling a little fibonacci but it’s not long before it becomes not so trivial.
"That was those - it was them - you got it." Lol
But i am a mathemagician so i'm gonna check for fingerprints...sounds convincing enough
He's a not a _real_ magician, so his delivery isn't all that great. From that perspective it makes total sense that he'd "check for fingerprints" as a mathemagician. :P
Here is the proof, for the true numberphiles:
This might look like a lot, but everything should be very easy to follow.
Define the function F by stating F(0)=1, F(1)=2 and F(n+2)=F(n+1)+F(n).
Define S(n) for natural numbers n, to be the set containing all values for F(k) with natural numbers k, such that 0≤k≤n.
Define the statement P(n) for natural numbers n, to mean 'There are no two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(n), such that x1+x2=y1+y2.'
To proof:
The statement P(n) holds for all natural numbers n.
Proof:
I will prove this by method of induction.
Base case:
In the sets S(0), S(1) and S(2) there are less than 4 values each. Therefore there are no two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(0), S(1) or S(2). So P(0), P(1) and P(2) all hold.
Inductive step:
Because F(0) and F(1) are positive, and every next term is the sum of positive numbers, we can conclude that F(m)>0 holds for all natural numbers m. This also means that F(m+2)=F(m+1)+F(m)≥F(m+1), so F(m+1)≥F(m) also holds for all natural numbers m.
Say P(k) holds for some natural number k≥3. So there are no two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(k), such that x1+x2=y1+y2.
Because k≥3, we can conclude that k+1≥4. So we can take two pairs of numbers (x1,x2) and (y1,y2) where all four numbers are distinct values in S(k+1). Because all four values are distinct values in S(k+1), and F(k+1) is an element of S(k+1), either one of the four chosen numbers is F(k+1), or none of them are.
If none of them are, then all four numbers are contained inside S(k). Using the induction hypothesis, we can conclude that x1+x2=y1+y2 does not hold.
If one of the four numbers is F(k+1), without loss of generality, we can say x1=F(k+1)=F(k)+F(k-1). Because F(m)>0 holds for all natural numbers m, we can conclude that x2>0 and therefore x1+x2>F(k)+F(k-1). Because F(m+1)≥F(m) holds for all natural numbers m, we can conclude that the largest sum possible for y1+y2 is F(k)+F(k-1). Therefore x1+x2>y1+y2 holds, and therefore x1+x2=y1+y2 does not hold.
We can conclude that P(k+1) holds.
Via the principle of mathematical induction, we can now conclude that P(n) holds for all natural numbers n.
Do note:
The function F is chosen rather arbitrary. The only property of F that was used in the proof was the fact that:
F(m+2)≥F(m+1)+F(m) and F(m)>0 hold for all natural numbers m.
Therefore we can generalize this proof to work on any function F such that F(m+2)≥F(m+1)+F(m) and F(m)>0 hold for all natural numbers m.
Pardon me but how can a mathematical proof be inductive in its reasoning? Surely then it is not a true proof.
+Ian Anderson
Proof by induction is just the name of a mathematical concept. It's one of the most popular proving methods out there and definately worth learning.
Say you have to prove a certain statement holds for all positive integers. This is often done with a proof by induction. This requires two steps:
1) Base case: Prove that the statement holds for the number 1.
2) Inductive step: Prove that when the statement holds for a number k, the statement must also hold for the number k+1.
For step 2 what you do is you assume the statement holds for the number k. This assumption is called the induction hypothesis. Then you reason how, from this assumption, you can conclude the statement must also hold for the number k+1.
+SmileyMPV couldn't this also be a deductive argument if one of your premises is "all numbers function in the same way"?
Ian Anderson There are a couple of axioms which define the natural numbers, and one of them literally is called the induction axiom and it basically states that the method of induction works on natural numbers.
+SmileyMPV thanks for your help!
"I'm a mathemagician"
Legend.
The best fib is a visual fib, where you get the spectator to think they saw something they didn't without saying a word.
Great video as always. Reminds me of Dr. Grimes video with the cards and the number guessing. Same principle. It's wonderful the way humans have used these principles or bumped into them out of necessity.
You are a mathemagician!
Phantom toll booth. Search it up.
MMM, subtraction soup. Man, I'm even hungrier than before, could I have another bowl? ...
This guy came to my school to give a lecture! He's an awesome guy
When the 1, 2, 3, 5 came out, I was like OH MY, THE TITLE REFERRING TO FIBONACCI :)
it hurts me how warped his cards are.
ikr
He has been practicing a lot.
I collect decks. I concur.
I cringed every time he riffled them without bridging. It felt like they were getting more and more bent over the course of the video.
Yeah, doesn't seem like they're plastic.
Well I can immediately tell he's not shuffling properly. He's keeping the same cards on top.
I like card tricks. Please make more Videos and teach us the Math Magic ;)
And now i will practice this trick.
+duden178 good luck!
I totally noticed his flawed shuffling at the beginning. Didn't suspect that was part of the trick, though.
*funny joke incorporating the Parker Square*
Top comment please
Your comment is not top, but currently 2nd or 3rd from the top. You could say...
...it's a Parker comment.
I found that way too funny
To the top!
I did notice that he wasn't shuffling properly, but I assumed he was just doing a math trick and wasn't practiced at shuffling. I really need to learn to stop assuming.
If he learned to do a better false shuffle it would be less obvious. A tabled faro is a classic and exploits some interesting math...
You're in Atlanta?! Leaving to go hang around Spelman....
He looks kind of disappointed when Brady doesnt react with amazement when he selects his cards correctly
That fake shuffle didn't fool anyone.
Mathemagician. This is so awesome.
Loving his tie...!
that cut right before reveling the cards looked a little suspicious
You can see it's the correct cards even before the cut if you pause at 2:16 - 2:17 :) He got it right, but yeah, it's a weird cut!
As soon as he put the 8 down in his explanation I started excited yelling "oh! oh! Shit, what is it called... oh! Fibonacci!" This channel has successfully made a math nerd out of me.
Nice to see another Irish lad on one of Brady's channels! Phil Moriarty has set a high standard!
A cool application of a trick I've done enough digging around to already know about. If you haven't done a video on phinary, you ought to :)
I never knew that about the fibonacci numbers. Very cool.
That's true for every trick though. Don't show the same trick multiple times. The first time they see it they're amazed, the second time they start analyzing
meeeh, you've covered a much better card trick including Brown's Criterion (?). The one with base 3. No cheat-shuffling, just sorting in a sophisticated manner!
These sort of card tricks make people assume that all card tricks are boring...
Great!Use of fibs makes it interesting.
awsome trick !
I very much like this card trick
great trick!
by the way the minimum sequence is oeis.org/A011185 , fibonnacci also has that property but not the minimum values
Do the lucas numbers work for this?
you should watch the Numberphile2 video!!!!
What about binary?
+VDX Switching bases wouldn't really do anything - you'd just write "10" instead of "2", "101" instead of "5", "1000" instead of "8", and so on. It's just a different representation, nothing about the math itself changes.
Watch "the Little Fibs (extra footage)" on Numberphile2
+Sethamajig No, because then it would be called the Little Lucas trick.
that cut as he reveals the cards, hmmmmm, something tells me a messup happened
Prime numbers and 1 would be little more effective, but instead of adding them, you would use multiplication
If I did this trick, to make the suits have the appearance of some randomness, I'd use one suit for evens, and another for the odds
:)
I would think that would make them look less random, not more random.
+NoriMori I meant rather than having all the same suit
That double-entendre, though
My new aspiration in life: to be a mathemagician
I thought he was Littlewood for a second after looking at the thumbnail lol
LITTLE FIBS, LITTLE FIBONACCI
when magician talk shit, you know is time to look at their hand
He is really hyped about his little trick -_-
You should do a Faro shuffle then a reverse Faro shuffle.
Cards in original order
What if the audience asked if they could shuffle the cards.
You guys should do a video on Johnson's Theorem ;)
His accent is so weird. It almost sounds American. This video has melted my brain.
Try Irish.
that was those. it was them.
When the shuffling at 2:14 doesn't change the cards he put at the top of the deck :p
Yes, and he admits to it...
Did you even watch the whole video?
lol yeah, doesn't make the comment any less valid though
Very neat.
I really enjoy his brogue
At 4:18 I knew it was going to be the Fibonacci Sequence.
so as we're this early we'd better get practising to do this before it gets round the Internet :-)
WOW K of hearts and 8 of clubs is my lucky poker hand :o
Oh I know it's not such a great hand, but it's my lucky hand, it's just like that. I draw this hand insanely often (well, let's say like 15 times in my life) and I won them all... Or most. You know, like a tennis player can have a lucky shirt because he seems to win every time he wears it even though it's not the best shirt and that it doesn't make sense, this is my lucky hand. Kind of a superstition I guess.
Can anybody give me the math behind this? I've known this trick since I was a kid but don't know why it's true.
1. 21 cards dealt out into 3 columns of 7, and have them memorize any card without telling you.
2. Have them tell you which column it is in, you pick up the columns, placing the one with their card in the middle of the other 2.
3. Deal out the 21 cards, one to each column, until each has 7 again.
4. Repeat step 2.
5. Repeat step 3.
6. Repeat step 2.
7. Repeat step 3.
8. Repeat step 2 one last time, then with all 21 cards in a pile in your hand again, instead of dealing them out to the columns just deal down 10 cards, their card will be the 11th.
How do you calculate volatility, statistics, and standard deviation or the VF formula
very cool trick! :)
Little Fibs. I see what you did there.
Clever trick. :)
I think it's time to start a prank channel.
I found his tie more impressive than his fibs
there is more suffering videos on the link?? is that the Riemann Roch theorem on his blackboard?
Fib-ulous
the camera turns away from the cards and there were cuts in the video, why don't you just do it in one cut without moving the camera from his hands so it seems more realistic? not that i doubt your integrity but it is kind of like a pet peeve of mine lol
Your cards are the '10.5 of clubs 'and the 'square root of 2 of spades'
Ahh do the bridge. I can see the cards getting warped
That pun though.
I am a massive fan of Numberphile, however, should we really be treading on the Magic Circle's territory? I mean they have like wizards and shit
So 2 cards sum can be guessed within 13. FN. 3 cards prime multiple.
Little lies
Little fibs
Little Fibonacci numbers
*Pottery*
Wait what?
NoriMori Silly internet reference dw
Fanofjambi That tells me nothing, but okay. XD Also, I don't know what "dw" means.
The veins in his eyelids distract me.
“But I’m a mathemagician”
I believe 2^n numbers have the same property, so I guess that should work too?
yes! but card numbers only go up to 13, so we would have just four cards to choose from (1, 2, 4 and 8). though with powers of two, _every_ sum is unique, unlike fibonacci numbers (1+2+8 = 3+8). so the mathemagician, their eyes closed, could let you pick any number of cards from those four cards, and they could still tell which you chose just from the sum.
Had a similar thought actually, after I posted that comment. 2^n numbers are quite fascinating!
Make a video on sprague grundy theoram
oh man he is ruining those cards... bridge your riffle shuffles for God's sake!
fib = federal investigation bureau
Connor Hill Have you heard of a game called GTA? Your general knowledge is bad.
Look up The Wisconsin Definition of a Fib
Question for you guys!
If you had a deck of cards. On every card there is a different number. Since there are infinite Number there are infinite cards. So, what is the chance that you pic the number 5(for example)?
Almost 0.
+Tsuyara I don't the exact anserw either but I thing its the first number after 0.
because thats the first number in the numberline (+) and its impossible to write it down just like the last number :D
(Almost) Every single magic trick, especially card tricks, involve a lie.
Who else recognized the fibonacci sequence before he told the viewers about it?
i gues >50% of this community
nice tie:-)
they're the FIBonacci numbers!
Smells like magicphile
Could you guys explain why if I had a bag of counters(9 red 1blue) and I pulled one out and put it back then obviously I'm more likely to get red, however if I were to do this lets say 1,000,000 times and I happen to get red every time then technically that is more likely (because there's a 9/10 chance each turn) to happen but at the same time not likely to happen because eventually you'd expect to pull out a blue one (I'm confused because the probability every turn never changes but over the course of 1,000,000 turns does it get more and more likely that I would pull out a blue counter?)
The apparent contradiction comes from the fact that you are mistaking two different probabilities to be the same probability. The probability that you draw a red counter given any number of previous red counter draws stays constant - 90%. This probability never changes because every draw is independent of all the others. However, the probability of drawing red a certain number of times in a row is different. Since multiple draws directly impact the result, the 90% probability of any one draw coming up red gets multiplied by itself for every draw we want to see happen in a row, so for n red draws in a row, the probability would be (0.9)^n.
TL;DR: The two probabilities you stated in the question are actually two different probabilities:
P(Red counter given n previous red counter draws) = 0.9
P(n red counter draws in a row) = (0.9)^n
wow. It's 1am and I have a lot to do tomorrow so....... I deccied to learn magic XD
Cards and suffering? Description, anyone?
I know very little about maths but if 0.99 recurring is equal to one why is the infinitesimal not equal to 0
How about Golomb-Rulers?
Love the Irish accent.
lol "more cards and suffering videos" in the description
when he explained it, it seemed like the lamest trick ever
but that's the beauty of maths, it gives us many lame things! :D
You made a mistake K is 14, and Q is 13, I know this since I was a little child!
No, after 10 there is Jack(11), Queen(12) and King(13) (And Ace can be 1 or 14 depending on your game). If you where right there is only Jack left but still need 2 card for 11 and 12...
Fib, nice pun
Some people also like cake :D
False cuts would be much more applicable. :)
Say Will! Will!
Say Wheaton! Wheaton!
Say Will Wheaton! Huil Hueaton!
i did this trick in a bar and I scored a million chicks
I only scored 832040 :(