We all know you canāt divide by the number zero. But in some sense the notion of ādividing by zeroā appears every time you use modular arithmetic! The structures that underlie this āmodding businessā are called equivalence relations and quotient sets. And thatās what Iād like to dive into today.
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco for supporting us at the Lemma level!
How to Divide by Zero | Infinite SeriesPBS Infinite Series2018-02-01 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What happens when you divide things that arenāt numbers?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
We all know you canāt divide by the number zero. But in some sense the notion of ādividing by zeroā appears every time you use modular arithmetic! The structures that underlie this āmodding businessā are called equivalence relations and quotient sets. And thatās what Iād like to dive into today.
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco for supporting us at the Lemma level!The End of An Infinite SeriesPBS Infinite Series2018-05-17 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Thank you everyone. This show was a joy to produce and it was the audience that made it incredible.
Imagine you have a square-shaped room, and inside there is an assassin and a target. And suppose that any shot that the assassin takes can ricochet off the walls of the room, just like a ball on a billiard table. Is it possible to position a finite number of security guards inside the square so that they block every possible shot from the assassin to the target?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Letās walk through this puzzle a little more precisely. First, instead of thinking of a physical room with actual people inside, I really want you to think of a square in the xy plane. Pick any two points in the square, and letās call one of those points A for āassassin,ā and the other point T for ātarget.ā Now a āshotā from the assassin is really just a ray emanating out of the point A which can, like a ball on a billiard table, bounce back and forth between the sides of the square. But unlike an actual game of pool, letās assume the trajectory has constant speed and that it can bounce back and forth for forever!
Written and Hosted by Tai-Danae Bradley Produced by Eric Brown Graphics by Matt Rankin Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco and Andrew Poelstra who are supporting us at the Lemma level!Instant Insanity Puzzle | Infinite SeriesPBS Infinite Series2018-04-26 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Imagine you have four cubes, whose faces are colored red, blue, yellow, and green. Can you stack these cubes so that each color appears exactly once on each of the four sides of the stack?
Now, the coloring on these cubes is very important. In other words: weāre only considering THESE four particular cubes. So, for example, cube 1 has exactly three red faces, and one yellow, green, and blue face, moreover, those colors appear on the particular faces as indicated. Similarly for the other cubes.
Written and Hosted by Tai-Danae Bradley Graphics by Matt Rankin Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Print off a template for the cubes shown in the video! bit.ly/2HWYNaY
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco and Andrew Poelstra who is supporting us at the Lemma level!Defining Infinity | Infinite SeriesPBS Infinite Series2018-04-13 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity? Learn through active problem-solving at Brilliant: brilliant.org/InfiniteSeries
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Set theory arose in part to get a grip on infinity. Early ānaiveā versions were beset by apparent paradoxes and were superseded by axiomatic versions that used formal rules to demarcate "legal" mathematical statements from gibberish.
Written and Hosted by Gabe Perez-Giz (@fizziksgabe) Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco and Andrew Poelstra who is supporting us at the Lemma level!Unraveling DNA with Rational Tangles | Infinite SeriesPBS Infinite Series2018-03-29 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How aboutā¦ knots? As in, actual tangles and knots?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
There is a special kind of mathematical tangle called a rational tangle, first defined by mathematician John Conway around 1970 which relates to biology and the study of DNA.
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco and Andrew Poelstra who is supporting us at the Lemma level!How Big are All Infinities Combined? (Cantors Paradox) | Infinite SeriesPBS Infinite Series2018-03-23 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Infinities come in different sizes. Thereās a whole tower of progressively larger "sizes of infinity". So whatās the right way to describe the size of the whole tower?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Check out the solution to the Geometry of SET challenge problem right here: bit.ly/2Ggpw1d
Talking about the sizes of infinite things is tricky in part because the word āinfiniteā is often used in two distinct ways -- to refer to the sets themselves, and also to refer to the *sizes* of those sets. In what follows, letās try to keep as sharp a distinction as we can between infinite sets and infinite set *sizes*, because doing so will let me highlight an especially paradoxical feature about infinite sizing that I don't think gets enough coverage. The technical term for a āsizeā, infinite or otherwise, is ācardinalityā, and I should probably use a term like ānumerousnessā or ānumerosityā rather than āsizeā because the idea it tries to generalize is the notion of "how many". Still, Iām going to say āsizeā a lot in this episode just because itās easier.
Written and Hosted by Tai-Denae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco and Andrew Poelstra who are supporting us at the Lemma level!The Geometry of SET | Infinite SeriesPBS Infinite Series2018-03-15 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
SET and Group Theory by Pavel Etingof (see p. 13ff) http://www-math.mit.edu/~etingof/groups.pdf
This episodes challenge question is: Among the 9 cards shown in this episode what is the maximum number of them that may not contain a SET? Can you rephrase this question in an equivalent yet geometric way and then answer it using the hint - SETs correspond to lines in the Z/3Z grid?
Email your answers to pbsinfiniteseries@gmail.com with the subject line "SET Challenge" along with your proof. A random winner will be selected among the submissions to win a PBS Digital t-shirt.
(Spoiler Alert!) Here's the solution to the SET challenge problem: bit.ly/2Ggpw1d
Let's talk about the card game SET. To play, you start with a deck of cards, each of which has a certain number of shapes in different colors and shadings. You deal out 12 cards and start looking for a SET---a collection of 3 cards that have either all the same or all different patterns. Now, once you deal those 12 cards, itās possible that there might not be a SET among them. When that happens, you just deal out 3 more cards. Andā¦ in some cases, there still might not be a SET. Soā¦ you can add 3 more cards. And this begs the question: What is the maximum number of cards you can deal that might not contain a SET?
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco and Andrew Poelstra who are supporting us at the Lemma level!What was Fermatās āMarvelous Proof? | Infinite SeriesPBS Infinite Series2018-03-08 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
If Fermat had a little more room in his margin, what proof would he have written there?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Recommended by a viewer for connections to formulation of numbers in computer science: https://softwarefoundations.cis.upenn.edu/
In 1637, Pierre de Fermat claimed to have the proof to his famous conjecture, but, as the story goes, it was too large to write in the margin of his book. Yet even after Andrew Wilesās proof more than 300 years later, weāre still left wondering: what proof did Fermat have in mind?
The mystery surrounding Fermatās last theorem may have to do with the way we understand prime numbers. You all know what prime numbers are. An integer greater than 1 is called prime if it has exactly two factors: 1 and itself. In other words, p is prime if whenever you write p as a product of two integers, then one of those integers turns out to be 1. In fact, this definition works for negative integers, too. We simply incorporate -1. But the prime numbers satisfy another definition that maybe you havenāt thought about: An integer p is prime if, whenever p divides a product of two integers, then p divides at least one of those two integers.
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco who are supporting us at the Lemma level!What are Numbers Made of? | Infinite SeriesPBS Infinite Series2018-03-01 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
In the physical world, many seemingly basic things turn out to be built from even more basic things. Molecules are made of atoms, atoms are made of protons, neutrons, and electrons. So what are numbers made of?
Recommended by a viewer for connections to formulation of numbers in computer science: https://softwarefoundations.cis.upenn.edu/
Any set N and function S that meet these conditions will *behave* , respectively, like the natural numbers and the operation "next" or "successor". You can even define operations that fully mimic run-of-the-mill addition and multiplication in terms of any suitable S, regardless of the details of how S works . In this sense, the Peano axioms distill numberhood down to its bare essentials.
Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco who are supporting us at the Lemma level!What Does It Mean to Be a Number? (The Peano Axioms) | Infinite SeriesPBS Infinite Series2018-02-27 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Are the natural numbers fundamental, or can they be constructed from more basic ingredients? It turns out that you can capture the essence of numberhood in a small set of axioms, analogous to Euclidās axioms in geometry. They will allow us to build a set N that will behave just like the natural numbers without ever explicitly mentioning numbers or counting or arithmetic as we do so. These axioms were first published in 1889, more or less in their modern form, by Giuseppe Peano, building on and integrating earlier work by Peirce and Dedekind.
Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Linda Huang Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco who is supporting us at the Lemma level!Telling Time on a Torus | Infinite SeriesPBS Infinite Series2018-02-15 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stick around.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Some configurations of a clock, like the hour hand at 3 with the minute hand at 12, represent "valid" times of day -- if the hands sweep around continuously at their usual steady rates, this configuration will actually happen every 12 hours, at precisely 3 o'clock.
Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose, Jason Hise, Thomas Scheer, Marting Sergio H. Faester, CSS, and Mauricio Pacheco who are supporting us at the Lemma level!Beyond the Golden Ratio | Infinite SeriesPBS Infinite Series2018-01-26 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
You know the Golden Ratio, but what is the Silver Ratio? Learn through active problem-solving at Brilliant: brilliant.org/InfiniteSeries
Cut a line segment into unequal pieces of lengths a and b such that the ratio a to b is the same as the ratio (a + b) to a --- that is, so that big over medium equals medium over small. This is how you construct the golden ratio Phi. If a rectangle has an aspect ratio of Phi, you can subdivide it forever into a square and another golden rectangle, and make fun logarithmic spirals by connecting the corners.
Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose, Jason Hise, Thomas Scheer, Marting Sergio H. Faester, CSS, and Mauricio Pacheco who are supporting us at the Lemma level!Proving Brouwers Fixed Point Theorem | Infinite SeriesPBS Infinite Series2018-01-18 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Analogous to the relationship between geometry and algebra, there is a mathematical āportalā from a looser version of geometry -- topology -- to a more āsophisticatedā version of algebra. This portal can take problems that are very difficult to solve topologically, and recast them in an algebraic light, where the answers may become easier.
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
REFERENCES
The functor in todayās episode is called āthe fundamental group.ā To learn more about the fundamental group and the proof of Brouwerās Fixed Point Theorem, check out:
Congratulations to Robby Weintraub for being the winner of the Topology vs "a" Topology Challenge Question. youtube.com/watch?v=tdOaMOcxY7U
Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.
Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose, Jason Hise, Thomas Scheer, Marting Sergio H. Faester, CSS, and Mauricio Pacheco who are supporting us at the Lemma level!The Mathematics of Diffie-Hellman Key Exchange | Infinite SeriesPBS Infinite Series2018-01-11 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Symmetric keys are essential to encrypting messages. How can two people share the same key without someone else getting a hold of it? Upfront asymmetric encryption is one way, but another is Diffie-Hellman key exchange. This is part 3 in our Cryptography 101 series. Check out the playlist here for parts 1 & 2: youtube.com/watch?v=NOs34_-eREk&list=PLa6IE8XPP_gmVt-Q4ldHi56mYsBuOg2Qw
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Symmetric single-key encryption schemes have become the workhorses of secure communication for a good reason. Theyāre fast and practically bulletproofā¦ once two parties like Alice and Bob have a single shared key in hand. And thatās the challenge -- they canāt use symmetric key encryption to share the original symmetric key, so how do they get started?
Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose, Jason Hise, Thomas Scheer, Marting Sergio H. Faester, CSS, and Mauricio Pacheco who are supporting us at the Lemma level!Topology vs a Topology | Infinite SeriesPBS Infinite Series2017-12-21 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What exactly is a topological space? Learn through active problem-solving at Brilliant: brilliant.org/InfiniteSeries
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Weāve talked about topology here on Infinite Series. Itās the branch of math where we study properties of shapes that are preserved no matter how you bend, twist, stretch or deform them. And youāve probably come across some cool examples of these shapes - or topological spaces - like spheres and tori, Mobius bands and Klein bottles. In this episode we discuss the the 3 axioms that underlie all of topology. If you want to dive deeper after watching this episode check out the links below:
Written and Hosted by Tai-Dinae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Meah Denee Barrington and Emma Dessau Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor, Yana Chernobilsky and John Hofmann who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!This Video was Not Encrypted with RSA | Infinite SeriesPBS Infinite Series2017-12-15 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Last time, we discussed symmetric encryption protocols, which rely on a user-supplied number called "the key" to drive an algorithm that scrambles messages. Since anything encrypted with a given key can only be decrypted with the same key, Alice and Bob can exchange secure messages once they agree on a key. But what if Alice and Bob are strangers who can only communicate over a channel monitored by eavesdroppers like Eve? How do they agree on a secret key in the first place?
Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!(Almost) Unbreakable Crypto | Infinite SeriesPBS Infinite Series2017-12-12 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Despite what many believe, the essence of encryption isnāt really about factoring or prime numbers. So what is it about? Thanks to Vanessa Hill for playing the part of our evil hacker! Be sure to check out Braincraft youtube.com/channel/UCt_t6FwNsqr3WWoL6dFqG9w
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
In previous episodes, Kelsey explained how you could crack RSA encryption with an algorithm capable of quickly factoring ginormous numbers into primes. That might give you the impression that fast factoring algorithms would compromise all digital encryption. But not so -- for instance, YouTube's encryption of this video would be unaffected. And that's because the essence of encryption isnāt really about factoring or prime numbers per se. So what is it about?
Written and Hosted by Gabe Perez-Giz Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!Associahedra: The Shapes of Multiplication | Infinite SeriesPBS Infinite Series2017-11-30 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What happens when you multiply shapes? This is part 2 of our episode on multiplying things that aren't numbers. You can check out part 1: The Multiplication Multiverse right here youtube.com/watch?v=H4I2C3Ts7_w
In our last episode, we talked about different properties of multiplication: associativity and commutativity are the most familiar, but theyāre just two of many. We also saw itās possible to multiply things that arenāt numbers, and in that case we may not have... associativity, for instance. But thatās not a bad thing. In fact, itās a beautiful thing!
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Meah Denee Barrington Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!The Multiplication Multiverse | Infinite SeriesPBS Infinite Series2017-11-23 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What happens if you multiply things that arenāt numbers? And what happens if that multiplication is not associative?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Multiplication of numbers is an associative property and we can make sense of āmultiplicationā between things that arenāt numbers but thatās not considered as associativity. And since weāre talking about associativity, you might wonder about that other property of real numbers: You know: when multiplying two numbers, swapping their order doesnāt change the answer. This property is called commutativity. But keep in mind: itās a very special property to have! Not everything in life is commutative. For example, getting dressed in the morning... putting on your socks and then your shoes is NOT the same as first putting on your shoes and then your socks.
Link to Resources:
The Fundamental Group: āLoop concatenationā http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Landau.pdf
Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!The Heat Equation + Special Announcement! | Infinite SeriesPBS Infinite Series2017-11-17 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What is the heat equation? And find out who the two new hosts of Infinite Series are!
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Imagine a giant -- endless, infinite -- sheet of metal. For mathematical convenience, letās overlay a grid. Now, imagine you light a very tiny and very powerful match directly underneath the origin, the point (0,0). This super special match instantaneously creates infinite heat at the origin, and zero heat everywhere else. Immediately remove the match and watch the heat diffuse along the surface, radiating out from the origin.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!Hilberts 15th Problem: Schubert Calculus | Infinite SeriesPBS Infinite Series2017-11-10 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Get 2 months of Curiosity Stream free by going to www.curiositystream.com/infinite and signing up with the promo code "infinite." It's said that Hermann Schubert performed the mathematical equivalent of "landing a jumbo jet blindfolded." Find out why.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
In the late 1800s, a mathematician, Hermann Schubert, computed all sorts of wild enumerative geometry problems, like the number of twisted cubics tangent to 12 quadrics -- which is apparently 5,819,539,783,680. And maybe that exact number doesnāt seem particularly important -- but the fact that Schubert was able to figure it out it is pretty amazing.
Schubert Calculus, Kleiman and Laksov -- jstor.org/tc/accept?origin=/stable/pdf/2317421.pdf 3264 and All That -- David Eisenbud and Joe Harris The Honeycomb Model of GLn(C) Tensor Products II -- Knutson, Tao, Woodward -- THE HONEYCOMB MODEL OF GLn(C) TENSOR PRODUCTS II:
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Special Thanks to Allen Knutson and BalƔzs Elek
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!Crisis in the Foundation of Mathematics | Infinite SeriesPBS Infinite Series2017-10-19 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What if the foundation that all of mathematics is built upon isn't as firm as we thought it was?
Note: The natural numbers sometimes include zero and sometimes don't -- it depends on how you define it. Within logic, zero is always included as a natural number.
Correction - The image shown at 8:15 is of Netwon's Principia and not Russell and Whitehead's Principia Mathematica as was intended.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Mathematics is cumulative -- it builds on itself. Thatās part of why you take math courses in a fairly prescribed order. To learn about matrices - big blocks of numbers - and the procedure for multiplying matrices, you need to know about numbers. Matrices are defined in terms of - in other words, constructed from - more fundamental objects: numbers.
References::
Probability website mentioned in comments: http://people.ischool.berkeley.edu/~nick/aaronson-oracle/index.html
Philosophy of mathematics (Selected readings) edited by Paul Benacerraf and Hilary Putnam
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!How to Generate Pseudorandom Numbers | Infinite SeriesPBS Infinite Series2017-10-13 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What is a the difference between a random and a pseudorandom number? And what can pseudo random numbers allow us to do that random numbers can't?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Computers need to have access to random numbers. Theyāre used to encrypt information, deal cards in your game of virtual solitaire, simulate unknown variables -- like in weather prediction and airplane scheduling, and so much more. But How can a computer possibly produce a random number?
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Special Thanks to Alex Townsend
Big thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!How Many Cops to Catch a Robber? | Infinite SeriesPBS Infinite Series2017-10-06 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Last episode, we used graph theory to figure out how a cop could catch a robber. But what happens when we introduce multiple cops? What happens if you have "lazy" cops or "drunk" robbers?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Cops and Robbers is played on a finite and connected graph - meaning that any two vertices are joined by a path of edges. The game begins by placing a cop and a robber each on a single vertex; we say it āoccupiesā that vertex. They alternate moving along the edges, from a vertex to neighboring vertex. Or, on any given turn, the player can choose to not move -- to stay where they are. Weāll assume that the cop always goes first. If, eventually, the cop lands on the robberās vertex, the game is over -- we say that the game is a āwinā for the cop. But, if the robber can avoid the cop indefinitely, we say that the game is a win for the robber.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Resources:
M. Aigner and M. Fromme -- A Game of Cops and Robbers: https://www.math.ucdavis.edu/~erikslivken/classes/2016_spring_180/aigner%20fromme.pdf
Special Thanks to Anthony Bonato and Brendan Sullivan
Big thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!PBS Infinite Series Live StreamPBS Infinite Series2017-09-28 | ...The Cops and Robbers Theorem | Infinite SeriesPBS Infinite Series2017-09-28 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Can a cop catch a robber? There's some surprising and compelling graph theory that go into answering that question.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Cops and Robbers is played on a finite and connected graph - meaning that any two vertices are joined by a path of edges. The game begins by placing a cop and a robber each on a single vertex; we say it āoccupiesā that vertex. They alternate moving along the edges, from a vertex to neighboring vertex. Or, on any given turn, the player can choose to not move -- to stay where they are. Weāll assume that the cop always goes first. If, eventually, the cop lands on the robberās vertex, the game is over -- we say that the game is a āwinā for the cop. But, if the robber can avoid the cop indefinitely, we say that the game is a win for the robber.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Resources:
M. Aigner and M. Fromme -- A Game of Cops and Robbers: https://www.math.ucdavis.edu/~erikslivken/classes/2016_spring_180/aigner%20fromme.pdf
The Game of Cops and Robbers on Graphs - Anthony Bonato and Richard Nowakowski
Brendan W. Sullivan, Nikolas Townsend, Mikayla Werzanski - āAn Introduction to Lazy Cops and Robbers on Graphs,ā to appear in College Mathematics Journal in 2017
Brendan W. Sullivan, Nikolas Townsend, Mikayla Werzanski "The 3x3 rooks graph is the unique smallest graph with lazy cop number 3" -- arxiv.org/abs/1606.08485
Special Thanks to Anthony Bonato and Brendan Sullivan
Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!Higher-Dimensional Tic-Tac-Toe | Infinite SeriesPBS Infinite Series2017-09-21 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Regular tic-tac-toe can get a bit boring -- if both players are playing optimally, it always ends in a draw. But what happens if you increase the width of the board? Or increase the dimension of the board? Or increase both?
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
The standard game of tic-tac-toe is too easy. How can we, as mathematicians, play with the combinatorics of tic-tac-toe? There are (at least) three easy ways to modify the game of tic-tac-toe: increase the width of the board - like *this* 5x5 board - increase the dimension of the board - like *this* 3x3x3 board - or increase both, like this 4x4x4 board.
Challenge Winner of the How the Axiom of Choice Gives Sizeless Sets: For Your Math
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco and Nicholas Rose who are supporting us on Patreon at the Lemma level!How the Axiom of Choice Gives Sizeless Sets | Infinite SeriesPBS Infinite Series2017-09-14 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Does every set - or collection of numbers - have a size: a length or a width? In other words, is it possible for a set to be sizeless? This in an updated version of our September 8th video. We found an error in our previous video and corrected it within this version.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
In this episode, we look at creating sizeless sets which we call size the Lebesgue measure - it formalizes the notion of length in one dimension, area in two dimensions and volume in three dimensions.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Mauricio Pacheco and Nicholas Rose who are supporting us at the Lemma level on Patreon!
And thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us at the Theorem Level on Patreon!Your Mind Is Eight-Dimensional - Your Brain as Math Part 3 | Infinite SeriesPBS Infinite Series2017-08-24 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
How Algebraic topology can help us unlock the connection between neurological structure and function. This is Part 3 in our Your Brain as Math mini-series. Check out Part 1 here: youtube.com/watch?v=M0M3srBoTkY Check out Part 2 here: youtube.com/watch?v=rlI1KOo1gp4
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Last episode, we learned that your brain can be modeled as a simplicial complex. And algebraic topology can tell us the Betti numbers of that simplicial complex. Why is that helpful? Letās find out.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco who is supporting us at the Lemma level!Simplicial Complexes - Your Brain as Math Part 2 | Infinite SeriesPBS Infinite Series2017-08-23 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What is a Simplicial Complex and how can it help us decode the brainās neurological structure? This is Part 2 in our Your Brain as Math mini-series. Check out Part 1 here: youtube.com/watch?v=M0M3srBoTkY Check out Part 3 here: youtube.com/watch?v=akgU8nRNIp0
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Last episode we saw that your neural network can be modeled as a graph, which -- weāll show in this episode -- can be viewed as a higher-dimensional simplicial complex. Soā¦ what is a simplicial complex??
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco who is supporting us at the Lemma level!Your Brain as Math - Part 1 | Infinite SeriesPBS Infinite Series2017-08-22 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
What does your brain look like when it's broken down mathematically? And what can this tell us? This is Part 1 in our Your Brain as Math mini-series. Check out Part 2 here: youtube.com/watch?v=rlI1KOo1gp4 Check out Part 3 here: youtube.com/watch?v=akgU8nRNIp0
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
In order to dive deeper into an exciting topic, we're mixing up the format. Over the next three days, weāll spend the next three episodes exploring an incredible application of seemingly purely-abstract mathematics: how algebraic topology can help us decode the connections among neurons in our brains, to help us understand their function.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Mauricio Pacheco who is supporting us at the Lemma level!Stochastic Supertasks | Infinite SeriesPBS Infinite Series2017-08-10 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Supertasks allow you to accomplish an infinite number of tasks in a finite amount of time. Find out how these paradoxical feats get even stranger once randomness is introduced.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
What happens when you try to empty an urn full of infinite balls? It turns out that whether the vase is empty or full at the end of an infinite amount of time depends on what order you try to empty it in. Check out what happens when randomness and the Ross-Littlewood Paradox collide.
The image of the 3D honeycomb sheet used at 7:33 and within the thumbnail image is a recolored/modified version of Andrew Kepert's "Tesselation of space using truncated octahedra." commons.wikimedia.org/wiki/File:Truncated_octahedra.jpg The original of this image is used again at 8:33 and 9:29.
The images of the Weaire-Phelan Structure, the truncated Hexagonal Trapezohedron and the Pyritohedron at 9:14 were created by Tomruen, links below:
Why is there a hexagonal structure in honeycombs? Why not squares? Or asymmetrical blobby shapes? In 36 B.C., the Roman scholar Marcus Terentius Varro wrote about two of the leading theories of the day. First: bees have six legs, so they must obviously prefer six-sided shapes. But that charming piece of numerology did not fool the geometers of day. They provided a second theory: Hexagons are the most efficient shape. Bees use wax to build the honeycombs -- and producing that wax expends bee energy. The ideal honeycomb structure is one that minimizes the amount of wax needed, while maximizing storage -- and the hexagonal structure does this best.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
In 1994, Intel recalled - to the tune of $475 million - an early model of their Pentium processor after they discovered it was making arithmetic errors. Arithmetic mistakes - like the one Intelās Pentium processors were making - are often rooted in computerās unusual version of the real number line.
What happened when a gambler asked for help from a mathematician? The formal study of Probability. Go to http://squarespace.com/infiniteseries and use code āINFINITEā for 10% off your first order.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com)
Throughout much of human history, people consciously and intentionally produced randomness. They frequently used dice - or dice-shaped animal bones and other random objects - to gamble, for entertainment, predict the future and communicate with deities. Despite all this engagement with controlled random processes, people didnāt really think of probability in mathematical terms prior to 1600. All of the ingredients were there -- people had rigorous theories of geometry and algebra, and the ability to rig a game of dice would have certainly provided an incentive to study probability -- but, thereās very little evidence that they thought about randomness in mathematical terms.
The theory of social networks allows us to mathematically model and analyze the relationships between governments, organizations and even the rival factions warring on Game of Thrones.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
Resources and Special thanks:
Network, Crowds and Markets, by David Easley and John Kleinberg :: https://www.cs.cornell.edu/home/kleinber/networks-book/ Cartwright and Harary :: http://snap.stanford.edu/class/cs224w-readings/cartwright56balance.pdf Antal, Krapivsky, and Redner :: http://physics.bu.edu/~redner/pubs/pdf/dresden.pdf Steven Strogatz Lecture :: youtube.com/watch?v=P60sWUxluyk
Special Thanks: Steven Strogatz
Commonly, in the field of social network analysis, one uses a graph - also called a network - where the vertices, or nodes, represent individuals and the edges represent something about the relationships or interactions between individuals. These networks might represent Facebook friendships, or help us understand the spread of disease.
This episode focuses on one model of a social network that encodes whether relationships are positive or negative -- in other words, if theyāre friendly or hostile -- and the notion of structural balance.
The bizarre Arrowās Impossibility Theorem, or Arrowās Paradox, shows a counterintuitive relationship between fair voting procedures and dictatorships. Start your free trial with Squarespace at http://squarespace.com/infiniteseries and enter offer code āinfiniteā to get 10% off your first purchase.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Different voting systems can produce radically different election results, so itās important to ensure the voting system weāre using has certain properties - that it fairly represents the opinions of the electorates. The impressively counterintuitive Arrowās Impossibility Theorem demonstrates that this is much harder than you might think.
What is the best voting system? Voting seems relatively straightforward, yet four of the most widely used voting systems can produce four completely different winners. Get 10% off a custom domain and email address by going to hover.com/InfiniteSeries
*Correction: The ballots at 1:20 were labeled incorrectly. At 1:20 the top ballot should read 1 Green, 2 Blue and 3 Purple and the bottom ballot should read 2 Green, 3 Blue and 1 Purple. Thank you to Hoarder who first noted this.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
With access to a complete set of ranked ballots - which means we know every personās opinions - it seems like a clear winner should emerge. But it doesnāt. The outcome of the election depends critically on what process you use to convert all those individualās preferences into a group preference.
When we mathematically abstract a 400 year old drawing tool called the Pantograph, we find that they have an incredible relationship with complex functions. Start your free trial with Squarespace at http://squarespace.com/infiniteseries and enter offer code āinfiniteā to get 10% off your first purchase.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
What does the inside of a tesseract look like? Pascalās Triangle can tell us. Start your 60 day free trial of CuriosityStream by going to curiositystream.com/infinite and using the promo code āinfinite.ā
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
What shape is formed by taking a diagonal slice of a 4-dimensional cube? Or, a 10-dimensional cube? It turns out that a very familiar mathematical object - Pascalās triangle - can help us answer this question.
Find out why Cantorās Function is nicknamed the Devilās Staircase. Try Skillshare at http://skl.sh/Infinite2 And check out the brand new PBS Digital Series Above the Noise youtube.com/channel/UC4K10PNjqgGLKA3lo5V8KdQ
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
Cantorās Function, also known as the Devilās Staircase, is exceptionally strange. After mapping out Cantorās Function, named after Georg Cantor, we find that its derivative disappears almost everywhere.
Can you turn your pants inside out without taking your feet off the ground? Start your free trial with Squarespace at http://squarespace.com/infiniteseries and enter offer code āinfiniteā to get 10% off your first purchase. And check out Vanessa Hillās documentary Mutant Menu right here! youtube.com/watch?v=NrDM6Ic2xMM
And special thanks to Danny Haymond Jr aka @slothman86 for for his incredible fan art!
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Thereās actually more than one way to build an infinitely long bridge. The traditional method is shown in many calculus classes but a super-fast method of building this bridge was demonstrated by two mathematicians in 2009.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
Classical computers struggle to crack modern encryption. But quantum computers using Shorās Algorithm make short work of RSA cryptography. Find out how.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Decrypting secure messages often involves attempting to find the factors that make up extremely large numbers. This process is too time consuming for classical computers but Shorās Algorithm shows us how Quantum Computers can greatly expedite the process.
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
Thanks to Spiros Michalakis for helpful discussions and feedback.
Only 4 steps stand between you and the secrets hidden behind RSA cryptography. Find out how to crack the worldās most commonly used form of encryption.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Euler's Big Idea: en.wikipedia.org/wiki/Euler%27s_theorem (I can find a non-wiki article, but I don't actually use this in the video. It's just where to learn more about the relevant math Euler did.)
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
Here's how you can get involved: 1. Tell us what you love about public media using #IlovePBS 2. Learn more about public media at http://pbs.org/value. 3. Find your representative at govtrack.us/congress/membersSolving the Wolverine Problem with Graph Coloring | Infinite SeriesPBS Infinite Series2017-04-06 | Viewers like you help make PBS (Thank you š) . Support your local PBS Member Station here: to.pbs.org/donateinfi
At one time, Wolverine served on four different superhero teams. How did he do it? He may have used graph coloring.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Graph coloring may seem simple but the mathematics behind it is surprising difficult and it pops up in a number strange places. Kelsey discusses Sudoku, the Four Color Theorem, the Hadwiger Nelson Problem and how graph coloring can be used to schedule the most effective way to save the planet. Find out how math can defeat the combined might of Thanos, Magneto, Kang, Dormammu, Ultron, Apocalypse and Dr. Doom.
Correction: At 3:58, "Four is the maximum number of required colors"
To understand finance, search algorithms and even evolution you need to understand Random Walks. Tell PBS what types of shows you want to see at surveymonkey.com/r/pbsds2017 25 random participants in the survey will receive PBS t-shirts.
Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com
Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com)
Random Walks are used in finance, computer science, psychology, biology and dozens of other scientific fields. Theyāre one of the most frequently used mathematical processes. So exactly what are Random Walks and how do they work?