# Web Video / Numberphile

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"Videos about numbers - it's that simple."

Numberphile is an educational YouTube channel about numbers and mathematics. Some videos are dedicated to a specific number, while others talk about a type of number, or a general mathematical topic. The channel is run by journalist Brady Haran*, and funded by the Mathematical Sciences Research Institute (MSRI).

Has a supplementary channel, Numberphile2, "for extra footage or stuff that didn't quite fit on the main channel".

## Numberphile and Numberphile2 provide examples of:

• Alternative Number System: There's a video about base 12 (a.k.a. duodecimal, dozenal), one about base 16 (a.k.a. hexadecimal), and one by Tom Scott that explores the surprisingly many different ways numbers are expressed in different cultures, including a group in Papua New Guinea that uses base-27. And naturally, any video relating to computer science will at least mention binary or hexadecimal.
• Deadpan Snarker: Matt Parker often works in sarcastic quips to his lessons, not unlike a stand-up comedian. Appropriately, his YouTube channel is named Stand-Up Maths.
• Early-Installment Weirdness: The channel's focus used to be more literal; videos were often about specific numbers or types of numbers. Over the years it has moved away from talking about particular numbers, and shifted towards covering a broad array of math concepts from many branches of mathematics.
• Eleventy Zillion: they do occasionally discuss numbers too big to be expressed in the normal -illion naming system, Graham's Number being a good example
• Everybody Hates Mathematics: Numberphile even has a video asking why.
• Obviously very much averted in the channel itself, whose name literally means "lover of numbers", and features people who do mathematics for a living.
• Somewhat heartwarmingly, many Numberphile viewers have found Numberphile to be the first — or only — thing that is capable of engaging them in anything math-related, or inspiring any appreciation for math. At least one viewer even claims that their dyscalculia never manifests while they are watching Numberphile.
• Hurricane of Puns: James uses the video on sexy primes* as an opportunity to unleash his inner Pungeon Master:
"Let's pick some…sexy triplets. Yeah, it's getting more exciting all the time, isn't it!"
"If they have a difference of five…what are we gonna call them? Quincy primes! That reminds me of Quincy — solving crimes on a boat."
"Difference of seven… That's going to be a…septic prime?"
"Difference of eight, what do you think that's going to be called? OCTOMUS PRIME!"
• Inherently Funny Words: In "3 is everywhere", James proves that almost all numbers contain the digit 3. When Brady correctly points out that this proof could be applied to any digit, it's revealed that James used 3 for the demonstration because "he just thinks it sounds funnier".
• Interface Screw: Their video on a now-fixed YouTube glitch about viewcounts temporarily freezing at 301 views has a viewcount permanently frozen at 301 views.
• LOL, 69: They have a video about 69!, referring to 69's factorial and how it's the biggest factorial that's calculable on most calculators.
• Ludicrous Precision: Perhaps surprisingly, this is often averted. At one point, Matt even lampshades the popular expectation of perfect precision in mathematics:
"People link mathematics with unnecessary precision. And they link mathematics with doing things that are pointless and over-the-top. And so for some reason, one of the first things people will do when they're learning maths in high school, and they wanna look smart, is write down an unnecessary number of decimal places. Because they think, 'Well it's more maths-y, the more numbers you write down, the more maths we're doing.' "
• One of Brady's related channels does a whole episode on this by showing that one really only needs 39 digits of pi to measure the size of the observable universe to within the width of an atom.
• Magic Square Puzzle: Matt's rather terrible quasi-solution to a magic square involves reusing two numbers and, even then, there's one diagonal with the wrong sum. This, and all of his future flawed solutions, are called the "Parker Square".note
• Misplaced a Decimal Point: This happens in almost any video where someone is doing a calculation in their head, or writing an expression/formula/equation from memory. Mistakes often get caught in post-processing; but sometimes the viewers are the first to notice. In any case, Numberphile certainly corrects any misapprehension that mathematicians are human calculators.
• MST3K Mantra: Comes up in Strange Spheres in Higher Dimensions, when Matt gets to the part about how spheres of 10 dimensions and higher are wider than the boxes containing them.
Matt: There's a trick you can use in mathematics called 'not worrying about it'.
• Nice Guy: The whole cast is quite a friendly bunch, but Brady and James stand out as examples.
• Not Hyperbole: "Graham's Number" opens with Tony Padilla stating that "If you actually tried to picture Graham's Number in your head, then your head would collapse into a black hole", and then clarifying that he means this very literally:
"The entropy of a black hole the size of your head carries less information than it would take to write out Graham's Number."
• Number of the Beast: Natch.
• Precious Puppy: Brady has a chihuahua named Audrey and a greyhound named Lulu, who occasionally show up if the interview is taking place in his house.
• Self-Deprecation: A fairly common occurrence, as some of the guests like to poke fun at their own nerdiness:
• In "Sexy Primes":
James: Yeah, we're doing sexy maths today. Right. So we're talking about sexy primes. Well, I'm not really qualified to talk about sexiness…
• In "Riemann Hypothesis":
Edward: Can I ask you a question, Brady? What is the most difficult way to earn a million dollars?
• Shout-Out: In "Stable Marriage Problem", the guest, Dr. Riehl, needed a group of 4 men and 4 women to explain her algorithm. So she named the women Charlotte, Elizabeth, Jane, and Lydia; and she names the men Bingley, Collins, Darcy, and Wickham. And she even sets up the problem so that they pair up the same way they do in the novel!
• Take That!:
• In a video about the difference between the long and short scales, Tony Padilla refers to short scale as "the incorrect American way".
• In "Tau vs Pi Smackdown", Matt and Steve take turns delivering "take thats" to tau and pi respectively — and to each other.
• Matt Parker has made a Running Gag out of delivering these to those who think the Fibonacci sequence is superior to the Lucas sequence.
• The Watson: Being the interviewer, a non-mathematician, and a journalist by profession, Brady serves this purpose by asking questions that viewers will likely have, as well as questions that are likely to elicit interesting information. Sometimes it's unclear if he's asking a question purely for the viewers' sake, or because he's wondering the same thing himself.
• He'll also sometimes playfully criticize an idea being presented, either in the spirit of fun, to elicit a clarification that will satisfy the viewers, or because he genuinely thinks it sounds like bollocks. Of course, sometimes it seems to be all three:
Brady: But why does this mean 1's not a prime? Maybe it's just a stupid theorem! Maybe the theorem's no good! Why does the theorem beat number 1 out?

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# The Busy Beaver Function

The "Busy Beaver" mathematical function, coined by Tiber Rado' in 1962, demonstrates the concept of a Turing Machine. To show how the function works in a simplified form, Numberphile and Computerphile show this rather neurotic little beaver-shaped droid who's both scared of the dark and conscious of its energy consumption (n=2), so it will work tirelessly until the amount of lights in a hall with infinite rooms is JUST the right amount where all of its needs are satisfied. This keeps going even if the amount of different compulsions it can get (n) is 10^100 or larger.

How well does it match the trope?