Kill the Mathematical Hydra | Infinite Series

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Mathematician Kelsey Houston-Edwards explains how to defeat a seemingly undefeatable monster using a rather unexpected mathematical proof. In this episode you’ll see mathematician vs monster, thought vs ferocity, cardinal vs ordinal. You won’t want to miss it.

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux

Comments answered by Kelsey:

Lucid Moses

Lorenz Zahn

QED

Rubbergnome

[requiembeeblebroxx]

Alternatively, try to make it regrow so many heads that its heart can no longer pump blood to all of them and it dies of hypoxia, OOTS-style.

[tfhark]

In case anyone gets confused wanting to learn more - the fact that all well ordered descending sequences terminate is not usually called the "Well Ordering Theorem", it's just a property of well ordered sets. The "Well Ordering Theorem" usually denotes Choice/Zorn's Lemma, which is a different statement.

[martixy]

Damn, this is not a video you can watch casually at 4AM. Gotta remember that about this channel.

[ocean_]

I just wanted to appreciate the awesome eye contact with the camera. It's a subtle detail but so often overlooked and underappreciated! So many channels have hosts blatantly looking back and forth at the script and it's a huge distraction. But here it's almost as if you're speaking directly to us which makes the videos subconsciously so much more captivating. Amazing channel, keep up with good work Kelsey and PBS!

[coatduck]

I think personally I subscribe to the theory that the best way to defeat a hydra is to cut off it's heads until it's just a big ball of heads. It's only a tactical advantage for so long . . .

[pedrocrb]

I think thats killing a mosquito with an atomic bomb

[talkingcowthatwasthereallalong]

What about the Hydra's feelings?











I can't do those maths, I'm a potato basically... Care about your hydracidal tendencies, not my potatoness...

[pixelfairy]

how do you survive N hydra head attacks while your busy chopping heads off?

[whatthefunction]

I've learned that mathematicians have way too much time.

[ShioPK]

Why advanced math on YT is so simple and logical, yet basic math on an exam makes no sense and looks like some form of black magic?

[DavidAnderson-cwoq]

2:40 my strategy: keep chopping off heads until it’s heart can no longer pump enough blood to all of them

[Karan-wzyg]

I have calculated the answer of four lined hyra challenge .It will have 7, 625, 597, 484, 987 heads and the total no. of steps to defeat this hyra are 11, 438, 395, 749, 194. I loved infinite series .Interesting mathematics. Pbs space time is also my favorite.

[morris]

Hercules is the Roman name. The Greek name is Heracles.

[vitorschroederdosanjos]

"You don't need to be a Greek hero, just a mathematician"
Pitagoras: am I a joke to you?

[joshuafife]

"You'll eventually chop off all the Hydras head"

Me-"Not if you die"

[bentupper]

Small correction at 6:55: The next limit ordinal after w should be w*2, not 2*w (omega = w). Since ordinal arithmetic is not commutative, these two are not equal. 2*w is actually equal to w.

[ViewtifulSam]

as someone whose research is mostly in combinatorial optimization (so I might say I'm conditioned to thinking really finitely), when you first mentioned ordinals to tackle this problem I was like "what, why??" but geez this solution is so pretty. I really like the way it elegantly encodes a very natural form of complexity on this tree. I wonder if it can be translated into finite things in an equally meaningful way, but anyway I'm more than fine with this proof. thanks for the great episode!

[anon]

This feels like using a hammer to push in a thumbtack.

There are never infinitely many heads so why resort to infinite ordinals for a proof?
I bet induction over natural numbers suffices. Since we're dealing with trees the induction probably is nested. One induction for the depth, and one for the height.

[MultivectorAnalysis]

Another great video! I see that some viewers already pointed out the issue with omega*2 vs 2*omega, but I noticed one more small typo. The graphic @9:48 has one too many nodes. The head immediately above the body should not be there. I really like this hydra example using transfinite ordinals. Keep up the good work!

[ravernot]

this channel is getting better- remember, don't be one of the other pbs channel hydra heads.