Building an Infinite Bridge | Infinite Series

Using the harmonic series we can build an infinitely long bridge. It takes a very long time though. A faster method was discovered in 2009.

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There’s 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

Comments answered by Kelsey:

MultiMurmaider

Marhsall Webb

10TinsThought

[Tehom]

Presumably the table is going to have an infinitely sharp edge. The rounded-corner illustration of the table edge at 1:00, while pretty, may not be the best choice to illustrate this.

You could say, of course, that the true edge of the table is just where the curve begins.

[matthewfennell]

Can beat all this.

Just use an infinitely long brick.

[KINoftheFLAMES]

a table with a curved top edge doesn't seem like a good choice for this discussion...

[keshav]

one of the best channels on YouTube :)

[fredericmazoit]

There is a (very) related riddle that I like.

There is a mathematical ant on a mathematical rubber band. The rubber band is 100m long and the ant starts on an end of the band and wants to reach the other end. Each day, the ant travel 1m. But each night, when the ant sleeps, an evil mathematician pull the band so that it is 100m longer.

To see what happens, at the end of the first day, the ant traveled 1m and the band is 100m. But the next morning, the band is 200m and since both the part before and the part after the band are now longer, the ant has traveled 2m.
At the end of the second day, the ant has traveled 3m but the next morning, the band is 300m long and the ant has traveled 4.5m. 295.5m to go…

The question is will the ant ever reach is final destination ? And if so, in how many days ?

The key to the answer is to see that on the n-th day, the band is (n+1)*100 m long, and thus on the n-th day, the ant travels 1/100*1/(n+1) of the band. So after n days, the ant will have traveled th of the band. But since the harmonic series diverges, this quantity will eventually be bigger that 1. And when this happens, this means that the ant will have crossed the whole band.

[TheRealFlenuan]

So this is what happens when you have -1/12 blocks

[kamryndanley]

I like the way that this introduces subdivision, and limits by using physical representations

[UB]

A bridge is a structure that connects two or more separate edges. If the structure is infinitely long, by definition, there is no second edge for it to connect to. (How can it stop somewhere if it doesn't stop?) What you have isn't an infinite bridge but an infinite diving board.

[Zerotan]

"Some infinite series are finite." Hopefully not this one :D

[MKD]

I watch the episodes twice. once to listen to her words explaining mathematics in that voice and again to see her hand expressions!

[Enboc]

Love your videos because you always put references in the description <3 <3 <3

[satiethetutor]

the Q&A at the end is a really neat concept!

[colinjava]

Very interesting, I prefer the classic bridge with the (1/2)ln n overhang.
It's so counterintuitive that it can overhang arbitrarily large distances.

[EchoLC]

Finally! A video I understand! I even know about the big O too!

[chongli]

In regards to Shor's Algorithm causing world economic collapse: no worries! We already have elliptic curve cryptography. There is no currently known algorithm for breaking it on a quantum computer. By the way, I would love to see a future episode on elliptic curve cryptography!

[agmessier]

In your first description, where you compare the proportion of the block to the right and left of the table edge, you actually determine the median position of the mass, not the mean position of the mass. This isn't necessarily the center of mass. Once a block is completely to the right of the table, it will be 100% to the right no matter how far away it is, but the CG will continue to change if it goes farther to the right.

In the second approach, where you consider point masses, you're actually considering the distance and computing the first moment, so that is the center of mass.

[debasishraychawdhuri]

What happens if you stack infinitely many blocks? the table collapses under its weight.

[vpremeru]

I love the "buts" and "wells." And, great content.

[adoxtnw]

Kind of off-topic/request: Could you make an episode on angles and rotation in general? covering degrees, radians and mainly: quaternions (which nobody seem to understand/explain). And also: why 360 degrees and not 100 ? ;) I love your channel, even if I struggle with it (me being an artist). Keep it up!

[shield]

Kelsey, have you heard of the Mathematics Genealogy project? I looked it up and you are adviser-descended from Isaac Newton!