Mar 10

How Enrico Fermi Takes Integrals

You know those interview questions? The ones where you’re supposed to make spurious assumptions and use them to compute something like: “How many piano tuners are there in Chicago?”
The correct term for one of these is a “Fermi Problem” after Enrico Fermi the physicist, who apparently was spectacularly good at such problems.
Legend has it he made a stunningly accurate guess at the power of a Nuclear Explosion based on how far some nearby scraps of paper moved.

The point of Fermi Problems—and the reason they’re so popular in interviews—is to find the quickest possible path to an answer.
Even if the answer itself isn’t close enough to be useful the intuition it gives you is.
And Fermi had a great love for finding this intuition in a problem.

Square Root

Integration is one of the most deceptively intuitive problems out there, in the picture above for example the answer is just the red.
This easy to digest definition is what you get in the first 5 minutes of a calculus class, and then the other 1795 minutes everything is complicated and unrelated to the red.
And integrals aren’t just hard for you, it really doesn’t take much to make an integral impossible for everyone.
For example \int \sin(x)^{\sin(x)} \ dx gets you a forlorn “no result found in terms of standard mathematical functions” from Wolfram Alpha. Math just doesn’t have a good answer for it.

But this shouldn’t sit well with any of us because you know, and I know that that function has some red under it.
And it really didn’t sit well with Fermi so here’s what he’d do: he’d draw the function out with pencil and paper, cut it out and then weigh it.
Divide that weight by that of a 1 by 1 square of the same paper and that’s the answer.
All he needed was the first 5 minutes.


Aug 09

The Netflix Zen Master Revisited

I was recently forwarded the response of the Netflix Zenmaster himself to my article about him. There were a few charming details I thought I might share with you. Apparently what I published was actually yesterday’s story. The Zenmaster has upped his game quite a bit since then. Nowadays content is stored on a 8TB file server he has setup in his home and streamed via wireless to all the computers and TVs in the house. It even allows for remote access through FTP. Here’s the truly golden bit: the movies have been edited to what they should have been. Annoying actors are completely edited out. As are superfluous scenes. Endings in particular are improved by this process. An example: his version of The Lord of the Rings has Frodo and Sam completely erased.

Aug 09

Don’t Always Do Your Best

I remember how my great-uncle Jerry
would sit on the porch and whittle
all day long.  Once he whittled me
a toy boat out of a larger toy boat
I had.  It was almost as good as the
first one, except now it had bumpy
whittle marks all over it. And no paint,
because he had whittled off the paint.
-Jack Handey

This idea–hilarious though it may be–is not such a terrible one.  Intel for example manufactured their Core 2 Solo processors by starting with a Core 2 Duo and disabling one of the 2 cores. Intentionally creating an inferior product to be sold at a lower price despite the fact that it cost them the same amount–more even if we consider the cost of disabling a core. However this seemingly paradoxical move actually makes perfect sense. By mutilating their product Intel gains something to sell to the segment for whom the Duo is too pricey. And it’s actually the best way to do it. The variable cost of the manufacturing process itself is negligible compared to the fixed cost of designing the chip before hand. Designing a new chip from the ground up to be a single core version of the Duo would double that design cost.  So with this simple little hack, they get to take full advantage of their prior research.

What’s so intriguing about this is that Intel could provide their Solo customers with the better product at the same cost. Which isolated seems like a no-brainer, you should do your best for your customers right? But to do so would undermine the sales of their pricier version, clearly not an option. So they swallowed their pride and did less than their best allowing them to cash in on a market they would otherwise have skipped over.

Aug 09

The Netflix Zen Master

I’ve always been a huge admirer of screamingly efficient systems. Participating in such system is more pleasurable still. This is part of why I enjoy my Netflix service so much: I get to feel like I’m part of the team. I don’t keep DVDs for weeks at a time without watching them or hold on to them after I’m done so that someone else can see them; because then the system grinds to a halt. And we can’t have that. That would be letting the team down. I prided myself on this, even kidded myself that perhaps workers at my shipping center talked about me in the lounge. All this was before I met The Netflix Zen Master, and learned what efficiency really was.

I was awoken by the sound of a man tearing down a hallway in thong slippers that slapped against the soles of his feet. From a brief shout to his wife I discerned the cause of the commotion: the mail had arrived. I barely rolled off the couch in time to see him race back down the hallway with 4 Netflix cover slips flapping in his wake. I followed him to a room where he already had each disc whirring away in  separate computers. When the rips finished he quickly collected the disks and loaded them side by side into a scanner, capturing the cover-art in one fell swoop. Then without a word he was gone. At the risk of destroying the beautiful dance, I followed him. He’d run out to the garage and already had the car running, a solemn nod indicated that I could come.

We sped down the road until our target became apparent: the mail truck. We quickly overtook it along the straightaway and pulled in a few houses ahead of it to drop the packages in a neighbor’s mailbox. We had done the impossible: gotten his DVDs and sent them back on the very same truck that had brought them in. That night I admired the product of his labor: 5 large binders filled with what he claimed to be 10,000 different titles all with beautiful cover-art. “10,000 films and nothing to watch” he said. Talking with him it became clear that he hardly liked movies at all.

In the interest of making this post about Internet business, I’d like to suggest that Netflix actually implement this competition as part of its service. Keeping a running scoreboard of the most efficient users, this would add an entirely new dimension to the service and would yield a great deal of publicity along the way. Now this really wouldn’t be too hard, in fact it already exists here and I can’t imagine it would be too pricey of an acquisition. You can be darn sure that if they offered me an “I’m the nth most efficient Netflix user” widget, then that would be going on my front page, and I would let it link to whatever they wanted it to. Free advertisement compliments of my competitive nature.

Jul 09

How Physicists Build a Bridge

Imagine the following, you have a room, twenty stories high and 50 feet across. You want to hang a Foucault Pendulum in this room. Here’s the catch: the ceiling is made of glass and can’t support the pendulum. The only way to hang it is with a cable that traverses the gap between the walls. Now we do have a little something to work with, on the other side of the walls are banks of offices from floors 1 to 20. Furthermore these offices have windows opening on to the room.

This is the situation physicists at Fermilab found themselves in when they wanted to hang a pendulum in Wilson Hall [ picture ]. Now they could call in a construction crew, build scaffolding up twenty stories and just connect the cable like that. Not pretty but it would get the job done. However they wanted something pretty. Firstly, things are a little easier. We don’t actually need to get the heavy duty cable across to begin with, we can start with a lightweight string, and use that to pull across increasingly heavy cables. The Niagara Falls Bridge for example started when a young boy flew a kite across the falls.

Unfortunately  kites don’t work inside. Well maybe we could have someone throw a baseball across the gap with the string pinned to it. Maybe but the physicists were more inspired by the 0 brawn approach: two people go up to 20th story offices, each with a ball of string. They drop the balls (holding on to an end) all the way down to the ground 20 stories below.  A third guy ties the ends together. Wind the string up. voila, we have our bridge.

Jul 09

What You Learned About How Asparagus Works Was Probably Wrong

It’s a small quirk of human metabolism that Asparagus makes our urine smell. Due to some research in the 80s we’re now pretty darn sure that the smell is caused by a triage of sulfur containing alkyl compounds citation. But a few decades before scientists pulled out the big guns and nailed down exactly what was causing this phenomenon, they looked at the much simpler question: “Who makes smelly urine?” Observations of the day held that many people met tales of Asparagus Urine with vacant stares, and a few studies revealed that the percentage of people making smelly urine was in the low 40s citation . (This study was done in The UK and would probably yield very different results in other countries.)

So the scientists concluded, this is a polymorphism, different phenotypes existing in the same population. Some people’s digestive tracks produce the malodorous compounds, and some don’t. Simple enough right? I’ve been told they even managed to find the corresponding genotypes, and the correlation they had was great. I heard it got as far as children’s textbooks, before someone pointed out a tiny flaw in the experiment.

The experimenters had been a bit shy in their work. They’d fed people asparagus and asked: “Now does your pee smell?” when they should have asked the more risque: “Does his pee smell?” Had they asked the latter they would have found that ≈40% of people said yes all the time, and  ≈60% said no all the time. Because it turns out that everyone digests asparagus the same way and outputs the same urine, it’s just that not everyone can smell it.

…transforms my chamber-pot into a flask of perfume -Marcel Proust

This post was inspired by an old Daniel Miessler post which surfaced yesterday on Hacker News entitled “ Why Planes Fly: What They Taught You In School Was Wrong .”