Insights by Danielle Fong

notes from a girl from the future

Category: Problem Solving

Reconstruction of Data from a Chart or Graph

I have here several charts of driving cycles. These are standard plots derived from real traffic data, of velocity versus time. Unfortunately I cannot find the data anywhere. So I hatched a plan: maybe there’s software that will reconstruct data from a graph or chart? Does anyone know? If not, I’ll just write it myself and open source it. It seems like a generally useful thing in engineering and science. It deserves an application (maybe even a web application).

Unified California Drivecycle

Timelessness

Many believe that technology simply gets better over time: that every class of invention can improve endlessly into modernity. That is not so. Most of the hard constraints on technology are imposed by physical or mathematical laws. These remain constant. Those who truly understand this may work, instead of towards the solution of individual problems, towards timelessness, and the ideal platonic form.

Wheel, Iran, from 2nd Millenium, BCE

Excavated at Choghazanbil Ziggurat, near Susa, late 2nd Millenium BCE.

Heisenthought.

heisenthought,

\ˈhī-zən-thȯt

alt. he-is-en-thought, as in, he is in thought, don’t disturb him… (thanks to Marc Chung @heisenthought)

noun.

1. A thought subject to mental collapse triggered by interruption.

2. A mental event or sequence characterized by coexistence of loosely related, sometimes contradictory, sets of knowledge or tasks. Highly dispersed in knowledge space, though it may support well defined momentum. Apt to tunnel through imposing technical or energetic barriers.

Collapse triggered upon the observation of the state of current knowledge by a third party. During the beginning states of observation, keen thinkers engage in a mad scramble to save mindstate, which may at some later time be partially reloaded. Status reports are heisenthought’s natural predator. Occasionally, members of a team will spontaneously ‘go dark’, in an attempt to think through some difficult problem — sometimes the only strategy which will work to extricate oneself from local extrema in solutionspace.1,2 Caution should be taken when observing said people, as doing so will both collapse their progress into a single, likely suboptimal path, and be likely misinterpreted as disloyalty, hubris or laziness, since they have disengaged from discussion with no apparent progress.

3. A mental event or sequence characterized by firmly specified and demarcated generating bodies of knowledge, and ill discernible forward movement. Induced by overspecification of problem, method, or solution. Collapse upon observation of current direction of progress by a third party. “‘Are we moving forward on this?’ ‘The heisenthought collapsed; we’re moving, just not in the right direction…'”

4. A coherent collection of thoughts sufficiently isolated from random outside influence. Obeys the relation Δknowledge Δmomentum ≥  ħ/2.

5. A tongue-in-cheek term invented to cast off workplace ‘pings’, ‘check-ins’, ‘status-reports’ and ‘how’s it goings?’.


Notes:

[1] – For example, read the interviews with Max Levchin in chapter 1 and Blake Ross in chapter 29 of Jessica Livingston’s Founders at Work.

Max discusses how he went dark for a year, and came up with the something that really mattered — a way to fight fraud.

We had this merger with a company called X.com. It was a bit of a tough merger because the companies were really competitive—we were two large competitors in the same market. For a while, Peter took some time off. The guy who ran X.com became the CEO, and I remained the CTO. He was really into Windows, and I was really into Unix. So there was this bad blood for a while between the engineering teams. He was convinced that Windows was where it’s at and that we have to switch to Windows, but the platform that we used was, I thought, built really well and I wanted to keep it. I wanted to stay on Unix. […]

I had this intern that I hired before the merger, and we thought, “We built all these cool Unix projects, but it’s kind of pointless now because they are going to scrap the platform. We might as well do something else.” So he and I decided we were going to find ourselves fun projects. […]

It was me acting out, but it was kind of a low time for me because I was not happy with the way we were going. Part of having a CEO is that you can respectfully disagree, but you can resign if you don’t like it that much. But then eventually I became interested in the economics of PayPal and trying to see what’s going on in the back end, because I was getting distracted from code and technology. I realized that we were losing a lot more money in fraud than I thought we were. It was still early 2001. If you looked at the actual loss rates, they were fairly low. You could see that we were losing money, but, given the growth of the system and the growth of the fraud, fraud was not that big of a problem. It was less than 1 percent—it was really low. But then, if you looked at the rate of growth of fraud, you could see that, if you don’t stop it, it would become 5 percent, 10 percent of the system, which would have been prohibitive.

So I started freaking out over it, and this intern and I wrote all sorts of packages— very statistical stuff—to analyze “How did it happen; how do we lose money?” By the end of the summer, we thought, “The world is going to end any minute now.” It was obvious that we were really losing tons of money. By midsummer, it was already on a $10 million range per month and just very scary.

[2] – Blake discusses how, by necessity, they closed up the source and process during the early stages of work on Firefox.

Phoenix was basically a fork of the Mozilla code base that we controlled. We closed off access to the code, because we felt it was impossible to create anything consumer-oriented when you had a thousand Netscape people in search of revenue and a thousand open source geeks who shunned big business trying to reach consensus. We just wanted to close it off and do what we thought was the right thing. We went through a couple name changes, Mozilla offered us more support, and that’s kind of how it all got started.

Thanks to Marc Chung and Joel Muzzerall for reading drafts of this.

On Naming Startups (with Ruby)

The name problem has been with our band of hackers for a while. At least we were not alone: judging by the perennial popularity of the topic on Hacker News, it would seem to stump many.

On such matters, an appeal to a higher power is appropriate. My friends use a variety of divination techniques, such as flipping a coin, tarot, or peyote. I, however, found myself reading an infrequently referenced blog post by Paul Graham (an orphan of the collapse of infogami).

“…as happened with lofts, the features that initially repelled people, like rough concrete walls, have now become a badge of coolness. Weird names are now cool, if they’re the right kind of weird. Nothing could be less cool, at this point, than calling a startup “cool.com.” A company with a name like that could not have arisen organically. “Cool.com” smells of a media conglomerate trying to create a web spinoff.”

and

“My favorite recent startup name is probably Writely. It looks so natural that even though it isn’t a word, you feel it should be. Anyone thoughtful enough to come up with a name like that is probably going to have good software.”

Even ordinary people have an extraordinary ability to glark meaning for a word newly encountered. A word that feels natural enough to exist in speech (‘I’m feeling ever so writely’) is quite a goal to aim for. People are sure to remember that.

I threw together a ruby script to create domain names from some simple rules and then check whois. I multithreaded it for throughput. (Ruby threads are easily invoked but apparently the threading system is not so powerful.)

Read the rest of this entry »

Blue Eyed Islanders. (A Logic Puzzle)

Terry Tao’s recent post on a classic logical puzzle has seeded a bloom of activity in the nerdsphere. A friend of mine introduced it to me over mugs of steamed milk in the graduate college coffee house; I was telling him of recent work I’d been doing on the soundness of emergence of Nash equilibria, and where sufficient conditions arise in real life.1 It was an enjoyable conversation, though I wasn’t afforded the luxury of working it out for myself. If you’d like to struggle through the problem on your own, read Terry’s post, and only return after the break when you think you’ve solved it. (why am I writing this? It started as a comment on news.ycombinator.com, and I couldn’t help myself)

This problem is subtle, and wording is important, so I’ve reproduced the statement from Terry’s blog (emphasis mine) [editor’s note: Terry didn’t intend for a particular subtlety, and so has reworded his main post. He says that it had an ‘unexpectedly interesting subtlety in its formulation, but was not the puzzle I had actually intended to write’. He’s posted the original here]:

There is an island upon which a tribe resides. The tribe consists of 1000 people, 100 of which are blue-eyed and 900 of which are brown-eyed. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and highly devout, and they all know that each other is also highly logical and highly devout.

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

One evening, he addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”.

What effect, if anything, does this faux pas have on the tribe?

I’ve italicized the statement hosting the subtlety. It is known to everyone that if any tribemember discovered his or her eye color, they would dutifully commit suicide at noon the following day. And yet. The statement cleverly leaves open whether every person knows that every other person is as logical, or as devout, or as committed to the duties of ritual sacrifice, as they are.

To jump the gun, the statement doesn’t explicitly state the logical nature and devoutness of all tribespeople as common knowledge.

Hopefully examples will deliver me from vagueness. Consider tribes with one, two, and three blue eyed people on islands Galileo, Hippasus, and Russell. 2,3,4

On Galileo, after the gaff, the sole blue eyed unfortunate notices that none of his people share his tint of iris, and reconciles himself to a midday doom.

On Hippasus, one day later, our fated blue-eyed duo, fully aware that the other would have extinguished were he or she the only blue eyed resident, are forced to draw the conclusion that they are blue eyed, and so they disappear.

But on Russell, confusion sets in. Three blue eyes islanders know the two others. They know that each would commit suicide if they discovered their eyecolor, and they know that on the previous two days, no such thing happened. It would seem that the group would meet a bitter end. As the reasoning usually goes, each of the three, knowing the other two, would infer that the others continued survival could only mean the existence of other blue eyes on the island — theirs!

But wait. Let’s examine this more closely: take the blue eyed islanders, let’s call them, err, Alice, Bert, and Cecil. Alice sees Cecil and Bert; she knows that they as well as the rest of the tribe, and knows they’d indeed follow protocol if either discovered their eye color. What she doesn’t know for certain is whether Bert knows that Cecil would kill himself over eye pigment (even though he in fact would). Therefore, she doesn’t know for certain that a tribe with two blue eyed members would homogenize itself on the second day, she only knows that this would be true were she one of the members. She therefore cannot deduce that she has blue eyes, and the tribe’s taboo keeps information from spreading any further. Our trio is saved. 5

What would happen if all islanders knew that all islanders followed the same rules (as is explained in the variant posted by xkcd)? Instead of confusion, Alice would be certain that Bert and Cecil wouldn’t have survived were they the only blue eyed people, and so she must be the last. They all would die on the third day. Indeed, any group of blue-eyed 6 islanders under the same conditions would all meet their fate the same way.

There are other variants, Anatoly brings up a very interesting metaproblem where proactive tribe’s members might decide to save the others through early self-sacrifice. The analysis of this, and other metaproblems, goes very deep. It will have to be the subject of another post.

In any case, I hope I’ve thoroughly explored the magic. Or at least spoiled it!

As Terry writes,

“The remarkable thing about the puzzle, to me, is how such a subtle and seemingly academic change in the knowledge environment eventually propagates to have a concrete and dramatic effect.”

Notes:

I’ve been meaning to write that article for ages, in fact I was urged to do so by my friends in politics, since models from game theory such as the Centipede Game, the Prisoner’s Dilemma, and Mutually Assured Destruction remain dominant teaching devices, and Nash equilibrium strategies continue to be prescribed and accepted as applicable by acolyte bureaucrats. Yet I’m writing this article, and not that one. The power of social news compels me.

Galileo was famously persecuted by the Church due to his advocacy of essentially logical methods and conclusions. (though you probably already know that)

The philosopher Hippasus was said to have been either expelled from the Pythagorians or drowned at sea for his proof that the square root of two was irrational.

While Bertrand Russell’s magnum opus, the Principia Mathematica, was doomed at inception due to the underexamined implications of self reference, in this case, letting meta-knowledge probe only so deep means our Russellian islanders are saved.

I’m aware that some may object: ‘but doesn’t “and they all know that each other is also highly logical and highly devout” imply common knowledge?’ I concede that this might be an interpretation in some English. Not mine; what kind of language distinguishes knowledge from meta-knowledge but not meta-knowledge from meta-meta-knowledge? Sounds illogical. Oh wait.

A common misconception is that the brown eyed people would die too. But that’s not quite right since none of them are sure that their eyes aren’t actually green, grey, or magenta.