What is an order of magnitude?

I’ve always wondered exactly how to define an order of magnitude. At ideas42 I had a particular colleague with a PhD in Econ; one time I mentioned that I think use it in a “fuzzy” way, and he responded that he always uses it in an exact way.

So what is the exact way? I think there are actually two ways to use the phrase. Is it a property or is it only a relation?

  1. Property: every number has an order of magnitude that is equivalent to its power of ten (so the OOM of 153 is 2 because 153 = 1.53 * 10^2). This implies a relation: two numbers have the same order of magnitude if each of them has the same order of magnitude, and you calculate the difference in their OOMs by subtracting one from the other.
  2. Relation: two numbers x and y, with x < y, differ by N orders of magnitude if

    (x * 10^N) < y < ( x* 10^(N-1) )

Notice that these two definitions have different “predictions”! Example: is 153 an order of magnitude more than 53? Definition (1) would say yes, but Definition (2) would say no.

The Wikipedia page actually uses both definitions without trying to explain the contradiction — the first sentence is a statement of definition (1) but the John Baez quote is definition (2).

The general principle is that objective-sounding, mathematical terms get used for rhetoric even when they are loosely defined; dig deep and nothing is as precise as it seems.

How do you use the phrase?

Architect Donald MacDonald

MacDonald is an old man with ( I assume) an illustrious past — his firm designed the new span of the Bay Bridge, at least. And in a few weeks he has the grand opening of a bridge in Portland.

His one good, well thought out big idea is 3D zoning. Right now in most places zoning covers the lot– but shouldn’t ground floor spaces have different rules than 4th story? I wish he had spent more time on that.

This talk was laid out (he claimed) starting from lowest-income housing and moving upwards. Really this meant 2 minutes of a box he designed for homeless people, three camper/RV style homes he designed, and then a bunch about his so-called “suburban villages” and “urban villages”. Ultimately I think he’s an architect of small things rather than big ideas. And his small thoughts are fascinating. In particular he pays a lot of attention to lines of sight, though he never summarized it in quite that way. But he talked about living spaces on top floors so that you see the good part of the tree rather than the trunk. And in the villages he’s designed, he angles nearby houses in such a way that you can see through gaps between other houses into the distance instead of just looking at the houses. And in the mixed residential-commercial buildings, 2-3 stories with the commercial space on the ground floor, he talked quite a bit about how he put the planters in such a way as to provide privacy on the deck.
The trouble came when it came to delivering on the title of his talk. “Democratic Architecture” sounds like a big idea. “Practical Solutions” was more his strength, but not to “Housing Crises”. Essentially his vision of housing is much the same in cities and in suburbs — small, self-contained, mixed-use “villages” about one city block square. A good example is this development in Oakland though he also showed a number of others. He talked quite a lot about affordability but seemed to think that most of the reason housing is so expensive in San Francisco is because of needlessly expensive building practices, rather than the price of land itself. This is why he thinks that the building height cap in San Francisco is no big deal. To support this, he mentioned a friend of his in London who was able to find a cheap apartment after looking at 100 others, seemed to me more like a counterexample. And he talked about some admittedly cool work he did a few decades ago in San Francisco where he was actually able to find decent lots that were undesirable by conventional standards (around Duboce Triangle).

Anyway, interesting issues. I asked a question about designing for homebuyers vs architects — since most of his talk was about homebuying (e.g. his units are designed to be expandable as you get more income) which he completely dodged. He also talked almost not at all about household size, which is important given that much of what he designs is small by conventional standards (14×17 including a lo
ft bed, in one case). He mentioned once that “asian” families “like” to have a lot of people in one space.

Finally, a small thing. He mentioned that it’s actually easier to build tall things on the hills of SF rather than the low-lying areas
because that’s where the bedrock is! And the Financial District is basically mud.

Get Broader

Convene five of your friends who collectively have some expertise in each of the following:

  • Physics
  • Chemistry
  • Medicine
  • International Politics*
  • Literature
  • Economics

Every two months, read one book / paper by each of that year’s Nobelists.  Meet and discuss. Make the economist wear a special badge.

*For the peace prize, of course. I couldn’t figure out what it means to be an expert in peace.

I wish I had read this at last night’s open mic

This is a poem I wrote months ago on a scrap of brown paper grocery bag, on the hood of a stranger’s car parked on Paris Street in San Francisco:

Any poem can sit unfinished in a typewriter for hours,
Sometimes you wait for the next word to strike.
Sometimes you sit down and think,
about what to do next.

The back of this scrap of paper has the name Michel Bouquet, who I saw in the film Manon. I don’t remember why I wrote down his name.

P.S. a good find from the forementioned open mic is filmmaker Arthur Valverde. I especially liked this film.

Uber Gets Insightful

Uber is sharing anonymized data with Boston policymakers.

The data will provide new insights to help manage urban growth, relieve traffic congestion, expand public transportation, and reduce greenhouse gas emissions.

This is an interesting dataset for an urban planner. And Uber did well to anonymize to ZCTA instead of giving individual addresses.1 NYC made a mess of things in June 2014 when trying to do something similar.

But using Uber’s data to actually make decisions is ludicrous. Urban planning, like most policymaking, is about how to best distribute scarce resources. It is political. Look at Uber’s example uses:

Uber’s transportation policy

If Boston actually uses Uber’s data to decide which potholes to fill first, they are not going to fill many potholes in poor neighborhoods. If Boston uses Uber’s data to add additional metro stops, they will not add metro stops in poor neighborhoods.

The first questions any data analyst should ask with a new dataset are:

  1. How was this data collected?
  2. What are its blind spots?

And the blind spots here are both large and systematic. Note, however, Uber’s vacuous language above: this data will provide “insights”. They are too smart to say explicitly “this is the only data source you should use for your city planning.” But without a similarly rich dataset on the whole city, the data will only provide “insights” about how to help rich folks.

And, by the way, be wary of people peddling insights. If an insight held up to rigorous analysis, we would just call it a conclusion.

What do you think about Uber’s influence on urban policy?

  1. Though some interesting data is lost here. For example, is the rider’s destination on a busy avenue (to a store/restaurant) or a residential street (personal visit)? []

Social Justice Mural

San Francisco is full of amazing murals! Here are some details from one I particularly like, on 25th and Mission.

The Genius of Peanuts

In the NYRB of 1985, Umberto Eco explores Peanuts (and Krazy Kat, which I’ve never read).

I find that literary criticism is at its worst when it makes an argument from authority and deep knowledge: “I am right because I am important and by the way look at this list of books I’ve read!”


On the other hand I love literary criticism which argues out of a sense of intimacy. Umberto Eco wrote this essay because he really loves Peanuts and it’s important to him that you come to love Peanuts, and for the right reasons. This kind of enthusiasm is infectious, which is why Harold Bloom’s Anatomy of Influence inspired my new Shakespeare book club. All of which is to say I want to go read some Charlie Brown adventures.

You should read the whole review but here are some fun parts:


The poetry of these children arises from the fact that we find in them all the problems, all the sufferings of the adults, who remain offstage. These children affect us because in a certain sense they are monsters: they are the monstrous infantile reductions of all the neuroses of a modern citizen of industrial civilization…

Charlie Brown has been called the most sensitive child ever to appear in a comic strip, a figure capable of Shakespearean shifts of mood; and Schulz’s pencil succeeds in rendering these variations with an economy of means that has something miraculous about it…

Aware of his vocation for the abyss, Pig Pen turns his plight into a boast; he speaks of the dust of centuries, an irreversible process: the course of history…

Snoopy knows he is a dog: he was a dog yesterday, he is a dog today, tomorrow he will perhaps be a dog still. For him, in the optimism of the opulent society in which one moves upward from status to status, there is no hope of promotion…

In this encyclopedia of contemporary weakness, there are, as we have said, sudden luminous patches of light, free variations, allegros, and rondos, where all is resolved in a few bars. The monsters turn into children again, Schulz becomes only a poet of childhood. We know it isn’t true, and we pretend to believe him. In the next strip he will continue to show us, in the face of Charlie Brown, with two strokes of his pencil, his version of the human condition.

All you need to know about the NFL’s Personal Conduct Policy

“Discipline may be imposed in any of the following circumstances:

  • [Various criminal offenses]
  • [Some other stuff]
  • Conduct that imposes inherent danger to the safety and well being of another person”

Tell. Me. More.

Seriously, everything that’s wrong with the NFL can be found in its Personal Conduct policy. The league sees itself as the national religion, transcending common concerns of law and operating according to its own moral standards. In truth it is distinguished from a neighborhood cockfight only by its scale and hypocrisy.

Did you know? The league office is a non-profit association which in 2013 paid $0 in income tax but $45 million dollars in salary and bonus to its moronic commissioner. Individual teams also benefit enormously from publicly-funded stadiums and tax breaks. Maybe this why the conduct policy is frantically trying to preserve “public confidence in the National Football League.”

Fundamental Attribution Error and the Master Race

I just re-watched Hitchcock’s Lifeboat and it provides a really nice demonstration of the Fundamental Attribution Error. (The film has other virtues too.)

Lifeboat is the story of an American merchant marine ship sunk by a German U-Boat during WWII. A few Americans find a lifeboat and pick up a German sailor amid the wreckage. They are short on food and water and are forced to row towards safety. For days, while the Americans bicker in thirst and hunger under a hot sun, German “Willy” steadfastly pulls oar.

The Nazi in Question. (Image found on http://www.cineoutsider.com/reviews/bluray/l/lifeboat.html)

The Americans come to see him as a superman. One character points out the contrast: “He’s made of iron, while we’re made of flesh and blood. Hungry flesh and blood!” Willy instead credits his endurance to “clean living”.

The Fundamental Attribution Error (and more generally, The Person and the Situation) say that when we see a person acting a certain way we think it’s because of who they are or how they were born. But instead it’s usually because of what they’ve done, how they’ve trained, or the context they face (that is invisible to us). So while the Americans think Willy’s physical endurance is genetic (“they truly are the master race”) he sees the years of physical training he endured, and perhaps even the additional pressure he faces, as the one German on the boat, to prove himself.

At least this is the story for about 15 minutes of the movie. In fact Willy is cheating. He has food and water squirreled away, which is the hidden context that really accounts for the observed behavior.