Posts tagged with utility

49 Plays

An interesting story about industrial rail in the United States. About 20 mins. From The Economist.

commercial railways in the United States

  • Europe has an impressive and growing network of high-speed passenger links
  • America’s freight railways are one of the unsung transport successes of the past 30 years.
  • Before deregulation America’s railways were going bust. … By 1980 a fifth of rail mileage was owned by bankrupt firms.
     
  • Since 1981 productivity has risen by 172%, after years of stagnation. Adjusted for inflation, rates are down by 55% 
  • Coal is the biggest single cargo, accounting for 45% by volume and 23% by value.
  • since 1990 the average horsepower of their fleet has risen by 72%
  • [since 1990] the number of ton-miles per (American) gallon of fuel [rose] from 332 to 457—an improvement of 38%
  • But the fastest-growing part of rail freight has been "intermodal" traffic: containers or truck trailers loaded on to flat railcars. The number of such shipments rose from 3m in 1980 to 12.3m in 2006, before the downturn caused a slight falling back.
  • one freight train can carry as much as 280 lorries can

(Source: )




Matt Ridley has written an entertaining book: The Rational Optimist, detailing all the ways in which life is great for rich people. (By rich people I mean the fraction of humans who make ≥5 figure salaries in $.)

For example Louis XIV had a hundred chefs make him 100 meals and throw away the 99 he didn’t want, but nowadays a New York City “peasant” has even more choice of dinner consumption, without needing to be king. (I’m not sure if this applies to the poorest person in NYC or the poor ones who can’t make it in … which is why I’m restricting the statement to ≥$10000 earners. Although maybe Mr Ridley would argue that even a subsistence farmer today has it better than Les Hommes de Cro-Magnon.)

But so, uh, why is this an interesting book? Nobody writes a book called Hey, did you know the sky is blue? Except at sunset when it’s pink or when it rains it’s grey. Isn’t that interesting?! Because everybody already knows that. The fact that Mr Ridley can sell a "provocative" book full of amazing facts and viewpoints about how prosperous we are sends a grave message the opposite way.

Why is it that we need a book from Mr Ridley to remind us how good we’ve got it?




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  • I like Indonesian food better than Japanese food i ⪰ j, and
  • I like Japanese food better than English food j ⪰ e.
  • I also like French food better than English food f ⪰ e, but
  • I see French food as so different from the “exotic Eastern” foods that I can’t really say whether I prefer French food to Indonesian f≹i or Japanese f≹j.

    I would just be in a different mood if I wanted French food than if I wanted “exotic Eastern” food.

So my restaurant preferences are shaped like a poset. In a poset some things are comparable  and some things ain’t . Popularity is shaped as a poset and so is sexiness. Taste in movies is a poset too. The blood types have the same mathematical form as a poset but only if you reinterpret the relation  as “can donate to” rather than “is better than”. So not really the same as ethnic food.

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Partial rankings | orders are transitive, so

  • (indonesian ⪰ japanese and japaneseenglish) implies indonesian ⪰ english.

That means I can use the “I prefer " symbol to codify what I said at the outset:

  • Indonesian  Japanese English
  • French English
  • neither⪰j nor⪰ f … nor⪰ f nor⪰ j (no comparison possible )


Posets correspond nicely to graphs since posets are multitrees.

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Total orders — where any two things can be ranked  — also correspond to graphs, but the edges always line up the nodes into a one-dimensional path. So their graphs look less interesting and display less weird dimensional behaviour. Multitrees (posets) can have fractional numbers of dimensions, like 1.3 dimensions. That’s not really surprising since there are so many kinds of food / movies / attractiveness, and you probably haven’t spent the mental effort to precisely figure out what you think about how you rate all of them.

Rankings | orders are a nice way to say something mathematical without having to use traditional numbers.

I don’t need to score Indonesian at 95 and score Japanese at 85. Scores generated that way don’t mean as much as Zagat and US News & World Report would like you to think, anyway — certainly they don’t have all the properties that the numbers 85 and 95 have.

It’s more honest to just say Indonesian ⪰ Japanese lexicographically, and quantify no more.




The Aboubakar family of Breidjing Camp in Chad.Food expenditure for one week: 685 CFA Francs or $1.23
Nothing speaks to me like this photo series. The families and their food.
This famous photo of the Aboubakars (taken in 2006 I believe) inspired me to eat more legumes and beans over the past few years. I figured—if 6 of them can get by on ~ $1/week, I can definitely lower my expenses by working what’s in those bags into my diet — crowding out the rich, expensive food (meats, pâté, cheese, hummus, butter, pre-made stuff).
Always fighting the hedonic treadmill. Thanks, Aboubakars (and Peter Menzel).
RELATED: Global Rich List, Angus Maddison’s History of the World Economy, Hans Rosling’s 2010 TED talk

The Aboubakar family of Breidjing Camp in Chad.
Food expenditure for one week: 685 CFA Francs or $1.23

Nothing speaks to me like this photo series. The families and their food.

This famous photo of the Aboubakars (taken in 2006 I believe) inspired me to eat more legumes and beans over the past few years. I figured—if 6 of them can get by on ~ $1/week, I can definitely lower my expenses by working what’s in those bags into my diet — crowding out the rich, expensive food (meats, pâté, cheese, hummus, butter, pre-made stuff).

Always fighting the hedonic treadmill. Thanks, Aboubakars (and Peter Menzel).

RELATED: Global Rich List, Angus Maddison’s History of the World Economy, Hans Rosling’s 2010 TED talk


hi-res




Work less. Spend less. Live more.

—chalked on a sidewalk at my college, years ago

I was reading economics at the time, so it made a lot of sense to cast the preference in terms of isoutility curves. As long as the level curves of 𝓤 over (consumption, leisure) space are sufficiently close to parallel the consumption axis, the above suggestion is rational, even optimal.

In terms of partial derivatives, 𝓤 / ∂leisure > ∂𝓤 / consumption at many points in (consumption, leisure) space. More to the point, the directional gradient along the budget constraint points leisureward even at the expense of consumption, for a meaningfully large fraction of the segment.




The wealth required by nature is limited and is easy to procure; but the wealth required by vain ideals extends to infinity.
Epicurus, Principal Doctrines, 300 B.C.




  • If you’re beautiful, you worry people talk to you because of your looks.
  • If you’re on top, you fear losing it all.
  • If you start a business, you notice that it’s less profitable than Microsoft.
  • If you write a book, you see that your work pales next to the classics.
  • If you get a Ph.D., you won’t get published in major journals.
  • If you get published in major journals, you won’t get a Nobel prize.
  • If you were born rich, you think your experience is less authentic or deserved.




Tychonoff’s theorem gives confidence that our definitions of compactness and product topology are the correct (i.e., most useful) ones.

(Tychonoff’s theorem says the product of any collection of compact topological spaces is compact.)

SOURCE: The Encyclopedia Wikimedia

true = useful!

Love seeing pragmatism amidst the supposedly aetherial pursuit of mathematical truth.

(Source: Wikipedia)




I wrote earlier about the many different ways to measure distance. One way I didn’t include is unmeasurable distance.

Sometimes A is

  • tastier,
  • sexier,
  • cooler,
  • more interesting,
  • or otherwise better endowed

than B … but it’s impossible to quantify by how much. No problem; just say that A≻B but that |A−B| is undefined.

It’s still the case that if A is sexier than B and B is sexier than C, it must follow that A is sexier than C.

Symbolically: A≻B & B≻C A≻C.

This concept opens up many parts of human experience to the mathematical imagination.

I will also express my view on moral rates of income tax using orderings ≻.

Oh, and if you’re into this kind of thing: using orders instead of measurable quantities kind of saved the economic concept of “utility”. Kind of saved it. At least instead of talking about 174.27819 hedons, nowadays you can just say X is lexicographically preferred to Y. Ordinal utility instead of cardinal utility.




The inequality of personal well-being is sharply down over the past hundred years and perhaps over the past twenty years as well. Bill Gates is much, much richer than I am, yet it is not obvious that he is much happier if, indeed, he is happier at all.

Tyler Cowen, writing in The American Interest

I’m on the fence about this one. Dr Cowen assumes that well-being is defined only by income and then plugs that through the log function. A clever trick, to be sure, but we don’t actually have measurements of well-being from centuries ago. This might matter if, for example, well-being is determined more by interactions with other people than by material wealth. Something like the privatisation of public land might increase material wealth but decrease the number of interactions with people and therefore decrease the number of friends and emotional contact.

I guess, absent further data, I’m filing this under troll.