If you’ve ever wondered what well above and well below mean, as opposed to far above and far below, Dan Weikel and Ralph Vartebedian at the Los Angeles Times have quantified it for us, in an article about the California High Speed Rail project.
Rail officials also say the latest cost estimate for the entire 500-mile project has been reduced from $68 billion to $64 billion, well below the $98 billion projection from several years ago, but still far above initial estimates of less than $40 billion.
I’d always assumed that far was further than well. But no, by their math, well is $34 billion but far is as little as $24 billion. Well is further than far.
So now, anytime someone uses far or its relatives to imply extremes — “the furthest corners of the earth” etc,, you can ask: Sure, they may be the furthest, but are they the wellest?
Jarrett, what do you think about medium and HSR systems and projects? Much of your postings deal with internal city transit, but increasingly there are regional-regional issues that need solving – transit between cities.
Rail seems like an excellent mode for city – city transit because often those distances are too short to go by plane, but too long for cars or motorways (limited to 100 km/hour) to be competitive against high speed rail services (200 km or higher).
My impression: once you get into the tens of billions, people lose all perspective of size. It’s as if differences don’t matter any longer when they get behind human comprehension. Doubling costs using bond financing doesn’t even register as a footnote most of the time. Of course if you’re trying to patch together a budget for education or housing the homeless, a billion or two dollars might open some eyes!
I guess it could be useful to also present the numbers in terms of millions a year for X years since that makes investments comparable to recurrent expenses or the total yearly budget.
I like what the British used to do (not sure if they do now) — billions have to be describes as thousand millions.
apparently they changed to the usual english-language scale in 1974.
It makes sense because if you speak English but use a different scale it’s a big problem when you read stuff and don’t know if a billion is a thousand million (i.e. a miliard) or a thousand miliard.
In Europe and most of the world one billion is 1,000,000,000,000 or 10^12 whereas in North America it is 1,000,000,000 or 10^9. That is why it is better to write it out as a number for international audiences.
I think it is always good to look at it per person. For example, the Iraq war cost about a trillion. Since there are about a third of a billion people in the U. S., that means about 3 grand per person.
64 billion is a lot of money. I would say it serves all of California, give or take a few (visitors will certainly benefit, while those in the far north won’t). This has ranged from about $1,000 (initially) to about $2,500, and now is around $1,600.
98m to 64m is (“only”) a 35% drop
40m to 64m is a 60% increase
I’m not going to propose hard and fast rules but if the numbers were $1m, $50m, and $100m would you have a problem with using a more extreme word to describe the 1->50 increase than the 100->50 drop?
64m to 98m is a 53% increase.
64m to 40m is a 37% drop.
Aren’t statistical math games fun?
In a situation where there’s by definition a minimum number (which for cost or revenue aggregates is the case: zero), comparing a percentage decrease to a percentage increase only shows that one is mathematically illiterate. If you want to compare such rates of change, the only defensible way is to compare logarithms. For an estimate, anyway, the order of magnitude is more meaningful than the number (and utility tends more towards logarithmic than linear, too):
log(98m) = 18.4 (using natural log for convenience)
log(64m) = 18.0
log(40m) = 17.5
So 40 64 is a little more significant than 64 98, but not hugely so.
As a physic geek I love answers by math geeks as they are so to the point and understandable, at least by us geeks.
There are only 10 types of people in the world. those that understand binary and those that don’t.
The $64 billion cost is still a little high. It includes $2.4 billion for LA to Anaheim, which is not strictly necessary in the 1st phase, and it also used the alignment via the Tehachapi pass and Palmdale. A route along the Tejon pass would save another $5 or more, according to this very well researched article, while making the route 7% faster and 34 miles shorter: http://www.cahsrblog.com/2013/06/the-truth-about-tejon/
Focus on the cost of SF to LA and change to the Tejon Pass route will bring down the total cost to $55 or $56 billion. Rethinking the northern route might lower the cost even further, though this is less likely to happen.
I agree that leviramsey’s comparison is the appropriate one, and therefore that Jarrett’s comparison in this post, which uses absolute deltas and concludes that 64->98 is greater than 40-64, is inappropriate (though I would not use a term like “mathematically illiterate”).
Laurence’s calculation of 64 “to” 40 or 98 ignores that the chronology was in fact the reverse. It is much more common to consider changes as a percentage of the starting value, rather than the reverse. Jarrett believes that the word choices in the article were based on special criteria dragged out by the authors solely for purposes of disparaging transit, I can’t read minds but I believe it is more likely, rather, that they looked at the 60% increase and the 35% decrease and chose their words based on those percentages – perhaps with inadequate consideration given to the fact that a given percentage decrease is, in a very real way, more significant than the same percentage increase (as leviramsey says).
The chronology of cost estimates is complicated, but one thing we know for certain is there never was an increase from $40 billion directly to $64 billion. So it is equally correct to say the 2008 estimate of $40 billion is 37% less the current estimate of $64 billion.
As for the motivations of the newspaper writers, I doubt they compared percentage changes. My guess is they looked at the $24 billion difference and thought, gee, that’s still a lot of money.