Tuesday, February 10, 2009

Today's Shared Google Reader Items, 2/10/2009

Here are today's shared items from Google Reader. Enjoy!

The Internets:
As always, leave your comments on these or anything else below.


Die Anyway said...

re: "but boo on the sig fig error (100 km/century = 60 miles/century, not 62, no matter what Google might tell you)."

I haven't had the opportunity to research this but you've got me curious. When I do running and racewalking races, a 10K race is 6.2 miles. That would make 100K = 62 miles. For that matter, when I wrote a program to compute race pace I found that 5K was 3.105 miles so that should make 100K = 62.1 miles.

Jon the Geek said...

It depends on the precision of the original measurement. In this case, clearly "100 km" was the original measurement, and then they converted that to miles. But the original measurement really could have easily been anything from 90 to 110 km, rounded to 100. When you convert but "unround" the answer, you're implying precision that isn't there.

In the case of a "10k", it's really pretty close to "10.0k", so 6.2 miles might even be a bit below the measured accuracy. Likewise, if you are being precise in your racewalk measurements, 3.105 miles/km COULD be the proper conversion factor. Or, rather... you should always keep lots of digits in your conversion factor, but your final answer should be rounded to the least number of digits in any of your measurements (roughly speaking).

The purpose of this is to avoid implying more precision than you actually have. In the case of the trees, the average isn't REALLY "62 miles/century," it's "about 60 miles/century." 62 implies precision that isn't there.

If you can't tell, this is kinda a pet peeve of mine. It's exacerbated because some professors try to claim that sig figs are a meaningless concept, when they actually have an important meaning. Sure, it's a shorthand form of error analysis, but it's quick and easy and can keep people from creating false meaning.

Die Anyway said...

Ok. It was obvious from the article that the distance was an approximation taken from averages over different species of trees and different areas. Still, if the report said 100k, I can't blame the article for equating it to 62 miles. Even if they had said 60 they would have been implying a degree of accuracy that wasn't supported. It was really something like 60 plus/minus 20.

Jon the Geek said...

Well, in sig fig terms, the last digit you report (the 6 in 60 in this case) is taken to be uncertain, while other significant digits are certain (the meaning of "uncertain" can be fuzzy, but usually it's "+/- 5 or so"). So when you say "62 miles," you roughly mean "somewhere between 57 miles and 67 miles." If you say "60 miles," it roughly means "somewhere between 10 miles and 110 miles." Converting from "100 km" ("somewhere between 50 km and 150 km," ie "roughly somewhere between 30 miles and 90 miles") to "62 miles" ("57-67 miles") rather than "60 miles" ("10-110 miles") is adding tons of certainty that isn't there.

Phoebe said...

I'd be curious to read your take on natural language search with Chrome! I expect that many of the first steps we'll see in semantic search will be vertical. For example at Jinni (http://www.jinni.com) we've developed a semantic search-and-recommendation engine for movies.

Die Anyway said...

Hmmmm.... so we would have something like this:

where 60 has magic multiplier power that its neighbors 59 and 61 don't have? Never thought of it that way, but I'm definitely not a mathematician so my thoughts on numbers pretty much don't count for much. :-)

Jon Harmon said...

Phoebe: I don't know if you're a real person or just some sort of spam bot, but my take on natural language (not so much semantic search) in Chrome (and Firefox) is here: http://jonthegeek.blogspot.com/2009/02/firefox-keywords-and-chrome-search.html

Jon Harmon said...

Die: The number you're talking about is "60." or "6.0x10^1". Most of the time people aren't picky about noting the difference in popular articles, but you can usually infer it from context. For example, the article was talking about "100 km," pretty clearly not "100. km" (1.00x10^2), nor even significant in the tens digit. The reason I say this is it's talking about km per century, so it's safe to assume that isn't known to a great deal of precision. I'll probably be writing a blog about this for work tomorrow, I'll link it here when it's done...

Jon Harmon said...

As promised: http://activeanswers.blogspot.com/2009/02/significant-figures-and-scientific.html