Comments on: The temblor forecast http://bit-player.org/2008/the-temblor-forecast An amateur's outlook on computation and mathematics. Wed, 23 Jul 2008 19:13:45 +0000 http://wordpress.org/?v=1.5.2 Comment on The temblor forecast by: Brian Pickering http://bit-player.org/2008/the-temblor-forecast#comment-1710 Thu, 26 Jun 2008 23:55:36 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1710 Regarding: ========================= To say there’s a 97 percent chance in Socal and a 93-percent chance in Nocal implies there’s a high probability (90.2 percent) of seeing both events in the course of the 30-year period. But the model is no longer valid after the first quake. ========================= Actually, the model isn't valid for predicting another earthquake in the same general area. For the most-part, NoCal and SoCal are far-enough apart that the changes in stresses due to an earthquake in SoCal, wouldn't hugely change the probability of an earthquake in NoCal. For example, the Loma Prieta and Northridge earthquakes each significantly affected the chances of another large earthquake in the SF and LA areas, respectively. That's because they changed the stresses in the immediate areas- relieving stress at/near the epicenter, but increasing it elsewhere in the area. The further away one gets, the less effect there is on the likelihood of another earthquake- there are simply too many other modifiers in between. If you think of a convention center full of people milling around, one person falling over will significantly affect the possibility of another person falling over in that immediate area. However, because of booths, moving people, etc., it's highly unlikely that one person falling over on THIS side of the convention center, will cause another person to fall over way OVER THERE. :-) Regarding:
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To say there’s a 97 percent chance in Socal and a 93-percent chance in Nocal implies there’s a high probability (90.2 percent) of seeing both events in the course of the 30-year period. But the model is no longer valid after the first quake.
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Actually, the model isn’t valid for predicting another earthquake in the same general area. For the most-part, NoCal and SoCal are far-enough apart that the changes in stresses due to an earthquake in SoCal, wouldn’t hugely change the probability of an earthquake in NoCal.

For example, the Loma Prieta and Northridge earthquakes each significantly affected the chances of another large earthquake in the SF and LA areas, respectively. That’s because they changed the stresses in the immediate areas- relieving stress at/near the epicenter, but increasing it elsewhere in the area. The further away one gets, the less effect there is on the likelihood of another earthquake- there are simply too many other modifiers in between.

If you think of a convention center full of people milling around, one person falling over will significantly affect the possibility of another person falling over in that immediate area. However, because of booths, moving people, etc., it’s highly unlikely that one person falling over on THIS side of the convention center, will cause another person to fall over way OVER THERE. :-)

]]> Comment on The temblor forecast by: Seb http://bit-player.org/2008/the-temblor-forecast#comment-1682 Thu, 24 Apr 2008 17:47:29 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1682 Thank you Brian and Barry. I want to say that "but" translates into whatever is needed to make my statement right (ja!). Now seriously, are you trying to convert me to a negative formula follower? I'm starting to see its "naturality". Since "p" includes "pq" and "q" includes "pq" substracting "pq" does the job. The sentence should be "p or q or both (but not both more than once!)". Venn diagrams are so simple and so clear, much easier to understand than these words. Thank you Brian and Barry. I want to say that “but” translates into whatever is needed to make my statement right (ja!). Now seriously, are you trying to convert me to a negative formula follower? I’m starting to see its “naturality”. Since “p” includes “pq” and “q” includes “pq” substracting “pq” does the job. The sentence should be “p or q or both (but not both more than once!)”. Venn diagrams are so simple and so clear, much easier to understand than these words.

]]> Comment on The temblor forecast by: Barry Cipra http://bit-player.org/2008/the-temblor-forecast#comment-1680 Thu, 24 Apr 2008 14:29:42 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1680 The real problem with Seb's interpretation is he doesn't say what "but" translates to. It seems to me it's a synonym here for "and", but (and?) "(p or q) and not (p and q)" translates to (p + q)(1 - pq). The closest one can get is to rewrite p + q - pq as p + q(1-p), which corresponds to "p or (q and not p)." One virtue of the "negative" formula 1 - (1 - p)(1 - q) is that that form makes it easy to see that the result is less than (or equal to) 1, which is less clear from the p + q - pq formula. The real problem with Seb’s interpretation is he doesn’t say what “but” translates to. It seems to me it’s a synonym here for “and”, but (and?) “(p or q) and not (p and q)” translates to (p + q)(1 - pq). The closest one can get is to rewrite p + q - pq as p + q(1-p), which corresponds to “p or (q and not p).”

One virtue of the “negative” formula 1 - (1 - p)(1 - q) is that that form makes it easy to see that the result is less than (or equal to) 1, which is less clear from the p + q - pq formula.

]]> Comment on The temblor forecast by: brian http://bit-player.org/2008/the-temblor-forecast#comment-1679 Thu, 24 Apr 2008 12:03:32 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1679 @Seb: That mapping between logical and arithmetical operators is appealing, but it always seems to lead me astray. The logical expression “p or q but not (p and q)” corresponds to the exclusive or relation. The mathematical expression “p + q - pq” calculates something else -- something that, translated into the language of logic, corresponds to the inclusive or. Think of a Venn diagram drawn in a square of unit area and containing two overlapping blobs labeled p and q. Following the logical formula “p or q but not (p and q)” we color p and we color q but then we erase the area of overlap, leaving p xor q. Whereas “p + q - pq” tells us to take the area of p, add the area of q, then subtract the area of overlap. But the result of this process is not p XOR q; it's p OR q -- the area of the square occupied by either p or q or both. The formula for the area of p XOR q would be p + q - 2pq. Which is why I always lean toward the "negative" formula, 1 – (1 – p)(1 – q). @Seb: That mapping between logical and arithmetical operators is appealing, but it always seems to lead me astray.

The logical expression “p or q but not (p and q)” corresponds to the exclusive or relation. The mathematical expression “p + q - pq” calculates something else — something that, translated into the language of logic, corresponds to the inclusive or. Think of a Venn diagram drawn in a square of unit area and containing two overlapping blobs labeled p and q. Following the logical formula “p or q but not (p and q)” we color p and we color q but then we erase the area of overlap, leaving p xor q. Whereas “p + q - pq” tells us to take the area of p, add the area of q, then subtract the area of overlap. But the result of this process is not p XOR q; it’s p OR q — the area of the square occupied by either p or q or both. The formula for the area of p XOR q would be p + q - 2pq.

Which is why I always lean toward the “negative” formula, 1 – (1 – p)(1 – q).

]]> Comment on The temblor forecast by: Barry Cipra http://bit-player.org/2008/the-temblor-forecast#comment-1678 Thu, 24 Apr 2008 03:24:43 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1678 Inclusion, exclusion. Inclusion, exclusion.

]]> Comment on The temblor forecast by: Seb http://bit-player.org/2008/the-temblor-forecast#comment-1677 Wed, 23 Apr 2008 16:10:51 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1677 I find it easier with the second formula. I think that "p or q but not (p and q)" is more naturally translated as "p + q - pq" where: "or = +" , "not = -" and "and=product". I find it difficult to "see" the other formula in this simple way. Anyway, two ways to do the same thing are better than one. I find it easier with the second formula. I think that “p or q but not (p and q)” is more naturally translated as “p + q - pq” where: “or = +” , “not = -” and “and=product”. I find it difficult to “see” the other formula in this simple way. Anyway, two ways to do the same thing are better than one.

]]> Comment on The temblor forecast by: brian http://bit-player.org/2008/the-temblor-forecast#comment-1676 Thu, 17 Apr 2008 13:41:36 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1676 Hmm. Math brain, computer brain.... There's also logic brain. I find the formula 1 – (1 – p)(1 – q) much more congenial, and more useful in practice, because it embodies a simple Boolean equivalence: "one or the other or both" is the same as "not neither." Understanding the formula p + q – pq in the same intuitive way requires a tad more thought -- and I have so little of that to spare! But perhaps there are people who have the opposite response? Hmm. Math brain, computer brain…. There’s also logic brain. I find the formula 1 – (1 – p)(1 – q) much more congenial, and more useful in practice, because it embodies a simple Boolean equivalence: “one or the other or both” is the same as “not neither.” Understanding the formula p + q – pq in the same intuitive way requires a tad more thought — and I have so little of that to spare! But perhaps there are people who have the opposite response?

]]> Comment on The temblor forecast by: Jim Ward http://bit-player.org/2008/the-temblor-forecast#comment-1675 Thu, 17 Apr 2008 11:18:55 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1675 I've been doing some reading on computational complexity, and in math brain the statement "1 – (1 – p)(1 – q), or p + q – pq" would zing by unnoticed, but in computer brain it scans as "he's replaced 3 subtractions and 1 multiplication with 1 addition, 1 subtraction, and 1 multiplication". It has given me an appreciation for the (unnamed?) discoverer of the distributive law. I’ve been doing some reading on computational complexity, and in math brain the statement “1 – (1 – p)(1 – q), or p + q – pq” would zing by unnoticed, but in computer brain it scans as “he’s replaced 3 subtractions and 1 multiplication with 1 addition, 1 subtraction, and 1 multiplication”. It has given me an appreciation for the (unnamed?) discoverer of the distributive law.

]]> Comment on The temblor forecast by: Lord http://bit-player.org/2008/the-temblor-forecast#comment-1673 Tue, 15 Apr 2008 19:56:24 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1673 There probably is some correlation since aftershocks are fairly frequent. Actually even if you are 30 miles away, this is not that significant. There probably is some correlation since aftershocks are fairly frequent. Actually even if you are 30 miles away, this is not that significant.

]]> Comment on The temblor forecast by: Anonymous http://bit-player.org/2008/the-temblor-forecast#comment-1672 Tue, 15 Apr 2008 17:40:02 +0000 http://bit-player.org/2008/the-temblor-forecast#comment-1672 If they were independent, it would be 99.8%. If they were negatively correlated, it would be more (up to 100%). Since it is less, they must be positively correlated---which is counterintuitive. A simpler explanation is just that the numbers have been rounded. If they were independent, it would be 99.8%. If they were negatively correlated, it would be more (up to 100%). Since it is less, they must be positively correlated—which is counterintuitive. A simpler explanation is just that the numbers have been rounded.

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