William M. Briggs

Statistician to the Stars!

Author: Briggs (page 151 of 537)

Richard Dawkins Is A Dangerous Man: Update

I’ll tell you how. He makes people feel smarter than they are. And in our world of self-esteem substituting for accomplishment and ability, his villainous power is especially poisonous.

For instance, he recently retweeted with approval these words: “Most abortions are performed on women, so men should not be involved in making laws about it.” Now I confess this made me giggle, and I replied, “Most murders are committed by men, so women shouldn’t be involved making laws about it.”

See what I mean? It is an objective truth that such a simple, sub-Freshman-level fallacy can be refuted by a business major with an SAT of 400 (total) who has spent the week on a bender pledging fraternities at the wrong campus. But I still felt pride in refuting it myself. I know that responding to his tweets is the equivalent of completing the TV Guide crossword clue “___________ in the Family”, sitcom (3), yet still I did it.

Worse, after answering, I felt I had done something, that I gave my intellect a workout, that I was ready to publish a Grand Unified Theory. All false.

But I had not yet reached bottom. Just like the poor student who can only study what he already knows, I couldn’t stop playing with Dawkins. Take this one (which I learnt from Wesley Smith):

I think I actually rubbed my hands together, so happy was I to see this. Where to begin? Pointing out pigs aren’t human but fetuses are? Stating that makin’ bacon and killing a life inside a woman are not equivalent nor comparable? So many possibilities! All trivial.

I was not the only sinner. Many responded to this tweet, which so disconcerted Dawkins that he answered several times.

  • “Human” features relevant to the morality of abortion include ability to feel pain, fear etc & to be mourned by others (link)
  • Yes, anything can be mourned. If you are going to mourn your fetus, you are free to not have an abortion (link)
  • Of course potential to be human is among fetus’ qualities. But my pig comparison was careful to specify “relevant to morality of abortion.” (link)
  • My hair and fingernails are human but don’t feel pain when I cut them. Embryo before brain develops doesn’t feel pain. Late fetus? Pig? (link)
  • Woman’s right to own body is good but not BEST pro-choice argument. Better argument would be abortus doesn’t feel pain. I’m pro choice. (link)

May the Lord forgive me, but I cackled and told myself how clever I was after thinking such “weighty” thoughts as these: A biologist who says his hair and fingernails are human? What’s next? Marches against the wholesale slaughter at nail salons and barbershops? A biologist who says a fetus only has the “potential” to be human? If it isn’t human, but will be, what is it now? What divine act makes it human? Stop me!

Dawkins (who isn’t alone; Sam Harris and others join him) supposes pain the universal moral standard in a universe without moral standards—a contradiction! Should I tell him? Those without pain can be killed. So it follows patients undergoing general surgery, and therefore in no pain, can be whacked wily nily? That the younger or drunker your victim, or the less likely you are to mourn him, the less culpable you are? Too easy! Too easy!

I became like the alcoholic who thinks one small drink won’t hurt him. I’ll have a sip and stop, I’ll respond to just one more tweet. But Dawkins is like an unlocked liquor store after the zombie apocalypse. He never stops providing opportunities for his opponents to gloat, and therefore darken their souls with pride.

Oh dear. A restrained man would let this pass. Instead my thoughts were uncharitable and simple, though I thought them wise. Through my fault, my fault, my most grievous fault, I kept reading.

A biologist who intimates identical twins are the same human being? Enough! If I continue, I’ll start watching The View or listening to NPR so that I can poke holes in their “profundities.” All that will be left to me is a recurring role as a talking head on MSNBC.

For a brief moment I comforted myself with the idea that if I found myself more intelligent than I truly was, Dawkins’s supporters, those poor souls convinced by his arguments, suffered far worse than I. But the comfort turned to grief when I realized the consequences.

Update I am incorrigible, an inveterate backslider. I ask for your prayers.

Update I’m going to have to cancel my Twitter account. “And if thy right hand offend thee, cut it off, and cast it from thee: for it is profitable for thee that one of thy members should perish, and not that thy whole body should be cast into hell.”

Climategate 3.0—Update: Hacker A Coder?

Whoever it was that snatched the cache of emails from prominent climatologists and created Climategate 1.0, then 2.0 has come forward, in a sort of way, to begin Climategate 3.0. He—sounds like a he, perhaps a Russian he?—sent an email to several climate scientists explaining why he did what he did, and including a password to open 200,000 files that have been previously hidden. (I wasn’t one of these; I don’t have the files nor the password.)

The hero/thief/activist/concerned citizen-of-the-world, call him what you will, I prefer jokester for this individual has a fine sense of humor, is clearly a computer geek and is careful covering his tracks. His missive can be read in several places, such as at Anthony Watt’s place.

I have not seen the file nor the password, but others have started burrowing through. Early results suggest, as Tom Nelson discovered, much boredom awaits. There has been a tidbit or two, such as one email from a serious, working, peer-reviewed and -reviewer climatologist that called Mann’s hockey stick “crap.” This curiously is the precise statistical word to describe Mann’s work, so perhaps it was a statistician and not climatologist who wrote those words.

This means the, the, THE, THE Consensus isn’t. Ah well.

The other (so far) slice of fun came from my pal Gav Schmidt, who in reaction to the refreshed controversy tweeted this:

This is the interest over time in Climategate. I must admit this curves tracks my attentiveness, too. But here’s why this is funny. A new email from Tom Wigley admits the pseudo-science (actually cheap journalism) of counting papers as proof of consensus or truth. After trying his own hand at counting citations, he said:

Analyses like these by people who don’t know the field are useless.
A good example is Naomi Oreskes work.

The press naturally loves Oreskes’s work, because journalists nearly always fall prey to and cherish the fallacy that interest equals truth. But Oreskes has always been engaged in persiflage.

So we now understand that plots of interest are a standard newsman’s dodge and reveal nothing but political hotness. This includes Gav’s plot, which is misleading even as a political thermometer, since it was taken before Climategate 3.0 hit.

Ah well, so much of science is theatre these days, yet another avenue for agitation. I’m guessing 3.0 doesn’t reach the peak that 1.0 or 2.0 did, since, though activist scientists haven’t yet ceased discovering new ways to announce the sky is falling, people have tired of hearing them.

But see this page for updates which I find of note.

Update May as well engage in amateur forensics. I think the hero-hacker is a coder. The facility with all things computer makes this easy to guess, but so does his language, which doesn’t sound like a scientist but with somebody who works with them. He also appears to be somebody who uses English for his day job, but whose native language is something else.

Probably a coder tasked with implementing parts of climate models (data assimilation, connectivity between modules, output generation, etc.) and who sees these creations resemble smelly sausage rather than prime rib. Somebody who is aware that the certainty and confidence publicly stated in the models is far more than is actually warranted.

How Long Do Popes Serve? Update

Update 14 March 2013. The Guardian has released the data on the popes. Its list and mine differ trivially, except that they were able to include the popes’ ages (starting from around 1400). It’s fun to compare the graphs they derived versus mine below. God bless Pope Francis.

Update 11 February 2013 (original date: 12 November 2012): Pope Benedict to Resign.

Easy stuff

Here, for no particular reason other than curiosity and because it’s Saturday, is a brief analysis on how long Popes have served. All data was retrieved from New Advent’s Catholic Encyclopedia.

The first Pope, St Peter, a buff fisherman nicknamed “The Rock”, had the longest go thus far, at about 36 years; perhaps not precisely 36 years because of course dates that far back are imprecise. Still, he had a good, long run.

The shortest term of office, rounded to the nearest year, was 0 years was by Stephen II in Anno Domini 752, who was made Chief “but on the third day after his election, whilst transacting some domestic affairs, he was struck with apoplexy, and expired on the next day.” And this was in the time before twenty-four cable news programs.

This picture shows the frequency of term of service in years (all dates rounded up to the nearest year; so that somebody serving 0 up to 12 months is counted as one year, etc.).

Frequency of Papal Years of Service

Serving just 2 years was the most common, with about half of all Popes serving 6 or fewer years Pope is a stress filled job, which might be why so many don’t last so long.

Blessed Pius IX, with 33 years served from 1846 to 1878 came in second place behind St Peter. Blessed John Paul II was second runner up and sat in office from 1978 to 2005. Lucky us! These last two data might indicate that Popes are serving longer terms lately. This next picture examines that.

Timeline of Papal Service Length

A vertical line representing the years of service for each Pope is drawn at the year in which they began office. Again, St Peter sticks above all the rest. A black dot is indicated for Benedict XVI, as he is still, thank God, beavering away. Update He made it eight years! The plots reveals that after about 1600 or 1700, longer terms of office were more common. Well, no surprise. This is when health took a turn to the north for all mankind on average.

Not for everybody, naturally. John Paul I served for only 33 days in 1978. And Pius VIII made it only 2 years starting in 1829. But all the other gents from 1670 onwards cruised through 6 or more years. Things were dicier for Popes between roughly 500 to 1200, but then this was a tumultuous time in history. Somehow, even with diets nearer to what is nowadays close to scientifically said to be ideal, people didn’t live as long as they do now. Science has no answer.

Natural comparisons to Popes would be presidents, kings and other leaders of large organizations. I’m guessing the distribution in length of service won’t be too different, especially in those institutions which appoint members for life.

I’m still collecting the birth years of the Popes and other information. When I have it (or people can point me to data sources where the collection is already done?) I’ll post new entries.

Update Not all Popes served for life, like Supreme Court judges. Example: Benedict IX took his turn in the Chair three separate times (he’s only given one entry for his total above).

Not so easy stuff

I wondered whether long periods of service were followed by short periods, perhaps because of institutional fatigue or suspicion. Or maybe the opposite was true and long periods were followed by long periods, perhaps because of good will. It could even be that both tendencies held but at different eras. The following picture helps.

Changes in Papal Service Length

St Peter served 36 years and his successor, St Linus, served only 10. Thus the first line is at -26, indicating the successor served twenty-six years fewer. And so on for the remainder of the Popes. The little “blips” at 0 indicate successors who served identical terms to their predecessors.

I can’t see any pattern, which doesn’t say too much, except that there is no pattern which strikes the eye. Counting shows that 123 successions were shorter, 17 were the same, and 122 were longer as their predecessors. The obvious and expected conclusion is that succession is a far more difficult process than captured in these simple numbers.

Paddy Power’s Pope Predictions—Update

Father Dougal is the farthest left

Update See below for main update.

The odds of Father Dougal Maguire (Craggy Island) being the next Pope are 1,000 to 1. You may say this is small, but it’s orders of magnitude a better chance than you have, or has Your Truly, who meets all the qualifications for the office: being a man and Catholic.

Don’t look for me in sitting in St Peter’s chair because, according to the odds maker Paddy Power, even Richard Dawkins has a better chance than I. He’s currently at 666 to 1.

Clearly, Paddy Power is posting these bets (he also has Bono at 1000 to 1) as a novelty, assuming people would pay a Euro or two for the joy of having a slip with Christianity’s self-appointed nemesis’s name printed on it as being the next Pope.

In top spot, as of this writing, Power puts Archbishop Angelo Scola (Italy) in the lead at 3 to 1. This translates into a probability of 0.25 (or 25%). Number two is Cardinal Peter Turkson (Ghana) at 3.5 to 1 (or 7 to 2), which is a probability of 0.222 (22.2%). These two gentleman have been switching places with other for the past couple of weeks. Now one will lead the betting, now the other.

The odds are set by Power with two constraints: the amount of money attracted by each of the various candidates and his (Power’s) goal of making a profit—not to say prophet. (That one is up to the Lord.)

If punters had a fly (or a bug) on the wall of the Conclave, and all their money was flowing to Candidate A, then Power would be forced to change the odds of this candidate. For example, if all the money were going to Turkson, and none to any other candidate, Power would put the odds of Turkson at (say) 1 to 10,000, which means betting 10,000 Euros would win you 1 if Turkson were elected. This would discourage most bettors, which is the point.

But suppose there were only two candidates (Turkson and Scola, say), and that money was flowing to both equally. Then Power would put his odds at close to, but not equaling 1 to 1. Odds of 1 to 1 translate to a probability of 50%. That 50/50 would reflect the “wisdom of the crowd” all right, but it would not allow Power to make any money. This is because all the money that was bet for the losing candidate would have to be paid out to those who picked the winner.

Power, like all bookies, makes his money by creating a “Dutch book” against the bettors. That is, he has to adjust the odds so that, no matter who wins, he takes a profit. That link explains the mathematics of Dutch books, but all we have to know is that the probabilities implied by the odds must add to more than 1. If they do, then Power is guaranteed to make money no matter which man is elected Pope.

This is why if there were only two candidates in the pool, setting them both at 1 to 1, which is 0.50 for each, is not a Dutch book. Obviously, (but not to graduates of New York City high schools) 0.5 + 0.5 = 1, which is not greater than 1. But if both had odds of 1 to 2, which is a probability of 0.66 (66%), then 0.66 + 0.66 = 1.33, which is greater than 1 and thus guarantees a profit for the bookie.

Having the sum greater than 1 implies the amount of money paid out by the bookie must necessarily be less than the amount of money he collected in the form of bets. And this is so no matter who wins. Without going into the guts of it, the further the sum of the implied probabilities are from 1, the more money the bookie keeps.

The sum for Paddy Power’s (current) Pope pool is 1.88, which is very far from 1, and which means that Power will make a profit, and a healthy one, no matter who is picked to serve (this assumes he is also adjusting the odds by the money bet, as discussed above, and which he is surely doing for the top candidates, but probably not for the bottom ones, meaning his profit will be less than the 1.88 implies). Discounting the three novelty bets (Maguire, Dawkins, and Bono) changes the conclusion not at all, since the odds for these non-starters is so long. Indeed, as said above, money for these gents is pure profit for Power (only Bono is eligible).

The mathematics thus hints at a strategy for the bookie: increase the number of candidates. On average, the wider the field the large the sum of the implied probabilities. Of course, the bookie has to have actual money bet on each of the candidates in the field. If he didn’t, then he could just put odds of a million to one on each member of the phone book (a strategy which would push the implied probability sum greater than 1 every time).

For what it’s worth, my money is on Turkson—but there may be a bit of wishcasting there, too.

Update If we assume only the top n candidates are having actual bets placed on them, then the sum of implied probabilities first rises above 1 for n = 8 (it’s 1.03). The lowest rank candidate of the eight has odds of 18 to 1. But this would leave out Cardinal Dolan at 20 to 1, who we can guess is drawing bets. If we include all those candidates 20 to 1 or better, then the sum is 1.22; a good profit.

Update I can’t believe I forgot renormalization! It’s a way to more closely estimate probabilities given the “vig” (one of the insider names for the Dutch book), and assuming calibration and other things that we’ll deal with another day. Idea is to take every implied probability and divide by the sum of probabilities. Assuming the 20 to 1 odds cutoff mentioned in the last update, this means that Scola has probability 0.21 (21%), Turkson 0.18 (18%), and anybody but these two 1 – 0.21 – 0.18 = 0.61 (61%).

If the implied probabilities already sum to 1 then renormalization does nothing, as it shouldn’t.

Update Since Power had (now) Pope Francis at 33 to 1, some are asking how much did Power lose since a long-shot came in. None. Power made a profit on the bets. That’s the point of making Dutch book against his punters. Power wins no matter what. See the link to Dutch Book for the mathematical details.

This is the same reason brokers charge “transaction fees.”

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