Friday, September 9, 2011

Probabilities and nincompoops

        Well, now we know why that fellow Mark Ward, attender at the Leeds Conference, exclaimed "Get this... the chances of the comet's data being naturally occuring coincidences is 44 billion to one!" He was citing Richard Hoagland's presentation on Comet Elenin, of course.

        While I was on my Spanish beach, on August 29th, Hoagland went through the pseudo-arithmetic that allowed him to make that claim, on Coast to Coast AM (hour 4.) He did it by cascading the probabilities of a given apparent magnitude, a given date of perihelion, a given anniversary, a given time of closest approach to Earth, and a given orbital inclination. Here are his figures. (CAUTION: Reading this may cause severe nausea and heart palpitation in anyone familiar with mathematics and/or statistical analysis. Proceed at your own risk.)

STEP 1: Apparent magnitude
        The first recorded magnitude, by Leonid Elenin himself, was 19.5. Oh, what a gift for the "theory" of hyperdimensional physics—even though, of course, an astronomical magnitude is totally irrelevant to an angle measured in degrees.

        Hoagland asks "WHAT ARE THE ODDS of a comet having this particular magnitude?" He answers himself "The brightest comet ever recorded had a magnitude of -17. The dimmest was +28.2. That's a range of 45.2. So the odds are 1 in 45.2."

STEP 2: Date of perihelion
        Hoagland still insists that the date is September 11th even though it's the 10th everywhere except Japan and Australia. He says the odds of that date occurring are 1 in 365.

STEP 3: Anniversary
        Even though he has the wrong date, he still insists that the attacks on 9/11/01 are important. He says that fact that this is not JUST ANY anniversary, but the tenth, allows him to factor in odds of 1 in 10.

STEP 4: Time of closest approach to Earth
        The time is 19:50 UTC on October 16th. Hoagland confuses the time of 19:50 with the decimal 19.5, but let that pass. He asks WHAT ARE THE ODDS of that particular time occurring and, multiplying 24 x 60, he arrives at 1 in 1440.

FINAL STEP: Orbital inclination
        Elenin's inclination is 1.84°. Hoagland figures the odds of that occurring are 360/1.84 or 1 in 195. (and of course he can't resist pointing out the magic 195 again.)

The odds are...

        Hoagland multiplies 45.2 x 365 x 10 x 1440 x 195 and arrives at 45,000,000,000. Stunning. Or not.

What's wrong with this picture?

        I feel sure many readers of this bloggery are ahead of me, and WAY ahead of Hoagland. Let's see what would happen if the figures were different. How about if the magnitude were 14.6, the date of perihelion were 3rd July, the anniversary were the 20th, the time of closest approach were 07:21 and the inclination were 2.02°?

Let's see... tap-tap-tap-tap... Oh, tens of billions.

        How about if the magnitude were -2.0, the date of perihelion were 10th June, the anniversary were the 21st, the time of closest approach were 21:21 and the inclination were 11.7°? Wow, tens of billions again.

        Hoagland has fallen slap bang into the ex post facto fallacy that so many other untrained and ignorant people have fallen into before him. This is like throwing snake eyes in a casino and claiming that your throw is unique in human history. It's true that you only have one chance in 36 of throwing that result, but the odds of the other 20 possible results are also long. WHATEVER you throw has a low probability—until you throw it, then the probability is 100%. Likewise, the parameters of Elenin have to have some values, and multiplying them out as though they were unique is going to yield nothing useful.

        Every single time someone throws a pair of dice, a long shot is pulled off, in other words. Using Hoagland's own perverse ideas, every single time a comet comes through, an event whose odds are 40 billion to one against also happens.



Chris Lopes said...

Actually he's even wrong where he's wrong. The time he states is for a very specific time zone (according to him) so he should have included the number of times zones in his calculations. Also, if you are going to be specific about inclination (BTW, what is special about 1.84?) you have to include the significant digits in your calculation. In this case, it would be 360/.01 or 36000 to 1. Of course since his basic assumption is completely bogus, little math errors don't matter.

Chris Lopes said...

Expat, you might want to cover the infamous "tetrahedral shield" issue (Don Davis did some work on that: and the disintegration (or not according to Hoagland)of Comet Elenin.

Anonymous said...

It's painfully obvious that RCH never had to sit down and solve an actual combinatorics problem in any probability course.
The range for a couple of those parameters could actually be tending towards infinity, depending on instrumentation, methodology and precision of the measurements.[ Apparent magnitude & Orbital Inclination].
Doesn't he actually make the case for the randomness of the event ?

Chris Lopes said...

Exactly right on the infinity argument. I hadn't thought of that.

Anonymous said...

EXPOSING PseudoAstronomy.

Episode 4 (BONUS): Comet Elenin Special

NOTE: This episode was slightly updated and re-posted as of September 10, 2011, 5:00 GMT.

Recap: For some odd reason, there are a lot of crazy claims out there about Comet Elenin. In recognition of its closest approach to the sun on September 10, this bonus episode addresses many of the common claims out there about the comet including an exposé into Richard Hoagland's magical numerology that apparently proves i'ts a spaceship.

Chris Lopes said...

That was a great link. He nailed Hoagland's calculations to the wall. The use of histograms to find the REAL probability was particularly helpful. I'll be going back to that site again, that's for sure.

Biological_Unit said...

I think yous probably spend more time thinking about RCH's bogus theories than his 'tards. They "feel" at issues!

Chris Lopes said...

I'm afraid you are right.

Tim Oldfather said...

I was actually embarrassed for Hoagland when I heard him venture into probability on C2C.
I believe the odds on rolling snake eyes actually is 1/36.

Chris Lopes said...

I'm not sure "embarrassed" is the right emotion on this one. Remember, he got PAID for that work both at Leeds and probably on the Camelot web-conference. He's also likely to use it at the conference he's doing on the 23rd. As mathematically absurd as it might be, it's working for him. I'm more appalled than embarrassed by that.

expat said...

I say 1 in 21 because there are repetitions. For example, a 6/2 is the same as a 2/6 because you don't care which die has the 6 and which has the 2. Small point.

Tim Oldfather said...

Yes a small point expat. there are 36 possible rolls 6 2 is different then 2 6. Consult a basic backgammon book and avoid the craps table :--)

1/36 is correct.

expat said...

Yep, you're right. I've corrected it. Slightly embarrassing since I was taking Hoagland to task for bad odds-calling. Thanks for picking that up.

Chris Lopes said...

At least you can admit your mistakes. Tim gently and jokingly suggested (on Hoagland's FB page) that Richard consult a mathematician before trying to work out probabilities. That comment was promptly taken out behind the barn and shot. The pseudo-scientific method in action. :)

Tim O. said...

Hoagland's tolerance for descent has certainly decreased. I had some interesting exchanges with him but now my posts are just deleted. Some of his supporters have expressed their displeasure at this "censorship".

expat said...

I just had a look and it seems plain that, by chasing away anyone with any kind of clue about physics and astronomy, he's left himself by default with the crazies. Perhaps that makes him happy.

Chris Lopes said...

For what it's worth, there is a downside to that strategy for him. He is constantly having to answer really stupid questions (like when is Elenin going to hit Earth) that interrupt his narrative. The faithful are as undisciplined as they are gullible.

Anonymous said...

Be on the look out for reactions to these:

expat said...

Is there a 19.5 anywhere in there? GOD I hope not...

Anonymous said...

There is.
We just don't know it yet.
:D :D :D

Chris Lopes said...

Well I'm sure it was 19.5 hours (using HD-Math) somewhere on the planet when the announcement was made, and that somewhere was somewhere IMPORTANT! :D

expat said...

While we're waiting for confirmation, we'll have to be content with jokes like this:

"We don't allow faster than light neutrinos in here" said the bartender.
A neutrino walks into a bar.

Virgins Online said...

As much as i think hoagwash is a cretin, I think you lot are as pathetic as him. I would not give him a second thought, you lot, seem to give him many thoughts, how sad is that?

expat said...

Virgins: Pretty sad, I guess. I'm in semi-retirement so I don't have to justify my time to anyone.

Thanks for the contribution.

Chris Lopes said...

Some of us just find discussing the crazy ideas of kooks like Hoagland and the people who follow him entertaining. If that's not your idea of entertainment, so be it. :)