Exposing PseudoAstronomy

August 30, 2011

Richard Hoagland’s Selective Numerology of Comet Elenin


Comet Elenin has been in the “alternative” media a lot for the past few months for reasons that I cannot fathom other than to think that the state of mind of most people has regressed several thousand years. I haven’t done any posts on it because there’s simply nothing to “debunk” as there’s nothing marvelous to report about it.

Putting that aside, Coast to Coast AM‘s science advisor, Richard C. Hoagland, was on last night (August 29/30) for two hours espousing more about his hyperbolic geometry and its relation to Comet Elenin. Far from being doomy and gloomy, Hoagland seems to believe that Elenin is actually an advanced spaceship sent from a previous advanced society from Earth to us to help get us out of trouble.

His evidence? Numerology.

The Magical Statistical Thinking of Richard Hoagland

Before I start, I have to say, I am not making this up.

Now that that’s out of the way, Hoagland claims that the chances of Elenin approaching the inner solar system as-is is less than 1 in 230 million. Therefore it has to be artificial. How does he get to that number? This way:

  1. The Russian mathematician, Leonid Elenin, who discovered his now namesake comet, did so when the comet had a magnitude (brightness) of +19.5 (this is actually really faint). Hoagland says the brightest comet observed was in the 1960s and was -17 magnitude, while the faintest is Halley with the Hubble Space Telescope in 2003 and it was at +28.2 magnitude. So with a range of 45.2 magnitudes, the chances of finding it at 19.5 is 1 in 45.2.
  2. The odds of Elenin visiting Earth on a particular day, in this case Sept. 10/11, is 1 in 365.
  3. The odds of it visiting on the 10th anniversary of the Sept. 11, 2001 terrorist attacks on the US, are 1 in 10.
  4. Elenin’s closest approach to Earth will be on a (unimportant to Richard) day but at 19:50 GMT (remember, 19.5 is a magical number to Richard). So that’s a 1 in 1440 chance (60 minutes times 24 hours in a day).

At this point, if we multiply these numbers together, we get a 1:237,571,200 chance. Wow!

Hoagland then makes a big deal about the comet being on a hyperbolic orbit (meaning that the eccentricity is >1.0 (e=0 is a circle, 0<e<1 is an ellipse, e>1 is a hyperbola)). He claims that this is the first comet ever found to be on a hyperbolic orbit.

But there's more that he then goes into:

  1. The comet has an orbital inclination of 1.84° to Earth. He takes the 360 degrees in a circle and divides by 1.84° to get 195 (remember, 19.5 is important to Richard).

Multiply that in and you get odds of 1:46,481,321,739. Wow!

Does Any of That Make Sense?

To put it succinctly, “no.” If you want the long version …

Point 1. Richard has to know with this point that he’s full of it. First, he’s wrong about comet C/1965 S1, AKA Ikeya-Seki. It reached magnitude -10, not -17. Because the magnitude scale is logarithmic, Richard is wrong by a factor of about 1000x in brightness. But besides this, comets are not discovered when they are at their brightest. They are usually discovered when they are around the position of Jupiter in the solar system and are somewhere in the upper teens on the magnitude scale. In the case of Ikeya-Seki, according to the all-knowing Wikipedia, the comet was “first observed as a faint telescopic object on September 18, 1965.”

In terms of how faint a comet can be and still be visible, Hale-Bopp will pass from visibility in about a decade when it nears +30 magnitude, so Richard is probably right about his +28ish as the faintest. But then, why did he use integers in his math? Why didn’t he say that the chances of it being discovered at 19.5 was one in 452 instead of 45.2? You could really make anything up here.

But regardless, as I said, the majority of comets are detected in the teens of magnitude, so I’ll give this perhaps a generous realistic probability of 1 in 5.

But even then, so what?

Point 2. This whole thing with the odds of something happening on a particular day really bugs me. It’s the same issue I have with the Global Consciousness Project in terms of what constitutes a “significant event.” In this case, Hoagland is claiming that the odds of its closest approach to the sun on a particular important anniversary in the US are 1 in 365. True. But what about it happening on Christmas? Thanksgiving? V-Day? D-Day? Pearl Harbor Day? A presidential election? Mother’s Day? What about Bastille Day? Guy Fawkes Day? Boxing Day? Cinco de Mayo?

And why just its closest approach to the sun? What about when it crosses Earth’s distance inboud? Outbound? Closest approach to Earth inbound? Outbound? Crosses Venus, Mars, Mercury, Jupiter?

This is the problem with a retrodiction — you can find almost anything significant somewhere in the world when you have a day and/or time as your constraint. I’m giving him even odds on this one, 1 in 1.

Point 3. I should probably combine the whole 10th anniversary thing with the previous point, but suffice to say, this is again nothing significant. If it were the fifth anniversary, he’d claim significance. Second, third, fourth, fifth, etc. And he’d continue to give the 1 in 1, 1 in 2, 3, 4, 5, etc. odds, despite these odds really not meaning anything because you could say, “What are the odds that out of a hundred anniversaries, it would be on the 10th? That’s 1 in 100, not 1 in 10!” So again, I’m giving him even odds on this one that he’d find something significant.

For those of you keeping score, we’re at 1:5, not 1:164,980.

Point 4. Yet again, the 19.5 number. Except, not. 19.5 hours GMT would be at 19:30, not 19:50. And, you could really choose any time zone around the world. So if Richard is allowing a ±20-minute window around 19.5 hours and we can choose any time zone, then this is a 2:3 chance, not 1:1440.

Point 5. There are a few things wrong with this. Well, two. First, 1.84 divided into (not by) 360 is 195.65217… . Rounding, this is 196, not 195. It’s also, well, 196, not 19.6. But besides this, his math is wrong because it “should” be 90/1.84. This is because if the comet were approaching from the “other” direction, it would still have that same angle relative to the plane of the solar system, so we’ve now cut our 360° circle in half to 180°. Second, if it were coming below the plane of the solar system, it would still be listed as having an inclination of 1.84°, so we’ve cut the circle in half again to 90°.

So it’s really a 1 in 48.9 chance that the inclination would be between 0 and 1.84°, a fairly insignificant inclination angle since most objects in the solar system orbit in roughly the same plane. You would have to multiply this into the probability distribution of inclination angles of known long-period comets to actually get the odds, and I’m not going to bother going through that math as I think we can agree at this point that it’s, again, an insignificant number.

So in the end, we have a roughly 1 in 5 chance that Elenin would have the level of significance that Hoagland places on it. Not 1 in 46 billion.

In addition to all this, though, Hoagland is wrong about this being the only comet on a hyperbolic trajectory. In fact, there are 259 known comets with hyperbolic orbits. And, while Elenin had an eccentricity of 1.0000621 early on, it was perturbed into that and is continuing to be perturbed such that when it exits the inner solar system should have an eccentricity of around 0.9991 (source).

Final Thoughts

I’m actually prepping a “bonus” episode of my podcast to come out on Sept. 10/11 to talk a bit about the Comet Elenin foolishness that’s going around the interwebz. But this was just too wrong to ignore as I was listening to Hoagland while doing work this morning. I hope that I’ve shown you that this particular brand of numerology is absolutely wrong and completely made up. Besides being magical thinking — he really just made up some of those numbers, completely ignored basic observational methods in others, and retrofitted to significance the rest.

It’s just wrong!



  1. I have not even bothered mentioning Calleman’s coverage of this comet on my blog. Of course, this is related to his distorted version of the Maya calendar…


    Comment by Johan Normark — August 30, 2011 @ 1:48 pm | Reply

    • Yeah, as I said, I wasn’t even really going to get into Elenin because it’s such a non-event that somehow exploded on YouTube and late-night talk shows. But while I was listening to Hoagland for 20 minutes, I kinda had to vent afterwards.

      Comment by Stuart Robbins — August 30, 2011 @ 6:04 pm | Reply

  2. Although I have always thought Hoagland to be a bit ‘iffy’….when I listened to him explain
    the latest on elenin, I found the geometry fascinating , I must admit.

    Physics isn’t always perfect…let’s not forget what happened with comet 17P Holmes, in 2007..exploding to be the size of the Sun! Comets are all very different…and our “genius” astronomers still don’t understand them. Let’s just wait and see….something is unusual concerning Elenin…I think there might just be some Magic in the Aire…

    Comment by G. Emerrich — August 30, 2011 @ 5:57 pm | Reply

    • Comet Holmes did not “explode to be the size of the sun.” Its coma grew to be about 70% the size of the sun, which is still impressive. That does not mean it has magical numerology associated with it that makes it a spacecraft sent by a previous terran civilization. It’s an argument from ignorance to state that all because astronomers “still don’t understand” comets means that we can start making things up and distorting the actual scientific facts to fit our own numerology.

      Comment by Stuart Robbins — August 30, 2011 @ 6:03 pm | Reply

  3. […] number magic). Numerology is a pointless endeavor (check out Stuart’s take on the numerology of Comet Elenin and you get another idea of how silly this can be). Apart from its pointlessness the 2012 […]

    Pingback by 2012: Maya numerology « Archaeological Haecceities — August 30, 2011 @ 11:24 pm | Reply

  4. Actually, you are correct…it didn’t “explode to be the size of the Sun”…the 17 m. brightened by a factor of nearly 1 million…and was the largest object in the solar system….larger than the Sun.
    The point being made that there is still the factor of unexplained event in the world of science…and yes, there very well could be a ‘magical numerology’ associated with events ….the universe is a great mystery….and I doubt humans have mastered it’s secrets….not yet.

    Comment by G. Emerrich — August 30, 2011 @ 11:49 pm | Reply

  5. it only got bright at all because of the sun G . [last sentence removed by mod due to new comment guidelines]

    Comment by Walter Walkie — August 31, 2011 @ 12:05 am | Reply

  6. I appreciate the sort-out on this as it was bothering me how Hoagland comes up with this stuff… a lot of what he says seems off the wall, and somebody like me doesn’t have the expertise to debate him, but clearly you do. The only thing that really interested me about this comet was the timing of its near Earth orbit passage with the high holy days of Judaism, and I am looking for the photos of it that supposedly show some sort of geometrical polyhedral shape in the impact of the solar wind on it (I guess from when the CME was supposed to have hit it around August 19…. which actually would be quite a rare event to see, wouldn’t it? I mean it’s not every day an object even the size of the Earth gets beaned head on by a solar CME.)

    Do you think Dr. Hoagland has lost his marbles?

    Comment by Harry Van Twistern — August 31, 2011 @ 5:53 pm | Reply

    • A few points here, Harry. First I’m not sure what to make of Mr. Hoagland. On its face, he certainly seems to be committable to a white padded cell, in my opinion. However, I have talked with several other people, who I will not name, who state unequivocally that he knows he’s making it all up and just keeps doing it anyway. In the end, I’m not sure it matters, though, since he’s still saying it and he still has a gigantic audience.

      On your other point about a CME, it’s not “every day” that objects get hit with CMEs, but it’s by no means a rare event. Off-hand, I think it’s at least once a month during solar minimum that the sun spits one out, and it’s likely several times a month during solar max. The probability of that CME hitting something is therefore not very rare since they spread out as they travel from the sun.

      I saw Hoagland’s image of the tetrahedral image of the comet, and I have to say I’m not impressed. The image shows the comet and what seems like it could be a bit of a coma that is then blurred into a few surrounding stars. This is something that Hoagland does >75% of the time — he uses under-resolved images, blows them up, and then claims structure in the artifacts. By the same token in that image, the star on the far left side is tetrahedral. The three objects on the far right are connected by lines, oh gee, I guess it’s a space bridge. In all objectivity, though, you need more resolution and need to image it in a few nights to see if those corner points are distant stars (so the comet will have moved) or whether they move with it. That would be the objective way to tell, if you don’t believe me that it’s an artifact.

      Comment by Stuart Robbins — August 31, 2011 @ 6:02 pm | Reply

      • Considering how Hoagland approaches critics on his own page, he most definitely knows he’s full of it. He’s just counting on the faithful knowing even less about science and math than he appears to.

        Comment by Chris L. — September 13, 2011 @ 10:25 am

  7. : is to, not in.

    Comment by Autymn D. C. (@alysdexia) — September 1, 2011 @ 12:00 pm | Reply

  8. And CMEs don’t travel! They fare or wend.

    Comment by Autymn D. C. (@alysdexia) — September 1, 2011 @ 12:03 pm | Reply

  9. A point you missed is that Hoagland’s method of computing the probability of Elenin’s exact orbital inclination is mathematically absurd. It creates a divide-by-zero for comets in the ecliptic, and assigns variable probability to inclinations other than zero — from very improbable at low inclinations to even-odds near 90°. Obviously all inclinations should have equal probability.

    I think he’s mad, quite frankly.

    Comment by Expat Stu — September 13, 2011 @ 9:18 am | Reply

    • Quite right — I got into that a bit with the whole magnitude thing, but I left it off with the inclination. Should’ve mentioned it again.

      Comment by Stuart Robbins — September 13, 2011 @ 4:20 pm | Reply

    • He uses discrete probability instead of continuous: a mistake so obvious, that anyone with a basic knowledge of calculus could’ve pointed it out. He pretends to have expertise in ‘advanced science’ but doesn’t even understand the basic rules of integral calculus, probably never even heard of it.

      Comment by Marco — March 19, 2012 @ 6:14 am | Reply

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