The Pyramid And The Garden


A recent breakthrough in pseudoscience: the location of the Great Pyramid of Giza encodes the speed of light to seven decimal places.

This is actually true. The speed of light in a vacuum is 299,792,458 meters per second. The coordinates of of the Great Pyramid are 29.9792458° N, 31.1342880° E (you can confirm with Google Maps that this gets you right on top of the Pyramid). The speed of light and the latitude number there have all the same digits. That’s a pretty impressive coincidence.

You might think this is idiotic because the meter was invented by 1600s French people. If ancient aliens or Atlanteans built the pyramids, why would they encode their secret wisdom using a unit of measurement from 1600s France? But there’s a way around this objection: the 1600s French people defined their meter as 1/10,000,000th the distance between the Equator and the North Pole. If the aliens also thought that was an interesting way to measure length, then they could have encoded their secret wisdom in it. So you wouldn’t need aliens who could predict the thoughts of 1600s Frenchmen. Just aliens who thought exactly like 1600s Frenchmen.

(actually, a different group of 1600s Frenchmen proposed a different version of the meter, defined as the length of a pendulum with a half-period of one second. This turned out to be 99.7% of the 1/10,000,000th-the-way-to-the-North-Pole definition, so either one works unless you want super-exactness. I think a much more interesting conspiracy theory would be that aliens designed the Earth to encode secret wisdom about the periods of pendulums.)

But realistically, aliens who think suspiciously like French people probably weren’t involved. So how do we explain the coincidence?


The following is indebted to user mrfintoil’s great explanation on

First, it’s not a coincidence to seven decimal places. Yes, that particular nine-digit sequence lands you atop the Great Pyramid. But that gives you way more precision than you need – cutting off the last three digits actually gets you closer rather than further from the center of the Pyramid. The only numbers that are doing any work are the 29.9792° N. So you really only get four decimal places worth of coincidence.

On the other hand, matching six digits is still pretty good. That’s literally a one-in-a-million chance.

So here the explanation has to go to how hard the pseudoscientists worked to find a coincidence of this magnitude; in other words, how many degrees of freedom they had.

Here’s an obvious example; as far as I can tell, the longitude of the Great Pyramid doesn’t encode anything interesting at all. So it’s not the equivalent of winning a one-in-a-million lottery with a single ticket. It’s the equivalent of winning a one-in-a-million lottery with two tickets.

A second issue: if the latitude of the Great Pyramid had been 10.7925 N, that would be the speed of light in kilometers per hour, which would be an equally impressive match.

So just taking these two degrees of freedom, we have four lottery tickets:

1. The one where the latitude is the speed of light in meters/second
2. The one where the longitude is the speed of light in meters/second
3. The one where the latitude is the speed of light in kilometers/hour
4. The one where the longitude is the speed of light in kilometers/hour

In other words, the number of lottery tickets increases exponentially as we get more degrees of freedom.

Let me list out all the degrees of freedom I can think of and see where we end up. I am going to try my best to be as fair as possible to the ancient aliens. For example, I was considering saying that since there are three pyramids at Giza, we have to multiply by three, but to be honest the Great Pyramid is clearly greater than the other two, and it would be less elegant if Menkaure’s pyramid encoded some amazing cosmic constant, so I won’t raise that objection. I am going to try to be really fricking fair.

1. Latitude vs. longitude (2 options)

2. Speed of light in meters/second vs. kilometers/hour vs. cubits/second vs. cubits/hour. I’m avoiding using feet/miles, because that’s even more arbitrary than meters. But I think it would actually be even more convincing if the calculation actually used the real Egyptian unit, which I understand is the cubit. So let’s go with (4 options)

3. Great Pyramid vs. Sphinx. Like I said before, the other two pyramids at Giza are noticeably less impressive than the Great Pyramid. But the Sphinx is pretty impressive, and the ancient aliens folks talk about it just as much as the Pyramid, so I think that would be an equally good hit if it had been true. (2 options)

4. Use of a 90 degree latitude system vs. use of a 100 degree latitude system. I’m a little split on this one, because it wouldn’t look anywhere near as impressive if the pseudoscience sites had to explain that they found a really cool coincidence but it only worked if you converted normal latitude into a different hypothetical latitude system that had 100 degrees. But since we know the aliens/Atlanteans use base 10 anyway (they’re encoding their wisdom in the base 10 representation of the speed of light) it makes more sense for them to use a base 10 latitude system instead of replicating our own bizarre custom of using base 10 for everything else but having latitude go from 0 to 90. On the other hand, if these were Earth-based Atlanteans, they might have gotten the custom of dividing the circle into 360 parts for the same reason we did – there are about 360 days in a year. And if they were aliens, maybe we got our bizarre latitude convention from them – the idea of 360 degree circles is really old and lost in the mists of time. Overall I can see this one going either way, so I’m going to give it as (2 options)

5. Decimal point placement. The latitude 29.9792 N matches the speed of light exactly, but so would the latitudes 2.99792, 2.99792 S, and 29.9792 S. I checked these other sites at the same longitude as the Pyramid to see if there were any mysterious features. But they seem to be, respectively, a perfectly ordinary field in Uganda, a perfectly ordinary field in Tanzania, and a perfectly ordinary patch of ocean. But a world where the pyramid was in Uganda and the ordinary field was in Egypt would be just as much of a hit as our current world. Therefore (4 options)

From these really simple things alone, we learn we’ve got 2 x 4 x 2 x 2 x 4 = 128 lottery tickets, reducing our 1/1 million chance of winning to something more like 1/10,000. Progress!

There are a few other degrees of freedom that I think are a little harder to judge, but still important:

6. What aspect of the Pyramid we’re looking at. That is, it would have been equally interesting (maybe moreso!) if its height or width matched the speed of light exactly. So that’s another (3 options). I guess if the ancient aliens were really good at what they were doing, they could have given the pyramid 299,792,458 sides, but I won’t hold that against them. This should really make the multiplication more complicated because I can no longer use all the different ways of representing latitude vs. longitude, but I’ll stick with the simple method for now.

7. Which site we’re looking at. This one is hard, because I don’t know if anywhere else has the ancient alien-related credibility of the Great Pyramid. The only equally mysterious site I can think of is Stonehenge, and maybe the Nazca Lines. I don’t feel comfortable saying it would be equally impressive if Tiwanaku or Yonaguni had the right coordinates. I’ll just say (2 options) for Pyramids and Stonehenge.

8. Which constant we’re looking at. Sure, the Pyramid encoding the speed of light is pretty cool, but what about the Planck length? Avagadro’s number? I’m split on whether I want to include mathematical constants like pi or e in here. I think if it encoded pi to some number of decimals places then I would just think that the Egyptians were more advanced at math than I thought but it wouldn’t necessarily be earth-shattering. The Egyptians knowing e would be pretty shocking but still maybe not worth believing in ancient aliens over. There really aren’t that many physical constants as cool as the speed of light, so I might just arbitrarily call this one (4 options).

So now we have a total of 128 x 3 x 2 x 4 = 3072 lottery tickets, for a 1/300 chance of winning the one-in-a-million lottery.

I would like to say “Ha ha, I sure proved those dumb conspiracy nuts wrong”, except that a 1/300 chance is still a pretty impressive coincidence – what scientists call p < 0.01. And now I've used up all my excuses. I think what’s going on here is that I’m still accepting the terms of the game – comparing only the exact categories used in the original calculation. Suppose that the latitude of the Great Pyramid was exactly 30.0000? That too would be impressive – it would prove that the pyramid builders knew the exact size and shape of the Earth and were able to build their Pyramid one third of the way between Equator and Pole. Suppose that the Great Pyramid was latitude 19.69724. That’s the date humankind first landed on the moon in yyyy/mm/dd format – clearly the Pyramid was built by a time-traveling Nostradamus! Suppose that the Pyramid was built of stones of four different colors, with blue stones always paired opposite red stones, and yellow stones always paired opposite green stones. Then the ancient Egyptians were trying to tell us about the structure of DNA. What if the Pyramid, viewed from above, looked like a human brain?

Is it fair to take all of that into account? If so, does the remaining coincidence go away? I wish I were able to give these questions a more confident affirmative answer.


I still believe that pseudoscience is helpful for understanding regular science. The loopholes that let people discover proofs of ESP or homeopathy are the same ones that let them discover proofs of power posing and ego depletion.

In the same way, numerology is helpful for understanding statistics. You can see the same factors at work, free from any lingering worry that maybe the theory you’re investigating is true after all.

Andrew Gelman writes about the garden of forking paths. The idea is: the scientific community accepts a discovery as meaningful if p < 0.05 - that is, if equally extreme data would only occur by coincidence 5% of the time or less. In other words, you need to win a lottery with a one-in-twenty chance if you want to get credit for discovering something absent any real effect to be discovered. But if a scientist forms their hypothesis after seeing their data, they might massage the precise wording of their hypothesis to better fit their data. If there are many different ways to frame the hypothesis, then they have many lottery tickets to choose from and a win is no longer so surprising. Gelman discusses a study claiming to find that women wear red or pink shirts during the most fertile part of their menstrual cycle, which sometimes involves red or pink coloration changes in primates. The study does detect the effect, p < 0.05. But there were a couple of different ways the researchers could have framed the problem. They could have looked at only red shirts. They could have looked at only pink shirts. They chose days 7-14 as most fertile. But they could also have chosen days 6-15 without really being wrong. They could have looked only at the unmarried women most likely to be trying to attract mates. A recent paper listed 34 different degrees of freedom that can be used in this kind of thing. Add up enough of them, and you have more than twenty tickets to the one-chance-in-twenty lottery and success is all but certain.

I used to call this the Elderly Hispanic Woman Effect, after drug studies where the drug has no effect in general, no effect on a subgroup of just men, no effect on a subgroup of just women, no effect on a subgroup of just blacks, no effect on a subgroup of just whites…but when you get to a subgroup of elderly Hispanic women, p < 0.05, apparently because it's synchronized with their unique biological needs. This is pretty obvious. The lesson of the Pyramid-lightspeed link is that sometimes it isn't. It just looks like some sudden and shocking coincidence. The other lesson of the Pyramid is that I cannot consistently figure this kind of thing out. I threw everything I had against the correlation, and I still ended up with p = 0.003. I don’t think this is because the Pyramid really was designed by aliens with a suspicious link to 1600s France. I think it’s because I’m not creative enough to fully dissect coincidences even when I’m looking for them.

This is always happening to me in real studies too. Something seems very suspicious. But their effect size is very high and their p-value is very significant. I can’t always figure out exactly what’s going on. But I should be reluctant to dismiss the possibility that I’m missing something and that there’s some reasonable explanation.

This entry was posted in Uncategorized. Bookmark the permalink.

162 Responses to The Pyramid And The Garden

  1. Jeffery Mewtamer says:

    Now that it’s been mentioned lower latitudes have higher probability, is there a simple formula for calculating that a random point on a spere will lie between two parallels?

    For meridians, you just take the degree difference over 360 or the radian difference over 2pi or tau, but I suspect the calculation isn’t so simple for parallels.

  2. joshmaundering says:

    My favorite mathematically justified pseudoscience is the “evolution is mathematically impossible” idea. Best laid out here I think:

    Each system can thus go through its 200 mutations in 100 seconds and then, if it is unsuccessful, start over for a new try. In 1018 seconds, there can, therefore, be 1018/102, or 1016, trials by each mutating system. Multiplying all these numbers together, there would be a total possible number of attempts to develop a 200-component system equal to 1014 (109) (1016), or 1039 attempts. Since the probability against the success of any one of them is 1060, it is obvious that the probability that just one of these 1039 attempts might be successful is only one out of 1060/1039, or 1021.

    All this means that the chance that any kind of a 200-component integrated functioning organism could be developed by mutation and natural selection just once, anywhere in the world, in all the assumed expanse of geologic time, is less than one chance out of a billion trillion. What possible conclusion, therefore, can we derive from such considerations as this except that evolution by mutation and natural selection is mathematically and logically indefensible!

    Plenty of refutations available, but I’m afraid to add any more links to this.

  3. uncle joe says:

    Seems like the point is, more or less, that you shouldn’t discard a model because it assigns a low probability to your actual observations.

    This makes perfect sense. Otherwise, when you flipped a coin five times and got TTHTH, you would immediately discard the hypothesis that the coin was fair (1/32 probability of that sequence) in favor of the belief that it had been rigged to land that way (100% probability).

    So you need the concept of priors, as we all know. But is there anyone actually applying this in published scientific papers?

    It seems like it would be very good to promote the idea that a paper must make the case that its result is not just statistically significant, but also is believable by someone with a reasonable prior. It’s either that, or accept that most scientific “findings” will be eternally suspect.

  4. daniel says:

    It strikes me like we’re missing on a whole lot of aspects, the main ones I’d count are surface size, volume, length of vertical edges, circumference of base, weight, and number of bricks.

    The obvious cop-out is that this is why we like bayesianism so much. A more on-point argument would be to discuss the conclusion – that judging this theory is equivalent to judging scientific studies, how about this rebuttal?
    Yes, it’s hard for one person to be creative enough to fully dissect all coincidences, that is supposedly why we have multiple people working on each study for extended periods of time & the peer review system. if you could dismantle each suspicious study you see in 5 minutes it would mean that these systems that try to maintain quality in articles are in a very poor state.

    I am very happy Scott included stonehenge, until I reached that that part I had a voice in my head going “but stonehenge also fits” on repeat.

  5. jlister says:

    Benford’s Law would increase the degrees of freedom. i.e. numbers tend to begin with low order digits (1 or 2). So both the speed of light and (even more so) the latitude begin with low order numbers. This would change the chances to about 1 in 30.

  6. pansnarrans says:

    Stonehenge was built by aliens. I saw it in Doctor Who.

    • Edward Scizorhands says:

      Wasn’t there a Sarah Jane Adventures episode that took place there? I can’t find anything on wikia about it.

      • pansnarrans says:

        Matt Smith. The Pandorica Opens. Unless I’ve gotten mixed up.

        • Edward Scizorhands says:

          You are right with that episode. But I was thinking specifically of Sarah Jane having to be there for some reason in her own series. It might have been some different set of standing stones.

  7. Hunter Glenn says:

    Sounds like Littlewood’s Law –'s_law

    “During the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of one per second. So the total number of events that happen to us is about 30,000 per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month”

    There are seven billion people on earth. So, every day, there are seven billion different days lived. One of those seven billion days has to be the most improbable day of all, a day so improbable it only happens once out of every seven billion days lived…there are about 30,000 days in the life of a 90 year old.

  8. Jeffery Mewtamer says:

    I knew of polar shifts, but I didn’t know the magnetic poles where supersonic jets compared to the techtonic plates.

    Hmmm. Since the Earth’s axis is tilted, could we take the axis of the Earth’s rotation plus the normal to the plane of the Earth’s orbit that passes through the Earth’s center to get a reference plane for longitude based on the Earth’s physical properties rather than the politics that lead to the prime meridian passing through Greenwich?

    Though, for putting coordinates to points on a sphere, is there any reason to prefer taking the angle between a reference plane and a ray from the origin(how latitude is measured) for one coordinate and the angle between a reference plane and a great circle intersecting the point in question(how longitude is measured) for the other coordinate? How would things change if we had parallels in both north-south and east-west or meridians in both, or north-south meridians and east-west parallels?

    Also, wasn’t the gram originally defined as the mass of one cubic centimeter of water?

    Let’s see, a cubic meter is 1M cubic cm, so a cubic meter of water has a mass of 1 megagram, more commonly called a metric ton.

    The Equator-Pole distance is roughly 10 Megameter, so a unit volume with this as our unit length would be 10^21 meter.

    Combining these results, we get that a cubic pole distance of water has a mass of 1000 Yottagrams, which if I’m reading Wikipedia’s orders of magnitude page for mass right, is roughly 1/6 of the Earth’s mass.

    And since Douglas Adams was mentioned, I’m curious what lies at (42, 42) in any of the coordinate systems I’ve hinted at.

    Also, what latitude would divide the equator-pole or pole-pole distance in Golden or Silver Ratio?

    For the record, I doubt there’s much, if any, cosmic significance to anything that lines up on a global scale, and I’d argue that anything found in architecture that lines up with something found in geometry comes down to architects being likely to draw aesthetics from Geometry and how all sorts of irrational and even transcendental lengths show up in even elementary geometric shapes(The diagonals of a Dodecahedron with unit edge length include phi, phi*root2 phi*root3 and at least one more length I haven’t been able to find, and all of this is derived from knowing the diagonals of a pentagon are phi and that the face diagonals of a dodecahedron form a cube and a little Pythagorean theorem).

    So, how fast is a pole distance per day? Are there any other units we could define in terms of the Earth Day and the equator-pole distance?

    • bean says:

      Hmmm. Since the Earth’s axis is tilted, could we take the axis of the Earth’s rotation plus the normal to the plane of the Earth’s orbit that passes through the Earth’s center to get a reference plane for longitude based on the Earth’s physical properties rather than the politics that lead to the prime meridian passing through Greenwich?

      No, because the Earth is rotating. That will give you a vector in fixed space.

      Though, for putting coordinates to points on a sphere, is there any reason to prefer taking the angle between a reference plane and a ray from the origin(how latitude is measured) for one coordinate and the angle between a reference plane and a great circle intersecting the point in question(how longitude is measured) for the other coordinate? How would things change if we had parallels in both north-south and east-west or meridians in both, or north-south meridians and east-west parallels?

      Yes. If you don’t, your coordinates get really weird. Let’s assume we take the Prime Meridian and make it the EWquator. Now, if you move purely north-south, you’re also changing your east-west coordinates unless you’re on the EWquator. You start at 90 deg E and go straight north. By the time you reach the north pole, you’ve also gone from 90 deg E to 0 deg E, despite being on the same meridian.
      Meridians for both is even worse, as latitude is obviously based on reality. It was much harder to figure out how to find longitude than latitude. Not only do you get the coordinate linking from the above example, but you also lose the ability to figure out latitude independently of longitude.
      Both are obviously bad when you have to do navigational math. The basic principle is that with one set of meridians and one set of parallels, the coordinate lines are always perpendicular to each other, which is obviously helpful. It’s the natural projection of X-Y coordinates onto a sphere, and one I would expect to be replicated by aliens.
      When they don’t work for some reason, you tend to use quaternions, although there might be some reason why dual meridians or dual parallels are helpful.

  9. coreyyanofsky says:

    Am I the only person who read “latitude go[es] from 1 to 90” and immediately thought whaaaa…? I mean, you could say latitude goes from 0 to 90 or 90°S to 90°N, but 1 to 90? That breaks my brain like Judge Doom doing the ol’ shave-and-a-haircut trick.

  10. kaleberg says:

    There are all sorts of global power points where aliens have concentrated energy on our planet. It isn’t just the Great Pyramid and maybe the Nazca Lines. Why not the Kaaba in Mecca or the Dome of the Rock in Jerusalem? I’ve heard all sorts of nonsense about Machu Picchu. Even Brasilia supposedly concentrated alien energy lines or something. Besides, why the speed of light? Why not the digits of pi or e or any number of mathematical or scientific constants?

    There should probably be a program like RIES for doing this. RIES takes a number and gives you an interesting formula for calculating it using simple numbers, pi, e and a few others. Type in your phone number with a decimal in it and you’ll find an amazing coincidence. Programs like this have an actual use. Scientists often compute various ratios. Then they dump them into something like RIES and find out that their answer is sqrt(pi/6) or something. Then they try to figure out why or whether it is just a coincidence. Sometimes it isn’t.

    Besides, anyone who studies general relativity and cosmology knows that the speed of light, like the gravitational constant is one. (Really, it makes back of the envelope calculations so much simpler.)

  11. pseudonymous says:

    The pyramid/speed correlation is actually crazier than that, though: it doesn’t really need anyone to use a base 10 system! If you notice, the meter is 10^-7th fraction of the equator-pole distance, and the latitude of the pyramid is also 10^-7th fraction of the speed of light. So even if your unit was just distance from north pole to equator, you could frame this as “Light travels latitude-of-Great-Pyramid units in one second”. Or if you wanted to be even spookier than that (without resorting to arbitrary systems like degrees), as “Light travels from the equator to the Great Pyramid in exactly 1/90th of a second”, and that would still be true to 6 significant digits!

    That invalidates points 2 and 4 (I would let 5 be because “1 in 90” is still something of an arbitrary figure, could as well have been “1 in 9” or “1 in 100” or something, so we might as well increase the options for 5). Even point 1 is not really fair because longitude is nowhere as “natural” as latitude: it also depends on what people later chose as the prime meridian, which is arbitrary, while the equator isn’t.

    The correct explanation, of course, is that this is a key facet of Adam Kadmon 🙂

    • dsotm says:

      That’s actually a good way to show there is little special about this, because light travels from anywhere to anywhere in some amount of time, so for this to be ‘interesting’ there needs to be something ‘interesting’ about ‘1/90th’ – the fact that the denominator within a small amount of decimal digits of an integer probably isn’t.

      But did someone already mention that 29.9792458 is awfully close to 30 degrees aka a 3rd of a hemisphere which probably had some meaning with shadows and sun dials in a sun-worshipping culture with base-6 math ?

      • pseudonymous says:

        Okay, let me restate that as:
        “The pyramid of Giza’s distance from the equator is precisely what light travels in 1/90.0000 seconds” 😀

        • dsotm says:

          But both Scott’s original article and multiple comments here shown that the precision isn’t actually that big depending on how close to the center of the pyramid you want to get at what point in time, earth datum etc.

          Also this is equivalent to saying that it’s a remarkable coincidence that we live in a universe where the speed of light in vacuum is close to being an integer multiple of the distance between the equator and the pole of our home planet divided by the 8th power of the number of our fingers (C = 299792458 ≈ 3*10^8), without mentioning the pyramid at all and crediting aliens/adam-kadmon with at least the creation of earth.

          Earth standard gravity g is 9.8 m/s^2 which is also within p=0.02<0.05 of 10 under the original reasoning (and here we actually have other planets with measured gravities as well as an underlying theory from which to calculate the values based on size and composition)

          The second is also not numerically/congruently independent of the meter – it was originally defined as 1/86400th of the time it takes a roughly-spherical earth to complete a full revolution around it's axis with meter being a 1/10^7 subdivision of the meridianal distance, in both cases the subdivisions are large integer multiples of 10 and 6 and are based on properties of the earth so we should assign expectation probabilities based on the distribution of the results of simple math expressions of these numbers being around multiples of 10 and 6 which at least intuitively (and hence retroactively) seems pretty high.

      • Autolykos says:

        Yup, a slightly badly measured 30°N is the most likely significance of the spot, if it has any at all. Probably the best theory yet, as it doesn’t require any knowledge the Egyptians didn’t have, and only being off by less than 1/1000 is still quite impressive.
        Choosing the tropic of cancer instead would’ve been pretty cool as well, but then the precision would be way less impressive. You could do that just with a string and a rock.

  12. dsotm says:

    Another thing to consider here is that this is a single observation being assigned a p-value, in the old-hispanic-lady analogy that would be like a paper claiming for a drug to be effective for old hispanic ladies based on a single case of old hispanic female patient who has made a miraculous against-all-odds recovery after taking it.

    Conversely if a group of old hispanic ladies was shown to have on average made recoveries that are both p<0.05 against the 'drug has no effect' hypothesis AND the 'drug has no effect on non old-hispanic-ladies' hypothesis this *would* have been a good reason to believe that there is something medically specific to old hispanic ladies and that the drug is effective for them, just like if out of 21 sites sharing similar well-defined characteristics 20 were found to be encoding physical constants in the beginning of their coordinates this would have been a good reason to suspect a causal relation.

  13. Ninmesara says:

    I’m afraid the lesson to take away from this is that the only real science is physics or anything else you can reproduce on a lab on demand with the desired precision given enough resources and the the rest is, as they say, stamp collection. And your stamps better agree with intuitons deeived from “real science”. 🙂

    • keranih says:

      Well, sociology is just a subset of biology.

      And biology is a subset of chemistry.

      And chemistry is a subset of physics.

      So…turtles quarks all the way down, eh?

  14. beoShaffer says:

    Bah, this is not a coincidence because nothing is ever a coincidence.

  15. Moon says:

    This reminds me of that idea that came out after 9/11 where if you fold a dollar bill in exactly a certain way, it will come out somehow looking like the Twin Towers looked after 9/11. How many hours must someone have spent folding dollar bills to get that?

    How many different physical, biological, and other laws and formulas and significant numbers must someone(s) have gone through before they came up with one that corresponded to the length, or width, or geographical coordinates or etc. of various pyramids, or steps of pyramids, or distances between the highest and lowest step, or distance from top to bottom measured diagonally, or measured straight up and down at a 90- degree angle, or whatever?

    If you are obsessive compulsive, you could easily entertain yourself by spending all the free time in your whole life living at the Great Pyramid, measuring every aspect of it, then going home and converting your measurements to all different kinds of units, and then looking up various numbers corresponding to various measurements in various sciences.

    You could look at distances between planets and all kinds of astronomical data too while you were at it, and then look for numbers that were one zillionth of those numbers, as pyramid dimensions.

    The Big Question here might possibly be: How obsessive compulsive and number focused can a person be? Yes, numerologists might be great at doing this.

    • Deiseach says:

      The Big Question here might possibly be: How obsessive compulsive and number focused can a person be?

      Pyramid inches. This is what happens when mathematicians have too much time on their hands 🙂 Charles Piazzi Smyth, a former Astronomer Royal, was an interesting case of it.

  16. Douglas Knight says:

    If the latitude were measured in degrees, minutes, seconds, then the arbitrariness of the 60s that show up in the definition of a second of arc and a second of time would cancel out, leaving only the arbitrary factor of 15=360/24 between dividing the circle into 360 degrees vs dividing the day into 24 hours. But the latitude was measured in decimal degrees.

  17. AnonEEmous says:

    all this discussion of “degrees of freedom” makes no sense…aliens created us and they encoded all the information into the world around you…you have zero degrees of freedom! and your sample size, is also zero…there’s no conspiracy just open your eyes…just kidding you also have zero eyes… and now you know the truth

  18. Squirrel of Doom says:

    The French did a decent job of measuring the size of the Earth, but they were a bit off. The Equator North Pole distance is actually 10,002 km, making these numbers 0.02% off.

  19. Doug S. says:

    You *can* find pi in the Pyramids; this is because they probably used wheels to measure distances when constructing it. (Counting rotations of a wheel is a very accurate method of measuring distance and surveyors use it today.)

  20. shakeddown says:

    Re: 4: another (actually more common) way to measure latitude is with degree minutes/seconds instead of decimals, so that’s another 2 degrees of freedom.

  21. The original Mr. X says:

    If the degrees in a circle come from the days in a year, wouldn’t we expect a circle to be divided into 365 degrees rather than 360?

    • quantummechanic1964 says:

      If the degrees in a circle come from the days in a year, wouldn’t we expect a circle to be divided into 365 degrees rather than 360?

      365 doesn’t have nearly as many factors as 360. IIRC, some systems used 12 months of 30 days, plus 5 extra-calendrical days.

  22. quantummechanic1964 says:

    If the Prime Meridian ran through Chelsea instead of Greenwich, would the longitude be a coincidence for Pi? I think it’s about 16 minutes difference.

    Then Douglas Adams and Carl Sagan would be proud of the aliens.


  23. Jeffery Mewtamer says:

    I think it worth noting that 24, 60, and 360 are all highly composite numbers, and are thus really useful for dividing things in a way that makes working with fractions convenient. A 24-hour day can be divided in 1/2, 1/3, 1/4, 1/6, or 1/12 or any multiple of these and get a whole number of hours. A 60 minute hour or 60 second minute adds fractions of 1/5, 1/10, 1/15, 1/20, and 1/30 and their multiples. Gradients divide the circle into quadrants of 100, but never really caught on because there’s so many fewer ways of dividing 400 vs 360. It’s also my understanding that duodecimal was the most common base for money prior to decimalization of currency, and 12 is also a highly composite number, and 5040, the number Plato chose as the ideal population of a city, is also highly composite, so the concept might have been known in ancient times. The odd thing about our time keeping is why 7, a prime number, was chosen for the length of a week, especially when it doesn’t devide 365 and why February is 28 days and we have 7 31 day months instead of 7 30 day months and only 5 31 day months.

    Usefulness of 12, 24, 60, and 360 aside, what latitudes correspond to 1 radian north/south of the equator or 1 radian form either pole? or 7/22 of a quadrant north/sourth of the equator or 7/22 of a quadrant/semicircle from the poles? Do any notable ancient sites lie on these?

    Do the Earth’s magnetic and rotational axes intersect at it’s center? If so, is the plane they define orthogonal to the plane of the equator? If so, what longitudes do they intersect the Earth’s surface at? Does anything interesting lie on radian or 7/22 radians from this plane?

    • quantummechanic1964 says:

      From Geomagnetic Pole:

      “The actual Earth’s magnetic poles are not antipodal—that is, they do not lie on a line passing through the center of the Earth.”

      Also the magnetic poles drift measurably over a short timescale. The North Magnetic Pole, in 2009, was “moving toward Russia at between 55 and 60 kilometres (34 and 37 mi) per year.”

  24. glorkvorn says:

    5. Decimal point placement. The latitude 29.9792 N matches the speed of light exactly, but so would the latitudes 2.99792, 2.99792 S, and 29.9792 S.

    But I can resolve both the meter and decimal place coincidence simultaneously! Using the equator-north pole distance as a measuring unit makes sense, but breaking it up into 1/10,000,000th pieces is arbitrary. What if the aliens simply used the distance itself as their basic unit? That would 10,000,000 meters, and in that unit, the speed of light is… 29.9792. No decimal place arbitrariness at all.

    (Admittedly that still leaves the coincidence of choosing the North latitude instead of the South, but you can hardly expect the ancient Egyptians to build their spaceship-pyramid in the ocean.)

  25. Perhaps I’m missing something, but while you discussed the question of why the aliens use meters, you don’t explain why they use seconds.

  26. mwk24 says:

    I feel it boils down to – what’s the chance of at least one incident on the planet of two mystical-esque measurements seeming similar.

  27. Chrysophylax says:

    Posterior ratio = Likelihood ratio * Prior ratio

    P(aliens|coincidence)/P(¬aliens|coincidence) = [P(coincidence|aliens)/P(coincidence|¬aliens)] * [P(aliens)/P(¬aliens)]

    You’ve only made an estimate of P(coincidence|¬aliens). You need to estimate P(coincidence|aliens) in order to work out whether this is evidence for aliens or not.

    If it’s less than 100% probable that aliens would try to leave an incredibly subtle and context-dependent clue in a single ancient monument, and not leave any substantial evidence of their presence or prowess, then the likelihood ratio is smaller and the evidence weaker. If I knew for a fact that aliens had visited Earth and left deliberate evidence of this, I’d expect to see something a lot more obvious. The additional probability of seeing a coincidence is barely higher with aliens than without aliens, so the likelihood ratio is barely greater than 1 and the evidence is tiny.

    We shouldn’t be trying to make this not be evidence or be evidence against aliens. Coincidences in pyramids are more likely with aliens than without. The proper objection is that they’re only very slightly more likely and our prior against aliens is enormous, so we still don’t believe in ancient aliens.

    The general lesson here is that when someone presents evidence and demands that you admit they’re right, it’s very easy to only argue that your hypothesis assigns significant probability to the observed result (and/or dispute the observation), and let them get away with pretending that their hypothesis assigns lots of probability mass to the observation. I think that working through the equation above is a good way to make sure that you assign sensible numbers to every component, rather than letting your update be hacked by a monkey politician.

    You also left out the likelihood of building an impressive pyramid at Giza. Khufu ordered a pyramid built there for sensible, non-alien reasons, and those reasons make the coincidence less surprising. I argued in another comment that there are only about ten degrees of freedom for the first two digits due to the size of Fourth Dynasty Egypt. If there were only a couple of suitable spots in the whole country, we might be looking at, say, a 1-in-30k lottery, giving us about a ten percent chance of winning with 3072 tickets.

    I don’t agree with the idea of treating this as a single lottery. It would be better to model it as multiple lotteries in sequence, since we could have the Great Pyramid and Stonehenge both encoding c in different ways.

    • AnonEEmous says:

      i think it’s worth noting that this information, too, is totally irrelevant unless you already knew about what it was. We didn’t even know much about “speed of light” being a thing until it was already being measured, so far as I can tell, and why would we think to look at the Pyramid of Giza? Not to mention specifically its longitude / latitude. It really seems like, at best, this was here to just help us “check our work” in case someone made this wild discovery, even though if you could come up with the first conclusion you probably could come up with better supporting evidence than “Pyramid of Giza latitude”?

      • Autolykos says:

        That’s probably the strongest argument against the theory. Once you know that “speed of light” is a thing, you have almost measured it already – you just need to grab a pencil and run the numbers. So there isn’t much point in encoding just its numerical value, unless you’re very, very precise. And we have a better way of encoding numbers than placing huge buildings on appropriate coordinates: We just write them down, with arbitrary precision and no measurement errors or shifts due to tectonic movements. If you want to be sure that your numbers will be read correctly, you start with counting, and maybe writing down a few dozen digits of Pi.
        If we had discovered the number 299,792,458 carved into the wall of the tomb inside the pyramid, ideally next to a carving of a meter-long measurement stick (or the speed of light in cubits/second, or the number using one of the pyramid’s dimensions as measurement stick), I would believe the Egyptians knew it.
        A civilization smart enough to calculate the speed of light up to six or more digits wouldn’t be stupid enough to use such a ridiculously bad way of recording it.

  28. uncle stinky says:

    If Wikipedia is trustworthy then plate tectonics? “The African Plate’s speed is estimated at around 2.15 cm (0.85 in) per year. It has been moving over the past 100 million years or so in a general northeast direction” 4000 years of that, (rounded for lazy maths), means it’s not where it started anyway. How significant would 80 or 90 metres be?

    • Autolykos says:

      An arcsecond is roughly 30 meters, so we’re talking about ~ 1/1000th of a degree. Which still leaves us with 4-5 significant digits.

  29. Jack says:

    It should be easy to show that the probability of a coincidence of this sort ever existing approaches one, and as people above have suggested if you are having trouble doing it you may need to take a few steps back.

    Whenever we think about the likelihood of things being true in the world we approach the issue with a complex structure of understandings that helps everything cohere. Even a simple question like, what are the chances of a coin flip coming up heads, depends for its motivation on a host of cultural factors and depends for its meaning on things like flipping, coming up, heads… If you are asking about a probability for a question before it is even motivated, you need to look not only at all the contingent meanings of the terms of the question, but also at all the contingent motivations that could have motivated different questions. Part of why it is not surprising that over ninety per cent of humans are under six feet tall is that we are not asking about skyscrapers and we think humans are not skyscrapers.

    All of which is to say, it would be a really remarkable failure of imagination if we could not produce a host of coincidences of this sort. And while this post appears to be an attempt to talk with conspiracy theorists in their own terms, we aren’t, because we are still approaching the question with a very different set of motivations and understandings.

  30. Maznak says:

    I am not the first one to point out, but you basically have many more degrees of freedom, once you accept that there was never a prediction beforehand of the sort “a latitude of very important ancient building codes for an important physical or mathematical constant”. So we might have this same discussion in case, I don’t know, the height of some gothic cathedral points to the charge of electron. But the space of all “similar things that might look very improbable” is really, really huge. So this thing is not such a big deal.

    • John Schilling says:

      There have definitely been predictions, or at least hypotheses, of the form “Very Important Ancient Buildings were probably built by Space Aliens, who would have left secret messages by which an advanced civilization would know it was them”. The values of fundamental physical constants are one of the few things universal enough to encode a message for a one-way message to a wholly alien (but technologically advanced) recipient.

      • John Colanduoni says:

        I’ve always been curious as to whether our theories and alien’s theories (and mathematics) would look similar enough to ours for the dimensionless constants to persist. I lean towards yes (especially because of all the symmetry group stuff, that seems hard to miss for an advanced civilization), but there are a lot of course corrections in the history of physics and mathematics that make me wonder.

        For example, intuitionistic logic (which denies that double negation of a proposition yields the original proposition) was gaining significant ground in mathematics at one point in history due to worries that this axiom could induce logical inconsistency. Mathematics in this world is very, very different: there’s two kinds of real numbers, our usual methods of calculus become much more difficult. But the really interesting thing is that models of intuitionistic logic actually match closely with models of quantum mechanical systems (in the abstract, qubit-level sense).

        What killed its popularity in our world was the proof that it couldn’t be a source of logical inconsistency in our theories of mathematics, so there was no risk in using it. It also came kind of late to shape quantum mechanics, and the link between intuitionistic logic and quantum mechanics was not discovered until much later. But if another civilization didn’t find that proof until it was too late, it’s quite possible on an alien world everyone would have used intuitionistic logic for virtually all mathematics for tens of generations before quantum mechanics was discovered. Combined with calculus as we know it being much more difficult to use, that could make these aliens take a totally different path when it comes to QM.

        What makes this idea especially interesting is that there are significant current efforts to look for other frameworks in with to do QM that look a *lot* different than our current ones. In addition to the intuitionistic logic stuff you have things like non-commutative geometry, partition logic, even category theory approaches. We could actually be trying to find a novel model for QM that another species found first while they try to find the one we started with!

        • Douglas Knight says:

          Constructive logic is popular in CS. Automated theorem provers use it. It hardly makes a difference.

          Maybe classical physics should be done with constructive real numbers. There is nothing quantum about it.

          • John Colanduoni says:

            It hardly makes a difference for automated theorem provers (and more importantly proof assistants) for a few reasons, none of them having anything to do with constructive logic “hardly making a difference” in general:

            1. People working on automated/assisted reasoning and associated theory (e.g. mathematical logicians) are usually studying constructive logics and mathematical foundations themselves (look at the day jobs of the developers of Coq). Naturally, if you want to study constructive logic, you should probably use constructive logic. In mathematics as a whole, where most people aren’t studying these directly, the effects of suddenly not having the law of excluded middle or the axiom of choice (which implies it) are more significant; reading a book on constructive analysis next to a classical one shows this pretty plainly.

            2. Usually inserting the law of excluded middle into a type theory is as simple as adding a new fundamental occupant of a certain type. So if you want to implement a computer system which can represent the objects of a type theory, there’s really no reason to build it in fundamentally and restrict your users. Non-type theoretic automated reasoning systems mostly use classical theories like Tarski-Grothendieck set theory.

            3. Most truly automated provers are really bad at dealing with infinite models, and real numbers in particular. Doing full-blown analysis without specific heuristics is completely out of the question. Combine that with the fact that when it comes to finite structures there’s usually little (if any) distance between constructive and classical mathematics, and it’s pretty clear why these systems are ambivalent about the law of excluded middle.

            That has nothing to do with constructive logic not being “different” enough to matter when it comes to doing everyday mathematical reasoning inside it.

            As for there being nothing quantum about constructive (or more specifically intuitionistic) logic, a decent examination of some of the most compeling and specific links is this paper.

          • Douglas Knight says:

            Wrong on all counts. Impressive!

          • John Colanduoni says:

            Care to explain how? At the very least your refutation for (2) should be succinct. If you have more time, I’m sure Schreiber and Schulman would appreciate the refutation (to an entire survey paper no less!) you’re so confident in.

  31. leoboiko says:

    I would like to say “Ha ha, I sure proved those dumb conspiracy nuts wrong”, except that a 1/300 chance is still a pretty impressive coincidence – what scientists call p < 0.01.

    All this tells me is yet more evidence to adjust my growing conviction that p is a useless measure and should be abandoned.

  32. bean says:

    Actually, this is made even more interesting by the fact that the French got this one slightly wrong. The Earth’s shape is really complicated, and the meter was originally defined based on the Rose Line through Paris. The aliens would have had to pick that line. More than that, Delambre and Méchain got their math slightly wrong, and it ended up being short of the intended definition by about 0.2 mm. If the aliens had done it right (which we assume they would) the relevant latitude would be 29.9669.
    Another possible DoF would be the encoding of latitude. They could have tried writing it in degrees minutes seconds instead, for instance.

    • Sixth Estate says:

      This objection is easily dispensed with by positing that these aliens were not only advanced in physical sciences but also social sciences, and therefore anticipated where the first global empires capable of establishing universal standard measurements were likely to emerge.

      Possibly this was assisted by time travel.

  33. “The loopholes that let people discover proofs of ESP or homeopathy are the same ones that let them discover proofs of power posing and ego depletion.”

    As I’ve remarked before in this kind of context, ego depletion is sufficiently proved from experience. So if you can’t confirm it by testing, you really do need to look for improved methods of testing.

    • Autolykos says:

      Introspection is really, really suspicious as a source of evidence, especially if you already know of the theory. You might be dealing with confirmation bias or placebo effect, for example. I’m still kind of divided on the ego depletion issue, even though it “feels” right for me, too.

      • I am saying that “I was tired of forcing myself to do that,” is not something that depends on the theory. It is a fact of experience (at least in my life) just as much as “I was tired of pedaling that bike.”

        • Autolykos says:

          Some people claim ego depletion stops if you believe to have infinite willpower. Sadly, I could never get that to work for myself, but I would not dismiss out of hand that it works for them. Placebo/nocebo effect is real and can be quite strong, after all.

          • If I believed that I had infinite spending power, I would spend money until all my cards stopped working, my wallet was empty, and so on, and soon I would be forced to stop spending money.

            But if Bill Gates believed he had infinite spending power, he would never run out, as long as he was just spending money on ordinary things. Nonetheless, he does not actually have infinite spending power, and it would be revealed if he tried to fund a mission to Mars.

            In a similar way, those people probably just have enough willpower to fund the lives they happen to be living. But if you increased the painfulness and difficulty of their lives enough, sooner or later they would run out, just like Bill Gates.

  34. R Flaum says:

    Would continental drift have measurably moved the Pyramid over this kind of timescale?

    • Sixth Estate says:

      Yes, but this only proves that the aliens, in their wisdom, realized that nobody would be able to make the connection for a few thousand years, and planned accordingly.

    • cmurdock says:

      Assuming the Pyramid was built ~2560 BC and going by the 2.15 cm/year speed of the African plate given by this website then it should have moved about 98 meters north-northeast. Which is nearly nine times the distance required to ruin the result: one ten-thousandth of a degree is about 11 meters.

      And of course, if we assume the Pyramid was built earlier, as ~Ancient Astronaut Theorists~ say, the discrepancy is much, much worse.

      • glorkvorn says:

        So what would it’s latitude have been when it was first built? 29.9792 – .0009 = 29.9784?

        Bean, below, wrote:

        Delambre and Méchain got their math slightly wrong, and it ended up being short of the intended definition by about 0.2 mm. If the aliens had done it right (which we assume they would) the relevant latitude would be 29.9669.

        So if they were *actually* much older than they appear, the continental drift could get us all the way to the “right” number of 29.9669.

        (No i don’t actually believe this, I’m just having fun playing with the argument)

  35. R Flaum says:

    Wait. If the origins of the 360-degree circle are lost in the mists of time, how do we know it comes from the (approximate) number of days in a year?

  36. Vladimir N says:

    What aspect of the Pyramid we’re looking at. That is, it would have been equally interesting (maybe moreso!) if its height or width matched the speed of light exactly. So that’s another (3 options).

    So now we have a total of 128 x 3 x 2 x 4 = 3072 lottery tickets

    You shouldn’t just multiply the size of {height, width, latitude} by the number of ways in which latitude could be special, because the number of ways in which height could be special is probably different.

    • Sixth Estate says:

      Indeed. What if the height of the period in metres is a multiple of the first three prime numbers and pi, plus 8 for the number of planets in the solar system and 37 light-years for the distance from our planet to their nearest base?

      This is clearly a message from the aliens proving that they understand important mathematical concepts and astronomy and are spacefaring. I don’t see how it could mean anything else.

  37. Galle says:

    One thing I think you missed is that the space of possible pyramidal latitudes is constrained. The Ancient Egyptians couldn’t have built a pyramid at forty degrees north, because the Ancient Greeks would have gotten very angry at them. I’m not entirely sure how much more likely this makes that exact latitude, but it seems worth considering.

    • Matt M says:

      Ah, but space aliens could build a pyramid wherever they damn well pleased!

      • Chrysophylax says:

        If the aliens were willing to leave obvious clues, they’d make something that couldn’t possibly have been built with the technology of the time, preferably incorporating written records and accurate sculptures of aliens. We have to assume the constraint that the clue must have plausible deniability.

        This reduces the possibilities by a lot. The Great Pyramid was built very early indeed and very few places had cultures remotely capable of doing something like that. This constrains the possibilities for the first two digits of the latitude. Being generous to the Third Dynasty, it ranged from 32N to 23N, giving only ten possibilities for the first two digits together.

        We do have to factor in other ancient civilisations potentially being chosen for the Pyramid, or the Pyramid being built later when Egypt stretched down to about 15N, but if we’re working with the hypothesis that aliens were in Ancient Egypt specifically, this is still a substantial reduction of the coincidence.

        Choosing to express the speed of light because that’s what they had the territory to handle is trickier to dismiss. I’m not going to do the work to try to figure out the coincidence if the degrees of freedom aren’t independent.

        • Scott Alexander says:

          The aliens obviously advanced ancient Egyptian culture to make them plausible pyramid-builders.

          • Chrysophylax says:

            Erratum: I meant the Fourth Dynasty.

            Egypt was a very good place for it. They couldn’t have built it in the Arctic Circle while retaining plausible deniability.

            They had very few options: Mesopotamia, Egypt, the Indus Valley and Norte Chico. Egypt and the Indus Valley both cover latitude 29.9N. Why is there no great monument in Pakistan?

          • Matt M says:

            I think a lot of this depends on your conception of the power/scale of involvement the aliens might posses. Perhaps they created the conditions necessary for the geography we recognize Egypt to support an early civilization.

  38. AnteriorMotive says:

    Also to consider when discussing numerology is that when the research in your field runs on back-of-the-envelope calculations, there’s a huge file drawer effect.

    Every deviation from the theory’s most straightforward prediction (aliens building a space elevator instead of a triangle) should be penalized. Numerologists don’t make predictions before announcing their “discoveries,” so they don’t get to say it confirms their theory when one pans out.

  39. williamgr says:

    An additional reason to reduce the number of significant figures in the agreement is the movement of tectonic plates — there is no reason to believe that the ancient aliens or Atlanteans would be aiming to impress people living at our exact time rather than their contemporaries, so we should consider the latitude of the pyramid at the moment of construction.

    According to Wikipedia, the African plates is moving NE at 2.15 cm/year and has been doing so for the past 100 million years. Taking the date of construction of the pyramids to be 5000 years ago and assuming that the motion is due north (I can’t be bothered to divide by sqrt(2)), the pyramid is now ~ 100 m further north that it was when build. This corresponds to 0.001 degrees of latitude, meaning that we now only have to deal with a one-in-a-hundred-thousand-chance and using your methodology we have p=0.03 (without even including the several other, reasonable degrees of freedom suggested above).

    This obviously doesn’t take away from the thrust of your argument that trying to control for degrees of freedom is hard.

    • dsotm says:

      this (only with 4500 years rather than 5000)

      A degree of lattitude around 29th is about 110835.75 meters according to
      which would make one meter be 0.00000902235966283442 degrees

      The google map link already puts the marker about 13meters from the center of the pyramid in about 45degrees, so let’s say 0.7 of that is in the latitude direction we get the center of the pyramid at 29.97932790347293
      – only three decimals rather than seven in common with C

      The tectonic movement can be similarly calculated to be about 80 meters over 4500 years as
      yielding 29.979965223308223

      The diagonal of the pyramid is as measured on google maps about 316m (click well enough and you get 314 meters!)
      so the pyramid itself also contains coordinates with only one decimal in common with C

      Edit: 4500 years, not 2500 year because BC

      • StellaAthena says:

        No, you can only go back about 200 years of drift. The metre was cast in 1799 and as everyone knows, Napoleon invaded Egypt in 1798 so that he could remeasure the location to determine how much it had drifted before casting the metre!

    • janrandom says:

      You beat me to it.

      There is another thing at the other end: Not only the location of the pyramid is moving. So is the pole in relation to which the measurement presumably is made. Just because for GPS and such the pole is fixed (where it was in 1900) doesn’t mean that it was at that place at the time the pyramids were built. And the movement of the pole is even faster then the tectonic plates: It can be 10cm per year which could accumulate to 500m since the pyramids were built.

  40. martinw says:

    Andrew Gelman writes about the garden of forking paths. [...] I used to call this the Elderly Hispanic Woman Effect

    Whereas xkcd fans know it as the Green Jelly Bean Effect.

    (Well, OK, I guess the principle illustrated by that xkcd strip is just the file-drawer effect. To illustrate the Garden of Forked Paths they’d need to compare not only different colors but also jelly beans versus M&Ms, etc.)

    • John Schilling says:

      Did you know that studies have proven that Elderly Hispanic Women prefer green jelly beans to all other flavors?

  41. Deiseach says:

    Oh, Scott. That linked article about Michaelangelo was so hideously awful I couldn’t even finish it. I know you mean it as an example of pseudo-science but good golly, Miss Molly. Warning: ranting about inside baseball in Catholicism, so for those likely to be bored, you can skip everything past the first half of what follows.

    The “completely rehashing standard 19th century Protestant polemic about the corrupt Romish church without realising we’re swallowing propaganda” is par for the course, but this part had me clawing at my own face:

    Pope Paul IV interpreted Michelangelo’s Last Judgment, painted on the wall of the Sistine Chapel 20 years after completing the ceiling, as defaming the church by suggesting that Jesus and those around him communicated with God directly without need of Church.

    “Jesus and those around him communicated with God directly”.

    Jesus. Could talk to God. All by Himself.

    As in “Jesus, believed by Christians – including that ol’ Biblical-literalist fuddy-duddy Paul IV pope dude – to be God made Man, second Person of the Trinity, God Himself”? Could talk to His Father? Without intermediary?

    That’s about as stunning, shocking and surprising a ‘belief’ as “I can talk to myself”. This is on a par with saying “Darwin upset the 19th century scientific consensus because he proved Lamarck was right” or something.

    This is not even understanding the religion you are trying to explain to outsiders. If they’re trying to say “Michaelangelo believed Jesus was not divine” (they’re not, they’re making such an unmerciful hash of the whole thing, but this is the strongest steelmanning I can do of what they’re burbling about), then yes, the pope would have been a teensy bit upset about a statement like that being depicted on the wall of a chapel, directly in front of and above the altar and the tabernacle.

    As for Paul IV condemning Michaelangelo for Spiritualism, where do I even begin with that? Spiritualism qua Spiritualism was condemned in an encyclical of the 19th century; I imagine they mean Spiritism or perhaps Quietism (though that was not formally condemned until under a later pope). To be frank, I have no idea what exactly they mean, and I rather suspect they don’t either.

    Plus, they’ve got their timeline screwed up. The ceiling of the Sistine Chapel was painted by Michaelangelo 1505-12, commissioned by Julius II (of the della Rovere family), the so-called “Warrior Pope”. The “Last Judgement” wasn’t commissioned until 1536 under Clement II – a Medici pope and we all know the Medicis hated art and science and learning, right? – and completed in 1541, under Paul III, who was busy with the Counter-Reformation but did take time for a bit of the oul’ art patronage. Also such a hater of science, that “It is to Pope Paul III that Nicolaus Copernicus dedicated De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres).” No wonder Michaelangelo had to hide his scientific anatomy from him, right?

    Yes, Paul IV cut off his pension – but this appears (ironically, in view of this article’s claim that “Michaelangelo was a simple man disgusted by the opulence and corruption of the church”) to be part of retrenching all expense on frivolities like art and secular pursuits, not because of heresy hunting (he did do that; the Wikipedia page informs me that he also set up the first ghetto in Rome and imposed heavy restrictions and penalties on the Roman Jews so, um, not an ecumenist to say the least). Okay, yeah, probably a bit of revenge for Michaelangelo thumbing his nose at him over the nudes in the “Last Judgement” involved as well, when he was still Cardinal Carafa:

    The Last Judgement was an object of a bitter dispute between Cardinal Carafa and Michelangelo. Because he depicted naked figures, the artist was accused of immorality and obscenity. A censorship campaign (known as the “Fig-Leaf Campaign”) was organized by Carafa and Monsignor Sernini (Mantua’s ambassador) to remove the frescoes.

    Charges of opulence and luxury are ironic, I repeat, because he was a reformer:

    According to Leopold von Ranke, a rigid austerity and an earnest zeal for the restoration of primitive habits became the dominant tendency of his Papacy. Monks who had left their monasteries were expelled from the city and from the Papal States. He would no longer tolerate the practice by which one man had been allowed to enjoy the revenues of an office while delegating its duties to another.

    All begging was forbidden. Even the collection of alms for Masses, which had previously been made by the clergy, was discontinued. A medal was struck representing Christ driving the money changers from the Temple. Paul IV put in place a reform of the papal administration designed to stamp out trafficking of principal positions in the Curia. All secular offices, from the highest to the lowest, were assigned to others based on merit. Important economies were made, and taxes were proportionately remitted. Paul IV established a chest, of which only he held the key, for the purpose of receiving all complaints that anyone desired to make.

    Also, he wasn’t responsible for “painting loincloths onto the nudes of the Last Judgement”. Controversy over this started when Michaelangelo was working on it at the time but was over-ridden by the pope (Paul III) of the time; Michaelangelo ignored Paul IV (the former Cardinal Carafa)‘s instructions to paint ‘more modest’ figures, and it wasn’t until 1565, about six years after his death, that the infamous loincloths and figleaves were painted on:

    The Last Judgment was an object of a dispute between critics within the Catholic Counter-Reformation and those who appreciated the genius of the artist and the Mannerist style of the painting. Michelangelo was accused of being insensitive to proper decorum, in respect of nudity and other aspects of the work, and of flaunting personal style over appropriate depictions of content.

    The Pope’s Master of Ceremonies Biagio da Cesena said “it was most disgraceful that in so sacred a place there should have been depicted all those nude figures, exposing themselves so shamefully, and that it was no work for a papal chapel but rather for the public baths and taverns”. Michelangelo worked Cesena’s face into the scene as Minos, judge of the underworld (far bottom-right corner of the painting) with Donkey ears (i.e. indicating foolishness), while his nudity is covered by a coiled snake. It is said that when he complained to the Pope, the pontiff responded that his jurisdiction did not extend to hell, so the portrait would have to remain.

    Two decades after the fresco was completed, the decrees of the Council of Trent urged restraint in religious imagery. The genitalia in the fresco were painted over with drapery after Michelangelo died in 1564 by the Mannerist artist Daniele da Volterra (who because of that got the nickname “Il Braghettone”, meaning “the breeches maker”), when the Council of Trent condemned nudity in religious art. The Council’s decree in part reads:

    Every superstition shall be removed … all lasciviousness be avoided; in such wise that figures shall not be painted or adorned with a beauty exciting to lust… there be nothing seen that is disorderly, or that is unbecomingly or confusedly arranged, nothing that is profane, nothing indecorous, seeing that holiness becometh the house of God. And that these things may be the more faithfully observed, the holy Synod ordains, that no one be allowed to place, or cause to be placed, any unusual image, in any place, or church, howsoever exempted, except that image have been approved of by the bishop.

    Painting figleaves on the nudes in the Sistine was all part of post-Council of Trent and the Counter Reformation; part of the Reformers’ complaints about luxury, opulence, corruption, decadence, etc. in the church was the patronage of the arts; can you imagine what Luther, for example, would have written about naked figures in a house of worship? “Harlotry and prostitution” would have been the first words but not the last! This turn towards modesty and proprietry was in response to the Reformation and Protestant criticism.

    Now, if they’re stuck to condemning Paul’s predecessor, Julius II, who was more interested in waging war, patronising the arts, and enjoying the fruits of wealth and power, they’d have a point – but Julius was not an enemy of science and the arts, so Michaelangelo’s alleged ‘hidden’ anatomical references wouldn’t have been a brave pseudo-Protestant freethinker’s efforts to strike a blow for SCIENCE!!!

    I think (a) if there are anatomical references, Michaelangelo did put them there deliberately, but not as hidden secret coded evidence of Reason Over Superstition; rather, showing off his art, skill and knowledge (b) any apparent “grotesque” or ungainly appearance in the painting up close neglects that it was never meant to be seen up close; it was viewed from below and from a distance and so exaggeration, distorted perspective and other effects were necessary to let the intended effects be perceptible for a ground-level viewer (the same as in Impressionism and Pointillism, you are not meant to look at the painting up close, as this breaks down into separately visible brush strokes and dots of colour; the effect only works from a particular distance).

    • The original Mr. X says:

      I think it’s a big red flag when these sorts of hidden codes promote some modern, progressive viewpoint; it looks suspiciously like people are projecting their own views onto someone who really didn’t share them. That’s part of the reason why I’d consider, e.g., theories about how “Shakespeare was a secret Catholic/a fan of scholastic philosophy, and put references to this in his works” to be more worthy of consideration than theories about how “Shakespeare thought that gender norms and social hierarchies are damaging and oppressive, just like I do, and put references to this in his works.”

      • Deiseach says:

        Coincidentally, just yesterday I did another art-historical post on Tumblr in response to a photopost and associated comments of a sculptural group of what looked like three hermaphrodites; the OP called it a two thousand year old Greek sculpture of trans women and there was approving commentary along the lines of how this proved transness was not a modern idea etc.

        I jumped in to explain about the Classical imagery of the hermaphrodite and how this wasn’t about transness; I also commented in a note to someone else that I didn’t think it was original but probably a 17th or 18th century work done in emulation of Classical originals (like the Borghese Hermaphroditus); basically, fetish porn in other words.

        Turns out it’s actually a photo-shopped image of an original “Three Graces” by a now-obscure Swiss French artist – that is, original Neo-Classical female statuary group with Classical or Neo-Classical statuary dicks added on 🙂

        I don’t know why I’m doing all this art history stuff, I have no training, never attended a class or course, or anything beyond “read a ton of popular art books along the lines of pop-science books”, apart from it makes me twitch when history is misinterpreted.

    • Matt M says:

      “It is said that when he complained to the Pope, the pontiff responded that his jurisdiction did not extend to hell, so the portrait would have to remain.”

      What is the 16th century equivalent of “rekt”?

    • DrBeat says:

      So, in your professional opinion, how much bullshit is that HBO show “The Young Pope” where they nominate a young guy to be pope and TURNS OUT HE’S A TOTAL DOUCHE?

      • Deiseach says:

        Oh, I haven’t even looked at that thing. I saw something about it with a photo of Jude Law and he’s probably supposed to be wearing a saturno but it looks more like a sombrero, to be blunt, so I’m expecting it’s going to make Dan Brown look like Eamon Duffy by comparison for historical rigour and accuracy. Probably along the lines of (wait for the Chesterton quote from “The Man Who Was Thursday”):

        “When first I became one of the New Anarchists I tried all kinds of respectable disguises. I dressed up as a bishop. I read up all about bishops in our anarchist pamphlets, in Superstition the Vampire and Priests of Prey. I certainly understood from them that bishops are strange and terrible old men keeping a cruel secret from mankind. I was misinformed. When on my first appearing in episcopal gaiters in a drawing-room I cried out in a voice of thunder, ‘Down! down! presumptuous human reason!’ they found out in some way that I was not a bishop at all. I was nabbed at once.

        I’m resisting the impulse to look up more about it because I know a column of boiling blood will come shooting out of the top of my head and I will keel over dead of an apoplexy 🙂

  42. liskantope says:

    I’ll comment here on my general reaction, although I think it’s more or less what several people above have been getting at. The fact that something was built in ancient times that has some coincidental property that occurs with a probability of .003 does not seem especially improbable, when you consider all the structures out there that we’ve discovered from ancient times. One of them had to have some property which satisfied some sort of unlikely coincidence. Maybe it still ends up looking very mildly improbable — after all, I take it the pyramid of Giza is one of the most magnificent wonders of the ancient world — but not more improbable than the interference of aliens.

    • Thecommexokid says:

      The reference class is not “magnificent wonders of the world”; it’s “stuff that crazy UFO people talk about all the time.” This numerical coincidence is meant to be taken as evidence that the conspiracy theorists have been on to something in constantly talking about aliens building the pyramids. There aren’t preexisting rumors that aliens built the hanging gardens of Babylon or the Colossus of Rhodes, so they aren’t comparable.

      I agree that the reference class should probably be bigger than just the Pyramids and Stonehenge, but the relevant additions would be things like Roswell or Area 51 rather than the other wonders of the world. We’re looking for evidence in defense of a preexisting alien conspiracy theory, not just any old interesting numerical coincidence.

  43. Robert L says:

    There is an important principle here, which is that when rebutting nutters over evolution, or pyramids, or whatever, you have to be hyper-careful about getting your arguments absolutely right, because rebutting a rebuttal can look quite similar to proving the original claim. It wasn’t Renaissance Frenchmen (you are about 2 centuries out) and fractions of the size of the earth are an objective, not an arbitrary, thing so deciding on them as a unit of measurement isn’t thinking “exactly like Renaissance Frenchmen”, any more than agreeing with them on the value of pi is thinking exactly like them. OK so it’s a slightly spooky coincidence if they count in base 10 (if they do – they might use different divisors than their base, like old English coinage), but we could construct an argument that evolved creatures are likely to have conveniently countable bits of anatomy on which they base their number system, so and that those bits are likely, for biological reasons I have not yet made up, to result in something between a binary and hexadecimal system.

    • Scott Alexander says:

      I’ve seen concepts of the Renaissance that last into the 1600s.

      Fractions of the size of the Earth are objective, but deciding exactly which fraction of which measurement to choose is pretty arbitrary. It would be very strange if aliens coincidentally used our 24-hour clock, even though “one twenty-fourth of the length of the day” is an objective measurement. This is especially true if the aliens don’t come from Earth.

  44. Furslid says:

    I think there’s a better reason for 360 degree circles. 360 has a lot of useful factors. 2x2x2x3x3x5= 360. So there are a lot of useful ways to slice up a circle and get a whole number of degrees.

    • Machine Interface says:

      There’s another interesting reason, which also explains why our hours have 60 minutes and our minutes 60 seconds: the Sumerian language, unlike most other human languages that count in base 10, counted in base 60 (though it didn’t have 60 different numerals from 1 to 60; rather, numerals lower than 60 were still encoded in base 10). The convention of this system were then partly retained by subsequent civilizations, who counted in base 10 but inherited a whole bunch of measurement systems constructed on base 60.

    • Incurian says:

      Fun fact: this is also why US Artillerymen decided there are 6400 mils in a circle, when there are only 6283 milliradians in a circle. Some other numbers adopted by other countries are 6000 and 6200.

  45. suntzuanime says:

    I’m sure you’re aware, but just to clarify: this is why the scientific method fetishizes advance predictions so much. The garden of forking paths can *sort* of be corrected for if you try, but it’s hard to figure out how to correct for “why are we considering the latitude of the Pyramid of Giza and not the height of the Mosque of Djenne”.

    • Matt M says:


      I don’t know much about statistics so maybe I’m explaining this wrong – but it seems to me you can’t just consider degrees of freedom in relation to pyramids and latitudes. You’d have to consider the entire set of “weird measurements of well known buildings and monuments” at which point you could start racking up significantly more degrees of freedom than you have now – up to the point where it wouldn’t be shocking that one ancient wonder has one measurement that strikes modern society as significant in some way.

      • AnteriorMotive says:

        When someone’s got you accepting the premise that they’re analyzing buildings and physical laws they’ve already got you. The trick with numerology and friends is to retrace their steps even further back in the garden of forking paths. If it wasnt pyramids encoding the speed of light, it would be the heiroglyphs for Akenaten translitering into ancient Greek as “star man.”

        • James Miller says:

          The claim that numerology is silly should be falsifiable meaning that there should exist potential evidence that would convince you that numerology is true.

          • Douglas Knight says:

            No, it shouldn’t. You should admit why you’re rejecting something, whether you gave it a chance, but you shouldn’t give everything a chance.

          • James Miller says:

            If a large number of people believe in something, there should be evidence capable of getting you to believe it too.

          • Chrysophylax says:

            “The claim that numerology is silly should be falsifiable meaning that there should exist potential evidence that would convince you that numerology is true.”

            Correct. If the world looked like Unsong, I would happily believe in the power of numerology (specifically, gematria).

            “No, it shouldn’t. You should admit why you’re rejecting something, whether you gave it a chance, but you shouldn’t give everything a chance.”

            You should not be infinitely certain of anything. If numerology starts being perfectly predictive tomorrow, you should not be stuck assigning it zero probability. You don’t have to assign a probability big enough to notice, but it needs to be non-zero, because that’s a claim that you have infinite evidence against it.

            “If a large number of people believe in something, there should be evidence capable of getting you to believe it too.”

            If people believe something, it controls anticipations and so is a meaningful claim under a correspondence theory of truth. If a million people claim to believe something, it is quite likely that the professed belief is not a meaningful truth claim. My refusal to be infinitely confident about it is entirely due to me being a fallible reasoner and nothing to do with popular opinions being sane.

          • suntzuanime says:

            See, this is what’s wrong with falsifiability fetishism, it’s doing a lot less good work than advance prediction fetishism. People take it to mean, “you have to admit that I could be right, or else you’re automatically wrong”. Even probability doesn’t quite work that way, much less human discourse.

          • Chrysophylax says:

            @suntzuanime: Please clarify what you’re arguing against. I’m not sure whether you disagree with me.

            Popperian falsifiability, taken totally literally, isn’t right because it claims that only disconfirmation is evidence. This is mathematically incoherent: your probabilities will never settle because the expected evidence will never balance out, and won’t sum to 1 because P(¬A) can’t increase when P(A) decreases.

            That doesn’t make the correspondence theory of truth wrong and doesn’t permit a finite agent to rationally violate Cromwell’s Rule. Every claim is true, false or meaningless, and every claim must be assigned non-zero probability unless you have infinite evidence of the validity of your own reasoning.

          • suntzuanime says:

            Sorry, I was quarreling with James Miller, not you. (James Miller was the one fetishizing falsifiability.)

      • Loquat says:

        That was my first thought on reading this post – I am extremely confident that the first person to notice (and make a big deal over) the Great Pyramid’s latitude matching the speed of light had not made any such prediction in advance, but was just reviewing all the numeric measurements of the pyramid they could get their hands on and comparing them to known Important Science Numbers like speed of light, pi, etc. That gives you plenty of tickets without even expanding your search beyond one building.

        • suntzuanime says:

          Well, that’s the premise of the post, and the idea is that you can correct for that, and Scott has attempted to correct for that and has decided there are not plenty of tickets.

          My point is that you do have to expand the search, beyond the point where it can be meaningfully corrected for.

          • Loquat says:

            Scott didn’t do a very good job of correcting – he only included latitude, longitude, height, and width, with a few different ways of measuring each. There are tons more numbers that measure various aspects of the Great Pyramid! Measurements of interior hallways and rooms, of distance between the Pyramid and various other important places, anything that forms an angle – if you’re not making advance predictions, you’re free to measure every conceivable thing about your chosen monument in the search for interesting coincidences.

    • jaimeastorga2000 says:

      “why are we considering the latitude of the Pyramid of Giza and not the height of the Mosque of Djenne”

      Because the latter is a random mudhut in Songhai, according to OT61.

  46. Sixth Estate says:

    I don’t know if it helps with your lottery ticket analogy, in particular, but the hypothesis that the location of the Pyramids is interesting can only be understood within the broader universe of hypothetical reasons why it might be interesting. The fact that something could have occurred by chance only 1 in 300 times doesn’t make it implausible that it did so, especially since we do have the Great Pyramid.

    To that end, if the reason for this exercise was to balance against the possibility of the ancient Egyptians having been given the pyramids by aliens, one would have to consider whether a 1 in 300 chance of an ancient civilization building an interesting structure at these coordinates by chance is greater or less than the chances of an otherwise undetected alien civilization evolving somewhere else in the universe, coming to Earth for unknown reasons, helping the Egyptians build the Pyramids for unknown reasons, locating the Pyramids so as to send a cryptic message to future humans (or other aliens) for unknown reasons, not bothering to leave rather more direct and obvious messages for unknown reasons, and then leaving Earth, again, for unknown reasons.

    I don’t know how many lottery tickets you will need to account for all of that, but I’m betting it’s lots.

    This was an interesting read and appears to be the pseudo-archaeological equivalent of the Bible codes.

  47. Markus Ramikin says:

    “I think a much more interesting conspiracy theory would be that aliens designed the Earth to encode secret wisdom about the periods of pendulums.”

    You made my day that much better, thank you.

  48. sovietKaleEatYou says:

    Applying Occam’s razor is notoriously hard. But roughly, what you want to do is rate the “importance” of every number as roughly the probability that at any given point when you are thinking about a concept that can be numerically encoded, you are in fact thinking about this concept. Since we don’t have statistics for such small probabilities, you might want to take the probability that at any given moment you’re thinking about the Pyramid of Giza — which is probably pretty high if you’re a fan of alien theories — and multiply it by the probability that you’re thinking about the concept of latitude in the context of a cultural artifact.

    Then you want to multiply this by the probability that you’re thinking of a number and you get the speed of light, which as you’ve pointed out is pretty important since we often think of fundamental physical quantities in terms of numbers. So I think of these two probabilities the first is a few orders of magnitude “less important” than the second, like maybe the first is 10^(-5 or 6) and the second is something like 10^(-2) and there are some other degrees of freedom of where to put the decimal point and such. I think that if you’re using this “for research purposes”, you shouldn’t cut off the last three digits (as the google maps latitude is one of the most likely numbers that would pop up when searching for “pyramid of giza latitude”, and we’re in human brain-space here), and for the same reason the ambiguities with units, etc. shouldn’t offset the factors. Since this seems like a rare and “newsworthy” event for the community involved, it is fair to say that the order of magnitude predicted by “Occam’s razor” should be quite close to the actual level of precision (in general it would of course be much smaller). Hell, trying to set up a blinded experiment in collaboration with the UFO community would be a great way to calibrate superpredictors at extremely low probabilities, sounds like something right up your alley!

  49. jaimeastorga2000 says:

    Longitude is measured from the Prime Meridian, which is an arbitrary convention. I don’t think it counts.

    • Sniffnoy says:

      Oh man, I totally meant to include this in my long comment, but I completely forgot…

    • John Schilling says:

      If Revolutionary Frenchmen can be enlisted in this conspiracy of coincidence, so can Victorian Englishmen. Longitude counts.

      So I’m counting twelve options on two degrees of freedom where Scott allowed for one degree with two options:

      29.9792 vs 2.99792 vs 0.299792 degrees, North vs. South vs. East vs West.

      Up to P=0.018; another factor of three and we can relegate this to the statistical obscurity it deserves.

    • Rob K says:

      The 360 degree circle seems like a fairly arbitary choice too, although I suppose the aliens could have been busily incepting the Babylonians with the idea for base 60 in their spare time.

      • Autolykos says:

        Which may be counted as weak evidence for the hypothesis that our alien ancestors have 60 tentacles…

  50. CatCube says:

    One other thing that occurred to me: what horizontal datum are you using? The coordinates 29.9792°N, 31.1342880°E falls on the Great Pyramid with WGS84, but if you use Old Egyptian 1907, that pin will be about 170 meters to the SW of where it shows on Google Maps, or somewhere in the neighborhood of 10 meters outside the pyramid. For Egyptian 1930, it could be as much as 200 meters south, or 85 meters outside the bounds of the pyramid.

    • Sniffnoy says:

      Yikes, now there’s a can of worms!

    • Wanderratte says:

      And why use the latitude? Why not the angle from the north (or south) pole to the Great Pyramid? And so on, and so on…

    • Ron says:

      So, can the pyramid-lightspeed thing be an eastern egg due WGS84 engineers?

      • bean says:

        Unlikely. Geodeticists don’t do that kind of thing, particularly ones working for the DoD.

      • John Colanduoni says:

        WGS84 uses an ellipsoid model (which means only a few parameters), so it would really hard to do that without making a lot of things way off. EGM08 (Earth Gravitational Model) on the other hand has thousands, so you could probably pull something there without it causing many noticable problems.

    • CatCube says:

      I misread the paper I was looking at. The quantities it gave were for the shift of the center of the reference ellipsoid, which are feeder numbers for equations to figure out transformations, not the transformations themselves. I knew that datum shifts aren’t constant over medium to long distances, so it should have jumped out at me that I can’t just take a constant set of numbers and the Pythagorean theorem. In my defense, hundreds of feet is a plausible shift, especially here on the west coast from NAD27 to WGS84.

      Doing it with a conversion site, the pin will move off of the near-center of the pyramid, but not outside it’s bounds for the Egyptian 1930 datum, and there’s very little difference for the Old Egyptian 1907–you can quibble with the rounding to argue it still works.

      It’s still silly, because you *do* need to specify a datum when you’re talking about super-precise coordinates, but it’s not quite the slam-dunk I made it sound like.

      On the bright side, I did figure out a little more about geodetic datums and transformations, which has been on my “to learn” list for a while.

    • Scott Alexander says:

      Aren’t modern datums (data?) just plain better than older ones, so that for a certain definition of latitude we would expect superadvanced aliens’ measurements and our own measurements to converge, and to both be better than 1907 people’s measurements?

      • mafi says:

        Older datums will often be less accurate but there are other reasons that they differ. The first is continental drift, a no net rotation constraint attempts to keep the things as unchanged as possible. The second is that the best datum for the world as a whole is different to the best datum for a given section of the world – so if you’re working in Australia it can be better to use an Australian datum rather than WGS84.

  51. CabbageControl says:

    You only remembered the initial correctly. It’s Revolutionary France not Renaissance.

  52. gronald says:

    I like which notes: “[there are] numerous other landmarks at the same latitude (it runs through the centre of New Orleans and Houston airport)”.

    (I suppose we could explain this by saying that the aliens who built the Houston airport were trying to tell us important facts about the speed of light?)

    • suntzuanime says:

      The Egyptians who built the Houston airport were trying to tell us important facts about the Great Pyramid of Giza.

    • Deiseach says:

      it runs through the centre of New Orleans and Houston airport

      Well, there we have it! New Orleans is plainly a reference to old Orleans, which is in France, which is where those Renaissance/Revolutionary Frenchmen lived with their metres! That’s the French Connection the aliens are citing! 🙂

    • Jaskologist says:

      Evidence for ley lines, clearly.

  53. Sniffnoy says:

    OK, I have a lot of nitpicks here, some of which you might even want to fix.

    1. The meter was invented way after the Renaissance! (I think you should probably fix this one.)

    2. The definition of the meter has changed quite a bit over time, though obviously it’s always kept the same approximate value. Currently, the meter is actually defined to be the distance traveled by light in 1/299,792,458 of a second, so that 299,792,458 m/s is the exact speed of light. Of course that just leaves the question of what the definition of a second is. In ordinary usage of course one second is a 3600th of an hour, which is is one 24th of a day, but officially one second is “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom”.

    OK, but what’s the point of all this? The point is that you’ve already noted that the “to 7 decimal places” bit makes no sense when you look at the latitude, as the Great Pyramid is wider than 10^-7 degrees, but it also doesn’t make sense when you look at the definition of meter or second being used. You noted at the beginning that one of the notions of meter you discussed was 99.7% of the other, but that’s only 3 decimal places, not seven.

    3. And again, why use seconds? Let’s go with the usual notion rather than the official one, for obvious reasons. Why would aliens divide the day into 24 hours? Why divide hours into 60 minutes and minutes into 60 seconds? There’s considerably more arbitrariness here than you’ve mentioned. Added: And this is all assuming that they’re using Earth days in the first place (I guess that bit makes some sense since they’re trying to communicate with us Earthlings).

    4. (Added) Here’s another bit of arbitrariness: The base you’re representing these numbers in, since by looking at strings of digits in base b in this way, you’re essentially allowing free multiplication by powers of b, so it matters what b is. Admittedly here you’ve kind of said that your choice of the meter fixes you to base 10, but in general this is something worth remembering, when you see numbers translated into strings of digits rather than used as pure numbers.

    5. (By the way, I have a suspicion you are misusing the term “degrees of freedom”? A little uncertain here.)

    6. Regarding decimal point placement, don’t forget the possibility of it being at 0.29 degrees latitude, rather than 2.9 or 29!

    7. Avogadro’s number isn’t a physical constant; it, and the idea of the mole, are pure convention.

    8. As for what physical constant the aliens would use, ideally they’d use a dimensionless one and avoid the whole units problem. Fine structure constant seems the obvious candidate there.

    Really, to my mind, any such comparison that relies on using a specific and arbitrary system of units (edit: or a particular and non-arbitrary choice of numeral system, or basically any convention that doesn’t have a good universal reason behind it) is pretty much automatically disqualified. Not that it would be that much better if it didn’t, but at least there would be a “real” coincidence that was unambiguously there, rather than one that only appears due to our particular convention.

    • John Colanduoni says:

      I think it’s a correct use of “degrees of freedom”. He’s trying to analyze the neighborhood of a particular point in the space of “all things that sound like crazy coincidences” by finding things he can independently vary without leaving the neighborhood of that point. Of course we don’t have a remotely formal definition of “neighborhood” here (or something like distance that would yield one), hence the debate over whether certain possibilities are “too far away”, but I think it’s a good analogy.

    • kboon says:

      The length of a day is not consistent to within seconds over timespans of thousands of years. They might also have used speed of light in water, or in air.

      Also they have a whole internet to help look for coincidences. IDK if these are actually true, but then I haven’t opened Google Maps to check Scott here either.

    • Scott Alexander says:

      The meter was invented in the 1670s or so. I don’t know a good name for that time period, but I think I’ve heard of people stretching the Renaissance in Northern Europe to last about that long.

      I think the argument from meter definition makes more sense as 1/10 millionth the size of a hemisphere than as the pendulum period, for the reasons you mention.

      Avagadro’s number is convention, but moles seem pretty natural if your unit of measurement is the gram, and the gram seems about as natural as the meter, ie somewhat but not very.

      I agree that an alternate base is a possibility, but it wouldn’t have been as “impressive” as seeing it all laid out in good old base 10, so I felt like it would have been wrong to include it.

      • Douglas Knight says:

        I don’t know the history of the meter, but your link does not support the claim that the 1670s meter was particularly French.

      • bean says:

        The meter was a creation of the French Revolution, not the 1670s. Yes, there were proposals that lead to it dating back that far, but the Earth’s shape is really complicated, so the actual meter we use today is based on a specific set of measurements done in the 1790s. The meter is actually slightly shorter than one ten-millionth of the distance between the equator and the pole, by about .2 mm. There was a math error during the creation of the standard bar, and the existing time and length standards were based on that.

        • Deiseach says:

          We should take into account Napoleon’s expedition to Egypt as well. He deliberately brought a team of scientists with him, who mapped and measured everything around them and more or less kicked off ‘modern’ Egyptology.

          Coincidence that his ‘military’ invasion started in 1798 and that the ‘official metre platinum bar’ was cast in 1799? Do we really believe that? 🙂

          (Honestly, linking the French to the Egpytians to ancient aliens is so easy and so fun!)

          • bean says:

            That’s a really good one. It’s so crazy it almost works, although it obviously requires the French to know the definition that will be adopted for the second, and the speed of light.

    • The arbitrariness of the second struck me as well. I wonder if it might have originated with the human pulse. A resting pulse rate of 60 beats a minute seems pretty close to normal.

      But that doesn’t solve the problem of explaining why the Altanteans use the same second we do, even if we assume they are humans, because it only gives a very approximate value, and varying the second +-5% gives you lots and lots more degrees of freedom.

      • Cerebral Paul Z. says:

        As I understand it “second” is short for “second minute”– i.e., what you get when you divide the hour by 60 a second time. So the 60 is inherited from the (arbitrary) decision to divide the hour into 60 minutes.

        • keranih says:

          So the 60 is inherited from the (arbitrary) decision to divide the hour into 60 minutes.

          As I understand it, not so arbitrary. Minutes and seconds are also measures of distance/angles – 60 minutes to a degree, 60 seconds to a minute.

          360 degrees to a whole circle, which is 6 groups of 60. Or 12 groups of 30, which were a pretty close match to the months of the year. The habit of making each daylight period 12 hours and every night twelve hours arose in several cultures, and is thought to be independent.

      • Fossegrimen says:

        If you go out and find a reasonably flat piece of sand or gravel and use a stick and a piece of string to try and construct an accurate sundial, you will find that the only sane numbers in the entire universe are: 6, 12, (24) and 60.

        This is dictated by basic trigonometry and I would be very surprised if it’s not the origin of the second.

        Aside: I believe the Swedes use a 400 degree circle, at least when I read a Swedish land surveillance tutorial they kept using right angles of 100 degrees.

        • Lucy Lynch says:

          The Swedish military used to use a 400 degree compass. I don’t think they do that any more, and in any case geometry classes use 360 degrees before introducing radians.

    • Spookykou says:

      Everyone seems convinced that the Renaissance was clearly over by the 1670, but Wikipedia tells me 14th to 17th centuries, which matches pretty well with my, admittedly less than stellar, education. Considering just how many people seem to think that Scott was ‘obviously’ wrong on this point, I was wondering if somebody could point me to a prominent alternative timeline from the one used by Wikipedia?

      • Douglas Knight says:

        No one other than Wikipedia ever extends the Italian Renaissance past the death of Galileo.

        Google is a pretty prominent source. It says 1300-1600. Most people say only 100 or 200 years. Ask your friends!

        Try this essay. Not for its precise definition of the Renaissance, but for its discussion of what definitions other people use, and why. Often one person will (illegitimately) use two definitions for different purposes. 1300-1650 is what you get by stretching to cover all those different periods.

  54. dtsund says:

    I’d omit Avogadro’s Number from the list of interesting constants; unlike the speed of light or the gravitational constant or the like, that one’s really entirely arbitrary, purely map rather than territory.

    • Autolykos says:

      Avogadro’s constant isn’t any more arbitrary than the speed of light. It’s closely linked to neutron and proton mass. So, basically, the arbitrary unit in there is not the meter, but the gram.

      • Sniffnoy says:

        Avogadro’s number is a dimensionless number used to count molecules because it makes it more convenient. The speed of light is, well, the speed of light. It’s fundamental, and, if we ignore the issue of what units to measure it in, is definitely not arbitrary. Avogadro’s number is the number of atoms in 12 grams of carbon-12. There’s no reason one even needs such a notion. Sure, it’s convenient to know if you’re actually working with the stuff, but even if we ignore the fact that the gram is arbitrary (as you point out) and imagine that it isn’t, Avogadro’s number would still be arbitrary and in no way fundamental. The only time it wouldn’t be arbitrary is if you were, in fact, working with just carbon-12 (and then of course it would still be arbitrary because of the gram-dependency you point out).

        • Autolykos says:

          Carbon-12 wasn’t an arbitrary choice, though (or rather, a different, equally sane choice wouldn’t have changed much) – it’s six protons and six neutrons, so an atomic mass unit is exactly the mass of one proton, one neutron and one electron, divided by two. If you took, say, one fourth of Helium-4, you would have gotten exactly the same number (well, almost exactly, because of mass-energy equivalence of the potential of nuclear forces). It is a useful concept for chemistry, and really completely defined by the gram. I’d expect any advanced alien civilization to have a similar constant based on their favorite mass unit.

          • Sniffnoy says:

            Oh, that’s a good point. I guess fundamentally it is the ratio of the gram to the amu (even though how it is used is just as as convenient number for counting things). So you’re right, all the arbitrariness there really is in the choice of the gram; there isn’t any additional as I claimed above. Of course, it’s still too far from fundamental to be a good candidate, but that’s a separate matter.

          • Douglas Knight says:

            But you do get a different answer with Helium-4. The AMU defined by Helium-4 is 1.00065 times the AMU as defined by Carbon-12. Wolfram Alpha lists two obsolete AMUs, too. Thus the AMU, up to such choices, only has 3 significant figures. (p+e+n)/2 is 1.0082, so down to 2 figures.

          • Autolykos says:

            @Douglas Knight: You’re right, of course. Up to iron, larger nuclei have less potential energy from nuclear forces, so they become slightly lighter than you’d expect from adding up their parts, due to mass-energy equivalence.
            Of course, encoding the number in the characteristics of a building isn’t much more accurate than two to three figures, either (like you’d get for the Great Pyramid, if Revolutionary Frenchmen had measured the circumference of the earth correctly).

  55. CatCube says:

    I think you’re putting too much weight on trying to say that there’s “still” p=0.003 “left.” Just because there’s only a 0.3% chance of this particular coincidence occurring doesn’t stop it being coincidence. I mean, it’s unlikely to go for 28 throws in a row in craps without sevening out, but I’ve done it. Sometimes the dice come up your way; there’s nothing mysterious about it. Similarly, if all you have is a data set giving you a correlation between two events, that’s only a starting point; you still need to do the legwork to show causation (including, in some cases, what direction that causation runs).

    The Birthday Paradox would seem to apply here. If you’ve got 23 people in a room there’s a 50% chance that two of them have the same birthday; however, there’s only a 6% chance that any of them have the same birthday as you. To apply it to your pyramid example, it’s not unlikely that some coincidence will occur, even if any particular coincidence is unlikely.

    Edit: For a funny coincidence, I looked up the probability of my sevening out after 28 rolls at the craps table. It’s 0.003

    • HeelBearCub says:

      In a world of 7 billion people, there are thousands of people who are “1 in a million”.

      Basically, we should expect to find out about 1 in a million coincidences all the time. There are so many events that occur, and the interesting ones are the ones that are “rare”.

      But what would be really, really weird is if rare things did not happen.

      • gerrydelasel says:

        As Terry Pratchett observed: “Scientists have calculated that the chances of something so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.

  56. John Colanduoni says:

    I would include dimensionless constants like the fine-structure constant in your degrees of freedom for sure, since then you remove the whole Renaissance French issue. The fine-structure constant itself is already big enough of a coincidence to get multiple serious physicists (like Pauli and Born) truly interested in numerological explanations.

    • Deiseach says:

      I think the simplest way to remove the Renaissance French notion is to remember that we are dealing with units of distance. No, the Egyptians didn’t work in metres and the French didn’t work in cubits (or whatever unit the Egyptians used). But we’re still “converting measuring miles into kilometres” for lightspeed, and “a meter is based on this much distance from the Equator to the Pole” and basically all measurements are derived from using human proportions – the French first had to measure from the Equator to the Pole, or take the best measurement of the time, then chop that up into “and this makes so many metres to the Equator-Pole distance”. They wanted a nice, tidy decimal measure so they fiddled around to get a metre that would give them one that fit into that distance; a metre is 39.37 inches which isn’t a nice round 40 inches, but a slight difference and it could have been.

      Since Egyptians and French are both humans, the basic foundations used for measurement “the length of an arm” or “the length of a stride” or “width of palm” are all going to be within the same range, so the units of measurement are going to be pretty similar in the end, so “gasp, the measure we measure light with is related to the measure we measure longitude with” is not a big deal.

      Is it a neat coincidence that there happens to be a significant building on that particular site? Yes, but it’s only a coincidence. There could equally have been nothing there (if Egypt had never developed as an empire, or if the Pharoahs decided to go for cremation instead of mummification and huge big tombs), or if lightspeed were slightly different or measured in a different way (we used boinkos per second, where a boinko is sixty spleeches and a spleech is ‘the width of your middle three toes’), the corresponding latitude could be in the middle of the Mediterranean or something.

    • fion says:

      I agree, but I would argue further that the *only* interesting constants of nature are dimensionless constants. Any dimensionful constant is really just a ratio between a natural quantity and an unnatural unit.

      So yes, the fine structure constant, also the ratios of masses of fundamental particles, perhaps the ratio of the Hubble time to the Planck time, the ratios of the SM gauge couplings…

      There are a *lot* of these!