# The Pyramid And The Garden

I.

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 110,000,000th 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 110,000,000th-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?

II.

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

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 11 mil­lion chance of win­ning to some­thing more like 110,000. 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 1300 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 1300 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.

III.

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.

• Just a small nit­p­cik­ing cor­rec­tion : the met­ric sys­tem wasn’t in­vented in the 1600s, but in the late 1700s dur­ing French Revolu­tion.

• A some­what mod­er­ate nit­pick, a lot of your de­grees of free­dom don’t mul­ti­ply with each other. For ex­am­ple, #4 and #6. We have 2 types of lat­ti­tude sys­tems, and we have 3 types of mea­sure­ments (lo­ca­tion, height, width) But this only gives us 4 pos­si­ble com­bi­na­tions, not 6 (lat­ti­tude 1, lat­ti­tude 2, width, height). And a lot of your other de­grees of free­dom don’t mul­ti­ply like lon­gi­tude/​lat­ti­tude, or lo­ca­tion also don’t mul­ti­ply with width/​height. Similarly, #3 and #7 don’t mul­ti­ply. You only have two de­grees of free­dom cor­re­spond­ing to differ­ent mon­u­ments if ev­ery al­ter­nate lo­ca­tion also has two valid mon­u­ments.

Some of this can be fixed by fus­ing some cat­e­gories and treat­ing them as ad­di­tive, but in gen­eral this means your num­ber of com­bi­na­tions should be smaller than you think (and more math­e­mat­i­cally com­pli­cated to com­pute).

• Thanks for point­ing that out; I no­ticed that too. This is per­haps partly made up for by the fact that he doesn’t count feet or the mouth of the Nile river as pos­si­bil­ities.

• There’s one fac­tor to ex­plain this co­in­ci­dence that is not refer­enced here and I couldn’t find it men­tioned on the SSC post ei­ther: po­lar mo­tion.

As a re­cap, lat­i­tude is the an­gle be­tween a given point (like the tip of the Pyra­mid) and the Equa­tor. The Equa­tor is the points at the sur­face that are equidis­tant from both poles. And the poles are the points where the ro­ta­tion axis in­ter­sects the sur­face. They’re the points the Earth ro­tates around, sort of.

Well, it turns out that the axis of ro­ta­tion is not fixed with re­spect to the sur­face. This is in­de­pen­dent of plate tec­ton­ics, the fact that some parts of the sur­face move with re­gards to each other. The Earth’s sur­face could be perfectly im­mov­able and we could still have po­lar mo­tion. The scale of the mo­tion is that, per Wikipe­dia, it has moved 20m since 1900, and re­cently the di­rec­tion has changed from 80 de­grees west to­wards the Prime Meri­dian.

To illus­trate this, imag­ine that some cos­mic force made the ex­act point where I’m cur­rently sit­ting writ­ing this com­ment be a pole. That is, the Earth re­volves around this very point in my bed­room. (I guess it’s a good thing I’m snug­gling un­der a blan­ket.) Then the Equa­tor would be this line be­tween the brighter and darker parts of the map (I used the near­est air­port, São Paulo-Con­gonhas, as the pole); it runs some­where near San Diego, just barely in­cludes all of Great Bri­tain and Antarc­tica, and crosses Egypt sus­pi­ciously close to the Pyra­mids. They’re ac­tu­ally 209 km from it on the op­po­site hemi­sphere as me, so their lat­i­tude would be just shy of nega­tive two de­grees.

Now, of course at the time the aliens Khufu’s slaves built the Pyra­mids the North Pole was some­where fairly close to its pre­sent lo­ca­tion, and not in trop­i­cal South Amer­ica. But it’d be very un­likely if it was at pre­cisely its cur­rent lo­ca­tion! (Or wher­ever it was at the time when the ver­sion of WGS84 Google Maps uses was made.) And since the pole can move 20m in 1.2 cen­turies, it could have moved way more than the size of the base of the pyra­mid, which mea­sures just over 200m, since the 26th cen­tury BCE.

• Another de­gree of free­dom comes from the num­ber of differ­ent top­ics there are where aliens are claimed to have med­dled. I ad­mit I can’t think of too many off the top of my head (crop cir­cles? maybe 9/​11?) but I’d be will­ing to bet there are at least 5 pop­u­lar, se­ri­ous claims to be had. That would bring the odds up to 160, or p = .017.

Maybe an­other de­gree can be squeezed out by say­ing that there are top­ics in pseu­do­science be­sides aliens, and top­ics to house crazy co­in­ci­dences be­sides pseu­do­science. I’m not sure how this could be counted, though.

One last thought, it’s not nec­es­sary to get p up to any­thing like 1. Coin­ci­dences do hap­pen, af­ter all.

• Pseudo-Science can be use­ful if you lack the time or the tools to do the real sci­ence cor­rectly. Any­one who’s ever stud­ied the Navier Stokes Equa­tion (NSE) knows you can more or less de­scribe a nice, warm sum­mer breeze in math­e­mat­i­cal terms with­out solv­ing all the way down tot he 4th or­der terms. The Co­ri­o­lus Force term in the NSE will not be large enough to bear any rele­vance to how strong or pleas­ant a breeze you ex­pe­rience. Some would say you are pseudo-sci­en­tific if you just short­hand your calcu­la­tion and only take tem­per­a­ture and pres­sure differ­ences into ac­count, but in re­al­ity, you are solv­ing in about twenty sec­onds of com­pu­ta­tional time what could take all day if you re­ally wanted to know how much ev­ery term of the equa­tion mat­tered.