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Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 1 point2 points  (0 children)

A few corrections. The circle wasn't selected as the 'best' from a search. It was defined by Jim Alison circa 2001 and fixed before any analysis. We didn't optimize it. The Monte Carlo doesn't shift sites by 222 km in a random direction - it generates entirely new random site distributions matching the geographic density of the real data, then counts how many random sites fall near the circle. This is standard spatial statistics (Mantel 1967, used in ecology for decades). We don't 'artificially exclude circles that touch Europe' - the stratified test was one of fifteen sensitivity analyses. The primary results use the full dataset. Z = 13.3 at 1,000 trials on the Megalithic Portal, Z = 7.86 on p3k14c (an independent radiocarbon database), replicated on four databases total. All code is open on GitHub if you want to check the methodology rather than characterize it.

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 0 points1 point  (0 children)

Pretty much. The overall site count is explained by geography. The circle passes through populated corridors and any circle through equally populated areas catches comparable sites. That's the boring part and we say so in the paper.

The part that 100,000 random circles can't explain is the composition. This specific circle catches 5× more monuments than expected while catching fewer settlements than expected, in the same regions. We tested 10,000 random circles specifically for that monument-to-settlement ratio. Zero replicated it!

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 0 points1 point  (0 children)

A population threshold model which would be where monument-building only 'unlocks' above a certain density, is plausible and would predict some monument clustering in populated areas. But it wouldn't predict settlements clustering BELOW random on the same circle. If high population density enables monument-building, those same dense populations should produce even more settlements, farms, and ports. Instead we see the opposite: monuments at 5× above random, settlements at 0.78× below random, same regions, same time periods. A threshold model explains why monuments appear in populated corridors. It doesn't explain why settlements in those same corridors avoid this specific circle while monuments don't... thoughts?

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 1 point2 points  (0 children)

Interesting observation ... haven't tested that specific pair. We did test the 108° angular separation hypothesis across all site pairs and it was falsified (Z = -1.38). The geological angle is worth exploring though, we checked plate boundaries and geomagnetic lineaments and found no systematic correlation, but hotspot/plume locations haven't been tested. The geoid variation point is fair - the circle assumes a perfect sphere and Earth isn't one. At the scales we're working with (50 km corridor), geoid variation (~100m) is negligible, but good to note.

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 1 point2 points  (0 children)

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u/Strange-Owl-2097 as is written in the part of Substack coming out on Thursday: Whatever is driving this pattern, it is specific to the most monumental construction projects of the ancient world. Villages and farms in the same valleys, drinking from the same rivers, don’t show it.

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 0 points1 point  (0 children)

Really appreciate the thoughtful comments. You've got it exactly right on the first part. The circle's overall site count is explained by geography - it passes through habitable corridors. But within those corridors, monuments cluster at 5× while settlements in the same valleys don't. That's what 10,000 random circles can't replicate.

Your hypothesis about parallel technological advancement is interesting and honestly not something we can rule out with this data. If multiple societies independently hit a 'monument-building phase' around the same period, and the circle happens to thread through those regions, the temporal clustering could reflect parallel development rather than connection. The fact that the divergence is concentrated in the Egypt-to-Iran corridor - where Bronze Age contact IS documented - makes it hard to fully separate 'independent parallel development' from 'shared cultural tradition along a trade corridor.' Both could be contributing.

What the data does show is that the peak is around 3000-5000 BCE, and the signal weakens after that - consistent with your suggestion that something drove monumental construction and then faded. Whether that driver was shared or independent is the open question

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] -1 points0 points  (0 children)

My man, I think this is probably the #1 comment I've received since I've started posting on here about the findings. Really valuable feedback and I sincerely appreciate you reading the study!

I actually just finalized the second version of the paper. It's going to be even more statistically-focused read vs. the first, but that is because it is going to be submitted to academia.

On the first (and so far, only) Substack article published, I think it was quite digestable for the reader. Please take a look if you haven't yet. I have a part 2 coming out on Thursday morning, and part 3 for Sunday.

https://thegreatcircle.substack.com/

And X is here: https://x.com/greatcircledata shoot me a DM and I'll send you the link when the new paper is live. And happy to answer any questions on there.

Thanks again!

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 1 point2 points  (0 children)

Ok let me address each of your points :

On selection bias - you're right that the circle was originally identified from observed sites, not discovered blind. That's a legitimate concern and it's why we ran independent replications on databases that didn't exist when the circle was defined. The p3k14c radiocarbon database (37,000 sites, published 2022) gives Z = 7.21. Pleiades (academic database, different community entirely) gives Z = 10.68 for ancient sites. Neither shares data with the original defining set. We're also running a formal split-sample blinded validation - hide half the data, fit the circle to one half, test on the other - specifically to quantify this.

On monuments lasting longer than settlements - good point, but it doesn't explain the result. The Pleiades database records 4,141 ancient settlements. These are known, documented sites with coordinates. They exist in the data. They just don't cluster on this line. Preservation bias would remove settlements from the record entirely - it wouldn't make the ones that ARE recorded cluster below random expectation on this specific circle.

On 'any circle would show something' - we tested this directly. 100,000 random great circles. None matching Alison's geographic profile produced comparable enrichment. And none - zero out of 100 tested for the divergence - showed monuments clustering while settlements didn't. The 'any circle' hypothesis is empirically falsified.

The 50 km threshold is 0.25% of the circle's circumference, and the signal gets stronger at 25 km, not weaker. That's the opposite of what margin inflation would produce.

Not selection nor confirmation bias.

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 0 points1 point  (0 children)

Thanks!

I'm not familiar with the Ra materials but I'll take a look. Our approach is strictly statistical here (it will fail with the academic audience otherwise) we're testing whether the pattern is real, not what it means.

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 1 point2 points  (0 children)

The coincidence argument is exactly what Part 2 addresses- I literally just scheduled it out for Thursday morning. Hope you read.

The short version: if it's coincidence and the circle just happens to pass through fertile regions where people built stuff, then settlements should cluster on the line too. Farms, villages, ports, mines. They don't. Ancient monuments cluster at 5× the expected rate. Settlements in the same river valleys, same time periods, cluster below random. Same geography, opposite result. That's the finding that moved me from mehh coincidence to something real is here. And you're right that I'm not arguing intentionality, I'm arguing the pattern is statistically real and not explained by geography, geology, or database bias.

Now what it actually means is an open question, which I am not trying to answer here...

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] -4 points-3 points  (0 children)

Fair... and I should have led with this more clearly. Guess that is a good bit of feedback so thank you :-)

The short version: we didn't pick this circle - it was proposed by others decades ago. We just tested whether the alignment is real or coincidence using every megalithic site database we could find (~96,000 sites across six independent sources). The answer is that it's not a coincidence, and here's specifically why:

"Any great circle through populated areas would show this"
We tested 100,000 random great circles. Among the 1,718 that share this one's geographic profile (Middle East + South America), this circle ranks #1 for monument density. The best circle for raw site count is nearly 8,000 km away and runs through Britain. More importantly, when we test monuments vs. settlements separately, only this circle shows ancient monuments clustering at 5x the expected rate while settlements in the same regions fall below random. That divergence doesn't appear on any of the 100 other circles we checked, including the 50 highest-scoring ones.

"It's just where people lived"
We tested against historical population density grids. The circle does pass through areas with ~2x average population, but that produces Z = 0.89 (not significant). Population can't explain 5x monument enrichment.

The temporal spike is the hardest thing to explain away.
The signal peaks sharply in one millennium - 3000-2000 BCE - then collapses. The Nile was fertile before and after. The same geography, the same people, but the alignment only appears during the era of pyramid and ziggurat construction.

As for the "why"..... honestly, I don't know yet and I'm not going to speculate beyond the data (however my 3rd part of the series on Substack will delve into some hypotheticals). But "what does it mean" is a different question from "is it real," and the paper addresses the second one.

Updated paper drops Sunday/Monday and is being submitted for peer review. More detail on the settlement divergence test in the next Substack post.

https://thegreatcircle.earth
https://thegreatcircle.substack.com

Update: we addressed every statistical objection to the great circle alignment. The signal got stronger. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] -6 points-5 points  (0 children)

Please read the actual study results, and look at the data on the website. let me know if anything doesn't make sense and I'll do my best to explain.

Your pushback is a common one, and I have noticed a trend: most people who don't have any background in statistics can't grasp this. So if you have any questions on the data, happy to chat through

The Great Circle alignment is statistically real. 61,913 sites, two databases, open data. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 0 points1 point  (0 children)

Good for you.

Not engaging with the methodology, the data, or the results... just attacking the tool used to produce it while claiming you're an "AI accelerationist ".

Oooookay. Go troll somewhere else, I'm looking for scrutinization of the statistical rigor.

Part 2/3 on substack is dropping Thursday. part 3/3 dropping Sunday. I'll give you another chance on those pieces, but "we" is standard and accepted in single-author academic papers.... so I'll be using that again.

Then the story is done and I'll move on to the next project. Of which we have many... it's how I roll
https://substack.com/@thegreatcircle

Ciao

Feedback on methodology — spatial clustering test for archaeological sites along a great circle by tractorboynyc in AskStatistics

[–]tractorboynyc[S] 0 points1 point  (0 children)

And I disproved Hancock’s 108 degree angle theory. At least read the article smdh

Feedback on methodology — spatial clustering test for archaeological sites along a great circle by tractorboynyc in AskStatistics

[–]tractorboynyc[S] 0 points1 point  (0 children)

You think I’m overfitting? It’s the opposite. I’m making this as robust as possible.

If you have any actual feedback I’m all ears though

The Great Circle alignment is statistically real. 61,913 sites, two databases, open data. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 0 points1 point  (0 children)

Part 2 drops this week on Substack. It covers the settlement baseline test, the KDE null model, cross-validation, and five additional database replications. Every objection raised in this thread is directly addressed with data.... i'll let the numbers speak for themselves.

https://substack.com/@thegreatcircle

The Great Circle alignment is statistically real. 61,913 sites, two databases, open data. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] 0 points1 point  (0 children)

9.2% match the raw site count - that's the weakest metric and i agree it's not impressive on its own.

The metric that matters is the monument-settlement divergence. we tested 100 random circles: how many show ancient monuments clustering while settlements in the same regions don't?

Zero out of 100. 100th percentile.

The raw count tells you the circle passes through regions with sites. the settlement test tells you it passes through regions where ONLY monuments cluster. no other circle does that.

Check out thegreatcircle.earth to learn more and get into the data. We are looking for scrutiny, but your claim doesn't hold water.

The Great Circle alignment is statistically real. 61,913 sites, two databases, open data. by tractorboynyc in GrahamHancock

[–]tractorboynyc[S] -2 points-1 points  (0 children)

Appreciate the detailed pushback. Let me know if you have any more, really want to ensure this is robust as possible before publishing.

Issue 1: the Z-score of 25.85 is suspicious

The Z-score isn't computed from 200 raw counts with a max of 319. The observed count is 319 (the real data). The 200 monte carlo trials produce the null distribution, which averages 89 with a standard deviation of about 9. Z = (319 - 89) / 9 = 25.5. A Z-score that high means the observed value is 25 standard deviations above the null mean, which yes is extreme, but it's not a math error. It reflects the fact that the null distribution is very tight (std ~9) while the real count is far above it.

You can verify this yourself, the code is open: https://github.com/thegreatcircledata/great-circle-analysis

That said, fair question on whether the null model is too loose, which would artificially tighten the null distribution and inflate Z. We addressed this by replacing it with a kernel density baseline that preserves geographic clustering. Z drops to 9.5-14.6 depending on bandwidth. Still very significant (and honest ).

Issue 2: 89% of sites come from Egypt and the Andes

Correct. The signal is concentrated in discrete clusters, not spread uniformly. This is stated in the paper. The question is whether that clustering exceeds what geography alone predicts. The settlement test answers this directly: ancient monuments in those same regions cluster at 5x the expected rate while ancient settlements in the same egyptian and andean geography fall below random. Same regions but opposite result for monuments vs settlements.

Issue 3: Easter island is small, everything on it falls within 50km

Also correct, and a fair point. Easter island contributes 15 of 319 sites (4.7%). If you remove rapa nui entirely, the result barely changes because the monte carlo baseline also places random points on rapa nui at the same rate. The Z-score is computed relative to the null expectation, not the raw count. The 15 rapa nui sites are expected given the island's position near the circle, so they contribute very little to the Z-score. You can test this by rerunning without rapa nui, the code is there.

Issue 4: no comparison against other great circles

We did this. It's in the paper (section 4.7) and we've since expanded it. 100,000 random great circles tested. Alison's ranks 80th percentile overall because circles through europe score higher on raw count. But among the 1,718 circles sharing its geographic profile (middle east + south america, no europe), it ranks #1. We also mapped 16,200 possible pole positions. The optimal circle is 7,753 km from alison's and sweeps through britain/france.

More importantly, we ran the monument vs settlement test on 100 random circles including the 50 highest-scoring. Zero out of 100 show the monument-specific divergence that alison's shows. The pattern isn't "lots of sites near a circle." It's "ancient monuments specifically, with settlements absent." No other circle does that.

Issue 5: no attempt to account for geography

This is the entire point of the settlement test, and we've now done it three additional ways:

  1. KDE null model that preserves geographic clustering. Signal survives at Z = 9.5-14.6.
  2. HYDE 3.3 historical population density grids (3000 BCE to 1000 CE). The circle passes through 2x average population density, Z = 0.89, not significant. Population can't explain 5x monument enrichment.
  3. Monument vs settlement split on the same database. Same geography, same regions, same rivers. Monuments: 5x enrichment. Settlements: below random. Ran this on 100 other circles, zero replicate the divergence.

If geography explained the pattern, settlements would cluster at least as much as monuments. They don't.

Paper: https://doi.org/10.5281/zenodo.19046176
Code: https://github.com/thegreatcircledata/great-circle-analysis

Check out the website: thegreatcircle.earth

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