A medieval map that made cartography into a science | Hacker News Reader

A medieval map that made cartography into a science

newscientist.com

56 pointsbryanrasmussen12 comments

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https://archive.ph/dgESt/again?url=https://www.newscientist....

Here's a much better photo[0] from the Wikipedia article[1].

Importantly, the map is "upside down", since it's oriented to have south at the top.

[0]: https://upload.wikimedia.org/wikipedia/commons/1/1b/FraMauro...

[1]: https://en.wikipedia.org/wiki/Fra_Mauro_map

It's also interesting that in the middle ages, the standard was to put east on top.

https://upload.wikimedia.org/wikipedia/commons/4/48/Hereford...

There's some historical discussion at https://en.wikipedia.org/wiki/T_and_O_map

It’s funny how bad I was at recognising the geography upside-down.

At the bottom of the article, it refers to a new map projection that's supposedly more accurate:

> A new world map published in 2021 by physicists J. Richard Gott, David Goldberg and Bob Vanderbei minimised such distortions.

Interested, I read the article and try to understand what makes their Gott-Wagener projection more accurate than others. Apparently this is determined by calculating 6 types of distortions, and then summing the squared error of those distortions, but only after normalising on the Equirectangular projection.

And I'm wondering: why that normalisation step? And why Equirectangular? Does that not introduce its own distortions? In particular, Mercator scores very poorly because in the category where it scores worst, Equirectangular scores pretty good, creating a big difference that gets emphasised by squaring it.

So I recalculate the summed squares without the normalisation, and I get very different results:

              Normalised:  not normalised:

  Equirectangular: 6       0.09959
  Mercator:        8.308   0.46488
  Lagrange:        6.556   0.32536
  Briesemeister:   6.193   0.49412
  Eckert IV :      5.8474  0.408
  Winkel-Tripel:   4.563   0.18284
  Gott-Wagener:    4.497   0.10969

So funny thing: Equirectangular is now suddenly the best, when it used to be average. Gott-Wagener is still better than Winkel-Tripel and only just after Equirectangular. Mercator is still bad, but Briesemeister is slightly worse.

So I've got serious doubts about this normalisation procedure. I suspect you get very different results depending on which projection you use to normalise on.

Gott & al. have a decent basic concept, but a highly questionable implementation of the idea. (At least, in the paper of theirs I looked at from a few years ago; this might be a slightly different one.)

They optimize for least squares distance errors for all pairs of distances across the map, but they consider points which are at opposite sides of a map across a discontinuity (but nearby on the globe) to have extremely high error, and therefore their optimization routine radically tugs those points towards each-other. The result is really scrunched up edges.

They'd get dramatically better results by either (a) ignoring very distant points altogether, (b) figuring out how to measure distance across a discontinuity, or (c) comparing distances on the map to distances on the globe if you go the "long way" around, i.e. following a similar path to the one implied to be shortest by the map.

There is a copy of this in the Museo Galileo in Florence as well, which I visited a couple of weeks ago. Highly recommended if you get the opportunity. They also have an extensive multimedia guide, which is also available online[1] (though they may be having server problems, it hasn't been loading 100% reliably for me).

[1]: https://mostre.museogalileo.it/framauro/en/

There's a different zoomable high-resolution scan available here: http://www.highres.factum-arte.org/Fra_Mauro_Map/shared/view...

Having not seen this map in person, it's not clear to me which of these two has the more accurate white balance.

And

"The transformative OpenStreetMap project turned cartography into a community-driven exploration."

--> https://www.openstreetmap.org

Very cool! It took me a while to figure it out, with Africa being on the north east sector. Once I spotted Italy it made way more sense! :)

Fun fact: the Fra Mauro crater on the moon is named after him. It was the intended landing site of the Apollo 13 mission. The next mission, Apollo 14, landed there.

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