GameStop and the Flat Earth

The recent GameStop saga seems to me to be more or less the economic equivalent of flat-earthism. The enthusiastic people going “all in” on GameStop seem to be frighteningly ignorant of such basics as how the stock market works, how options work, why trades in batches of 100 occur, and how Robinhood can offer “free trades” (after all, TANSTAAFL).

When helpful people offer sensible advice, or when an inaccurate model of the world clashes with unfolding empirical data, the discrepancies are all too often explained using conspiracy theories or ignored in a self-reinforcing “echo chamber,” rather than being seriously addressed. I’m thinking specifically of certain corners of reddit.

At the same time, with GameStop, people seem overly greedy for profit and/or for revenge against “evil hedge funds” (both motivations appear to be in play). So much so that the impossibility of pushing GameStop stock up to the desired $1 trillion or so (i.e. 2% of the total US stock market) is simply not recognised. I very much fear that it will all end in tears for many people.

Sunset on a flat earth

Earlier, I wrote a post on why people know that the earth is round. Evidence such as star movement, the obscuring of distant objects by the earth’s curvature, and aircraft flight times shows that the earth is not flat:

In this post, I want to temporarily put on the “hat” of a flat-earther. They claim that the sun is a “spotlight” which travels across a circular flat earth like this:

That is at least a well-defined model, crazy though it might be, and therefore can be tested. Here is a computer render of the spring sun at sunset on that assumption (as seen from, say, San Francisco, at the moment that the sun disappears from view):

Three obvious problems with the flat-earth model are visible in this picture:

  • The sun is much too small: only 40% of its noontime diameter (because it is 2.5 times as far away as at noon)
  • The sun appears oval, rather than circular, because the “spotlight” is being seen obliquely (click to zoom if you can’t see the shape)
  • The sun is much too high in the sky (24° above the horizon)

In reality, of course, the sun at sunset is a circular disk that gradually slips under the horizon. Oops. No, the earth is not flat.

Four worlds

The picture above shows four possible worlds: a (slightly oblate) sphere, a torus, a disc, and a Klein bottle (images © Anthony Dekker). The darkened end of the Klein bottle is shifted through the fourth dimension to connect with the other end, making it a one-sided surface (like the Möbius strip). How do we know which world we live in?

Australians know that the world is round

Following up on my earth-measuring post, people have known for more than 2,000 years that the earth is round. In 350 BC, Aristotle wrote “The evidence of the senses further corroborates this [that the earth is spherical]. How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave-but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth’s surface, which is therefore spherical. Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent.” (On the Heavens, II, 14).

Around the year 700, Bede wrote “We call the earth a globe, not as if the shape of a sphere were expressed in the diversity of plains and mountains, but because, if all things (terrestrial) are included in the outline, the earth’s circumference will represent the figure of a perfect globe. Hence it is that the stars of the northern hemisphere appear to us, but never those of the southern; while on the other hand, the people who live on the southern part of the earth cannot see our stars, because the globe obstructs their view.” (De Natura Rerum). Australians verify his statement about stars every night.

I have commented previously on how the medieval poet Dante described time zones on a round earth:

In more recent times, we have pictures from space:

Aristotle and Bede mention the stars. Not only do the visible stars vary with latitude, but in the Northern Hemisphere they rotate around Polaris, while in the Southern Hemisphere they rotate around the South Celestial Pole, as in this photograph taken in Chile:

Sailors at sea have long known that the earth is round. From a vantage point 20 metres above sea level, one can see a complete ship 17 km away. Beyond that, the distant ship goes “hull down,” and only the upper parts of it are visible (from 34 km away, the lower 20 metres of a distant ship will be hidden). Closer to sea level, the distance is much less. This photo, taken in Spain by “Santifc,” shows the phenomenon (and similar observations can be made at some Australian beaches):

And, of course, the aircraft flight times to and from Australia can only be explained by the fact that the earth is round: