2769: Overlapping Circles

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Overlapping Circles
"The Venn diagram of the sun and the moon is a circle." --someone being snarky at totality
Title text: "The Venn diagram of the sun and the moon is a circle." --someone being snarky at totality


The comic shows two overlapping circles. This is a simple example of a Venn Diagram, which is a way that set theorists often illustrate the relationships between sets. Venn diagrams can consist of a number of overlapping shapes to describe the similarities and differences between any number of objects. Up to three overlapping circles can be used to represent every combination of membership of those separate sets. Beyond this, circles cannot suffice and other shapes (ovals or even concave shapes) are needed, but just two such areas is as trivial as shown, with the portion of the diagram where the two circles overlap represents the intersection of the sets (items that are in both sets). There are several other comics about Venn diagrams.

The two sets in this diagram are set theorists and astronomers. Set theorists would find the shape here interesting because such diagrams would appear regularly in their work. Astronomers also find overlapping circles interesting, because this is what they see during eclipses, when one astronomical body is directly or partially in front of another. In the overlapping section in the middle would be people who are both set theorists and astronomers. The joke here is that these people would be particularly excited by the shape, because it represents the overlapping of both their fields of study.

Note that Randall seems to have chosen humor over scientific accuracy. Read literally, this diagram appears to be saying that the only people who are excited about the shape are those who are both set theorists and astronomers. The label that is in the intersection of the two circles should properly apply to their union. However, a pedantic person might note that the label is actually within the union of the two circles, so perhaps all is well after all.

A common snarky comment on the Internet is "The Venn diagram of [x] and [y] is a circle" (for example, "fanfic writers" and "virgins"), implying that the two sets are identical. Totality describes a total (full) eclipse, when one astronomical body completely blocks the light from another. During totality, the shape of the eclipse is a circle. The title text references the totality that occurs during a total solar eclipse and its corresponding shape (or "Venn diagram," as the title text phrases it).

This comic was released 8 days after the Solar eclipse of April 20, 2023, which was visible across parts of South East Asia and Australia, and of which an excited astronomer would certainly be aware.


[The comic is an image of Venn diagram, which is used to compare groups of objects.]
[The Venn diagram in the comic has two overlapping circles. The leftmost circle is labeled "set theorists," the rightmost circle is labeled "astronomers," and the intersection between the circles is labeled "people who get excited about this shape."]

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Incorrect. I’m sure there are set theorists who get excited about that shape who are not astronomers, and astronomers who get excited about that shape who are not set theorists, and people who get excited about it who are neither. 23:16, 28 April 2023 (UTC)

Hmmm, I'm not a set theorist, but I don't think that's what the Venn diagram is trying to say. My understanding is that both set theorists and astronomers get excited about that shape, not that only people who are both astronomers and set theorists would be excited. Alcatraz ii (talk) 23:20, 28 April 2023 (UTC)
I agree with Alcatraz ii. The original poster has a point that there are people who agree neither set theorists nor astronomers and get excited about this shape, but a Venn diagram does not imply that the people in the overlapping section are both set theorists and astronomers. Python (talk) 23:31, 28 April 2023 (UTC)Python
Actually, it does. That's what overlaps in a Venn diagram mean, it's the set of entities that satisfy both conditions. Nitpicking (talk) 02:25, 29 April 2023 (UTC)
You're right. People who get excited about the diagram would be the union of the two sets, not intersection. Unless Randall is saying that only astronomers who are also set theorists are so enamored of the two diagrams that they get excited about it. Barmar (talk) 04:52, 29 April 2023 (UTC)
Hmmmm... I initially understood the comic the way Randall intended - that these two groups like this shape - but you have a point, that's not how Venn diagrams work. The left circle is labelled as the set of "set theorists", the right circle is the set of "astronomers", making the joined section the set of "astronomer set theorists". As a Venn diagram this should be ONE circle, "People who enjoy this shape", with "set theorists" and "astronomers" inside it, and as one circle it WOULDN'T have this shape, LOL! I guess a second circle to make this shape, "People who enjoy space", then put "astronauts" in it, and move "astronomers" to the junction? NiceGuy1 (talk) 06:21, 29 April 2023 (UTC)

On title text: I'm pretty sure that if two sets are represented by a single circle rater than two, it's no longer a Venn diagram but merely an Euler diagram. 00:22, 29 April 2023 (UTC)

A single circle can be either. Two (or more) intersecting circles/loops-of-whatever-shape can be either, but might disqualify themselves from being strict Venns if they do not exhibit exactly 2ⁿ different sub-regions from n basic standalone partitioning regions. (This includes the whole surrounding one, not within any single partition, which purists might deem needs an "everything else"-sort of label/manifest, if you're putting things inside other parts, but that maybe can be taken as read.)
You can't but help having 2 regions (inside and outside) from an n=1 circle. (And one region from being constrained by n=0 partitioning boundaries!)
It's once you have two or more that you start to get the Euler-not-Ven exceptions, like entirely unintersecting groups (notably misnamed, by this comic) or only partially supporting all groups (misnamed by Cueball, in-Universe), unless you make effort to have some (singly unique) areas covering all combinations of all options.
But an annular eclipse probably doesn't count. In 9ne, you cannot see/infer a point upon the Moon's surface that is not also where the Sun 'is' – albeit obscured – though you do see bits of Sun-surface that have no Moon coincident to your view (during the phase of maximum coverage). One assumes that non-annular eclipses (or hypo-annular ones, where the Sun's bodily 'cross-section' is at a minimum compared to the Moon's) are just onzerved as perfect fits. And this must exclude the upper-atmosphere/corona of the Sun (the Bailey's Beads/Diamond Ring effects being the limiting factors), so that you theoretically have a single circle and announce to yourself that all that you see within that is on a sightline which intersects both Sun and Moon, and all sightlines outwith that circle intersect neither. No room in your defining diagram/worldview/skyview for one XOR the other (like having a region for "red cars", but handling red non-cars and non-red cars (and all things that are neither red nor a car) as possibilities. 03:47, 29 April 2023 (UTC)
The way I’ve heard it (though I can’t remember where), it’s a Venn diagram iff it’s a Euler diagram with two congruent circles that overlap without regard for proportion; any other type of Euler diagram is not a Venn diagram. Which is to say, there is no such thing as a Venn diagram with an almost complete overlap or no overlap. I’m not sure where to find an authoritative definition though.

Edit: And according to Wolfram MathWorld, I’m completely wrong about the shape. They have Venn examples that use several blobs. But what’s important is that every possible intersection has its own region, and size doesn’t matter. — 06:10, 29 April 2023 (UTC)

The shape formed by the intersection of two circles is called a lens. Lenses are also of interest to astronomers for telescope manufacture. A lens shape causes spherical aberation when used as an optical element, leading to the use of aspheric lenses and mirrors on higher quality telescopes. Quantum7 (talk) 05:25, 29 April 2023 (UTC)

Uhhh, the first commenter has a point, that's not how Venn diagrams work. The left circle is labelled as the set of "set theorists", the right circle is the set of "astronomers", making the joined section the set of "astronomer set theorists", i.e. people who belong to both sets. As a Venn diagram this should be ONE circle, the set of "People who get excited by this shape", with "set theorists" and "astronomers" inside it, and as one circle it WOULDN'T have this shape, LOL! I guess a second circle to make this shape, "People who enjoy space" for example, then put "astronauts" in it, and move "astronomers" to the junction? Or these are set names of aspects of these professions, like putting "study the night sky" in Astronomers, and "math experts" in Set Theorists (IDK, LOL!), with the Excited thing being an aspect they have in common... I think the explanation needs to be updated to note that the Venn diagram was made somewhat wrong... NiceGuy1 (talk) 06:46, 29 April 2023 (UTC)

The Sun and Moon are spheroids and so they do not appear as perfectly circular. [email protected] 08:49, 29 April 2023 (UTC)

Others who enjoy this shape, travellers relying on Mastercard.

wrt earlier comments, an easier fix than changing the shape would be changing the text:

Left - Things set theorists get excited about

Right - Things astronomers get excited about

Middle - This shape 18:24, 30 April 2023 (UTC)

why was there a div tag at the bottom of this page? 00:30, 1 May 2023 (UTC)Bumpf