1944: The End of the Rainbow

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The End of the Rainbow

Title text: The retina is the exposed surface of the brain, so if you think about a pot of gold while looking at a rainbow, then there's one at BOTH ends.

Explanation

Megan appears to reference the myth that at the end of every rainbow lies a leprechaun's pot of gold. Instead of claiming that leprechauns and their gold don't exist, Cueball offers the refutation that, technically, rainbows are circles, so they do not have an end. This is true for an idealized rainbow, and for some actual rainbows: if the viewer has an unobstructed view of the light-reflecting substance creating the effect for the whole of the circle's circumference, they could see a full circle. In practice, the circle is often broken by the horizon or, for example, discontinuity in cloud cover.

However, Megan counters that if one considers the path that light takes to form a rainbow, then it forms a two-cone structure, where the Sun (the vertex of the outer cone) emits light rays that move towards the Earth (forming the faces of the outer cone), then reflect off water droplets located at just the right angle (the circular base) to reach our eyes (the vertex of the inner cone). Thus, such a rainbow structure can be said to have "ends", represented by the vertices of the two cones: one at the eye of the viewer, and another at the light source (usually the sun). A common rainbow (for which the base is formed by a water droplets in the Earth's atmosphere) can not be viewed as that. The Sun's diameter is orders of magnitude greater than Earth's one (even including the outer layers of the atmosphere), and we would expect the apex of a cone to be much smaller than its base. Thus a two-cone rainbow which ostensibly starts in Sun shall have its effective base formed in the outer space (or, rather, be a smudged out sum of all point origins lying within the near-hemisoheric visible glowing atmosphere of the Sun.

Megan then says that the Sun is indeed a pot of gold. The Sun is approximately 1.989 × 10³⁰ (1 nonillion 989 octillion) kilograms, and its abundance of gold is approximately 0.3 parts per trillion (ed: this value is incorrect - values in the paper are not in ppt - see comments below). Based on these numbers, the sun contains 5.967 × 10¹⁷ (596 quadrillion 700 trillion) kilograms of gold. This equates to 5.967 × 10¹⁴ (596 trillion 700 billion) metric tons of gold. As such, Megan's statement that the sun contains "quintillions of tons of gold" is off by a factor of roughly 4000, but the amount of gold within the sun is, nonetheless, far more than a pot's worth.^{[citation needed]}

The amount of water in the oceans is about 1.35 × 10¹⁸ (1 quintillion 350 quadrillion) metric tons. If we assume that Megan is still talking in terms of mass rather than volume or molecule count, then her next statement (that there is more gold in the sun than water in the oceans) would have been true had she been correct in her previous claim, but in fact there is more sea-water than sun-gold by a factor of roughly 2300.

Cueball then asks about leprechauns (perhaps ironically, since Megan's theory at this point appears to involve astronomy/physics, not mythical creatures/beings). Megan replies that the leprechauns all died when the Sun formed, building on the irony of Cueball's question (and opening questions about the role of leprechauns in the early formation of our solar system).

The title text suggests that, since the pot of gold exists as an idea in the brains of people thinking about it, and the retina is the foremost part of the brain for light perception, it can be argued that, in addition to existing in the sun as the comic explains, the gold (and leprechauns) also exist at the perceiver's end of the cone, as long as they are thinking about a pot of gold at the time (and then it's gone as soon as they stop thinking about it). Many neurologists would agree with the concept that ideas in your mind can be said to be physically located in your brain. However, this seems to go further, and suggest an idealist ontological position, that things, in this case a pot of gold, exist by virtue of our having an idea of them.

Transcript

[Megan and Cueball are walking.]

Megan: There's a pot of gold at the end of the rainbow.

Cueball: Rainbows are circles. They have no end.

Megan: Not quite!

[In a borderless panel, a multi-part graphic is shown depicting what Megan is describing off-panel: a short cone inside a longer cone, with the longer cone having its point starting at the Sun, the shorter cone having its point at a miniature Cueball's head, and both cones sharing the same circular base. The diagram is repeated from 3 different perspectives to make the structure easier to grasp.]

Megan (off-panel): A rainbow is light leaving the Sun, bouncing off the clouds, and converging on your eye. It's an inside-out two-ended cone.

[Megan and Cueball are still walking.]

Megan: One end of that cone is your retina.

[A wider view of the same scene, with Megan and Cueball walking on a dark ground.]

Megan: The other end is the Sun—which contains quintillions of tons of gold. There's more gold in the Sun than water in the oceans.

Cueball: So there is a pot of gold!

Cueball: What about leprechauns?

Megan: All incinerated as the sun formed. Very sad.

Trivia

As of January 19, 2017, the value of gold is 42,692.98 USD per kilogram. Based on this, all of the gold in the sun is worth 2.5474901 × 10^22 (25 sextillion 474 quintillion 901 quadrillion) USD. Of course, if you tried to sell the gold in the sun, the market would be saturated and the value of gold would plummet astronomically. You would never be able to cash out.

The idea that the Sun is valuable in monetary terms is also present in 1622: Henge.

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Discussion

Hey, an early comic that I understand! Typed up a transcript (though the description of the first panel was already there, and the empty explanation already had the Incomplete Explanation set as "Created by a LEPRECHAUN"), but using an iPad and typing in Notes to avoid editing conflicts, so I can't see the comic while I'm typing. So the inherent magic of the Telephone Game comes into play, where the mind likes to summarize and put into different words, LOL! I think I managed to get it completely accurate, though. I'll see if I can come up with an explanation shortly. NiceGuy1 (talk) 07:10, 19 January 2018 (UTC)

If you think about leprechauns while thinking about pots of gold then there will indeed be leprechauns at both ends.162.158.166.125 08:09, 19 January 2018 (UTC)

There is a *huge* difference between 10^-7 and 10^7... just fyi162.158.2.82 08:12, 19 January 2018 (UTC)

This is one of those cases where the phrase "Orders Of Magnitude" comes in, LOL! Kind of glad someone else beat me to providing an explanation now, not my goof. LOL! NiceGuy1 (talk) 08:22, 19 January 2018 (UTC)

I don't think that the part about solar gold volume is correct. The density used only applies to gold in solid state in room temperature, and the Sun is neither. In a way, gold indise Sun has the volume of the Sun itself. 162.158.90.168 10:41, 19 January 2018 (UTC)

Yes I realized that a few minutes after posting my original edit, and added a parenthesis to explain that I used the volume that much gold would have on Earth-like conditions. Not that the fact has any concrete application anyway, but I thought it would show that the claim that there is more gold in the Sun than water on Earth can't simply be pictured as an ocean volume of gold. Maybe there's a sea somewhere that's about the right volume and you could say "taking all the gold from the Sun would fill <that particular sea>" 141.101.88.16 11:21, 19 January 2018 (UTC)

There may be more gold in the sun than water in the oceans but the oceans have a higher concentration of gold than the sun does. 172.69.62.136 11:40, 19 January 2018 (UTC)

Leprechauns live on the night side of the Sun to avoid being incinerated, that's why we can't see them from this side. Zetfr 12:46, 19 January 2018 (UTC)

The night side... Of the sun... Is there a cartoon about this? I feel like there needs to be a cartoon about this. Just one observation: On the night side of the sun, there's no moon? Or if there is, what's lighting it up?  ;D This is even better than the "dark" side of the Moon. ProphetZarquon (talk) 15:33, 19 January 2018 (UTC)

Reminds me of this Reddit conversation 162.158.167.138 09:42, 20 January 2018 (UTC)

That is amusing. On that flag, I'm more concerned with why there's a massive explosion depicted on the moon at the top of the flag: It can't be the sun, because the sun goes behind the moon, not the other way around, therefore that starburst must represent a catastrophic explosion of some kind. It's like a space exploration flag made for people with no understanding of astronomy. ProphetZarquon (talk) 19:03, 24 January 2018 (UTC)

"far more than a [...] leprechaun's pot of gold" - I'm pretty sure a leprechaun's pot of gold is self-refilling, and therefore infinite.162.158.111.204 13:06, 19 January 2018 (UTC)

Oh no, the pot is just a container they had handy; The pot of gold is the measure of their ransom. ... No idea why I feel so sure of that. I don't think I want to re-read all the lore I studied as a kid to find the source... ProphetZarquon (talk) 15:33, 19 January 2018 (UTC)

did anyone else notice that the cone from the clouds to your eye isn't actually a cone, since it's slightly truncated at the point, otherwise we'd see an ideal point (i.e. not see it.) just me, then. --162.158.88.170 13:08, 19 January 2018 (UTC)

Wellllllll the cone comes to a point inside your eyeball, assuming you have perfect far vision, and then redisperses to project the image onto your retina upside-down and backwards. But we're really starting to split the hairs of 'what is a rainbow' here, as the rainbow is visible from a wide variety of vantage points, and the paths of light (and positions at which the light bounces off the cloud particles) are all different, some minutely, some vastly. Our eye is not a pinhole camera, and different views of the rainbow will enter it and hit the retina at slightly different spots. But the rainbow isn't this set of particular projections. It seems more arguable that the rainbow is either the rough set of cloud vapor that happens to reflect the light from the areas the rainbow is visible combined with this light reflected (a partial, fuzzy circle, and a partial, fuzzy cone) ... or simply the phenomenon of the water and light forming this image to us. Where is the rainbow???? If you move closer, it will move too! It's over there if and only if you are over here. It's certainly in that direction ... right? Or is it just in your brain? Maybe the rainbow is in your eyes for perceiving scattered light at all. Rainbows kind of violate the consensus we've come to in language about referring to objects. Perhaps they show that our language is insufficient to describe all of our experiences accurately. It looks pretty in the sky over there. That's a rainbow! It looking pretty in the sky with a curved band of color. Like a blur. Where is the blur? Okay; now I agree with Randall; the rainbow exists on your retina, and in the projected image you see, which forms a cone shape. But somebody else can see the same rainbow, and their cone is different! So clearly that's insufficient. It's like having the idea of a shared projected image. Like a reflection. Where is the reflection? There we go. Perhaps if the reflection is in the mirror, the rainbow is in the clouds.Baffo32 (talk) 18:26, 20 January 2018 (UTC)

Two monks were watching a flag flapping in the wind. One said to the other, “The flag is moving.”

The other replied, “The wind is moving.”

Huineng overheard this. He said, “Not the flag, not the wind; mind is moving.” --162.158.88.170 13:58, 22 January 2018 (UTC)

I think the logic of the title text is: gold is at the other end of the rainbow is there, because in that moment the person (his/her brain) is thinking about the gold. To put in a dumber way: when you think about gold, then gold is in your brain, ergo if your brain is one end of the rainbow, and you're wondering if there's gold at the end of the rainbow, then in a self-fulfilling way, it is. 162.158.238.82 13:53, 19 January 2018 (UTC) .tnm

I don't think the current title-text explanation makes any sense: The title-text portion of the comic doesn't seem to reference leprechauns at all. Was the comic edited after being posted? ProphetZarquon (talk) 15:33, 19 January 2018 (UTC)

I fixed the title text explanation. Also does this comic imply that if someone thinks about carnivorous giant neon zombie tomatoes while looking at a rainbow, then they exist at one end? ;) PotatoGod (talk) 15:45, 19 January 2018 (UTC)

I'm pretty sure the numbers are completly wrong, 0.3 parts per trillion probably comes from here (because the same article was used as a reference at some point in the history of the explanation), but I think this is the ratio of atoms, not mass. The answer on quora uses the same value of 0.3 parts per trillion but instead of 6*10^17 kg of gold, deduces from that number that there is 10^20 kg of golds. One atom of gold is ~195 times as heavy as one atom of hydrogen, and since the Sun is mostly hydrogen and also some heavier elements, the mass of gold over the average mass of atoms in the Sun should be a little below 195. The ratio between 10^20 and 6*10^17 is 167. There's still a ratio of 20 between that value (10^20 kg) of the mass of gold on the sun and the one from wolframalpha, and I'm quite expecting Randall to have used the latter, which is of 2 quintillion tons of gold on the Sun, IE "quintillions of tons" as expressed by Megan. Maybe that value is wrong, but I think it should be mentionned to show that Randall probably didn't just make up a number. 141.101.88.16 17:42, 19 January 2018 (UTC)

I've attempted to get to the bottom of this - Wikipedia gives limited sources. A search for [on WolframAlpha] gives 10^-7% by mass, but again, their references don't seem to support that (at least from a brief scan). Quora cites [1968 paper but I can't read that very well - I've attempted to analyse their data but I'm afraid I've been unable to determine how Quora reached their ".3 parts per trillion" from that paper. (I might drag out some textbooks and try again later.) In any case these two numbers are in wild disagreement, even if we assume Quora meant atomic ratios and multiply their number by 197 (atomic mass of gold; gold only has one stable isotope).

As mentioned, WolframAlpha's number gives 2.0x10^21 kg, or 2 quintillion tonnes, whereas Quora's gives 6.0x10^17 kg, or 0.0006 quintillion tonnes (0.12 quintillion tonnes if we mutiply by 197).

Of course, none of these results are small! I'd be happy with a pot of gold of even half a quadrillion tonnes. Cosmogoblin (talk) 20:26, 19 January 2018 (UTC)

How can 'more than' be off by a factor of anything, given that it's non-specific? It could be 'fractionally more than' or 'a thousand times more than'.162.158.111.204 18:07, 19 January 2018 (UTC)

In this case, because the true amount is LESS than, not more than. (The author of that part of the explanation assumed the minimum amount that could be called "quintillions" is 2 quintillion, and the calculated true amount is 4000 times smaller.) Cosmogoblin (talk) 20:30, 19 January 2018 (UTC)

Okay, I've got a different quibble about sizes here. Despite the fact that the sun is so far away from the earth that it appears as a relatively small disk in the sky, the sun is thousands of times LARGER than our planet. As such, the longer cone in Megan's explanation is such a gross oversimplification of the way light from the sun works as to be wildly inaccurate. If anything, this cone should be reversed (larger at the sun's end) to illustrate the portion of the sun's light energy that actually hits the whole planet, let alone just the area that any person is looking at when they see a rainbow. (Granted, the angle of the cone would be extremely shallow due to the distances involved, but it would still be larger-to-smaller, not smaller-to-larger as explained here.) The cone as she describes it only makes sense if we're talking about a very small portion of the sun's surface emitting that light. It's unclear to me if this was meant to be a flawed, oversimplified or metaphorical explanation (in which case it's not very clear), or if Randall was actually attempting to explain how this works, but this particular comic feels pretty far "off" to me in that respect, compared to similar comics he's done in the past. KieferSkunk (talk) 02:27, 20 January 2018 (UTC)

That occurred to me as well. The cone is just from a single point (in the comic's diagram, the centre of the apparent disc of the sun).

A ray diagram would show that each ray traces a single path, which means it does in fact come from a single point on the sun. For a given colour, therefore, this is correct; the various paths for the rainbow's ring of colour would indeed trace out a cone, from a single point. Other colours would trace out a different cone, but the difference would be the arrival point (on your retina), not the departure point (on the sun).

My explanation is slightly lacking, in that (a) I haven't considered the variable distances to each individual raindrop, and (b) a verbal description is nothing compared to a diagram. I may try to draw one later, if I have time. Cosmogoblin (talk) 18:19, 20 January 2018 (UTC)

The color a cell on your retina sees is not from a single ray. It's from multiple rays that have passed through the area of your pupil, from the area of the sun disc, through the areas on the surfaces of the water molecules that produce the correct angles for each combination of points in your pupil and on the sun given the index of refraction for the water. That's why rainbows look so blurry! Baffo32 (talk) 20:39, 20 January 2018 (UTC)

I think the reality is that it isn't a two-ended cone, it's just... a cone. Wide end at the sun, point on your retina, rainbow is where the cone is bent back, bounced in your direction. Megan's explanation is probably just a simplification due to it being difficult to think of the sun as anything but a point. NiceGuy1 (talk) 00:06, 21 January 2018 (UTC)

Given the sun's great distance from the Earth and the Earth's minuscule size in proportion, it is safe to assume that all light rays from the Sun are parallel. This is an assumption made in countless contexts and is close enough to reality for all practical purposes. As such, you've got parallel rays from the sun that get refracted by the rain drops, causing some wavelengths to focus on your retina, forming a cone (with the point at the focal point of your eye's lens). So the shape we're probably really talking about is a cone from your eye (apex) to the apparent position of the rainbow and a cylinder from there to a similar-sized circle on the sun's photosphere. At least it seems plausible to me. Shamino (talk) 21:32, 21 January 2018 (UTC)

Extra credit to Baffo32 for "the value of gold would plummet astronomically". :o) 162.158.111.204 23:42, 20 January 2018 (UTC)

The accuracy of Megan's statement is being discussed in https://astronomy.stackexchange.com/questions/24590/how-much-gold-is-there-in-our-sun and their conclusions are contradicting the one published here. I haven't still checked but I think somebody should.--Pere prlpz (talk) 11:46, 21 January 2018 (UTC)

Relating to the trivia section, couldn't you hold the gold and increase the supply at roughly the growth rate of the economy, which would keep the value consistent? (I mean, technically you couldn't store that much gold, but since we're considering selling it I think we can assume you have a Bag of Holding or something and can store it.) I don't know if I'm misunderstanding economics with this idea though. Also, I don't know how long it would take to sell everything with that strategy, but I imagine you could get your future generations into the scheme, and they could profit too. 198.41.230.172 12:04, 22 January 2018 (UTC)

I wonder if the light which refracts in the raindrops to create the image of the rainbow actually come from ONE POINT on the surface of the sun, or come from a 'circle' on the surface of the sun with a radius the size of the apparent rainbow. (The sun is, after all, SEVERAL TIMES the size of the earth.) I remember in physics classes we always treated 'rays of sun' to be parallel to each other, but that may have just been due to the angle between them being so very small. 162.158.79.29 17:56, 22 January 2018 (UTC)

The author giving 0.3ppt of gold has misinterpreted the referenced paper. The values in the paper are NOT ppt! The concentration (mass fraction) is calculated as 197 * 10^(0.32 - 12). The value of 0.32 is from the table in the paper, and the value of 197 is the atomic mass ratio of Au to H. This gives a mass concentration of 0.4ppb (0.4 x 10^-9). I have not changed the explanation of the comic because it would require a complete rewrite. Note that other sources give different values for Au. For example, [[1]] gives a value of 0.92 in the Sun's photosphere, which, if assumed to hold for the entire sun, gives a mass fraction of 1.64ppb! Sigma9 (talk) 01:27, 23 January 2018 (UTC)

Megan says in panel 3: “One end of that cone is your retina”. Another cool thing about this comic is that the neural cells tiling your retina, transducing photon energy into neurochemical signals and thus beginning the pathway through which visual information is transmitted to the rest of your brain, are your “cone” photoreceptors. So - at the end of all those “inside-out two-ended” optical cones, arising from each point emitter in the sun, are a set of neural cones essential for discerning the rainbow’s poem-inspiring colours. Unweave the rainbow, indeed! ☺ - Andrew 162.158.2.58 03:41, 31 January 2018 (UTC)

"Inside out"?

No-one's worked out what an "inside out" cone is then? 198.41.238.70 07:50, 13 February 2018 (UTC)

The "inside out" cone is a reference to the second cone, between the circular reflection of the light and the point it is received in the eye. This cone is "inside out" because the surface which is usually on the interior of a hollow cone is on the outside of the completed shape. A hollow cone would typically be closed off by a circle where the rainbow appears, but because the shape is formed by the path of light from the sun, the shape is instead closed by another cone outside of the one in question - because the closing cone encompasses what is usually considered the outside of the cone in question it becomes the inside, and vice versa, making the cone "inside out"

--162.158.158.7 23:11, 11 November 2020 (UTC)

The problem with that is that if the cone doesn't have an end cap then it doesn't *have* an inside and an outside, being topologically equivalent to a disc. 172.70.86.44 10:16, 27 June 2022 (UTC)