3283: Size and Lifespan

Size and Lifespan

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Title text: With their 13 years recording and performing together and two humans worth of mass, the White Stripes are sandwiched neatly between gray wolves and blue whales.

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Explanation

This comic presents a correlation between the size (in kg, therefore more accurately, the mass) of different objects with colors in their names, and their lifespan. It is similar to common charts that map the size versus lifespan of various animals, showing that, broadly, the larger they are, the longer they live, demonstrating biological allometry principles such as Kleiber's law. Here, however, it covers entirely unrelated classes of objects (animals, features of the Earth, and even astronomical bodies), appearing to suggest that there is some universal cosmic trend across all entities named with a color.

Black holes are complete outliers due to them (theoretically) being of many different sizes, and having a different relationship of size to 'life-expectancy', with evaporation through Hawking radiation making their effective lifespan scale with the cube of their mass. The subset of possible black holes that fit within the upper and lower time-scale limits of the comic (from the lower-limit origin of the graph out beyond the upper limit of the graph and all the way to the very top edge of the comic frame) therefore relate to a restricted subset of possible masses. The line widens towards the top, possibly to represent the uncertainty of mass for a given lifetime (and vice-versa) that may be due to the rate of accretion they can possibly undergo (to effectively extend their lifetime) according to their local environment. It produces a trend-line that is angled entirely across the general trend of all the other combined items.

Similarly, at either end of the scale, white blood cells and stars are 'smeared' across the chart. White blood cells are split into two different clumps (representing two separate types of white blood cell) which, together, 'cross' the general trend of the chart. The chosen spectrum of star types follow a continuous line, also crossing the general trend-line, which actually has an actual inverse slope (the more massive end of the line has a shorter lifetime than the least massive end), so can only tangentially support the basic premise of the rest of the graph, while demonstrating a departure from the more widely implied size/lifespan relationship.

The vertical (lifetime) axis starts from a single second at the bottom and ends at the top with the expected life-time of the longest lived stars (red dwarfs). The black holes still shown in the graph above the end of the time axis would therefore last a thousand times longer than those longest lived stars, which themselves are expected to last longer than the current age of the universe, so any black hole with a comprehensible life expectancy would be extremely small — just a few magnitudes more massive than a blue whale.

Somewhat dubiously, the chart conflates typical lifespans in some cases with lifetime to date in others.

Items listed

Object	Size (kg)	Lifespan (seconds)	Approx. lifespan (human-readable)	Explanation
white blood cells	10-11±0.5	104.5±1.5 and 108.25±0.75	6 hours–12 days and 1–30 years	The graph separates memory lymphocytes (which need to be replaced only every few years) from the other kinds of white blood cells (which the body replaces every few days).
yellowjackets	10-4±0.5	107.25±0.5	60 days–2 years	Example of a long insect lifespan
gray wolves	101.5±0.5	108.5±0.5	3–30 years	Example of a typical mammal lifespan
blue whales	104.5±1	109±0.5	10–100 years	Example of a long mammal lifespan
black holes	<105.5 to >1011.75±1.25	<100 to >1025	<1 second to >300 quadrillion years (20 million universe lifetimes)	Black holes eventually evaporate away due to Hawking radiation. 'Smaller' black holes can be surprisingly short-lived for celestial objects; however, this log-scale graph would have to be roughly four times taller to account for stellar-mass black holes (~1075 seconds, or >1057 universe lifetimes) and six times higher to account for the largest known black holes (over 10100 seconds, or >1082 universe lifetimes). Equally, the smallest theoretical black holes, which could be close to the Planck mass, would evaporate so quickly that to include them would require the chart to extend for about twice its current height below where it does. The smallest known black hole is roughly four times the mass of the Sun, meaning most of the line depicted covers ones that are only theoretical. The largest known black hole is TON 618, with an estimated mass of 10 41 kg. The evaporation time of a black hole not fed is an easy formula. As evaporation time per mass is cubic, on a double-logarithmic scale this is a linear line with a gradient of 3:1. As the horizontal resolution is around half of the vertical, that makes it a visible gradient of 6:1 — almost a vertical line. Once a black hole gets big enough, it is more likely to pull in new mass from the surrounding area and thus extend its lifetime before evaporating. Variation in the amount of material locally available will affect how much it is extended, resulting in a range of possible lifetimes for any given mass, shown by the thicker line at the top of the graph. Smaller black holes are too small to catch enough mass to make much difference, so the line is thinner at the bottom. That all black holes with lifetimes comparable to anything else familiar to humans would have a mass between that of a blue whale and that of the red sea might be the observation that triggered the creation of this comic.
Red Sea	1017.5±0.5	1015±1	3–300 million years	The time probably references the end of the desiccation of the Red Sea.
Greenland	1020±0.5	1016.75±0.5	0.6–6 billion years	An autonomous territory of of Denmark, Greenland is the world's largest island. Greenland makes an interesting pairing with the Red Sea, because red is the opposite of green and sea is the opposite of land, a juxtaposition famously made by Rockapella that might have been internalized by Randall in his childhood and repeated here.
red dwarfs to blue giants	1029 to 1032.5	1021 to 1013.5	1 million to 30 trillion years	Stars are probably some of the largest single things in the universe and often imagined to be longest-lasting, too. As can be seen on this diagram, though, many kinds of stars are more short-lived than some phenomena on Earth, like landmasses or seas. The inverse relationship between mass and lifespan (which goes against the overall suggested relationship of the chart) is because massive stars fuse hydrogen to helium far faster. The charted region is effectively an inverse of the famous Hertzsprung–Russell diagram, with the stellar classification (surface temperature) being inversely proportional to mass, and luminosity (rate of fusion) being inversely proportional to lifespan.
The White Stripes (title text)	102	108.65	13.5 years	The White Stripes were a rock duo from 1997-2011 made up of Jack and Meg White.

Transcript

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Discussion

I am surprised black holes have so little mass. Can this be correct? 163.116.173.198 a black hole

Black holes can come in a vast range of masses - we're only seeing the relatively tiny short-lived ones, but they extend well off the chart into much more massive and long-lived ones. 82.13.184.33 12:20, 10 August 2026 (UTC)

I assume for Black Holes mass is not in kilograms, but in solar masses. 193.210.0.32 (talk) 13:53, 10 August 2026 (UTC) (please sign your comments with ~~~~)

No - black holes can, theoretically, come in any mass - from hundreds of thousands of solar masses down to a Planck mass (including blue whale sized (and bowl of petunias sized)) - so the line would extend both well above and well below what's shown on the chart. 82.13.184.33 14:05, 10 August 2026 (UTC)

Actually, 'well above' is debatable - as far as I can figure, Randall's chart already goes a couple of orders of magnitude beyond the current age of the universe, so how much further there is to go is uncertain. 82.13.184.33 14:15, 10 August 2026 (UTC)

Since the vertical coordinate is lifetime, it does go "well above" and "well below" the graph as well, as a black hole's lifetime is proportional to M³ (e. g., a 2 kg BH has 8× longer lifetime than a 1 kg BH (41.86 qs and 5.2325 qs, respectively), a BH with mass equal to the Planck mass (c. 21.76 μg) has lifetime equal to the Planck time (c. 5.39124e-44 s)). So expanding the graph, it goes 43.269 orders of magnitude below 1 s and many magnitudes above 10²⁰ s. 2001:4C4D:12C8:C800:5D8E:47D2:C546:908 18:55, 10 August 2026 (UTC)

Even a 1 solar mass black hole would have a lifespan in excess of 10⁶⁷ years, which would place it well outside the bounds of this graph, and heavier ones would have even longer lifespans. Zmatt (talk) 13:41, 14 August 2026 (UTC)

I definitely want to know why white blood cells have two "clumps" of area instead of a contiguous area. AdmiralMemo (talk) 12:30, 10 August 2026 (UTC)

See the table here - certain lymphocytes have a lifetime of years, whereas for other white blood cells it's only hours or days. 82.13.184.33 12:39, 10 August 2026 (UTC)

The table is wildly off and doesn't match the graph. Wolves weight 1 kilogram? Blue Whales weigh 100 kg? 2803:7260:110:270:ad6d:487c:fa3:ce0 (talk) 12:35, 10 August 2026 (UTC) (please sign your comments with ~~~~)

Table re-measured to the nearest quarter-increment. SomeDee (talk) 12:57, 10 August 2026 (UTC)

Logarithmic scale. 10^10=10*10*10*10*10*10*10*10*10*10=10000000000 Inevitablepotato36 (talk) 00:01, 11 August 2026 (UTC)

yeah it does seem a litlle off actually- Inevitablepotato36 (talk) 00:02, 11 August 2026 (UTC)

Does anyone know what the title text is talking about? I feel like it's referencing some sort of sport thing, but I'm not sure MiquelFire (talk) 14:24, 10 August 2026 (UTC)

The White Stripes were a two-person band active between 1997 and 2011 - see Wikipedia link in the table. 82.13.184.33 14:40, 10 August 2026 (UTC)

Does Greenland's mass include the ice cap? Should mention this. DKMell (talk) 16:07, 10 August 2026 (UTC)

The age of Greenland on the chart appears to be roughly the age of the Earth. In one sense I suppose that makes sense, in that the material that now makes up Greenland came together at around that point, but I would have expected it to have been set at the point when it separated off from the continent due to ice sheet collapse. 82.13.184.33 16:29, 10 August 2026 (UTC)

Given that everything else is a lifespan rather than an age, I think it may be referring to time remaining until the Sun becomes a red giant and consumes the Earth (Greenland included). Zmatt (talk) 13:25, 14 August 2026 (UTC)

Is there a joke I'm missing in the fact that everything is a color?

Not sure you're missing anything - that kind of is (a large part of) the joke - the only thing that ties them together is a colour in the name, which makes them a silly set of things to graph together. 82.13.184.33 08:26, 11 August 2026 (UTC)

I don't understand why there are no velociraptors in this chart. Their fans are _very_ colorful. 2601:647:4001:656B:5DEB:C9F7:C93D:4E77 18:23, 10 August 2026 (UTC)

Black holes in the middle? Given that black holes cover the full range of mass, and the population is weighted (heh) towards the top, why did Randall put them in the middle of the graph? 37.19.220.64 19:00, 10 August 2026 (UTC)

Where else? It would be equally incorrect to have them either at the low end (many are enormously massive) or the high end (theoretically, there were Planck mass black holes at the Big Bang). Nitpicking (talk) 22:07, 10 August 2026 (UTC)

The graph includes only very small, theoretical block holes (up to <10¹³ kg, or 5x10^-18 solar masses) because larger ones take a very long time to evaporate. If it showed the largest supermassive black holes, which would indeed extend over to the right edge of the graph, it would have to be six times as tall - and if that were scaled to still fit on your screen, you couldn't see the detail of any of the things you see here. DKMell (talk) 23:27, 10 August 2026 (UTC)

If it were to include all black holes, including the tiniest theoretical micro black holes, it would have to be even taller (and wider), as the scale would have to be extended well off the bottom as well. 82.13.184.33 08:34, 11 August 2026 (UTC)

Me again. Understood. However, given that the range of black holes starts smaller than the smaller objects and finishes larger than the largest objects, I would recommend putting it on the left or the right of the graph - and include an inset zoomed out to a relevant scale. There's no justification for putting it between blue whales and the red sea. 158.173.67.152 16:36, 11 August 2026 (UTC)

That would just be inaccurate. It's a scatterplot. A black hole with a lifespan comparable to a blue whale has a mass somewhere between a blue whale and the red sea. They're exactly where they should be. 2600:1010:B217:A158:540C:84F2:8D25:8BC5 17:53, 11 August 2026 (UTC)

Sorry, you're right. I think I just have a headache seeing that the black hole range goes off both ends vertically; I keep fixating on smaller and smaller ones, and on larger and larger ones and where *they* would fit. I just think the graph needs an insert for the full range of black holes. 158.173.21.22 18:08, 11 August 2026 (UTC)

Trivia: the White Stripes released an album called White Blood Cells. Nitpicking (talk) 22:12, 10 August 2026 (UTC)

True - although those White Blood Cells would ruin the spurious graph, being CD-sized or vinyl-sized (or bits on a computer-sized) and having a lifespan of 25 years and counting already. (Randall has snuck in another 'making you feel old' reference here, probably without even realising it!) 82.13.184.33 08:38, 11 August 2026 (UTC)

Non-Living data points: The idea of treating large systems using the same law of scale is also discussed by Geoffrey West in his book "Scale". https://www.organism.earth/library/document/scale -- Jh6p (talk) 22:38, 10 August 2026 (UTC) (please sign your comments with ~~~~)

He has left out oranges and "purple" items (purple martin, purple mountain majesties, etc). Also, I cannot find any things that are known as "magenta X" or "cyan X", perhaps there isn't any well known enough. SDSpivey (talk) 02:35, 11 August 2026 (UTC)

Cyanobacteria seems like an obvious choice for that. I don't know anything magenta-named that would fit. 02:35, 11 August 2026 (UTC) 125.236.215.22 03:32, 11 August 2026 (UTC)

There's Magenta from Rocky Horror. 82.13.184.33 08:29, 11 August 2026 (UTC)

Why does the black hole line get thicker higher up? Is it due to uncertainty in how fast it grows at this scale, or is the constant unknown? (I assume not uncertainty in rate of Hawking radiation, as I thought that uncertainty is on the small end and is about the contribution of non-photon emissions?) 2003:EB:5F1C:AF00:19B6:547E:51CC:9C29 07:34, 11 August 2026 (UTC)

Why do black holes get bigger uncertainty at the top than at the bottom? 159.224.64.162 08:30, 11 August 2026 (UTC)

I guess because the larger they get, the larger the sphere of surrounding matter that will get pulled into them, so the lifespan will depend somewhat on how much matter is within that sphere. 82.13.184.33 09:05, 11 August 2026 (UTC)

Seems like BH becomes the size of a proton at ~10^11-10^12, and the size of an atom at ~10^17 159.224.64.162 13:14, 11 August 2026 (UTC)

I think this is a reference to star colors and lifespans. Thoughts? Capycapybara (talk) 10:37, 11 August 2026 (UTC)

Next time add proton lifetime :D 46.182.184.167 (talk) 13:45, 11 August 2026 (UTC) (please sign your comments with ~~~~)

Given the discussed range in Black hole sizes and lifespans wouldn't they simply fill the chart? 158.95.0.132 (talk) 21:38, 11 August 2026 (please sign your comments with ~~~~)

No, not 'the whole chart', because size and time(-left) is a fairly connected ratio. What we're seeing is the lifetimes that range from 10^0 seconds (1 second) to 10^20 seconds (approximately pi long-billion, or short-trillian, years) by the top of the axis (maybe a hundred times longer than that, if you count until the comic's frame-top). These limits relate to black-hole masses of maybe 315ish tonnes to an order of around 1/10¹²-ish the mass of the Earth (less than the mass of the Red Sea or Greenland, you'll note from the graph). This is an absurdly small black hole to consider, for most practical purposes.

The top black holes are several million solar masses (blue giant stars are maybe 200 solar masses), but just don't appear on the graph at all unless you extend the time axis up far enough to accommodate that range. And the mass one far enough right. But it would still be just a (potentially widening) line on the mostly white graph with barely a smudge of anything other than this line, down in on this bit that we're 'zoomed-in on' for the actual comic.

...to put it another way, you don't have a million solar-mass black hole with a second of lifetime, nor a microscopic one with a lifetime of much more than a blink of an eye. Though you (may) have ones that fit across both ranges, they're values that are tied (more loosely, at the top end, for various possible reasons) directly to each other, only drawing out a line of sorts, not enclosing an entire area-block. 92.23.0.28 22:22, 11 August 2026 (UTC)

Did Randall mix up mass and time? Why are Greenland more massive than every black hole so far and well into the next million universe life-spans? 83.209.137.72 (talk) 06:35, 13 August 2026 (UTC) (please sign your comments with ~~~~)

What you're seeing isn't every black hole so far - it's possible black holes. 82.13.184.33 08:41, 13 August 2026 (UTC)

More precisely, it's the (theoretically-)possible black holes that fit within the comic frame. Follow that black hole plot up far enough and it will eventually slide over into star-sized mass territory (but at very much more time than can be plotted there).

Also, Greenland is only at about "the age of the universe so far", by my reckoning (without looking at the Explanation table, so may include an original mistake upon my part), depending on exactly where in the blob you measure to. But that might include how long more it is supposed to 'live' on top of how long it has existed on Earth so far.

Black holes and (redder) stars do go significantly into older-than-the-universe territory. Depending upon what future cosmology will turn out to be, that may well be what we could effectively get. 92.23.0.28 19:15, 13 August 2026 (UTC)
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