i did the hemospectrum lifespan math. turns out, the hemospectrum is ridiculous.
as you can see from my maths sheet (with some explanations hastily added here and there,) the references I used were from canonical sources (hussie and the comic itself) stating that:
the burgundy bloods live about 30-50 human years
lifespans begin to go over a century with the greens
ceruleans can outlive “dozens” of midbloods
the fushia bloods can live a Long Fucking Time, which i quantified for math purposes
my “evidence only” chart uses only those first three canonical facts, with some guesstimates for fuchsia.
i plotted those on a chart, realized it was ridiculously exponential, then plotted the ln of the values on a chart, which you see. i then tried out some fits on the max values, and found a second degree polynomial was almost perfect.
this made a formula for maximum really simple - just use the fit formula and raise e to it.
i needed to come up with something a little arbitrary for min though, since i only had two points. so i decided that i wanted the difference in the ln of maximum and minimum age to increase either linearly or polynomially - meaning that the difference between actual maximum and minimum age would increase at a very fast exponential rate. this makes sense, because there are lots of things that can kill trolls early in their lives, but being higher on the hemospectrum does give them quite a bit of toughness. so their minimum age should increase significantly, but not nearly as fast as the maximum age.
i ended up using a cubic increase - i got that magic d#3 number by simply dividing the difference in the fuchsia and burgundy age gaps by the cube of 12, then multiplying that magic number by the cube of the index (with maximum of 12) in the actual difference formula. add that to the base difference and subtract it from the ln of the maximum age and raise e to the whole thing, and bam, minimum age. math!
as you can see, the math gave me the desired realistic result.
it turns out that in order to display the hemospectrum differences, you need four separate overlapping column charts. if you try to plot all 12, you can see violet and fuchsia and nothing else. (the obvious solution would be to display it as an ln, but then you couldn’t appreciate the magnitude of the increase! it just ends up looking nice and smooth:)
the middle chart is how many lives of lowbloods each highblood can expect to live. i.e. a fuchsia blood can expect to live the lives of 307 thousand burgundy bloods, and 11 violet bloods. if you follow the diagonals, you can see the exponential increase by the fact that the diagonals are increasing! (e.g. olive lives about 2 lime lives, while violet lives about 8 purple lives.)
some perspectives on this:
the blood caste with the lifespan closest to that of a modern human are the lime/candy red bloods. note that, in mutant form, they have the same blood color as humans.
highbloods would be extremely lonely; they would outlive most people they knew by far. to a fuchsia blood, adjusted to a human lifespan of about 80 years, a violet blood’s life would only last about 7 years. and a burgundy blood’s life would only last about 2 hours.
teal bloods are the first caste who truly begin to experience the phenomenon of lowbloods’ lives being shortened into obscurity. even a jade blood should be able to form a meaningful relationship with a burgundy, whose adjusted lifespan would be about 8 years to them. but to a teal, a burgundy’s adjusted lifespan would be under 3 years, and even a lime’s just a little over 5 years. this is notable because teal bloods are generally considered the first tier of midblood bureaucrats.
under non-sgrub conditions, to vriska, terezi’s life would last about 20 years. and to mindfang, the summoner’s life would last about 265 days.
to kanaya, rose’s life would last about 16 years.
karkat and dave would age together perfectly, with karkat starting out one year younger.
to the disciple, the sufferer’s life would last about 20 years. to the dolorosa, his life would last about 8 years. to the e%ecutor, his life would last about 102 days.
to equius, nepeta’s life would last about 205 days; on equius’s timescale, their moirallegiance would end swiftly with nepeta’s death of old age.
at the beginning of sgrub, aradia was 30% of the way through her average life expectancy (about 24 human years adjusted), nepeta was 7% of the way through hers (about 6 human years), equius was 0.04% of the way through his (about 11 human days), and feferi was .0001% of the way through hers (about 42 human minutes.) sgrub was literally fetching highblood infants.
THE EXTENDED SIGN LIST MEANS THAT IN BLOODSWAPS, UNLESS THE BLOODSWAPS ALSO EXCHANGE ASPECT + LUNAR SWAY, THE SWAPPED TROLLS WOULD HAVE DIFFERENT SIGNS.
karkat’s fuschia now?! BOOM
(all jokes aside I’m sure other people have pointed this out and I ain’t gonna tell anyone how to do their AUs, this is just a realization that struck me out of the blue and I got very weirded out about it. “sign of the confidante” seems to fit him pretty well though!)
