transhumanisticpanspermia:

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:

1. the burgundy bloods live about 30-50 human years
   
2. lifespans begin to go over a century with the greens
   
3. ceruleans can outlive “dozens” of midbloods
4. 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.)