IMPORTANT: please do NOT read this post until you have read this metapost at this site here:
An apology to this site (including a heart-felt "thank-you" note)
Are the 240 roots of $E_8$ in ANY special relationship with any PARTICULAR set(s) of 1296 elements of $E_8$?
If the answer to this question is "yes", then I can probably go away and stop bothering you good people, at least for a few weeks.
Because if the answer is "yes", then the answer will probably tell me exactly how $E_8$ is instantiated in the energetics of the particular biomolecular subsystem which my team has been studying for quite a number of years.
So, if you'd like me to go away, at least for a while, please take a moment to think about this question. And thanks as always for whatever time you can afford to spend doing so.