Hyper(tasks/computation)

I’m particularly interested in super/hyper/ultra tasks & hypercomputation / digital physics / virtual particles.

In Surreal Time & Ultratasks, some interesting ideas are presented:

If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (a sequence which includes one task done for each ordinal number—thus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible.

This is similar to what I have been thinking about regarding tiny time, however for that model we use games (pseudo#s).

Day Zero Ultratask

For each ordinal , an -task could be done in a finite-length interval of moment-less time so long as the interval contains an -length sequence of pairwise non-overlapping subintervals. Perhaps there is a pointless analog of the system of surreal numbers, along with other pointless continua that contain infinitesimal intervals.

We have & . So we can (at least in theory) have an length sequence on day (maybe w/ as the “event horizon” of Day 🤔).

In Hypercomputation: computing more than the Turing machine they present a figure (7 - pg.31 ) which looks identical to the game tree for 👀

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I was also thinking about loop(y) time again, this time inspired by affine games (they give other forms born on Day besides !). We could have a game tree w/ as the root & as the first steps. Maybe can be seen as types of ultratasks (maybe every loopy game can) 🤷‍♀️