Updated preprint: Scale Invariant Dynamics in Market Price Momentum - with connections to information geometry and thermodynamic coupling. SSRN: papers.ssrn.com/sol3/papers.…

Hamilton’s equations have been hiding a Clifford algebra in plain sight. I first wrote this up as a mathematics thesis but came back to it because it supplies some of the ingredients for recent work, much more to follow. If we properly observe the conjugate tensor structure, we pass to the unitary form and then see that Cl(1,1) emerges naturally. A circular mass-spring network makes the eigenmode picture concrete. Paper: doi.org/10.5281/zenodo.22837… Animation Caption: Solving Hamiltions in unitary form gives exactly the eignemodes that are available in the systems. These are shown collectively by the "excited" brighter states of motion.

Silicon Senescence: Gompertz Mortality in a Fielded GPU Population I asked a simple question: do GPUs age the way people do? I’d heard these devices have been failing at high rates (a few years) and wondered what the replacement costs might be at datacenter scale. But what if ~1% of GPU performance could buy dramatically more hardware life? The public Titan GPU dataset indicates that failure risk can accelerate with age. So I built an age-aware governor and asked what happens if GPUs are run closer to their rated operating point instead of the default boost? The estimate that comes back shows that losing only ~1% of compute reduces GPU removals by ~49%. But that is just one operating point. The governor is like a knob that trades compute performance against hardware life. So compute performance is likely mis-priced relative to the cost of GPU replacement and failures. Perhaps not a big surprise to the folks optimizing these systems, but I found it fascinating and learned a lot putting this together. I'd expect datacenter folks to be the most interested because you'd sell longevity to who owns the depreciation, not who sells the replacement. Paper + code reproducing the Titan analysis: doi.org/10.5281/zenodo.22801… Animation Caption: What if ~1% less compute could buy a much larger reduction in hardware loss? Silicon Senescence connects GPU aging, operating stress, and survival, then asks whether hardware life can be treated as something datacenter operators choose to spend.

If you want to know whether a system is being driven or at equilibrium, you need its probability current. Getting this from actual dynamical trajectory data has been the hard part. To help solve this I've been developing a Delaunay-Voronoi Fokker-Planck (DVFP) instrument. DVFP turns scattered, irregular, time-ordered phase-space observations into an empirical Fokker-Planck description. The distinction is simple: Geometry tells us what is nearby. Time tells us what happens next, and these are handled properly in this construction. From here we obtain density, drift, diffusion, and probability current, which is what detailed balance and entropy production are built from. Paper and DOI: doi.org/10.5281/zenodo.22759… Animation: As the underlying dynamics evolve, the DVFP instrument adapts its local weighting while preserving the temporal ordering of the observations.

Super interesting.

Right on, excellent observation.

This is awesome stuff, takes me back to numerical work on the double-pendulum, a great little testbed for chaotic dynamical systems.

Very nice work, deriving masses from one input is elegant.