What I've Been Up To

hHihi! iI've been absolutely absorbed in independent research for the past few months. iI hope to bring the fruits of this research to share very soon. hHere's a taste:

eEpistemic pPhysics

tThe big one for me that's been taking up the past month! oOn aAugust 12, 2026, while exploring the concepts of negative and complex evidence in the context of valence networks (below), iI made the connection between special relativity and bBeta-distributed evidence. tThe main significance is creating connections, predictions, and insights between fields, especially epistemology, statistics, and physics. iI'll have a full writeup of this soon, and iI'm working on an academic manuscript that's taking forever, but iI'm hoping to have substantive human-written blog posts about it soon! cCurrently iI have my aiAI slop website about it epistemicphysics.com just to share the ideas, but aiAI is terrible at writing and explaining to a human audience effectively. aAnything on that website that sounds understandable was probably curated by a lot of prompts from me. aAfter writing blog posts and maybe the manuscript, iI might get around to de-slopifying it.

bBeta vValence nNetworks

iI created what iI believe is a novel type of artificial neural network - stochastic beta valence networks. aA "neuron" has a beta distribution (or beta mixture), and its supporting and opposing evidence are treated as excitatory and inhibitory input. tThe stochastic part comes from sampling from the resultant distribution during training and inference. tThis can also be extended to static versions, fully dynamic spiking versions, episodic spiking versions, and more.

sSloth.ink and gGated eEpistemic cCalculus

aAll my time has been on epistemic physics and other projects, but it feeds back into sloth.ink too! iI created a suitable way to represent beliefs on the number line using the concepts of epistemic physics and an analytic distribution that's been derived before but not named - so iI'm calling it the wWeighted bBayesian bBootstrap distribution. iIn addition, the fuzzy tally logic of gated epistemic calculus has been developed further, taking into account the lineage of the evidence and creating an alternate method of doing bBayesian inference. hHopefully iI can put out a blog post about all the interesting updates. tThe fuzzy tally logic and evidence lineage concepts also feed back into epistemic physics, so it forms a nice feedback loop.

mMachine lLearning

uUsing a swarm of dynamic flying "agents" iI created a dimensionality reduction (drDR) method that can alternate between preserving geometry better than almost all state-of-the-art drDR methods and clustering better than most too. tThe main cost is computation time, which iI'm still working on.

drDR also illustrated a tradeoff that led me to develop a theory of learning and creativity based on transformation and geometry. iI start by stating dimensionality reduction and learning can be related to art in the sense of projecting and transforming between dimensions. yYou necessarily lose information when doing drDR past the intrinsic dimension, so the question becomes how do you keep what is valuable? bBy thinking through that you can come to some interesting conclusions about different forms of creativity, manifold or sheaf geometry, and what learning is. aAlso transformation underlies everything we value, so it's kind of a "trans theory of everything" xdXD.

rRandom iIdeas

sSome other ideas iI've been throwing around are strapping and syncing a long-range rfidRFID reader to a robot vacuum to form an in-home map of all rfidRFID-tagged objects. tThis way you wouldn't need 3-4 readers for triangulation. iIt could use epistemic physics to do sensor fusion and investigate areas of higher uncertainty, and could be enhanced with some calibration rfidRFIDs at different heights.

mMy math isn't the strongest, but aiAI has been helping me explore that direction. fFirst, there's a beautiful connection between epistemic physics and the rRiemann zeta function - the difference between the distribution of draws of rapidity-transformed uniform beliefs has the zeta function in it!

𝐸[𝐷𝑠]=21−𝑠(𝑠−1)Γ(𝑠+1)𝜁(𝑠),𝐷=|Φ1−Φ2|$$ E[D^s] = 2^{1-s}(s-1)\Gamma(s+1)\zeta(s), \qquad D=|\Phi_1-\Phi_2| $$

iIn addition, multiplying uniform beliefs together can result in increasing zetas too!

𝐸[11−𝐵1𝐵2]=𝜁(2)=𝜋26$$ E\left[\frac1{1-B_1B_2}\right] = \zeta(2) = \frac{\pi^2}{6} $$

𝐸[11−∏𝑛𝑖=1𝐵𝑖]=𝜁(𝑛),𝑛>1$$ E\left[ \frac1{1-\prod_{i=1}^nB_i} \right] = \zeta(n), \qquad n>1 $$

sSo interesting - it makes sense there's a connection since bBrownian bridges are related to the rRiemann hypothesis, see this youtube video by aAlmost sSure, and epistemic physics beliefs at zero velocity basically recreates bBrownian motion.

sSecond, iI've also been playing with relativistic hydrodynamics with aiAI help. aAfter a many iterations, iI landed on

𝜕𝑓𝜕𝑡+𝐯(𝐩)⋅∇𝐱𝑓+𝐅⋅∇𝐩𝑓=Γ𝜏(𝐽[𝑓]−𝑓)$$ \frac{\partial f}{\partial t} + \mathbf v(\mathbf p)\cdot\nabla_{\mathbf x}f + \mathbf F\cdot\nabla_{\mathbf p}f = \frac{\Gamma}{\tau}\,\big(J[f] - f\big) $$

velocity $𝐯$\mathbf v$$
$𝑓(𝐱,𝐩,𝑡)$f(\mathbf x, \mathbf p, t)$$ - distribution of how many particles have momentum $𝐩$\mathbf p$$ at position $𝐱$\mathbf x$$ , time $𝑡 $t$$
$Γ$\Gamma$$ - relativistic correction to the rate, 1 when flow is slow
$𝜏$\tau$$ relaxation time
$𝐽 $J$$ - the local equilibrium, computed from $𝑓 $f$$

iI'll have more details if this works out further in a blog post, but basically this puts a speed limit of $𝑐 $c$$ on the velocity, keeps counts positive preventing spikes in momentum and energy, and has a linear gradient rule. iIt's basically a modified relativistic bBoltzmann with aAnderson-wWitting relaxation.

tThere's actually so many more ideas (one of my favorites is the epistemic cCauchy mean and variance demo) but this post is getting a bit long, so iI'll end here!