Escaping Flatland: A Retrospective
A common theme in all my software developments is recognizing that true state is continuous, relational, and non-local. Therefore this blog's "tongue-in-cheek" title referring to the Flatland: A Romance of Many Dimensions novella. Building upon this geometric analogy, classical software is very similar to what we humans perceive as "flat normality", that is a Euclidean geometry. Continuity in a Euclidean geometry are dualities (e.g. volume integral vs surface integral). In classical software, continuity is also expressed as dualities (e.g. commit-request vs commit-commit phases in a DB). But what if your geometry is not "flat", not Euclidean? Then maybe your continuity has more than two parts! In physics, for example, three mode continuity exist to express flow or topological continuity. What about in software? And how do we even define "non-Euclidean" software designs?
To express what is a non-Euclidean" software design, we need mention hyperbolic geometry, and its most fundamental property of having "too much" surface integral relative to volume integral. Or more pragmatically: most seats in a stadium are "in the back" because the edge of the stadium has more room to fill than the stadium's center! In software the data is at the center of the stadium, the ways to get to that data is at the edge "of the stadium"! That translates to: you can index data sets in multiple different and yet self-consistent ways! To simplify, "flat" designs just access data "one way", "non-flat" software have multiple sparse properties, we reject binary and integer-based absolutism, and instead "map data" using inner properties of the data itself. I call this software design approach "fractional mapping", as it covers concepts like sparsity, secondary keys, probabilistic data structures, and more, in a mathematically rigorous way.
I have designed and led designs of in high-demand industries from semiconductor physics and algorithmic trading to distributed ledgers and industrial security. These systems on built on fractional mapping and reject "flat" designs.
Below is a selection of these projects. Whether you are an organization seeking strategic architectural guidance, or an engineer looking to master advanced fractional design concepts in my upcoming workshop, this portfolio illustrates the power of a well-engineered "non-flat" designs.
Constrained auto-layout of analog CMOS cells
Domain and Context: Analog Layout Automation, I joined the ILAC (Interactive Layout of Analog CMOS Circuits) team, which I later led (CSEM, my first role).
Fractional Mapping: Invariants are areas and symmetries, not shape. Cell routing is first a topological flow, then a geometrically sensitive routing.
Core Algorithm: Three steps: topological, physical, optimized.
Outcome: ILAC was tthe world's first automated analog layout tool, it's licensing to Silicon Compiler Systems Corporation was then acquired by Mentor Graphics, which then failed to commercialize it. Stuck in the famous Falcon Framework fiasco, the resulting penalties covered the project's development's costs.
Optimal Symbolic transfer function approximant
Domain and Context: Analog Circuit Design Automation, I helped IDAC (Interactive Design for Analog Circuits), an analog CMOS cell sizing tool from desired specifications (CSEM, my first role)
Fractional Mapping: Transfer function as ordered hierarchical approximation.
Core Algorithm: Recursively optimally cut and refine a symbolic transfer function using minimum-cost bipartite matching.
Outcome: Production code used only hand calculated transfer functions. A few years later a better minimum-cost matroid matching based approach was introduced.
Hybrid grid-graph simulation engine
Domain and Context: TCAD Device Simulator capable of simulating electrical and thermal characteristics of silicon-based and compound semiconductor devices (my PhD)
Fractional Mapping: Everything is one unified indexable hierarchical sparse multi-model.
Core Algorithm: A generic "god's eye" global to local to global sparse indexing scheme across a full system supports a hybrid mesh-graph continuous time simulator based on a Newton-like solver (e.g. gradient descent).
Outcome: Dessis, the simulator was later acquired by Synopys and has been the #1 TCAD simulator for the last thirty years!
Derivative market making
Domain and Context: Non-proprietary derivative market making system with optimized connectivity to major electronic exchanges. (CTO at Actant AG)
Fractional Mapping: Short term "static" goals are optimally mapped to near instantaneous exchange "dynamic" actions. Instrument risk is consolidated to portfolio risk which is projected back to instrument as goal adjustments.
Core Algorithm: Incremental "optimizing" trading spooler
https://patents.google.com/patent/US20110246389A1/en . Muli-dimensional math as pre-calculated interpolatable and differentiable tables. Outcome: Part of the Actant system.
Smart contract of distributed rights and obligations
Domain and Context: Distributed Ledgers (as Product Owner and CTO at Elevence, seed-funded by BearingPoint Ventures).
Fractional Mapping: A comonadic structure allows extraction and compution of partial relativistic state.
Core Algorithm: Privacy preserving comonadic partial-state rewrite engine secured by a distributed store.
Outcome: The engineering team and foundational architecture were acquired by Digital Asset, contributing to the genesis of DAML. Digital Asset has since successfully scaled this paradigm to tokenize global financial infrastructure. (
https://www.bearingpoint.com/en/about-us/news-and-media/press-releases/bearingpoint-spin-off-elevence-joins-forces-with-digital-asset-holdings/
Real-time continuous state from distributed sensors
Domain and Context: Protecting subsea and land based industrial assets, as senior advisor
Fractional Mapping: Everything is one incremental hiearchical dense or sparse multi-model.
Core Algorithm: Incremental computations over DAG of streams of data chunks.
Outcome: Passed external audit and handed over.