Boolean logic reaches far beyond the substrate beneath software. It is a massively parallel, dynamic, reactive computing medium that can attack problems sequential processors struggle to express or finish.

Brian Greenforest places the multiplexer at the center: one physical choice, composed across space, becomes an alphabet for entire machines.

Stay in the Switching Domain

MUXes map directly to if-then-else, binary decision diagrams, routing, arithmetic, control, and reconfiguration. Registers add time, and feedback turns combinational choices into evolving systems.

One FPGA output can drive a neighboring configuration input, letting the fabric change parts of itself through ordinary logic. That move turns reconfiguration into application behavior.

Build the Machine From Boolean Relationships

Good layouts and interconnects expose parallel structure that an instruction stream hides. Search and combinatorial problems can exploit many simultaneous decisions instead of serializing every branch.

Explore MUX algebra, the Cartilage Core, and the visual language. Then contribute a circuit, layout, or application that uses Boolean structure at its full scale.

Build Boolean Logic From the MUX Up

MUX Algebra and the Boolean construction derive universal switching; Cartilage Core and its visual language carry that logic into an executable spatial machine.

MUX Algebra · Boolean Algebra Is All That Is Required · Cartilage Core · public source repository · The Physical MUX Tile Alphabet · Cartilage Visual Language

Originally posted on LinkedIn

Brian Greenforest · Thursday, June 17, 2021 at 6:34:31 PM PDT (2021-06-18 01:34:31 UTC)

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Boolean logic is everything. It is massively parallel. It is dynamic. It is reactive. No need to reinvent the wheel. But an extreme need to raise appreciation. And use it instead of software to solve problems which software never can solve in reasonable amount of time. With right layouts and interconnects, even NP-complete problems can look much easier in Boolean logic. Think about it. Appreciate switching circuits. Holy Multiplexers! Amen!

Comments added by Brian Greenforest on LinkedIn

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Comment 1 · Thursday, June 17, 2021 at 6:51:11 PM PDT (2021-06-18 01:51:11 UTC)

Let me elaborate on the "dynamic" argument clearer. Imagine you connect reconfiguration pin of one FPGA to an output of another FPGA. Everything is still made of multiplexers, pure Boolean logic. There is no emergent magical effect anywhere, but your Verilog suddenly becomes dynamic: you can stream and orchestrate your configurations all over the place. Which makes ALL EXISTING ASICs ever built to have the same POWER! Power to change the shape of your object-oriented system dynamically, adaptively, to instantiate more subtle structure. That power was always with us! Perhaps not often used, but definitely available! If you never tried to build a large VLSI digital circuit in Verilog, give it a try ASAP. It you wrote code your entire career, and you never knew that massively parallel scalable programming does exist, order an FPGA, and try to configure it! Learn WHAT EXACTLY Boolean logic is. Because it's absolutely NOT about the ugly condition checkers (which always hurt my brain, too!) in if/else if blocks!

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