modular arithmetic

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

MinutePhysics explains Shor's algorithm, showing how a quantum computer factors large integers by finding the period of a number modulo N. It walks through the modular arithmetic and number theory that give the exponential speedup over classical factoring, and why this threatens encryption.

Zack Freedman introduces Gridfinity, his free, open-source modular workshop storage system of 3D-printable bins and baseplates. The video walks through the design, the parametric templates and the many module types that fit parts, tools and accessories.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

John Gustafson presents posits, a proposed drop-in replacement for IEEE 754 floats that is simpler in hardware and more flexible in precision. The seminar includes a live demo and machine learning results.

A 95-minute recorded debate at the ARITH23 computer arithmetic conference between John Gustafson, proponent of unums/posits, and William Kahan, architect of IEEE 754 floating point. They argue the merits of the new number formats versus conventional floats and interval arithmetic.

Physicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion. He argues that steady percentage growth cannot be sustained on a finite planet and that most public discussion ignores this.

A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.

Professor Ruzic explains modular micro-reactors: self-contained nuclear units with passive safety whose fuel lasts about 20 years. He covers their use for process and district heat and where they can compete with diesel generation.

Johns Hopkins APL shows Les Baugh, a bilateral shoulder-level amputee, controlling two Modular Prosthetic Limbs by thought after a short training period. Nerves rerouted to his chest drive the arms.

Matt Parker of Stand-up Maths explains why people keep making the same mistake with millions and billions, using a Bloomberg cash calculator example. He looks at the unit slip behind the repeated arithmetic error.

Time-lapse of Broad Group erecting a 30-story prefabricated hotel (J57) in Changsha, China in about 15 days. The description touts modular construction's precision, speed and low waste.

Andrew Tanenbaum's FOSDEM 2010 talk on MINIX 3, a microkernel OS built for high reliability and security. It shows how the system detects and recovers from device driver crashes, and addresses microkernel performance concerns.

Physicist Albert Bartlett's full-length lecture on how steady exponential growth in population and energy use collides with finite resources. It uses examples like bacteria in a bottle and covers peak oil.

Nicholas Zakas of Yahoo discusses architecture for large, modular JavaScript web applications. He lays out the theory behind building front ends that scale in complexity.

Rachel and Jun film Toyota Home Aichi installing a prefabricated house unit in Japan, with the assembly and roof waterproofing completed in about half a day.

Numberphile's James Grime makes the case for base 12 (dozenal) over base 10, showing how twelve's many divisors make arithmetic and everyday fractions easier.

A 1969 BBC Tomorrow's World segment about Nellie, a school computer used by pupils at Forest Grammar School to solve equations and play music. Students learn programming and maintenance, and act out binary arithmetic.

A short Art of the Problem clip explaining Diffie-Hellman key exchange, using a paint mixing analogy for one-way functions and touching on modular arithmetic and discrete logarithms.

Bill Dally of NVIDIA gives a University of Washington lecture on trends in deep learning hardware. It covers numeric formats, specialized instructions, energy per operation and co-design of hardware and software.

Linus Tech Tips reviews the first Framework Laptop, a fully repairable and upgradeable machine. The reviewer expected a flimsy chunky device and was happily surprised.

Tom Scott-style absurdist tour by Tom7 of SIGBOVIK chess projects: a tournament of 30 weird chess algorithms used to rate a color- and piece-blind chess program. Topics include mirrors, arithmetic encoding, perverted game tree search and a diluted Stockfish.

jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.

Matt Parker explains the history behind NTSC television running at 29.97 frames per second rather than 30, tracing it to the backward-compatible addition of color. He walks through the arithmetic behind the odd ratio.

David MacKay's TEDxWarwick talk uses basic arithmetic to show how much land and energy renewables would need to power a country like the UK. It explains the limits of sustainable options and why they should still be pursued.

Aditya Siram introduces ATS, a statically typed ML-like language that compiles to C and offers type-safe pointer arithmetic and a full proof language. The Strange Loop talk shows off C interop, concurrency and verification features with non-trivial examples.

Christof Paar's university lecture introducing Galois fields and finite-field arithmetic as used in AES. It covers the mathematics behind the AES S-box.

A short CGP Grey animation showing how the US electoral college lets a candidate win the presidency with as little as about 22 percent of the popular vote. It lays out the arithmetic of winning states by narrow margins.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

Lex Fridman's long podcast conversation with Chris Lattner, creator of Swift, LLVM and MLIR and co-founder of Modular. Topics include the Mojo language, the future of programming and AI, and hardware.

Luke Wagner of Fastly explains what a WebAssembly component is, how it relates to familiar concepts, and what the Component Model enables. It emphasizes security, composability and modularity.

Julia co-creator Jeff Bezanson candidly lists fundamental problems with the language at JuliaCon 2019, including modularity, types and compiler latency, and how they might be solved.

Linus Sebastian of Linus Tech Tips discloses that he has invested in Framework, the modular repairable laptop maker. He explains his reasoning and the commitments he is making to viewers about future coverage.

Linus Tech Tips covers Framework's newly announced devices, including its first desktop, with comments from Framework's CEO about the company's design decisions.

OpenAI cofounder Greg Brockman explains the design principles behind ChatGPT and demos unreleased plug-ins at TED 2023. In the follow-up, TED head Chris Anderson presses him on the timeline of development and the risks of releasing such a tool.

Jim Keller, CTO of Tenstorrent, talks at Samsung Foundry's SAFE 2021 about building AI silicon through modular, provable design. The talk also touches on Tenstorrent's RISC-V Ascalon core.

A short GRASP Lab (University of Pennsylvania) demo in which teams of quadrotors autonomously assemble tower-like cubic structures from modular parts. The drones are given the target structure and work out the assembly plan themselves.

A London Haskell talk on the algebra of algebraic data types, showing how sum and product types behave like arithmetic. It frames types as numbers obeying algebraic laws.

Rob Miles discusses GPT-3 on Computerphile, covering how scaling parameters kept improving results over GPT-2 and how the model nearly learned arithmetic without anyone knowing exactly how.