interval arithmetic

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.

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.

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.

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.

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

Andrew Huang teaches the basics of music theory in about half an hour, covering intervals, chords and patterns. He stresses understanding how music works over memorizing terminology.

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.

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.

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.

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.

A short demonstration comparing just intonation with equal temperament, played so you can hear how the tuning compromise changes intervals and chords. It includes a Bach prelude played in both tunings.

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.

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.

Geoff Cumming uses a simulation to show how wildly the p value varies from one replication to the next because of sampling variability. He argues for estimation and confidence intervals over null hypothesis significance testing.

PBS Space Time explains how spacetime geometry and light cones determine the order of events and what can cause what. It visualizes causality in special relativity.

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.

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.

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.