Xah Talk Show 2026-07-07 Ep804. math. exponential, log, hyperbolic sin, JavaScript, Wolfram language
Video Summary (Generated by AI, Edited by Human.)
In this episode of the Xah Talk Show (Ep804), Xah Lee conducts a coding and mathematics work session focused on exponential, logarithmic, and hyperbolic functions, primarily using the Wolfram Language and JavaScript.
Key topics and highlights include:
JavaScript Documentation and Design: Xah discusses his long-standing "JavaScript in depth" project (2:46) and expresses frustration with modern web design trends, particularly "gray on white" text which he considers an accessibility failure (9:02-17:52).
Mathematical Computing:
Exponential Functions: Demonstrates plotting the exponential function e^x and discusses the function expM1 (representing e^x-1) in JavaScript (29:00-32:20).
Logarithms: Covers plotting natural logs as well as log base 10 and base 2 (54:14-1:04:11).
Hyperbolic Functions: Creates a new documentation page for hyperbolic functions, plotting functions like sinh cosh tanh, using Wolfram Language (1:21:28-1:41:51).
Software and Programming:
Emacs and Lisp: Touches on the history of various Lisp-based Emacs implementations (20:10-25:15) and his personal workflow within GNU Emacs.
Numerical Analysis: Spends time discussing the complexities of floating-point arithmetic and the limitations of binary representations for decimal fractions (1:04:27-1:11:31).
The word grey, has 2 different orthography! Aka spelling. The american way, is gray, with AH. The brit way, is grey, with Eh.
- add plot
- JS: Math exponential and logarithm
- numerical analysis
- why we need the function Math.expm1.
- ask ai.
- happens in JavaScript, python, golang, fsharp, emacs lisp, etc.
in js, you have Math.expm1(x). does this happen in python, or golang, or fsharp
Plot[E^x, {x, -2, 2}, AspectRatio -> Automatic] Plot[Log[x], {x, 0, 6}, AspectRatio -> Automatic]
- redo the image in Wolfram language
- Exponential Curve
- plane curves, add a new page, on hyperbolic functions sinh cosh etc
- Hyperbolic Trig Functions
- add link to plane curves page
- add code examples for all
- add plot for each
- JS: Math hyperbolic functions. sinh, cosh, tanh, etc.