- Miscellaneous Fun Stuff
- Biology, Ecology, Earth and Climate
- Chemistry
- Astronomy
- General Physics
- Classical Mechanics
- General Relativity
- Quantum Mechanics
- Quantum Field Theory
- Quantum Gravity
- Mathematical Physics
- Mathematics - Pure Beauty

- advice - advice to young scientists.
The advice on how to give good talks is needed even by most old scientists.
- books - how to learn math and physics.
- crackpot - the "crackpot index"
for physicists.
- illusion - an infuriating optical
illusion.
- inches - why there are 63360 inches
per mile.
- information - how many bits
are in all the words ever spoken, and other fun statistics
about information.
- interviews - some interviews.
- favorite - some of my favorite music.
- music - my own music.
- paper.info - information on
how to get all sorts of math and physics papers electronically -
for free!
- photos - photos, mainly from my
math and physics-related travels.
- poems - poems by my wife, Lisa Raphals.
- puzzles - some fun puzzles.
- teaching - how to teach stuff.
- voynich - The Voynich Manuscript: the most mysterious manuscript in the world.

- biology -
short fun posts on biology.
- earth - a brief history of the
Earth, and why physicists should find this place interesting.
- extinction - the five big
mass extinctions, and the one we are causing now.
- limits to growth - a
classic model of population growth and resource depletion, which
runs on your browser.
- nimbios - lectures on information and
entropy in biological systems, at NIMBioS, the National Institute
for Mathematical and Biological Synthesis.
- stochastic -
a very simplified climate model that runs on your browser.
- subcellular - stuff about subcellular
life forms, especially some of the weird ones like viroids.
- temperature - a story of ice ages, global
warming and other bouts of climate change.
- timeline - a brief history of the universe.

- chemistry - short fun posts on chemistry.

- astronomy -
short fun posts on astronomy.
- doomed - the tale of a doomed galaxy.
- end - the end of the universe, briefly
summarized.
- entropy -
What's going on when galaxies and starts form - is the force of gravity
making entropy decrease?
- lagrange - what's a Lagrange
point, and what lives there?
- stars - stuff about stars, especially
some of the weird ones like R Coronae Borealis stars.
- toutatis - the asteroid that gave
us our nearest brush with death this century.
- vacuum - what is the energy density
of the vacuum?
- virial - the virial theorem made
easy.
- wobble - the wobbling of the earth and other curiosities - a brief foray into celestial mechanics.

- condensate - what's a fermionic
condensate?
- constants - how many fundamental
physical constants are there?
- distances - a chart of various
distances, ranging from the Planck length to the radius of the
observable universe.
- lengths - a tour of 4 basic length scales in
physics.
- neutrinos - neutrinos and the
mysterious Maki-Nakagawa-Sakata matrix.
- open questions - what
we
*don't know*about physics. - penrose - summary of a chat
with Roger Penrose.
- physics -
short fun posts on physics.
- physics FAQ - Answers to frequently asked
physics questions, compiled by many authors. Please don't send me
comments about this! It's run by Don Koks; I am merely one of many
hosts.
- segal - my memories of Irving Segal.
- time - a book review of
H. D. Zeh's book "The Physical Basis of the Direction of Time". This
appeared in the Mathematical Intelligencer.

- classical - course notes and
problems on classical mechanics.
- gravitational - mysteries of the gravitational 2-body problem.

- einstein - the meaning of
Einstein's equation: a brief introduction to general relativity.
- gr - a tutorial on general relativity, featuring the "Adventures of Oz and the Wizard", in which a hapless apprentice learns relativity the hard way.

- bayes - a collection of old posts and
email on Bayesianism in probability theory and quantum mechanics.
- lie - an introduction to
Lie groups and quantum mechanics, by my friend Michael Weiss.
- quantization - a brief
outline of how geometric quantization works, to go along with the
series of articles about geometric quantization on
the sci.physics.research archive.
- quantum theory and
analysis - lecture notes on the spectral theorem, Stone's theorem,
Kato-Rellich theorem and applications to Schrödinger operators.
- spin - an introduction to
the theory of spin in quantum mechanics, by Michael Weiss.
- uncertainty - the uncertainty principle as applied to time and energy.

- cstar - what are C*-algebras good for?
- guts -
The algebra of grand unified theories, with John Huerta.
- elementary - some guided
exercises about elementary particles in the Standard Model. Part of
the Spring 2003session of the
Quantum Gravity Seminar.
- photon - excerpts
from the infamous "Photons, Schmotons" thread,
in which Michael Weiss and I went through a lot of quantum theory,
leading up to some basic quantum electrodynamics.
- renormalization -
renormalization in quantum field theory and statistical
mechanics made easy.
- spin_stat - a sketch of the proof of the spin-statistics theorem.

- area - some
puzzling possible progress on determining the quantum of area.
- background - what is a background-free
theory of physics, and why are they important?
- black hole - a picture of a
quantum black hole as we imagine it in the spin network approach
to quantum gravity.
- edge -
What I've changed my mind about: should I be thinking about quantum gravity?
- connect - a short story by
Greg Egan about future of loop quantum gravity. It's called
"Only Connect" and it appeared in the journal Nature on February
10, 2000.
- foam - information
about spin foams, compiled by Dan Christensen. If you know some
math and want to learn about spin foam models of quantum gravity,
check out the archive of his conversation with me about this stuff.
- hamiltonian - my paper
"The Hamiltonian constraint for quantum gravity in the
loop representation", which is an introduction to Thiemann's work on
that subject. This is not for the faint-hearted; a
less demanding
versioncan be found in Jorge Pullin's
newsletter, Matters of Gravity.
- penrose - Roger Penrose's papers on
spin networks, "Angular momentum: an approach to combinatorial
space-time" and "On the nature of quantum geometry",
in electronic form.
- planck - my
paper "Higher-dimensional algebra
and Planck scale physics", a not too technical introduction to current
ideas on quantum gravity.
- quantum - my paper
"Quantum quandaries: a category-theoretic perspective",
which is a followup to the previous paper.
- QG - notes from the Quantum Gravity Seminar here at U. C. Riverside. A vast amount of stuff.

- the
art of math - an article by Sophie Hebden about my work on
categorification and physics.
- boosts - according to Emmy Noether,
symmetries give conservation laws - but what does symmetry under
Lorentz transformations give? You won't find the answer in most
books!
- braids - some rambling lectures on knot
polynomials, braids, anyons, noncommutative geometry, and lots of other
neat things.
- butterfly - the butterfly, the gyroid
and the neutrino: how beautiful mathematics and physics can be found on
the wing of an iridescent butterfly.
- categories - a sketch of category
theory and how it relates to quantization.
- harmonic - discreteness and the role
of compact groups and double covers in the quantum mechanics of spin
and the harmonic oscillator.
- inverse cube - the inverse cube
force law in classical and quantum mechanics.
- information -
an introduction to information geometry and related topics.
- kostant - lecture notes and a
video of Bertram Kostant's lecture
entitled "On some mathematics in Garrett Lisi's E
_{8}theory of everything". - networks - an exploration of
network theory.
- noether - Noether's theorem in a nutshell.
- nth quantization - the story
of nth quantization. A strange tale with infinitely many chapters,
of which only a few have been written so far.
- symplectic - symplectic, quaternionic,
fermionic - what's the relationship?
- symmetries - an account of the
appearance of symmetry groups in physics.
- tangles - a primer on the category of
tangles.
- tenfold - the ten kinds of matter,
the ten dimensions in string theory and other aspects of the "ten-fold way".
- torsors - torsors made easy, so even physicists can learn to love them.

- algebraic topology - a basic
course on algebraic topology, roughly following Munkres' book.
- bigness -
large numbers, some of them infinite.
- ADE - a rapid introduction to ADE
theory, by John McKay.
- curious
quaternionsand ubiquitous octonions - two interviews of me by Helen Joyce
of Plus Magazine.
- dodecahedron - tales of the
dodecahedron: from Pythagoras through Plato to Poincaré.
- erlangen - Felix Klein's famous Erlangen
program, translated into English by M. Haskell.
- egyptian - Archimedean tilings and
Egyptian fractions.
- 4d - the
beauty of the 4th dimension.
- 42 - the answer to life, the universe
and everything.
- games - a course on game theory.
- geometry -
short fun posts on geometry.
- golden - tales of fool's gold and
the golden ratio.
- groupoidification - an introduction
to "groupoidification", a process that
reveals the bare bones of combinatorics beneath the flesh
of linear algebra.
- icosahedron - who invented
the icosahedron?
- involutes - the involute of the cubical
parabola: a puzzle relating singularities and the icosahedron.
- klein - Felix Klein's quartic curve, the
most beautiful Platonic surface.
- M13 - the amazing Mathieu group M
_{12}, and its big brother: the Mathieu groupoid M_{13}. - math power - the beauty and power of math.
Slides for a talk to school kids.
- normal - What's a normal subgroup?
And what are they
*like?* - numbers -
a tour of some of my favorite numbers:
five,
eightand
twenty-four.
(But don't forget forty-two.)
- octonions - an
introduction to the octonions and their connections to
geometry, topology, group theory, and mathematical physics.
- platonic - Platonic solids in higher
dimensions - otherwise known as regular polytopes.
- six - a tour of some amazing properties of the
group of permutations of 6 elements, and its relation to the icosahedron.
- rolling - there's a lot
of beautiful math lurking in rolling circles and balls
- roots - the beauty of roots:
strange patterns in the roots of polynomials with integer coefficients.
- square root - a puzzle about the
"square root of complex conjugation". I already know the
answer, but don't ask me what it is.
- strangest - the strangest numbers
in string theory: a
*Scientific American*article on the octonions by John Huerta and me. - surprises - surprises in logic:
Chaitin's incompleteness theorem and the Kritchman–Raz proof of
Gödel's 2nd incompleteness theorem.
- tilings - pretty pictures of tilings,
suitable for background wallpaper on your computer.
- topos - topos theory in a nutshell.
- trig - trigonometry and complex
numbers.
- visual insight - beautiful pictures of mathematical objects, with explanations.

© 2016 John Baez

baez@math.removethis.ucr.andthis.edu