Recent Updates:

The page for the Concertina II computer architecture has been recently updated once again. I have drastically simplified the available headers, and I have eliminated alternate sets of 32-bit instructions by moving them to the standard 32-bit instruction set. This meant only allowing 16-bit instructions within blocks with a header that indicates variable-length instructions.

The page about the game of Backgammon has been updated with the rules of the Milton Bradley game of Kakeba, also called by them "Japanese Backgammon", although it has nothing to do with Sugoroku.

The page about the game of Chivalry, and the related games Camelot, Grand Camelot, Cam, and Inside Moves, as well as King's Court, Chinese Checkers, Halma, Hexagony, Reversi, and Ploy, among others, had been updated, particularly with respect to its coverage of Inside Moves, and it has now been further updated with photographs.

The description of the German SG-41, a lug and pin machine similar to the Hagelin machines, has been updated, thanks to new information from the Crypto Museum web site.

My page about A Limitation of Color Photography has now had an example added to it of what can be done in digital photography, where that limitation no longer applies.

I have now added a page concerning a little-recognized Canadian contribution to the popular game of Cribbage.

Given that I had a page on model train gauges in my section on units of measurement, it should not be surprising that I eventually got around to adding a page with a few images of various railroad trains throughout history, primarily focusing on the era of streamlined steam. Also, on the bottom of that page about train gauges, I have now revealed the answer to the greatest mystery of life! We know about D cells and C cells, and AA cells and AAA cells. But how big are B cells and A cells? The answer is here!

It has been claimed that it would be quite impossible to build a bridge linking Vancouver Island to the mainland of Canada, since such a bridge would have a span longer than any in the world. On this page I show an alternative, involving several bridges, which ultimately connect Vancouver Island to the Lower Mainland of British Columbia, not requiring either any impossibly long bridges, nor the building of a new passage across the Rocky Mountains to add to the existing ones to Prince Rupert in the north and to Vancouver in the south.

I have turned my attention once again to the section on Map Projections. Only a few projections have been added, such as the Bartholomew Tetrahedral and the BSAM projection. But what I have added in a number of places are actual examples of maps on a few of the projections mentioned from older atlases or U.S. Government publications. Thus, these pages are now more richly illustrated. Also, as there have been updates to Justin Kunimune's program Map Designer, I have some additional illustrations of conformal projections using the Dixon elliptic functions.

There is now a page at the link for The Gamma Function, however it is only a stub page.

In my page of featured images, I've now added an image which brings together the ordinary Tangram, the much less well-known fifteen-piece Tangram, and the Ostomachion, which is a puzzle similar to the Tangram, but of Western origin, together in one place perhaps for the first time on the whole Internet!

A series of pages discussing the history of the 35mm SLR camera has been added to this site; some of its prececessors are also mentioned, such as the Ermanox and the Leica.

A new Mersenne prime has been discovered, and this fact is reflected on my pages here.

A new page has been added, concerning the 19th-century game of The Siege of Paris.

Recently, there was added a new page giving a history of computers in general, and the microcomputer revolution in particular. This page has now been considerably expanded, with the addition of numerous illustrations, and it has been split into several pages because of this. And, since this was first announced, additional illustrations have been added along with descriptions of more computer systems of the past which I have thought to be of significance.

Now included among the items mentioned on these pages are: the Antikythera Mechanism and the Whirlpool Aero Cable Car (not a computer, but noted for its historical significance as being associated with the famous computer pioneer Torres y Quevedo), along with the IBM 305 RAMAC, which introduced the hard disk to the world, and a type of computer that is nearly forgotten now, the Digital Differential Analyzer; the Control Data 6060 Remote Calculator, a large additional assortment of supercomputers, which now have their own page, the HP 9845, an early desktop computer with 3D graphing capabilities, the Symbolics 3600 computer, and the GRiD Compass computer (and covering that computer gave me an excuse to include a couple of NASA photographs featuring some famous stars of stage and screen; some additional TV stars - including one who was also in the movie - also appear now from an advertisement for the IBM Personal System/2 on another page). And these new items, of course, are alongside many other computers.

A page has been added containing a brief chronology of the typewriter, highlighting various technical innovations in its history. Illustrations of some of the kinds of typewriter discussed have now been added. Another thing added, to this page, part of a discussion of extending the capabilities of the Selectric Composer, are samples of text typed on the IBM Executive Typewriter and the IBM Selectric Composer, and even the Vari-Typer, so that the reader can get some idea of their print quality. That discussion continues to, and concludes on, this page, which goes step by step through how I start from the principle of combining the capabilities of an ordinary Selectric typewriter with those of the Selectric Composer in a single machine, and continue by adding features to overcome some of the perceived limitations of the Selectric Composer. The pitfalls one runs into when trying to make a single machine so versatile are exhibited, and in some cases discussed. More recently, I have added this page, which, as it discusses recent events with respect to video cards, is related to that history of computers.

Do you live in Australia? This page explains why you have a unique opportunity to prove that the Earth is not flat, after all.

Recent additions continue on the page Latest Additions and also What's New.

Also check out the page Featured Items.

Pencil and Paper Systems • Electrical and Mechanical Cipher Machines • Telecipher Machines • The Computer Era • Public-Key Cryptography • Miscellaneous Topics

Cylindrical Projections • Azimuthal Projections • Conic Projections • Pseudocylindrical and Pseudoconic Projections • Polyconic Projections • Conventional Projections • Other Conformal Projections • Other Equal-Area Projections • Miscellaneous Projections

A Brief History of Computers in General, and the Personal Computer in Particular • How Does A Computer Work? • What Computers Are Made From • Computer Arithmetic • The General Layout of a Computer • The Subroutine Call • The Old Days: Computing Without RAM • The Old Days: Decimal Computers • Interleaved Memory and Stride • Pipelined and Out-of-Order Processing • Classic VLIW • The Perfect Computer? • Minimizing Change • Not Quite RISC • A Historical View of FORTRAN • Remembering APL • Computer Architectural Preferences • Computer Front Panels • The Punched Card • Print Train Trivia • Printing Terminals and Proportional Spacing • Digital Magnetic Tape Recording • Reforming ASCII and Unicode • From the Annunciator to the Nixie Tube

Large Keyboards • Keyboards for Genuinely Large Character Sets • Comments on the Keyboard of the IBM PC • Keyboard Arrangements • The Keyboard Overlay Problem • Making Keyboards More Compact • An Attempt at a Popular Keyboard • Another Problem in Applied Geometry • Scan Codes Demystified

The Slide Rule • Infinity • Archimedean Solids • The Golden Ratio and Friends • Space-Filling Polyhedra • Sphere Packings • Polycube Puzzles • The Fourth Dimension • Rotations of a Dodecahedron • Examples of Groups • Two Famous Equations • Euler's Constant • Squaring the Circle • The Weird World of the Gudermannian • The Gamma Function • Gödel's Theorem and the Halting Problem • Magic Squares • The Mandelbrot Function • Diophantus at the Printer's Shop • Change Ringing • Notations for Fractions • Alternate Number Bases • A Cute Diagram • Bayesian Statistics and the Doomsday Argument • A Magical Set of Dice • Probability

The 17 Wallpaper Groups • Pentagonal Tilings • Octagonal Tilings • Dodecagonal Tilings • Heptagonal Tilings

The Rules of Chess • A Little History

A Few Openings • Chess Notation • The Immortal Game (Anderssen-Kieseritzky) • The Immortal 50th Game (La Bourdonnais-MacDonnell)

Comments on the Rules • The Crisis in Chess • Dynamic Scoring • A Proposed Rating System • Tournament Tiebreaking

Well-Known Forms of Chess • Traditional Enlarged Forms of Chess • Warring States Chess • The Game of the Three Kingdoms • Jetan, Barsoom's Game of Chess • The Game of Battle • Chess-Draughts • Hexagonal Chess • Hexagonal Chess, Part 2 • Triangular Chess? • S. Waider's Chess for Three Players • Enlarged and Improved Chess • Four-Player Chess • The Game of War • Three-Dimensional Chess

Leaping Bat Chess • Random Variant Chess • Chess 2016 • Corrected Random Variant Chess • Original Random Variant Chess • My Own Three-Dimensional Chess • Engagement Chess • Five-Player Chess • An Unusual Board for Three-Player Chess • Spectral Realm Chess • Half-Shogi Chess • Temporary Marsellais Chess • Antimatter Universe Chess • An Ordinary Variant • Antimatter Universe Flag Chess • Yet Another Ordinary Variant • Rotating Spaceship Chess • A Problem Corrected • Prequel Chess • Reformed Shatranj • Two Off-Centre Ordinary Variants • Snake Chess • Tomorrow's Chess? • Tiebraker Chess • Exciting Chess • Winning Chess

Two-Move and Three-Move Restrictions • The Perfect Game [of checkers]? • Other Forms of Checkers • Hasami Shogi, Seega, and Other Related Games • Ludus Latrunculorum • English Gothic Double Checkers

Board Games Other Than Chess • A Few Board Games of Interest • Comments on Wei Ch'i (or Go, or Baduk) • Other Uses for a Go Board • The Greatest Modern Board Game of Skill • Backgammon • The Jungle Game • Rithmomachy • The Perfect [board] Game? • Making Wargames More Complicated • Making Full Use of Three Ordinary Dice • The World is Round • Making Board Games More Complicated • Space Battles in Three Dimensions • The Real Game of Bridge • Siberian Semi-Contract Whist (or Bridge) • Bridge for Six: Trivial Whist • Counting Tricks Before They're Hatched • The Semi-Tarock Deck • A Canadian Invention

A Comment on Quantum Mechanics • A Space Habitat Design • Travel to Mars • Lining up the Planets • The Equation of Time • Introducing Special Relativity • The Inconstant Moon • The Einstein-Podolsky-Rosen experiments • The Fine-Structure Constant • A Few Words About Stars • Punctuated Equilibria

How a Telescope Works • Kinds of Telescopes • Telescope Mountings • Eyepieces • Introduction to Geometrical Optics

Perpetual Calendars • A Luni-Solar Calendar • A Simplified Calendar Proposal • Julian Day Numbers • A Martian Calendar • A Modest Proposal for the Abolition of the Leap Second • Happy Easter! • Happy Hanukkah! • The Mayan Calendar

Printer's Units • Temperature Scales • From Gold Coins to Cadmium Light • Gauge is Not Scale • The Size of the Piano Keyboard • Some Unusual Units of Length • Old Feet and Old Pounds • Avoiding the Metric System

The Musical Scale • More Complicated Temperaments • A Bit About Musical Notation • Some Interesting Keyboards • A Bit About Chords • Approximating Equal Temperament • The Hammond Organ • A Minor Mystery: The Chorus Tone Generator • How Does a Violin Work?

Memory-Reference Instructions • Additional Instructions • Basic Architecture • Tagged Operation Modes • Restricted Functionality • Off-Chip Processing

Instruction Set

Basic Information • Writing an EXALT Program • Arithmetic Statements • Control Structures • Type Declaration • Storage Classes • Subprograms • Parallel Processing • User-Defined Types • Program Source Modification • Expression Evaluation • Input/Output • Database Management • Exception Handling • Advanced Features • Appendix II: Implementation Notes