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Welcome to my personal home page. There are many pages on this site concerning various topics of an entertaining, yet somewhat technical, nature that many visitors should find fascinating.

Recent Updates:

On my page about the Korean typewriter, having finally found significant new information about the mysterious Selectric element for typing in Korean, I have added this information at the bottom of that page. Also, on my page about large keyboards, I've accompanied the existing diagram of the Space Cadet keyboard by one of the Knight keyboard and one of the SAIL keyboard which preceded it, and I have also included a diagram of the keyboard of the 9210 Scientific Descriptive Printer, which was used for preparing programs in COLASL to run on the IBM STRETCH computer (the prototype of the IBM 7030). As well, on my page commenting on the keyboards for the IBM PC, I've added diagrams of the keyboards for the SANYO MBC-550 computer, the Spectravideo SV-328, and the Fortune Systems 32:16, as well as replacing the small diagram of the keyboard of the Radio Shack Model II computer with a larger one.

On my page of featured images, I now illustrate a possible form for The Computer of the Future! This is located at the top of the page, immediately prior to a brief mention of telephone dials.

I have added a brief page about hyperbolic trig functions and the Gudermannian. In addition, in the page about special scales in the section on slide rules, I have fleshed out the description of the scales of the Hemmi 153 slide rule, as well as adding information about the Flying Fish 1018 slide rule. As well, in the course of other minor corrections and additions to my pages on the slide rule, on the final page of that section, I have (finally!) added a diagram and an explanation to help provide a deeper understanding of how a slide rule works and is designed, by explaining how the manipulations involved in multiplying a series of numbers, and the way the cursor works, create a fundamental distinction between the sliding portion of the slide rule, and the stock within which it moves.

On this page, I've finally added a diagram and some text in which I acknowledge some new developments in amateur astronomy: Meade's Advanced Coma Free telescope, Celestron's EdgeHD telescope and their Rowe-Ackermann telescope, as well as the Hyperstar accessory from Starizona.

Just in time for Halloween! In my section on ways to handle 36-bit, 48-bit, and 60-bit data in a world built around the 8-bit byte and the 32-bit word, I have now added the page Triskaidekaphobia which considers using 60 bits out of every 64 bits to provide five 12-bit storage units from every 64 bits of memory... and then turning around and making four out of every five of those storage units, in effect, 13 bits long. Since not all of them have that extra bit, limitations are imposed on the EQUIVALENCE statement which, if disregarded, could lead to some... interesting... program bugs. So it could lead programmers to think of the thirteenth bit as unlucky, hence the title.

On a new page in the mathematics section, I discuss Bayesian Statistics and the Doomsday Argument.

After a long period of inactivity, my pages on Map Projections have, as their first addition of the current new series, a page concerning the conformal projection of the world on an ellipse! And (without waiting to complete the project of updating my own BASIC program to draw this one as well) I have also added on the following page the Adams-Cahill conformal projection of the world on the surface of an octahedron by means of the Dixon elliptic functions. Since then, another five pages have been added: one on the new Equal Earth projection, one on the Boggs Eumorphic projection, one on the Strebe projection, and one on perspective projections, as well as the page noted in the paragraph below on the Dietrich-Kitada projection. Additions have also been made to several other pages, including the ones about the Mercator projection, the Bonne projection, the Mollweide projection, the Hammer-Aitoff projection, Lambert's Conformal Conic projection, and even the Winkel Tripel projection. Possibly of particular interest, my page on the Ginzburg Projection now has coverage of the closely related Latitudinally Equal Differential Polyconic Projection, widely used for world maps in the People's Republic of China.

And now I have perhaps made the most exciting addition to the section on map projections yet. Many years ago, at the library specializing in maps at the University I attended, I noticed an old German book with a lot of maps in an unusual projection I hadn't seen before. It stuck in my mind. Eventually, I learned about the Van der Grinten IV projection, and assumed that this was the map projection I had seen so long ago. But I learned that I was mistaken. A forum post by a noted cartographer, on the web site of his company, noted that one Bruno Dietrich wrote an unusual book with many thematic maps in a novel map projection, not described, and years later, a Japanese cartographer, Kozo Kitada, assuming the projection was equal-area, as it appeared to be, worked out what the construction of the projection must have been. The forum post described enough of its properties that I was able, particularly with the aid of maps on-line in that projection to let me see what I was aiming at, to also work out how that projection would have had to work. So my site now has a page on what that map projection really was - it turns out that instead of being a conventional projection like the Van der Grinten IV, it was equal-area - and (after a difficult debugging session) I got my little BASIC map-drawing program to handle that projection (it may be the second map-drawing program in existence that does so), so now I present my web page about the Dietrich-Kitada projection.

Do you live in Australia? This page explains why you have a unique opportunity to prove that the Earth is not flat, after all. UPDATE: A note has now been added to show that Flat Earth believers might still have a possible fall-back position available to them.

Having on this site both a page discussing, at length, measurements used by printers and a page going into detail about unit systems used for some typesetting machines, I have finally decided that it would also be appropriate to add a page illustrating the development of typefaces over the years. This brief page goes very quickly over the highlights of the story that can be found in many introductory books about printing.

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. There is also a new page giving a history of computers in general, and the microcomputer revolution in particular.

Finally, I have added to this site a page concerning one of the most popular mathematical subjects:

I had long delayed doing so, despite the topic being a natural for this page, as there are many other excellent pages on this subject on the Web. At present, it is quite a modest page on the subject, and I do expect to expand it.

Cryptography Entry Page
Index Page

Pencil and Paper SystemsElectrical and Mechanical Cipher MachinesTelecipher MachinesThe Computer EraPublic-Key CryptographyMiscellaneous Topics

Map Projections Entry/Index Page

Cylindrical ProjectionsAzimuthal ProjectionsConic ProjectionsPseudocylindrical and Pseudoconic ProjectionsPolyconic ProjectionsConventional ProjectionsOther Conformal ProjectionsOther Equal-Area ProjectionsMiscellaneous Projections

A brief page with a few annotations about the Girl Genius web comic, for which a link banner appears to the right, is now on this site.


Featured Images

A Short History of Type

A Brief Chronology of the Typewriter

Signal Flag Systems
The Vocalization of Hebrew
Introduction to HTML
Color Charts
Building Blocks and the Pythagorean Triangle
Efficient and Flexible Text Encoding
Design for a Tall Building

Movie and TV Aspect Ratios
A Limitation of Color Photography
Color Filter Array Designs

Don't Touch That Dial!
Color Television Madness
Four Speakers from Two Channels?
A Problem in Applied Geometry

Chinese Character Encodings

A Phonemic Alphabet
Two Schemes For Elections
Patterns in Nature and Myth

A Note on Large Numbers
A Unified Architecture for Telephone Numbers
On Philosophy and Ethics


A Brief History of Computers in General, and the Personal Computer in ParticularHow Does A Computer Work?What Computers Are Made FromComputer ArithmeticThe General Layout of a ComputerThe Subroutine CallThe Old Days: Computing Without RAMThe Old Days: Decimal ComputersInterleaved Memory and StridePipelined and Out-of-Order ProcessingClassic VLIWThe Perfect Computer?Minimizing ChangeNot Quite RISCA Historical View of FORTRANRemembering APLComputer Architectural PreferencesComputer Front PanelsThe Punched CardPrint Train TriviaPrinting Terminals and Proportional SpacingDigital Magnetic Tape RecordingReforming ASCII and Unicode

Keyboards Entry/Index Page

Large KeyboardsKeyboards for Genuinely Large Character SetsComments on the Keyboard of the IBM PCKeyboard ArrangementsThe Keyboard Overlay ProblemMaking Keyboards More CompactAn Attempt at a Popular KeyboardScan Codes Demystified


The Slide RuleInfinityArchimedean SolidsPolycube PuzzlesThe Fourth DimensionRotations of a DodecahedronExamples of GroupsTwo Famous EquationsEuler's ConstantSquaring the CircleThe Weird World of the GudermannianSphere PackingsGödel's Theorem and the Halting ProblemMagic SquaresThe Mandelbrot FunctionDiophantus at the Printer's ShopChange RingingNotations for FractionsAlternate Number BasesBayesian Statistics and the Doomsday ArgumentProbability

Tilings Entry/Index Page

The 17 Wallpaper GroupsPentagonal TilingsOctagonal TilingsDodecagonal TilingsHeptagonal Tilings

Chess Entry/Index Page

The Rules of ChessA Little History

A Few OpeningsChess NotationThe Immortal Game (Anderssen-Kieseritzky)The Immortal 50th Game (La Bourdonnais-MacDonnell)

Comments on the RulesThe Crisis in ChessDynamic ScoringA Proposed Rating SystemTournament Tiebreaking

Well-Known Forms of ChessTraditional Enlarged Forms of ChessWarring States ChessThe Game of the Three KingdomsJetan, Barsoom's Game of ChessThe Game of BattleChess-DraughtsHexagonal ChessHexagonal Chess, Part 2Triangular Chess?S. Waider's Chess for Three PlayersEnlarged and Improved ChessFour-Player ChessThe Game of War

Leaping Bat ChessRandom Variant ChessChess 2016Corrected Random Variant ChessOriginal Random Variant ChessThree-Dimensional ChessEngagement ChessFive-Player ChessAn Unusual Board for Three-Player ChessSpectral Realm ChessHalf-Shogi ChessTemporary Marsellais ChessAntimatter Universe ChessAn Ordinary VariantAntimatter Universe Flag ChessYet Another Ordinary VariantRotating Spaceship ChessA Problem CorrectedPrequel ChessReformed ShatranjTwo Off-Centre Ordinary VariantsSnake ChessTomorrow's Chess?Tiebraker ChessExciting Chess

Checkers Entry/Index Page

Two-Move and Three-Move RestrictionsThe Perfect Game [of checkers]?Other Forms of CheckersHasami Shogi, Seega, and Other Related GamesLudus LatrunculorumEnglish Gothic Double Checkers

Board Games

Board Games Other Than ChessA Few Board Games of InterestComments on Wei Ch'i (or Go, or Baduk)Other Uses for a Go BoardThe Greatest Modern Board Game of SkillBackgammonThe Jungle GameRithmomachyThe Perfect [board] Game?Making Wargames More ComplicatedMaking Full Use of Three Ordinary DiceThe World is RoundMaking Board Games More ComplicatedSpace Battles in Three DimensionsThe Real Game of BridgeSiberian Semi-Contract Whist (or Bridge)Bridge for Six: Trivial WhistCounting Tricks Before They're HatchedThe Semi-Tarock Deck

Science Entry/Index Page

A Few Words About StarsA Space Habitat DesignTravel to MarsLining up the PlanetsThe Equation of TimeThe Inconstant MoonThe Einstein-Podolsky-Rosen experimentsThe Fine-Structure ConstantPunctuated Equilibria

Telescopes Entry/Index Page

How a Telescope WorksKinds of TelescopesTelescope MountingsEyepiecesIntroduction to Geometrical Optics

Calendars Entry/Index Page

Perpetual CalendarsA Luni-Solar CalendarA Simplified Calendar ProposalJulian Day NumbersA Martian CalendarA Modest Proposal for the Abolition of the Leap SecondHappy Easter!Happy Hanukkah!The Mayan Calendar

Unit Conversions Unit Conversions

Printer's UnitsTemperature ScalesFrom Gold Coins to Cadmium LightGauge is Not ScaleThe Size of the Piano KeyboardSome Unusual Units of LengthOld Feet and Old PoundsAvoiding the Metric System


The Musical ScaleMore Complicated TemperamentsA Bit About Musical NotationSome Interesting KeyboardsA Bit About ChordsApproximating Equal TemperamentThe Hammond OrganA Minor Mystery: The Chorus Tone GeneratorHow Does a Violin Work?

A Computer Architecture
A Computer Architecture
Entry/Index Page

Memory-Reference InstructionsAdditional InstructionsBasic ArchitectureTagged Operation ModesRestricted FunctionalityOff-Chip Processing

Concertina II
Entry/Index Page

Instruction Set

A Computer Language
A Computer Language
Preview Page

Basic InformationWriting an EXALT ProgramArithmetic StatementsControl StructuresType DeclarationStorage ClassesSubprogramsParallel ProcessingUser-Defined TypesProgram Source ModificationExpression EvaluationInput/OutputDatabase ManagementException HandlingAdvanced FeaturesAppendix II: Implementation Notes

Contact Information and Notes

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Copyright (c) 2000, 2001, 2002, 2004, 2005, 2008, 2010, 2011, 2012 John J. G. Savard