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Click on the Ukrainian flag to the left for a timeline of events relating to the current tragic events in that country: this timeline covers three major subjects, past activities of the Russian state aimed at suppressing the Ukrainian language and national identity, the history of the fall of the Soviet Union, including the transfer of power from Boris Yeltsin to Vladimir Putin, and the current conflict in Ukraine as well as the previous invasions of Crimea and later Donetsk and Luhansk.

After finally locating a reference on the Web about how Gary Kasparov had to give up his bid for the Russian Presidency on December 12, 2007 due to a contrivance, I was reminded how the novel 1984 pointed out that the "memory hole" was one of the things that made people vulnerable to the lies of tyrants. It helped that I had also recently read a transcript of a speech by Vladimir Putin which included the lie that Russia has a genuinely democratic and representative political system which just happens to be different from the Western one.

Click here for some reflections of mine on the serious crisis in which this situation has placed the world as I see it.

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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.

The striking image on the entry page is from the section on the Mandelbrot Function.

I have now come up with a solution for what computer keyboards should look like, in order to facilitate touch-typing, and to be compatible with the typewriter-pairing APL/ASCII standard:

(Of course, for compatibility with the APL/ASCII standard, the characters < and > would need to be switched to being accessed in the conventional manner, with SHIFT, rather than with CTRL, as shown here.)

A Meditation for which I have found no place:

When I was young, I had watercolor paint sets with perhaps six colors or twelve. But I had remembered seeing some with a great many colors, and I had always wanted one, but I never seemed to see a store with them on sale.

These days, with the Internet, with the mighty search engine Google, and the marketplace of eBay, I had been able to solve the mystery of what those sets were and who made them.

It turns out that the water color sets I was thinking of were made by a British firm by the name of "Page of London", and they came in many different sizes, with up to as many as 108 colors.

Recent Updates:

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

The page about three-player variants of Chess has now had a diagram and a description of the most common recent three-player variant of Chess added to it, as well as some other information. Also, a new variant of Chess, which uses the regular board and men, but in which the Queen's move is changed back to its ancient value of only one square diagonally, which is designed to make checkmate easier, and therefore more common, is now described both on the page about Dynamic Scoring, and the page about the variant Winning Chess.

The page about Aperiodic Tilings Within Conventional Lattices has been updated with the addition of the news that an aperiodic tiling of the plane by just one tile has now been discovered! An image of part of this tiling is shown below:

A further update to this page has been made, concerning the revised tiling, involving a new shape called the Spectre, which constitutes a tiling based on a true aperiodic monotile, as the previous one required both the shape called the Hat and its reflection.

The page on The Mysteries of the Dodecahedron has been updated to include a diagram which shows explicitly how one particular matrix form for the Golay Code is related to the icosahedron.

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.

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 recently added a diagram of the keyboard of the Control Data PLATO terminal's keyboard, and previously 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). Also added are keyboard diagrams for both the Laning and Zierler system and the Klerer-May system. As well, on my page commenting on the keyboards for the IBM PC, I've recently added a diagram of the keyboard of the Fujitsu Micro 16s, and previously I had added diagrams of the keyboards for the SANYO MBC-550 computer, the Spectravideo SV-328, the Televideo TS-1603, 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. Also, more accurate diagrams of the appearance of the original keyboards for the IBM Personal Computer and the IBM Personal Computer AT, as well as the IBM Enhanced Keyboard, have been added.

The page concerning Dice of Other Shapes has been considerably enhanced, with a number of photographs, most of which have now been moved to a page of their own, as well as a few diagrams added. These updates have been accompanied by an update to the page on the Archimedian Duals, to which images have also been added. And then, first a following page has now been appended to the page about dice of unusual shapes, featuring a systematic survey of the Archimedian duals with a complete set of illustrations of them and of the Archimedian solids from which they are derived, then the text of the original page was split into three pages, the original page, one page after the diagrams of the Archimedian solids, and another page after the page with the photographs, so that the discussion would proceed in proper sequence.

In the section on Units of Measurement, the page From Gold Coins to Cadmium Light had been expanded with new images and additional text; these additions continued, until the page was split in two, with the new content being placed in a new page specifically devoted to coins.

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 had 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. Subsequently, three additional pages have been added which go into more detail about specific groups of typefaces, following that page.

A new page has been added, which discusses how it might be possible to design a variant of Chess which is at once both Three-Dimensional and Hexagonal, by arranging the hexagons (or squares!) according to the Face-Centered Cubic symmetry. A new page about Space-Filling Polyhedra has also been added, so as to provide more information related to the Face-Centered Cubic symmetry, in addition to what is already provided on the page about Sphere Packing.

It has been a long time since I have updated my pages on cryptography, but I now have two very exciting updates, concerning two cipher machines the workings of which were declassified back in 2006. On this page there is now a description of the KL-7 rotor machine, and on this page there is now a description of the KW-7 electronic cipher machine.

A new page concerning the implementation of Hexagonal Chess on a computer discusses what would seem to be one very minor and trivial issue: how the hexagonal board should be represented. But it is seen that there are potential pitfalls, as there are important issues to be considered, if a wide range of Hexagonal Chess variants are to be supported.

A brief chronology of telescopes for the amateur astronomer has been added to this page about different kinds of telescope.

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.

My page on Floating-Point Formats now mentions the floating-point format used by the TC-16 computer in the People's Republic of China, and by the Model 709, which was the prototype for it, as well, which is the first format I have encountered that does not seem to fit in my categorization of floating-point formats as belonging to three fundamental groups.

I have now added a page about devices used for lettering to the end of my pages about keyboards, as the legends on many keyboards were originally drawn using such devices rather than being printed with printer's type.

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.

Unfortunately, I now realize that there may have been errors in my calculation of how the Dietrich-Kitada projection worked. I have corrected one, but there is likely to be another error as well.

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.

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

The Search for Awe

Handy Table of Powers

Dice of Other Shapes

Playing Cards

A Short History of Type

A Brief Chronology of the Typewriter

Signal Flag Systems
The Flags of the United States
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
On Human Rights
The Name of the United States


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 UnicodeFrom the Annunciator to the Nixie Tube

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 KeyboardAnother Problem in Applied GeometryScan Codes Demystified


The Slide RuleInfinityArchimedean SolidsSpace-Filling PolyhedraSphere PackingsPolycube PuzzlesThe Fourth DimensionRotations of a DodecahedronExamples of GroupsTwo Famous EquationsEuler's ConstantSquaring the CircleThe Weird World of the GudermannianGödel'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 WarThree-Dimensional Chess

Leaping Bat ChessRandom Variant ChessChess 2016Corrected Random Variant ChessOriginal Random Variant ChessMy Own Three-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 ChessWinning 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 TimeIntroducing Special RelativityThe 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