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The image above is a photograph of the skyline of Edmonton, Alberta, where I live, which I myself took some years ago.

The image above is a detail from a photograph taken by Edmonton artist Carrie Wheeler, which I have retouched and otherwise modified.

The city of Edmonton, like many cities in Western Canada, is home to a significant minority of Ukrainian origin.

In the nearby town of Vegreville, also in Alberta, Ukrainian culture is celebrated by a giant metal sculpture of a Pysanka egg, which is an egg on which colored designs are painted by a traditional method involving covering parts of the egg to which a specific dye is not to be applied with wax. These eggs are crafted for Easter celebrations.

This sculpture was unveiled in 1973, in association with national celebrations of the centennial of the founding of the Royal Canadian Mounted Police.

Also, therefore, it should not be regarded as surprising that Edmonton is also home to a monument, pictured at left, intended to serve as a memorial to those who lost their lives in the Holodomor, a famine deliberately created in Ukraine by Josef Stalin.

This monument, unveiled in 1983, was Canada's first public memorial to the Holodomor.

(Incidentally, as I live in Edmonton, it should not be surprising that the picture at left is my own work; but for a while initially, as I was both busy and feeling indisposed, I had been using a Creative Commons-licensed image instead. But I finally managed to pass by City Hall.)

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.

From inside, some comments I had made concerning the recent conversation between Volodomyr Zelensky and Donald Trump and J. D. Vance at the Oval Office:

After hearing the encouraging news that European governments are stepping up to the plate, and preparing to increase their aid to Ukraine, I engaged in some further reflection on these events.

It seemed to me that there was a real danger that some people in Europe would resent having more of their tax money go to Ukraine, because one man couldn't have controlled himself just a little more.

However, since the "disrespect" consisted of "litigating" the issues around the conflict, rather than raising his voice or any other actual disrespect, there is another important factor to consider. Not just that this diminishes the blame Volodomyr Zelensky bears for the contretemps, because that wouldn't matter to people focusing on the practical matter of their tax dollars.

No; instead, we must look beyond what actually happened, which we had the chance to see, to also think about what could have happened, but didn't.

Because what Zelensky would have had to have done to placate Trump and Vance further would have been to indicate agreement with the Putin talking points they were presenting.

And where's the danger of that?

Right when they come back to Zelensky with this wonderful peace agreement they were able to obtain from Vladimir Putin - which he would have to sign, or else make himself out to be a liar, because that would show he didn't really believe all those things he had assented to in this meeting.

So Zelensky didn't fall into their trap; he avoided the deadliest prong of a two-pronged trap that was designed so that there was no way to completely escape it.

Integrity isn't a stupid move: it's the only winning strategy.

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

The article at this link recounts the facts about Donald J. Trump's mishandling of the COVID-19 pandemic; it was even worse than I remembered.

According to a news item of June 18, 2024, Justin Trudeau called out "Slava Ukraini!", which means "Glory to Ukraine", while outdoors in connection with an international summit on peace for Ukraine.

One Russian propagandist reacted to this by calling our Prime Minister a "Bandera Nazi Thug". I checked on Wikipedia; while it is true that the slogan "Slava Ukraini!" was used by the OUN, it was not originated by them; it was used during Ukraine's ill-fated War of Independence from 1917 to 1921. And, of course, given that Ukraine had been under the heel of Stalin, and had just experienced the Holodomor, a more nuanced understanding of the OUN than simply dismissing them as Nazi collaborators is also in order.

But in another sense, perhaps Justin Trudeau's outburst is not entirely immune from criticism.

As "Slava Ukraini!" is the battle-cry of the Ukrainian soldier, echoing it, of course, is an entirely appropriate expression of solidarity with Ukraine.

However, in its historic struggle against brutal and utterly unprovoked Russian aggression, Ukraine is already crowned with glory, whatever the outcome of the current conflict may be.

Instead, we should be wishing for Ukraine things that either it does not have, or things that it does now have, but is in danger of not retaining. Let us wish Ukraine what it needs, not what it has in abundance.

Thus, at right, I illustrate three additional Ukrainian phrases, in addition to "Slava Ukrainii!", Glory to Ukraine. They are: "Peremoha Ukrainii!", Victory to Ukraine; "Swobodu Ukrainii!", Freedom to Ukraine; and "Miru Ukrainii!", Peace to Ukraine!

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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.

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.

They'll Be Rewriting All the Textbooks:

Through a YouTube video, I learned of the following paper, published in Proceedings of the National Academy of Sciences: Evolution of the Iodine Cycle and the Late Stabilization of the Earth’s Ozone Layer by Jingjiun Liu, Dalton S. Hardisty, James F. Kasting, and Noah J. Planavsky.

The discovery disclosed in this paper is this: Iodine, a natural consituent of the Earth's atmosphere, which, like the chlorinated fluorocarbons (CFCs) now banned, causes the breakdown of ozone in the Earth's atmosphere, was once present in the Earth's atmosphere in larger quantities than at present. This is due to the fact that only recently did the Earth's soil and oceans start absorbing iodine at a sufficient rate to prevent it from accumulating to a significant extent in the Earth's atmosphere. And this is the explanation of why plants and animals only colonized the Earth's land surfaces after they sat empty for about four billion years while life flourished in the oceans.

This is what precipitated the Ordovician-Silurian extinction event.

While Iodine is a solid at room temperature and pressure, water is a liquid at room temperature and pressure, not a gas either. However, water vapor is a constituent of our atmosphere: and, like water, solid Iodine still has a nonzero vapor pressure.

	Entry Page Index Page	Pencil and Paper Systems • Electrical and Mechanical Cipher Machines • Telecipher Machines • The Computer Era • Public-Key Cryptography • Miscellaneous Topics
	Entry/Index Page	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 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. Miscellaneous: 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 Canada 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 A Few Cameras 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 How We Know the World Is Round
	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
	Entry/Index Page	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 • 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 • Bayesian Statistics and the Doomsday Argument • A Magical Set of Dice • Probability
	Entry/Index Page	The 17 Wallpaper Groups • Pentagonal Tilings • Octagonal Tilings • Dodecagonal Tilings • Heptagonal Tilings
	Entry/Index Page	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
	Entry/Index Page	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
	Entry/Index Page	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
	Entry/Index Page	How a Telescope Works • Kinds of Telescopes • Telescope Mountings • Eyepieces • Introduction to Geometrical Optics
	Entry/Index Page	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
	Unit Conversions	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?
A Computer Architecture	Entry/Index Page	Memory-Reference Instructions • Additional Instructions • Basic Architecture • Tagged Operation Modes • Restricted Functionality • Off-Chip Processing
	Entry/Index Page	Instruction Set
A Computer Language	Preview Page	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