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On January 20, 2025, Donald J. Trump was inaugurated as the 47th President of the United States of America.

As you may have guessed, I am less than thrilled about this.

Of course, I may be biased, as I am a Canadian, living in Canada, a country upon which, like Greenland, Trump has cast covetous eyes.

There was once a time when I looked more favorably on the prospect of a union between Canada and the United States. When John F. Kennedy was President, and Americans were engaging in the first steps of the exploration of space, with the rest of the Free World left to do no more than look on in admiration. But that was then, and today Canada faces more problems and difficulties than it did then, but so does the United States - to even a greater extent, apparently. Problems which we would rather not join Americans in enduring.

A statement by U.S. Vide President J. D. Vance made in a Fox News interview about Greenland on Sunday, February 2nd, 2025 is extremely concerning. Aside from its insulting tone towards Denmark in particular, and the nations of the European Union in general, it revealed that the concerns voiced by the U.S. about Russian and Chinese activity in the Arctic are merely a pretext, and the real goal is to begin the exploitation of the mineral resources of Greenland, despite the extreme fragility of the ecosystem in an area with as challenging a climate as that of Greenland. This motive, to plunder natural resources by force, as opposed to taking urgent defensive measures against a genuine threat to the Arctic, would, of course, brand the United States as an aggressor nation pure and simple should it use military force in pressing its plan to acquire Greenland.

I do, however, still have faith that someday the American people will come to their senses, and no longer elect people like Donald Trump as their President, and the normal situation of close and friendly relations between our two countries will be restored.

However, if you wish, as do I, to be able to forget for a time that this ever happened, you may click here, and send the page back to normal.

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 sup

I do, however, still have faith that someday the American people will come to their senses, and no longer elect people like Donald Trump as their President, and the normal situation of close and friendly relations between our two countries will be restored.

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.

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

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

Therefore, it should not be regarded as surprising that it is also home to a monument intended to serve as a memorial, pictured at left, 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.)

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 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
	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 Few Words About Stars • 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 • 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