A Win Against Fritz

From time to time, I'll insert a chess game into this blog, played against Fritz on Chessbase. My main purpose in doing this is to keep practising how to insert a chess game into a blog or else I'll forget how to do it before very long. A secondary purpose is to keep a record of interesting games, preferably ones that I win but not exclusively. Here goes:

[White "Sean"] [Black "Fritz Club Level"] [Result "1-0"] [Termination "Fritz resigned"] 1.Nf3 d5 2.d4 h5 3.c4 Nf6 4.Nc3 e6 5.Bg5 Bb4 6.Qa4+ Nc6 7.a3 Bxc3+ 8.bxc3 Bd7 9.Qc2 dxc4 10.e4 e5 11.Bxc4 Qe7 12.0-0 0-0-0 13.d5 Na5 14.Bd3 Rde8 15.h4 c6 16.c4 b6 17.Rfb1 Kc7 18.Nd2 Kb8 19.Nb3 Nxb3 20.Qxb3 c5 21.a4 Qd6 22.Bd2 Kc7 23.a5 Ra8 24.f3 Rhb8 25.Qa3 Rb7 26.Bc2 Rab8 27.a6 Nxd5 28.cxd5 Ba4 29.Bxa4 Ra8 30.axb7 Rb8 31.Bc6 Rh8 32.Qxa7 Kd8 33.b8 Qxb8 34.Qxb8+ Ke7 35.Qb7+ Kf6 36.Bg5+ Kg6 37.Ra7 Rf8 38.Rxb6 Kh7 39.Be8 Kh8 40.Bxf7 Rd8 41.Be6 Rd7 42.Qxd7 Kh7 43.Qxg7#

There is a glitch in this game. White's 33rd move is 33.b8+Q, meaning that the pawn queens with check, but this was not recognised and play stopped at Black's 32nd move. The only way that I found to proceed was simply to write 33. b8. Ah well, nothing's perfect. To be honest, I blundered in this game on my ninth move. I forgot that my queen was vulnerable to a discovered attack from the black bishop after the knight moves away. In the original game, I played 9.e3 and black countered with 9...Nxd4. Oops! After my reconsidered 9.Qc2, I didn't make any more blunders and went on to win in grand fashion against a handicapped Fritz playing at club level.

The Cambrian Explosion

According to Wikipedia:

The Cambrian explosion or Cambrian radiation was an event approximately 541 million years ago in the Cambrian period when most major animal phyla appeared in the fossil record. It lasted for about 20–25 million years. It resulted in the divergence of most modern metazoan phyla. The event was accompanied by major diversification of other organisms. 

Before the Cambrian explosion, most organisms were simple, composed of individual cells occasionally organised into colonies. Over the following 70 to 80 million years, the rate of diversification accelerated, and the variety of life began to resemble that of today. Almost all present animal phyla appeared during this period.

An article in NEW ATLAS caught my attention with the following heading:

 Ancient crystals suggest Earth's core is
4 billion years younger than the planet

This is somewhat confusing but the article goes on to explain that the Earth's inner core, in its current solid form, only formed about 565 million years ago. 

A new study dates the Earth's inner core to just 565 million years old,
much younger than the 4.5-billion year old planet

I'll quote the article in full:

The Earth is almost 4.5 billion years old, but it's young at heart – literally. Researchers from the University of Rochester have now dated the solid inner core of the planet to just 565 million years, making it a relative toddler compared to the rest of Earth. 

Since Earth started life as a growing clump of rock, it's easy to assume that the core is the oldest part of the planet, but that's not quite the case. Today, it's divided into two regions: a solid ball of iron in the inner core, which is surrounded by a swirling pool of liquid iron. When exactly that inner core solidified has long been up for debate, with conventional thinking placing it somewhere between half a billion and 2.5 billion years. 

But now the Rochester researchers have narrowed it down to the lower end of that scale. The key to the discovery is the magnetic field that surrounds and protects Earth, and measuring how that's changed over time. 

To do so, the team collected samples of ancient crystals from the Sept-Îles Complex in Quebec. Inside these crystals are tiny magnetic needles that preserve a record of the magnetic field at the time they were first locked away in the mineral. The researchers found that about 565 million years ago, the Earth's magnetic field was the weakest it's ever been – about a tenth of its current strength – and was on the verge of collapse. 

Since life is still here today and we're able to go outside without being bombarded with deadly cosmic radiation, the magnetic field obviously bounced back from that low point. But how? The Rochester team says that a newly-formed solid inner core could be responsible.
The Earth's magnetic field is generated by the flowing fluid iron, in a process called a geo-dynamo. 

The team says Earth has probably had a weak geo-dynamo for billions of years, created by a core that was mostly molten iron. But this process slowed down over time, until that turning point 565 million years ago when it was stabilised, possibly by the arrival of the solid inner core we know today. 

"This is a critical point in the evolution of the planet," says John Tarduno, corresponding author of the study. "The field did not collapse because the inner core started to grow and provided a new energy source for the formation of the geo-dynamo." 

The team says the idea is backed up by other data sets and simulations, but at will need more work to confirm it. The study doesn't just help us understand our own planet a bit better – it could aid in the search for exoplanets that are capable of supporting life. 

"The same factors that drive dynamos on Earth might affect the magnetic shielding on exoplanets," says Tarduno. "It could be the case that some planets don't have long-lived dynamos and those planets would not have the magnetic shielding we have, meaning that their atmosphere and water might be removed." 

The research was published in the journal Nature Geosciences.

John Tarduno's comment "This is a critical point in the evolution of the planet" is quite telling and its tempting to surmise that the reason for the Cambrian explosion was the solidification of the inner core and the resultant increase in strength of the Earth's magnetic field and the resultant protection that magnetic shielding gave to emerging life forms.

Left: Earth's core and magnetic field 565 million years ago, at
its weakest point. Right: Earth's current core and magnetic field

Making Musical Progress

The reason my mathematical knowledge continues to expand is that I've gotten into the habit of analysing my diurnal age on a daily basis. It's one of the first things I do in the morning after breakfast. Usually I'll pick out a sequence in the OEIS (Online Encyclopaedia of Integer Sequences) that contains that number and also piques my interest. I'll investigate the mathematics involved and later I'll see if I can reproduce the sequence using SageMathCell. I often find additional information on Numbers Aplenty. The point is that this routine consistently introduces me to new mathematical concepts and improves my coding using SageMath.

However with music, even though I play most days, I tend to play the same old songs and, far less frequently, I'll learn a new song. Only very occasionally will I learn some new technique. I want to improve my playing and so I need to enforce some discipline on myself regarding my music. I should strive to learn a little bit every day. To that end I'm starting with Marco Cirillo's FINGERPICKING GUITAR IN 7 DAYS series of videos. Here's the first of his videos.

 

The same could approach could be applied to my chess playing. It would be nice to make a little progress each day by learning a new opening or endgame technique, finding out a little more about the history of the game or exploring one of the many variants of the game. I've certainly made progress in both my musical and chess proficiency since retiring but I can do better. However, back to the musical exercise:

Figure 1: music notation and tabs for first part of the exercise

Figure 2: music notation and tabs for second part of the exercise

Figure 3: music notation and tabs for third part of the exercise

I'll practise this exercise and then move on to his other videos.

Chess: A Personal History

I've just finished reading "The Immortal Game" by David Shenk. It's a brief history of chess set against the backdrop of the so-called Immortal Game played on June 21st  1851 in London between Adolf Anderssen (White), a famous player and informal world champion of the mid-19th century, and Lionel Kieseritzky (Black), another strong player of the day. It's an interesting approach: drip feeding the moves to the reader over the course of the various chapters while at the same time expatiating upon the historical, psychological and cultural aspects of chess in general.

A brief discussion of the moves involved in this famous game can be found on WikiBooks. Unfortunately for Kieseritzky, he died not long after playing this game. To quote from the book:

Kieseritzky ... would forever carry the moniker “Immortal Loser.” Upon returning home to Paris ... he was soon forced to fold his failing chess magazine as he struggled with his finances and his health. He died in a Paris mental hospital in 1853, just two years after his loss in the Immortal Game. He had no money to his name. No one in the chess world contributed to give Kieseritzky a decent burial. No one stood by his grave.

This got me thinking about my own chess history and I've chosen to document a little of my story here. Oddly, the story begins with my father when I was about eleven years of age. One day he decided that we should learn to play chess. I was agreeable. We went off in search of a former boarder in our house who was now living elsewhere but whom we remembered as having been a keen chess player. I can clearly remember him playing, some years before, against an opponent who was a boarder at my maternal grandparents' house. This would have been my earliest memory of a chess game.

My father and I never did find our former boarder. He had moved elsewhere. Regarding that other boarder who was English, he later returned to Britain but revisited Australia years later with an Irish bride in tow. By this time, I had learned to play chess and we played several games together when I was in my mid-teens. Back to the beginning and not long after our failed attempt to find the boarder, I somehow acquired a small fold-up chess set with magnetic pieces that included instructions as to how to move and thus I learned the basics of the game from this. My relationship with my father was never close and only worsened in my teenage years and I don't think he ever learned to play.

I can't remember the exact chronology but around 1964, the year that I was in Grade 10 of high school, I started to take the game very seriously. I purchased several books, amongst the first was Irving Chernev's "Logical Chess" of which I still have a physical copy. It's one of the very few books to survive from my youth. Up until the composition of this post, I'd not been able to find an electronic version of the book but happily I have now obtained one. It's been converted into algebraic notation whereas the original edition that I had used descriptive chess notation (P-K4 etc.). The latter was the most widely used notation in the 1960's and I found it quite difficult to adapt to the algebraic notation that came to dominant in the 1970's. It's as if my brain had been hard-wired with the classical notation but the algebraic to me lacked "magic". I felt there was something magical about 1. P-K4 whereas I felt nothing for 1. e4. Strange, I know, but there you have it.

There has been some criticism of Chernev's book in later years (read these forum comments on chess.com) but to me, at the time, it was a wonderful book and I pored over it in an effort to improve the quality of my play. My best friend at school also became interested in the game and during our remaining high school years we played a great many games. I subscribed to a chess magazine (the name of which eludes me) and I read other chess books including Lasker's "Common Sense in Chess" and "My System" by Aron Nimzowitsch. This was an exciting time for chess. Bobby Fischer's star was on the rise and the supremacy of the Soviet chess machine was being challenged.

Grandmaster Yuri Averbakh

During my year at University (1967), I remember watching a simultaneous exhibition by the well-known Russian grandmaster Yuri Averbakh. This was my first ever time seeing a grandmaster in action. He is still alive believe it or not, aged 96. I've included a photo of him here in his prime rather than one of him as he now looks. My friend from school also attended University but he was beginning to show signs of the paranoid schizophrenia that would overwhelm him in the early years of the next decade. His interest in chess was declining and I guess my initial enthusiasm had faded as well. I did play correspondence chess on and off for a couple of years in the early 70's which was quite tedious because a letter needed to be posted for each move. For most of the decade however, I just played in a desultory fashion.

For some reason, in the early 80's I joined a local chess club and enjoyed a brief flush of fame when our team headed off one evening to play a rival team. The team size was eight as I recall and we were comprehensively beaten 1.5 to 6.5 with all players beaten except for me, who secured a win with the white pieces playing a Ruy Lopez, and another team member who managed a draw. Not longer after that I headed off with my family to Britain and while travelling around there, my interest in the game was rekindled. I remember buying a copy of Reuben Fine's "Basic Chess Endings" and studying it very enthusiastically.

What I lacked over the years since my schooldays was a regular opponent and it was only between 1985 and 1987 that I become friends with a German guy who enjoyed chess and Stratego. On many Friday nights during that time, I would drop by his unit and we would enjoy wine and nibbles while playing firstly a few games of Chess before finishing up with a game of Stratego. I remember he bought what must have been at the time one of the first electronic devices capable of playing chess. I knew that the limitations of such devices were most glaring in the end game and so, on the few occasions that I played it, I usually managed to win by simplifying as quickly as possible into an advantageous end game. However, I much preferred my human antagonist and I have fond memories of that period and all the wine-sodden games that we played together.

At various times during my high school teaching career I've supervised school chess teams but that usually involved driving the students to the opposing team's venue or hosting the opposing team at our school. The students who signed up for the team could already play and I didn't really spend much time teaching them about chess. With the advent of computers and later smartphones, I played many desultory games against my electronic adversaries but it was only after retiring in 2015 that I found I had a lot of spare time and my enthusiasm for chess was rekindled. I became aware of the extensive resources available online for playing chess, improving one's level of play and just finding out more about the game in general. An interest in learning about the personalities and styles of the leading players of the day had characterised my early association with chess and now more than 50 years later, that same interest had been rekindled. I've come full circle.

Toroidal Chess

I'd heard about toroidal chess but thought such a game was rather silly because how could you practically play chess on a toroidal board. Even with magnetic pieces attached to a metallic toroidal board, playing comfortably would be almost impossible. It came as something of a revelation that this variant of chess could be played quite easily on a standard chess board.

Diagram 1

To see how, let's start with a cylinder chess which, as the name suggests, is played on a cylindrical board in which the left hand side of the board is joined to the right hand side. Here are some excerpts from what Wikipedia has this say about cylinder chess:

The game is played as if there is no edge on the side of the board. When a piece goes off the right edge of the board in cylinder chess, it reappears on the left edge; when a piece goes off the left edge, it reappears on the right edge (see Diagram 1) ... bishops are more valuable in this variant ... the game is sometimes played with changed rules for castling ... some cylinder chess problems allow moves that don't change the position (null moves). 

In Diagram 2 an example of such a problem is shown. The solution is to put Black in zugzwang by playing 1.Rh4-h4. Now, after any move by Black, White has a mate. The move 1.Rg4 doesn't work because of 1...Ka5 threatening to capture the rook on h6.

Diagram 2

It took me a while to understand what was happening in Diagram 2 but I eventually got it. Certainly it takes some getting used to. However, things getting far more difficult once the bottom of the board is joined to the top to create the torus. This also brings the White and Black back ranks up against each other, which necessitates a repositioning of the initial starting position of the pieces.

This revised starting position is shown in Diagram 3. Note that "in the starting setup, the rooks protect each other, while being threatened by the opponent's rooks. They are supported by the knights on the sides of the board, making their positions more defensible" . A reason for moving the Knight from its usual position is that if "the knight starts from its normal starting square, say g1 ... (then) moving through h1 to a1, it can then make the orthogonal move to a8, potentially taking a rook!" Further advice is to "watch out for diagonal attacks from pawns positioned on the side of the board" and to "note that the queens threaten the rooks at a1 and a8, making the rooks on that side of the board slightly less secure than the king's side rooks"(link).

Diagram 3

I should add that there is no castling and only pawns on the a, b, g, and h files can move two spaces on their first turn, and consequently, those are the only pawns that en passant can apply to. A piece cannot move eight spaces and wrap around to its starting position and be considered to have moved - all moves must change the board position. There seems to be a site where one can play toroidal chess on the Internet. I checked it out but there weren't any other online players at that time. There is another site where a wide variety of chess variants can be played, including Cylinder Chess and Fischer Random Chess but not apparently toroidal chess. The site seems to be quite active although I haven't tested it out.

I'm not all that keen to attempt to play either cylinder chess or toroidal chess. I find the conventional game demanding enough and there's something comforting about having all the action confined to the 64 checkered squares with rigid borders at the top and bottom, left and right. Once one or both of the borders are removed, the nature of the game seems to be fundamentally altered. It's interesting nonetheless and I was drawn to it via the mathematical problem of how many ways can two non-attacking amazons be placed on an n X n toroidal chess board. I wrote about this in a post to my mathematics blog titled The Mathematics of Chess.