Tuesday, 2 August 2022

“In the abbess”!

Last month, as I have watched a little of the 1989 Ashes series for the first time (at least since it was played), I was more convinced than ever before that English bowling at the tail end of the 1980s really was worse than at any other time in the history of cricket.

The abysmal line and length of English bowlers throughout the series really confirms what the 1990 and 1991 Wisdens were saying about the inability of English bowlers of the time to master even the basics. It demonstrates beyond the smallest doubt that the “Year of the Bat” in the following 1990 season — when not a single England-qualified bowler bowling minimally 1,000 balls averaged under 26 and the average number of runs per wicket in county cricket rose to a whopping 38.72 — had absolutely zilch to do with the quality of the batting. The extraordinary scores of 1990 were due to a combination of

  1. rigged pitches
    1. these were due to changes designed to reduce the effectiveness of county medium pacers, alongside full covering introduced to be more favourable to television broadcasting interests
  2. abysmal bowling standards as described above

One amazing but funny mishearing occurred last month when I said English bowling in the late 1980s was

“in the abyss”

was heard by my brother as

“in the abbess”!
My brother even joked about an abbess being an English bowler — of course utterly ridiculous! Nonetheless, the joke still resonates with me because although “a-biss” is not the same sound as “a-bess”, the correct pronunciation of abyss is “a-biss”, as with acidic (which I very frequently mispronounced as “a-si-dic” when reading chemistry textbooks in school).

Monday, 4 July 2022

The 473,268th and 473,269th centuries — how few primes do you need?

In recent days, as I recover from a series of “bugs” (viruses) that badly affected me all through June and made me feel much chillier than usual in typically cool Melbourne winter weather, I have looked again at old prime number lists on the Encyclopedia of Integer Sequences.

Over eight year ago, I published a post on the 16,719th century, the first to contain no prime number, and some other sequences with very few primes. Today, using the trusty Alpertron factoring site, I turned my attention to the 473,268th and 473,269thth centuries — the first consecutive centuries void of prime numbers. The factors of numbers not divisible by 2, 3, or 5 in the 473,268th and 473,269th centuries are tabulated below:

  • 47,326,703 = 43 × 73 × 15,077
  • 47,326,709 = 23 × 2,057,683
  • 47,326,711 = 331 × 142,981
  • 47,326,717 = 2,939 × 16,103
  • 47,326,721 = 13 × 53 × 149 × 461
  • 47,326,723 = 67 × 706,369
  • 47,326,727 = 7 × 233 × 29,017
  • 47,326,729 = 89 × 643 × 827
  • 47,326,733 = 2521 × 18,773
  • 47,326,739 = 19 × 19 × 31 × 4,229
  • 47,326,741 = 7 × 11 × 614,633
  • 47,326,747 = 13 × 3,640,519
  • 47,326,751 = 41 × 1,154,311
  • 47,326,753 = 29 × 1,631,957
  • 47,326,757 = 5,477 × 8,641
  • 47,326,759 = 17 × 2,783,927
  • 47,326,763 = 11 × 131 × 32,843
  • 47,326,769 = 7 × 1,291 × 5,237
  • 47,326,771 = 1,399 × 33,829
  • 47,326,777 = 19 × 199 × 12,517
  • 47,326,783 = 7 × 6,760,969
  • 47,326,789 = 43 × 61 × 18,043
  • 47,326,793 = 17 × 523 × 5,323
  • 47,326,799 = 13 × 3,640,523
  • 47,326,801 = 23 × 31 × 66,377
  • 47,326,807 = 11 × 257 × 16,741
  • 47,326,811 = 7 × 29 × 37 × 6,301
  • 47,326,813 = 307 × 154,159
  • 47,326,817 = 431 × 109,807
  • 47,326,819 = 109 × 434,191
  • 47,326,823 = 2,753 × 17,191
  • 47,326,829 = 11 × 4,302,439
  • 47,326,831 = 6,793 × 6,967
  • 47,326,837 = 1,279 × 37,003
  • 47,326,841 = 1,777 × 26,633
  • 47,326,843 = 349 × 135,607
  • 47,326,847 = 23 × 2,057,689
  • 47,326,849 = 73 × 73 × 83 × 107
  • 47,326,853 = 7 × 19 × 355,841
  • 47,326,859 = 139 × 340,481
  • 47,326,861 = 17 × 2,783,933
  • 47,326,867 = 7 × 379 × 17,839
  • 47,326,871 = 743 × 63,697
  • 47,326,873 = 11 × 151 × 28,493
  • 47,326,877 = 13 × 1,187 × 3,067
  • 47,326,879 = 1,931 × 24,509
  • 47,326,883 = 101 × 619 × 757
  • 47,326,889 = 6,073 × 7,793
  • 47,326,891 = 19 × 2,490,889
  • 47,326,897 = 1,277 × 37,061
The square root of 47,326,900 is approximately 6,879.454920268029491. The largest prime smaller than the square root of 47,326,900 is 6,871, and 6,871 is the 872nd prime number. If we tabulate all factors from the table above, we find that the following primes smaller than 6,879 divide numbers in the 473,268th and 473,269th centuries:
 
Prime # of numbers divisible by
7 7
11 4
13 4
17 3
19 4
23 3
29 2
31 2
37 1
41 1
43 2
53 1
61 1
67 1
73 2
83 1
89 1
101 1
107 1
109 1
131 1
139 1
149 1
151 1
199 1
233 1
257 1
307 1
331 1
347 1
379 1
431 1
461 1
523 1
619 1
643 1
743 1
757 1
827 1
1,187 1
1,277 1
1,279 1
1,291 1
1,399 1
1,777 1
1,931 1
2,521 1
2,753 1
2,939 1
3,067 1
4,229 1
5,237 1
5,323 1
5,477 1
6,073 1
6,301 1
6,793 1
In other words, only fifty-seven primes out of 872 are needed to divide numbers in the first pair of consecutive primefree centuries (excluding number divisible by 2, 3, or 5 which may also have other factors smaller than 6,879). Put another way, just 6.53 percent of the primes that could potentially be the smallest factor of a number in the 473,268th or 473,269th centuries actually divide any number therewithin. With similar sequences in seven-digit centuries — just one order of magnitude smaller — the proportion of primes required is three times greater, which I find somewhat surprising. It obviously suggests that “pairing” of factors rapidly becomes more difficult as numbers become larger, so that it is more difficult for possible factors to occur in rapid succession as happens during the persistent record gap between 1,327 and 1,361.

Sunday, 15 May 2022

A surprising non-recognition

Non-recognition of governments is a rare occurrence, usually occurring where the formation of a government is viewed as illegitimate and there is an alternative legitimate government that possesses support but is not in control of that territory. Important examples of non-recognition of governments are:

  1. The Soviet Government after the Bolshevik Revolution up to 1924
    1. Some countries, like Japan and Yugoslavia, did not recognise the Bolshevik Government until the 1940s
  2. East Germany outside the Soviet Bloc and West Germany inside it during the Cold War
  3. The Peking Stalinist Government vis-à-vis the Taipei Government in China
  4. The PDPA regime in Afghanistan (1978-1991) outside the Soviet Bloc
  5. The Taliban in Afghanistan between 1994 and 2002
Even when strongly opposed, there are rarely even protest demands at times of intense class struggle for non-recognition of the most repressive governments. For instance, there were never working class demands in Western Europe to not recognise the Nazi regime in Germany or the Fascist regime in Italy. However, I have recently discovered that there was one case of non-recognition of a right-wing dictatorship in Europe, even if on a relatively small scale. Nine countries never recognised the Franco government as the legitimate government of Spain. Instead, these countries — Mexico, Guatemala, Venezuela, and the Stalinist regimes of Poland, Czechoslovakia, Hungary, Yugoslavia, Romania, and Albania — viewed the Spanish Republican government-in-exile as the legal government of all Spain throughout Franco’s rule. Undoubtedly, the great majority of workers in Western European nations also privately viewed the Spanish Republican government-in-exile as the rightful government of Spain.

The critical question is why was Spain different in this respect from other democratic collapses — and perhaps even the Stalinist dictatorships?

The answer is that, unlike the Hitler, Mussolini and Dollfuß-Schuschnigg regimes, the Nationalists in Spain came to power as a result of a lengthy civil war rather than a technically legal coup. This meant that there was a much clearer alternative government than in Nazi Germany or Fascist Italy, or even Dollfuß-Schuschnigg Austria where a short civil war did occur. For another comparison, the Stalinist nations of Europe also never had viable alternative governments for the West to recognise, while the Whites in Russia were so fragmented even during the Civil War that there was never one clear alternative rightful government. Additionally, outside North America and Australia working class protest during the early 1920s was so intense that hosting a Russian government-in-exile would have increased the risk of spreading socialist revolution. In North America and Australia — especially the United States — there was little sympathy for Russians and the Orthodox Church was regarded as an alien culture, so it would have been difficult for a Russian government-in-exile to establish there either.
 
Thus, despite ruling classes’ extreme hostility towards socialism and Bolshevism, non-recognition of the Bolshevik Government in no case lasted so long as a few nations’ non-recognition of Francoist Spain. All this demonstrates how:
  1. revolutionaries and right-wing dictators alike desire overwhelmingly to avoid any possibility that the outside world could view their government as illegitimate or unjust
  2. the best way to avoid this possibility is to take power in a manner that prevents any clear alternative government from emerging
  3. that if an alternative government does exist, there is a significant possibility that it will be recognised by some nation as rightful

Tuesday, 10 May 2022

A circuitous trip and a famous joke from time past

In the late 1990s — the same time I first studied Socialist Alternative, Socialist Worker and Green Left Weekly and was startled at how they demonstrated political reality as completely different from what I learned in school — I briefly collected bus timetables in Melbourne. I was quietly appalled by the quality of service vis-à-vis what books like Environment, Capitalism and Socialism or even the more moderate Public Transport Users’ Association demonstrated as requisite for sustainable transport in Melbourne.

At the same time, my brother was critical of my interest in travelling on buses — an interest that has continued to this day. I often joke that
“if you want to understand global warming, ride on Melbourne’s bus services”
because it is clear to me that the woeful quality of bus and other public transport serves is a critical reason why Australia is rated the worst-performing nation in the world re greenhouse gas emissions. (At the same time, ecology increasing demonstrates Australia is required to be by far the best performed nation, as far ahead of the pack as Port Adelaide in the 1914 SAFL or Yorkshire in the 1901 County Championship).

Yesterday, after a brief conversation with my mother, I was allowed to spend my first day riding buses since the COVID pandemic. Before COVID, I would often spend days riding buses around Melbourne, and enjoyed it even though there often is not much to see from inside a bus.

I had had a plan to go on a bus route that I recall laughing about with my brother a great deal during the late 1990s — the bus from Moonee Ponds to Niddrie via Strathmore. My brother called that route, then numbered 501,
“a classically circuitous route”
at the same time as he complained a great deal about how circuitous almost all bus routes were vis-à-vis trains or trams. When I took this “classically circuitous route”, I was taken by what I thought was a joke saying (as I strongly recall it):
WHY IS THIS BUS
THE 501?
BECAUSE THAT IS THE PROBABILITY THAT IT WILL
BE EARLY OR LATE:
5/1

When I first read that, I presumed that meant the odds of it being early or late were 5 to 1 — which means it was on time five times out of six. My brother, however, said that it is much more likely that the old writing I had seen — if I recall correctly near Strathmore shops — was not a joke but an angry response to a user’s experience. That is, it was either early or late five times out of six, and on time only one time out of six. Actual experience does not tell me which is right, although I have ridden on buses many times, and they are often late though rarely outright cancelled as trains sometimes are.

At the same time, of course, the 501 could not plausibly have actually received its route number from being early or late five times out of six!

Yesterday, my first plan was to ride on the “classically circuitous” route, now part of the 469 alongside a modified Niddrie to East Keilor section from the old route 475. When I did this, I scanned reasonably carefully but could not see the old 501 writing noted above — it may well have been removed long before the route was modified — but I did find the long circuitous trip and the beef burger at Milleara Mall quite interesting. The terrain around Strathmore Heights is quite steep, even scenic, as is the lake area to the south of the Calder Freeway. 

Saturday, 7 May 2022

Are the “Big Five” dictators a correct assumption?

 For many years, I have assumed that the worst dictators in (at least) modern history have been:

  • Joseph Stalin (lived 1878-1953)
  • Adolf Hitler (lived 1889-1945)
  • Mao Zedong (lived 1893-1976)
  • Pol Pot (lived 1925-1998)
  • Saddam Hussein (lived 1937-2006)

The reason for this is that Stalin, Hitler, Mao and Pol Pot were the largest killers from famines and/or genocides, whilst Hussein was both an extreme warmonger and also genocidally exterminated many Kurdish populations with poison gas in northern Iraq.

Most people around me have found this an absurd list, but after re-watching the Evolution of Evil series on YouTube tonight, I googled for a list of worst dictators and found ‘The Top 10 Worst Dictators in History’ by Larry Slawson — who received his Masters Degree at UNC Charlotte and specializes in Russian and Ukrainian history.

Slawsons’s list was:

  1. Mao Zedong
  2. Genghis Khan
  3. Joseph Stalin
  4. Adolf Hitler
  5. Leopold II
  6. Pol Pot
  7. Saddam Hussein
  8. Idi Amin
  9. Vlad the Impaler
  10. Ivan the Terrible

It surprised me a lot to see the familiar “big five” dictators (in bold) were in the top seven, separated from each other only by two older rulers. This does suggest to me that — perhaps not as usually as I would wish because of inability to be sceptical without clear refutation about extreme views — my judgment is reasonably accurate. The list could also be a reflection of potential bias, given that the death tolls attributed to Stalin and Mao by writers like Paul Kengor do not seem to be accepted by academic scholars away from the conservative “Christian madrassas” (as my brother calls them) like Kengor’s Grove City College or Benjamin Wiker’s former Franciscan University of Steubenville. Still, I was oddly surprised by what I read on such a brief glance.