Monday, 25 July 2022

How abysmal is Australia’s climate performance?

Ever since the Kyōtō Protocol clearly failed despite the efforts of Europe, I have always believed that there were deep and fundamental flaws with the whole process of climate protocols.

For many years, it has been clear to me that emissions reductions by resource-impoverished nations may be worse than useless. The resource-rich nations — mostly lying in the ecologically fragile arid regions of the globe as these are unaffected by resource-destroying orogeny and glaciation — can if one country divests from fossil fuels simply shift their sales to another country, neutralising the best efforts of resource-poor nations to divest from fossil fuels, and indeed making it a disadvantage to do something serious about greenhouse gas emissions. Because climate protocols have never been able to mount the smallest demands upon the resource-superabundant nations of Australia and the Gulf Cooperation Council, those countries have been — despite being the worst polluters in the world before the Kyōtō Protocol — invariably given carte blanche to increase emissions. Under such a scenario, it is impossible to stop global emissions skyrocketing. Australia, the Gulf States and other fossil fuel-rich desert nations like Iran, Kazakhstan and Turkmenistan will always have someone to sell their fossil fuels to.

In 2018, Dimitri Lafleur’s thesis Aspects of Australia’s fugitive and overseas emissions from fossil fuel exports demonstrated that one can quantify national emissions debits much better by tracing them to the beginning of the pipeline, rather than the end as published figures generally do. Lafleur’s figures show that Australia’s emissions — abysmal by conventional measurements — are by an extraction-based measurement three times higher than by the “territorial”-based measurement under which climate protocols have been carried out. Recent history implies that if emissions are not regulated at the beginning of the pipeline, efforts to regulate them downstream will fail because extractors will always sell them elsewhere. Lafleur is actually quite conservative when he says:

“We are not suggesting that extraction-based accounting should replace territorial based accounting under the international negotiation framework. Rather, we argue that an extraction-based accounting framework could complement the standard territorial one. While domestic emissions reductions are, and should remain, the prime focus under the Paris Agreement, an extraction based emission inventory could inform the discourse on ‘means of support’ for mitigation, adaptation, or loss and damage elsewhere. Given the economic benefits accruing from the extraction and sale of fossil fuels, that linkage between extraction-based emissions accounting and provision of support could also be reasoned indirectly, i.e. via an argument of capability.”

The severe failure of emissions protocols, however, made me without knowing of the idea of extraction-based emissions think that the territorial-based system was too flawed to be useful. Additionally, the idea of extraction-based emissions was not invented by Lafleur, but was developed with less quantification by Michael Lazarus and Peter Erickson in the early 2010s, by when I was already of the view that there must be a serious flaw in emissions calculations given that efforts to transform to clean energy in Europe had no impact globally. Lazarus and Erickson do contend, if implicitly, that extraction-based emissions completely replacing territorial-based emissions in negotiations would be a good idea.

It has for over two decades angered me that so ecologically fragile a country as Australia has been so consistently ranked as one of the worst performers in climate policy — and in recent assessment as the worst. The unique ecological traits of Australia, as noted by such writers are Tim Flannery, Tom McMahon, Gordon Orians, and Antoni Milewski, require Australia to be the world’s leader in energy and emissions policy by a large margin, and to be consistent ranked as by far the best performing country according to CCPI criteria! It is equally untenable that the best-performing countries according to CCPI are:

  1. of negligible conservation value due to having floras and fauna that are wholly postglacial, vis-à-vis the extremely ancient Australian flora and fauna adopted to conditions much more typical fo geological history
  2. negligibly small extractors of fossil fuels and thus (as noted above) entirely unable to have any influence upon global emissions outside their territory

2020 Climate Change Policy Institute rank for correctly included countries — dark red = Very Low; orange = Low; yellow = Medium; light green = High. Countries in white are incorrectly included and would be excluded from an extraction-based assessment. Countries in dark grey are incorrectly excluded but necessarily included for a usable extraction-based assessment

Thus, I created the map above from the 2020 CCPI report to see just how bad Australia is when compared to other major extraction-based emitters. I “whitened out” countries whose inclusion would be worse than unnecessary under an extraction-based scheme, and colored in dark grey countries whose omission would be untenable for any such scheme.

A major problem, although an inevitable one, is that policy details may not be available for many major extraction-based emitters. This does naturally mean that their ranking under CCPI criteria would almost definitely be Very Low. This is almost certainly true for Iraq, Venezuela, Libya, and several sub-Saharan oil producers. Assessing Kuwait, Qaṭar, the United Arab Emirates and Turkmenistan — all very important emitters — is made difficult by the very limited access to information provided by their governments. The fact that CCPI could assess Sacudi Arabia, however, suggests that these problems are not insurmountable.

If every country colored dark grey on the above map scored Very Low, it would not excuse Australia’s abysmal record, although it would make it relatively less bad. It would demonstrate that countries who do no extract fossil fuels need to be much more united to demand both repayment and energy reform from the major polluters, many of whom are extremely wealthy and able to afford this. Such a contention is supported by the poor scores of almost all other major polluters — Sacudi Arabia, Russia, the United States, Iran, Canada, Kazakhstan. If some of the countries colored dark grey scored better than Very Low, it would highlight how bad Australia’s performance is. However, unless a country scores significantly worse than Australia — which may not be possible if I recall correctly — it remains necessary to highly how badly Australia has performed and how important it is to remedying and paying the costs of climate change.

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 473,269th 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
  • 47,326,781 = 829 × 57,089
  • 47,326,783 = 7 × 6,760,969
  • 47,326,787 = 137 × 345,451
  • 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
137 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
829 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-nine 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.