I am beginning to wonder if the American political system is truly broken beyond repair.
I wonder what this means for Canada. No change? Will we become a safe haven for refugees from Gilead, as in The Handmaid’s Tale? Or will we be this new America’s Ukraine?
I am afraid that we will find out.
Someone reminded me that 40 years ago, when we developed games for the Commodore-64, there were no GPUs. That 8-bit CPUs did not even have a machine instruction for multiplication. And they were dreadfully slow.
Therefore, it was essential to use fast and efficient algorithms for graphics primitives.
One such primitive is Bresenham’s algorithm although back then, I didn’t know it had a name beyond being called a forward differences algorithm. It’s a wonderful, powerful example of an algorithm that produces a circle relying only on integer addition and bitwise shifts; never mind floating point, it doesn’t even need multiplication!
Here’s a C-language implementation for an R=20 circle (implemented in this case as a character map just for demonstration purposes):
#include <stdio.h>
#include <string.h>
#define R 20
void main(void)
{
int x, y, d, dA, dB;
int i;
char B[2*R+1][2*R+2];
memset(B, ' ', sizeof(B));
for (i = 0; i < 2*R+1; i++) B[i][2*R+1] = 0;
x = 0;
y = R;
d = 5 - (R<<2);
dA = 12;
dB = 20 - (R<<3);
while (x<=y)
{
B[R+x][R+y] = B[R+x][R-y] = B[R-x][R+y] = B[R-x][R-y] =
B[R+y][R+x] = B[R+y][R-x] = B[R-y][R+x] = B[R-y][R-x] = 'X';
if (d<0)
{
d += dA;
dB += 8;
}
else
{
y--;
d += dB;
dB += 16;
}
x++;
dA += 8;
}
for (i = 0; i < 2*R+1; i++) printf("%s\n", B[i]);
}
And the output it produces:
XXXXXXXXX
XXX XXX
XX XX
XX XX
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X X
XX XX
XX XX
XXX XXX
XXXXXXXXX
Don’t tell me it’s not beautiful. And even in machine language, it’s just a few dozen instructions.
I am reading an article in The Globe and Mail, with an attention-grabbing headline: Unvaccinated disproportionately risk safety of those vaccinated against COVID-19, study shows.
Except that the actual study shows no such thing. Nor does it involve actual vaccines or actual people.
What the study shows is that the simple (dare I say, naive) epidemiological model known as the SIR (Susceptible-Infected-Removed) model, when applied to a combination of two (vaccinated vs. unvaccinated) populations, indicates that the presence of the unvaccinated significantly increases the chances of infection among the vaccinated as well.
D’oh. Tell us something we didn’t know.
But the point is, this is a purely theoretical study. The math is elementary. The results are known (in fact, it makes me wonder why this paper was published in the first place; it’s not that it is wrong per se, but it really doesn’t tell us anything we didn’t know simply by looking at the differential equations that characterize the SIR model.) Moreover, the actual nuances of COVID-19 (mutations, limited and waning vaccine efficacy, differences between preventing infection vs. preventing hospitalization, death, or “long COVID” — in other words, all those factors that make CODID-19 tricky, baffling, unpredictable) are omitted.
So what will such a study accomplish? The authors’ point is that the model’s simplicity is a strength, as it also offers transparence and flexibility. I think in actuality, it will just muddy the waters. Those who are opposed to vaccination, especially mandatory vaccination, will call this study bogus and naive, an example of ivory tower theorizing with no solid foundations in reality. Conversely, some of those who are in favor of vaccination will present this paper as “proof” that the unvaccinated are selfish, irresponsible extremists who should be marginalized, ostracized by civilized society.
The Globe and Mail article is already evidence of this viewpoint. A quote from one of the study’s authors serves as a representative example: “In particular, when you have a lot of mixing between vaccinated and unvaccinated people, the unvaccinated people actually get protected by the vaccinated people, who act as a buffer – but that comes at a cost to the vaccinated.”
Does anyone think that pronouncements like these will help convince those who are ideologically opposed to vaccination or bought into the various nonsensical conspiracy theories about the nature, dangers, or efficacy of COVID-19 vaccines, especially mRNA vaccines?
Came across a question tonight: How do you construct the matrix
$$\begin{pmatrix}1&2&…&n\\n&1&…&n-1\\…\\2&3&…&1\end{pmatrix}?$$
Here’s a bit of Maxima code to make it happen:
(%i1) M(n):=apply(matrix,makelist(makelist(mod(x-k+n,n)+1,x,0,n-1),k,0,n-1))$
(%i2) M(5);
[ 1 2 3 4 5 ]
[ ]
[ 5 1 2 3 4 ]
[ ]
(%o2) [ 4 5 1 2 3 ]
[ ]
[ 3 4 5 1 2 ]
[ ]
[ 2 3 4 5 1 ]
I also ended up wondering about the determinants of these matrices:
(%i3) makelist(determinant(M(i)),i,1,10); (%o3) [1, - 3, 18, - 160, 1875, - 27216, 470596, - 9437184, 215233605, - 5500000000]
I became curious if this sequence of numbers was known, and indeed that is the case. It is sequence number A052182 in the Encyclopedia of Integer Sequences: “Determinant of n X n matrix whose rows are cyclic permutations of 1..n.” D’oh.
As it turns out, this sequence also has another name: it’s the Smarandache cyclic determinant sequence. In closed form, it is given by
$${\rm SCDNS}(n)=(-1)^{n+1}\frac{n+1}{2}n^{n-1}.$$
(%i4) SCDNS(n):=(-1)^(n+1)*(n+1)/2*n^(n-1);
n + 1
(- 1) (n + 1) n - 1
(%o4) SCDNS(n) := (------------------) n
2
(%i5) makelist(determinant(SCDNS(i)),i,1,10);
(%o5) [1, - 3, 18, - 160, 1875, - 27216, 470596, - 9437184, 215233605, - 5500000000]
Surprisingly, apart from the alternating sign it shares the first several values with another sequence, A212599. But then they deviate.
Don’t let anyone tell you that math is not fun.
Move over, general relativity. Solar gravitational lens? Meh. Particle physics and the standard model? Child’s play.
Today, I had to replace the wax ring of a leaky toilet.
Thanks to this YouTube video for some useful advice, helping me avoid some trivial mistakes.
I’ve been finding parallels between the events in Ukraine and 1914 (when Austria-Hungary attacked Serbia), 1938 (when the Western world acquiesced to Hitler’s annexation of the Sudetenland in the hope that it would bring “peace for our times”, to use Chamberlain’s words), 1939 (Hitler’s attack on Poland) and 1943 (Hitler’s historic defeat at Stalingrad.)
But perhaps it’s 1904-1905, when the Russian Empire waged a naval war against the Japanese Empire.
The specifics are different (for starters, the Russo-Japanese war was started by Japan), but the similarities abound: The general expectation was that a major European power, Russia, will easily prevail over the perceived inferiority of an “Asiatic” empire. Instead, Russia was humiliated, and the political backlash directly led to the 1905 revolution, itself a precursor to the 1917 Bolshevik revolution.
And here we are, in 2022, with Russia humiliated again by an enemy that was widely perceived as inferior. Beyond the tactical defeats, the strategic, political blunders are palpable: threats of Russian aggression have not only breathed fresh life into the NATO alliance, but also prompted traditionally (and fiercely) neutral Sweden and Finland to take concrete steps towards NATO membership.
And now, the Moskva. I am not sure but I am beginning to think that this 12,500 ton guided missile cruiser is the largest warship sank by enemy action since WW2. I mean, if this does not reek criminal recklessness and incompetence on behalf of the Russian leadership, both political and military, I don’t know what does.
Does this mean that a revolution is in the works? Are Putin’s days numbered? Perhaps, but I wouldn’t bet on it. And the nuclear wildcard is… there. Perhaps Putin will resort to nukes if all other options fail. Or perhaps a palace revolution widens into civil war, and the world may yet witness the consequences of the first ever nuclear civil war. Whatever happens, I doubt it will be pretty.
Acting as “release manager” for Maxima, the open-source computer algebra system, I am happy to announce that just minutes ago, I released version 5.46.
I am an avid Maxima user myself; I’ve used Maxima’s tensor algebra packages, in particular, extensively in the context of general relativity and modified gravity. I believe Maxima’s tensor algebra capabilities remain top notch, perhaps even unsurpassed. (What other CAS can derive Einstein’s field equations from the Einstein-Hilbert Lagrangian?)
The Maxima system has more than half a century of history: its roots go back to the 1960s, when I was still in kindergarten. I have been contributing to the project for nearly 20 years myself.
Anyhow, Maxima 5.46, here we go! I hope I made no blunders while preparing this release, but if I did, I’m sure I’ll hear about it shortly.
Our work on the Solar Gravitational Lens, complete with some diagrams created by yours truly, now made it onto TikTok.
@toknerdytome Solar Gravitational Lens #learnontiktok #tiktokpartner #science #space #astrotok #alien #nasa #physics #astronomy #technology ♬ Interstellar- Main Theme – Geek Music
How about that.
Last week, Hungary’s Orban won a resounding victory in Hungary’s elections.
I was not happy about it, to be honest, and many of my liberal-minded friends were bitterly disappointed.
But a few of them began to look more deeply into the reasons behind this outcome. A recent article* by my friend László Mérő, a Hungarian mathematician and publicist, was illuminating. László decided to volunteer in the elections process as a scrutineer. He ended up in a rural electoral district, where he had a chance to talk to many of the voters who cast their ballots, including both the roughly 30% who voted for the united opposition, but also the majority who chose Orban’s government instead.
His conclusion? There was no fraud. The process was conducted professionally, transparently, and cleanly. The government may dominate traditional media (indeed, this is one of the cardinal sins of Orban’s autocratic government) but the voters were not uninformed. They were aware of the opposition, its message, and its goals. They didn’t favor the government because they were brainwashed. They favored the ruling party because those candidates did a much better job on the ground. They were known to the voters, unlike the fly-by-night opposition.
And anyone who thinks Orban represents some fringe must think again. Just days after his resounding victory (he not only retained, he even increased his two thirds parliamentary supermajority) we were reminded by press releases that CPAC, the Conservative Political Action Conference, was already set to hold its next meeting in Budapest. Orban will be the keynote speaker.
Wait, CPAC? The conference series held by one of the most respectable American conservative organizations, the American Conservative Union, dedicated to the foundations of conservatism, including personal liberty, freedom, and responsible governance?
That’s no fringe.
And, I strongly suspect, at least one of the reasons why Trump, Orban and other “illiberal” leaders and opinion-makers managed to hijack conservatism is that liberalism, in turn, was hijacked by the “woke” culture: a culture that is ready to “cancel” anyone who disagrees with whatever the canonical view of the day happens to be on race, gender, and related issues. I mean, J. K. Rowling? For real?
The fact that it all happens in a geopolitical context, allowing the likes of Putin to use his propaganda machine to try and divide the West even as his murderous horde of ill-equipped, badly led soldiers is rampaging in Ukraine, behaving like the worst of the Nazis (and prodded by Kremlin propaganda outlets to erase Ukrainian national identity) while pretending to “denazify” a country led by a Jewish president, is just the icing on this proverbial cake.
Elections are under way in France today. A possible Le Pen victory might have dramatic consequences.
*Magyar Nemzet, 2022.04.06 — In Hungarian
The news we get from liberated areas of Ukraine are getting grimmer every day.
Army general Mark Milley, the Chairman of the Joint Chiefs of Staff of the United States, America’s highest-ranking military officer, told us in his Congressional testimony today that “we are witness to the greatest threat to the peace and security of Europe and perhaps the world in my 42 years of service in uniform”.
I made up my mind. If we want to preserve at least a tiny chance of keeping this world both peaceful and decent, we must take the Churchillian step of openly and boldly confronting evil.
If I were in charge… I would make Ukraine unconditionally a full-fledged member of NATO, effective immediately, with all the protections of NATO’s Article 5 implied. I would at the same time announce that a large contingent of NATO troops are entering the country, in cooperation with Ukraine’s legitimate, elected government, to guarantee the country’s original (!) borders, yes, including Crimea and Donbass.
And let’s do this while the Russian military is led by the same nincompoops who thought that the most important item for an invading army to carry is dress uniforms, or that digging in the Red Forest, in the world’s most contaminated soil with radioactive fallout, is a smart idea.
Mr. Putin, then, it’s your move. You push your button, we push ours, and the world as we know it ends. But I am betting that you are, in the end, just a worthless coward. Waste of skin.
His followers probably dismiss these as “fake news”, in the wonderful tradition of Joseph Göbbels, Donald Trump and the rest of their heroes.
But we know that these are not fake news. Like this image of a dog not leaving the body of his dead master.
Or how about distressed parents writing their names and contact information on their children’s backs, in case they get separated or killed? When I saw this image, I must admit I felt like I was viciously kicked in the gut.
Putin must answer for these crimes. His followers, his enablers, his supporters must bear responsibility.
Whatever it takes.
Until and unless that happens, this world will not be whole again.
Hungary’s elections are coming to a close. All indications are that not only did Viktor Orban win, he won big: it appears he will retain his two -thirds constitutional supermajority in Hungary’s parliament. Yey-ho, illiberal democracy!
And they had the audacity to campaign as the party of peace: by confronting Putin, they argued, the opposition wants war and it is the government’s cowardly attitude that will somehow save the country from getting bogged down in conflict. (Because, you know, this attitude worked so well in the last major war in Europe, which witnessed Hungary as Hitler’s last ally, deporting over 600,000 of its own citizens to Nazi death camps, and having much of the country destroyed when the frontlines finally reached it in 1944-45.)
Meanwhile, Putin’s popularity in Russia is through the roof: The “Nazis” of Ukraine must be crushed, say people on the streets, and perhaps then Poland is next!
In America, Trump’s followers are regrouping, hoping to take back the House, the Senate, and eventually the White House, lining up behind their authoritarian leader to whom the rule of law means nothing unless it serves his personal interests.
Even here in Canada, all in the name of democracy of course, hundreds of unruly truckers blocked my city for nearly a month, and what is worse, their effort was (and remains) supported by millions. Perhaps still a small minority but still: It is a minority that is supporting a movement that is openly unconstitutional and insurrectionist.
And the sad thing is, we’ve all seen this before. The world went through something eerily similar a century ago. The Bolsheviks were popular in Soviet Russia. Mussolini was popular in Italy. Franco was popular in Spain. Hitler was popular in Germany. Even in places like the US and the UK, the likes of Charles Lindbergh or Oswald Mosley had considerable following.
I could ask the pointless question, why? Social scientists and historians probably offer sensible answers. But that doesn’t help. So long as people, even well-educated people, are willing to believe pseudoscience, ridiculous conspiracy theories, half truths, insinuations, and above all messages of hate: the compulsion to hate (or at least fear or distrust) someone, anyone, be it Ukrainians (or Russians), hate “migrants”, hate liberals, hate homosexuals, hate “others” however their other-ness is defined…
Screw you, world. I’m going back to physics. Just leave me alone, please.
With apologies to the late Dr. Seuss (indeed I have no delusions about my talents as a cartoonist), I felt compelled to make a few, ahem, creative adjustments to one of his classic caricatures, as the message appears just as relevant today as it was more than eight decades ago, when some overly “patriotic” Americans were trying to be BFFs with another murderous tyrant.
The original was published on June 2, 1941. The lessons of history should not be forgotten.
Very well. I have now become convinced that Putler’s army in Ukraine is led by criminally incompetent clowns whose expertise is limited to cruelty and wholesale murder.
So they decide to occupy the Chernobyl Exclusion Zone. It’s an Exclusion Zone for a reason. Not because Ukrainians are fond of the Strugatsky brothers’ amazing novelette, Roadside Picnic, which describes similar Zones (albeit zones left behind by visiting, “picnicking” extraterrestrials.) They might be; the story really is good (and it formed the basis for Tarkovsky’s film Stalker, as well as the amazing S.T.A.L.K.E.R. series of video games. Scenes from which, incidentally, now bear alarming resemblance to the ruined cities of Ukraine.)
No, it is called an Exclusion Zone because it contains, you know, radioactive fallout from the world’s worst nuclear disaster: the explosion at reactor 4 of the Chernobyl Nuclear Power Station that happened in 1986.
Fallout that, until now, was mostly safely buried under fresh soil, causing relatively little harm. That is, until Russian conscripts, led by the aforementioned nincompoop murderers, dug it up with trenches. Soldiers who are now ill with signs of radiation sickness. With generals like the ones leading them, they need no enemies. They are perfectly capable of defeating themselves even without Ukrainian help.
For the first time in my life, I exercised my right as a Hungarian citizen and voted.
Before I left Hungary, voting was pointless: my choice was the Hungarian Socialist Workers’ Party or else. The “or else” meant nothing.
More recently, I didn’t feel it kosher to participate in elections in a country where I do not reside and do not pay taxes. Then again, thanks in part to the current government, a great many Hungarian citizens who do not reside in Hungary or pay taxes there have gained the right to vote… so perhaps it’s not unethical for me to do so as well.
So I did.
Incidentally, the Parliament building in Budapest is quite an impressive edifice.
Outside Lviv’s railway station, this last Saturday I believe.
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A friend of mine was wondering about Putin’s motivation.
I offered my take on Putin’s “dream”, starting with his remarkable statement from decades ago, expressing his opinion that the collapse of the USSR was the greatest political catastrophe of the 20th century.
Many of Putin’s generation feel the same way. They spent their formative years in a Soviet Union that finally stepped over the shadow of Stalin’s terror rule. A country in which life became worth living again, and which was poised to deliver, after much toil and struggle of course but still, a Utopian communist state that in many ways is almost exactly like the Utopia of Star Trek and its United Federation of Planets.
And this was a post-racial, transnational dream. To be sure, Russians, their culture, their language, their civilization were to assume a leading role but not as oppressors, rather as leaders and teachers, bringing the benefits of Utopia to all, including both the polyglot citizenry of the USSR and peoples beyond the Soviet borders.
The collapse of the USSR meant the end of this dream. Many wept (literally) when the red Soviet flag was taken down from the Kremlin at the end of 1991. Perhaps even Putin was one of them.
Fast forward to 2022. To those who were weeping in 1991, the state of affairs that saw essential parts of the USSR as independent countries was deeply offensive and unnatural. The eventual reunification of these nations was, to them, a foregone conclusion. What stood in the way? Apart from corruption and petty politics, a hostile West that supported the independence of these newly created nations, even incorporating them into its military alliance that exists for the sole purpose of threatening and intimidating Russia.
And that leads to the grand strategy. Divide the West. Sow the seeds of division within Europe, support Brexit, spread conspiracy theories that create mistrust in the media and in the institutions of liberal democracy, help promote a narcissistic TV personality to the presidency of the United States by spreading propaganda through social media, drive wedges between the West and its closest allies such as Turkey, and in the meantime make gradual advances in the territories of the former USSR, a “salami tactic” approach, recovering what was lost one county, one province at a time, but with the ultimate goal being even uncoupling the Baltic states from the West, re-establish a land connection to Kaliningrad and reincorporate Lithuania, Estonia and Latvia into the reforming USSR.
And it almost worked! Europe seemed more divided than ever, with populist autocrats emerging in places like Hungary and Poland who seemed more loyal to Moscow than Brussels. The Brits completed Brexit. Turkey bought the S-400 air defense system against express US wishes. And while Canada was briefly immobilized by a “freedom” convoy, in the US a near-plurality of voters were willing to believe that the last presidential election was “rigged”.
So the time seemed ripe to take the next step, the biggest prize in the re-establishment of the USSR: Ukraine.
But this strategy presumes that successor countries like Ukraine are actually unwilling pawns in the hands of a hostile West; that the majorities in these countries would in fact welcome the “ancient regime”, would welcome becoming part again of a great, united superpower that covers 1/6th of the land area of the planet and commands economic resources to match any rival.
Based on that assumption, the expectations are easy to see. Once Russia’s army enters Ukraine, the country’s corrupt, ineffectual leadership (led by a former TV comedian who, being Jewish, probably has no loyalty to Ukraine anyway) would flee the country at the first opportunity, the regime would collapse and the population would welcome the tanks (several of which were decorated with Soviet — not Russian, Soviet! — flags) with great happiness.
The next step would be Georgia and of course, once the might and invincibility of Russia becomes clear to a weak, divided West, the Baltics: Kaliningrad, Lithuania, and the rest of them. The dream is fulfilled, and Putin is revered as the greatest Russian statesman since, say, Peter the Great.
So I think this is what Putin wanted or hoped for. Instead, he managed to accomplish in mere three weeks what took more than three years for Hitler: progression from the initial crossing of the border (like Hitler entering Poland in 1939) to his version of the Battle of Stalingrad.
It is clear that the Russian army no longer has the initiative. Reports today are about a destroyed Russian warship, Ukrainians not only pushing back against Russian forces near Kyiv but encircling some 10,000 of them, and NATO updating its estimates, now saying that over 15,000 (15,000!!! That’s a staggering number, considering that the invasion force numbered less than 200,000 to begin with) Russian servicemen have been killed already.
The wildcard is WMDs: Will Putin deploy chemical weapons? Go nuclear? History is no guide here. Or perhaps those in his close circle, knowing that he is finished and seeing the harm that his continuing “leadership” brings to their power, wealth, lives, will finish him off soon? That would be a relief.
But even if that happens, we need to be mindful of the broader context. Our reaction should be carefully calibrated by pragmatism, not petty vindictiveness. An opinion piece from Bloomberg that begins with the thoughts of Keynes echoes my concerns exactly. We may “win” this conflict and Putin may be deposed. But beyond the immediate needs of Ukraine, we must also look at the broader picture and make sure that we create a post-war world that is sustainable. In short, we’ll need to help Russia to become a valuable member of the international community (like Germany and Japan were helped after 1945) instead of punishing Russia (like Germany was punished in 1919) and sow the seeds of more division and conflict.
Do you know what wealth is?
It’s not superyachts. It’s not million dollar mansions. It’s not private jets or a chauffeured Rolls Royce. Those are pricey toys.
Let me show you real wealth. Guess which of the two objects in the image below is worth more:
On the left, a Canadian quarter. That is, 25 Canadian cents. This is the amount that a resident of Ontario, working for the legally mandated minimum wage, earns in exactly one minute.
On the right is a 540 milliliter can of sliced pineapples, in pineapple juice. All the way from Indonesia.
That is to say, someone planted those pineapple plants and nurtured them. Someone picked that fruit. Others mined the iron and coal from which the soft steel was made, eventually rolled into sheets and formed into cans. Yet others operated the machinery of the cannery, slicing those pineapples, filling and sealing the cans on July 5, 2021 according to the stamped label on the can. The cans were then put into crates, loaded into containers that were put on trucks, taken to a port, transferred to a ship which then sailed to Canada. The container then made its way, through the railways and on trucks, to a warehouse and ultimately, to the grocery store here in Ottawa, all the while protected from the elements, from excess heat and excess cold that would have ruined the contents. Finally, someone placed the cans on a shelf where they must have sat a little longer than usual, until either a human manager or maybe an algorithm decided that they should be marked down.
And then my beautiful wife picked up a pair of these cans… paying the grand total of 48 Canadian cents for the two.
That is, a large can of sliced pineapples, all the way from Indonesia, here in the final days of an Ottawa winter… costing less than a quarter. Even working at the Ontario minimum wage, for the equivalent of less than 60 seconds of our labor.
That’s what wealth really is.
Between a war launched by a mad dictator, an occupation by “freedom convoy” mad truckers, and other mad shenanigans, it’s been a while since I last blogged about pure physics.
Especially about a topic close to my heart, modified gravity. John Moffat’s modified gravity theory MOG, in particular.
Back in 2020, a paper was published arguing that MOG may not be able to account for the dynamics certain galaxies. The author studied a large, low surface brightness galaxy, Antlia II, which has very little mass, and concluded that the only way to fit MOG to this galaxy’s dynamics is by assuming outlandish values not only for the MOG theory’s parameters but also the parameter that characterizes the mass distribution in the galaxy itself.
In fact, I would argue that any galaxy this light that does not follow Newtonian physics is bad news for modified theories of gravity; these theories predict deviations from Newtonian physics for large, heavy galaxies, but a galaxy this light is comparable in size to large globular clusters (which definitely behave the Newtonian way) so why would they be subject to different rules?
But then… For many years now, John and I (maybe I should only speak for myself in my blog, but I think John would concur) have been cautiously, tentatively raising the possibility that these faint satellite galaxies are really not very good test subjects at all. They do not look like relaxed, “virialized” mechanical systems; rather, they appear tidally disrupted by the host galaxy the vicinity of which they inhabit.
We have heard arguments that this cannot be the case, that these satellites show no signs of recent interaction. And in any case, it is never a good idea for a theorist to question the data. We are not entitled to “alternative facts”.
But then, here’s a paper from just a few months ago with a very respectable list of authors on its front page, presenting new observations of two faint galaxies, one being Antlia II: “Our main result is a clear detection of a velocity gradient in Ant2 that strongly suggests it has recently experienced substantial tidal disruption.”
I find this result very encouraging. It is consistent with the basic behavior of the MOG theory: Systems that are too light to show effects due to modified gravity exhibit strictly Newtonian behavior. This distinguishes MOG from the popular MOND paradigm, which needs the somewhat ad hoc “external field effect” to account for the dynamics of diffuse objects that show no presence of dark matter or modified gravity.
Today, we saw President Putin in public, at a celebration commemorating the annexation of Crimea 8 years ago.
Suddenly that reminded me of something else: Germany celebrating the Anschluss, the annexation of Austria that occurred in March 1938.
But Putin, it seems, had eclipsed Hitler as the all-time genius of national greatness. After all, he managed to accomplish in mere three weeks what took Adolf more than three long, painful, blood-soaked years.
Putin managed to get from his equivalent of the Polish border to his Stalingrad in just three weeks.
That is, what initially began as a form of Blitzkrieg, or lightning war, rapidly deteriorated into an unwinnable war of attrition, with long, unsustainable supply lines, fighting against a much better motivated, better led, better supplied foe.
Ukraine is paying an incredibly heavy price, but by their fierce resistance, they might just be saving the world from global thermonuclear war.
Of course, rather than losing (which will likely see him hanged, just like other incompetent autocrats before him, with Mussolini serving as a relevant example) Putin may well decide that burning much of the world is preferable. At that point, I hope that those around him, however subservient or corrupt, will find the moral courage, the spirit of true patriotism not to carry out orders that would amount to much of humanity (including Russia) committing a form of collective suicide. That they won’t let this murderous sicko, this petty KGB thug turn our magnificent civilization into ashes and dust, into radioactive mushroom clouds.