And that infinity and one is still infinity. This hazy number play sets up the kid's intuitions. Especially where it doesn't work. Infinity is not part of the structure that lets us play the number game. It needs new rules. — Banno

Exactly, and we aren't understanding those rules yet. What we see are paradoxes and we simply want to avoid them or assume there's something wrong. There isn't anything wrong, it's that we start from the wrong axioms.

Indeed it's very interesting. I have just later understood when grandfather, a math teacher himself, just shook his head and said it was too difficult, when at first grade at school they started teaching math with set theory. But so progressive and courageous were math-teaching in the 1970's in Finland.

Yet I think mathematics will suprise us some day... once we really understand infinity, it likely is something that can be taught at school for kids. Mathematics is just so beautiful.

I think the real breakthrough will be in when we understand that there is the mathematics that is not computable and thus doesn't start with addition, but is inherently important to mathematics. Yet we (and I think other animals too) have started using mathematics from the practical side of it. "No lions, one lion, two lions, many lions." could be the "mathematical system" for a zebra in the African Savannah, which is very useful for it's survival. It doesn't need calculus, it doesn't ponder infinity. Yet for us when we want to make mathematics a logical system. For the grazer on the Savannah it might be enough, but for us the "0,1,2,many" system isn't enough at all. We need calculus, infinity is obvious in mathematics. Yet if we assume that everything in mathematics starts from counting, from finite natural numbers, we are making a mistake.

We don't need much ontology. Quantification will suffice. — Banno

As the popularity of this post shows, we do need clarity on the mathematical object called infinity.

In my view the question comes down to simply just what does it really mean when Cantor showed us that the natural numbers cannot be put into 1-to-1 correspondence with the reals. The standard answer, that the infinity is simply larger, and thus we have larger infinities etc. doesn't really answer everything. It simply lacks the rigorous logic that is so ever present in mathematics. The problem with the Continuum Hypothesis shouldn't come as a surprise.

It isn't clear to me which is effect and which is cause however. — BenMcLean

An active policy change comes from the alliance status. Yet what is also happening is that the US is losing it's share of the global economy as other countries have emerged back. The dominance of the US economy in the 1950's has an obvious reason: WW2 had destroyed Japan and Europe and Russia and China attempted to achieve communism with the disastrous centrally planned socialism.

No, it really hasn't. Whole generations of Americans have found themselves disposessed of their jobs, homes and status within their own land because of the international market our taxes make possible forcing us to be in economic competition with the entire world for everything. — BenMcLean

That your corporations have moved production to countries that have far lower wages and that you have an oligarchy in control as there is hardly any labour movement to demand it's share is the fault of the US itself, not the alliance system. As I stated above, your manufacturing has benefitted vastly from arms sales into Europe especially during the Cold War. That's what you have gotten from the alliance. But naturally the nativist line is that foreigners are the reason. Trump is simply making things far worse for you.

Just look at where in the long run have American weapons been exported to:


In my export oriented little country the politicians have always said how important it is for us to be competitive and how utterly destructive would it be to attempt hide behind tariff walls. Yet exports aren't at all so important to the US itself.

Maybe being the reserve currency benefitted the American government, but how exactly that compensates the American people for not just the taxation but the intergenerational economic degradation they've seen is not going to be clear to most voters even if you could make the case for it. — BenMcLean

First and foremost: the unequal distribution of wealth is something inherent to the American society. You simply cannot blame it on others. No other Western country is as inequal as the US.




That your government works for those that have the ability to lobby for their own agendas is again not something that is caused by your alliances.

A current account crisis is something that Americans have not heard of. Yet the obvious result if there's a currency crisis is that a) interest rates ought to be higher and b) exports are more costly. Or if you don't raise interest rates, you will have a lot of inflation. So ask yourself: have you experienced higher interest rates and inflation?

I can see that moving towards subscriptions and rents is better business than selling people copies of software. That seems to need continuous updating anyway, so what's the point of owning it?
Still, the OP has a point. And I'm sure there's be a healthy trade in the data we all keep on the cloud. — Ludwig V

It's an obvious trick to get the customer to be dependent of the service provider. Even the change from manufacturer to "service provider" tells what is happening. Why make a product that people can buy once and then use it for many decades? I think that only really valuable wristwatches are made for working for very, very long.

And the majority of people don't want the hassle of a local computer. They don't know how to program it. Basically everything will be just buy once... and then it continuously updates and you pay an annual payment.

Quite so. I think there may be people who think that things will get better once Trump's term ends. We'll see. — Ludwig V

Here's the real tragedy in all of this.

Perhaps Trump simply ends up in such a catastrophe that wearing a red MAGA hat in post-Trump USA will be as offensive as wearing now the Nazi red and white arm band with the Swastika in Berlin. But that won't matter.

The Americans have now voted Trump twice into power. Hence there will be the feeling that they might possibly do it again. And that at least part of America are truly hostile towards Europe and do favor a dictator like Putin, because they support Trump.

It would be like if there would be a revolution in Russia and Putin would be ousted and the new reformers would want to embrace democracy and join the West. Would we in Europe embrace them? Perhaps, but we would always worry that if the Putinists, the Russophiles would make a comeback. We would fear that the "Westernizers", which Russia has seen in it's history, would we just a passing movement and perhaps in the future the Imperialists would take over. It would take many decades, perhaps a generation, for this feeling to go away.

With Trump there's now an obvious rift between the US and it's treaty allies both in Europe and actually also in the Far East.

But perhaps enough of security politics. There's ample threads about that.

I think the OP is still a very interesting topic to debate. I don't see it as a political thing, but more of an economic and commercial development that can be seen in many things.

Up until Elon Musk turned out to be such a complete a***hole, I was really impressed with him. It's depressing to see such obvious brilliance yoked to such malevolent politics. — Wayfarer

Yes, I've never seen such image and brand suicide as Elon did with taking a political position in the Trump regime and getting totally completely drunk on power. Otherwise Tesla and SpaceX would have been such great brands.

One prominent paper concluded that $100 spent on A.I. safety saves one trillion future lives — NY Times Review

Lol.

Yeah, about 117 billion human beings have ever lived on this Earth and likely we'll see soon "Peak Human Population", so getting to a trillion people in the future will take a looong time. And even with $200 spent on A.I. safety isn't yet that much.

also because Europe fundamentally does not pay for its own military defense. It isn't completely devoid of military spending and is improving in this area but Europe is still heavily dependent on the United States for security its taxes do not pay for and ours do. — BenMcLean

This is a bit off the topic, but I come from a country that has now only for three of years "enjoyed" US defense protection, but the whole Cold War and until the 2020's, we were totally on our own.

And furthermore, do note that this has been especially by design by the Americans themselves: only France has basically sought a totally independent military industry and has called this strategic autonomy. The end result is that for France their military is far more capable and yet cheaper than what Germany or the UK have, which spend similar amounts on defense. The US has insisted on Europeans being dependent on American defense industry, which worked totally fine ...until Trump. Now it's obvious that your current administration is outright hostile to Europe, and Europe cannot at all rely on the US or it's military industrial complex.

The United States should have started charging some kind of rent for reliance on its defense network at that point, not because we don't want to be generous, but simply because no system, no matter how strong, can survive a permanent downward trend. — BenMcLean

You should understand that the actual rent you have gotten is from your currency being the reserve currency. That has been a political decision. And thus you have been able to take on debt without any problems. That has been a quite large rent to you.

Do understand that the US dollar being a reserve currency is thanks to your alliances. That the US dollar is the reserve currency isn't at all because of your economic position: otherwise we simply would have had a basket of currencies and there the US would have been the largest, but not the only, currency. You defaulted already once in the 1970's, and your alliance with Saudi-Arabia saved you, which created the petrodollar. That is why there is this insistence on invading countries with oil like Iraq and Venezuela.

And Europe has been totally OK with the position that the US has enjoyed, because you have provided that safety and the basis of the international order.

But now Trump is dismantling it, so good riddance to Pax Americana. It's very sad, because the system worked. The problem is that American politicians never explained the actual benefits that the US enjoyed from being a Superpower, whose alliances other countries sought voluntarily to join. And when Europe takes care of it's own military, that's a huge loss to American defense industry. And when the dollar isn't so important anymore, good bye to a lot of that prosperity you have enjoyed.

Do you think that a socialist or quasi-socialist system could actually pay for itself without turning into Soviet style tyranny the way the libertarians assume? — BenMcLean

Never underestimate just how similar in reality European system is to the American one. You spend just like European countries on Health Care and social security, with the exception that you don't have universal health care or free higher education. Yet somehow you pay a lot more per capita than European countries (even Norway with it's vast oil revenues spends less on health care than the US).

This is far more about political and economic discourse, not actually on the reality. Soviet style Marxism-Leninism isn't found anywhere and the few actual socialists are Venezuela, Cuba and North Korea plus China (who think they are Marxists).

What Europe should do is sent a stupid amount of troups to Greenland in order "to defend it from the Chinese and the Russians". — ChatteringMonkey

They are doing exactly that. And the amount may be literally stupid.





Ok, it's just a recon/advance force to get ready for an exercise. But still is perhaps more than that 1 Danish dogsled that Trump keeps talking about.

Anti-liberal wokeness isn't just inherently wrong in itself -- although it totally is -- but is also a distraction from what having a left wing should be good for: being suspicious of capitalism. Keeping megacororate power in check. The Left should have listened to Bernie Sanders. — BenMcLean

Basically European social democracy attempts to run exactly like that: these "socialist" understand that market capitalism does work, but the excesses have to be cut. Then the question simply becomes just what is "excess" and when has capitalism gone "too far". Issues that people can have differences.

The one and only scientist ever to be sent? — magritte

Yes. Only one ever. Harrison Schmitt.

Harrison Hagan "Jack" Schmitt (born July 3, 1935) is an American geologist, former NASA astronaut, university professor, and former U.S. senator from New Mexico. He is the most recent living person—and only person without a background in military aviation—to have walked on the Moon.

But I have become sceptical of the 'colonize Mars' narrative. — Wayfarer

That's scifi fantasy and I reason it to be "pep-talk" to get people excited about space travel. Good luck in achieving a "permanent" moon base for starters. One of the most expensive joint enterprises that the human race has been able to do is the International Space Station. After that ends, what then? Again, good luck getting that kind of international cooperation now! It's possible that Mars could be explored, but a colony? Far more easier and less difficult would be to make Sahara a huge forest.

Jezz Bezos, on the other hand, wants 'a trillion people living in a fleet of giant cylindrical space stations with interior areas bigger than Manhattan.' Also fantasy, plainly. — Wayfarer

The hubris of the multi-billionaires. Well, unfortunately these private enterprises are one stock market crash from the dreams collapsing totally. Yet that future stock market crash and currency crisis can also put all the government space programs around the world into a shoestring budget. And that's why I do worry if we will go backwards when it comes to space.

. That's the kind of pioneering spirit that made NASA great in the day. Whereas Musk and Bezos owe more to Star Wars than to down-home technological smarts. — Wayfarer

SpaceX has made advances in the re-usability of the rockets, which wass quite a leap. And let's remember that NASA has basically become a bureaucratic organization, just like the military-industrial complex: when funding is dependent on getting votes from various politicians, then the whole production line is sprinkled all around the country thanks only to budgetary politics whereas SpaceX has attempted to have everything together, which is reasonable.

This idea that we have to 'colonize other planets' to 'escape Earth' is a sci-fi fantasy. We have a perfect starship, one capable of supporting billions of humans for hundreds of milions of years. But it's dangerously over-heated, resource-depleted, and environmentally threatened. That's where all the technology and political savvy ought to be directed - to maintaining Spaceship Earth. — Wayfarer

Yet things like being in space might help in this.

Technological advances happen quite differently then we think. We often assume that in order to solve our problems, we should gather "the best scientists" and then they come up with solutions to the issues we see as our obvious problems. The problem with this is that what is adapted is a very centralized and hierarchial R&D environment. Actual innovations often come from totally surprising places.

Let's think about just how perverse technological leaps are. One of History's worst moment for human kind gave us a huge technological boost: all the technological advances during WW2 starting from nuclear power.. and for spaceflight the first rockets that reached space. How much tech in the US has basically been supported by various projects of the defense department? During the Cold War, a lot. And space programs? Basically they've been a sideshow of the ICBM-programs.

(Besides the Mir, the Soviets had for a while also a military space station: the Almaz)

We deplore this side, yet it tells really a lot about us ourselves.

Still, investing in technology and R&D usually gives a lot more in the future than just to spend that money on transfer payments or welfare. Yet obviously when there's poverty, many can obviously make the question that "Why are we spending money in things like space programs, when there are so many people that are poor?"

(India's space program in 1962 and today)

Thanks for a great OP! :up:

I don't know so much about computers, but I've always had a distaste of everything being in a cloud. Few comments:

Seeing this is actually one of the things that has made me decide I have to explicitly reject libertarianism. If libertarianism was true, then the free market would naturally correct this by bringing more suppliers into the consumer computer hardware market to meet the high demand indicated by this massive price spike. — BenMcLean

Libertarianism is an political philosophy, while obviously the global economy we have now isn't at all libertarian. The global economy is basically dominated by Oligopolistic competition (in every field there's a few large corporations which dominate the market and thus create an Oligopoly). Now the Oligarchs might publicly champion libertarian values and talk that kind of bullshit, but in truth what they value is the oligarchy that they are part of.

And this isn't about open source either -- this is about open platforms and individual private property ownership vs enclosure and rent-seeking. This should concern everyone, not just open source advocates. — BenMcLean

This ought to be important.

But I think this is something that has happened, or is push forward, in other areas than just computers.

Think about cars or tractors.

I had an Economic history professor, who only bought cars that were older than one specific year in the 1970's (which I've forgotten). His reasoning was that any car before that year, he could himself repair anything in the car himself and thus he only needed to buy the spare parts. But after that year there came electronics, which he couldn't do. And now look at our moders cars. WTF can an ordinary car owner do? Well, if it isn't an electric car, then just add fuel and water/washing fluid for the windscreen viper. Something else? Go to your dealership or face penalties.

This is even worse with modern tractors, which are extremely expensive and are also computers on wheels, which heavy limitations on just what the farmer can do. It's no wonder that many farmers use age old tractors.

I think that this is something very similar to what you told about computers and local computing. And your story goes on steroids when we take into account that actually for the vast majority of people the real computer they daily use is their smartphone. It seems there's a desire to make our local computers as dependent of the manufacturers/service providers as out smartphones are now.

The Dutch. You talked about the Dutch giving a bad time to the Inuits in Greenland.

Not the Danes.

Two different people, you know.

The upcoming Artemis ii mission has gotten me thinking: are there any real good reasons to spend millions and millions of dollars on manned spaceflight? The only two reasons that I have been given are “an expensive joyride for the ultra rich” and “nationalism”, neither of which are “good reasons.” — an-salad

Yes, there are indeed very good reasons for spaceflight and manned spaceflight in general. And yes, I understand that you are questioning here only the validity of manned space flight, but unfortunately they do come together:

Manned space flight makes it vastly more difficult and complex, but then again, one geologist on the moon can do a hell of a lot more than our best rovers. The environment in space is so absolutely difficult and lethal to humans, that there has been a lot of things that we have gotten, even to our own ordinary lives from spaceflight.

The most obvious example that comes to my mind would be a space blanket from the 1960's, which is generally used by first responders, but also used by campers etc.



There are medical advancements thanks to the space program, improvements in laser eye surgery to artificial limbs and so on. Naturally the technology of spaceflight in general has been important: for example the first solar cells were developed for vehicles in space, satellites and manned vehicles.

I think now the "expensive joyride for the rich" has tainted a bit space exploration, just like we have been made aware just what a huge asshole Elon Musk is. That is unfortunate. Yet that space travel is now a playground for billionaires does tell that the it's not only the Superpowers who can go to space. Quite telling example is that for the money that Hollywood created the Space Movie "Gravity" with Sandra Bullock and George Clooney, India launched a satellite to Mars. Hence the idea that it's "too expensive" can be challenged.

” Is there something that I have overlooked? — an-salad

Yes. What happens when we aren't anymore capable of going into space if manned space flight withers away. That is totally a possibility, actually.

When investments are cancelled, the ability to do something is usually lost. It is something we don't usually accept happening and we can be in denial about it. I'll give an example of this. There's the British example of their "space program" that in the 1960's and 1970's was planning to have the capability to produce rockets.

But then in the 1970's government came to the conclusion that the UK didn't need a space program and anyway, it was cheaper to buy American SLBMs (submarine launched ballistic missiles) than have anything British. It so expensive and useless.

Hence after the program was terminated and to the horror of the UK government, the British program launched their own satellite into orbit and it performed flawlessly.

(The British technology of the Black Arrow was unique, which can be seen that the "Lipstick" rocket didn't create huge vapour clouds as other rockets as it used HTP fuel)


And thus Britain never got into the lucrative satellite launching business!

All thanks to the short-sightedness of the British administrations who could not think that launching satellites would be profitable. All from the country that was the birthplace of the industrial revolution and gave firsts like the jet aircraft etc.

Here's a great video explaining how the UK went with it's rocket program, which is a case example how the UK has undermined it's technological lead.


So the answer is that you can overlook at some dramatic advances that we can have with manned spaceflight in the future... that we don't now know. And then the outcome when we lose the technology.

If manned space flight ceases to exist, then there's absolutely no other way to see it as technological retreat and destruction, like Europe suffered when Antiquity turned into the Early Middle Ages and technological know how was lost. It's not an issue of nationalism or the eccentricities of the ultra-rich. It tells where are we in history.

It's a very bleak future for us, if it would happen.

How things are going, it is extremely likely that the last astronaut that walked on the Moon may die of old age since we go back to the Moon, if we go anymore there. Going to Mars is even more questionable. Actually here Neil Armstrong (first on the moon) and Paul Ciernan (last on the moon) are asked that question on the future of manned space flight. Now both are dead and nobody has gone to the moon back. I think the youngest Apollo astronaut that walked on the moon is now 90 years of age.

From I guess 2011:

Well, the Danes met the White House Maga-people.

They basically agreed to disagree. Fundamentally. And hold further talks. Hope they (the Danes) succeed in holding those talks until Trump is kicked out and normal, rational people take control of the White House.



And anyway, now Trump is hellbent to take control of Iran. Or do something. And as @Tzeentch commented earlier, Iran might really have a revolution at hand.

I guess Trump has had enough issues to keep him in the limelight and think that he can focus somewhere else. But now it's obviously bullying time:



But this "I want Greenland because it would be awesome for my legacy" -craving from Trump will surely be one of the most strange and eccentric issues ever to rock the North Atlantic relations.

I've seen several videos from prominent indigenous Greenlanders who want it annexed due to the disgusting treatment by the dutch over time. Interesting... — AmadeusD

:lol:

By the Dutch indeed.

At this point there is nothing of substance left to discuss. — Esse Quam Videri

Yep.

And Banno, you were right.

There's no need to list all of the elements. All this talk about constructivism, intuitionism and finitism misses the point ( I do not subscribe to any of these -isms nor do I have to in order to be internally consistent. )

PROOF

1) To say that S is larger than S' means that S' is a proper subset of S.
( A definition that applies to all sets, regardless of their size. )

2) N is a proper subset of N0.

3) Therefore, N0 is bigger than N.

This is an indisputable proof. As indisputable as 2 + 2 = 4.

However, if you're convinced by a fallacious proof, you will normally deny the validity of this one, like a cancer attacking healthy cells.

FALLACIOUS PROOF #1

The first fallacious proof they use to show that N and N0 are of the same size is the observation that, if you add 1 to infinity, you still get infinity. This is true but only in the sense that the result is also an infinite number ( i.e. larger than every integer. ) They make a mistake when they conclude that, just because "infinity" and "infinity + 1" are infinite numbers, it follows that they are equal. It's like saying that 4 equals 5 merely because 4 and 5 are integers. — Magnus Anderson

What else would this be than finitism?

You don't accept the infinite to be different from the finite and obviously treat infinite like it would finite by arguing that "infinity" and "infinity + 1" aren't equal. Just look what the axiom of infinity is, which @Magnus Anderson clearly thinks is incorrect. That n < n+1 is simply how finite numbers work.

It doesn't even work for finite sets. Think what it would mean if you could only compare the sizes of sets and their subsets. You couldn't say, for example, that there are more apples than oranges on the table, because neither is a subset of the other. — SophistiCat

I think that @Magnus Anderson seems to think that if you take one out of an infinity set then number 1 is really missing from there.

The NATO secretary general Mark Rutte is asked about Trump's threats to take Greenland. And Rutte replies with saying that ...everybody shares the worry about Russia and NATO is taking action to defend the Arctic and Greenland.



Hence he doesn't at all answer the question.

And why would he? It would extremely humiliating for Trump for the NATO secretary general to say the obvious (as it would be for NATO itself). Like referring to article 1. of the treaty that basically NATO members don't threat by force each other. Or that NATO would die if the US would take military action to annex Greenland.

Hence NATO members respond the in the classic diplomatic way when a totally unacceptable proposal is given. Just to assume that the proposal was about something totally else, security in the Arctic, and respond to this. And that basically what the Arctic Light 2025 exercise in Greenland was last year and what possible deployment of French and German troops to Greenland will be: strengthening the collective defense of Greenland ...against Russia and near Arctic country China.

(Danish F-16 in the US space base Pituffik)


That Trump has changed his rambling and smoke and mirrors to other countries, like now writing bellicose posts toward Cuba. Anything away from the Epstein scandal and the economic situation. And perhaps as a toddler that got a little bit too excited about an awesome performance (the kidnapping of Maduro) then wanting more and showing signs of a tantrum, the US armed forces try to get Trump's attention somewhere else.

(Now for rants about other countries... As long as taking over Greenland isn't mentioned, good.)


The next step we will seen tomorrow on Wednesday when the Danish Foreign Minister Lars Lokke Rasmussen and his Greenlandic counterpart Vivian Motzfeldt meet Marco Rubio and JD Vance in the White House. Trump seems not to be in the meeting. Likely a "deal" to be made about Greenland is as likely as Putin accepting peace in Ukraine tomorrow. Perhaps here just how the Danes and the Greenlander will be treated will show much. If it's a bully session like with the White House meeting with Volodymyr Zelensky, that's bad. If it's just a bit awkward, that would be good.

Slightly optimistic, but you cannot know for sure with this White House.

There are people in the world who research deadly viruses. There are other people in the world who, if given access to deadly viruses, would use them against millions of innocents. — flannel jesus

Or then there are people that hide from their own citizens and the rest of the world when people researching deadly viruses simply fuck up and the virus leaks out by accident and seven million die around the world. :wink:

Let’s hope so. — Tom Storm

Paradoxically, the reason I'm confident that NOW we aren't there yet is because of Trump himself.

He had the perfect situation to really do an autocoup on Jan 6th, but what did he do? Told he'd walk with his supporters to Capitol Hill, but was then whisked away to the White House by the Secret Service where he sat and watched on TV his supporters breaking into the Capitol Complex. And at some point, he finally listen to his daughter (or someone else) that's it's enough and they should go home.

But OMG, would you have a more capable populist leader like Victor Orban, you really should be scared. Or American would have already been living under President Trump for nine years with no end in sight.

So are you saying that Trump does not currently have enough key military personnel aligned with his administration to enforce his authority beyond constitutional or legislative limitations? — Tom Storm

As @jorndoe commented above, when it comes to invading Greenland and annexing territory for a NATO member and thus creating the possibility of the dissolution of NATO, it's quite obvious that the view would be that it is an illegal order. Beyond stupidity, I say.

Yet if it's blowing up some boat in the Caribbean, a JSOC commander wouldn't and did not put his career on the line (as we can see from how general Bradley has acted).

Notice that the generals don't have their position totally dependent on Trump as their career has gone through the system, even if the political leadership has appointed them. If a general is totally dependent on the support of Trump and has no support in the military, then it would be different situation.

Like if somehow Trump would promote retired lieutenant general Mike Flynn to four star general and appoint him the chairman of the joint chiefs of staff, Flynn would know that once Trump is out, he will be too.

The US Military isn't there yet.

Exactly — politics is about compromise, so claims to absolute truth throw a wrench into it. Yet it is also true that religion is simply an inextinguishable part of life and does bear on moral/ethical questions. Previously, we would say things like 'religion is a private matter' or 'religion belongs in the private sphere.' I question the feasibility of this view, yet I remain sympathetic to it. — BitconnectCarlos

I'm sympathetic to it also. For example it's a very reasonable etiquette let's say in a workplace. Yet if we talk about for example Middle East politics and the Israeli/Palestinian conflict, not to take into account religion would be an huge error.

Any rational person should be cautious against the centralization of power. Yet sometimes it is necessary. FDR circumvented Congress to provide material aid to the UK prior to WWII, when the US public and Congress were largely isolationist. There are many examples of the centralization of power being used in beneficial ways. Of course, it is right to be cautious of such a thing. — BitconnectCarlos

Politics is many times a complex balancing act.

How long do you think some parts of the US military elite will hold out against a maverick US president? — Tom Storm

Until he gets military people like Kash Patel, Pam Bondi and Kristi Noem to be man the crucial leadership places in the military. And it's totally possible: just start from a lieutenant general like Mike Flynn and put him in charge to first pick totally loyal MAGA people from the ranks of the military and then purge others. Luckily this would need real leadership qualities, which Trump doesn't have. But a true purge of the military would be needed if the Trump needs a totally loyal armed forces for himself.

Let's remember that former national security advisor (for 22 days) general Mike Flynn advised Trump to use the military to seize the voting machines when Trump lost to Biden. I think he would have the Trump character to attempt to make the armed forces loyal to dictator Trump.



Until that day, there might be too many generals like Mark Milley, who Trump loathes so much that the White House immediately when his second term started demanded his picture to be removed from the Pentagon, his security clearance was suspended and Hegseth is looking ways how Milley could be demoted now when retired.

So that's symbolic purge light.

Yes, this is the time. Let’s hope they do and let’s face it, if they don’t, they will be a laughing stock. — Punshhh

What is worrisome that NATO's secretary general Marcus Rutte has stayed silent. The guy that called Trump "Daddy". Seems to be an example of the European laughing stock.

The Daily Mail has come out with an interesting article (see Greenland Invasion Plot) which states that after the outstanding success of Maduro operation Miller and Trump have put the JSOC (Special Forces Command) to plan for the invasion of Greenland.

Admiral Bradley, current commander of JSOC got into the limelight earlier with the "doubletap" on Venezuelan boats.


What is encouraging is that the Daily Mail reports this planning is resisted by the joint chiefs of staff as an illegal order. This can be really the outcome: when it comes to the President commanding the military leaders to plan an attack on Greenland and thus a NATO ally, that they will say it's illegal is quite probable. Destroying NATO and attacking an ally without the approval of Congress sounds simply stupid.

Two retired American NATO commanders, general Breedlove and general Hodges were asked in different interviews what would the do if the President would ask to plan an invasion of Greenland. Both answered the same way: they wouldn't do it, because it's an illegal order. Both understood that their action would put them into trouble.

Now this actually might indeed have happened. Trump might already have gotten a cold silence from the military. Yet naturally what really has happened is something that we can verify only from history books. Nobody, both Trump or the Joint Chiefs of Staff, want to make public if this kind of breach has happened. Yet if top leaders start to retire before their term ends or Trump sacks the top generals, that is a very ominous event.

If the "Greenland thing" dies down, perhaps having a meeting with the Danes which will be continued in the future and then dropped, then it's likely Trump has been given a clear "NO" from the military.

But the Europeans are still alarmed. UK's Starmer is thinking of sending troops to Greenland, if necessary.

British Prime Minister Sir Keir Starmer warns that talks within NATO on a possible UK military presence in Greenland form part of a broader effort to safeguard international order, while former US President Donald Trump's forceful foreign policy rhetoric stokes deep concern among European allies.Sir Starmer has underscored that any discussion of British troops in Greenland is framed within NATO's collective defence strategy. Government ministers have indicated that such deployments form part of routine strategic engagement with allies to deter potential Russian aggression in the Arctic Circle.

I've stayed away from -- not even reading-- threads about war because the topic becomes a series of postings about current events.

There is the political philosophy proper to discuss this:
The just war theory and ethics in the battlegrounds.
The ethics of diplomacy and negotiations should also be included here. — L'éléphant

It's inherently a structural part of our societies. It's so frighteningly normal. Has been since the time of Plato and Aristotle and thus our views about war and military don't actually differ so much for the Greek philosophers.

Yet talking about war, the military or deterrence is very difficult to do in a philosophical way, because there's the need for moral posturing and grandstanding. The perfect example is a discussion of nuclear weapons.

And indeed the just war theory, the laws of war and rules of engagement are very interesting topics philosophically in a situation there basically are no rules and no limitations.

The institutionalization of warfighting and military is also interesting. In a way, human beings rationality, practicality and ingenuity emerge in warfare a very bizarre way in a very deadly competition.

You're missing the point. What has to be shown is that the fact that one can think of f(n) = n - 1 means that there exists one-to-one correspondence, or bijection, between N and N0. To do that, you have to show that f(n) = n - 1 is not a contradiction in terms. — Magnus Anderson

With finite set there's a contradiction.

With infinite set there isn't.

(In fact just look up the axiom of infinity in Zermelo-Fraenkel set theory. Or the definition of Dedekind infinity).

Sorry, but I don't think you grasp the example of Hilbert's Hotel, which above @Banno gave you. So you write:

Suppose we have a hotel with a number of rooms equal to the number of natural numbers.

Suppose each room is occupied by a single guest.

That gives us a nice bijection between the set of guests and the set of hotel rooms.

R1 R2 R3 ...
G1 G2 G3 ...

Guest #1 ( G1 ) is in room #1 ( R1 ), guest #2 ( G2 ) in room #2 ( R2 ) and so on.

If there exists a bijection between N and N0, then it follows that we have a spare room for another guest. Let's call that guest G0.

---- R1 R2 R3 ...
G0 G1 G2 G3 ...

There is no longer a bijection between the two sets. G0 is not in any room. And if you try to add it to any room, you will either end up having two guests in a room ( not bijection ) or you will have to kick out one of the guests ( still not bijection. )

There's no way out of this conundrum . . . other than to pretend. — Magnus Anderson

OK, you really don't understand the Hilbert Hotel.

How Hilbert hotel works, at first:

R1 R2 R3...
G1 G2 G3...

And then when one gest, let's say G1, leaves, it's still full (meaning there's a bijection) because:

R1 R2 R3 ...
G2 G3 G4 ...

And if another guest comes, that G0, then the hotel fills up:

R1 R2 R3 ...
G0 G1 G2 ....

Please understand when many people are saying the same thing to you. Perhaps this video would help, because it's talking exactly about the same thing, although it really shows in what circumstance there isn't any bijection:



And if you are interested in finitism, I have a great professor to listen to or watch his lectures...

It's about more than just politicians. Land. Universities. In any case, our original topic was the role of religion in political discourse, or the use of appeals to God/absolute truth in the political sphere. — BitconnectCarlos

The "custom of the land" as often corruption is referred to.

Politics deals also with moral and ethical questions, hence it is no wonder that in religious societies God (and hence absolute truth) would play a part. Yet politics in a democracy is about compromises to get agreements and a consensus. Political polarization makes that very difficult.

Basically every political party and movement should at all times be frightened of losing elections and power. A very entrenched political system where that isn't a problem is one reason (among others) that increases the possibility of corruption. And if the legal system isn't working or itself is corrupt, then corruption is rampant.

Perhaps conservatism might be a problem for the right if those "old values" are things like corruption, yet there's ample ideology in the right to eradicate these problems starting simply with the rights of the individuals and the ever important separation of powers.

Centralization of power, usually to one leader, is a cause for corruption and the destruction of the institutions necessary in a republic. This has been the real problem in leftist ideology (which doesn't care about separation of powers and the necessary institutions), but can also lead the right-wing astray when people want "strong leaders" to fix things.

The dispute concerns the notion of Dedekind Infinity. — sime

It's not just Dedekind Infinity, it simply is Infinity in general. Galileo Galilei noticed the puzzling aspects of infinity a long time before Dedekind or Cantor (which in my view are best explained by the example of the Hilbert Hotel).

Recall that Hilbert believed that finitary proof methods could be used to ground the notion of absolute infinity that he considered to be indispensible for mathematics — sime

I think the term would be actual infinity that you should refer here to. Absolute Infinity is something totally else, which contradicts the Cantorian hierarchy of larger and larger infinities. Cantor simply preserved Absolute Infinity for God and as he was a deeply religious man, that shouldn't be overlooked. Yet for Absolute Infinity Cantor had no clue how to reason it.

and which the incompleteness theorems conclusively debunked — sime

The incompleteness theorems didn't debunk actual infinity, what they debunked was Hilbert's aim to formalize mathematics and to prove its consistency and completeness by having a general answer (algorithm) to the Entscheidungsproblem. Mathematicians are usually just happy having infinity as an axiom in ZF and don't worry so much about it.

Cheers. Useful stuff. When someone makes such obvious mistakes, it's probably not worth giving detailed responses, because chances are they will not be able to recognise or understand the argument. The result will be interminable. — Banno

If someone is willing to learn something, on the contrary.

I really would hope that if I make a mistake, some fellow PF member will say that I have made a mistake and try to thoroughly explain to me what my mistake was. Not just "Read high school math 1.0".

But yes, usually the response is just an angry outburst.

What makes you think so? Haven't you noticed that a lot of what the Trump administration does is performative. A lot of them are podcaster, newsanchors, social media-figures... even Trump made his name in showbizz. A lot of the time there's a 'show'-element to it.

I bet if Europe stands united together and doesn't blink first on Greenland, nothing happens. — ChatteringMonkey

The only thing that makes Trump forget Greenland is that something else captures his imagination or demands his focus.

Remember that the "Let's buy Greenland" was a thing that already came to light in the first Trump adminstration. Then the Danes reacted just the way you assume Trump to be.

It's the foreigners who buy up large plots of land and make large donations to politicians and universities. Everyone notices the poor foreigner; the rich are more subtle but far more dangerous. — BitconnectCarlos

If your politicians can be bought to play the tunes of foreigners, which especially now they surely can be (starting now from Trump himself), you should blame your own people, not the foreigners for this.

If your country is corrupt, don't blame others for it.

I would hope actually that there would be a philosophical debate about war in this forum. Too easily it becomes related to current events and ongoing wars. And this is already this OP is found the lounge, not in "ethics" or in "political philosophy".

The real problem is that we have been learnt a way to discuss war and the military and many times they come to be more like a lithurgy. "I'm against war and for peace" is something very obvious that we can say all the time. But so is "I'm against crime and people being violent and hurting each other" would be also similar. Or "All weapons, especially nuclear weapons, should be destroyed" is also very simplistic. Yet we just reach to the moral high ground and not accept just how institutionalized war and warfighting is in every society that there is.

Well, it's definitely happening. — Tzeentch

You might be right on this, which makes me sad if it happens. :sad:

(Notice btw. that this Pro-Trump Reuters article leaves conveniently away the fact that the Greenlanders have no desire to be Americans and would like to be part of the EU if (when) they are independent. But who cares of some 50 000+ people made up mostly of Inuits.)

I think he understands more that you give him credit for. I think he sees everything as a negotiation to get the best deal... that's why he never rules anything out. If you rule out military action for Greenland then that is something you cannot leverage to bargain for it. That doesn't mean he is willing to do it. — ChatteringMonkey

Oh, he is really willing to do it. He needs Greenland, he needs to expand the territory of the US.

The real question is if the US government is really willing to let him do it. Luckily there are some signs that the Republicans won't swallow Trump's stupidity (see Thom Tillis' remarks above).

And if the Congress and the military will let him do it, annex Greenland, break NATO, the next real question is what will the Americans themselves not let him do.

And I'm sure that when (if) he does this, annexes Greenland, then will appear the "realists" that will say that Denmark has to give up Greenland and this actually doesn't mean anything for NATO, that the alliance is intact. And Trump will see what Europeans are really the degenerate surrender-monkeys (or cucks, as the favorite definition in MAGA world goes) as they have appeared to him.

:lol:
— Banno

For a grownup man, that's a pretty childish response. — Magnus Anderson

Sorry Magnus, but this what you say is wrong:

That a bijective function exists, cretin, does not mean that the two sets can be put into a one-to-one correspondence. — Magnus Anderson

A bijection does mean that sets can be put into a one-to-one correspondence.

If the word "function" is defined the way mathematicians define it, namely, as a relation between two sets where each element from the first set is paired with exactly one element from the second then, if a bijective function... — Magnus Anderson

No. There are injections and surjections, which aren't bijections (both injection and a surjection) and they are also called functions.

Let me just remind you of this. It's looks simply, but actually it is difficult to grasp especially with infinite sets:

But I don't think he wants to push it that far that the US effectively loses all its allies, because that is part of what makes the US so powerfull. — ChatteringMonkey

I'm not sure if Trump understands that American power comes from the alliances it enjoys. I think he truly believes that US alliance with Europe has been only a financial burden without anything gotten back. He has stated this so many times, just like in his own mind the EU was formed to be against the US, again a totally bogus historical reason. He also has said so many times that "If we would need them, they wouldn't come", which just goes against history as the US did get help in Afghanistan the only time article 5 was used (after the 9/11 attacks).

(Danes in Afghanistan, back then few years ago)

He could do that and might do that — ChatteringMonkey

Latest interview starts really hinting on that. The easy or the hard way. This is bad.

After his term, the next administration would have to affirm their willingness to enforce it over and over, — ChatteringMonkey

Then the damage has already been done. NATO has already been done and the US has been seen as a threat itself. And how humiliating is it then give back US territory ...assuming there are MAGA-lunatics still around in US politics?

And 2) he does still have to consider his political base somewhat. — ChatteringMonkey

Does he, really? Does his base really want the US to be in NATO? Does his base think it's important to have good relations with those puny Europeans? No, they will just cheer for their President to have the audacity to do what he wants. He will surely have his "base", no matter how small it is.

I wouldn't be so sure if there are going to be midterms the way things are going now. Do notice what he wants: he wants to use the insurrection act, he does want wars all around. It cannot be simply disregarded the possibility that he simply puts on hold midterms.

Remember this President in January 6th: he wanted to join the crowd in the assault on Congress, but his Secret Service simply drove him to the White House. This time it isn't so. He has loyalist in the political positions in the military and in the Justice Department. Do you think they would say no? The military might say no to literally attacking NATO allies, but he just can declare himself to be in control of Greenland and it's US territory. How well that will go on the Europeans?

So like I said in my first post here, whether or not they turn over Greenland will probably also depend on how much economic pain Europe is willing to accept for it, if the US wants to play it that hard that is. — ChatteringMonkey

First, Europe should play hard.

Yet let's just think of this for a moment.

What does stop Trump simply from flying to Pituffik Space Base and declare that now Greenland is part of America, announce that Greenlanders will be given an American citizenship and perhaps 10 000$ and those who will not take the citizenship are to be deported to Denmark. And then it's just a huge ICE operation for those who don't take the money and the citizenship.

Once he has done this, Trump can then say that any resistance, be it the Danish military or the civilian population, is a threat to the US and will be dealt with maximum force of the US armed forces. He can obviously then enforce the insurrection act, perhaps martial law in the new territory formerly named Greenland now to be called Trumpland.

There will be ample amount of MAGA media-people cheering for their GodEmperor Trump and break up in U-S-A, U-S-A, chants once he has done this and they will just laugh at anybody criticizing the action. The interesting question is what ordinary Americans will do.

In this way he doesn't at first ask the military to plan to attack Denmark, which many in the Joint-Chiefs-of-Staff, the highest generals, would take as an illegal order. He surely doesn't need "Shock and Awe". It's the other way around: if the Danes use force, then it's natural that Trump can defend the US and it's citizens.

Why would this above be illogical? Trump already has declared that he is in charge of Venezuela, which he isn't in charge of. This would be a totally similar action.

perhaps it would be good to combine all these threads into a 'Recent geopolitical developments' thread, or something like that. A mod might be able to help with that, if you like the idea. — Tzeentch

Well, that morphs into a Trump thread, because there's always 'Recent geopolitical developments'... just as there will be the US president and his policy actions debated.

The fact is that some of threads may end and be forgotten... WHICH WOULD BE A SPLENDID OUTCOME!

It really would be great if this annexation of Greenland ended as being as one of the odd eccentricities of Donald Trump which created confusion, yet something that didn't end up in a tragedy or as a divisive infamous event (as his actions on January 6th became).

Remember that the Ukraine thread with it's 18.1k responses is called the "Ukraine Crisis" as the war hadn't yet happened when the thread was started (and earlier the discussion was on the Biden thread). Yet a war that has killed hundreds of thousands in Europe is something worth commenting.

That's also the story of UK, actually. Yet here Germany shot itself on the foot by getting rid of nuclear energy.

Yet here's the issue: if those high prices of energy happen because of pressure from another country, if let's say the US halted energy shipments to Germany in order to pressure Germany, that backfires.

You see, people are angry if the economy is tanking because of government mismanagement. If we in Finland would start to have cuts in our energy production in the middle of the winter suddenly, we would be angry and likely the present administration would lose in the next elections. Yet if Putin would start, out of the blue, bombing or sabotaging our energy power plants and thanks to that we would have blackouts, the blame wouldn't be on the government. Heck, then you just put on clothes, use candles and buy an aggregate!

Germany and the European countries aren't poor. If they have to buy with a higher cost energy from somewhere else, they will do it. Trump pressuring Europe will simply just backfire in this case as every move to pressure Europe into something that it doesn't want will reinforce the need for strategic autonomy. (Hence Trump demanding that Europe would spend on more on defense was taken happily on by the Europeans.)

And yet there's still little in the way of socialism in Europe. That's because the EU controls economic policy, and it's firmly neo-liberal. Again, what you're pointing to as evidence of European leftism is just government handouts in an otherwise liberal domain. — frank

One note to the discussion that you and @I like sushi are having: the political discourse is obviously quite different between the continents, but the actual government spending is quite the same. Which is quite surprising as the US doesn't have universal health care etc. Even if the US usually denies it and thinks the European countries are the "welfare nanny-states", the similarities are obvious.



Just compare this to let's say German budget in 2020, when the rearmament issue hadn't emerged: