I admire, and envy, your optimism. IMO, the liklihood of Trump being impeached, and removed, is maybe 5%. — Relativist

If Trump would be just an ordinary president, it would be after all 5% (or well, with an ordinary prez I guess the percentage would be 0,05%), but he's not. Greenland, Minneapolis, mocking the NATO members in Afghanistan... it's not going to end there.

I think in reality Trump getting impeached or being sidelined is about 11%. Him dying (of natural causes) is more like 20%. Alzheimers runs in the family. All those tests he brags of doing tells something real.

In reality, there may also be the "Biden moment", when he is just put aside when he is totally incapable of ruling. If the Dems did it to Biden, it can indeed happen to Trump. He just needs to be in a worse condition.

In fact,

My little country which thinks it's a good democracy had an experience of this. A President that had basically destroyed the opposition and had the backing of the Soviet Union, simply got too old and demented. And then it wasn't great political drama, but a small announcement that he has retired for health reason. Not with a bang, but with a whimper.

(Last moments of Urho Kekkonen as the President of Finland, here assisted by the Iceland's President, Vigdis Finbogadóttir and his Finnish army adjutant in August 1981 in Iceland, next month the president "took" sick leave and then died in 1986.)


Trump's health simply going down is a real possibility. If Alzheimer takes hold, then the "ouster" is quick and easy.

Trump's action, giving him control of this money, is unConstitutional. The Constitution gives Congress the sole right to allocate funds. In a fair world, Trump would be impeached and removed from office for this. But partisanship rules, and the net result is near-dictatorial power. — Relativist

And what do you think happens if after the Midterms Trump and the GOP would lose both the House and the Senate majorities? It is a possibility.

Still, impeachment needs a majority in House and in the Senate a 2/3 majority. Now there's 35 seats in the Senate in election and those 65 that don't have elections 35 are Dems and 31 GOP. So if the GOP get only 10 Senate seats and the Dems (or people willing to impeach Trump) 25, that makes in my arithmetic 60 seats, which is the 2/3 majority. But then, even if the Dems don't get the 2/3 majority, still the GOP senators can see the writing on the wall and do what they would have done to Nixon.

That's why Trump isn't so keen to have the midterms.

And any, even the Venezuela thing hasn't come to an end.

That's not a serious picture or anything, right? — AmadeusD

No. Supposed to be Trump's humor.

But posting maps where countries are part of another one is actually no laughing matter. I just remember the maps that circulated of NovoRossiya after the takeover of Crimea. Or the maps published by ISIS of their future Caliphate.

You're right - we don't know. — AmadeusD

The good thing is that afterwards we will know. History will put these issues into context.

Just imagine the historical films done about Trump decades from now. Biden might be forgotten like Gerald Ford. Trump won't be. That's for sure.

What are the first five? I have a feeling a huge amount of rhetoric is doing lifting in response to this thing. — AmadeusD

Look at the map: US with Canada and Greenland. The US is larger than Russia. And look at the people who Trump is telling these facts. From left to right: Starmer, Meloni, von der Leyen, Merz, Macron, Stubb(!!!), Zelenskyy, Rutte (I guess).

(Yep, it's nice that my tiny country's president is among those European heavy hitters.)

I think he really got excited about Greenland. It was outrageous. It was totally surprising. Totally out of the ordinary. But he assumed it could be done, because he really thinks so little of Europeans. Just the idea of a real estate tycoon finishing his career with the biggest deal of the Century with buying the largest island in the World.

Trump posting himself (or, at least, someone in his feed) this AI picture tells more than a thousand words:


Yet let's think about this:
- Denmark wasn't going to sell it
- Greenlanders didn't want to become Americans
- Americans didn't want to buy and especially not to invade Greenland
- The military likely viewed it as an unlawful command as the NATO treaty is actually something as a law when the US has signed the treaty.
- The Republicans in Congress were not so hot about annexing territory from an ally.
- The only ones enthusiastic about this were the Russians.

What cards did Trump have? How is this a great opening?

Then of course there's the idea that all of this was part of the "Art of the Deal". That this was 4D Chess and Trump gives first an outrageous and demeaning bid, and then takes home something totally else.

Well, if so, just what on Earth did he get? What did Denmark now "reasonably" accept that made everything first to be worth it? We don't know.

This idea simply doesn't make sense. What makes sense is that the markets panicked of a sudden possibility of a trade war because of Greenland, and Trump had to quickly back down. And there was Rutte to give the hasty exit for the US president as this wasn't going anywhere.

And now Trump can focus on the "Bored of Peace"-thing.

What we have are ways of talking, language games, a grammar, or a paradigm - whatever you want to call it. Infinity is a mathematical notion that we can use to calculate physical results. It is not an ontology. — Banno

And we do use it. It is, well, essential.

What we don't have is a proof. Or how it fits everything else.

What we have is threads like this constantly coming up. That itself tells something.

Now, am I crazy to argue that there might be something more to be said here? Perhaps I'm annoying in repeating myself, but I think this is a topic worth wile to talk about.

And ontology? Well, what is the relationship of infinity with numbers?

If we define numbers being arithmetic values that represent a certain quantity over all other quantities, what if we skip away the "arithmetic" part? What if we say that infinity represents a certain unique quantity over all quantities also?

For starters, I think we can agree on what space is. What is time and how it relates to space is another question.

One can argue that calculus doesn't solve Zeno's paradoxes as we don't have yet a clear understanding of infinity.

He was against the reckless expenditure when he was the prime minister of NL; now he is pushing for more expenditure just to woo Trump. Are they clowns, or am I the blind dude who is not seeing what is going on? — javi2541997

I don't think you are blind.

That talk "reckless expenditure" I assume is before his last years of being a prime minister (2010-2024). The Russian invasion of Ukraine change a lot. Prior I lived in a nonaligned country where nobody was seriously demanding the country to join NATO. It was an possible option in a theoretical future. So a lot has changed.

Well, @AmadeusD, I'm surely not in the Trump-lovers line.

Time will tell, and I have an extremely hard time thinking this is bruise on the US or Trump. That seems an emotional reading. We'll see. — AmadeusD

A bruise isn't something dangerous. An open cut which isn't treated might be. A mortal wound is truly something else. So that for the "figures of speech" here. So I'm not in the camp of declaring NATO to be dead.

Really apprecaite this exchange so far. — AmadeusD

I do too.

I can't conceive of what you're talking about. The current claims about any kind of widespread racism in the US seem, factually, ridiculous. The tenuous connection you're making between Nazism and US policy is unserious, sorry to say. I can't really engage it. — AmadeusD

I think you understood me incorrectly as this has nothing to do with US policy.
In "American racism" you have Caucasians, whites. In European racism you make difference with West-Europeans (Germans etc) and with Slavs for example. Well, Russians and Poles, Czechs etc. are white in the US. This just to show how illogical racism is.

And racism is something that every country has, btw. There's ample amounts of those here too.

True. But in-group bias is a Human standard. Racism is a somewhat direct consequence of tribal values. In modern times, we've had the privilege to construct tribes of multiple ethnicities. It wasn't so in the past. — AmadeusD

Racism is extremely illogical and basically is a result of bigotry, hubris of oneself and shows the lack of needed social cohesion in a society. So when the current American-style racism is marketed in Europe, it seems very odd at first, because the classic "Untermenschen" of the Nazis are White Europeans also, starting from the Poles and Russians.

Yet "Tribalism" shouldn't be so negative as we use it now. Things that tie strangers together are actually needed in any society. Just like if religion gives us fundamentalism, we shouldn't forget all the positive aspects that people get from religion and their faith.

I completely dislike him. What a twat. — javi2541997

Calling Trump "Daddy" and all that... :razz:
Rutte definitely is always saying that thanks to Trump, NATO countries are increasing their defense expenditure, which is something Trump likes a lot (as Obama wanted also this, but failed).



Well, Denmark might really have increased it's defense spending because of Trump and his actions. But the real reason is naturally Putin's Russia invading Ukraine. That's the obvious reason, which nobody says around Trump. Why get the baby into a tantrum? Just look at what the response was to the Norwegian prime minister, when the baby didn't get his Noble Nobel-peace prize.

I guess he forgot he's European when he changed his NL suit for the NATO one. — javi2541997

Remember what ALL republicans said about Trump, starting from JD Vance or someone like Lindsey Graham before becoming total toadies and yes-men for him. But Republicans just love Trump, just like Americans for some reason unknown to everybody else love to pay the most in the World for health care services and still have a mediocre health care system without universal health care.

Yet Rutte has been straightforward: he publicly repeated that he NEVER will take sides if two member states argue, and that he will follow similar actions that secretary generals made to keep the calm between Turkey and Greece.

NATO's article 1 is actually very important. To have all European countries in an military alliance is there to avoid the possibility that Trump put in front of everybody. Just like the EU started from an union that made rearmament difficult, so has NATO also this effect as NATO armies usually operate with each other. And lastly, NATO is actually an US created organization for US objectives, which the orange idiot never has understood (and basically the American establishment seems to have failed to reason to one part of the American public).

As I've said, without NATO there surely would have been after 1945 a war between Turkey and Greece. And now we saw that even the Trump the lunatic didn't go through with taking Greenland.

Hopefully he plays now with his new Mar-a-Lago based "Bored of Peace" -project and has there other country leaders making him feel important and at center stage.

(Donald just loves to be the center focus. Look at that smile.)

Globalists apparently express such polarity when the intersection and interests of national and regional democracy and tribal values don't facilitate the ease of their projects towards ideologies and abstract social utopia. — Alexander Hine

I wouldn't say that tribal values have to be racist. And being against racism isn't in my view an abstract social utopia.

I think we should consider the fact that Newton and Leibniz didn't invent calculus for the purpose of solving Zeno's paradox, but for describing trajectories under gravity. — sime

No, but the issue in the core of Zeno's paradoxes. And we should note that calculus had problems with the infinitesimals, like the famous critique from bishop Berkeley.

And basically logism and the set theoretic approach hoped to find some rigorous ground for calculus, but the paradox resisted to die with Russell's paradox. And with Cantor's hierarchial system, there's still questions...

I really think that there's more to it than we know now. Math is just so beautiful and so awesome.

Zeno mistook an infinite description of motion for an infinite obstacle to motion. — Banno

Or it was a critique of Plato and other mainstream philosopher's idea of the potential infinite.

We should remember that we unfortunately have lost Plato's original book, where likely the Eleatic school would have made their own viewpoint. Now we have just the texts of those who were against the Eleatic school, the "mainstream" Socratic-Platonic school.

Boy, would that book be nice to resurface. It's said that Zeno had even more paradoxes. Loved to have known what they were.

So next move from Trump is the "Board of Peace", which he has invited countries and Jared, Witkoff, some billionaires etc. to the executive Board. Of course, Chairman Trump is a member for life.

(with Donald, everything has to be golden)


Wonder how many meme's there are about the spelling.

Shouldn't it be "Bored of Peace?" :wink:

Trump lovers will say: "This is the art of the deal!" "4D Chess!!!"
Trump haters will say: "This is TACO!"

End result: The US alliance system got a really a beaten and bad bruise which cannot be hidden and Europeans won't forget this, that Americans can attempt to annex territory from their allies and impose tariffs or other sanctions if this annexation is imposed.

Speaking of idiots, the Danes are sending troops to Greenland, ready to die for their monarchy and the last vestiges of their colonial empire. — NOS4A2

No.

They're hosting NATO exercises, which guarantees the actual safety of Greenland.

Which Trump seems to go with now Rutte.

Your a bit off here. Trump already caved in. For the time, at least...

And now, finally.

I think this absurd thread will like be ending soon as Trump finally gave in. For now. Until someone asks him if he is still thinking of buying Greenland, to which he will say "Of Course..."

And then this continues... But now:



Sanity seems to have prevailed. :smile:

American Presidents will choose always later inflation from losing the next elections. If there hasn't been a dollar crisis yet, perhaps there isn't one in the next two years.

Both Biden and Trump have been very consistent on this.

But Trump, being hte mover he is, is probably aware of this. — AmadeusD

Lol. The only thing he is looking at is the midterms. Huge win might get finally an impeachment that goes through. That's why he wants the economy to be fine, and what better would be is to lower interest rates. Nevermind the inflation later. So, I think gold might be going still up, even if the fears of military annexation of Iceland Greenland by USA from Denmark isn't on the table.

It's estimated that the future Fed chairman will be perhaps between two Kevin's:

Kevin Hassett, a long-time conservative economist and key Trump economic adviser, is seen as a top contender to succeed Powell.

A Trump loyalist, Hassett, 63, served as chair of the White House Council of Economic Advisers during Trump's first term and now leads the National Economic Council.

Hassett has been a stalwart defender of Trump's economic policies, downplaying data showing signs of weakness in the US economy and repeating allegations of bias at the Bureau of Labor Statistics.

Or then it might be Kevin Warsh:

The 55 year-old economist, a fellow at the right-leaning Hoover Institution who serves on the board of UPS, had also been considered for Fed chair during Trump's first term. He briefly overtook Hassett in prediction markets this month before falling back to second place.

"I think the two Kevins are great," Trump told the Wall Street Journal this month.

Warsh has been an outspoken Fed critic, lambasting everything from the central bank's heavy reliance on data to its use of assets on its balance sheet. He has escalated his rhetoric since emerging as a contender for the top Fed job this year, calling for "regime change".

Warsh had a relatively "hawkish" reputation as Fed governor, meaning that he tended to favour higher interest rates and focused on concerns about inflation.

But he is now seen as a voice that would support lower rates in the near term. He has argued that the Fed should shrink its balance sheet in order to bring down short-term interest rates, though some have questioned that logic.

"He thinks you have to lower interest rates," Trump told the Journal. "And so does everybody else that I've talked to."

Let's remember that Trump has wanted to oust the present chairman for a long time.

Indeed. Well, he got Iceland and Greenland mixed up. But he promised he won't use force to take Greenland. They way I see it, the US military wouldn't have been so crazy. He just got too excited about the successful Maduro kidnapping perhaps.

Simply put it: Danes have to keep the heads cool. Trump is a demented idiot and people around him will repeat everything what he says, but the US establishment aren't made of demented idiots. It's something we never should forget here.

Let's just wait if Trump really puts on tariffs to Europe in the end of the month ...or he has forgotten it then.

$850 billion is the highest it’s ever been. It’s only gone up. — Mikie

First, there's inflation (as @Tzeentch noted). Secondly, the defense expenditure has been a far higher percentage of the GDP during the Cold War. Let's remember that also the armed forces were back then larger. There were more men, more ships, more aircraft and more ...nuclear weapons. A way lot more.

Correct.

In fact, payments on the national debt are now larger than the defense expenditure. During the Cold War the spending was far higher.

? I understand i need to divest of talking about Trump here, but it almost seems liek you're saying we must remain party to agreements which don't benefit us. I don't really see that working. — AmadeusD

You think that changing tariffs less than in one year is rational? What international investments and trade simply needs is stability. Think about, if someone really plans to do large investments to the US, plans building a factory etc. it takes basically years to build one and locks the company for many years onward. If you don't know what is happens, that there's the possibility of some politician making Trump angry and then all your plans go bust, then you simply avoid doing anything and stay on the sidelines.

Or make deals with China as Canada has done now. Earlier, when the US was an ally to Canada, the country basically didn't allow Chinese electric cars on their market (as Biden wanted). Now the Canadian market is open for Chinese electric cars.


Why alienate countries that had good relations with you? It's all just the US shooting itself in the foot, which is hugely benefitting Russia and China.

You're right, though. If Trump is (I can't quite see what you're seeing, but that's not surprising to me) renegging on several agreements, particularly on trade, then yeah thats bollocks and geopolitically unstable. — AmadeusD

Political instability isn't good for the economy. Just look at how gold is doing.

If, however, he's doing it as leverage to dominate the international landscape with a view to securing American interests - i don't quite know what I think anymore. — AmadeusD

Is he really dominating the international landscape? What really is the benefit of this domination? What are these interests? That he himself gets vast amounts of money? How is that helping actually the US? He definitely is in the spotlight, sure. It's really a global reality show around him, which he obviously likes.

It's actually something that the Russians do (earlier the Soviets did) a lot. Many Nordic countries simply start from the assumption that international treaties once agreed on are upheld and that is that. They won't dare to question them afterwards and take them for granted.

Russia has a totally different way to think about it: if things are great, then those treaties are upheld, no problem. Yet if there's problems with the relations Russia wants to push some agenda, perhaps there's a problem here or there and the treaty isn't so clear anymore. If for example before the FSB (acting as border guard in Russia) did keep people from wandering from Russia into my country, somehow later there was a huge influx of migrants without the needed papers coming to our and Norway's borders. When asked why they are there, they tell that they were told that the border was now open and the FSB was helping them to go to the border. So basically everything is on the table, negotiable.

This creates simply an environment which makes for example international trade very difficult and everything is basically very political. Political ties to the leadership becomes very important, which gives rise to corruption. This basically creates a large country risk, which is the cause that money doesn't (and didn't) flow from the West to Russia ...or many developing countries. International trade and investment needs strong reliable institutions.

So this is where Cantor specifically went wrong: he should have interpreted diagonalization as showing that a surjection cannot always exist between countable sets. But instead, Cantor started with the premise that a surjection A --> B must always exist when A and B are countable, which forces the conclusion that diagonalisation implies "even bigger" uncountable sets, which is a conclusion that Cantor accepted because it resonated with his theology. — sime

OK, this might be difficult to understand as I don't have a clear way to say this, but I'll try to be as clear and as simple as possible:

Cantor's diagonalization, just as the example with Turing's machine, is basically about negative self reference and this negative self-reference and it's effects are the key issue. With Cantor's diagonal argument, one way to say is that it's about showing that there's a real number which isn't on the list of real numbers where every real number ought to be. With Turing, it's about another Turing Machine that does the opposite of the first Turing Machine, where the first Turing Machine should be capable of computing and giving an answer on everything. Both cases, the limitation is, de facto, negative self reference. Negative self refence simply means that it's not possible for me or anybody to do something, that I or they, don't do.

I myself have used many times the following example of how negative self reference, how easily this diagonalization works:

Forecast what number, 1 or 2, I will write in my next response and make the forecast before I respond (in a day, at least). I will follow exactly these lines: If you say I will write 1, I will write 2. If you say I will write 2, I will write 1. If you don't answer anything, just copy this or answer something else or disregard this, I will write 1.

In game theory, the answer is obvious:
_You say_/_I say_
__1__/__2__
__2__/__1__
__"something else"__/__1__

Is it easy for anyone else than you to forecast correctly what I will say. Yes, very likely it's going to be 1, because usually people won't even bother to participate in this simple forecasting game of mine. But you cannot write the correct forecast because the correct forecast will be what you don't write. Hence the negative self-reference. Is there a correct number to be forecasted? Definitely, yes, but it depends on your action.

Let's put this back into the context of what we have been talking about:

Is Cantor-Schröder-Bernstein theorem correct? Yes, it is.

Just as Gödel's completeness theorem goes perfectly with his incompleteness theorems, the real question is what changes in the more complex systems?

You argue it this way:

So let's take P(N) to be the decidable subsets of the natural numbers. Then is CSB true or false?

1. We know that we can construct an injection P(N) --> N via Turing machine encoding of decidable sets. (|P(N)| <= N)

2. We can build 'any old' injection f : N -> P(N) to show that |N| <= |P(N)|.

3. Hence according to CSB, the set of decidable sets of P(N) has the same size as N.

And yet f cannot be a surjection: For diagonalising over f must produce a new member of P(N), but this isn't possible if f is surjective. Hence f cannot be a surjection, and this is the reason why diagonalization can produce new members of P(N), without P(N) ever being greater than N. — sime

OK, perhaps I don't get 100% of this, but I assume your on the correct track.

Yet does diagonalization really "produce a new member"? I don't think so. Diagonalization shows us the limits of computability or in the case of Cantor the futility of trying of treating an uncomputable set as a computable set. Remember that the diagonal proof is a Reductio ad absurdum proof. A list of all real numbers cannot simply done. That it cannot be done means that it's uncomputable. Yet is there the set of real numbers? Yes. And obviously there's a bijection from the set of real numbers to the set of real numbers.

I would argue that the limits of computability and provability just show where the line between objectivity and subjectivity go. The part of mathematics that is uncomputable tells actually a lot about subjectivity and being part of the universe, which creates problems for objectivity.

Looks to me like Trump reinstated an already existing programme because it was the opposite of what Obama did. Now in his second term he has become expansionist and will probably want to add the moon to his new list of colonies. — Punshhh

When the issue is Trump, to view it this way is totally rational. I think the Trump thing here just works against any successful program. I'm quite sceptical of the future of a manned spaceflight in general.

Even if we shouldn't forget that during the Apollo missions the US was also in political turmoil.

Never in the last hundred years or so, have I been able detect any meaningful influence of the American public on US long-term strategy. — Tzeentch

Really?

How about the opposition to the Vietnam war? I think the Domino-theory was a long-term strategy.

Or the Civil Rights movement? The policy towards blacks in the south was a long-term strategy too.

How Russian media is viewing the possible US annexation of Greenland? With praise, it seems, from one fellow imperialist to another, from the Rossiyskaya Gazeta:

(translation) If Trump achieves the annexation of Greenland by 4th of July 2026 when America celebrates the 250th anniversary of the Declaration of Independence he will undoubtedly become one of the historical figures to assert the greatness of the United States. With Greenland, the United States will become the second largest country in the World after Russia, surpassing Canada in area. For Americans, that outcome will be on par with such "planetary" events as the abolition of slavery by Abraham Lincoln in 1862 or the territorial conquest of the Napoleonic Wars. Everyone will quickly forget the current diplomatic contacts with the Danes on the future of Greenland as something momentary and, in fact, useless. But if, thanks to Trump, Greenland comes part of America, this will be forever. For sure the American people will not forget such achievement.

But standing in the way of the US president's historic breakthrough is the stubbornness of Copenhagen and the mock solidarity with it of a number of intransigent European capitals, including the so-called friends of America - Britain and France. Europe does not need the greatness Trump is promoting. Brussels is counting on "drowning" the US President in the midterm congressional elections, on not letting him conclude his greatest deal of his life.

Unless i'm missing something big in what you're suggesting... — AmadeusD

Yes, you indeed are missing my point.

Trump and the EU made last year a trade deal... which is now ripped open because basically of his own vanity in getting Greenland. And this vanity is obvious on the reply Trump made to the Norwegian prime minister (who btw or his government doesn't decide who gets the Nobel peace prize).

So less than a year has past and Trump already is changing what was decided.

This is the reason why I said that you cannot make a deal ...and basically assume that Trump would himself go along with what has been decided.

Now he's trying to blackmail Europe into selling him Greenland. Utterly absurd. — Michael

You simply cannot make a deal with Trump. And that's why everybody is rapidly making deals with other (Canada with China, EU with Mercosur) because of Trump.

Remember that with the first tariff stupidity the egomaniac wrecked the agreement that his first administration had done with Canada and Mexico. Hence you cannot never trust Trump. (Perhaps only if you are Putin. Doing Putin's bidding has been extremely consistent.)

Lol, so my country, just as Norway, that sent two officers to Greenland to recon for future exercises, is facing Trump's 10% tariffs and later 25% tariffs.

And Trump's lies are so ridiculous. First he (and Vance) say that Denmark isn't taking care of the defense of Greenland and jokes that they have added one dogsled to the defense of Greenland making it two, and when Denmark does increase the defense of Greenland, it's creates according to Trump a "very dangerous situation for the Safety, Security, and Survival of our Planet.” It's totally clear that Trump wants the largest territorial expansion of US soil since US buying Alaska (or the US-Spanish war) to make himself important. Greenland's new name could be really Trumpland, if Donald get's his way.

I hope that Denmark and the other NATO countries hold their line, and don't back away from the bully, but just stay calm, firm and let Trump implode himself.

We have to always remember that only a minority of Americans accept what Trump is doing now.

Just to comment on the actual Artemis program, and NASAs manned space program in general:

The program came after the cancelled Constellation program (2005-2009), which planned the return to the Moon no later than 2020 with a planned budget of 230 million. Only one unmanned launch was made before the cancellation (of the program with 25 planned missions). Artemis picks up from that. Artemis program has less than half of the intended money of the Constellation program and has ten missions planned ten missions ending at 2035. The Artemis I was launched 5 years behind it's original schedule.

Artemis II is basically what Apollo 8 did while it will be Artemis III, planned next year, that mimicks the famous Apollo 11. Artemis III is planned to stay on the moon 6,5 hours and make two EVAs. Artemis III waits for the Space X Starship lander.

Artemis phase I (plans that obviously didn't make the timeline)


So let's just compare this with the Apollo program. The Apollo program planned for 20 mission in it's entirety with ten manned moon landings, but the last three were cancelled. Yet what is crucial is the program times: the Apollo program was intended to be from 1963 to 1972, only nine years. The Artemis program, with half of the missions that Apollo had is planned to end in 2035 and then will have been around for 18 years. Twice the time for half of the missions than over 50 years ago. And that is just that plan.

Btw, has anybody noticed how Greg Bovino looks like Colonel Lockjaw from the "One Battle after Another", the role acted by Sean Penn? Bovino is so close to the film's fictional character. Named just as an "Commander-at-Large" by Kristi Noem and operating outside the command structure of the Border Patrol and reporting directly to the secretary of Homeland Defense, it is a bit similar to the movie.

The movie was made in 2024 and the story is from a 1990's book, so Bovino inspired the movie. Perhaps it has been the other way?

I never really took the Trump being a 'Putin agent' all that seriously, and I still think that is somewhat farfetched — ChatteringMonkey

I don't think it is at all far fetched. Let's remember that:

a) His bromance with Putin has been for a long time. He genuinely likes the guy. He likes tough guys, who are rich and powerful.
b) Russian customers saved earlier Trump from bankruptcy. He has known Russians for a long time.
c) Trump is really delusional. No seriously, the whole Greenland and Canada the 51st State are such lunacies that you can see that power has really gone to the head with Donald.
d) He is genuinely doing what the Kremlin wants. The Kremlin has wanted to break the NATO alliance and severe the ties between the US and Europe. The Kremlin doesn't at all like EU as it makes far more difficult for Russia to attempt to influence European countries as they stick together. Just look at what Donald is doing.

Anyway, we got a reminder that not all Americans are such lunatics as the people in the White House are with bipartisan delegation of the US Congress meeting their counterparts in Denmark.

The whole thing is a disgusting cesspit of robber-baron colonialism. — Wayfarer

That an enthusiastic Trump just bloated out. Just like he has now said that he isn't so keen to have the midterms anymore.

It's going to be interesting to see just when Americans have been humiliated enough by Trump.

Is it when he cancels the midterms? When he grabs even more power?

The hypothesis that every real number can be listed by an algorithm, is equivalent to knowing the limiting behaviour of every computer program. So what Cantor actually showed, is an indirect proof that the halting problem cannot be solved, and not that there are "more" real numbers than natural numbers. — sime

It's really good that now people are more and more noticing the simple link with Cantor and undecidability resuls of Turing and Gödel. Negative self reference is a very powerful tool in logic.

Part of where Meta and Magnus have difficulty is in their insistence that one way of talking is right, the other, they call variously incoherent or inconsistent, both without providing an argument and in the face of demonstrations to the opposition effect. — Banno

Indeed. And this is why it's actually very informative and interesting to listen to actual finitists as they can make valid criticism of ordinary mathematics. Just like every school in philosophy or economics or whatever, also in mathematics various schools make interesting viewpoints that shouldn't be categorized as being either right or wrong.

Within cardinal arithmetic, ∞+1=∞ is true; within ordinal arithmetic, ω+1>ω is true. Cross-applying the rules is what generates the illusion of contradiction. — Banno

The first uncountable ordinal is the interesting question. What is it, what does it mean and what is the logic then?

I think the main problem is that proving something is inherently close to computation, thus no wonder that we have the undecidability results lurking with the uncountable.

Tough nut to crack, but actually it's great that some large basic questions are still open in math and not everything has been done before us. Because that's the error many do: Russell and Whitehead thought that as everything is already there, they just had to write everything out then in a "small" book.

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.