• Ukraine Crisis
    It doesn't look good for the Ukrainians. Russians are slowly getting the initiative.

    Although Ukraine likely isn't going to collapse. But likely this conflict will end like the Korean War. Technically it won't end, just like the Korean war.

    You know, I think there's this attitude that people have forgotten Ukraine or don't want to hear about it, so you have to instill something to get the focus of the people in Western Europe.

    Russia does what it does. It's an Empire and does things Empires do. When it reaches objectives that Putin can say were the original objectives, then it can declare it has won a great victory. And Putin can die happy that he has made it to history as one of those Great leaders of Russia.
  • Israel killing civilians in Gaza and the West Bank
    What if I were to say, "the US and Britain surely cannot beat the movement called Nazism, but only their present military units"... I suppose I would be technically right also but not making much of a point. Nazis do still exist.BitconnectCarlos
    Because what is offered to the Palestinians by the current Israeli government is to move away, to Sinai or Jordan, or somewhere else. That's basically it. Or be second-class citizens with different laws applied that Israelis. The majority of Israelis don't want a Palestine state and also don't want the Palestinians in their state. And this administration of Bibi is determined to do something about this.

    The Germans got back their country, you know.

    In fact the US helped Germany with aid and also made a huge effort by the Berlin airlift. Do note that the East German staged an uprising while in West Germany nothing like that happened, so the way you treat people matters. I'm sure that similarly the West German response would have been different if you would have based the occupation on that Germany and the Germans are a death cult, the should be an agrarian country without any industrial base that they can (and will) use to attack the West. Such ideas were very common after WW2 and if the politicians would have followed the "will of the people" in this way, I'm sure that the Bundesrepublik hadn't emerged to be what it is now.

    So no, it won't go that way here as it went with Germany (and Japan) after WW2. Just as Iraq didn't go as Germany. Or Afghanistan.

    Hopefully Israel won't need to "mow the grass" in another decade or two if real, systemic changes can be made and if the Rafah campaign is successful.BitconnectCarlos
    Hopefully? Of course it will. The infants of today will be all military age in 20 years. Then at least the next serious mowing of the grass.

    Besides what "systemic changes" are you talking about? Well, the ethnic cleansing might do the trick. Have Gaza empty of those human animals and build there nice Jewish settlements. Perhaps a museum to celebrate ancient Kadytis. Israelis are great in building museums. And if all the neighboring countries collapse into civil wars like Lebanon and Syria, then Israel can easily bomb them all the time without any problem. It will just show how incapable the Arabs are of anything, right?

    Or I get it: The Palestinians simply have stop being a death cult and stop attacking peaceful Israelis. And perhaps just move somewhere else and "get on with it!". I mean it's just a place where you live. One place is as good as another. For nobody the place they live is a "Holy Land", right??? :grin:
  • Postmodernism and Mathematics
    I don't understand what you are getting at. I provided plain proof that there are indeed people who deny mathematics for political (leftist) reasons.Lionino
    Where? An WSJ article? So someone really has the problem with actual arithmetic? If you provide "plain proof", the just give the reference...even if this is just five pages, it's hard to find.

    Maybe she (whoever) didn't, but many did.Lionino
    Remember to give the actual quotes, not someone referring to something.

    Actors such as JBP and Shapiro are doing a disservice to their own cause when they bring up Derrida and Foucault, all the while the people they want to fight are seldom named — some might say they are poisoning the swamp, but realistically they are just ignorant.Lionino
    This is an important point here. It's just like talking about leftist thought in general where words that have specific definitions are used as vague adjectives and called "marxist", "maoist" or "woke". Well, in this forum there are a lot of leftist members and usually their views and comments have nothing to do with what is portrayed by Shapiro and JBP (Jordan Peterson?).

    In fact, the ignorance of for example Jordan Peterson is clearly when he had a debate with Slavoj Zizek. And naturally that in the discourse of 'leftism' that social democracy isn't discussed shows how shallow this right-wing rhetoric is. As shallow as, well, leftists analyzing the right-wing.

    Hence back to the subject of mathematics. The first question is, is it really about the formulas of mathematics or is it about the teaching of mathematics?
  • Postmodernism and Mathematics
    Maybe those people are not real post-modernists, but they do exist:Lionino
    You surely can get a clueless person that has only been taught something what you would call 'post-modernist' to say something incredibly stupid.

    That's the way how the "culture war" works: find the most stupid, most fringe remark from the social media (very easy to do) and then declare: "Look at these idiots!" You aren't engaging in discussion, trying to understand the others point of view or to get the most sensible argument. Nope. You are there to win the argument and warn how dangerous the other side is.

    And there's a lot of ignorant views there. The basic problem is simply when you teach the critique of something, but not the actual school of thought or philosophical view being criticized, the person is simply clueless.

    But let's take for instance one of these "pomo" attempts that was declared to be the threat for mathematics (I forgot by whom). So I listened to the lecture. She didn't say 2+2=5. The basic reasoning was to find examples closer to the lives of the pupils and understand when the lack basic skills and how to operate then.

    I did have a thread of Decolonizing Science which was basically the same subject matter, not "pomo", but still.

    I think I've just become a bit cautious of those that warn about this pomo-leftism in science or math. In the end they aren't interested in the actual math, so one shouldn't be so angry about it. It's just the present way of virtue-signalling.
  • Postmodernism and Mathematics
    It's maths I'm interested in precisely because maths seems to offer a type of perfection and certainty that science and certainly philosophy do not. My question is niche not general. If postmodernism has a tendency to devalue or critique foundational thinking, how this applies to maths seems more interesting to me than how it applies to science - It's interesting to note that while some believe pomo can come to a conclusion that 2 + 2 = 5, those with knowledge of the subject here suggest this is a straw-man and a fit up.Tom Storm
    Exactly, do not make the mistake that people engaged with the "culture war" make here.

    As I was saying, the objectives of social sciences when approaching math is different from math. Postmodernism is similar: if it's focus is how the past modernist agenda is over and how it's about "an acute sensitivity to the role of ideology in asserting and maintaining political and economic power", it's nonsense then to talk about 2 + 2 = 5, because any postmodernist that is against 'naive realism' isn't trying to debunk arithmetic with natural numbers. He or she may be interested in what questions we want to use arithmetic and where not, especially when it comes to applications and modelling the real world. Just look at the role we give the indicator GDP or GDP per capita. Yes, calculating the GDP you do use math, mainly arithmetic actually, but obviously the calculation has a lot of implications to political and economic power. And counting the GDP is really in the field of economics and other social sciences.

    This kind of answer (that pomo makes 2+2=5 OK) is simply from someone who doesn't know and doesn't care to know what the pomo/sociel science gobbledygook is about. It's just nonsense, period. Hence it's a danger! And that seems to be what for example mr White above is saying that you quoted.

    And of course there is postmodernist nonsense. The laxness of rigor was shown very well by Alan Sokal and he does have a genuine reason for being critical where "leftist" academics is going. Yet I can assure that similar nonsense can be find also in the 'hard sciences': it's just usually hidden in such complicated math and jargon, that nobody can clearly understand what kind of nonsense it is. If you would put the end conclusions in plain English, which is totally forbidden, then only the layman would notice the crap the 'academic' study is. Especially the use of math is a culprit here as if you don't understand the math, you don't understand what the whole thing is about.

    A previous similar attitude between the 'hard' (true) sciences and social sciences was by C.P. Snow and his book two cultures from 1959. There Snow paints this picture of one scientific culture, the hard sciences, still upholding the true foundations of science and then there being this soft underbelly, the social sciences and those academics who study them and their utter ignorance of nearly everything.

    Now some might argue that Snow only attacked the ignorance of social science people about science (and thus the issue simply would be that academic people have too narrow and specific areas of study), but that's actually not the case. Snow's hubris and arrogance can be seen actually from the end of the book. There he purposes that since the "other culture" has so badly lost itself, the 'true' science ought to tackle the most difficult problems of the current era, namely the Cold War and nuclear weapons armament! Well, science didn't solve the Cold War, MAD kept the politicians from not starting the war and economic realities made the Soviet Union to collapse. Something that C.P. Snow was clueless about among others.

    Yet many even now purpose that since postmodernism (or whatever leftism it supposed to be) has so badly crippled the social sciences, then natural science should take their role too!
  • Israel killing civilians in Gaza and the West Bank
    For the time being. There are elements with the government that are tired of Bibi, but sadly, many of the alternatives to him are even worse, which is hard to comprehend.Manuel
    Yes, there surely are those who are tired about Netanyahu and question how October 7th was possible. Yet the response isn't so much criticized by Israeli politicians. Just look at for example interviews of former prime minister Ehud Olmert. He's really not a Bibi fan in any way, but the response to destroy Hamas is quite there. It's as if on 9/11 we would have had a democratic administration of Al Gore: it would have gone also to Afghanistan. Not perhaps later to Iraq, but it would have gone there. To handle 9/11 like a police matter was simply out of the question. And so it is for Israel: it's at war. The real question is if another administration would want to enlarge the conflict as Bibi evidently does.

    It risks escalating into an even bigger war this time, I don't believe that, once this is over, whenever it is, Israel will ever be the same again, nor will Gaza. I see the logic you are presenting, similar to what many in the government are presenting, but it has its drawbacks too, most notably civilian losses for Israel.Manuel

    Yet civilian losses, just as in 9/11 and in October 7th, were needed to justify the war at the first place. Assume if the Al-Aqsa Flood operation had been a disaster for Hamas, if the IDF had been tipped of and it had it's forces on alert and had started the battle at the wall, then wiping out Gaza wouldn't have been tolerated! Hamas would look like the bumbling fools that in general Palestinians look like for Israelis as it is hubris that caused the breaching of the multi-million wall in the first place (because it wasn't designed against a large concentrated military operation, but small breaching attempts)..

    When there's a credible threat, a genuinely traumatic experience, it will harden the attitudes. As you said, both Israel and Gaza (and the Palestinians) won't be the same after this.

    Well, a lot can happen, but my feeling is, even if they go to war with Hezbollah, which they may very well do, Israel is no longer guaranteed long stretches of peace, that is, they won't be able to avoid significant large wars, if they do not give up some land. So this is a band-aid for a missing arm, only more troubles for everybody.Manuel
    I agree. Basically if Netanyahu overplays his hands, the end result may be a peace deal. But that would mean that the Israel lobby in the US loses it's position on the US. That is a big if.
  • Postmodernism and Mathematics
    I am interested in what postmodernism has to say about mathematics.Tom Storm
    I think it would be better to ask what postmodernism has to say about the sciences in general, not narrowing down to math. What does postmodernism say about logic? What does postmodernism say about philosophy?

    I would argue hardly anything itself.

    Postmodernism is more concentrated on society and how society works, human behaviour and those reflect on things like mathematics etc. And this very common also to for example the history of science and how social sciences look at the sciences. They aren't interest in the subject matter itself, they are interested more on the community that makes up the scientific community and how it behaves.

    Hence for example the findings of Thomas Kuhn and "Kuhnian paradigm shifts" only show how this community works and doesn't tell us of the actual science matter itself. And mathematics is in this same category.

    Yet on many occasions the mathematicians or scientist don't understand this. They think for instance Kuhn, from all people, is somehow degragading their actual field of study as if it would say about something about the science or math itself. It doesn't.

    This is something that people should understand here. It's about just how much people are Platonist and how much constructivists and what has happened for this to change. Not exactly on what post-modernism says about Platonism and Constructivism philosophically. Then you end up with nonsense.
  • Asexual Love
    Valentines Day ought be about more kinds of love.Moliere
    As already pointed out, Valentines Day is more about couples and children having friends. Especially for young girls Valentines Day is important. For boys, not so much.

    A lot of love is asexual: people love their children and their parents and their grandparents. Some even their brothers and sisters and more distant family members. And that has nothing to with sex, only that sex created families in the first place. Yet that is hardly erotic, but simple natural biology. You really have to be a disgusting pervert or a pedophile for that relationship to be erotic.

    It would be also whimsical if you would celebrate on Valentine's day your love to your country. Another literally asexual love by every way.

    Except for some idiot perverts, that is:
    b22ae3001f142a69a0b671243386797f15-29-president-trump-american-flag-cpac-20.rhorizontal.w700.jpg
  • Israel killing civilians in Gaza and the West Bank
    I don't see how they can beat Hezbollah, if they can't beat Hamas. And then what? A defeat against Hamas and Hezbollah?Manuel
    Isreal and Bibi react. Then think about tomorrow. 'The distant future' is not on their minds.

    And note, IDF cannot surely beat the movement called Hamas, but present military units of Hamas the can take out or degrade to a point that they can say to the Israeli public that Hamas isn't a threat. And that's it. That's the objective. Same is for Hezbollah they have a huge stockpile of rockets, so the issue is to destroy the existing capability. Those physical rockets and present leadership and present fighters. And with the October 7th attack having a similar effect of the 9/11 attacks, this logic can easily prevail. Why not? It's an opportunity.

    Plus Israel can justify it's actions that Hezbollah operates south of the Litani river and thus poses a threat that Israel simply cannot live with. (Of course Hezbollah argues that this is because Israel hasn't kept it's side of the deal.)

    Reminding of the slaughter on October 7th is an easy way to enlarge the war. 9/11 showed just how long this feeling will continue. The attack on Iraq on fabricated reasons happened and was very popular. Remember the time of "Freedom Fries"? Hence for Israel to deal with Hezbollah now is an opportunity. It's not when things are calm.

    So my view is that it is more likely that Israel will attack and try to destroy Hezbollah than that this war wouldn't escalate from the tit-for-tat war that it is now. Yes, the current level of conflict can be a possibility: a historical example of a tit-for-tat war is the War of Attrition that went on a bit over three years.

    Yet that hardly is what Bibi would like and the likely at least in a years time those Israelis living now in hotels somewhere else in Israel would get angry.

    Naturally "Genocide Joe" is against this. Yet it will be harder and harder for the US to keep this stance when it's already fighting it's war against Hezbollah in Iraq!

    (from nine days ago)


    Perhaps Bibi hopes that the US can get mixed up to this. After all, Bibi's objectives are portrayed as "Israel defending the US and the West". And also hopes for his friend Trump to arrive on the scene.
  • Israel killing civilians in Gaza and the West Bank
    But they couldn't "swat the fly" in 2006, when they only focused on Lebanon. How could they do so now, when they are in a worse condition, militarily speaking?Manuel
    Are they in a worse condition? I don't think Bibi thinks at all like that.

    Remember that 2006 war, which lasted for 34 days, happened because a cross border raid that left three IDF soldiers dead.

    A little bit different that what happened in Oct 7th. Just as 9/11 response was a bit different to the 1993Twin Towers bombing (when that terrorist attack was a police matter, in which the FBI caught the terrorists and put them into an ordinary US prison).

    When you have the people wanting revenge, you go all in with the war! It's an opportunity of a lifetime. Time to mow the lawn in Lebanon too?
  • Israel killing civilians in Gaza and the West Bank
    The issue then is, can the Israeli economy, and the Israeli's themselves (the citizens) be able to sustain an in-depth fight with Hezbollah?Manuel
    The question you should ask: Will Bibi be OK with a hundred thousand or more Israelis having fled their homes in the North and now having live somewhere else?

    let's remember:
    (Times of Israel, 22nd Oct 2023) Some 200,000 Israelis have been internally displaced in the ongoing Israel-Hamas following the terror group’s October 7 massacre in southern Israel, and amid escalating skirmishes on the Lebanon border in the north with terror group Hezbollah and allied Palestinian factions, according to Israeli authorities.

    About half of the 200,000 were instructed to evacuate from 105 communities near the Gaza and Lebanon borders in the south and north, while half left areas close to the front of their own volition, a spokesperson for the Prime Minister’s Office said Sunday.

    The Defense Ministry, through its National Emergency Management Authority (NEMA), said it was giving services to about 120,000 displaced Israelis ordered to evacuate from 25 communities up to four kilometers from the Gaza Strip, and from another 28 communities up to two kilometers from the Lebanon border, according to a Defense Ministry announcement.

    - You think those Israelis living close to Lebanon are happy to just come home and wait for the tens of thousands of Hezbollah rockets to be fired at them at some time?

    - Second of all, when Israel is already in a war. Why not try to kill two flies at the same time? You are already running around with the flyswatter and not minding your peaceful doings, so why not?
  • Israel killing civilians in Gaza and the West Bank
    that there won't be a wider fight with Hezbollah.Manuel
    Has it been peaceful in Southern Lebanon? I don't think so.

    F240208AMA07-640x400.jpg

    I still hold that they will go to war with Hezbollah. Because it has started already in slow burner. Perhaps after the Rafah operation.

    The enlargement of this war seems to be like how the media and the politicians treat an economic depression. First there's the denial the everything is OK. Then it's just a temporary hickup.
    And finally when the politicians admit that it's a economic depression, well, they don't have to admit it because everybody knows it and it has been on for years. They'll start to talk about it as old news.
  • Infinity
    (I think that's right, but perhaps there could be objections?)TonesInDeepFreeze
    I think it's right. But anyway, even the notion of reals would go against this argument that mathematical objects "cannot be carried out, cannot be completed" and hence are "nonsensical". And when you throw out real numbers as "nonsensical", your mathematics is quite illogical. We do need number like pi!

    Another common crank fallacy is claiming that mathematics is false by way or arguing that mathematics uses words in ways different from their ordinary meanings or different from their meanings in certain other fields of study.TonesInDeepFreeze
    The most irritating answer type is that if you ask something about mathematics and mathematical objects, people answer by referring to physics and for instance quantum physics. No, an observation of the physical reality, that we model by a mathematical model, doesn't tell if a mathematical object is true or false.

    We start from the need to move something and then build a carriage to move it, not that we just build a carriage without requirements and then try to find something that can be moved with it. Furthermore, it's even more wrong to start arguing that our primary task, need to move something in the first place, is wrong, we shouldn't even think of it, because our carriage can't move it.
  • Infinity
    Finitism can get simply ridiculous at some point.
  • Ukraine Crisis
    Russia doesn't want to be nuked by North Korea or some other rogue nation or terrorist cell either.boethius
    Why would Russia be nuked by North Korea???? Would the US be nuked by the UK or France? I don't think so.

    North Korea has just given a massive assistance to it's de facto ally Russia with the million or so munitions given to the Russian army to fight the war in Ukraine.

    Let's remember the facts here: Soviet Union created North Korea. Kim il Sung was put to be the leader of North Korea by Stalin. Soviet Union provided support to North Korea during the Korean War, where air regiments of Soviet fighters fought it out on "MiG Alley" with the Americans over North Korea. Russia has a treaty of "Friendship, Good-Neighborly Relations and Cooperation".

    FKKrHRXXIAQRTfb?format=jpg&name=900x900
    brezhnev-i-kim-ir-sen.jpg
    Vladimir_Putin_with_Kim_Jong-Il-2.jpg
    putin-un-141805705-16x9.jpg?VersionId=c2n4pQSsXLYGdXIEr6cMFazwm.prYrLu&size=690:388

    North Korean leader Kim Jong Un told Russian President Vladimir Putin on Wednesday that his country offers its “full and unconditional support” for Russia’s “sacred fight” to defend its security interests, in an apparent reference to the war in Ukraine, and said Pyongyang will always stand with Moscow on the “anti-imperialist” front.

    It's hilariously ludicrous to think that for Russia, North Korea is any kind of threat. It's one of those few loyal allies it has.
  • Infinity
    So we find this mistake commonly with examples such as what ssu suggested a bijection between the natural numbers.Metaphysician Undercover
    No, you are making a mistake.

    I suggest you to read an elementary school book on set theory. There indeed are infinite sets and there can be a bijection between these sets. It's not just "mistake" like you think.

    From "cuemath" describes this perfectly well:

    A finite set is a set with a finite number of elements and is countable. An infinite set, on the other hand, has an infinite number of elements, and an infinite set may be countable or uncountable. Yes, finite and infinite sets don't mean that countable and uncountable. There is a difference. For example, sets like N (natural numbers) and Z (integers) are countable though they are infinite because it is possible to list them. In other words, we can have a one-to-one correspondence (bijection) from each of these sets to the set of natural numbers N, and hence they are countable. On the other hand, the set of all real numbers R is uncountable as we cannot list its elements and hence there can't be a bijection from R to N.

    And furthermore, just how important is a bijection in the definition of cardinality:

    Cardinality of Countable Sets
    To be precise a set A is called countable if one of the following conditions is satisfied.

    A is a finite set.
    If there can be a one-to-one correspondence from A → N. i.e., n(A) = n(N).
    (This point is used to determine whether an infinite set is countable.)
    If a set is countable and infinite then it is called a "countably infinite set". Some examples of such sets are N, Z, and Q (rational numbers). So, the cardinality of a finite countable set is the number of elements in the set. On the other hand, if it is an infinite countable set, then its cardinality is equal to the cardinality of the set of natural numbers.
    See Cuemath: cardinality

    Perhaps you should start here:
    Lecture on infinity and countability

    Or here, just what is an infinite set:
    Mathworld Wolfram: Infinite set

    Or simply the axiom of infinity in ZF-logic:
    Axiom of Infinity

    Or if you think that there is no set of the natural numbers N, I think your contribution to any set theoretic discussion or to the subject of infinity is quite limited, to say at least. Otherwise I do value your opinions and remarks on various other subjects.
  • Israel killing civilians in Gaza and the West Bank
    I understand it, even the outside international order of the Masters of the Universe doesn’t reason in terms of “humanitarian concerns”, “international laws”, “war crimes”, “equal rights” deep down. Therefore, as far as I’m concerned, framing the Israeli-Palestinian conflict in terms of “humanitarian concerns”, “international laws”, “war crimes”, “equal rights” to obfuscate the above considerations is kind of a noble mystification, to be kind.neomac

    Yes, why should we care about international law, war crimes, equal rights and humanitarian concerns? All meaningless mystification! Why would we care about these issues when it comes to be the war in Ukraine or in Gaza? Silly nonsense, noble mystification.

    Ahhh...the argument of it's all realpolitik, baby.

    If there's real mystification, it's the idea of "Israel being the Holy Land", "Judeo-Christian heritage", or Israel being some kind of bulwark of Western values and defender of the West. As I've repeated over and over again, for Evangelists the support of Israel is a matter of faith. Isn't that mystification? The Muslims surely have similar bullshit mystification too. And even more mystification is all the crap importance that three religions put to Jerusalem. It makes the beautiful old city actually repulsive as the people that give it special importance to it (or who in history have wanted to build a new one) are repulsive themselves.
  • Ukraine Crisis
    However, the Russian perspective (at least according to Putin) was they were willing to renegotiate ABM and other treaties to deal with rogue nuclear threats while maintaining the non-proliferation architecture.boethius
    Good insert that according to Putin. Because when you look at modern surface to air missile development, the longer range systems are all basically developed to engage ballistic missiles. So the idea of any ABM treaty now is a bit hypocritical. So it's not only the Russians who are here hypocrites.

    For example Israel had no trouble of hitting the Houthi ballistic missiles and the success of the Arrow system obviously can be seen from the simple fact that the Houthis aren't lobbing long range missiles to Israel anymore. Much time has gone from the time Saddam Hussein was firing Scuds to Israel and basically got half of the USAF fighter bombers searching in vain the empty vast desert of Western Iraq.

    Now, all I've tried to explain on the subject is that building ABM missile bases closer to your nuclear opponent is a noticeable increase in first strike capability (certainly worth analyzing and placing on the list of risks to consider mitigatory action). Obviously for the Russians it's a big enough concern to take diplomatic action against.boethius
    Of course it's a concern to the Russians. But basically those ABM sites in Poland would basically protect... France and the UK. It's a simple fact that Russian nukes launched from Russia will fly over the Arctic, over Canada to hit continental US and the USAF missile silos in the center of the US. If those sites were planned to be in the tundra wastes of northern Canada, then the role would be totally obvious. ABM missiles have to be very close to the actual flight paths of the missiles as simply there isn't much time to defend against an ICBM launch.

    IMG_3171.jpeg?resize=1024%2C1365&ssl=1
  • Infinity
    That's a bijection which cannot be carried out, cannot be completed. It's a nonsensical proposition.Metaphysician Undercover
    Nonsensical?

    Seems you confusing ideas about set theory. Or ignorance about the subject.

    Set theory is part of mathematics, but of course you can be with your idea that it's "nonsensical".

    Sorry, but I did assume this thread was about mathematics.
  • Infinity
    What????

    Isn't there a bijection between the set of natural numbers and the set of natural numbers?

    If so,

    Isn't there also a bijection between the set of natural numbers and the set of rational numbers also? And a bijection between the set of natural numbers and the set of algebraic numbers? This is the reason why we have the "Hilbert Hotel" example and actually, the axiom of infinity in ZF as it's written.

    I think there is as it's the way that set theoretic books describe it and the way I've learned Cantorian set theory.

    That there isn't a bijection the set of natural numbers and the set of real numbers is basically why there is all the fuzz about aleph-0 and aleph 1. And here we get to the Continuum Hypothesis already.

    Hence infinity is actually very puzzling to us. Still.
  • Infinity
    Yes, and as I've shown over and over again, that definition of "=" is not representative of how "=" is actually used in mathematics. Therefore it is a false definition, designed for some other purpose, foreign to mathematics.Metaphysician Undercover

    So when the issue is set theory, isn't then more correct just to talk about a bijection?

    Or is that problematic too?
  • Ukraine Crisis
    We just recently experienced Trump threatening to turn North Korea into a lake of fire, maybe there's someone even more unhinged in power in the future.boethius
    We've recently experience Trump being the best of friends with Kim Jong Un. No other US president ever has met with the North Korean dictator. So go figure.

    SingaporeSummit.jpg

    And btw during Trump's administration, North Korea tested quite large nuclear weapons in 100+ kiloton range. So at least now the US isn't in denial about the North Korean nuclear weapon... as it for the first test said it might be just a large conventional explosion. But a 6,9 earthquake on the Richter scale you don't get with conventional explosives.
  • Israel killing civilians in Gaza and the West Bank
    Tell me more about Panarabist and Muslim Brotherhood's grievances, I too miss caliphates, jihadism, and sharia so badly, bro.neomac
    Muslim Brotherhood's lowest point came when their assassin tried to shoot Nasser from a short range, emptied his pistol and MISSED! Nasser just stood and continued his speech. So there's the start of the grievances between the brotherhood and the Egyptian military. At the start the Muslim Brotherhood had supported Nasser. Some say this was a conspiracy, but likely it was real (hence not a good assassin). And of course the islamists were more successful with the successor President, general Anwar Sadat, who made peace with Israel and thus was killed in a military parade. That terrorist group, Egyptian Islamic Jihad, actually merged with Al-Qaeda. It just shows how deadly is peacemaking to Middle Eastern politicians.



    Yet you should start with the history of Pan-Arabism, if you aren't familiar with it. Especially when Syria and Egypt became one country. Unfortunately Nasser fucked it up pretty quickly, even if there was genuine grass roots support for "United Arab Republic". Didn't take long that the Syrians revolted and the Egyptians to be forced out of Syria. Yet it does remind that Pan-Arabism was a quite serious movement. It's very interesting part of history.

    Nasser in Damascus in front of an enthusiastic crowd:
    Nasser_addressing_Damascus%2C_1960.jpg
    In fact, the failure of secular Pan-Arabism, especially after the Six Day War, is a result why the turning to islamism in the long run in the area. Also 1967 is very crucial to the US-Israeli relations.
  • Infinity
    Set theory begins with the assumption of mathematical objects, hence it is based in Platonic realism.Metaphysician Undercover

    You don't need to believe in Platonic realism to use set theory. Its axioms are just rules to follow when "doing" maths.Michael

    I agree. I didn't say you need to believe in the truth of the principles you employ. However, it's hypocrisy to say "I'm a mathematical antirealist" and then go ahead and use set theory. But that sort of hypocrisy is extremely commonplace in our world, it's actually become the norm now. Very few people make the effort to understand the metaphysics which they claim to believe in, and whether it is consistent with the metaphysics which supports the theories which they employ in practise.Metaphysician Undercover
    Is it hypocritical for a mathematical formalist to use set theory? I think the differences between the philosophical schools in mathematics don't actually matter so much because the differences are in the realm of metaphysics. If for a Platonist the abstract mathematical objects exist and for the formalist it's just basically something compared to an eloquent game, what's the actual difference?

    The way I see it the difference between anti-realists and realists (Platonists of some sort?) is things like if mathematical truths are discovered or invented. It doesn't change the math!

    The math in set theory is mainly about injections, surjections and a bijection, which we mark usually with "=".
  • Israel killing civilians in Gaza and the West Bank
    Jordan's king in the White House yesterday:



    According to some news agency, some Egyptian forces have been deployed to the Sinai. 40 tanks means a tank battalion reinforced with mechanized troops.

    (REUTERS) Egypt has sent about 40 tanks and armoured personnel carriers to north-eastern Sinai within the past two weeks as part of a series of measures to bolster security on its border with Gaza, two Egyptian security sources said, Reuters reports.

    The deployment took place ahead of the expansion of Israeli military operations around Gaza’s southern city of Rafah, where much of its population has sought safety, sharpening Egyptian fears that Palestinians could be forced en masse out of the enclave.
  • Israel killing civilians in Gaza and the West Bank
    Even if Hamas declared that it isn't interested in politics of other nations, naturally an organization that has very close ties to the Muslim Brotherhood isn't viewed friendly by a President that came to power in a coup deposing the Muslim Brotherhood from power in Egypt. Even if Sisi won democratic elections just short time ago, I think this reality hasn't been forgotten.

    And even if the Arab States have the Arab league and other international Muslim organizations where the Muslim countries cooperate, the Arab countries are far from being an effective group as the EU is. The EU even with Orban's Hungary. Case example is Libya and how "allies" somehow ended up backing different sides. Or then the rift between Saudi-Arabia and Qatar, which nearly went to war yet still being on the same Gulf Cooperation Council, which fought alongside the US and allies to liberate Kuwait. When you don't have democracy grounded in institutions, then military coups, self-coups or physical violence is not only something theoretical.

    Hence the instability isn't just due to the Palestinian (and the Kurdish) issue.

    And this is fine with Israel. The last thing they would want is to deal with neighbors speaking with one voice. In fact I guess that Netanyahu wouldn't mind if all were failed states and in civil war like Syria.
  • Infinity
    I think there is still a lot for us to understand about infinity.

    One reason that comes to my mind is that we haven't gotten much applied use for Aleph-2, for Aleph-3, or Aleph-4 etc. Usually correct math has a lot of applications. Physics and engineering and science uses it all the time. Cantor doesn't help it with then speaking of an Absolute Infinity. Now people dismiss this as irrelevant and just being Cantor's religious ideas (that God is Absolute Infinity), yet I don't think so. He simply didn't understand it and didn't get that kind of relevation as he did with noticing that the cardinality of the natural numbers isn't the same as with real numbers.

    Yet once you assume that there actually would be theorem for Absolute Infinity that we haven't discover, then that theorem has to clear Russel's Paradox, the 'set of all sets', or the sometimes called Cantor's Paradox or Burali-Forti Paradox. When we have a paradox, obviously our reasoning about the premises aren't correct. Because mathematics is logical.

    I think the problem is in counting itself and giving a proof in Mathematics. Mathematics has started from a need to count, not from let's create a logical system and call it math. Hence humans have made discoveries in math: that there are irrational numbers. That there are many types of geometries. Hence we can come up with new ways to think about math.

    I'm not sure if this is correct, so I'll ask here: is counting basically a way to give a proof? Because let's assume that we have true but unprovable entities in Math (or with counting, uncountable numbers). What would you get if you would try to prove and unprovable entity in Math?

    I guess you would get a paradox, because you cannot prove the unprovable or count the uncountable. The paradoxical nature is quite obvious. And the problem won't go away even with Cantor's hierarchial system.

    Perhaps the problem is that people have tried to solve the paradoxes yet still hold on to their premises, as if everything is already there in the foundations of math and paradoxes can be kept away by restrictions. Like ZF.

    I'm not saying that I know the answer, but saying that there might be here something for us to still discover.
  • The Sahel: An Ecological and Political Crisis
    Now the political turmoil has hit Senegal where a President doesn't want to end his term even if there are term limits. Senegal has never had a military coup, even if it has had to remind politicians that to uphold the constitution in political crisis earlier. Now lets see what happens, but if there would be military coup there to "restore order" or even to "defend the constitution", then you would have a straight flush in the Sahel states from the Atlantic to the Red Sea with military juntas ruling. The President has uparmed The National Gendarmerie, which is part of the Armed Forces yet a separate branch. Worst possibility would be to have a situation like in Sudan.

  • Israel killing civilians in Gaza and the West Bank
    Welcoming 1.5M desperate brother Palestinian refugees is WORSE than going to war with Israel, go figure!neomac
    With refugees, like the millions of Ukrainians in Europe, there's still this idea that they return back once the war or crisis is over. That's the whole reason why Poles and others accepted Ukrainian refugee...especially when the men of warfighting age stayed in Ukraine. But here there would not be any return. Actually Egypt taking them would be seen quite clearly as helping the Netanyahu government in it's ethnic cleansing... sorry, "voluntary moving". Not only the Egyptians know this, also the Palestinians themselves understand this. In 1948 they didn't and the idea was to come back once the war is over.

    I think the Egyptian president makes it quite clear in the article:

    El-Sisi said Egypt was concerned about Hamas elements launching attacks on Israel from the Sinai.

    “We do not want Sinai to become a base for launching terrorist attacks against Israel,” he stated.

    “The uprooting of Palestinians from Gaza to Egypt will lead to the uprooting of Palestinians from the West Bank to Jordan,” el-Sisi claimed. “We reject the uprooting of Palestinians from their land. What is happening now in Gaza is an attempt to push civilians to seek refuge and emigrate to Egypt.”
  • Israel killing civilians in Gaza and the West Bank
    My point is that, up until now, the BEST CHANCE for the Israeli-Palestinian conflict to be resolved in the best interest of both and on their own initiative was at the end of the British mandate, because, later on, the historical grievances THEY BOTH had at the end of the British mandate just kept badly growing on BOTH SIDES.neomac
    Well, then indeed you paint a very bleak picture...if that chance then was the best.

    And as I said, during that time it wasn't only the Palestinians (the non-Jews living in Mandate Palestine, if for some Palestinians don't exist). Don't forget all the neighbors who wanted a piece of the land for themselves too.
  • Ukraine Crisis
    Everything I've explained is not just "my theory about it", it is literally the New York Times explaining to us the Russia's views on the topic. I'm simply explaining the common reasons someone would have to express such an opinion.boethius
    Fine. Yet this is Russian rhetoric to give one reason more against the ABM sites. It is political rhetoric. Because just why would you put attack cruise missiles in a fixed well known position? Cruise missiles are subsonic. Did the US field ground launched cruise missiles? Actually yes, during the Cold War they had few BGM-109G Ground Launched Cruise Missile, and they were mobile. Something you hide in a warehouse... somewhere, not in fixed site with actually not much if any protection to the missiles. And FYI, those were scrapped in the INF treaty.

    1280px-BGM-109G_Gryphon_-_ID_DF-ST-83-09866.JPEG

    What's the purpose of having a slow moving weapon on a fixed, well known site? There is absolutely no logic to this, but for the Russians there is the logic to give more reasons why those ABM bases should not be deployed.

    Ok, so please explain why the New York Times writes:

    It is also equipped with missile launchers known as MK 41s, which the Russians worry can be easily repurposed to fire offensive missiles like the Tomahawk.
    — On the Edge of a Polish Forest, Where Some of Putin’s Darkest Fears Lurk

    Key word "easily".
    boethius

    Hey, those Mk 41. VLS can also easily repurposed to fire the RUM-139 VL-ASROC, an anti-submarine missile. Or they easily be repurposed to fire the Nulka decoy system to leer away anti-ship missiles.

    Key word "easily" too!

    If you would think about or understand military thinking, the Mk 41 VLS is obviously for a layered air defence system as obviously you won't use the ABM missiles to shoot down things like slow aircraft of attack drones. Because obviously forward based installations can be attacked by a plethora of various weapon systems. Layered air defence is the way you deal with different kinds of threats.

    Note the three kinds of different weapons protecting here Russian Hmeymin air base in Syria:
    1123928.jpg


    you again repeat the obvious: "they present a challenge to either a first strike or a counter strike."

    The fact forward deployed ABM present a threat to counter strike is what makes them a first-strike enabling system.
    boethius
    Yes, I think we agree on this.

    And thus both Russia and the US have put effort to make their GBAD systems capable in the ABM role. S-400 and the S-500 are quite capable in this field, so much that actually the A-135 might be replaced by the S-500. The dubious and questionable nuclear tipped ABM missiles of the 20th Century are now history. After many decades the ideas of Reagans "Star Wars" are emerging into reality. The US has built it's capability around navy warships, which by moving around on the oceans make them far more difficult target than some fixed emplacement that has permanent map coordinates.

    Rear deployed ABM protecting your own silos is where you'd put your ABM if you were just concerned about surviving a first strike and maintaining a counter strike deterrence (to then hopefully dissuade a first strike).boethius
    Or, if the possible actor has just few ICBMs and has a limited territory to shoot them from, you put an ABM site between your country and the launch site. Just look what is the shortest range between Washington DC and one certain Middle Eastern country the US hates so much. Which btw the US insisted on being the reason. :smirk:

    Russian ICBM go over the Arctic Sea and Canada into the US. Not over Poland. ABM sites in the tundra of Canada and Alaska would be a different issue.
  • Ukraine Crisis
    Why was the US concerned about missiles in Cuba when the Soviets had silos, and submarines and aircraft launched missiles and free fall bombs and so on?boethius
    Because they were actual offensive weapons! Not just SAM sites.

    By your (and others') logic here, the Cuban missile crisis was about literally nothing.boethius
    Real strawman there. Now your way off.

    Do you understand what nuclear weapons the US, France and the UK have? Those weapons don't need ABM missile sites or any kind of fixed forward sites to operate. In fact, bringing them closer to Russia just increases the ability to Russia to strike them. Please educate yourself first on the nuclear strategy of the Western powers. A fixed site has severe disadvantages: it can be targeted itself by nukes and other weapon systems. Hence there's a reason just why the US fixed silos are in the center of the US. And why Russian fixed silos aren't on the Russian border. Or that fixed Chinese sites are in the middle of China, not on the seashore.

    Russia doesn't like missile bases close to itself for the same reason the US doesn't like missile bases close to itself.boethius
    Yes. But NOT for the reason you gave. Converting ABM sites to offensive missiles sites is nonsense. The fact is simple: ABM systems shoot down ballistic missiles and thus they present a challenge to either a first strike or to a counter strike. Hence the whole reasoning for an ABM treaty.

    For example, let's say the ABM treaty was still a thing, and indeed it's as you say that the A-135 could "wiggle" out of the ABM treaty, then one may naturally wonder if enough such bases and enough such missiles all around Russia would have the same overall strategic effect that is banned by the treaty. Whether it's technically "legal" or not, obviously Russia wouldn't like that and would react to it.boethius
    A-135 is operational. They basically have it for one place: Moscow. That the way to counter MIRVs and basically the complexity of hitting an extremely fast tiny object that actually slows down extremely fast when hitting the lower parts of the atmosphere has been to use an airburst nuke. Well, even if that doesn't have the similar effect than an ordinary nuke, I wouldn't like to be under the detonation. But I guess it's OK for other places around Moscow.

    And simply there are economical limits to such costly weapon systems. If they would be cheaper, I guess the Soviet Union would have built them a lot more.



    As a military man, I'm sure you understand that the Russians view de facto US bases close to Russia as long term strategic threats.boethius
    Of course.

    Therefore, it's a prudent strategic move to try to prevent these bases getting even closer to Russia's border. You can argue that invading Ukraine wasn't the best way of doing that, but it is a way.boethius
    I think the disagreement is only in that I think that there were also other crucial reasons than just NATO enlargement for Putin to invade Ukraine. Putin has made them quite clear in his writings, speeches and actions.
  • Ukraine Crisis
    Go through this exchange and maybe consider the fact that not only is my position correct from the start:

    1. ABM bases can be converted to launch nuclear missiles.

    2. ABM is anyways a first strike risk.
    boethius
    Two things incorrect here. ABM bases being converted to nuclear launch sites is absolute nonsense. Just look at the Western nuclear deterrence: it's made up of land based missile silos in the heart of the US, submarine launched missiles, aircraft launched cruise missiles and free fall bombs. What is there to "convert" in ABM bases for these weapons? Just what system needs some fixed site?

    Secondly, Russia has had actually the first ABM system in operation for decades. It's first operational system was the A-35, which came operational basically in the late 60's early 70's. It's most modern version is the A-135 (Nato codename ABM-4) Gorgon and a newer system is in the works (A-235 Samolet-M). Modern Russian GBAD (Ground Based Air Defense) systems are also capable of target missiles: even a BUK-M1 can destroy a Scud missile (if the target is known and the air defense system is ready for the incoming missile). The S-400 is quite capable, and actually many say that Russian GBAD missiles are better than Western ones as they have focused on the missile development so much (whereas the West focuses on air power).

    Thus US created it's Nike Zeus ABM missile, btw also using a nuclear warhead as it's Russian counterpart, but the system was canceled I think by McNamara. Patriot was a lame version and actually didn't shoot anything down in the Gulf War decades ago. Only know Israeli and Western missiles have improved to the level of taking out ballistic missiles.

    And thirdly, the ABM treaty talked (perhaps intentionally) only vaguely about "strategic" missiles, namely ICBMs and SLBMs. Hence the A-135 could wiggle it's way out of the ABM treaty. There were Theater Missile Defense negotiations, but these didn't go anywhere. And the Gulf war showed that TMD was something that wasn't limited to US/Russia confrontations.

    So again to say that it was US that is breaking the ABM treaty is biased, if and when you don't take into account that Russians never actually cared so much about it and have had ABM systems operational far longer than the US had any.
  • Joe Biden (+General Biden/Harris Administration)
    I think there's a resiliency to the American identity, with a particular hang up on democracy (as if they invented it), that you'd sooner have civil war than a full blown autocracy.Benkei
    Yet the paradox here is the extreme faith in the Presidency to be this power of change, if there's something wrong with the system. (The US president is this kind of superstar, that people pin hopes upon. Just look at the Hollywood movies and their portrayal of the US president.) And be it Ross Perot or Donald Trump or anybody else, this is a very far fetched idea, but shows the thinking that the US President is this all powerful person who if not omnipotent, is something nearly so. Especially when the President doesn't have a loyal party backing him or her in the Congress. In short, it seems that many people don't like that power is decentralized.

    Thus I personally favour the president / prime minister model: the prime minister being the head of the administration, yet the president having credible power and the ability to blow the whistle and stop things if the prime minister is out of bounds. Because in the US system when the opposition party takes control of both houses, the President is simply a lame duck. Now, should there be a prime minister, that party in control has to do something, not just say no to basically anything the President proposes.

    Of course in the Parliamentary model one thing that can be hard for people to accept is that they don't personally choose the prime minister, especially in a multi-party system. The party that got the most votes might not be able to create an administration and there can be an impasse. Something that you perhaps know well.
  • Joe Biden (+General Biden/Harris Administration)
    The system is designed to resist change.Fooloso4
    Never underestimate just what voters can do.

    But yes, the voters can play with the balls given to them and not care about anything else. But once there is a will, there's a way.

    Yet actually the GOP ending up with Trump has made people believe in the system of "primaries" and biparty system, where you can change parties from inside.... and not simply have new parties.
  • Joe Biden (+General Biden/Harris Administration)
    Questions about both the mental and physical health of candidates has long been used as a political weapon. Biden might not remember it but Reagan suffered from Alzheimer's and Trump's mental health has from the start been called into question by mental health professionals - narcissistic personality disorder, antisocial personality disorder, and paranoid personality disorder.Fooloso4
    Come on... Joe Biden, the guy is like Breznev at the end. Similar vitality!!! Just look at the following and see the similarities.



    Now compare to the elan of Biden, when he's talking about Mexico being run by President Sisi and having a border with Israel:



    We just had our Presidential election. Two decent candidates, whom many said both could have been good to win.

    In the US, I just feel sorry that Americans still believe in these two parties.
  • Israel killing civilians in Gaza and the West Bank
    And furthermore, I think @Benkei already mentioned that even Hamas has changed it's view from the "River to the Sea" objective. But here...not so obviously as the PLO did, so it's easier to put aside.

    (The Guardian, May 1st 2017) Hamas has unveiled a new political program softening its stance on Israel by accepting the idea of a Palestinian state in territories occupied by Israel in the six-day war of 1967.

    The new document states the Islamist movement it is not seeking war with the Jewish people – only with Zionism that drives the occupation of Palestine.

    The new document also insists that Hamas is a not a revolutionary force that seeks to intervene in other countries, a commitment that is likely to be welcomed by other states such as Egypt.

    The response from Israel:
    Israel rejected the document before its full publication, with a spokesman for the prime minister, Benjamin Netanyahu, saying: “Hamas is attempting to fool the world, but it will not succeed.”
  • Israel killing civilians in Gaza and the West Bank
    Educate! Counterexamples?tim wood
    First of all, when PLO laid down it arms and recognized Israel, that naturally means that there is a state of Israel. Or just what do you think recognizing a sovereign state means?

    Ok, let's start with hitting two flies at the same time, the lie that there hasn't been any peace proposals from the Arab side (from the start of this millennium, there has been a second one later):

    The Arab Peace initiative

    The initiative offers normalisation of relations by the Arab world with Israel, in return for a full withdrawal by Israel from the occupied territories (including the West Bank, Gaza, the Golan Heights, and Lebanon), with the possibility of comparable and mutual agreed minor swaps of the land between Israel and Palestine, a "just settlement" of the Palestinian refugee problem based on UN Resolution 194, and the establishment of a Palestinian state with East Jerusalem as its capital. The Initiative was initially overshadowed by the Passover massacre, a major Palestinian attack that took place on 27 March 2002, the day before the Initiative was published.

    The Palestinian Authority led by Yasser Arafat immediately embraced the initiative. His successor Mahmoud Abbas also supported the plan and officially asked U.S. President Barack Obama to adopt it as part of his Middle East policy.

    but of course...

    The Israeli government under Ariel Sharon rejected the initiative as a "non-starter" because it required Israel to withdraw to pre-June 1967 borders.

    And do notice that some on the Palestinian side weren't so excited about the peace plan... just what I talked about extremists taking the helm.

    And then, to give just one example, Jasser Arafat stated even in 1988:

    (LA Times, Dec 12th 1988) PLO Chairman Yasser Arafat will recognize Israel within its pre-1967 borders in his address to the United Nations in Geneva, Arafat’s political adviser Bassam Abu Sharif said in an interview published today.

    Sharif told the largest-selling Israeli newspaper, Yedioth Ahronoth, that Arafat will clarify resolutions passed in Algiers last month by the Palestine National Council at the U.N. General Assembly’s debate on Palestine on Tuesday.
    And yes, there are many examples, but I guess even one tells the story

    So this guy simply is full of bullshit... yet the guy clearly shows what Israelis and especially Zionists think. We can be in our own reality where actual facts don't matter. People simply live in parallel realities.
  • Israel killing civilians in Gaza and the West Bank
    A South African could have said quite the same things about white South Africa. They had a democracy too... for whites. And I mean, just look at South Africa's neighbors! How many democracies do you find in black Africa? And didn't the white Afrikaners fear that the blacks would take them out? Isn't Rhodesia a good example of this?

    Of course the guy doesn't take the example of Jordania. And gives a typical bullshit lie that "all their Palestinian leaders have said they want it all". It simply isn't true. But who cares, all the Arabs want is to kill all the Jews is perfect for the current state of mind of the Israelis. And Pan-arabism of course means that Palestinians don't exist! Great logic there. Yet many Israelis think as this guy and there is nothing, absolutely nothing that will change their minds.

    Thus you have a war where both sides are adamant in their view that all the other side has these genocidal aspirations and thus no negotiation is simply impossible with these awful people. And one side is far more powerful than the other.
  • Israel killing civilians in Gaza and the West Bank
    he reason why I focused on the Palestinians is just because you seemed to question my views and suggest that Palestinians would opt for peace, stability and prosperity in the region with good relations around to the present clusterfuck.neomac
    I think the misunderstandings are mutual: my point is that ordinary people would opt for peace, stability and prosperity if that chance would exist. It doesn't.

    It is a fact that historical grievances on the Arab/Palestinian part prevailed against the UN resolution which Israel accepted.neomac
    It is a fact that Israel doesn't accept a huge number of UN resolutions, even Security Council resolutions, so what is your point?