The Ramsey number R(m,n) is the minimum size of a fully connected graph with edges colored red or blue such that there is either an m-sized blue clique or an n-sized red clique. R(3,3) is 6, which is stated as every group of 6 having 3 mutual friends or 3 mutual strangers. Ramsey showed that these exist for every m and n, I think.
But they grow very rapidly. Ramsey theory has usually the biggest constants found in mathematical papers.[1] There is a famous quote by Erdos:
"Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack."
What always gets me about Graham's Number is that you can't even write down how many digits it has using the entire observable universe ... but "the last 12 digits are ...262464195387".
It's so big that going from the number itself to the number of digits (i.e. taking its logarithm) is not even something worth talking about. It's like blowing a kiss to an exploding nuclear bomb.
You just get dizzy even thinking about it. The observable universe is just not really that big when talking about this stuff, there are not even 100 orders of magnitude in the universe from smallest to biggest. Anything that you can have a conception of (even stuff like the number of possible lottery tickets or possible books that could ever be written etc) is just indistinguishable from mundane everyday sizes when dealing with googology. You're trying to roar but it comes out as a whisper. You have to explicitly design these. Most of the time if you think "but wouldn't it be comparable if we counted the XYZ) the answer is no.
It's like an adult equivalent of a kid saying "I get that galaxies are big, but are they also bigger than really big houses? How about a house with its own swimming pool? Really really big mansion of a big movie star?"
Edit: Tone is difficult in writing, I don't mean to be condescending, I'm getting dizzy myself when thinking of this and remember my frustration and amazement when first hearing about these.
Another fun property of this is that you can use it across bases. For example, how many bits would I need to represent 34812923 in binary? log2(34812923) = 25.05 -> round up to 26 bits.
Thank you for posting this. The significance of this statement was lost on me until you pointed it out. Going by MathOverflow, it's slightly more complicated than that, but it's pretty close.
And, as it always goes with the Gramham's number, all your physical metaphors for how ridiculous small metaphors go are so ridiculous small that if I try to convey the factor with a metaphor it will make almost no difference.
Or, in other words, blowing a kiss against a nuclear blow? That absolutely hugely more relevant than taking the log of the Graham's number. I can't even say how hugely more relevant it is without an almost equally irrelevant comparison.
(And yes, I am certain you know this. It's a pedantic clarification, I hope it made the point clearer.)
Yes, I agree, but your correction also doesn't make that much of a difference, even after realizing this, we're still far.
On the other hand there is just maybe a page of explanation needed for a somewhat educated layperson to understand the construction of Graham's number.
So on one hand it's unexplicably big to the point where it's even unexplicable how unexplicably big it is etc, on the other hand it can be compactly described. It's an example of the power of thought and reason and deliberate design, making so much of so little.
Add Turing to the list, having him around during the naissance of molecular genetics and the flowering of computation would have made those fields all the more lively.
I rather think making arguably the biggest individual contribution to winning the biggest war in history is a pretty big contributor to his game. His role in the founding of computer science also doesn't hurt.
In terms of a metric akin to "mathematical DALYs", Galois was perhaps the most impactful early death of all, followed by Abel. Both Galois and Abel founded entire branches of mathematics before the age of 25.
Good question, maybe he shouldn't be on that list. I'd read a long biography about him in German ("Wer ist Alexander Grothendieck?"), and was left with the impression that he was unfulfilled and unhappy at the end of his career; of course he lived to old age and there were certainly worse fates on that list, so perhaps its inclusion is not so appropriate.
And doubtless several more. By the way, not only are Scholze and Tao outstanding talents, but very nice and humble, as in ACTUAL nice and humble, and they (especially Tao) write in a crystal clear way so they are wonderful as expositors and academic writers. Makes one chuckle comparing that to so much unrestrained ego online.
Yes, my favorite thing about Tao is how well he explains concepts on his blog [0] and on mathoverflow[1]. He does not put on airs of being an unapproachable genius. I guess he knows he has nothing to prove
This is much more satisfying way to think of these concepts. The idea of thinking of convolution as a 'fuzzy' optical phenomena, the idea of thinking of n-dimensional space as a probability distribution.
It's interesting the way he grounds his intuition in practical applications. For convolution for example, a common application is to convolve a 2d image with a gaussian kernel to fuzz the image. I know that, but always still had a not-very intuitive, but very dry and technical understanding of convolution as a sort of dot product of two vectors representing the underlying image and the kernel. Terence Tao in contrast exploits the practical intuition of 'fuzziness' in this process to suggest thinking of convolution as a fuzzy (probablistic) addition of functions. It's a subtle step, but giving some sort of physical, or visual intuition for mathethematics like this is so helpful.
Yep being a lowly engineer who loves math I always wanted to learn a more rigorous approach, but then again I am lazy, so for example I started with Rudin, but gave up as soon as I couldnt grasp something, same with other analysis books and lecture notes. Then comes Terry with his 2 jewels of books on Analysis, but I thought to myself, no way I am going to understand anything from arguably the best mathematician in the last decades. But not only the prose is clear and unpretentious the motivation of why analysis is "needed" is presented perfectly, the books are self-contained and the progression is very smooth,no pun intended. Highly, highly recommended.
He thinks in a very expository way, it seems. There's aother guy, Gromov, who is the opposite. He is famously mysterious (people sometimes joke about "speaking Gromovian").
I'm so curious what it must be like to have that kind of mind. Just did a quick Google and his IQ is around 230. I mean, it's hard enough to really understand what anyone else's subjective experience is like, but I think it's literally impossible to get a true sense of what it would be like to be that intelligent (for those of us who are nowhere close). With that great a difference it's got to really be a difference in kind, not just degree.
Owing to the way IQ is defined, nobody has an IQ over 200.
IQ doesn’t measure absolute intelligence, but rather assumes it is a normal curve and maps that to human friendly numbers: mean 100, standard deviation 15 or 16 depending who you ask.
The same thing has the curious side effect that if the number of people in comas at any given time is greater than 1, then coma patients must have an IQ > 0.
OK, so if all IQs could be mapped accurately onto a normal curve with a SD of 15-16 you wouldn't expect anyone over 200. But standardized IQ tests can most definitely give results over 200, and do. And presumably someone who scores 250 on an IQ test is likely to be more intelligent^ than someone who scores 200 on the same test.
^in the sense that it measured by IQ tests, anyway. Point being it shows a real difference; deltas over 200 aren't meaningless.
Terence Tao's intelligence is not predicted by IQ. Plenty have higher IQ and achieve less. Some lower and achieve more.
IQ is total pseudoscience nonsense of zero value to anyone or anything.
It's one genuine use is as a fig leaf for the very worst kind of racism. Treat it and anyone touting IQ an indicator of anything with extreme suspicion. Nazis love IQ. Goodwin's. /Thread
Why do you consider IQ to be pseudoscience? It's the bedrock of psychometrics. Just because some people use some IQ data to justify racism doesn't mean the measure is unscientific. Nazis loved nuclear physics too, it doesn't mean the field is pseudoscience.
Take any large multivariate problem and look for a regressor against some dimension. Say, car speed. You will find that there is a good variable that links that. But that variable won't be explanatory or even correct.
I know this isn’t your main point, and I might just be remembering British wartime propaganda (my parents told me several things that later turned out to have been that), but…
Wasn’t the Nazi nuclear program severely delayed by their race-based hatred of Einstein for being Jewish?
This is an argument against doing physics the way the Nazis did (ie deriding certain theoretical paths as "Jewish physics"), not an argument against doing nuclear physics at all because the Nazis did.
The latter is what this thread is talking about: it's obvious that we shouldn't be studying psychometrics the way the Nazis did, but it's not obvious that we shouldn't be doing it at all because they did (as with nuclear physics).
Hilariously, even harry8's complaint that the Nazis loved IQ is precisely backwards: Hitler banned IQ testing for being "Jewish" too.
EDIT: I actually was curious about this last claim, so I checked the source that the Wikipedia article points to. While this text was written by one of the most-cited psychologists in history, there's little else out there to concretely corroborate or refute that IQ testing was _banned_ by the Nazis. The evidence indicates that their attitude was somewhere between apathy and hostility towards the tests.
No you're a bit too literal. Nazis sadly are not dead and gone, not limited to 1930-45 Germany.
IQ is loved by Nazis as proof of master race bullshit. Really.
Treat IQ with contempt. It's an indicator of idiocy in a discussion. (All of us are capable of idiocy in discussions, including me, don't fall for the IQ trap. You're above it. We all are).
Environmentalism is an important part of neo-Nazism (and other strains of fascism) too. Do you think that automatically tars anybody who thinks we should pollute less? I appreciate the point you're trying to make, but you're letting labels do the thinking for you (or as I've heard it put recently, "engaging in idiocy").
I don't personally believe that racial IQ differences are significant or salient to differences in population outcomes, nor am I convinced that claims are well-founded that IQ determines individual outcomes to a significant degree. But I don't advise treating it like a magic word that shuts off the thought centers of your brain. If you think it's a useless concept, you should be able to articulate why by pointing to the science (or lack thereof), not by letting Nazis tell you what you're allowed to think critically about.
This is getting closer to making a reasonable claim, but unfortunately, an unsupported assertion is the _beginning_ of making an argument, not the end.
Most of the relevant scientific community disagrees with your assertion that IQ is purely pseudoscience. From Wikipedia:
> Clinical psychologists generally regard IQ scores as having sufficient statistical validity for many clinical purposes.[25][68][69] ... "On the whole, scholars with any expertise in the area of intelligence and intelligence testing (defined very broadly) share a common view of the most important components of intelligence, and are convinced that it can be measured with some degree of accuracy." Almost all respondents picked out abstract reasoning, ability to solve problems and ability to acquire knowledge as the most important elements.
There's plenty more on the topic, and as always, Wikipedia is a great place to start your search for sources.
In what way is your blanket dismissal of the scientific consensus different from anti-vaxxers ("the only use of vaccines is support for Illuminati mind-control!!) or flat-earthers ("the only use for a round earth theory is support for, uh, the globe industry!")? Or for that matter, what makes you different from IQ essentialists like neo-Nazis, that take a nuanced scientific concept and flatten it into an all-or-nothing perfect predictor of outcomes? Hell, at least they're _directionally_ in agreement with the scientific establishment about the validity of the concept.
The onus is on those making the claim to provide the evidence. A claim without evidence can be dismissed without evidence.
There is no evidence. Dig into anything that is claimed as evidence and it's clearly invalid, at best. As a statement of the overwhelimingly obvious: the field of Psychology has issues. It knows this. You've heard of the "replication crisis." There are those trying to right it and treat it like it is actually science and rip out all the pseudo-bs that psych is redolent with. Good luck to them. Maybe they'll even remove the utterly discredited stanford prison experiment from every single first year psych textbook? Or keep it as yet another example of collective delusion in the discpline caused by faked research? Yet another one. But in every textbook. Credibility?
"On the whole, scholars with any expertise in the area of intelligence and intelligence testing (defined very broadly) share a common view of the most important components of intelligence, and are convinced that it can be measured with some degree of accuracy." - Anyone who disagrees and asks for the evidence is defined as lacking expertise. It's frigging comical. But it does screw up lives and justify racism so, there's that. Get told you're stupid as a child, there's a good chance that's self-fulfilling.
There is ovewhelming evidence that vaccines work. Seen a polio case, well, ever? There is none that IQ is a useful scientific metric. See Egas Moniz's Nobel prize for how psychology can move as a discipline on mass without evidence. Or maybe butchering brains and getting nobel prizes for it isn't clear enough evidence that you can't take anything in psychology "on trust" anymore than you can physics.
IQ is a disgrace. It is already and will continue to be increasingly sighted as how bad the discpiline of psychology has been for the past 100 years. May they own their shame and do better. Your IQ score being higher than mine means absolutely nothing. My IQ score being higher than yours means nothing. Absolutely nothing. Zero. But yeah, you can convince people it's has meaning and use it mess up lives - even if you don't intend to do that. Like the altruistic motives behind lobotomy and the success they had with the Nobel committee.
I wonder if you constantly challenged yourself to see and feel from others perspectives, all the time. Perhaps one day you may understand what it’s like to have that kind of mind. At that point, would your IQ also be around 230?
I think challenging yourself to see from other people's perspectives is probably a great thing to do. But no, it's not going to somehow increase your innate intelligence to super-genius level.
Why does it need to be replaced? Get rid of it entirely. Intelligence comes in myriad forms and trying to reduce it to a single three digit number is such a naive, ignorant idea to begin with.
So how do we measure whether someone has an intellectual disability and needs special schooling? How do we decide who we can draft into the military? (It used to be an IQ of at least 83)
But would the tests be measuring something that a generalized IQ test wouldn’t? It seems better to have one standardized way to measure whatever it is IQ tests are measuring and then use applicable thresholds for your domain.
Is the test for a driver’s license the same as the test for a calculus exam? Of course not. I see no reason why the educational system or military draft is any different. As I said before, intelligence comes in a variety of forms, so the focus should be on fixing the system to account for this, not categorizing certain students with so-called learning disabilities because they don’t fit into the institutionalized definition of intelligence, which is measured on this extremely oversimplified scale known as an IQ test.
IQ tests are perfectly reliable for predicting learning disabilities. If someone scores very low on an IQ test, they will not function well in a normal school. Neither will the function well if they score very high. They’d be bored out of their minds.
I’m struggling to understand your problem with IQ tests. If you have an IQ of between 90 and 110 as per a standard test no one really cares. You’re “normal”. Score higher maybe a bit more intelligent at spacio-temporal problems and it’s probably a good predicator that you’ll do well at mathematics.
If you score below 75 you almost certainly have an intellectual disability and need help. You can give these people any other test you like, it will make no difference. They won’t “function” in a society where the mean IQ is 100 (which it is).
As a previous commenter said Terence Tao is a living genius currently. But also, some people that (somewhat) recently rose to fame in the field of mathematics are:
Andrew Wiles, for providing a proof to Fermat's Last Theorem.
Grigori Perelman (and Richard Hamilton), solver and winner of the Millenium Prize Problem: Poincare's Conjecture.
Euler is really the master in terms of sheer volume and mathematical scope. You supposedly could get a theorem named after you if you discovered it in Euler’s notebooks (though probably well picked over by now).
Not that well picked over. After about 100 years of work and several volumes being published, the work on producing the complete collected works of Euler is not done.
Judged by the number of multiple-surname ‘things’ on both pages, Gauss seems to have been more of a collaborator, or more of his discoveries were also made by others at about the same time.
> Lydia made the mistake of remarking, “What a beautiful tree,” presumably too casually, whereupon Wittgenstein glared and demanded, “What do you mean?” and she burst into tears.
There’s lots of great stuff in Ramsey theory. In some sense it feels quite different to a lot of other mathematics. It also has the great property that it is typically very hard to look at a statement in Ramsey theory and know if it is likely true or not, or even if it will likely be easy to prove or not.
For example consider a recently disproven long-standing problem of Ramsey theory:
Is it possible to colour the natural numbers with two colours such that no Pythagorean triple is all one colour?
This question was asked by Ron Graham many years ago with a $100 prize for the answer, assuming it would be reasonably easy to prove. It was recently solved with an absolutely enormous multi-terabyte computer proof. It turns out you can colour everything up to 7824 fine but no choice for 7825 is sufficient.
If anyone from the New Yorker sees this, here is what your user interface looks like to the average reader of your online newspaper: https://imgur.com/a/kCoxLHR
Given the media industry's history, I'm sure if anyone relevant does see your post, that white space is simply going to be used as display ad real estate.
>>Discounting the interests of future people, Ramsey wrote, is “ethically indefensible and arises merely from the weakness of the imagination.
Climate change, the federal debt, increasing shareholder value over anything else, I wonder what Ramsey would have to say about the current state of the world.
He might well say that the problem is that it is not growing fast enough and that concerns about the federal debt or climate change are morally indefensible. (An example of this: the coronavirus crisis has exposed the scleroticism and poverty of the present, and the extent to which the 'unseen' has been sacrificed by regulators and how other less important issues have distracted from important things like pandemic prevention.)
If you take Ramsey's ideas about intertemporal consumption and the bliss point seriously and you try to do an empirical calculation, it generally implies that the utilitarian thing is to have savings/investment rates anywhere up to 98% (!!!) vs the current savings rate of ~0%: https://plato.stanford.edu/entries/ramsey-economics/#NumeEst... See also 'turnpike theory' which builds on Ramsey and also finds that generally, the optimal thing is to grow as fast as possible to hit the limits as quickly as possible and only then start consuming: https://en.wikipedia.org/wiki/Turnpike_theory
I don't think you mean this... But it sort of sounds like you are saying it doesn't matter how we increase the number after the dollar sign as long as we manage to do so.
Climate change is bad but the federal debt is good. It allows the private sector to be net savers and creates overall stability. It’s also clearly sustainable, hundreds of years and counting.
Presumably there is some threshold at which debt (or the rate at which we acquire it, or one of the aforementioned adjusted for population) is a bad thing and unsustainable, right? This is a genuine question—macroeconomics is counterintuitive to me.
It is bad when it causes excessive inflation. The "debt" in itself can never be unsustainable, since it is denominated in USD, which is a floating fiat currency that the US government controls. The US government is the source of all dollars, so it can never 'run out of dollars'. However, printing too many dollars can lead to inflation. So the deficit could be called unsustainable if it causes unwanted inflation.
Debt does not (necessarily) mean high taxes in the future.
Deficit is Government spending - Tax collected. High deficits might lead to inflation. One way to control inflation would be to increase taxes(draining money out of the economy)
> In general, when the government consumes a lot, the private sector can consume less of the national product.
This is not exactly true. When there is still "slack" in the economy(it is not at full employment, the private sector isn't investing for other reasons etc.), government spending tends to have low inflationary pressure. It is only when the economy is operating at peak productive capacity that government consumption crowds out private sector consumption.
> Debt does not (necessarily) mean high taxes in the future.
You are right, that's why I called it another possibility. To list them all explicitly.
Higher debt now means that the future either has default, higher (than anticipated) inflation or higher taxes.
(A steady inflation doesn't do anything to debts: at the time the debt is incurred, any anticipated inflation shows up in the nominal interest rate. Similarly, getting a reputation for defaulting increases your nominal interest rate. A reputation for high taxes doesn't do anything to the interest rate directly.)
Responsible governments try to avoid default and ever increasing inflation. That leaves taxes. Or taking on less debt in the first place.
About slack:
Modern central banks target inflation. If there's slack like you describe, a competent central bank will inject more money until inflation is at the target.
Central banks wire their profits to the treasury. That includes the seigniorage income they make from propping up inflation back to the target.
That's just bog standard monetary policy. And doesn't crowd out private sector investment and consumption and is perfectly capable of picking up any slack.
(That's not to say the fiscal side of government doesn't have any effects at all. But that's more on the supply side.)
ISTM just looking at the federal debt as a single number is a bit misleading. Any treasury debut held by the Federal Reserve (in US terms, or similar central banks of other countries) is effectively interest-free, so it is certainly sustainable. The only downside there is the potential for inflation if it's done too much.
Debt help by citizens of the country is also somewhat neutral in terms of sustainability. The government needs to pay interest on it, but the money ultimately goes into the economy, so that might also be sustainable in larger amounts than might be intuitive.
Foreign-held debt is another matter, and I'm not enough of an expert to speak on the ramifications there. But I do think in general it's important to recognize that national governments which control their own monetary policy are a very different beast than a household or a business, and so their debt liabilities can't necessarily be thought of in the same way.
Foreign held debt is not much of a problem in principle, if the interest is lower than what the country earns from owning foreign assets.
But government debt is a problem even if the government doesn't go bankrupt:
You are right that a government that can print its own money can hardly go bankrupt financially. But it's perhaps not ideal for the government to consume ever increasing portions of what the nation produces? Forget about money and finance for a second: given the same material resources the private sector is usually more efficient at satisfying human wants.
> given the same material resources the private sector is usually more efficient at satisfying human wants.
I think this is a very dangerous simplification. There are certainly areas where private sector does a much better job than the public sector. But there are also areas where the public sector in general is superior. Examples are things like healthcare, infrastructure and education.
It’s not obvious that the public sector does a better job in healthcare, infrastructure or education. Rather we as a society feel that those things which should be available to all regardless of ones circumstances.
If you only educated those who could pay, they would be able to get educated more cheaply than our current system. However, this would eventually destroy the economic productivity of our country.
The private sector tends to do poorly in any area where the returns on an investment are not captureable by the investor individual but instead accrue to society as a whole.
The returns to education mostly accrue to the one get educated. So the private sector is perfectly capable of providing education. (And we see that in practice.)
If you believe 'The Case Against Education' the individual captures more than 100% of the net returns from education, ie there are negative externalities. That means society consumes more education than is optimal on utilitarian grounds.
That conclusion is counter-intuitive, but the argument is simple: education is mostly a signalling arms race.
> Caplan argues that the primary function of education is not to enhance students' skill but to certify their intelligence, conscientiousness, and conformity – attributes that are valued by employers. He ultimately estimates that approximately 80% of individuals' return to education is the result of signaling, with the remainder due to human capital accumulation.
There is certainly a LOT of signaling involved in education. As a college dropout and self taught developer this is intimately clear to me.
However, I have traveled enough of the world and lived enough places to see what happens when education systems are weak or non-existent. I think you underestimate the degree to which high levels of illiteracy and innumeracy absolutely destroy the potential for economic growth and prosperity.
It is possibly true that we (the USA) consume more education than is pragmaticly optimal. However, removing public education would result in a loss of economic output that far exceeds the savings. Predicting who will need that education sufficiently accurately is imposy for both society as a whole and for individuals contemplating their future.
Hypothetically - actually not so much - this was one of the issues in 2008.
If the financial system creates such quantities of debt, that the regular capital and interest repayments exceed the available money supply, that would be a hard threshold. This is quite a large number if you calculate, even with high interest rates, so highly unlike in practice. Plus bank lending has a side effect of money creation, which stops it happening within the banking system.
However government debt and company bonds are non-bank debt, and securitised loans also don't have the money creation property, so one of the issues in 2008 can be presumed to be that the expansion of the debt supply relative to the money supply probably did become an issue in some countries.
Probably, but it will depend on the interest rate.
The lower the interest rate, the higher the safe level of debt.
Right now federal bonds have a negative interest rate, so perhaps there is no limit to the amount of debt, and in fact that there might be a minimum safe lower bound. Or maybe not; we don't have much experience in dealing with this sort of situation since it was seen to be impossible.
Putting that aside, the UK had debt around 200% of GDP after the Napoleonic Wars, and eventually paid most of it down. So the "bad & unsustainable level" appears to be well above that.
That was in the midst of the Industrial Revolution and during a time when the UK also had direct and indirect control of exploitable colonies, I don't think the debt to GDP figures of the time are particularly relevant to modern nation states.
Japan has avoided financial collapse with a giant debt to GDP ratio for years now, I think the advent of QE and owning your own debt via central banks has made the whole thing seem a bit silly.
The question is: can you think of any that involved debt nominated in the country's own currency?
All examples I've ever read or heard of involved foreign currency debt, or to be more precise, debt in a currency that the country in question didn't control (e.g. developing countries with USD-denominated debt, Euro-zone countries, historical cases with debt denominated in gold, etc.).
> By the mid-1920s, interest on [British] government debt was absorbing 44% of all government expenditure, [...]
That definitely sounds like an issue. Without the debt, they presumably could have cut taxes in about half.
(And gold standard or not doesn't make too much of a difference, if you have a firm commitment to keep inflation in check and not to default on your debt either.)
> > By the mid-1920s, interest on [British] government debt was absorbing 44% of all government expenditure, [...]
That definitely sounds like an issue. Without the debt, they presumably could have cut taxes in about half.
That's not an issue if, by taking on the debt, the government allowed the economy to grow sufficiently faster.
The conservative analogy to a household budget doesn't make sense. Analogizing to a startup where you're best off taking on debt for more capital, to increase growth, also don't make sense. But it's an open question, which of these makes the least sense.
> That's not an issue if, by taking on the debt, the government allowed the economy to grow sufficiently faster.
Perhaps. Though that's a big If. Most government expenditures in practice are more like consumption than investment. (In Britain's case, the expenditure was sui generis: the first World War.)
So the yardstick for 'sufficiently faster' is not some absolute positive return, but the comparison to what the private sector would have done with the resources.
> The conservative analogy to a household budget doesn't make sense. Analogizing to a startup where you're best off taking on debt for more capital, to increase growth, also don't make sense. But it's an open question, which of these makes the least sense.
Please explain. As far as I can tell, making the household budget analogy work is almost the definition of competent monetary policy. So that analogy is more of an 'ought' than an 'is'.
The 'startup analogy' is perhaps more apt for small open economies. Though even there the total amount that foreigners are willing to lend the country as a whole is probably finite and limited by the country's total future earnings. Those total future earnings have to pay back the debt; either directly in the private sector, or indirectly via taxes.
Now, IF you have incompetent monetary policy, then indeed the household budget analogy breaks down. Incompetent monetary policy means that total nominal spending in the economy is not stabilized, and so fiscal stimulus MIGHT make sense.
(Interestingly, the conceptually simplest way to have competent monetary policy is to have no monetary police. Ie leave note issuing to a private laissez faire financial sector. That tends to stabilize total nominal spending in the economy. See the Canadian experience https://www.alt-m.org/2015/07/29/there-was-no-place-like-can... for a close enough approximation in the real world.)
Crowding out in the sense of preventing the private sector from using resources would only happen hand in hand with inflation, which an earlier commenter already identified as the real limit of deficits.
Crowding out in the traditional sense of discouraging the private sector from investment is really a function of interest rates. For a government that runs its own, free-floating currency, interest rates are a policy variable independent from deficit and debt.
That even competent monetary policy cannot be relied on to make the household analogy work was proven empirically beyond any reasonable doubt via the famous "zero lower bound".
There is also the question of whether monetary policy should even try to make the household analogy hold. This is ultimately a political question, and especially in a democracy there a good reasons why it shouldn't.
> That even competent monetary policy cannot be relied on to make the household analogy work was proven empirically beyond any reasonable doubt via the famous "zero lower bound".
The zero lower bond is not a problem. You can still do unlimited QE, independent of interest rates. Or you can do what Singapore does and not use interest rates as a policy instrument at all (they use foreign exchange rates; the US could use eg a basket of commodity prices, if they wanted to).
Venezuela, Russia and Ukraine all defaulted in debt in their own currency as recently as 1998. Argentina has had an ongoing partial default in peso denominated debt.
I don't know much about what you're referring to, and a cursory search did not provide any evidence that the root cause of sustained high inflation in Brazil was debt at any time, much less debt in Brazil's own sovereign currency.
Nobody disputes that bad governance can lead to high inflation. The point of dispute is whether we have to reduce debt today because in the future that high debt may lead to hyperinflation, recession, or some other negative economic outcome that is so bad that its badness would outweigh the badness of austerity measures implemented today.
Honestly, I have never seen any serious debate on the issue, mostly because I don't know of anybody that from the late 70's up to 94 that even contested it was caused by the ever growing domestic debt.
But yes, now that you have cited it, there aren't many mainstream media articles in English that say it. I couldn't find any either.
In fact the compromise that led to the location of Washington DC, was one factor that led to New York being the major money center of the United States. Hamilton (of New York) wanted the new federal government to assume the unpaid revolutionary war debt of the States of which New York had quite a bit. Virginia had responsibly paid off all of its revolutionary war debt, and felt it ought not be saddled with other states debt, so as a trade off the new Federal district was moved down to Virginia. When the state debt was federalized, much of it was held in NY which became the place to buy and sell it.
Another amusing story about US sovereign debt is the Louisiana purchase. As the story goes Napoleon sold Louisiana to the United States to raise money to finance his wars. The US didn’t have cash on hand to pay, so they floated the Louisiana 3’s which were bonds that paid 3% to raise the money. The agent for the bond sale was Barings, and they were sold on the London and Amsterdam markets. So it was largely the British investing class who were literally financing Napoleon.
If there's one thing sorely lacking from the public discussion about what you mentioned, it's a balanced and thorough evaluation including reliable estimates for the effects.
The federal debt has had no observable effect whatsoever for decades, the dollar is as strong and internationally valued as ever. Climate change has not made anything measurably worse in the 3 decades people have been screaming about it. The bit about shareholder value is too unspecific.
> (As an Oxford mathematician, Martin Gould, has explained, Ramsey theory tells us, for instance, that among any six users of Facebook there will always be either a trio of mutual friends or a trio in which none are friends.)
What is the sensible/true version of this? Clearly it’s not correct as stated. You could have three pairs of two mutuals. You could have five mutuals and a singlet. Or six mutuals. Is it more a statement about probabilities?
Thanks. I still think the wording of the original description isn’t great. If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are friends, not that all of them are friends and therefor three of them are friends.
But I suppose I will choose not to die on the hill of slightly misleading language and admit I was just wrong.
This is a classical joke among new students to Mathematics to break the habit of the English language description being translated to the Mathematical problem statement.
It goes in a question and answer format something like: "You knew a girl in high-school. In situation A, you find out years later that she is a stage actor and a dancer. In situation B, you find out years later that she is a stage actor. Compare how likely the second one is to the first one" In plain English there's an implied meaning of "she is a stage actor and not a dancer" in situation B. But that is not the statement. Situation B is as likely or more than Situation A but not if you use the English language description which suddenly is under-specified without real-world information.
Obviously you pick the things to play to the priors of the person you're asking so that if they think actors frequently dance you put that in there. That leads them down the false rabbit hole of whether it's "stage actor and dancer" vs. "stage actor and not dancer" that you're comparing.
> If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are friends, not that all of them are friends and therefor three of them are friends.
In pragmatics (a subfield of linguistics) this is called "conversational implicature" - in particular it's an example of the "maxim of quantity".
Which is to say, you are correct about how the language works and mathematicians are a little weird.
Let the 6 nodes be users, and color edges between two users red if they are friends, blue if they are not. I think it's true as stated, as another comment claims.
