Wrong paradox, Tim. The wiggly curve converges uniformly to the line segment [0,1] while its length tends to infinity. Sorry I don't have the image. — jgill

What paradox is this? I tried to look it up but only found the staircase paradox itself. Is there a path that converges uniformly to the unit interval but whose length is infinite?

It's a perfectly respectable opinion all over the media, certainly not original with me.
— fishfry

Ugh. Come on. — Xtrix

I'd let this go but I'm really curious to understand your thinking.

I agree Hillary as the nominee is unlikely. But you think even mention of it is somehow beyond the pale. But I have seen much speculation along those lines from both the right and the left side of the commentariat for months. I just don't see why you think even mentioning the idea as a speculation is somehow wrong. I mean, Hillary's been all over the place in public the past few months, and when asked about her intentions she coyly says, "I never say never."

How do you figure that's not sufficient justification for raising the question?

Please try to answer this in complete logical sentences, not "Ugh . Come on," which is not helpful.

Of course there will be involvement with private hospitals and private insurance, to a degree. — Xtrix

Those involvements are exactly what makes Medicare so popular; and they're exactly what Bernie and Liz want to abolish.

You've made it clear you're not interested in learning anything "in detail," so why bother? — Xtrix

Your reading comprehension issues noted.

I did not say I'm not interested in learning. I'm actually quite knowledgable on health care policy and economics. I stated that I don't feel like talking about it right now in this thread. Needless to say you couldn't help yourself not to lie about what I said.

So you don't. You might have stated this clearly from the beginning and not waste my time. — Xtrix

Any time you spent in my presence made you less ignorant. It was time well spent.

Bernie would not accept. Trump has been part of the political corruption on both sides of it... the buyer and the seller of public policy. — creativesoul

I think he would. Of course Trump would never do it. It's just an idea. But I do think that if they did, that ticket would win 50 states. The US is on the verge of a populist revolution. If the establishment doesn't crush us first.

↪fishfry So Whoopi is secretly a fan of Trump — Benkei

I used that example to illustrate the fact that while it is no doubt highly unlikely that Hillary will be the eventual nominee; it is nevertheless not completely beyond the pale to so speculate. That was my only point.

How? — Benkei

I'm afraid I'm talked out on health care policy for now. Thanks for your good questions, I'm worn out!

Isn't that what Medicare did already? And you've noted it but I'm not sure what your ethical position is in it. — Benkei

Well Social Security too. That's FDR's legacy. FDR and LBJ, the two great liberal creators of our social safety net. I'm all for a social safety net.

The problem isn't ethics so much as demographics and economics. I don't feel like looking up the numbers but you know that at the time of FDR there were a lot more workers supporting each retiree than there are today. And modern medicine is keeping geezers alive a lot longer.

I don't know what the optimum reforms would be. I do have a personal experience though. When I was young a friend of a friend who was an insurance salesman sold me a health care policy. I was broke and the policy was cheap. Long story short I was in an accident and the insurance took care of everything and I had no problems. Since then even as a sometimes self-employed person I've always made sure I have health insurance.

The kind of policy I got is illegal under Obamacare. I could never have afforded the Obamacare premium and like most young people today, I would have just paid the fine and not had health insurance. My life might be very different if I hadn't had the excellent care I got at the time.

You are right that with Medicare the young subsidize the old. But it's much worse with Obamacare. I don't know the numbers. I only know that the policy that practically saved my life decades ago is flat out illegal today. I don't think that's a good idea.

From a pure numbers game, the greater the group mutualising the risk the cheaper the insurance becomes. This explains why, on average, healthcare costs rose less than the years before Obamacare.

For me, policy that benefits the greatest amount of people at the least cost makes the most sense economically. Besides, young people grow old. They will benefit eventually and they can see it as paying more now so they can pay less later for coverage. So I also see a benefit at the personal level. — Benkei

Not buying it. Had an experience to the contrary. Obamacare specifically made things worse for young people to a degree never before seen. My own life would have been radically worse if Obamacare had been in effect. So you will never make your point with me on this.

Sometimes it's OK to just say "Yeah, that was silly." This is an online forum - no need to save face. Why go on defending the indefensible? Because I can't get myself to believe you actually believe what you're saying. You're smarter than that. — Xtrix

I figured out the election.

What do you think of Trump dumping Pence and choosing ... Bernie! Right now the left is angry that the DNC has schemed to prop up Joe Biden in order to "coalesce" around cognitively impaired Joe. And the same people who were themselves calling him that just a few weeks ago, are now pretending to be outraged that I would dare call him that. Why, it's just like those vile health smears on Hillary in 2106. Yeah till the day they had to throw her in the back of a van like a sack of potatoes.

So where do the Bernie bros go? Some will stay home, some will vote for Trump, some will hold their nose and vote for sleepy Joe. What if Trump dumps Pence -- which he should anyway, Pence has a very weird and creepy vibe and adds no value to the administration at all -- and picks Bernie. And explains it: "Yes we disagree on specifics, but we both know things in this country have to change! And we are listening to the people!"

I say that ticket wins fifty states.

You're such a fan of my outlandish ideas that I thought I'd run this by you. What do you think?

By the way Whoopi Goldberg just said Hillary should run as Joe's VP. I am curious as to why you think my idea is so outlandish when Hillary's name is in the news every single day, usually linked to speculation about her either being VP or stepping in when Biden inevitably needs to be replaced. I can agree with you that this is an unlikely scenario. But for you to say my idea is so ridiculous as to be unworthy of consideration ... I don't get that. It's a perfectly respectable opinion all over the media, certainly not original with me. My Bernie idea is original.

https://www.washingtonexaminer.com/news/she-would-be-brilliant-whoopi-goldberg-says-hillary-clinton-should-be-vice-president

I even said early on that collapse of the economy as soon as possible, since that is arguably the only thing which will dramatically reduce fossil fuel use, may well be the best thing for the planet and humanity overall. — Janus

Are you saying that you'd welcome the death of three billion people worldwide as long as you could have your precious environmental fantasies? This is the trouble with leftists. They claim to love humanity but they hate people. And if you don't agree with them they'd just as soon see you dead.

There is of course an important choice to make if what you describe is true. Do you mutualise risk across the board resulting in lower health insurance costs on average or do you mutualise per age category allowing for differentiated premiums? — Benkei

As I've noted, Obamacare makes the young subsidize the old and the risk-tolerant to pay for more risk reduction than they want or can afford.

Medicare is a government-run program. — Xtrix

Medicare is a public/private partnership. Bernie and Liz's plans for M4A would abolish the private component. You're simply wrong on the facts.

Saying I should "do my homework" is childish -- either you have an argument based on evidence, or you don't. — Xtrix

Or, as I've stated, I haven't sufficient interest in the topic of health care policy to drill down another level of detail. It's clear to me from what you write that you don't know how Medicare works. It's ok, nobody does till they get old enough to have to find out. That's why Dem candidates can get away with saying M4A and the public doesn't realize that what they're proposing is a much less flexible and much worse system than Medicare as currently implemented. You don't seem to know about Medicare Supplemental and Medicare Advantage. Those two programs are the reason Medicare is so popular. And they're what Bernie (and Liz before she backed off M4A entirely) want to abolish.

Of course this is now all moot as Joe is against M4A.

See; https://www.investopedia.com/articles/personal-finance/071415/did-obamacare-make-premiums-go.asp — Benkei

Thx.

I read the article. I don't believe a word of it. It says nothing about the effect on young people, who used to be able to get low cost plans that covered catastrophic situations. Now those plans are outlawed and the premiums for the young need to be far higher than the risk profile would suggest, in order to subsidize premiums for the old and sick. Many young people chose to pay the fine (or tax, if you're John Roberts) and forego being insured. This is bad policy. That article is cherry-picked and misleading according to my understanding of the issue.

Same issue with self-employed people. Allowing people to choose higher deductibles to keep their premiums down is a good deal for a lot of people. Outlawing that means that the self-employed got killed by Obamacare premiums. Most people with employer health coverage never see that aspect of things because to them their health care is inexpensive. They don't see the actual costs and they don't pay those costs. Self-employed people do.

That article obscured more than it revealed in my opinion.

But besides Joe Biden, who's defending Obamacare these days?

The investopedia link I sent does not paint such a black and white picture for Obamacare. It might be worth a read. — Benkei

I may have missed the link and didn't see it scrolling back a bit. If you live in a country with a competent, caring government, I envy you. I don't live in such a place. My sense of the US government is more aligned with the title of this book: A Government of Wolves: The Emerging American Police State. I haven't read the book but I've read many of John Whitehead's essays.

I really, really, really don't want Nancy Pelosi running every aspect of my health care. I really don't. I'll take my chance with the semi-free market and the miserable insurance companies and corporate health care we have now. That's the lesser of two evils, if I'm given a choice.

I do think Obamacare was as bad as reported, by the way. I was on Obamacare for a while. Very high premiums.

A game theoretic scenario entails that both players have an equal chance at winning... — Shawn

There are mathematical games in which one or the other player has a forced win with perfect play. You're redefining what game theory means. I'm curious. Where are you getting your definition from? You're correct that memorizing perfect play wouldn't be fun; but the idea of game theory is abstract, it's not about you and Uncle Fred sitting down for a friendly game of checkers.

https://en.wikipedia.org/wiki/Solved_game

Doesn't count. Otherwise it wouldn't be much of a game if one had to memorize a certain causal chain in a deterministic tree to ensure victory at all times.

Does that make sense? — Shawn

No, that's not what game theory's about. You seem more interested in the practical aspects of playing games. In that light your comments make more sense. When I think of game theory I think of the formal mathematical discipline of that name.

Then you ought be more than willing to push the agenda of one who knows the issues and how to correct them... yet you rail against Bernie. — creativesoul

I like Bernie personally. It's just his politics I don't like. I've already said I'm not a socialist and don't support M4A. Not sure what I could add. Bernie's policies, which I did take the trouble to glance at on his website, are all big government programs. It's perfectly sensible to be against a "democratic socialist" if one distrusts big government. Yes I'm aware that Trump has implemented his own brand of big government, completely blowing up the budget. I'm not happy about that.

Winning strategies is something that can only exist for participants of a deterministic game where mistakes can be made. Once you have a super-rational player that is immune from making mistakes via forward and backward induction, along with no asymmetrical information problems, then winning becomes next to impossible.

Agree? — Shawn

No, that's simply wrong. There are games in which one player or the other has a forced win with perfect play on both sides. I gave you an example of one earlier.

This is basic game theory, 101. Should I go on? — Shawn

By all means, since you claim a solution to an open problem.

In any sufficiently complex game, given enough iterations, it can be demonstrated that both players become hyper-rational, and thus a winning strategy cannot be entertained. — Shawn

It's certainly the case that some games with perfect information (both sides know the current state of the game at all times) do have winning strategies. The example I thought of is a little technical but it's an interesting story I happen to know so I'll talk a little about it.

To be fair this is an infinitary game, it consists of a countably infinite sequence of moves. When mathematicians talk about game theory this is one class of games that's studied.

Choose a subset of the closed unit interval, $X \subset [0,1]$. There are two players, Alice and Bob as they're often called in these scenarios. Alice goes first, choosing a zero or a one. Bob then chooses a zero or a one, and so forth. They continue for a countably infinite sequence of moves, defining an infinite sequence of zeros and ones.

If you put an implied binary point in front of the resulting string, you have the binary representation of some real number in the unit interval. If that real number is in $X$ Alice wins; otherwise Bob wins.

Is there a winning strategy for Alice or Bob? Clearly it depends on which set $X$ we choose. For example suppose $X = [0, \frac{1}{2})$. That's the half-interval that includes 0 but excludes 1/2. Then Alice chooses 0 as her first move, and no matter what Bob does, Alice has already won the game.

I hope this example is clear. Any binary number .0xxxxxanything is automatically in the left half of the unit interval.

So it's clear that at least for SOME sets, there is a winning strategy for one player or the other.

The statement For every set there is a winning strategy is known as the axiom of determinacy. It's one of the alternative axioms set theorists like to play with. It's inconsistent with the axiom of choice which is why it's not generally adopted. It's been proven true for various interesting classes of set of reals.

[The description of the game in the Wiki article is a little different than how I described it but it's equivalent].

I admit this is the example that popped into my head when you claimed that with perfect play all games must be draws. This is not true.

Even for finite games, which can in principle be completely analyzed, some games have winning strategies and others don't. And as far as chess is concerned, it's unknown whether there is a winning strategy. The problem space is so vast that even though it's finite, our current computers can't evaluate the entire game tree.

ps -- Here is a reference for the solvability of chess.

https://en.wikipedia.org/wiki/Solving_chess

Damn. I should've asked this question pages ago because this fear I can understand, given the system you have. — Benkei

I think I might not have realized this myself a few pages ago. I just can't see the US government pulling this off without making things much, much worse. Obamacare was sold with lies, did not "bend the cost curve" as they kept telling us, and you could not "keep your doctor," it was passed in a 100% partisan manner, self-employed people got financially destroyed, and it made premiums very expensive for healthy young people, causing them to have to forego health insurance altogether.

I would say that I have arrived at the highly defensible position that I under no circumstances want the current Democratic party running my health care. They are neither moral nor competent.

Do you think the type of welfare State like the Netherlands is better or worse than the USA? And why? — Benkei

Not familiar with the Netherlands at all. What if I said I have no objection in principle to universal state-run health care, but that I deeply distrust the US government to provide it? That might be closer to my actual position. There are a lot of problems with the American system. None of them can be solved with M4A as envisioned by, say, the Dem candidates of the past few months.

I don't live in the US, so I don't have to worry about it, personally. Excepting doctor's visits, I get my healthcare for free. Ergo, it's a theoretical argument for me. And you're not engaging. — Baden

Well FWIW the corporatized American system of medicine is problematic. I don't dispute that. And I'm not engaging. Haven't I said enough about health care? It's not even one of my hobby horse subjects. I don't care about it enough. I've stated my opinions to the level of detail I have an interest in discussing. I hope this is ok with you because I just don't care that much about health care policy except for opposition to M4A.

If you are happy with your health care that's great. I'm an American and I am very happy with my health care although the bureaucracy can be frustrating.

What motivates corporations is PROFIT. — Benkei

I agree that Marx had it right when he described what a disaster late stage capitalism would be. No question the system's not working. Hence Trump and Bernie. I just don't think socialism's the answer. If capitalism's not the answer either, what then? I have no idea. What Uber does is very exploitive. It would be pointless for me to try to defend what's become of capitalism. Our system's broken. That doesn't mean I can't call out the worst of the bad ideas that have been suggested to fix it.

You keep saying "socialist", "socialist" without responding to anything I said and then you say you're done. Nothing I've said is "socialist" in the way you've implied. I repeat, it's conservative policy here too. We can talk about socialism another time. — Baden

I had a flood of mentions and have not kept track of everyone's individual positions. If I misconstrued your position I apologize. But if I simply failed to respond to your substantive remarks, it's because I only noticed the insults. But as I say, I cut all the Bernie fans a lot of slack since you all must be totally devastated this week. M4A is the worst idea ever. If you disagree then we disagree. See if you can get more people on your side next time.

I don't vote and I'd certainly not vote for a senile fossil like him. Not my side in any case as the Dens and Reps are two sides of the same coin. — Benkei

Thank you so much for that. I agree completely. And I'm not a socialist, which upsets a few handles on this site. The entire Dem electorate just rejected them the past two weeks, they must be despondent.

Why is anyone taking fish seriously he thinks Hillary might be nominated this disqualifies him from adult conversation. — StreetlightX

Are you representing to me that (a) You read a wide variety of political news and opinion; and (b) that you have never heard such speculation from professional pundits and observers?

Maybe read and respond to what I wrote instead of repeating hysterical nonsense. — Baden

Done politicking for the day. Not productive to debate socialists who don't even see the wealth around them that liberty and free enterprise have produced.

By the way what motivates private entities to do well by consumers is competition. All the kids with iPhone in their hands use them to tweet against corporations. It's to laugh.

I'm honestly politicked out., no more replies today else this could go on without end. FWIW a lot of people in this thread should be writing to the DNC and yelling at their fellow Dems who just resoundingly rejected their socialistic ideas.

The price increases for Obamacare are exaggerated and actually less than historic trends, with possible outliers in certain states. — Benkei

You'll be a good Biden voter then. Hope you're happy with what your side has done.

Seriously, just sit down and think. — Baden

I've sat down and studied the twentieth century. I lived through a good chunk of it. Socialism is the most brutal, dehumanizing system ever imagined. A boot stamping on a human face as Orwell put it. Think of the awful cybertotalitarian regime in China. That's not my vision for the future. That's my vision of the thing I will stand up and oppose to my dying breath.

We need socialism in order to get rid of stupidity. Capitalism is melting people's brain, just look at fishfry — Maw

Funny how facts have been replaced by insults in my last couple of mentions. You like Stalin, Mao, and Castro? Good for you. "Oh but that wasn't REAL socialism, nobody's ever done it right." LOL. Now THAT is dumb.

It's amazing how insurance companies and other vested interests have managed to convince tools like fishfry that a system that costs twice as much as it should, is half as good as it should be, and makes them billions is in his and the public's interest. All the data in the world won't wake the guy up to reality. Pure ideological blindness. — Baden

Perhaps I just lived through the disastrous Obamacare rollout and watched over the next few years as everyone's premiums went through the roof. Perhaps, unlike most people, I spent decades paying for my own health care out of my own pocket and thereby know a lot more about how health care costs and how it's paid for than the average office worker with a company-supplied insurance plan.

Perhaps I don't trust the government to run my health care. I don't trust them to run my foreign policy, do you? And for what it's worth, Joe Biden is opposed to Medicare for All and wants to extend Obamacare. 100 million Democrats can't be wrong, right? LOL. Cognitively impaired Joe is their savior. Point being that the Democratic party has decided against your chimera of a government takeover of healthcare. Your argument is no longer with me. It's with the entire Democratic establishment. Sorry Bernie bro's. And if I'm a tool, I'm a whammin' slammin' jackhammer baby.

If it's not a woman, perhaps Joe should take Bernie as vice president.

Vice president isn't so important, but Biden should really get the progressives with him.

(And think of how scared that would make Republicans if Joe has health problems.) — ssu

Only way Biden will get anyone under the age of 60 to vote for him.

But I see your point, I think. IF numbers work as they did when we all first learned math (rigidly), then normal mathematics is objectively true. — Gregory

Oh no, not at all. I make no claims of truth for math. Only logical coherence and interestingness, those are the criteria by which mathematicians judge math. If you have a logically coherent, interesting system in which 2 = 9 you have every right to pursue it. Math is not about truth; only about whether given assumptions entail particular conclusions.

As Bertrand Russell said:

“Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.”

https://www.goodreads.com/quotes/577891-pure-mathematics-consists-entirely-of-assertions-to-the-effect-that

Where does it say my taxes will "go through the roof"? — Maw

I appreciate your and everyone else's passion on this topic. Medicare for All is dead as a campaign issue. Biden is on record as opposing it and wanting to extend Obamacare. I've said my piece and will leave it at that.

Tragically, and I know you'll be personally devastated to hear this, they just cancelled the rest of the XFL season. Looks like I'm stuck here for the duration for my entertainment. I just washed my hands so it's ok.

Oh, like chess? Have you played chess against a computer?

Why don't you test it out. Set a chess engine like Rybka, against Shredder, or Rybka vs Rybka, and see what happens? — Shawn

This has nothing to do with the well-known fact that it is an open question as to whether white has a forced win with perfect play on both sides.

You have claimed a demonstration, your word, to the contrary. Have you got a link?

Nope — Maw

It is pure fantasy to believe that the access and quality Americans enjoy today would hold if private insurance were abolished.

https://www.nytimes.com/2020/03/09/opinion/medicare-for-all-cost.html

Most Americans are perfectly happy with their health care.
— fishfry

Hah! — creativesoul

You could look it up.

https://news.gallup.com/poll/245195/americans-rate-healthcare-quite-positively.aspx

https://www.washingtonpost.com/opinions/2019/05/03/sorry-bernie-most-americans-like-their-health-insurance-way-it-is/

Where I see her showing up possibly is on Biden’s cabinet. — 0 thru 9

Why do you think Hillary specifically declined to endorse cognitively impaired Joe a few days ago? She knows the Dems will be looking for an actual candidate soon. They can't hide Joe forever.

https://www.hollywoodreporter.com/news/hillary-clinton-says-she-wont-endorse-anytime-soon-1282664

And where would I get such a crazy idea that Hillary still wants to be president? From She Who Must Not Be Indicted herself.

'I never say never': Hillary Clinton refuses to close the door on a 2020 presidential run

I think this response is disingenuous. I was illustrating that not everything the government does is awful, nor do the public view it that way. Now you want to say that the reason it's popular is because of the private aspect of it, or otherwise "people would hate it." Heads I win, tails you lose. — Xtrix

Yes, that is exactly the case. Straight Medicare would be very unpopular. It doesn't pay enough benefits and it offers no flexibility. It's the private component that makes it work. You should do your homework on this issue. What I state is well-known fact.