Ha, ursula, you have no idea of the kind of menatal torture have been through since last summer, surrounded by scepticd who constantly tried to destroy my dreams. But I have not allowed them to be destroyed - I have merely receded in to a shell.

I noticed your interest in such stuff some time ago, in the genetics thread, and was waiting for this faceoff.

Tell me, what do you want to know about the new world?

hi, bubka. first of all i apologize you for not being ursula  :) .

new world. revolutionary new world. that reminds me on one book of a. huxley.

do you know it? well, just the main idea of the storyline?

Is that the one called Brave New World and is all emo and stuff?

Anyway, there is no such thing as a perfect world but the closest thing will be everchanging, meaning it cannot be set in stone.

a revolutionary world here refers to a world after the revolution. you are welcome to make your queries about it.

And what Revolution is this? Any Revolution we choose that we think will make the world better (and possibly perfect in your eyes) ?

The socialist revolution folowed by the communist revolution.
You are a fan of socialism, aren't you? :wink:

Oh and if possible the anarchist revolution.

[quote="bubka"]Ha, ursula, you have no idea of the kind of menatal torture have been through since last summer, surrounded by scepticd who constantly tried to destroy my dreams. But I have not allowed them to be destroyed - I have merely receded in to a shell.[/quote]
I find it weird that you write "mental torture" while you yourself write stuff like "communism solves everything " and "Saddam is a martyr".  If you write stuff like that, don't feel "tortured" when people disagree and tell you they do.

[quote="bubka"]
I noticed your interest in such stuff some time ago, in the genetics thread, and was waiting for this faceoff.[/quote]

Oh my God you've been keeping an eye on me. Don't become obsessed you hear :) But yes, I'm concerned about the situation thousands of milllions live in, about environmental issues and yes, I think the present world order is unsustainable(that is the fashionable word). But don't misunderstand me. I'm not interested in repeating the USSR or Mao's China history. They are there so we know what can not be done.

[quote="bubka"]Tell me, what do you want to know about the new world?[/quote]

OK,
1.- Are you theorizing for the galaxy or are you thinking in a revolution for our Earth with our human beings? Notice I'm only interested in the second option.

2.- What will be your economic order? Will it be worldwide? Who owns the production? How do you distribute it?

3.- Commerce. How do you organize it? Will it be free commerce? Will you have money?

4.- Political system. Will it be democratic? If it will, what will you call a democracy? What will you do with dissidents? (people who do not agree with your utopia)

5.- Media. Newspapers, TV, who owns them? How do you ensure they won't become biased? Notice it is important because they highly influence the opinion of people.

6.- Government. What will be it's powers? How will you make new laws? For instance in modern democracies the powers are separated.

7.- Science and technology. What will be their purpose? An easy answer is to match human necessities. What are the human necessities? Will we work to produce say mobile phones? Does somebody tell me what I actually need? This question also fits in the first and second item. Suppose I want some avocado produced in the distant Mexico, do I get to have it considering there's a great deal of resources spent in order to [i]bring[/i] the avocado to me?

8.- Work. A scientist life is a happy one, he is all the time doing what he pleases. However, most people do not like what they do, working in a bar until 3am is very unpleasant. They only do it for the money. I wonder, in your utopian society, what will you do with all the people that work with displease? Suppose they don't work anymore, do you continue to provide for them?

Oh I could go on, but it's too much. If you want to set some tyranny the answers are simple, but I'm not interested. Thinking utopicly some answers might still be simple without falling in a dictatorship. At least I think I can provide partial answers for most of those questions. Anyhow, wha interests me the most is how we can get fom where we are to the frommy point of view better society. And it is much harder, you have to consider alot of more questions given such adverse initial conditions.

[quote="deimos"]
new world. revolutionary new world. that reminds me on one book of a. huxley.
do you know it? well, just the main idea of the storyline?
[/quote]

Even worse than falling in a Brave New World kind of society (in which at least they could have sex all the time and remember? they even were designed to like what they were designed to be) is falling in a 1984(orwell) kind of society that is just oppresive. Much more similar by the way to the kind of society we saw in the USSR or in the eastern european countries.

[quote="bubka"]
Oh and if possible the anarchist revolution.
[/quote]

Anarchists do not have the organization, because of their same definition, to produce a revolution.

[quote="Ignite"]Anyway, there is no such thing as a perfect world but the closest thing will be everchanging, meaning it cannot be set in stone.[/quote]

Yes but everchanging = everascending, I hope. Once everyone lives according to the Declaration of Human Rights I hope there's not coming back.

Ursula

At last, some sensible questions.
1. The Earth.
2. The world will of course be one huge integrated economy. There will be no country nonsense.
3. There will be no money.
4. Political system will be somewhat democratic, but there will be no opposition parties. And since the dictator will be perefectly just, people who want to depose him will be ignored.
5. Media will be in government hands. Unofficial media will be neither acknowledged nor banned, but there content will be subject to censor.
6. Legislature, executive and judiciary will be integrated.
7. Science and technology will continue unimpede. However, they will come into use only when there is enough for all. The government may use them for strictly official purposes. The news of any advancement will immediately be announced using the media.
8. The toughest question. If you are satisfied with the above, we can get into that in detail.

You seem to think the answer to my questions is pretty simple which I should have expected. You go nowhere that way. If I gave you a brand new world tomorrow for you to build your utopia you wouldn't know what to do with it.

[quote="bubka"]At last, some sensible questions.
2. The world will of course be one huge integrated economy. There will be no country nonsense.
[/quote]

This is what is nonsense. One huge integrated economy destroys the Earth. Besides you don't answer anything. I didn't even mention countries in my question! I'm asking what will be the economic system. What will be the relationship between the people and the things they produce? Who owns the resources, the factories and the products? Will your economy be planned? What about private initiative? This were just warmup questions agains which refer the real of the answers.
And at this point I don't expect you to answer every one of them. But you could think a bit more on the world you want. It's not just about going around and proclaiming the revolution

[quote="bubka"]
3. There will be no money.
[/quote]
Again simplicity. Well, you will have to provide me a way of adquiring goods. This you forgot to address.

[quote="bubka"]
4. Political system will be somewhat democratic, but there will be no opposition parties. And since the dictator will be perefectly just, people who want to depose him will be ignored.
[/quote]

Assume, theoretically speaking, that somehow, unexpectedly, the dictator becomes mad, or he just start to do bad things. Of course this would be a very unlikely thing to happen to your dictator, but say it does. [i]Do you have the means to depose him?[/i] You, the people. Take a look at history, to the dictators [i]you[/i] don't like. What if people who want to depose him become majority? Will you continue to ignore them?
And that is actually a minor issue easily fixed.
What I'm concerned about democracy is about giving people the real possibility of ruling on the things that affect them.

[quote="bubka"]
5. Media will be in government hands. Unofficial media will be neither acknowledged nor banned, but there content will be subject to censor.
[/quote]

And the media in the government hands, will it be subjectto censorship? This answer is actually the one I agree the most, only that all media should be subject to a soft scrutiny from an external corporation. Only to ensure everybody is well informing.

[quote="bubka"]
6. Legislature, executive and judiciary will be integrated.
[/quote]

Too much power, my friend. It could work, but too much power.

[quote="bubka"]
7. Science and technology will continue unimpede. However, they will come into use only when there is enough for all. The government may use them for strictly official purposes. The news of any advancement will immediately be announced using the media.
[/quote]

The idea is good, science and technology must be advanced but there should be a planning of their usage. However, the infinite power of your government makes it easy for them to do whatever they want. Like producing new technology and not telling you. Your world will be divided by the ruling class and the working class just as it has happened before. But counting with utopian people is a great advantage. Give the power to decide to them.

This exhausted me

Ursula

I seem to have answered only one question successfully.
Let me try again, more carefully this time.

2. I must quote a famous to the point of cliched but nevertheless very effective line: "To each according to his need, from each according to his need." (Just for variety, I switched it around) One huge integrated economy is the only sensible solution.

3. Again, there is no need to acquire goods: they will be provided.

4. Of course the party will depose him (and dispose of him) immediately. The people will not be bothered about such petty issues. :)

5. Very dumb. Both the censor board and the official media will be part of the government, so the latter will not of course publish anything that the former may censor.

6. Get habituated to handling power while being upright yourself, lady.  :wink: It will come handy in those days.

7. Of course, it is the same idea. The government [i]can[/i] do whatever it wants, but it [i]will[/i] do what is honest and just.

I think you can see the key idea here. In a dictatorship, the government can do whatever it wants, so it can always do what is best. But in other stupid systems, the government can't do whatever it wants, therefore it is almost never possible for it to do the best.

That is why dictatorship ROCKS!

Oh and if you gave me a brand new world tomorrow, of course I would fail to do anything with it at all because the revolutions must be backed up by years of conscious evolution and remodelling, which is necesasry for the removal of bourgeois legacy.
Think simple. :)

Cheers,
bubka

Okay.

Given that your dictator is 100% benevolent, 100% incorruptible, 100% competent, and in general 100% perfect, and the command economy actually works, you might be fine.

Until then, we'll wait.

Go read some Ayn Rand and some history textbooks...

I love how you assume the dictator will do what's best for the people and not what's best for himself...

Chillax, friends! [quote="Scrambled"]Oh no. What if your version of George W. Bush become dictator? His party hasn't disposed of him yet. The opposing party hasn't disposed of him yet. The US hasn't even disposed of him yet.[/quote]Becoming a dictator is not that easy. For example you need to be able to count up to twenty, spell bourgeoisie correctly, evaluate a + b whole squared, and tell an Iraqi mountain peak from a nuclear missile launcher while looking at satellite photos.

Anyone, let's see what more mature people have to say on this. (I am looking forward to the responses of fred, Xevarion, deimos, and of course ursula.)

[quote="bubka"]
2. I must quote a famous to the point of cliched but nevertheless very effective line: "To each according to his need, from each according to his need." (Just for variety, I switched it around) One huge integrated economy is the only sensible solution.

[/quote]

I think you have a typo here. The quote (attributed to Marx) is supposed to be: "From each according to his ability, to each according to his need."

I must question this about your society: what is the incentive for labor? If I am living in this Communist Dictatorship and the product of all my labor is given to the state, why do I bother to work at all? Do I do it out of the kindness of my heart? Do I not receive goods from the state if I do not work? (do I get more benefits, the harder I work?) If I am working in a factory but happen to come up with an innovation that would revolutionize the whole industry, is there any reason at all I would tell the state about it?
In a capitalist society, profit is the incentive for labor. If I create wealth by doing labor, this wealth (minus the costs) becomes my own profit.
In a Communist society, why should I do any work at all? Or anything more than the bare minimum required? Historically, the answer has been that otherwise, you will be shot. What is your answer?

yes thanks for pointing out the typo.

Well you have raised ursula's eighth and most difficult question. You can call it kindness of heart, you can call it sense of duty, but it is more or less the same thing. Actually you do profit if you work hard, but so does everyone else. You will never be able to live a better life than your neighbour, but you can improve the general living standard. Also you'll get the honour because your hard work or innovation will be officially acknowledged.

Not much of an incentive, true, but 'why should he share the profit of my hard work' is what we call bourgeoisie mentality. It is in fact the difference between communism and socialism. I will discuss that later in detail.

[quote="bubka"]
2. I must quote a famous to the point of cliched but nevertheless very effective line: "To each according to his need, from each according to his need." (Just for variety, I switched it around) One huge integrated economy is the only sensible solution.[/quote]

Define 'need'.  Who tells the things I need? Is it I? If I say I need a Porsche, will you give it to me? Or is the government? Which is ironic, how can the government know what are my needs? What if the government declares that everybody's needs are plenty of rice and beans to survive every month?
The issue of what are the human needs is a crucial one, if you want to know my answer to this question, at least one point of view I'm ready to share up to some extent, read Max Neef. I must send you to read some modern stuff, maybe you will be convinced things are not that simple as you still think.

I realize I must restrict your utopia a bit further. Perfect people won't do, if everyone is perfect including your dictator, you are clearly able to build a perfect society. From this point on, assume you work with mostly utopian people, but all capable of doing the bad. Also assume all the mechanisms in society are aswell subject to failure. The unique party of yours can also, in the long run, become sick from within, sick and rotten of power. This scenario is closer to reality as history shows. So enough of mental orgasms. In real life you need control mechanisms for the power structure so that it renews itself and for it to be revolutionary all the time. What you actually need is transfer power to the people, not to the government.

[quote="bubka"]3. Again, there is no need to acquire goods: they will be provided.[/quote]

See last question, what if I want something you don't provide me? I can aftually accept this with my utopian mind -or without it, even today people are able to accept they can not have it all - but I must know why. How do you plan to justify the distribution of goods is what concerns me?

[quote="bubka"]
4. Of course the party will depose him (and dispose of him) immediately. The people will not be bothered about such petty issues. :)
[/quote]
Or the party will be so benefitted from the presence of such a dictator that will haveno interest in deposing him. They won't even think they are doing wrong. Of course,  you don't believe in democracy which amazes me because your beloved Marx ultimately did. Your dictatorship of course can be taken to practice. It is easy to imagine a one party dictatorship but whether it turns out to be forever good for everyone remains very dubious. Go and study some history. But choose impartial references. Fingers of my hand are enough to count the surviving systems similar to yours and it remains to be seen if they can survive much longer. There is North Korea with evident problems, there is Cuba which is a country I know well and they have some remarkable features there but with a lot of problems nonetheless and I don't even know whether to include China or VIetNam anymore.
And how can you say the people won't be bothered by such issues? Do you mean a world where people don't care about politics? Or the party is such an incredibly efficient machine that the first step the dictator takes out of the line will be enough to instantly depose him?

[quote="bubka"]
5. Very dumb. Both the censor board and the official media will be part of the government, so the latter will not of course publish anything that the former may censor.
[/quote]

You are repeating everything that has been tried before. I have a couple of questions for you, one of which I will ask right now. Why do you thing the USSR failed? They had everything you say, one aprty, one fine dictator who did everything for the common good, censorship and media integrated within the government and yet, they left us, extinguished from the political systems realm. Why do you think that happened?

[quote="bubka"]
6. Get habituated to handling power while being upright yourself, lady.  :wink: It will come handy in those days.
[/quote]

jajaa! this is so funny, but thanks for the advice, I'll keep in mind when I get to be dictatortress.
Nevertheless, when it so happens, my piece of advice to you is get habituated to my abusing of power over... you for instance. ;)

[quote="bubka"]
7. Of course, it is the same idea. The government [i]can[/i] do whatever it wants, but it [i]will[/i] do what is honest and just.
[/quote]

Well, me utopian girl from the twenty third century(ok maybe twenty third millenium) won't support that government. I just don't think a government that can do what he wants will do always the honest. However you coud try to guarantee the honest and just is always done by some means. So you must attack the reasons for which the government nowadays doesn't. As it turns out I think it needs a complete restructuring of the competences of the government and of course a redefinition of democracy.

[quote="bubka"]
I think you can see the key idea here. In a dictatorship, the government can do whatever it wants, so it can always do what is best. But in other stupid systems, the government can't do whatever it wants, therefore it is almost never possible for it to do the best.
That is why dictatorship ROCKS!
[/quote]

This has worked in some countries you know, but only for a few years. I'm thinking of Guinea who lived under a dictatorship and made some social progress at first. What you fprget in your statement and in the whole post and in your whole life is that for a government if it is true they can't do the best most times, they can't also do the [i]worst[/i] and that's is more valuable. Because building takes time and effort but destroying is very easy. Maybe Bush will be pleased to bomb Iran, LIbia SIria or whatever other very evil country. It is good he cannot just do it. What is needed is a government always [i]able to do the good but unable to do the bad[/i]. So although I see the system you imagine, I think it is very simplistic and doesn't address the things in which that kind of systems tend to fail. That without mentioning other issues in the economical region.

My final questions to you are about you pointing Stalin and Mao as your paradigms. I wonder what is your knowledge of this two guys in particular. What is according to you their contribution to history and theory? There are numbers of more than twenty million deaths unver Mao's regime during the Cultural Revolution and all the purges. Stalin  falls a bit behind, more than ten million deaths. The number of people who were affected in one way or another is much bigger, including some of the greatest intelectuals of our time who happened to be russian or eastern europeans. Is it just that you don't know any of this or just that you agree with it of choose to ignore it? Do you know there was this guy called Trotski, Stalin seems to have had a dislike for him and after pursuing him a bit around the globe finally his agents managed to kill him in Mexico?
This kind of ideas  are either a product of a very bad information or of a sickness of the mind . Have you met somebody who lived in Russia under Stalin's era or even later? They lived there under constant delusions of persecution and they were  justified. Had you been Stalin, the most probable place where you could find [b]me[/b] right now would be Siberia because of my unorthodox opinions about your creed. I'm guessing you are not Stalin after all because you seem to enjoy the argument. But read about Zhukov(not a good guy) or Lev Landau or Solzhenytsin.

Ursula

[color=red]Edit:[/color]
[quote="boostage"]
In a capitalist society, profit is the incentive for labor. If I create wealth by doing labor, this wealth (minus the costs) becomes my own profit.
[/quote]
No, no, in a capitalist society, you create some wealth by doing labor, this wealth minus the costs of production which [i]include your salary[/i] is called the surplus and is taken by the capitalist. You produce way more than what is given to you.

You don't quite get it. The problems of the present system cannot by addressed by changing the system itself - it must be solved by something i mentioned before that you carefully avoided - [i]conscious evolution[/i].

Which brings up Mao. I think the Great Proletarian Cultural Revolution is by far the most stunning and brilliant political idea of this century, and one of the top five all time greats. The fact that he was not able to put it into effect is entirely a different matter. Presently the GPCR is being carried out by the International in many third world countries, including India.

And as for Troitsky, he is one of those from the higher class who foresaw Lenin's rise to power, got into the party and became very loyal to Lenin in the hope of succeeding as party head and assiisting the counter revolution. Lenin saw through him before dying and bequeathed leadership to Stalin. Troitsky stoopd low enough to call Staling an Asian barbarian, as he was from a peasant family in Georgia and not Europe. I wonder how some people call this base schemer a communist. (It is worth mentioning that Khruschev, who murdered Stalin and sabotaged the party, was a follower of Troitsky.)

[quote="bubka"]You don't quite get it. The problems of the present system cannot by addressed by changing the system itself - it must be solved by something i mentioned before that you carefully avoided - [i]conscious evolution[/i][/quote]

Oh I do quite get it. And what I'm telling you is that the kind of conscious evolution you expect is unreal. That is what I precised in one of the first paragraphs. Almost utopian people. And anyway, how much must we expect to address the problems of the present system? If we are going to wait until your perfect mind is reached we could aswell do nothing and see what the future has prepared for us. An evolution of the minds is neccesary directed to a more social thinking but but don't expect the conscience of the people to be perfectly oriented towards the common good. But the evolution needed is only such that people will be able to understand the need of mechanisms to ensure that within the reasonable, society is more important than the individual.

In your defense of Mao and Stalin, you forget to address the crimes of both and provide a justification though you might aswell not spend the effort. You don't build a revolution with mass crimes against all who oppose your views. One thing is the war that accompanies those revolutions and other is the constant persecution to which was subjected every citizen that had a funny smell. In both cases you are foregetting the huge adoration that was practiced in both countries. The Cultural Revolution even assuming the concept was good, it was poorly taken to the practice and Mao [i]knew[/i] what his People's Army boys were doing around. In the case of Stalin you tell me that since Trotsky was an upstart he should be persecuted around the globe and ultimately killed. In modern democracies, people call each other things not far from asian barbarian all the time, they don't tend to be well seen but they can tell what they please. For using that language in an official political argument he can be punished and that would be among the competencies of democracy. Your statement that Lenin backed Stalin is false as far as I know. Lenin couldn't make up his mind because he didn't like the options he saw. Particularly he proposed the [i]removal of Stalin as a Secretary of the Central Comittee[/i] in what is now known as the [url=http://www.werple.net.au/~andy/bs/1922vil.htm]Lenin's testament[/url]. You forget many things, my friend, particularly I repeat, you forget the crimes, the killing and the terror in both states. [i]The magnitude of them is not comparable to any other in human history except Hitler, and what I ask is, are you telling me it was worth it?[/i] Why if it was so fine, it has fallen and now everybody rejects it??

Ursula

PS: By the way, so long and thanks for all the fish is the worst of all five books. Or was it six? Whatever, actually the only one worth it is the Hitchhikers's Guide. It serves at least toi know why 42 is the answer so you can get points in freak tests. Oh and the part of the whale is veery funny :)

What about the freedoms of the people, bubka? Say I want a math book. I go to the local store, get a job, and after a few hours minus taxes, I get the math book. How do I get this math book in your country?

If there are enough copies for everyone, you can get one for free. But you are also xpected to return it when you have no use for it and somebody else needs it. If there are too few copies, you can borrow it from the local library. It's only fair.

@ursula: There are five books in the trilogy in four parts, and SLATFATF is the fourth. And it is quite good. And by the way, here is a quote from book 1:  "in fact the message was this: So long, and thanks for all the fish. - Final message from the Dolphins, as they escape just prior to Earth's destruction".

You are also forgetting that we are not actually here to critically analyze past leaders. Mao was no angel - nobody is. Ho Chi-min was the only communist leader - in fact, one of the very few leaders of all time - to be successful yet maintain a spotless character. Also there is ample doubt what the actual fact was, and arguing over fact is of no use.

But I am puzzled at how you limit the conscious evolution. If you didn't get it, I am aiming at anarchy as the ultimate fantasy, and I can never get to it if I think that check and balance is always necessary. It is human weakness that the new war is against. There lies the brilliance of Cutural Revolution. The theory of GPCR has come a long way since Mao, and this time, we hope it won't fail. :(

bubka

One: some of the satellite images became public; I didn't see you outcrying their artificiality at the time.

Two; Iraq had a nuclear reactor. It bought one from France, and no one is denying it. It wasn't operational during the war, but maybe until you should buy the brains to be smart enough to tell apart the Al Tuwaithan Osirak Nuclear Facility from a mountain before you start talking.

Three; My USA argument still holds. The US is taking your "dumb" Bush, the people are taking him, and even the UN accepts him. Why wouldn't these people of our new world? And

Four; You don't need to spell Boregiose to be smart or competent. You could probably ask on the boards and very few people will know how to spell it.

Five; If you had any idea of history, Lenin wanted Stalin exiled from the USSR, but the Communist Council voted it not to be revealed. Launch whatever conspiracy theory you want against this, but make sure its sourced and backed with history documents.

Six; what if Adolf Hitler becomes our new dictator? Hitler was accepted by his people.  Why wouldn't he be by this "new world"'s?

"Brilliance of Cultural Revolution"; by this, I can only hope you aren't referring to THE Cultural Revolution, but to a general cultural revolution.

One: I had more important jobs, like relieving my bowels, thanks.
Two: Nuclear reactors and nuclear missiles are two different things.
Three: The "dumb" US is taking my "dumb" Bush, the "dumb" people are taking him, and even the "dumb" UN (probably in spite of the fact that it could very easily instead declare, let's say, Sri Lanka as the most powerful nations and call Bush an A. Hole in his face and get away with it) is accepting him. Now which of these exactly do you compare with the new people?
Four: You don't need to be smart or competent for the boards either.
Five: Stalinists claim the Lenin Testament was faked by Troitsky, but as this can't be resolvec by arguing, forget it.
Six: There is no what if, because he won't. Read through the thread first.

I am referring to theGPCR theory.

P.S.: You see Scrambled, we plan to teach the world a new dance, as Mumble did. Then they won't accept the old penguins like Buh any longer.  :wink:

[quote="bubka"]
Five: Stalinists claim the Lenin Testament was faked by Troitsky, but as this can't be resolvec by arguing, forget it.
[/quote]
No.
This argument has no historical evidence surrounding it. Stalinists blamed Trotsky for everything. It was a hobby. You know what? Give me a singe shred of evidence besides for your own predilection to be true. Historical dating gives the document to be at the time before Lenin died, not to mention authentically Lenin written. Unless your so ignorant of history that your going to steadfastly deny something that obviously happened, and something that everyone except the hardliner Stalinists who want to save face accept, then arguing about this has no more point than arguing whether the holocuast happened; but you have to obviously defer to it being genuine, rather than treat it as if it was a neutral point.
And maybe I don't get it, but you're saying that people would throw a bad dictator out before the people learned a "new dance". How does this happen?

You are just saying what you have been told. You have NEVER seen the original copy of Lenin's testament. And of course the date is befoe Lenin's death - if Troitsky faked it, he wouldn't put a date that would give him away, would he?

But you must understand that I am not proclaiming the Stalinist point of view as true. What I am saying is that it is irrelevant in the context of the revolution. Whether we accept Stalin's teachings or not cannot depend on whether Lenin in his deathbed approved of them or not. The whole idea of this revolution is largely objective - materialism and Stalinism can't go hand in hand.

When did I ever say the bad dictator would be thrown out first? Again I repeat: read the thread.

[quote="bubka"]If there are enough copies for everyone, you can get one for free. But you are also xpected to return it when you have no use for it and somebody else needs it. If there are too few copies, you can borrow it from the local library. It's only fair.
[/quote]

Who makes the copies? What is their incentive for doing so, seeing
as the capitalist incentive has been removed?

Why would I want to be a cititzen in a dictatoriship like this when I can enjoy the same math book, but get it quicker via money, in a capitalist society?

Also, what if your leading party becomes corrupt and self-serving? How do we get rid of them?

Aww not again! :(

If the leading party get corrupted, get rid of it through an armed capitalist revolution liek the French revolution. Happy now? :mad:

The people who can't afford a maths book in the capitalist society will join it, and they far ounumber those who can, who will be ignored.

[quote="PenguinIntegral"]
Why would I want to be a cititzen in a dictatoriship like this when I can enjoy the same math book, but get it quicker via moey, in a capitalist society? [/quote]

Because you [i]know[/i] that, for instance, you can only produce a lot of books by first cutting down a lot of trees. And you understand that it is not good for humanity to cut down more trees than what it sows. What makes no sense is the enormous quantity of books being printed that no one buys. Besides hopefully technology will come to help us on this since there's no environmental cost in producing digital books. But you can see it better with cars. You won't be able to have a car even if you want to, in my world either. And you just understand this. Of course the public transport will be awesome, but cars are simply unsustainable. And there's a great deal of resources spent for you to have a car. Imagine more than a billion chinese guys each with a car. Of course there [i]will be[/i] cars. But they will be saved for particular purposes. You will be able to rent them but not use them everyday.
Actually the way things are, we better stop using cars some time soon. It seems that finally we have a UN report were a good lot of scientists warn explicitly about global warming. Cars and planes are a main source of emission of contaminant gases. So humanity right now is like a parachutist who knows what the consequences of not opening the parachute are, but still he doesn't open it to enjoy the feeling of flying.
There will be a lot of stuff you are able to have now that you won't be ablt to have in an earthly utopia. It is a problem for the utopia if people consider them essential for happiness.

[quote="PenguinIntegral"]
Who makes the copies? What is their incentive for doing so, seeing
as the capitalist incentive has been removed?
[/quote]

I'm speaking of hte world I imagine now, not bubka's. That is a hard question. But in my world I don't give you the book as he does, I will sell it to you although at a reasonable price -that means, way cheaper than now -. You will receive a salary for your work but the salary spectra will be of course much reduced. You could see as an incentive for working -doing the copies, in your case- the fact you will perceive such a salary. You will also understand the importance of your work for society. Notice all of this involves an evolution of the mind which may seem impossible at this stage. I'm not particularly optimistic about it but in the other hand, I don't see many other solutions to the problems concerning poverty, energy and the environment humanity is likely to face this century.

[quote="bubka"]
You are just saying what you have been told. You have NEVER seen the original copy of Lenin's testament. And of course the date is befoe Lenin's death - if Troitsky faked it, he wouldn't put a date that would give him away, would he? [/quote]

This happens with every news, every event you know about. You never saw a nazi killing a jew with your eyes. All of this you have been told. So what are your reasons to believe in it? There are things that appear dubious for the great amount of contradicting information about them and there are things that seem clear not only because informations differ little but also because it is logical, plausible, easy for it to have happened and you don't see reasons on the people claiming it to be lying. Sort of Occam's razor. and according to those guidelines I believe Lenin did write the testament.

[quote="bubka"]
@ursula: There are five books in the trilogy in four parts, and SLATFATF is the fourth. And it is quite good. And by the way, here is a quote from book 1: "in fact the message was this: So long, and thanks for all the fish. - Final message from the Dolphins, as they escape just prior to Earth's destruction".
[/quote]
Yes I know, actually I only read two of them Hitchhiker's Guide and The Restaurant at the End of the Universe, but said it only to make fun of you :)  I like the first, did'nt like the second and quitted.

[quote="buba"]
You are also forgetting that we are not actually here to critically analyze past leaders.
[/quote]

Maybe you aren't. Which seems very convenient to me when it comes to analyze the crimes of them, since when you want to talk of their achievements the words melt in your mouth. You declare without shame your aadmiration for these people so you must be ready for me to ask you what it takes to be admired by you. Is it that it doesn't matter how many deaths hang upon me, if I made some contributions to communist theory? And actually there is not much of a doubt about facts in USSR or Mao's China. At least in the main facts and based in the Occam's razor above. I understand this is not the point of the discussion, nevertheless sorry but you won't convince me that was good thing that this two people had happened.

[quote="bubka"]
But I am puzzled at how you limit the conscious evolution. If you didn't get it, I am aiming at anarchy as the ultimate fantasy, a
[/quote]

I can't imagine an anarchist world. And thinking on it largely limits my capacity of action about the world we do live in. Anarchy is not my aim. Humanity might at some point evolve to anarchy but we are so far from that point that to me is irrelevant. So if you want I rephrase my question and state it about the world before anarchy. Before the perfect minds you talk about because then we will have anarchy and not some perfect dictator - why do we need him?-. Before the conscious evolution reaches that point? Do you think we might be having a better world or we must sit and wait? About that world I'm more concerned, is the one we should try to build.

Ursula

[quote="bubka"]You are just saying what you have been told. You have NEVER seen the original copy of Lenin's testament. And of course the date is befoe Lenin's death - if Troitsky faked it, he wouldn't put a date that would give him away, would he?
[/quote]
YOU DIDN'T WANT HISTORY TO HAPPEN SO IT DIDN'T

no. Thats bull crap. I am willing to wager more than 1,000,000 dollars on 1000:1 odds that if we carbon dated the document, the isotopes would reveal 100 years. You have no ground for your statement except truthiness. I personally think strong historical evidence as well as the testimony of everyone there besides Stalin is sufficient ground to make it true.  If you're going to make an absurd claim that you believed to be true, at least show some evidence that Trotsky faked it; in fact, did Stalin even say this? As it stands, this structure of this argument is strikingly similar to that of Holocaust deniers.

Obviously, you being a rebel, have seen passed all the BS that history class tries to teach us and know the truth of this matter. Why don't you cite a single source, even a Stalinist, to give some evidence that it was fabricated.

Oh, and did I mention that Trotsky a large portion of his powers around 1926 to Stalin?

I found something yesterday, so I'll keep my post short:
[url]http://www.awtw.org[/url]

But I still have a question for ursula: what is [i]your[/i] world?

I find it odd that there's so much discussion about the problems of choosing a dictator who will always do what is "best" for the country, as if this utopia we're talking about were indeed better than any other system, were it not for the fact that it is hard to prevent the government from abusing its power. Even if you had a perfect, ideal dictator who flawlessly represented the Will of the People, this would not be an utopia in my eyes, but a dystopia. Indeed, even if the government is not corrupt, it is perfectly possible for it to make wrong decisions or otherwise prevent society from maximizing collective happiness. Allow me to explain:

[quote="bubka"]You can call it kindness of heart, you can call it sense of duty, but it is more or less the same thing. Actually you do profit if you work hard, but so does everyone else. You will never be able to live a better life than your neighbour, but you can improve the general living standard. Also you'll get the honour because your hard work or innovation will be officially acknowledged. [/quote]

This is no incentive at all, unless everyone shares the same communist views from the beginning. Most real-life people do not think like this: they may feel a vague sense of satisfaction knowing that somebody, somewhere, will have an extra pair of socks to wear, but they would work harder if they knew they could themselves take the extra pair of socks. The end result is that people just won't try to do their best, and [i]everyone[/i] will suffer as a consequence. The only case in which this wouldn't be a problem is if everyone were perfectly communist (i.e. getting the same pleasure from consuming some goods as they get from knowing someone else consumes them), but no real country or community is like this; you'd have to brainwash them first, by means of a dictatorship which... right, you can't implement because people will not work efficiently (as they are not yet brainwashed).

[quote="ursula"]No, no, in a capitalist society, you create some wealth by doing labor, this wealth minus the costs of production which include your salary is called the surplus and is taken by the capitalist. You produce way more than what is given to you.[/quote]

This is an arbitrary value judgement. As I see it, part of what you "produce" is in fact produced by you, and the other part is produced by capital goods. Both your labor and the capital goods you use are paid for. The capitalist does not "take" part of it from you but instead you willingly surrender part of "your" production in return for using his capital goods, without which you would be nowhere near as productive. Still, the price for using capital goods is "fair" because in most cases there is no monopoly on them.

On to my main point: the main reason I see for you to reject capitalism is that it leads to an unfair distribution of wealth (not in my opinion, but I can accept that you think so). I fail to understand why this means we should reject not only the capitalist system for distributing wealth, but also the free market system for assigning factors of production to different uses and then assigning the final goods to different people. Putting aside the issue of distribution of wealth, the free market does a remarkably good job of organizing the economy without a huge and costly bureaucracy (which, no matter how huge and costly, would do a lousy job in comparison anyway).

[quote="bubka"]If there are enough copies for everyone, you can get one for free. But you are also xpected to return it when you have no use for it and somebody else needs it. If there are too few copies, you can borrow it from the local library. It's only fair.

The people who can't afford a maths book in the capitalist society will join it, and they far ounumber those who can, who will be ignored.[/quote]

You are being too easy on yourself. "Enough copies for everyone"? [i]What?[/i] Perhaps a capitalist society does not distribute its production equally, but (with government regulation in some cases, i.e. monopolies, contamination, etc.) it assures that an efficient level of production is reached, that is, there is no way of redistributing the factors of production in the economy to produce more of every good; to produce more math books, you will have to produce fewer hamburgers. It is a sad truth, but you will not be able to satisfy everyone's needs so easily (depending on how you define "needs"). The point is that you will not be able to dramatically raise the standard of living, unless wealth was insansely centralized in your original society, where insanely=far more centralized than it actually is.

In the case of math books, you might have meant "enough copies of everyone without producing any more books", so perhaps you plan on taking away books from people who have lots of them sitting on their personal libraries and giving them to those who have no books. That won't raise the standard of living by much; in fact, if those books were useless to the people who have them, they would have sold them.

Besides, you face the problem of infinite demand. "You can get one for free"? That may result in everyone demanding more and more math books, even if they have little use for them. How do you determine who "deserves" the math book more? In a capitalist society, between two people similarly wealthy, he who can make better use of it will be willing to pay more for it, and he will get the book. Here you have no way of telling them apart.

Basically, you will give everyone the same set of goods, possibly with some minor differences (I'm guessing a mathematician would need more math books than a waiter). This not only implies that you are equally distributing wealth, but you are also inefficiently distributing goods. Indeed, perhaps A has a thing for hamburgers, while B has a thing for tomatoes; normally A would buy more hamburgers and B more tomatoes at the market, but you force them both to eat equal quantities of each. This [i]lowers[/i] the general standard of living, which is not determined only by how many goods are consumed but also by whether they are consumed by those who enjoy them most.

You are also unable to efficiently distribute factors of production. In a capitalist society, if demand for hamburgers rises while demand for tomatoes declines, hamburgers will become more expensive and thus more profitable, leading to a higher investment of capital goods in the hamburger industry. In your utopia, you may be producing lots of some goods which people don't want, while not producing enough of others which they really want.

This also applies to labor: consider two jobs which require little qualification, but one of which is more enjoyable than the other. For example, you may work as a forest keeper or you may, I don't know, clean sewers? Assume both jobs required similar ability. Still, more people will be drawn to the forest keeper job because it's pleasant. In a capitalist society, this results in forest keepers being paid less than sewer-cleaners. In your society, I don't see how you prevent a flood of forest-keepers. How do you force people to do unpleasant, more difficult, more dedicated, etc. jobs if they aren't better paid? If you let them choose, the job distribution will be a disaster. If you force some randomly chosen people to clean sewers... I wouldn't like to live in your society.

[quote="ursula"]I'm speaking of hte world I imagine now, not bubka's. That is a hard question. But in my world I don't give you the book as he does, I will sell it to you although at a reasonable price -that means, way cheaper than now -. You will receive a salary for your work but the salary spectra will be of course much reduced. You could see as an incentive for working -doing the copies, in your case- the fact you will perceive such a salary. You will also understand the importance of your work for society.[/quote]

What is a reasonable price? Why are the current prices be much higher than reasonable? Well, math books are a bad example because the dynamics of writing and publishing a book are a special case (it requires some form of monopoly to work out), so take something more typical, like tomatoes. Is the reasonable price of tomatoes much lower than the current one, too? If you lower salaries proportionally, you won't be lowering real prices (thus no change to the standard of living). If you do lower real prices in general, you will not achieve a higher standard of living; you will find that suddenly everyone is demanding more and more tomatoes, hamburgers, math books, .... And you won't be able to provide for them, because your economy has a limited output. Since you can't magically raise production, if you keep prices that low, the result will be hundreds of people queuing up for hours to get a few hamburgers. This is a waste of time and labor, which actually lowers the standard of living.

That was a nice post [b]Severius[/b], :), let me first reply to the part  that concerns me and then add some stuff

[quote="myself"]
No, no, in a capitalist society, you create some wealth by doing labor....
[quote="Severius"]
This is an arbitrary value judgement. As I see it, part of what you "produce" is in fact produced by you, and the other part is produced by capital goods. Both your labor and the capital goods you use are paid for. The capitalist does not "take" part of it from you but instead you willingly surrender part of "your" production in return for using his capital goods, without which you would be nowhere near as productive. Still, the price for using capital goods is "fair" because in most cases there is no monopoly on them. [/quote][/quote]

Well, to say that the axe with which I'm cutting down some trees is actually producing part of the goods is quite something. However it could come the time when human labour is dispensable. For instance, all te farm work could be done by machines in a near future. But this is not the case I'm speaking of. Indeed in this case, the fruit of the work of such machines would be property of the owner and it would be the same as when people wore their axes and cut down some wood to sell it, now the machine playing the role of the axe. The problem appears when human labour is needed -the machines actually are not able to function without the intervention of humans-. Of course, this issue is in the foundations of capitalism itself and it is one of the reasons of its appearance. The working man doesn't have anymore the tools needed to perform his work, all he has is his expertise. So what he does is to sell his work to the guy [i]who does have[/i] the tools receiving a compensation which is nowhere close to the earnings of the guys whose merit is being the owners of the tools. I'm questioning the fairness of there being one reduced set of people getting a lot of money from some work they haven't done [i]as opposed to[/i] the earnings coming from the same work being distributed among the people who do it. The first of this situations is the one we have now in the world, I'm not saying it is not fairer than feudalism, nor that there aren't working people who go home hapy with what the earn.  I'm questioning about the possibility of achieving something better. Whether I [i]willingly[/i] surrender part ofmy production or not is [i]very[/i] debatable. As it is, there is not much of a choice, either I work for a company or I don't work at all -state doens't provide jobs for everyone-, and one [i]must[/i] work. I also recognize that kind of system ultimately leads to a world that can not sustain.

The problem about stating such theories is that people tend to just walk away from them. It is one problem facing most social movements nowadays. People think you are telling them you are going to take away their petit business or their house or whatever from them to make it all one big public property. That is wrong. For tomorrow's world one can not propose the abolishment of private property and it is not clear it is the best for a final world without the problems of this one. What is clear is that the aim of major private enterprises is to increase the level of life of a very reduced set of citizens and almost always attempting directly or indirectly against the level of life of many more and [i]in more fundamental ways[/i]. That must be changed with urgency.

[quote="Severius"]
On to my main point: the main reason I see for you to reject capitalism is that it leads to an unfair distribution of wealth (not in my opinion, but I can accept that you think so). [/quote]

It depends of course on what you think as fair. However, I think you are seeing the main reason everybody wants to see in people who reject capitalism. For that [i]is not[/i] themain reason I have stated. The main reason is that capitalism as it is founded leads to [i]an unfair and inhuman world order[/i]. Capitalism as you see it today [i]can not exist[/i] without roughly one half the population of the Earth living precarily. It is not because I earn two thousand and the guy next door earns two million which [i]I[/i] clearly don't care. Capitalism would be good if the minimum salary would be two thousand. Take a look at the places where the cloth you use are made. And that happens with all the products at the bottom of the production line, all the primary resources and the reason is simple, you can not pay people laughable salaries in the US or the EU. Besides the human factor, companies prove to be careless about other stuff such as the environment which I think should be taken care of.

[quote="Severius"]
I fail to understand why this means we should reject not only the capitalist system for distributing wealth, but also the free market system for assigning factors of production to different uses and then assigning the final goods to different people. Putting aside the issue of distribution of wealth, the free market does a remarkably good job of organizing the economy without a huge and costly bureaucracy (which, no matter how huge and costly, would do a lousy job in comparison anyway).
[/quote]
First of all, I must say that I wouldn't reject completely free market, but modulate it, at least in a first epoch. I don't think free market, as a way of assigning a value to work, should be rejected absolutely. But I tell you what I would reject. In a free market system, if the demand for cars grows, first the prices will go up, but the likely thing to happen later is the appearance of companies that produce cars so the price of a car goes down again making it accesible to many people. This goes on to benefit the buyers of cars and the owners of such companies. Indirectly though it doesn't benefit a lot of people who will be affected by the climate change the emission of greenhouse gases the enormous amount of circulating cars will produce. So no, there can not be all the cars you want, and this can be regulated either directly in the market -setting minimum prices for cars- or either in the production -limiting it-. Also, it can not be that for every global warming warning I see on TV, I see 3 or 4 hundred car advertisements. Because it is not [i]more important you having a car than people being displaced because of desertification[/i]. So I encourage a considerable intervening of the government in the production and the market, but not mainly in the book market and certainly not in the food market, at least the local one which is the one I think economies shoud depend on. There will be food produced for everyone and its cost will be according to the rules of free market, i.e, it will cost according to the demand of it there is and to the offer.

[quote="Severius"]
What is a reasonable price? Why are the current prices be much higher than reasonable? Well, math books are a bad example because the dynamics of writing and publishing a book are a special case (it requires some form of monopoly to work out), so take something more typical, like tomatoes. Is the reasonable price of tomatoes much lower than the current one, too? If you lower salaries proportionally, you won't be lowering real prices
[/quote]
Here I must refer to the utopia. The point is not that with your salary you will be able to buy a lot more tomatoes than what you are now. In my paragraph I was referring particularly to the book example - or art in general - because in that particular case, the price of the book is exaggerated by the presence of a company who puts a price on the book to match its expected earning. Authors usually perceive little percent of this. But I'm losing the thread. The point is that you will be able to buy tomatoes or hamburgers or books with your salary. You won't be able to buy cars because of reasons I've said before. You say that if I lower real prices in general every one will be demanding more tomatoes and more hamburgers, I don't understand this since you can only eat a finite number of tomatoes and hamburgers and if you eat hamburger you can't eat also chicken because it's too much and anyhow what I'm telling you is that if we run out of tomatoes you will [i]understand[/i] why this is so - utopia -. Indeed if I lower the prices of tomatoes and hamburgers and everyone starts to buy a lot more tomatoes and hamburgers and everybody is buying what they can eat I can only conclude that [i]they were hungry before![/i] And then the world was wrong.
Ultimately in my utopia you will be feeding mostly of what is cropped near the place you inhabit. It is possible that the tomatoes we produce are not enough for everybody everyday to have a couple of them. I'm also telling you that you won't have tomatoes in spring because there is a great deal of resources spent for you to have tomatoes in spring. My point is that ideally [i]you won't have to worry for such issues[/i]. We will crop according to the demand - if people wants tomatoes instead of carrots there will be more tomatoes than carrots - and there will be plenty of food in general and you will be able to buy it.

Got tired, I'll continue later

Ursula

[quote="ursula"] Well, to say that the axe with which I'm cutting down some trees is actually producing part of the goods is quite something. [machines...]
The problem appears when human labour is needed -the machines actually are not able to function without the intervention of humans-. Of course, this issue is in the foundations of capitalism itself and it is one of the reasons of its appearance. The working man doesn't have anymore the tools needed to perform his work, all he has is his expertise. So what he does is to sell his work to the guy who does have the tools receiving a compensation which is nowhere close to the earnings of the guys whose merit is being the owners of the tools. [/quote]

I want to make a few comments about this. Of course, I'm not talking about self-sufficient machines but capital goods which require human labor. In this case, the situation is symmetric: the working man cannot produce anything by itself; capital goods are not productive by themselves either. Thus an arrangement must be made: the working man and the capital owner combine their factors of production, and the output is distributed between them according to supply and demand of labor and capital. Side comment: in fact, the working man [i]could[/i] choose to produce stuff by himself with the basic tools they used before the IR; considering that the real exchange rate between different goods hasn't changed by much, he could have a similar standard of living to the one he had before the IR with this production. Of course, he will not choose to do this but he will work with the capitalist, because it is a better deal for him: the standard of living you can achieve with a given salary is much better than what you can achieve with pre-IR equipment.

[quote="ursula"] I'm questioning the fairness of there being one reduced set of people getting a lot of money from some work they haven't done as opposed to the earnings coming from the same work being distributed among the people who do it. The first of this situations is the one we have now in the world, I'm not saying it is not fairer than feudalism, nor that there aren't working people who go home hapy with what the earn. I'm questioning about the possibility of achieving something better. Whether I willingly surrender part ofmy production or not is very debatable. As it is, there is not much of a choice, either I work for a company or I don't work at all -state doens't provide jobs for everyone-, and one must work. I also recognize that kind of system ultimately leads to a world that can not sustain. [/quote]

This fairness thing is, of course, very subjective. I do not find it unfair that owners of capital goods can charge a fee for their use, as long as there is no monopoly on them. Ironically, there has been a trend towards a sort of monopoly of labor, which is what trade unions do. The fact that capitalists have a much higher income than working men is a coincidental result of 1) the distribution of wealth/capital goods, and 2) the amount of available capital and labor in the economy. In economies where there are plenty of capital goods (rich economies), they are cheaper; that is, owners of capital do not have such a comparatively high income because it is not so scarce as it is in countries with hundreds of millions of people and little investment. What I am saying is that this "unfairness" is not so bad everywhere; it is worse in poor economies. Thus, a rich economy has little need of changing its system for distributing wealth.

About whether you voluntarily surrender part of your production: well, you can work for a company, or you can choose not to work at all and die of hunger, or... you can do some job which requires no more capital goods than that which you own. For example, you can buy a small parcel in the country and grow crops, you can make your own clothes with primitive tools... etc. I know, this sounds ridiculous, but I am trying to highlight the fact that we are privileged to have neighbors who lend us their capital goods - I do not feel they are cheating us by charging a fee, as long as there is no monopoly.

[quote="ursula"] What is clear is that the aim of major private enterprises is to increase the level of life of a very reduced set of citizens and almost always attempting directly or indirectly against the level of life of many more and in more fundamental ways. That must be changed with urgency. [/quote]

The aim of major private enterprises is to increase the standard of living of their owners. I do not see anything wrong in this although, of course, it will lead to some people having a much higher income than others. But why do you say this goes against the interests of the masses? I just don't understand. Private companies do not hurt anybody; they do not steal from anybody, and they force nobody to buy their goods, nor can they force citizens to work for them. By sharing their capital goods for production they actually increase not only the standard of living of their owners, but also the standard of living of the general population. Of course, in the particular case of contamination, private enterprises work against the interests of the population, and this should be efficiently regulated by the government; but it is a particular case. Most companies are not harmful to the interests of society, unless you think that the owners' refusal to [i]give away[/i] their wealth=being against the interests of society.

[quote="ursula"] It depends of course on what you think as fair. However, I think you are seeing the main reason everybody wants to see in people who reject capitalism. For that is not themain reason I have stated. The main reason is that capitalism as it is founded leads to an unfair and inhuman world order. Capitalism as you see it today can not exist without roughly one half the population of the Earth living precarily. It is not because I earn two thousand and the guy next door earns two million which I clearly don't care. Capitalism would be good if the minimum salary would be two thousand. Take a look at the places where the cloth you use are made. And that happens with all the products at the bottom of the production line, all the primary resources and the reason is simple, you can not pay people laughable salaries in the US or the EU. Besides the human factor, companies prove to be careless about other stuff such as the environment which I think should be taken care of. [/quote]

Well, I thought the issue of distribution of wealth is the one you're against (as opposed to free market); my apologies if I was wrong. However, what is an "unfair, inhuman world order"? Inhuman? In any case, I find selfish capitalism to be more akin to human nature than a socialist utopia. Well, perhaps you mean that extreme poverty is inhuman. Yes, it probably is. However, I don't see why you blame capitalism for this. In developed countries it is only a small percentage of the population who lives in poverty, and that can be handled -if the population so decides- by means of a competent safety net. In fact developed countries do have safety nets. My point is, do you need to switch to socialism in order to deal with poverty? In developed countries, that is unnecessary. In poor countries, chances are that an equal distribution of wealth will not be enough for everyone to have their needs satisfied. If you mean that rich countries should make huge donations to poor ones as to guarantee a similar standard of living anywhere in the world... I do not know whether that would be fair. Most likely, developed countries would not want to join your utopia.

On the environment issue: yes, there should be efficient government regulations, since it is a particular case in which the free market fails to do a good job. However, government regulations concerning externalities are by no means incompatible with capitalism; this problem can be solved independently of whether you have a socialist superstate, etc., etc.

[quote="ursula"] First of all, I must say that I wouldn't reject completely free market... [/quote]

That part was directed mainly to bubka, because he is rooting for a no-private-property, no-money, nothing-outside-the-State economy.

[quote="ursula"] In a free market system, if the demand for cars grows, [...] This goes on to benefit the buyers of cars and the owners of such companies. Indirectly though it doesn't benefit a lot of people who will be affected by the climate change the emission of greenhouse gases the enormous amount of circulating cars will produce. [/quote]

This is another case of externalities. Of course, these things should be regulated depending on how grave the harm to the environment is. If they are not well regulated, it is either because it has been decided that the problem is not so serious, or because the government is incompetent, but this has nothing to do with capitalism vs socialism.

[quote="ursula"] So I encourage a considerable intervening of the government in the production and the market, but not mainly in the book market and certainly not in the food market, at least the local one which is the one I think economies shoud depend on. [/quote]

Can you give me an example of a market in which you would want the government to intervene, which doesn't have to do with externalities or monopoly? If you have none, then your government would be environment-friendly rather than socialist.

[quote="ursula"] The point is not that with your salary you will be able to buy a lot more tomatoes than what you are now. In my paragraph I was referring particularly to the book example - or art in general - because in that particular case, the price of the book is exaggerated by the presence of a company who puts a price on the book to match its expected earning. Authors usually perceive little percent of this. [/quote]

My apologies. I have little knowledge of the book publishing industry, so I would prefer not to comment on that. I thought that when you said "much cheaper than they are now", you were referring not to books in particular but to many other goods in general. If I knew more about the books subject I might agree with you, but the point is that this discussion started with someone asking "Say I want a math book. ..." and he took the math book as a random example, not expecting that it would be a special case. So instead of math books we should consider a random example, which is what I attempted with hamburgers.

[quote="ursula"] You say that if I lower real prices in general every one will be demanding more tomatoes and more hamburgers, I don't understand this since you can only eat a finite number of tomatoes and hamburgers and if you eat hamburger you can't eat also chicken because it's too much and anyhow what I'm telling you is that if we run out of tomatoes you will understand why this is so - utopia -. Indeed if I lower the prices of tomatoes and hamburgers and everyone starts to buy a lot more tomatoes and hamburgers and everybody is buying what they can eat I can only conclude that they were hungry before! And then the world was wrong. [/quote]

Again, it turns out that hamburgers and tomatoes are not random enough examples because they are food. Pretend that we were talking about a good which you wouldn't get obese from consuming more of. Then people would indeed demand more if it, if its real price were lower. My point is this: if you do lower the real prices of goods and people demand more of them, you will not be able to provide for them. Instead you will run out of food (or whatever random good we're talking about). My point is that you may raise the standard of living of the poorest, but you can't magically raise the general standard of living by lowering prices, unless you can magically multiply the output of the economy- which is impossible (unless you're Jesus).

[quote="ursula"] I'm also telling you that you won't have tomatoes in spring because there is a great deal of resources spent for you to have tomatoes in spring. [/quote]

So what? If it truly makes me happy to have tomatoes in spring (happier than if I spent those same resources on something else), why should I not have them? Suppose there are two kinds of fruit, A and B, and in this season we can grow A locally but not B. Then, it is twice as costly to get B to my country, than it is to get A. Suppose that, at the same time, the foreign country produces B, but it is twice as expensive for them to get my A fruit. Now, suppose that the people in both countries are willing to pay for the expensive fruit - it makes them happier to have one foreign fruit than two units of local fruit. Why should trade be forbidden?

That was long... I hope I can take a break now :wink:

Severius

I liked the part about the peutunia potted plant that when falling thought, "Oh no, not again."  Note that this has shown up in Halo and Halo II when a gunt is stuck.  (Those of you that don't know Halo, never mind.)

These thoughts are not very evolved and not very deep.  For example, how do we go from where we are to where you want everyone to be?

Bush is supported by about half of America.  You will remove him, the Congress and all the US government to do what?  How will that work?  All of those that produce many times more than average, how will you continue to have them spend 12-18 hours/day when there is no upside for them?  When they don't how will you absorb the global depression that results?  How will you censor the unofficial media?  China doesn't seem to have found a way, even with a willingness to kill?

Even startup companies, where two partners agree on the goals often find themselves at each other throats within a couple of years.  Why else were the founders of Apple thrown out, ony to have Jobs return after it looked like the company was tanking.  Now he has stolen money from Apple shareholders and the government by lying about the date set for stock options he had his friends grant himself.  I don't understand how these types of people will be able to live in the world society you suggest.

Take all of you.  Are you willing to give up your efforts/fun on this web site and become starving to allow some of the excess that you "waste" here spent to bring the standard of living up for the most unfortunate in the world?

I didn't think so.

What happens when some try to give support to the most needy is that their neighbors steal it, war breaks out and the like.

What will you do if someone resists?  Have them killed?  Have their villiage killed, since you can't find them?

The reason the current governments are set up the way they are is that it tends to work best with the folks we have.  If a better idea comes by, it will be tried.  The good ones are kept and emulated, the bad ones, such as those you propose, are discarded and show up in fiction.

I just wanted to tell you [b]Severius[/b] that I haven't had time to answer your post, I know it will take me at least an hour. But I have not forgotten it and I hope to answer it during this week. Forgive me.

[b]wizard[/b], my plan try is to convince as many people as possible. If people think something is wrong within this system let's hope the democracy we have today does give us the means to change it. Unfortunately I don't think my efforts o anyone's will be enough. You are right, it is a much more difficult task to change the world now than to imagine a better one. Even people who think there are things wrong often do nothing, mostly because it is too uncomfortable.
Your question about us leaving the commodities is illogical. First, you don't know how we live, all you can guess is that I have an internet connection and you might be wrong because I might connect at work. If my going hungry would be of any good to people, say it will save [i]one african child's live[/i] I don't think I would doubt much. I know a lot of people who wouldn't. In my case, I also try to do things I can and I understand are helpful. I belong to an NGO of international reach. I also don't think I propose unreal or discouraging things. But it is very very hard to convince people who believe to do things, not to mention to convince of something people who don't believe at all.

Ursula

The "oh no, not again" is explained much later, when Stavromueller Beta comes in.

I have also not had time to answer the posts. And I got too confused when these two started. Say, are you two grown ups?

[quote="wizard2378"]What happens when some try to give support to the most needy is that their neighbors steal it, war breaks out and the like.[/quote]

I'm trying to parse this statement and the thought behind it: are you suggesting that charity causes "war and the like," or are you saying something else?

Also, just for the record, approximately a third or less of Americans approve of Bush's overall job approval, not half -- he's below 50% in every single state (he just recently lost a majority of Utahns for the first time).


function
superior algebra
superior algebra unsolved

is it true or false, and why:

"every nonzero positive element of a $ C^*$algebra is invertible"

the claim is equivalent to: a real-valued nonnegative non-zero function on a compact space has no zeroes. which is clearly false (take e.g. $ p\equal{}(1,0) \in \mathbb{C}^2$).


what are the codes to different fonts? i know textbf and textrm and mathbb. what else is there?

[url=http://tug.ctan.org/tex-archive/info/lshort/english/lshort.pdf]The Not So Short Introduction to LaTeX2e[/url] Section 6.2 Fonts and Sizes pp 111-115.


And so we address the complexity of the greatest machine ever- the human nervous system.

We begin on the level of the smallest living functional unit- the cell. Nerve cells are called neurons and there are just a few types that I will explain- motor neurons, sensory neurons, and interneurons.

Each neuron consists of a cell body, an axon and some dendrites (these little extensions that attach to other neurons.) I mean, they have to be in close vicinity if they're going to transmit singals to one another.

A neural signal is dubbed an action potential and occurs when a neuron is stimulated enough that sodium channel gates open and let in some sodium ions. This is called depolarization. If only one neuron fires, say one sensory neuron, we may not know it because we our brain has a threshold for stimuli- there needs to be enough stimulation in order for sensation to occur. The action potential is propagated along an axon (which you can read more about online, like about saltatory conduction and unipolarity and bipolarity and hyperpolarization and stuff.)

So pretty much it works like this: you sense stuff by having your sensory neurons (which are all over your body) stimulated. The signal travels up the spinal cord and the thalamus sorts it to where in the cortex it needs to go. That's how it works in simple words.

If we want to move, we use our motor cortex which at the back of the frontal lobe just anterior to the sensory cortex. Here we can propagate a potential and use motor neurons to send these potentials to effectors (muscles, and I guess glands too, but those are mostly involuntary.)

I'm kind of getting tired so I will post later. I hope this has helped.

He didn't ask a very specific question, so I have him a simple answer. I mean, Spoon made me a little mad earlier because he was getting on Zyloch's (I think) case for not being super specific in his answer. If this guy had asked what the function of acetylcholinesterase is in the nervous system, then that'd be a different story.

Remember, we're here to have fun in the coolest science EVER! Biology! Woo hoo!!!!!

[quote="warut_suk"]How does brain and nervous system send information?[/quote]
[hide]
Little receptors on the sensory nerves react to stimuli, such as heat, etc. The sensory nerves send the information through the axon to the dendrites which send the information to the next sensory nerve cell.
The process is repeated until the information reachs the CNS (Central Nervous System). The interneuron cells inside of the CNS interpret the information and send instructions to the motor neurons which send the information in the same way the sensory neurons did to the parts of the body where the instructions are obeyed(example: removing your hand from a hot stove). [/hide]
This is just the basic way. adidasty's way is much better :)

Is it within the realm of possibilities that we may one day engineer the connections between interneurons? Not necessarily in a person's brain but in some medium composed of a small community of neurons? I've heard that some proteins guide axon extremeties to connect to other neurons. The reason for my asking is that if we could build the basic logic gates (AND, OR, NOT) with a handfull of neurons we would be able to build a CPU which, unlike common processors, is not immutable and final, but actually dynamic. Suppose that we were to have such a CPU and that we were to implement an instruction which allocates neurons and connects them accordingly. How cool would that be? :)
Of course we would have to prevent the neurons from just connecting to each other with their own natural protocol, these connections might disrupt the integrity of the circuit. This wouldn't be easy though. Perhaps we could implement a system wherein connections that are not created by the processor's instruction would be little used and eventually deteriorate.
Actually, such a processor would be too dynamic, and change with the input over time. It's chaos, i'm surprised the brain works. I guess at a higher level, the changes on individual neurons aren't meaningful enough to alter the system significantly. This means that we probably need a significant number of neurons in order to have a somewhat stable system.

Those are interesting concepts, Job. I think you'd be very interested in long-term potentiation and the physiology of memory and neural connection. You are correct, some proteins may guide adjacent neurons to come into contact if action potentials are common enough on pathways that include both neurons. I learned about this much more in psychology class than I did in biology class. I think you'd enjoy it.


Let $ x_n \equal{} \sqrt{n\plus{}\sqrt{n^2\minus{}1}}$ for all $ n \ge 1$. Express $ \frac{1}{x_1}\plus{}\frac{1}{x_2}\plus{}...\plus{}\frac{1}{x_{49}}$ as $ a\plus{}b\sqrt{2}$ for some integers a and b.

I believe you mean $ \textcolor{red}{5} \plus{} 3\sqrt{2}$

Thx, edited.

Motivation: conjugate to get $ \frac {1}{x_i} \equal{} \sqrt {i^2 \minus{} \sqrt {i^2 \minus{} 1}}$

Then, find p,q s.t. $ (p \minus{} q\sqrt {i^2 \minus{} 1})^2 \equal{} i^2 \minus{} \sqrt {i^2 \minus{} 1}$

Which gives a very easy system which solves to get what we want.

Thank you very much, fofler and metafor.


Let $ m,n > 1$ are integers which satisfy $ n|4^m \minus{} 1$ and $ 2^m|n \minus{} 1$. Is it a must that $ n \equal{} 2^{m} \plus{} 1$?

[quote="dyd"]Let $ m,n > 1$ are integers which satisfy $ n|4^m \minus{} 1$ and $ 2^m|n \minus{} 1$. Is it a must that $ n \equal{} 2^{m} \minus{} 1$?[/quote]
I guess you mean $ n \equal{} 2^m \plus{} 1$ ^^

Sure it is...

Let $ 4^m \minus{} 1 \equal{} kn$ and $ n\minus{}1 \equal{} j \cdot 2^m$
Then we have $ 4^m \minus{} 1 \equal{} kj2^m\plus{}k \Longrightarrow k \equal{} \minus{}1 \bmod 2^m$ so we set $ k \equal{} 2^mp\minus{}1$
And so $ 4^m \minus{} 1 \equal{} (2^mp\minus{}1)(2^mj\plus{}1) \Longrightarrow p\equal{}j\equal{}1$ But then $ k \equal{} 2^m\minus{}1$ and n = $ \frac{4^m\minus{}1}{2^n\minus{}1} \equal{} 2^n\plus{}1$

[hide]$ n.2^m|(4^m \minus{} 1)(n \minus{} 1)$ opening paranthesis we get $ n.2^m|4^m \plus{} n \minus{} 1$ so $ 4^m \plus{} n \minus{} 1\geq n.2^m$
$ 4^m \minus{} 1 \geq n.(2^m \minus{} 1)$       and  $ 2^m \plus{} 1\geq n$  from given criteria $ n \minus{} 1\geq2^m$ we reach $ n \equal{} 2^m \plus{} 1$[/hide]


modular arithmetic
number theory
number theory theorems

:?:
Can someone please explain fermat's little theorem to me.  I understand that $ a^p\equiv a \pmod p$, but how do you use that to get something like this:

$ 98^{70}\equiv 1\pmod{11}$
$ 98^{70}\equiv 1\cdot 3^{2}\pmod{5}$

or

$ 101^{52}\equiv 1\cdot 2^{2}\pmod{11}$
$ 101^{52}\equiv 1\pmod{5}$

 :?:

If $ a$ is not divisible by $ p$, then $ a^p\equal{}a\cdot a^{p\minus{}1}\equiv a\pmod p$, and $ a^{p\minus{}1}\equiv1\pmod p$.  This also means that, given $ a^b\equiv c\pmod p$, you may divide write $ b\equal{}t(p\minus{}1)\plus{}u$, and if $ a$ is not divisible by $ p$, then $ a^b\equal{}\left(a^{p\minus{}1}\right)^t\cdot a^u\equiv a^u\pmod p$.  If moreover you write $ a\equal{}tv\plus{}w$, then $ a^u\equiv w^u$, and you can simplify rather drastically the congruence.

For example, assume that we are asked to find the remainder of $ 113^{2009}$ divided by $ 11$.  Clearly $ 113\equal{}11\cdot10\plus{}3$ is not divisible by $ 11$, so $ 113^{10}\equiv1\pmod{11}$, and $ 113^{2000}\equiv1\pmod{11}$, and it suffices to find the remainder of $ 3^9$.  Since $ 3^2\equiv(\minus{}2)\pmod{11}$, then $ 3^8\equiv(\minus{}2)^4\equiv5\pmod{11}$, and finally $ 113^{2009}\equiv4\pmod{11}$, unless my calculations are wrong.

Now you can do yourself the examples that you propose, go for it!

So if we're looking for $ 98^{70} \pmod {11}$, then 98 is not divisible by 11.  Then we get $ 98^{10}\equiv 1 \pmod {11}$.  So $ 98^{70}\equiv 1 \pmod {11}$.  Oh, awesome. I get it.  Now with the rest.

$ 98\equal{}5\cdot 19 \plus{}3$ so $ 98^{70} \pmod{5} \implies 98^4\equiv 1 \implies 98^{68}\equiv 1\implies 98^{70} \equiv 1\cdot 3^2 \equiv 4 \pmod 5$

$ 101\equal{}9\cdot 11 \plus{}2$ so $ 101^{52} \pmod {11} \implies 101^{10}\equiv 1\implies 101^{50}\equiv 1\implies 101^{52}\equiv 2^2\equiv 4 \pmod{11}$

$ 101\equal{}20\cdot 5\plus{}1$ so $ 101^{52}\pmod 5 \implies 101^4\equiv 1\implies 101^{52}\equiv 1 \pmod 5$

Awesome.  Thanks

No problem, just glad I could help.  Good job in solving your original cases!


quadratics
algebra
polynomial
USAMTS
algebra unsolved

Interesting.

[hide]
Repeated substitution of the given expression into the RHS yields $\sqrt{a-\sqrt{a+\sqrt{a-\sqrt{a...}}}}$.  Makes for a slightly more interesting problem, IMHO.
[/hide]

Anyway, the beginning of the solution (I think):

[hide]
Squaring both sides and rearranging gives $a-x^2 = \sqrt{a-x}$.  Squaring again gives $a^2 - 2ax^2 + x^4 = a - x$.  I'll finish this as soon as I get time to look up Tartaglia's formula, unless there's a better way :).

[/hide]

I assume we're supposed to reach a closed expression. Otherwise justdudxit already gave the solution:
[hide="Solution"]$x=\sqrt{a-\sqrt{a+\sqrt{a-\sqrt{a...}}}}$[/hide]

:o

I just looked up the formula...unless something reduces with our particular equation, that's one hell of an answer.

I tried to factor the polynomial into two quadratics $(x^2+Ax+B_1)(x^2-Ax+B_2)$ before reading lordwings's answer but encountered trouble determining the coefficients.

If this problem comes from a competition then you probably should be able to solve the problem without the formula (like the quartic on USAMTS round 3). Would the question writer likely request memorization of a byzantine formula (like Cardano's) or massive and tedious computations?

[quote="lordWings"]I used software that supposedly uses that formula, and surprisingly the four roots are really simple:
$x=\frac{1\pm\sqrt{4a+1}}{2}$, $x=\frac{-1\pm\sqrt{4a-3}}{2}$.
Maybe using $a+x\geq 0$ and $a-\sqrt{a+x}\geq 0$ we can eliminate three of them to reach the solution we're looking for:
$x=\sqrt{a-\sqrt{a+\sqrt{a-\sqrt{a+...}}}}$[/quote]

Could you plz tell what software did u use to get such nice roots?

[quote="cats..."]the  equation justdudxit has is a quadratic in $a$.[/quote]
That's it!
First solve for $a$, it's just a quadratic equation with two easy solutions: $a=x^2-x$, $a=x^2+x+1$.
And then solve for $x$ two easy quadratic equations to get the four solutions I gave before.

[quote="RohanSingh"]Could you plz tell what software did u use to get such nice roots?[/quote]
I used a very old student version of Maple.

[quote]the equation justdudxit has is a quadratic in $a$.[/quote]

Wow, I didn't think of viewing it from that angle. *slaps forehead*

I'm trying to solve this strictly.

We're trying to solve for $x$
$f(x,a)=\sqrt{a-\sqrt{a+x}}=x$.
Squaring twice (we'll have to be careful: squaring can add fake solutions to the original equation), we reach $a+x=(a-x^2)^2$.

It's a complicated equation to solve for $x$, but it's a simple quadratic equation in $a$, $a^2-(2x^2+1)+(x^4-x)=0$, and the solutions are:
$a=\frac{2x^2+1\pm|2x+1|}{2}$. So, $a=x^2+x+1$ or $a=x^2-x$.

We'll check the solutions with the original equation:
[b]Case 1)[/b]
$f(x,a=x^2+x+1)=\sqrt{x^2+x+1-|x+1|}=x$ iff $x\geq -1$ and $x\geq 0$ ($x\geq 0$, $a\geq 1$).
Solving for $x$ the quadratic equation $a=x^2+x+1$, we have $x=\frac{-1\pm\sqrt{4a-3}}{2}$.
The only solution in this case is $x=\frac{-1+\sqrt{4a-3}}{2}\geq 0$, with $a\geq 1$.
[b]Case 2)[/b]
$f(x,a=x^2-x)=\sqrt{x^2-x-|x|}=x$ iff $x\leq 0$ and $x\geq 0$ ($x=0$, $a=0$).
The only solution in this case is $x=0$, with $a=0$.

So, it seems that the solution
$\boxed{x=\sqrt{a-\sqrt{a+\sqrt{a-\sqrt{a+\dots}}}}}$
only converges if $a\geq 1$ or $a=0$, and then
$\boxed{x=\frac{-1+\sqrt{4a-3}}{2}}$.

Nice.  Goes to show you should get your hands dirty on this sort of problem.

yeah this problem is extremely cool. it appeared some days ago in the high school forum somewhere. can u generalise? (for which fourth degree plinomials is it happen?)


calculus
integration
trigonometry
calculus computations

Let $ f(x)\equal{}x^{2}\plus{}|x|$. Prove that $ \int_{0}^{\pi}f(\cos x)\ dx\equal{}2\int_{0}^{\frac{\pi}{2}}f(\sin x)\ dx$.

$ \int^{\pi}_{0}f\left(\cos x\right)dx\equal{}\int^{\frac{\pi}{2}}_{0}f\left(\cos x\right)dx\plus{}\int^{\pi}_{\frac{\pi}{2}}f\left(\cos x\right)dx$
Let $ x\equal{}\frac{\pi}{2}\minus{}t$ then $ dx\equal{}\minus{}dt$ and:

$ \int^{\pi}_{0}f\left(\cos x\right)dx\equal{}\int^{0}_{\frac{\pi}{2}}f\left(\sin t\right)(\minus{}dt)\plus{}\int^{\minus{}\frac{\pi}{2}}_{0}f\left(\sin t\right)(\minus{}dt)\equal{}\int^{\frac{\pi}{2}}_{0}f\left(\sin t\right)dt\plus{}\int^{0}_{\minus{}\frac{\pi}{2}}f\left(\sin t\right)dt$

but because $ f(\sin x)\equal{}f(\sin(\minus{}x))$ we have: $ \int^{\frac{\pi}{2}}_{0}f\left(\sin t\right)dt\equal{}\int^{0}_{\minus{}\frac{\pi}{2}}f\left(\sin t\right)dt$

and we're Done! :)

Here is the links in which Virgil Nicula have posted the related something to this problem.

[url=http://www.mathlinks.ro/viewtopic.php?t=23498&search_id=1960244277]Take a look[/url]


geometry inequalities calculus rotation trigonometry function derivative

What is the maximum possible area for a triangle inscribed in a circle of radius r?

So the triangle must be an isosceles one. How do we know that, and how do we prove that? And then how should we proceed?

Thanks!

the scarlet macaw

There are a couple of ways of doing it.  You can use a geometric method (fix one side; to maximize the other side the remaining point must lie on the perpendicular bisector of that side, so the triangle is isosceles - apply it again and we get that it's equilateral)

You can also use Jensen's inequality (write the area of the triangle in terms of $r$ and $\theta$)

You can also use AM-GM (although I forget exactly how to make this one work)

Finally, you can use calculus/lagrange multipliers.

I was wondering if the Lagrange Multipliers will lead to an application of AM-GM on this problem.  Would it?

Do you know how to use lagrange multipliers?  Anyways, you can prove AM-GM via lagrange multipliers.

Yes, that's what I mean.  I meant to ask if we use langrange multipliers in this case. will it somehow lead us to the same applications of Am-GM in this problem, or woudl it be very different from AM-GM?

Masoud Zargar

I don't think so - the AM-GM is quite ugly if I remember correctly.  The Jensen's solution is the cleanest.

Here's a calculus approach.

Assume the triangle is formed by three points on a given circle. We might as well assume that the radius of the circle is 1.

Let's set all this in the complex plane, on the circle $|z|=1.$ WLOG (we can rotate if necessary), one of these three points is $1.$ So assume the three vertices of the triangle are $1, e^{i\alpha},$ and $e^{i\beta}.$

Here's a useful formula for the area of a triangle whose vertices are $z_0,z_1,z_2.$

Area $= \left|\frac12\text{ Im}\left(\overline{z_0}z_1 +\overline{z_1}z_2+\overline{z_2}z_0 \right)\right|.$

(You can extend this formula to any polygon; if we always trace the polygon out in a counterclockwise direction, we don't need the absolute value.)

In our specific case, we get $\frac12\text{ Im}(e^{i\alpha} + e^{i(\beta-\alpha)} +e^{-i\beta})$

$=\frac12(\sin\alpha+\sin(\beta-\alpha)-\sin\beta).$

This is a function of two real variables, $\alpha$ and $\beta.$ We set the partial derivatives equal to zero to look for critical points:

$\cos\alpha-\cos(\beta-\alpha)=0$
$\cos(\beta-\alpha)-\cos\beta=0$

So $\alpha,\beta,$ and $\alpha-\beta$ all have the same cosine.

From here on, we do all arithmetic $\pmod{2\pi}.$

Either $\alpha=\beta$ or $\alpha=-\beta.$ But if $\alpha=\beta$, then $\beta-\alpha=0$ and thus $\alpha=\beta=0.$ This, with all three points being the same, gives is the minumum area, which isn't what we were interested in.

Thus $\alpha=-\beta\pmod{2\pi}.$

$\alpha=\beta-\alpha,$ so $2\alpha=\beta=-\alpha$ and thus $3\alpha=0\pmod{2\pi}.$

This makes $\alpha=\frac{2\pi}3$ or $\alpha=-\frac{2\pi}3.$ With $\beta=-\alpha$ that makes our three points equally spaced around the circle, hence the vertices of an equilateral triangle.

Letting $\alpha=\frac{2\pi}3$ and $\beta=\frac{4\pi}3$ we get that the area is

$\frac12\left(\sin\left(\frac{2\pi}3\right)+\sin\left(\frac{2\pi}3\right) -\sin\left(\frac{4\pi}3\right)\right)=\frac{3\sqrt{3}}4.$

Question: can you extend this method to the question of the $n$-gon of maximum area inscribed within a particular circle for general $n$ ?

Oh, okay, thanks.  Abbreviations seem to be everyone. :P

Here is a sketch of the proof using Jensen's inequality:  Given triangle $ABC$ with sides $a,b,c$, angles $\alpha,\beta,\gamma$, circumradius $R$, and area $K$, we have $2R\sin\alpha=a$ (and so on for $\beta,\gamma$) and $R=abc/(4K)$

We may rewrite this as

$K=2R^2\sin \alpha\sin \beta \sin \gamma$

We may rewrite this again as

$K=2R^2\exp(\ln(\sin\alpha)+\ln(\sin \beta)+\ln(\sin \gamma))$.  It is straightforward to check that

$\frac{d^2}{dx^2}[\ln\sin x]<0$ for $x\in(0,\pi)$.  Also, $\alpha+\beta+\gamma=\pi$ (triangle condition)

So we're pretty much there.  Applying Jensen's inequality inside the exponential, we get

$K\leq 2R^2\exp\left(3\ln\sin\left(\frac{\alpha+\beta+\gamma}{3}\right)\right)=2R^2\sin\left(\frac{\pi}{3}\right)^3=\frac{3\sqrt{3}}{4}R^2$

Since equality is attained in the equilateral triangle, we're done.  Oh, and I lied, that wasn't a sketch, that was the whole thing.


If anyone needs an iTest team, and feels they have some significant talent to offer, post here!

I have no talent to offer but I wouldn't mind participating...

I didn't mean like IMO talent.  Just being an AoPSer pretty much qualifies you.  :wink:   Anyway, I sent you a PM with the details.

[quote="Ignite168"]What's iTest? The site leaves me still confused.[/quote]
This site??
http://www.ahsimc.com/index.htm

I'd join, but i have no talent. on practice amc's, about 140 on amc 10s, about 115 on amc 12s, and 6-8 on aime.

Yes, lotr, that was the right site.  Since we can only have 5 people, please post your grade and AIME/AMC 10/AMC 12 scores as well.

I would join a team, although I'm not a genius-type.... :D

I haven't taken any AMC tests :rotfl: but on the practice amc 10s ive taked, i'm in the 135-145 range, amc 12s 95-115, aimes 1-5 :blush:

Well I haven't taken any AMC10s/12s/AIMEs either so I guess I'll just make my own team.

Edit: The actual iTest site is really, really, really, bad.

I might have some talent.  I get like 7-10 on AIME and 135+ on AMC 10 and 12 both.

[quote="mysmartmouth"]I moved this to RT, since NO ONE reads Other US Contests.[/quote]

And I moved it back, because it doesn't belong in RT.

...and I locked it, since the iTest has already started!


$ x^2 \plus{} y^2 \plus{} z^2 \equal{} 1993$ then prove $ x \plus{} y \plus{} z$ can't be a perfect square:

[b]Problem from Romania TST 1993[/b]
[hide="Proof"][color=darkblue]Suppose $ x \plus{} y \plus{} z \equal{} a^2$, $ a\in \mathbb{N}$.
We have $ x^2 \plus{} y^2 \plus{} z^2 < (x \plus{} y \plus{} z)^2\le 3(x^2 \plus{} y^2 \plus{} z^2)$, that is $ 1993 < a^4 < 2\cdot 1993$, so $ 6 < a < 9$. Because $ a^2 \equal{} (x \plus{} y \plus{} z)^2 \equal{} x^2 \plus{} y^2 \plus{} z^2 \plus{} 2(xy \plus{} yz \plus{} zx)$ and $ x^2 \plus{} y^2 \plus{} z^2 \equal{} 1993$ is odd, we obtain that $ a$ is odd too, so $ a \equal{} 7$.
$ x \plus{} y \plus{} z \equal{} 49$, $ y \plus{} z \equal{} 49 \minus{} x$ and $ (y \plus{} z)^2\geq y^2 \plus{} z^2$, that is $ (49 \minus{} x)^2\geq 1993 \minus{} x^2$ or $ x^2 \minus{} 49x \plus{} 204\geq0$. We obtain that $ x\geq \dfrac{49 \plus{} \sqrt {1585}}{2}$ or $ x\le \dfrac{49 \minus{} \sqrt {1585}}{2}$. In first case $ x > 45$, so $ x^2 > 1993 \equal{} x^2 \plus{} y^2 \plus{} z^2$.
In the secod case $ x\le 4$, similiarly $ y \le 4, z\le 4$, contradiction....[/color][/hide]

We will take congruences mod 5. Since a square is = 0,1,4 (mod5) and 1993=3 (mod 5) we have that if x^2+y^2+z^2=3(mod 5) we easily conclude that x,y,z are equal to 1 mod 5 or two of them are 4 and the other 0 mod 5. So we have that x+y+z=3 mod 5 but if it were a perfect square it wolud be 0,1 or 4.
Hope it is correct , if you don't understand just ask :)

Daniel

[quote="lambruscokid"]if x^2+y^2+z^2=3(mod 5) we easily conclude that x,y,z are equal to 1 mod 5 or two of them are 4 and the other 0 mod 5[/quote]
I think we conclude that $ x^2,y^2,z^2$ are equal to 1 mod 5 or two of them are 4 and the other 0 mod 5...

oh you are right, I'll keep thinking the problem
Thank you!


algebra
polynomial
calculus
algebra proposed

Let $ P(X)\in\mathbb R[X]$ ,$ P(X)\equal{}a_{n}X^{n}\plus{}a_{n\minus{}1}X^{n\minus{}1}\plus{}...\plus{}a_{0}$ with $ n$ even,satisfying the following conditions:
a)$ a_{0}>0$, $ a_{n}>0$
b)$ a_{1}^{2}\plus{}a_{2}^{2}\plus{}...\plus{}a_{n\minus{}1}^{2}\leq\frac{4\cdot min (a_{0}^{2},a_{n}^{2})}{n\minus{}1}$
Prove that $ P(x)\geq 0,\forall x\in\mathbb R$

According to the conditions, the signs of $ a_{i}(0 < i < n)$ don't matter. So it's enough to prove that: (because $ a_{n}x^{n}\plus{}a_{0}> 0$ for all x)
$ \ a_{n}x^{n}\plus{}a_{0}\geq\sum_{i \equal{} 1}^{n\minus{}1}a_{i}x^{i}, a_{i}> 0$ for 0<i<n and x>0
using cauchy:
$ \sum_{i \equal{} 1}^{n\minus{}1}a_{i}x^{i}\leq ((a_{1}^{2}\plus{}a_{2}^{2}\plus{}...\plus{}a_{n\minus{}1}^{2})(x^{2}\plus{}...\plus{}x^{2n\minus{}2}))^{0.5}\leq 2min (a_{0},a_{n})((x^{2}\plus{}...\plus{}x^{2n\minus{}2})/n\minus{}1)^{0.5}$
By weighted AM-GM: $ \ a_{n}x^{n}\plus{}a_{0}\geq (x^{n}\plus{}1)a_{n}^{x^{n}/x^{n}\plus{}1}a_{0}^{1/x^{n}\plus{}1}$
if we assume that $ a_{0}\equal{} < a_{n}$ than it's enough to show that:
$ \ (x^{n}\plus{}1)a_{n}^{x^{n}/x^{n}\plus{}1}a_{0}^{1/x^{n}\plus{}1}\geq 2a_{0}((x^{2}\plus{}...\plus{}x^{2n\minus{}2})/n\minus{}1)^{0.5}\to (x^{n}\plus{}1)(a_{n}/a_{0})^{x^{n}/x^{n}\plus{}1}\geq 2((x^{2}\plus{}...\plus{}x^{2n\minus{}2})/n\minus{}1)^{0.5}$
It's equivalent to:
$ (*)(x^{n}\plus{}1)\geq 2((x^{2}\plus{}...\plus{}x^{2n\minus{}2})/n\minus{}1)^{0.5}.$ Can someone prove this?
Second case:  $ a_{0}> a_{n}$ -> the same as the first case, I think.

Can someone prove\disprove (*)?

well, I think I proved (*) with calculus: I generalized it as $ (G+1)/2\geq\sqrt{A}$ (G is geometric mean and A is arithmetic mean), and then it's almost trivial:
$ F(x) = (G+1)/2-\sqrt{A},x = (x_{0},....,x_{n})$
$ \frac{d}{dx_{i}}\left(F(x)\right) =\frac{1}{2n}(\frac{G}{x_{i}}-\sqrt{A}) = 0\to$ iff all $ x_{i}$'s are equal to 1, so the minimum value is achieved when x=(1,....,1), and then $ F(x)\geq F(1,1,..1) = 0.$
I know that this proof is not formal enough. Can someone find another proof, or validate this one? And is this result known? Because I really like it!  :P
EDIT: this generalization is of course wrong (choose x=(1,2)...)  :( but I think it can still be proved by Lagrange multipliers, but I am too lazy to do it, and still looking for a non-calculus solution...  :idea: