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July 15th, 2013, 03:02 PM   #11
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Re: Utopia

For example, I cannot predict what you will say next CRG, no matter how much I try.

All that exists will enumerate itself, and you will force a decision that my so called "all seeing eye" will therefore enumerate whether you post again here or not. I certainly hope that you do!
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July 15th, 2013, 03:08 PM   #12
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Re: Utopia

I'm a little confused by all this ... starting with, why is this in a math forum?

But I like politics too, so I'll play.

Given human nature, how would you deal with, say, Nazi Germany? Should the rest of the world have just submitted on the grounds that war is universally bad? Surely you can see that you are dealing with real-world situations in which you are not able to control the actions of 7 billion human beings and their power-mad leaders.

What exactly are you proposing?
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July 15th, 2013, 03:08 PM   #13
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Re: Utopia

I once asked if anyone knew of an axiom that could make sets jump on pogo sticks, do tricks, and back-flips.

The thing is, such an axiom existed the moment I thought of it. My brain cells recall it to this day, and again, my all-seeing-eye enumerated the possibility.

That is my true illusion. We can never actually enumerate everything of course, at least not in our heads, but the Universe does, and it always adds up.
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July 15th, 2013, 03:13 PM   #14
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Re: Utopia

Uhh...

"Bounded rationality" is the study of actors who do not act rationally but merely approximate rationality. It doesn't mean "constrained by rationality"; for that, you could search [rational irrationality].
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July 15th, 2013, 03:13 PM   #15
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Re: Utopia

Quote:
Originally Posted by Maschke
I'm a little confused by all this ... starting with, why is this in a math forum?

But I like politics too, so I'll play.

Given human nature, how would you deal with, say, Nazi Germany? Should the rest of the world have just submitted on the grounds that war is universally bad? Surely you can see that you are dealing with real-world situations in which you are not able to control the actions of 7 billion human beings and their power-mad leaders.

What exactly are you proposing?

I despise violence...

It was the responsibility of the citizens of Germany, along with the people of the world, to mutually agree not to kill each other. I realize that people will follow to insane ends with little explanation. Despite all of this, the Universe does not flinch. It continues doing simply what it does.
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July 15th, 2013, 03:20 PM   #16
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Re: Utopia

Quote:
Originally Posted by Maschke
I'm a little confused by all this ... starting with, why is this in a math forum?
This topic is (to my mind) at the intersection of math and economics. Game theory, social choice theory, mechanism design... all fairly standard stuff.

Quote:
Originally Posted by Maschke
Given human nature, how would you deal with, say, Nazi Germany? Should the rest of the world have just submitted on the grounds that war is universally bad? Surely you can see that you are dealing with real-world situations in which you are not able to control the actions of 7 billion human beings and their power-mad leaders.
Indeed. That's why I'd like to see a solution that does not rely on universal adherence. Perhaps you could have most people following this idealistic path, but surely there will always be Hitlers and Amins. If a method could be found that would stop crazies and the ill-incented with some not-too-huge majority (say, < 99%) that would be encouraging.
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July 15th, 2013, 03:28 PM   #17
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Re: Utopia

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by Maschke
I'm a little confused by all this ... starting with, why is this in a math forum?
This topic is (to my mind) at the intersection of math and economics. Game theory, social choice theory, mechanism design... all fairly standard stuff.

Quote:
Originally Posted by Maschke
Given human nature, how would you deal with, say, Nazi Germany? Should the rest of the world have just submitted on the grounds that war is universally bad? Surely you can see that you are dealing with real-world situations in which you are not able to control the actions of 7 billion human beings and their power-mad leaders.
Indeed. That's why I'd like to see a solution that does not rely on universal adherence. Perhaps you could have most people following this idealistic path, but surely there will always be Hitlers and Amins. If a method could be found that would stop crazies and the ill-incented with some not-too-huge majority (say, < 99%) that would be encouraging.
Let's pretend for a second that a legendary mathematician existed, and he started a sequence that enumerated all true statements the Universe could ever make. To do so, he chose a starting point that was his frame of reference (thanks Einstein).

His enumeration was correct in theory, so he whipped out his legendary supercomputer with an infinite amount of memory and a processor infinitely fast. Immediately, he could return answers to questions. Not just some questions. All questions.

It would be nice, to be that legendary mathematician. Let me know if you figure out his name.
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July 15th, 2013, 03:47 PM   #18
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Re: Utopia

By the way, with a name like Utopia, you have expect at least some theoretical crazy talk, right?

Speaking of crazy talk, I am someone who is crazy enough to be religious in my own way (ie... we all are in our own way, as for example, we are not all priests).

Since again I want to keep a mathematical focus here and not a religious one, I will simply pose a question, does anybody think mathematics and religion have anything to do with each other? Personally, I do not...

The notion of a utopia is a long considered "thing." So is the "all-seeing-eye" and such. I do not buy into dooms day theories and I do not wear a tin foil hat. I actually am simple in that I just like everybody and everything as long as they are not doing something 'bad' to me or others. Easy enough, I presume.

To salvage this thread, we covered some mathematical concepts that were of interest to me and that expanded my brain (game theory, bounded rationalization, etc.). I end on the note that all we know and do is a subset of all that exists. All that exists seems to operate according to laws of our so-called universe, and I consider it my job as a curious explorer to observe those laws. I realize mathematicians all adhere to this basic quest.
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July 15th, 2013, 03:59 PM   #19
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Re: Utopia

Quote:
Originally Posted by krausebj0
Let's pretend for a second that a legendary mathematician existed, and he started a sequence that enumerated all true statements the Universe could ever make. To do so, he chose a starting point that was his frame of reference (thanks Einstein).

His enumeration was correct in theory, so he whipped out his legendary supercomputer with an infinite amount of memory and a processor infinitely fast. Immediately, he could return answers to questions. Not just some questions. All questions.

It would be nice, to be that legendary mathematician. Let me know if you figure out his name.
The supercomputer you describe is called a Zeno machine. I can think of a number of people you might be referring to (Borges, Zeno, Hardy, Russell, Goedel) but it's a bit hard to guess.
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July 15th, 2013, 04:05 PM   #20
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Re: Utopia

Hey CRG, I know this thread is a little out there, but it really is supposed to be a number theory thread?

The point is to acknowledge some basics (game theory, rational bounds, the set of all possibilities, the set of all that exists, etc.).

The foundations of mathematics seek to solidify and provide an axiomatic model of our number system. Set theory is the starting point for me and is my focus (not particularily war, religion, etc.). The premise has always been that if all the elements of a complete model (all the axioms, or true statements) can be enumerated, then mathematicians are in theory able to calculate "purely."

The goal of any purist is to solidify the foundations of mathematics. Pure mathematics and applied mathematics are able to be the same things...
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