July 13th, 2013, 06:54 AM  #1 
Senior Member Joined: Nov 2011 Posts: 599 Thanks: 0  Utopia
I am about to head out again for the rest of the day, but want to drop an experiment on you guys. As we all know, I love when things add up. This experiment is of a mathematical sense only, and I do not mean to make any sort of political statement by it personally. I choose to discuss politics elsewhere if at all. There are infinite possibilities when it comes to starting a war. Of these possibililities, each can be assigned a unique sequence of occurrances leading up to the possibility itself (ie... someone was broke, so they joined the army because it paid, someone else joined for a different reason, and so on, and an army resulted in one country, etc.). No matter what the case, reality will in fact contain such a list of occurances leading up to the end possibility of war (historically speaking, as wars have existed, so thus is the case if another war is to exist). In order to prevent war, we can mathematically reason with the possibilities and occurrances leading up to them. I will provide a basic example: Assumption: All armies must feed and pay their troops Mechanism: All countries are banned from feeding and paying troops Imperfection: Countries do not want to be defenseless... ... I post this because it is close to the 4th of July, and again, I will be watching fireworks tonight. 
July 13th, 2013, 12:08 PM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Utopia Quote:
The field of mathematics most often applies to such situations is game theory or social choice theory. You may be interested, for example, in the hawkdove game and the implications of its mixed strategy on this problem. (This is a very simple example  of course the fields go much deeper, but it's usually best to start with something relatively simple.)  
July 14th, 2013, 05:46 AM  #3 
Senior Member Joined: Nov 2011 Posts: 599 Thanks: 0  Re: Utopia
Hi there CRG. Just call me Brendon. I need to apologize for being a bit of a clown. Thanks again for all of your help here. I agree there are imperfections in my logic, namely, that it requires unconditional faith in everyone when it comes to the utopia example of preventing war. "preventing war" can be switched to "watching the sunrise" where one has to seek a path in which one gets to watch the sunrise. We are all capable of adding things up. I want to make my experiment one that is easily performed by kindergardeners. 
July 14th, 2013, 07:03 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Utopia
I think that the condition that all people cooperate is too strong to be useful in the realworld. I could imagine 60% support, even 99% support, but not 100%. I wouldn't want a system where there is peace but devastating war can break out if there is just one person who desires it. That's why I suggested the hawkdove game: its analysis (or rather, the analysis of a slightly more complicated game) leads to a strategy by which incomplete adherence to a particular strategy leads to peace by discouraging hawks (as long the the threshold of hawks is not too large). The keyword to search for is "evolutionarily stable strategy". 
July 14th, 2013, 07:06 AM  #5  
Senior Member Joined: Nov 2011 Posts: 599 Thanks: 0  Re: Utopia Quote:
By the way, I never addressed martian attacks either... that is another imperfection.  
July 14th, 2013, 10:57 AM  #6 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Utopia
I suggest you learn about this! It's fascinating and not hard. Any introduction to game theory textbook should cover games like dove and hawk, and the better ones will cover ESSs. Once you understand the basics you should be in a much better position to think about and create potentiallyworkable solutions to this and other problems. Another famous game theory problem related to establishing a stable peace is the iterated prisoner's dilemma, which should similarly be covered in any good introduction. I can give book recommendations, if you like, or you can find material online. 
July 14th, 2013, 06:16 PM  #7 
Senior Member Joined: Nov 2011 Posts: 599 Thanks: 0  Re: Utopia
Thank you for the suggestion CRG. While I continue to contemplate your wisdom, please allow me one more "amatuer" explanation of my thought process. Throughout history, we (scientists, including mathematicians) have performed experiments. As the joke goes, we do not know who really invented explosive devices for the first time. Now days, we tend to realize if our work has any sort of danger aspect, so to speak. Utopia seeks to do the opposite in the sense that it was eliminating dangers (like war). Personally, it freaks me out to think that people had the nerve to create an atomic bomb. What were they thinking? It freaks me out to think that a curious person could trigger an explosion, earth quake, volcano, black hole, etc. My point is this: I want to make sure my work has a familyfriendly label. I do this by being an accountant and playing with numbers. For the sake of people like me who are happy with what they have, I request that we never go too far by failing to see what we are doing. I love the ideas of solar power, clean water, space travel, and so forth. Let's get there safely! 
July 15th, 2013, 04:34 AM  #8 
Senior Member Joined: Nov 2011 Posts: 599 Thanks: 0  Re: Utopia
Thanks CRG. I have received my basic introduction to Game Theory now, including your Hawk and Dove examples and the prisoner's dilemma. We know how much I love Wiki, so I will use it: https://en.wikipedia.org/wiki/Game_theory Game theory is a study of strategic decision making. More formally, it is "the study of mathematical models of conflict and cooperation between intelligent rational decisionmakers". As expected, I am to turn around and somehow dismiss game theory. Let's see... I think it has to do with the "rational decisionmakers" part. Hawk and Dove are imaginary (comic book characters) and never really have to make a single rational decision. The prisoners are in no position to make a rational decision, despite their ability to. Free will is more powerful than any mathematician's attempts to predict the future. The present is always dictated by the past, as is the future, so we can all be prophets and seers. The near future is much easier to predict. I assume I will go to the corner store today (which just so happens to exist in the first place) among other things, so am I a fortune teller? No, clearly not, but I am probably successful in predicting the future, as I plan to go to the corner store here shortly. I control my own prophecy. Utopia is idealistic. It is applied to anything and everything by everyone, without even realizing it. In fact, utopia is our natural process. Everything always adds up. There is no family friendly label that I can place on my work. Imagination is left to consume those who let it, and the case is no different with my mathematical paradoxes. While I see my work as fun and a joke, others may not. I cannot control others. Let us agree that my utopia has already been addressed by mathematicians of the past then. It is nothing new. Thank you for your input, and pointing me towards game theory CRG. 
July 15th, 2013, 05:05 AM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Utopia Quote:
 
July 15th, 2013, 02:50 PM  #10 
Senior Member Joined: Nov 2011 Posts: 599 Thanks: 0  Re: Utopia
Again, thanks for pointing out bounded rationality. I agree we are on the same page now, except one last tiny detail. My model is not bounded by rationality. Utopia is the all seeing eye. It is an axiomitization of our Universe. We are the ones bounded by rationality... 

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