Where Did Prot Holo Come From?

[JusticeRetroHunter.7684]

1 hour ago, Crozame.4098 said:

I mean, seriously, think of some other games: publics good game, Cournot completion, common value auctions etc. For these games, the  equilibrium is the centre of the mass? LMAO.

 

Seriously dude, all your statements are meaningless if you are not rigorous. 

 

 

If it obeys a function, it can be mapped out to phase space, and if it has a fixed point solution it will look just like the picture above in that phase space.

 

Do you...know what a phase space is man just curious?

[Crozame.4098]

34 minutes ago, JusticeRetroHunter.7684 said:

 

If it obeys a function, it can be mapped out to phase space, and if it has a fixed point solution it will look just like the picture above in that phase space.

 

Do you...know what a phase space is man just curious?

So, you are using more and more definitions to explain "simple definitions" that you made for other people to understand a concept better.

 

And for the record, I do not know what is a phase space, because I do not need it in my daily life nor in my research. But, when I need to explain something in this forum, I usually give simple examples or counter examples and I do not use vague terms and I do not post hour long vids that might be totally irrelevant.

 

Also, when I provide inaccurate information in some of my other posts, I admit my mistake. I do not try to invent "thousands of" excuses to cover them up. 

Edited June 18, 2021 by Crozame.4098

[JusticeRetroHunter.7684]

19 minutes ago, Crozame.4098 said:

So, you are using more and more definitions to explain "simple definitions" that you made for other people to understand a concept better.

 

Actually you're just being thick headed and don't want to go and learn a few things to understand very simple simple discussion point here...I'm here right now trying to explain to you WHY there is a notion of SIZE to fixed points...you're refusal to learn why we are talking about it like this is not anyone's fault but you own.

 

Quote

 

And for the record, I do not know what is a phase space, because I do not need it in my daily life or in my research. But, when I need to explain something in this forum, I usually give simple examples or counter examples and I do not use vague terms and I do not post hour long vids that might be totally irrelevant.

 

 

Alright so this is definitely the reason why you're having trouble. I'm not gonna explain to you what phase space is... but it's the reason why it makes it easy for me and maybe Kolzar to talk about the size of fixed points. You don't need to draw phase space graphs to understand this problem (in fact for correspondence you probably can't draw one very easily)...but if you did you'd understand very easily how their is a convention of size involved with these points.

 

I don't know what you do for a living...nor do I need to know...but if you haven't learned what a phase space is or why it's used, that's something as very primal and basic as set theory. I didn't know much set theory before this forum post...but I went to go and learn it a bit more so i could talk about this in some kind of meaningful detail with Kolzar...I suggest you do the same because phase space is really fundamental math stuff so I can hardly believe you research anything in the real world without using phase space diagrams.

 

Honestly, I'm done here trying to help you out because this topic is already 12 pages deep and it's just a circular talk with you. Do your own diligence and nitpick all you like, but you are the one that's failing to understand the conversation here it's on you to either ask questions to get them answered, or to go and look it up on your own and sort out why we are talking about the game in this way.

Edited June 18, 2021 by JusticeRetroHunter.7684

[Crozame.4098]

19 minutes ago, JusticeRetroHunter.7684 said:

lright so this is definitely the reason why you're having trouble. I'm not gonna explain to you what phase space is... but it's the reason why it makes it easy for me and maybe Kolzar to talk about the size of fixed points. You don't need to draw phase space graphs to understand this problem (in fact for correspondence you probably can't draw one very easily)...but if you did you'd understand very easily how their is a convention of size involved with these points.

First of all, I did not have trouble understand the concepts. All I pointed out was that you were not using them in a rigorous manner.

 

Your statement like "phase space is really fundamental math stuff" is also shacky. I did calculus, probability theory, some mathmatical analyses, and some set theory, I never encountered a term called fundamental math stuff. This is like all of your posts, trying to sound smart by using some technical terms, but mate, use them accurately...

 

Lastly, if you really want to help us. Stop pumping ambiguous defined stuff on this forum.

Edited June 18, 2021 by Crozame.4098

[JusticeRetroHunter.7684]

Just now, Crozame.4098 said:

First of all, I did not have trouble understand the concepts. All I pointed out was that you were not using them in a rigorous manner.

 

Your statement like "phase space is really fundamental math stuff" is also shacky. I did calculus, probability theory, some basic mathmatical analyses, and some basic set theory, I never encountered a term called fundamental math stuff. This is like all of your posts, trying to sound smart but not....

 

Yea, Phase Space is fundamental like Algebra is to Calculus....like you need to know how to add X and Y before you can integrate them. Set Theory is also fundamental in that it's like a different version of algebra but for things and sets of things. 

 

Phase space is actually just a graph...plotting X and Y on a Euclidian grid is a phase space. As a tool it's a bit more powerful then just a graph though, because it allows you to plot all possible states a system can be in onto a simple XY grid, and allows you to watch how the entire system evolves through time. It's a very fundamental set up in order to make predictions, in every STEM field.

 

If you look into a bit of history, the first Fixed Point Theorem, by Brouwer, was based on the work of Poincare...the guy who made phase space. Poincare was similarly trying to find out the equilibrium solutions to Newton's work...finding the trajectories of celestial bodies required knowing their fixed points...he needed to create the mathematics of phase space in order to do that. Poincare actually developed the first fixed point theorem, it was just never fully realized until Brouwer came along and put the pieces together. 
 

[Crozame.4098]

1 hour ago, JusticeRetroHunter.7684 said:

 

Yea, Phase Space is fundamental like Algebra is to Calculus....like you need to know how to add X and Y before you can integrate them. Set Theory is also fundamental in that it's like a different version of algebra but for things and sets of things. 

 

Phase space is actually just a graph...plotting X and Y on a Euclidian grid is a phase space. As a tool it's a bit more powerful then just a graph though, because it allows you to plot all possible states a system can be in onto a simple XY grid, and allows you to watch how the entire system evolves through time. It's a very fundamental set up in order to make predictions, in every STEM field.

 

If you look into a bit of history, the first Fixed Point Theorem, by Brouwer, was based on the work of Poincare...the guy who made phase space. Poincare was similarly trying to find out the equilibrium solutions to Newton's work...finding the trajectories of celestial bodies required knowing their fixed points...he needed to create the mathematics of phase space in order to do that. Poincare actually developed the first fixed point theorem, it was just never fully realized until Brouwer came along and put the pieces together. 
 

Oh, if it is such a fundamental thing like algebra to calculus, why it is not in high school or undergraduate curriculum? Again, you are falling for your own delusion, making statements without any grounds.

[JusticeRetroHunter.7684]

2 minutes ago, Crozame.4098 said:

Oh, if it is such a fundamental thing like algebra to calculus, why it is not in high school or undergraduate curriculum? Again, you are falling for your own delusion, making statements without any grounds.

 

Did you not read anything I just said? A Euclidean X by Y grid is a phase space...it's the first thing you learn in school ever.

[JusticeRetroHunter.7684]

13 minutes ago, Crozame.4098 said:

Oh, if it is such a fundamental thing like algebra to calculus, why it is not in high school or undergraduate curriculum? Again, you are falling for your own delusion, making statements without any grounds.

 

Look I'm really tired of saying the same things over and over again, each time just being berated as if I'm not throwing a bunch of links at you that are all reputable sources that all say the same thing.

 

Want to see RPS represented in phase space? Here you go

https://www.siue.edu/~evailat/Rock-Paper-Scissors.htm

 

Want to know what Phase Space is and how it applies to our conversation and is fundamental to all system analysis? Watch this video

 

I won't bother replying anymore if you don't want to take the initiative to learn anything on your own time with your own effort. Honestly if you don't know how phase space is or how it's being used here, you won't understand the conversation between Kolzar and myself, why our views are the basically same with very minor exceptions. The end

[Crozame.4098]

1 hour ago, JusticeRetroHunter.7684 said:

 

Did you not read anything I just said? A Euclidean X by Y grid is a phase space...it's the first thing you learn in school ever.

LMAO, then why they dont use that term? Why the text book is about x and y axis?

 

And you still dont understand the point about whether I understand your statements and they way you present your statements. I mostly refer to the latter point.

Edited June 18, 2021 by Crozame.4098

[JusticeRetroHunter.7684]

32 minutes ago, Crozame.4098 said:

LMAO, then why they dont use that term? Why the text book is about x and y axis?  Whats wrong with you....

 

Because phase space is the correct term obviously... There's nothing wrong with me you just don't want to learn what it is.

 

You have an X and Y axis. The X axis is an integer, the Y axis is another integer, together they create a coordinate (X,Y) and this is your typical Euclidean graph that you learn in middle school. Instead of using a single integer value for X or Y, you can instead have Y be a vector which has 2 values that define it (Length and direction) and the X axis have 3 values that define it to indicate a position (XYZ), So now the Y axis is a vector, and the X axis is a position in a 3d space. Now you can map the position of some object along the X axis, and a vector that determines how far it travels along that axis at intervals of time to give you a description for how that object is moving in a system through time. This graph therefor describes the entire system, and placing an element anywhere in this system describes where its going and where it will end up because all coordinates on this graph have a unique trajectory. 

 

Go and watch the video the guy clearly explains it, and he even talks about the fixed points you find when you graph a system in phase space. 

Edited June 18, 2021 by JusticeRetroHunter.7684

[Crozame.4098]

2 hours ago, JusticeRetroHunter.7684 said:

 

Because phase space is the correct term obviously... There's nothing wrong with me you just don't want to learn what it is.

 

You have an X and Y axis. The X axis is an integer, the Y axis is another integer, together they create a coordinate (X,Y) and this is your typical Euclidean graph that you learn in middle school. Instead of using a single integer value for X or Y, you can instead have Y be a vector which has 2 values that define it (Length and direction) and the X axis have 3 values that define it to indicate a position (XYZ), So now the Y axis is a vector, and the X axis is a position in a 3d space. Now you can map the position of some object along the X axis, and a vector that determines how far it travels along that axis at intervals of time to give you a description for how that object is moving in a system through time. This graph therefor describes the entire system, and placing an element anywhere in this system describes where its going and where it will end up because all coordinates on this graph have a unique trajectory. 

 

Go and watch the video the guy clearly explains it, and he even talks about the fixed points you find when you graph a system in phase space. 

I mean, you dont even know the point of the issue... You are just avoiding stuff that you are certainly wrong, and repeat the same kitten everytime.

 

And btw, X and Y should be Real numbers in Euclidean space, not integers. Again, not rigorous~

[JusticeRetroHunter.7684]

 

6 hours ago, Crozame.4098 said:

And btw, X and Y should be Real numbers in Euclidean space, not integers. Again, not rigorous~

 

Integers are real numbers.

[Crozame.4098]

6 hours ago, JusticeRetroHunter.7684 said:

 

 

Integers are real numbers.

So you think the the x and y axis only consists of integers?