another Ron Paul post

[Religious Dick]

You think no one is hurt by ownership of property? Ask yourself how many people died so you, a white man, can own the land you live on today.

Apparently not enough of them. Where's Augusto Pinochet when you need him?

[Plane]

This is an unbelievably dumb thing to have to argue Plane. It is common sense that when dealing with economics, a number is either finite or infinite. But, for your pleasure I had an Oxon friend provide a more detailed explanation:

?For the Maths, the answer?s ?No, but.? In set theory, a set is finite if there is a one to one correspondence between the set and a proper subset of the set of natural numbers, with the empty set being given as finite. From there, the definition of infinite is a set that is not finite (you then get this definition subdivided into 2, with countably infinite being a set with a one to one correspondence between the set and the natural numbers and uncountably infinite being everything else). This definition doesn?t take into account proper classes  http://mathworld.wolfram.com/ProperClass.html (e.g., the class of all sets), but proper classes are bigger than sets, so would automatically be classed as infinite. That, however, looks at just sets, and not things with mathematical structure on them. To look at things with mathematical structure on them, the obvious ideas that spring to mind concern Measure Theory http://mathworld.wolfram.com/Measure.html. I don't really know much about this at all (I know quite a bit about Lebesgue Integration mentioned in the link, but nothing about Lebesgue measure, for example). The essence of measure theory is to put measure on things, giving you a concept of quantity, but as the functions all fall into the real numbers, your measure of quantity will always be finite (infinity is not a real number). Going back to the mathematical structure setup, the standard way to work with something in maths is to work in a Category http://mathworld.wolfram.com/CategoryTheory.html, or if your being really crazy, you work in higher categories  http://en.wikipedia.org/wiki/N-category. From there, you have the notion of small category, where the objects are sets rather than a proper class, and there are lots and lots of ways to count and put quantity on categories, objects in categories, morphisms in categories etc, but 99.9% of these are useless, don't tell you anything, and are just you (you in general, not you in particular) just making up bullshit that no one would care about. Categories are something I know a lot about (my PHD is currently based around working with something called the stable homotopy category of equivariant spectra), but I know nothing about classing categories by size (except for classifying k-tuply monoidal n-categories, which you really, REALLY, don't want to know about). Finally, you can obviously classify (weak) n-Categories by the n, and this leads onto lots of cool stuff being developed at the moment on infinity categories, and the theory there is tending towards classifying them in the form (infinity,1), (infinity,2) etc, suggesting that actually, although these things are in a sense "infinite", there's a lot more to it than that. Sorry if this answer makes no sense!?

 My point is easily made that his point that everything is either finite or its not, in which case it?s called infinite, is what I was saying! Especially when he says ?infinity is not a real number?! I knew that one! His use of infinity 1, etc, is done not to confuse the non-mathematicians where aleph-hull, aleph-one, etc would be used instead.

I know you can't tell it ,but this guy is in near agreement with me.

From there, you have the notion of small category, where the objects are sets rather than a proper class, and there are lots and lots of ways to count and put quantity on categories, objects in categories, morphisms in categories etc, but 99.9% of these are useless, don't tell you anything, and are just you (you in general, not you in particular) just making up bullshit that no one would care about.

How true!

I agree that there is no infinity of resorces but you needn't get hung up n such a minor point. Consider that the world has very many times more wealth now than it did fifty years ago, this wealth was created . Acording to your understanding this cannot be so even though it evidently is.

Ther is no finite amount to wealth , nor is it finite.

Most capitol is created the same year it is consumed .

[Plane]

JS I hope you are not getting too frustrated with our argument seeming to get hung up on something that you would consider an axiom .


Lets just skip to the next thing leaving unsetled whether a number can have a state that is neither infinite or finite. I don't consider it important actually, only interesting .

   If I am a potter and I sell a lot of pots I will dig more clay , one might argue that there is no infinity of clay and this is true , but there is a lot of clay.

    In curcumstances in which there is a limited amount of raw materiel ,price must rise as the raw materiel becomes scarce , if the raw materiel becomes too rare substitutes must be found and the high price will support the search for the substitute.

    Both of these situations occur in reality some things are made from plentiful raw materiels and some are made from scarce raw materiels , but in both cases value is added by work done , and capitol is created.

[Plane]

This is an unbelievably dumb thing to have to argue Plane. It is common sense that when dealing with economics, a number is either finite or infinite. But, for your pleasure I had an Oxon friend provide a more detailed explanation:

?For the Maths, the answer?s ?No, but.? In set theory, a set is finite if there is a one to one correspondence between the set and a proper subset of the set of natural numbers, with the empty set being given as finite. From there, the definition of infinite is a set that is not finite (you then get this definition subdivided into 2, with countably infinite being a set with a one to one correspondence between the set and the natural numbers and uncountably infinite being everything else). This definition doesn?t take into account proper classes  http://mathworld.wolfram.com/ProperClass.html (e.g., the class of all sets), but proper classes are bigger than sets, so would automatically be classed as infinite. That, however, looks at just sets, and not things with mathematical structure on them. To look at things with mathematical structure on them, the obvious ideas that spring to mind concern Measure Theory http://mathworld.wolfram.com/Measure.html. I don't really know much about this at all (I know quite a bit about Lebesgue Integration mentioned in the link, but nothing about Lebesgue measure, for example). The essence of measure theory is to put measure on things, giving you a concept of quantity, but as the functions all fall into the real numbers, your measure of quantity will always be finite (infinity is not a real number). Going back to the mathematical structure setup, the standard way to work with something in maths is to work in a Category http://mathworld.wolfram.com/CategoryTheory.html, or if your being really crazy, you work in higher categories  http://en.wikipedia.org/wiki/N-category. From there, you have the notion of small category, where the objects are sets rather than a proper class, and there are lots and lots of ways to count and put quantity on categories, objects in categories, morphisms in categories etc, but 99.9% of these are useless, don't tell you anything, and are just you (you in general, not you in particular) just making up bullshit that no one would care about. Categories are something I know a lot about (my PHD is currently based around working with something called the stable homotopy category of equivariant spectra), but I know nothing about classing categories by size (except for classifying k-tuply monoidal n-categories, which you really, REALLY, don't want to know about). Finally, you can obviously classify (weak) n-Categories by the n, and this leads onto lots of cool stuff being developed at the moment on infinity categories, and the theory there is tending towards classifying them in the form (infinity,1), (infinity,2) etc, suggesting that actually, although these things are in a sense "infinite", there's a lot more to it than that. Sorry if this answer makes no sense!?

 My point is easily made that his point that everything is either finite or its not, in which case it?s called infinite, is what I was saying! Especially when he says ?infinity is not a real number?! I knew that one! His use of infinity 1, etc, is done not to confuse the non-mathematicians where aleph-hull, aleph-one, etc would be used instead.

This guy would be interesting to talk to.

I am not entirely up on his jargon but he makes some good points.


I wouldn't have said that everything is infinite unless it isn't , but that is true as far as it goes .

The sands on the beach are finite but what is the water in the river?

From moment to moment the volume of a river changes due to its continual emptying and refilling, the only way it could possibly be considered to be finite would be instantaneously, for an instant the quanity of water in a river would have a one for one match up with a set which was a finite number.

This is not a usefull distinction but a forced one , from haveing to shoehorn everypossible state into either infinate or finite.

It isn't necessacery or usefull to make such a distinction , it only comes up in this context because the point is attempting to be made that all games are zero sum.

[_JS]

This guy would be interesting to talk to.

I am not entirely up on his jargon but he makes some good points.

He is a very interesting individual, and I'm not up on all the jargon either. In fact, he purposefully tried to put this in layman's terms so that I could better discuss it. This is what an Oxford Mathematician sounds like. I know a little about his statement on categorizing infinities and in this case he simplified it for us by not using the terms aleph-null, aleph-one, etc (he simply used "infinity,1...").

I wasn't really hung up on this aspect of our discussion Plane, in fact I think we agree more than we disagree. I think it is more a matter of how we apply the terms to it. Obviously I'm not arguing that there does not exist untapped capital. The existence of untapped capital does not make it a non-finite number. It simply makes it a variable, just simple algebra. Also, I'm well aware that there does exist real-term growth - one of the questions is who benefits from that growth and by what degree?

I apologize if I've done a poor job debating, and I feel that I have. Honestly, I have a lot going on in life right now and I just don't have the time or inclination at the moment.

 

[Plane]

This guy would be interesting to talk to.

I am not entirely up on his jargon but he makes some good points.

He is a very interesting individual, and I'm not up on all the jargon either. In fact, he purposefully tried to put this in layman's terms so that I could better discuss it. This is what an Oxford Mathematician sounds like. I know a little about his statement on categorizing infinities and in this case he simplified it for us by not using the terms aleph-null, aleph-one, etc (he simply used "infinity,1...").

I wasn't really hung up on this aspect of our discussion Plane, in fact I think we agree more than we disagree. I think it is more a matter of how we apply the terms to it. Obviously I'm not arguing that there does not exist untapped capital. The existence of untapped capital does not make it a non-finite number. It simply makes it a variable, just simple algebra. Also, I'm well aware that there does exist real-term growth - one of the questions is who benefits from that growth and by what degree?

I apologize if I've done a poor job debating, and I feel that I have. Honestly, I have a lot going on in life right now and I just don't have the time or inclination at the moment.

 

I have been enjoying the discussion , but it is always volentary and dependant on your generosity to continue , please quit before it causes a problem.

Please don't think that I want you to place an unrealistic priority on answering me. Answer weeks later if that please you.

I think what I would like to narrow down is the idea of creation of capitol , which I beleive happens constantly .

Not just from the tapping of natural resorces , but also from the work and thought of Human beings.

My Idea of Capitol is of a system of exchange in values which allows Capitol to be constantly created and consumed , so that speaking of its total value is like speaking of the water in a river.



BTW, your mathmatical buddy is welcome here , if he doesn't mind the sad state of our math.