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Any of you work in quant finance?


HeartThais

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It's all about continuity and countability.

 

Dooyeweerd clearly states that the quantitative aspect has as its kernel discrete quantity (see his lengthy arguments in NC II:79-95ff). He places continuity within the spatial aspect, whose kernel is 'continuous extension', with a strong retrocipation to this aspect. For example, he argues that irrational numbers are not in fact true numbers (but rather functions). I found difficulty in accepting this, having been brought up to see number as essentially continuous. But I have now changed my mind.

 

In fact I have recently been discussing integer and 'real' (continuous) numbers with a mathematician. The discussion centred on two types of infinity. That related to real numbers is larger than the infinity related to integers! Due to the continuous nature of spatial numbers (continuous extension). So, he was saying, 'reals' are a fundamentally different kind of number, and require a different kind of mathematics. This recognition of a fundamental difference is indicative of crossing an aspectual boundary. So, since the main use of reals is to cope with spatial factors, indirectly if not directly, then it might seem that they are attached more to the spatial aspect.

 

Also Andrew Hartley (you know Andrew don't you) sent me the following expansion on this theme:

 

"I went back to some of your Dooy web pages and felt I must sometime soon come to grips with Dooy's idea that the real numbers belong to the spatial mode and not the quantitative one. ... I have an idea that it is all related to the concept of "countability," e.g., as in the language of Nancy McGough who said 'In 1874 Georg Cantor discovered that there is more than one level of infinity. The lowest level is called countable infinity and higher levels are called uncountable infinities. The natural numbers are an example of a countably infinite set and the real numbers are an example of an uncountably infinite set. In 1877 Cantor hypothesized that the number of real numbers is the next level of infinity above countable infinity. Since the real numbers are used to represent a linear continuum, this hypothesis is called the Continuum Hypothesis or CH.'"

 

It is interesting to find that Dooyeweerd, a lawyer, understood this deep mathematical idea, and saw the kernel of the spatial aspect as continuous extension rather than shape, position, distance, curvature, or whatever.

 

Got it?

 

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"Cantor hypothesized that the number of real numbers is the next level of infinity above countable infinity."

 

Could you rewrite this?

 

Does not that mean the brown stain in my shorts doesn't really exist because it has not permeated into the air yet and that nobody is qualified to detect that particlar odor as a result of not being in close proximity of where my shorts are?

 

I think you have gotten my defluxia over working again which means I am going to get fluxed up again. :applause:

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Cantor was a real genius. The idea of countable and uncountable infinities is indeed a fundamental concept for mathematicians, though there's a whole branch of mathematics that doesn't believe at all in the idea of infinity.

 

It's actually relatively simple to grasp the difference between countable and uncountable, though it would take more space than I'm willing to devote here (and more time, I'd have to refresh my memory), but usually when people invoke concepts like this in real life, they're just trying to intimidate people--trying to make people feel like they people who know about uncountable numbers are superior and 'in the know.' Many times the actual concepts they talk about are unrelated to countability in any substantial sense.

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Is there anyone here that works in derivatives or a similar field in Asia? If you do, please contact me. I'd like to get your insights.

 

I had a relative who worked in a field, it was near Wexford in Ireland so not Asia I'm afraid, he was a farmer.

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