First of all I wanted to link a couple things : Ten good free Linux ebooks online at linuxhaxor. And a link to an interesting scenario that happens in business at randsinrepose.
Topology. The problem in topology, as I see it, is that is misses that connection to the universe that is critical to having a method which produces proper results. What I am talking about specifically is the fact that space can be viewed as isolated or bounded. It is a very well populated science, which lacks universal foundation. The key problem is in defining the basics. In a universe that is wavelike in its structure and where a point or singularity can continuously be compressed, there is no place where another element cannot be fit between or through something else. The problem is that in an ocean, there is never really a surface. It may seem so in the abstract, however there is no way to isolate space in such a way that anything has a real continuous surface. In the mathematics it has application and it is useful, but it is like Bayesian analysis, it needs to be seen for what it is and not applied where it represents things which are not productive. When you mix probability waves and topology, you get a very strange soup that tastes like paradox.
It is my personal opinion that any scientist that does not take advantage of programming in their area is missing about 99% of what they could achieve with the same effort. By actually writing equations ( in program form ) that match the principles I study, I gain a deeper insight and ways that they can be combined to produce new insight at speeds that I could never hope to match in my brain alone. To some extent we have become connected and addicted to our computers, as I/we have become dependent on that extension to achieve a product which cannot be produced without the symbiosis of the two.
We stand on electronic stilts of our imagination and design to rise above the chaos.
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