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Journal Journal: Keeping the faith, thinking in four dimensions, ...

Keeping the faith

Lately I've become increasing disgusted with the state of affairs on both Slashdot and the internet at large. There seems to be a growing number of people with nothing better to do but sit at a computer and post garbage replies to people who actually have something good to say. While these people obviously have some growing up to do, saying so will only cause one to get flamed again. I'm sure that this has been going on for a long time, but I've only recently begun to realize how big the problem has become. Just when I get to the point of leaving the discussions behind, however, someone writes an intelligent and engaging reply -- and it is they who keep me here.

Thinking in Four Dimensions

The other day -- yesterday, actually -- I started thinking about what a four-dimensional sphere might look like. The introverted and highly abstract train of thought that followed was one of the most profound I've had in some time.

Since a sphere is the (n-dimensional) set of points that are equidistant from a singular "center" point, it follows that beyond three dimensions there would be some overlap -- that is, some of the points from dimensions n > 3 would occupy the same space as points from other dimensions. We know that this cannot occur in our universe, so other dimensions must be fundamentally disconnected from those that we can see.

To illustrate this example (and to make it easier to think about), I used the concept of color. Consider a red sphere in three dimensions. It would look like a large rubber ball with no holes or textures. For the sake of this example, we will assume that all the points in dimensions 4, 5, and 6 are colored blue. We initially see the ball as being red, but logic tells us that once the other three dimensions (4-6) are introduced and the aforementioned overlap takes place, the ball will become purple.

This resolves -- or, rather, simplifies -- one of the issues I was fumbling with: even if we could see beyond three dimensions, how would we know? My guess is that, similar to our ability to recognize color, we would be able to recognize that something is fundamentally different about the extra dimensions.

These thoughts also led to more thoughts about Klein Bottles and other such manifolds. Topology is a highly fascinating subject -- one that I hope to learn more about soon.


Why can't it be a requirement that bosses take some management classes? My boss seems to think that this philosophy will run a business well:

  • If nothing is wrong, a boss should sit in his cubicle and say nothing to his employees.
  • If something goes wrong, immediately get upset and berate the employee who caused the problem -- or berate the employee who could have prevented the problem, no matter how far out of the employee's hands it was.
  • Pay some new employees (with same education and less experience) more than those who have been there for 4-5 years.
  • Promising raises to a certain payrate and then actually paying considerably less.
  • Much more like this...

I'm planning to write a long letter about all this when I resign, since it needs to be said.

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