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Posts tagged with: Musings


While reading about Galilean transformation and electromagnetism (as a prelude to the implications of the special theory of relativity on quantum mechanics, which I’m reviewing since I never did that well in my quantum mechanics class at Princeton), I learned something about ether that I didn’t know before. To me, ether was always either a classification for organic compounds, an item that restored manna to RPG characters, or an archaic word for “space.” Now, I just learned that ether was actually the name given by early physicists to the medium through which electromagnetic radiation was thought to propagate (just as sound, for example, propagates through air).

As the Michelson-Morley experiment would later show, electromagnetic waves are indeed capable of propagating without a propagation medium (see explanation below). This in turn allowed Einstein to develop his special theory of relativity as we know it today. So, the “ether” coined by those early physicists was nothing more than an imaginary construct created to help people of that time understand electromagnetic phenomena. Fascinating, isn’t it?

The Michelson-Morley experiment didn’t explicitly disprove the existence of ether. It did, however, show that light travels at the same speed in perpendicular directions, which, assuming ether did exist, wouldn’t be possible unless the ether frame moved in sync with the Earth’s rotation, which would be a preposterous claim. (They believed the ether frame was rooted either in the solar system’s center of mass or in the center of the universe.) It was Einstein who later used these experimental results to assert that there is no ether frame, which means the velocity of light is only relative to the observer’s own frame, which would then result in the famous concept of a “constant speed of light, c.” Einstein then used this idea to arrive at his famous postulate:

The laws of electromagnetic phenomena, as well as the laws of mechanics, are the same in all inertial frames of reference, despite the fact that these frames move with respect to each other. Consequently, all inertial frames are completely equivalent for all phenomena.

This was an incredibly bold statement at the time, because it meant that Maxwell’s equations and Galilean transformations could not both be correct (one of them had to be wrong). Even bolder, Einstein chose to modify the Galilean transformation, which meant he was challenging the fundamental equations of Newtonian physics!

The Math behind Google’s Pagerank

Pekkle sent me a link a while ago to an article at AMS about how Google determines the importance of a page, also known as its pagerank. It’s actually a very interesting paper and a pleasure to read, especially the first few pages where the author takes you through some elementary logic to arrive at an elegantly simple representation of the entire world wide web’s pageranks as the eigenvector of a square matrix described simply by the number of links on each page. If you’re like me and derive gratification from seeing real world problems reduced to abstract mathematical constructs, you’ll have a blast with this one. I also found this short review of eigenvalues and eigenvectors helpful, as it’s been a while since I’ve touched any linear algebra.

Defense Spending in America

While it’s good for contractors and vendors, defense spending as I’ve come to discover can be a total waste of taxpayer money. I’m going to be very vague here because I don’t want to get into any trouble. During my visit to a certain well-known Department of Defense client of ours in Washington, DC last week, one of their network engineers complained to me about how his department is throwing a significant amount of money (easily into eight figures) into a highly costly technology that not only doesn’t improve their network, but actually decreases their network’s fault tolerance and survivability. This wasn’t a case of opinion or personal preference; any network engineer would come to the same conclusion.

Apparently the only reason why this was allowed to happen is because a certain person in a high level position, who seems to not really understand networking technology, gave his approval to this project. Even when others eventually saw that the project was a total waste of money that did more harm than good, they didn’t dare bring this to the attention of the high-level-position-person for fear of “embarrassing” him and getting on his bad side. There was also speculation that this HLPP either had a substantial investment in the stock of the vendor for this project, or was getting some nice kickbacks in return for his support.

The point of all this is just to serve as an anecdote of a personal encounter with incompetence protected by political bureaucracy resulting in a deplorable waste of taxpayer money. I’ve heard stories before, but I’ve never seen it first hand until now. I guess I’m not surprised, but it’s certainly going to leave a bitter taste in my mouth when I finally get around to doing my taxes.