Ciro Santilli @cirosantilli 35

TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.

Vectors with the index on top such as $x^i$ are the "regular vectors", they are called covariant vectors.

Those in indices on bottom are called contravariant vectors.

It is possible to change between them by Raising and lowering indices.

The values are different only when the metric signature matrix is different from the identity matrix.

The length of its cycle.

Bibliography:

It is quite amazing to read through books such as The Supermen: The Story of Seymour Cray by Charles J. Murray (1997), as it makes you notice that earlier CPUs (all before the 70's) were not made with integrated circuits, but rather smaller pieces glued up on PCBs! E.g. the arithmetic logic unit was actually a discrete component at one point.

The reason for this can also be understood quite clearly by reading books such as Robert Noyce: The Man Behind the Microchip by Leslie Berlin (2006). The first integrated circuits were just too small for this. It was initially unimaginable that a CPU would fit in a single chip! Even just having a very small number of components on a chip was already revolutionary and enough to kick-start the industry. Just imagine how much money any level of integration saved in those early days for production, e.g. as opposed to manually soldering point-to-point constructions. Also the reliability, size an weight gains were amazing. In particular for military and spacial applications originally.

They died so completely, Googling "ICL" now has higher hits such as Imperial College London.

Once upon a time, when Ciro worked at a company, one day the company decided to give everyone a 20% raise.

The likely reason was that Apple was coming to town, and was sucking the fuck out of the company's talent.

Nothing ever drove it so clearly into Ciro's heart the obvious fact that even for skilled jobs, companies don't pay you what you're worth. They pay you as little as possible so you won't quit to join someone else. It is pure market forces in play.

The annoying thing is that people are highly non-fungible, so much like painting auctions, you can only estimate your price by putting yourself on auction and seeing what people will pay for you, i.e. interviewing for new jobs.

Another point is that people have all sorts of stupid restrictions such as not wanting to work on certain areas for moral reasons, or not wanting to move away from a certain area they like. Companies will of course readily exploit such weakness to be able to pay less. Silly non-rational beings.