How many colors do you need to color countries on a map such that no two adjacent countries have the same color? Only four.
The problem is solved by representing a map as a planar graph. The solution comes from the graph theory.
Unfortunately this is not true for non-planar graphs. Every non-planar graph can be represented in three dimensions and it is possible to connect each vertex with all the other vertices, therefore in the worst case one would need as many colors as there are vertices in order to avoid two interconnected vertices having the same color.
I suspect that this has something to do with the fact that our space is three-dimensional. Not two-dimensional and not four-dimensional. I think there must be some connection. Perhaps three dimensions are sufficient and a fourth dimension of space would be redundant? I am sure some physicist has already thought of it and wrote a nice thesis.
We got the MacBook White over 5.5 years ago. It withstood the trial of time. A year after we got it, it survived a spill of tea, which killed the IR sensor for the remote. Two years later the inverter cable went flaky – the backlight became intermittent, so we stopped closing the lid, otherwise it was difficult to restore the backlight. Then the fan started being loud. I replaced the fan with a new one. Then I upgraded the memory to 4GB and upgraded the OS. A year ago the battery died, so I replaced it. A few days ago the kids inadvertently pushed it off from the coffee table and a day later the hard drive died.
That’s it, I will stop trying to keep it alive and I will let it die.
Until its last minutes, the MacBook White worked very well, almost the same like when it was new. The only reason to ever reinstall the OS was to upgrade it. After the memory upgrade it was able to even run Lion without any problems.
I expect the new generations of MacBooks sold today to be even better.
- The very nice looking plastic of which MacBook White was made was nevertheless – plastic. There were tiny cracks here and there and tiny pieces chipped off on the edges of the keyboard. All current MacBooks are made of aluminium and are not susceptible to this kind of damage as easily.
- The lid hinges in the aluminium MacBooks feel much more solid, not sure if his is because the hinges are better, but I have no problems whatsoever with the one I’ve been using for over 3 years now.
- The latest generations of MacBooks don’t have hard drives. Hard drives are delicate. Some people rightfully call them the spinning discs of rust. The latest MacBooks have flash-based non-volatile memory instead of hard drives, which should theoretically have longer average life time and is more reliable than mechanical hard drives.
Apple’s MacOSX integrates really well with the hardware. But one can also run Linux or Windows just fine on MacBooks, either in a virtual machine or natively. It’s certainly a piece of hardware worth recommending. It is expensive, but it is worth every penny spent on it.