We all know Moore's law, but very few seem to understand the inevitable logic that it implies. Moore's law states that the number of transistors on a silicon chip doubles every 12 to 18 months. In practice chips are all pretty much the same cost (within an order of magnitude or so), thus we get double the capability every 18 months. The long term consequence of this is that everything becomes digital and every digital device is eventually a single chip.
I will not waste your time you with a comprehensive history. It is sufficient to highlight a couple of trends. The first trend is to digital media, starting with music in the CD and then MP3, then video and books, and now we are on the verge of digital broadcast TV and radio. A second trend is towards the single chip implementation of all electronic devices, starting with watches and calculators in the 70's then consumer electronics like CD players, stereos, radios and TV's. Currently we have just achieved the single chip cell-phone. The trend to digital media helps with the movement to single chip implementations because it is much easier to do an all digital device than one that has both analog and digital circuits.
One device that has so far avoided becoming a single chip implementation is the personal computer. A typical motherboard has about 6 to 8 processing chips, a bunch of memory chips and some driver chips that do nothing more than pass on a strengthened signal from a processing chip. One day all these chips except for the driver chips will coalesce into a single chip, because there will be nothing else better to do with all the available transistors.
So, last week when AMD announced that they were buying ATI, I knew what it was about. AMD has the single chip personal computer on their long term road map, and they need the display drivers and other peripherals that ATI has to complete their vision. AMD has already moved the memory controller onto the processor chip. Next I expect them to announce a low end chip with all the rest of the peripherals integrated. Over time the single chip processor implementation will move up to the mid range and high end. Sometime thereafter, the single chip computer with integrated memory will become first possible and then inevitable.