Moore’s Law Redux

Moore law is an axiom not a fundamental law of physics. It is a riule of thumb that is generally held to be sustainable in the short run. Leave it
to drab and over-anayltic minds to turn an exciting prospect into techno-babble. Yet somethiing important that is missing her is the social change that is gradual coming about with the advent of technology, - to the vast majority of the populace, - the internet is but a cursory beginning into the vast and exciting possiblities that are about to take place with the dawn of the information age, - thw way we live, the way we do business, and the eventually the way we percieve
life itself.

MOreover when we talk about computing - we are currently talking about Silicon based binary logic. JUst imagine if multi-level logic becomes feasible, one has just increased the bandwith of computers multi-fold almost instantenously -given existing semiconductor processes.

There are other areas in experimental stages, such as the advent of neural computing, and the cross-pollination of ideas between the biological & computational worlds, that open the possibiities of rational thought by artificial beings.

Actually I think the editor is barfing on the use of certain symbols, so here it goes again ... :-)

Now where is this headed to, let me ask you this: what do you think will be the constraint on the growth of cpu power given that signals cannot exceed the speed of light. If the minimum distance that a signal needs to travel is x, then the fastest possible cpu cannot be more than c/x Hz. Let me put some numbers here: Let x be of the order of one nanometer. Then the time taken for the signal to traverse this distance will be 3 billionths of a nanosecond. This corresponds to a rate of 300 million GHz. If I accept 300M GHz to be the fastest possible computer, then according to Moore`s law, I should get there in about 30 lifetimes of 18 months each, or about 45 years. After that everything should start to flatten out.

My previous message got chopped off by the replies editor, so here is the last paragraph again ...


Now where is this headed to, let me ask you this: what do you think will be the constraint on the growth of cpu power given that signals cannot exceed the speed of light. If the minimum distance that a signal needs to travel is x, then the fastest possible cpu cannot be more than c/x Hz. Let me put some numbers here: Let x be of the order of one nanometer. Then the time taken for the signal to traverse this distance will be 3x10

It was a very interesting article, but somehow I think that Moore`s law is not as mysterious or fundamental as some people say. May I suggest that it is not a coded message at the end of pi, neither is it an indication of some undiscovered order in the universe. I think it is derived very easily by a college freshman who knows elementary calculus:

Let N be the measure of the level of whatever technology one is interested in at time t, then I can simply say that the rate of change of the level of a technology is directly proportional its level at that time. i.e the more advanced the technology, the faster its growth. This translates into a simple ODE:

dN/dt = kN

which yields the Moore`s law:

log2(N/N0) = t/T

(where T=1/k, and N0 is the level at starting time. The choice of log base 2 is of course equivalent to that of a natural base through appropriate scaling of T)

The choice of the lifetime T, is dependent on what technology one is interested in. This simple analysis also shows why other technologies may also follow the same behavior. The choice of T may be directly related to the amount of work being done in a field.

I`m very intrigued by the notion of a fundamental universal law residing somewhere in the scaling of a particular techonology. I`m also very curious about where this scaling is headed off to.

About the first issue, Moore`s ``law`` is probably as fundamental as Hooke`s ``law``, which related the extension of a spring to the tension applied to it, i.e. an empirical observation that fits the data very well, but is not fundamental. Other such laws include Rydberg`s law for explaining the emission spectra of hydrogen. In the latter two cases, the observed data were found to follow a given trend quite well, but no explanation was given about the reason for the trend. In the case of Hooke`s law, in the regions that it is applicable, it is the form of inter-molecular potential. In the case of Rydberg`s law, it was the energy splitting of a quantum mechanical oscillator in a potential well. This probably offers a hint on what could possibly define a physical law. Feynman, in his classic book, ``The Character of Physical Law``, suggests that one should look at the comprehensiveness of a hypothesis and its verifiability before characterizing it as a law. The laws of quantum mechanics, for example, are comprehensive, because they apply to an enormous range of phenomena, and are uniquely predictable and verifiable in every domain. This is not the case of either Moore`s Law, Hooke`s law or Rydberg`s Law. (In fact, as you state it, it is not even clear what exactly is doubling every 18 months!)

Now if one were to take the issue that Moore;s law is an approximate mathematical model of the growth of a complex system then one has to pose the problem in terms of the dymanics of a complex system. Even there, although there are a lot of issue relating to the dynamics of an abstract complex system, I do not think that Moore;s law teaches us anything about the fundamental laws of the universe. The scaling of a particular system is dependent on many factors which are not universally determined but a result of a convention or a historical accident. What is so fundamental in the way one technology developed before another? Didn`t the Nazis almost come to the threshold of making an atomic weapon, but why is it that the Allies did that first? Interesting question, but in my view, sheer random chance explains it well enough without invoking extra mysterious reasons.

Now where is this headed to, let me ask you this: what do you think will be the constraint on the growth of cpu power given that signals cannot exceed the speed of light. If the minimum distance that a signal needs to travel is x, then the fastest possible cpu cannot be more than c/x Hz. Let me put some numbers here: Let x be of the order of one nanometer. Then the time taken for the signal to traverse this distance will be 3x10

Brilliant article. Incredible storytelling style. but I wonder, are we saying the unabomber had a point?