Moore's Law: Is the exponential growth of semiconductors a law of nature? A Satire on Scientific Explanation via Lewis’s Best System Account
Edy Fung, October 2023, Stockholm
Laws of nature play a role in differentiating what is considered a scientific explanation from a non-scientific one. It is one of the premises constituting the explanans in the deduction nomological account. In order to validate scientificity, we need to be able to determine what makes a law of nature.
Cartwright states the most entrenched view of laws of nature are the ones that “describe the facts about reality” and names this view the facticity view of laws.[1] That is, according to Rosenberg on how logical empiricists would put it, laws of nature are universal statements that look like “All a’s are b’s,” or “Whenever an event of type C occurs, an event of type E occurs.”
The reverse direction of these statements is not necessarily true—not all universal statements that describe facts about reality are laws of nature. One of the main challenges about the laws of nature is that it can never be absolutely clear whether those “facts about reality” are merely singular, unique events. There are patterns in the world that are consistently occurring enough to be observed as regular, but perhaps too local and particular for the time and space they belong to. If we cannot answer whether the observation still holds true outside the time and space it belongs to, this can end up as an accidentally true generalisation; and even if the observation does hold, regularities do not automatically equate laws of nature.
One of the philosophical views which can help us unpack the topic of laws of nature is the system’s approach by David Lewis.
Moore’s Law
Moore’s Law has been circulating in the semiconductor industry for at least 50 years. It describes,
“the number of transistors on microchips doubles every two years.” [3]
This claim was posited in 1965 by Gorden Moore, the co-founder of Fairchild Semiconductor and Intel. It first appeared when Moore estimated the possible amount of transistors produced due to the rate of downscaling of integrated circuit size and increased performance of chips. His projections were popularised in the field and today it is widely perceived as a target that the industry has tried to fulfil for the last 50 years.
In most cases, Moore’s Law is not treated as a real law of physics. Here we can test if Moore’s Law is a law of nature using Lewis’s best systems account. Lewis states,
“Regularity is a law if and only if it appears as a theorem or axiom in that true deductive system which achieves a best combination of simplicity and strength.” [4]
We can analyse Moore’s Law according to the components in this statement. First, it is an empirical regularity that Moore’s Law describes. Moore’s Law describes a factual occurrence within transistor manufacturing. Transistors are very tangible entities. The manufacturing of transistors is measurable in numbers. It is verifiable by observation or experience rather than logic and therefore empirical. Statistics have shown the number of transistors doubled every two years between 1970 and 2020 (see Figure 1) and validates this regularity.
Next, Moore’s Law contains an axiom—a sentence assumed to be true. Moore’s Law when expressed in a mathematical equation,
In terms of simplicity, Moore’s Law is a one-line statement. It satisfies the requirement of being simple in its axiomatisation. In terms of strength, one can argue that Moore’s Law is not strong enough when it only applies locally to transistor manufacturing instead of broader applications in the laws of economics. It is uncertain how many more predictions can be expanded from the axiom, across the field as well as how far stretched in the future. Within the field, one can find out the period of time required for any given number of transistors to be produced, or the number of transistors obtained via any given period of time. It seems to be limited to these two aspects. But specialists can extend a few further steps by deducing the trends for cost and labour as a result. [5] Moore’s Law works like a physical law which is incredibly beneficial within the parameters of the world of semiconductors. Another point is that if we consider to what extent Moore’s Law applies in the future, the strength of the law can increase if it stays true for another 50 or 100 years. For if it holds true for a longer period of time, the degree of consistency increases; the data sample accumulates for better statistical modelling and thus provides a stronger foundation to predict future data. There is arguably room for this regularity to satisfy the strength element when viewed in different timespans.
The benefit of the Best Systems account is that it can function as a rule of thumb to conduct straightforward tests on whether a claim sounds like a law of nature. The strength component in the Best Systems account encompasses the universal scope that the claim should aim for without having to declare universality and its vagueness. Weighing the law via a spectrum between strength and weakness seems to allow small and local exceptions and does not completely exclude unknowns that are not yet universal.
It also helps us construct claims for better understanding and applications. The strength of Moore’s Law could increase if certain boundary conditions are appended. For example, if it is reconstructed as,
Given that the supply of silicon on Earth and the energy required for the extraction process is not finite, the total number of transistors on microchips doubles every two years.
The clause would lose simplicity, but gain universality and thus is more lawlike. However, the Best Systems account still plays no role in “debunking” false claims from accidentally true generalisations. The transistor industry is relatively recent in the history of civilisation. There are no other precedents for us to compare and find out if this is a unique occurrence. Best Systems account in itself cannot analyse any false laws arisen from false generalisations even with empirical data present. Lewis himself says, “A version of the violated law may still be simple and strong enough to survive as a law”. [6] Perhaps the Best Systems account still leads to a metaphysical extravaganza of open interpretation of law versus generalisation.
Conclusion
We have examined via Lewis’s Best Systems account and demonstrated ways to view Moore’s Law as a possible law of nature, given that precise boundary conditions are considered and we look at how the law sits with time from a different angle. This is admittedly a bizarre conclusion, especially since our common sense tells us Moore’s Law should be an accidently true generalisation. Opponents of this regularity would argue that Moore’s Law is a self-fulfilling prophecy, and that the industry must have made a conscientious effort to keep the law true: how could a projection target become a causation of a phenomenon? Did the act of making the law in itself instantiate the truthiness; in other words, would the number of transistors still double if Gordon Moore never made such a proposition? Perhaps a better rephrasing could be: the number of transistors on microchips doubles every two years, whether or not Gordon Moore has said so, which leads to a series of different discussions about counterfactuals and causality. If Moore’s Law never exists and we come to measure and trace the empirical data today or from the future, we would then observe the exponential growth of transistors no different from other natural phenomena in our organic world. Borrowing Feymann’s words, “There is [...] a rhythm and a pattern between the phenomena of nature which is not apparent to the eye, but only to the eye of analysis; and it is these rhythms and patterns which we call Physical Laws.” [7] The exponential growth of transistors follows the same “rhythms and patterns” as the number of microorganisms and nuclear chain reactions. Would we then change our perspectives on this regularity with transistors?
Nevertheless, the weird case of Moore’s Law suggests that sometimes an accidentally true generalisation is not in any way less beneficial than a law of nature, even if it cannot be certified as a scientific explanation. Generalisation gives a functional value to our society even if it might not be universally true; or we cannot know or care to what extent a fact still applies, not in a spacetime bounded by our limited human knowledge and our finite experience.
[1] Nancy Cartwright, “Do the Laws of Physics State the Facts?”, How the Laws of Physics Lie (Oxford, 1983; online edn, Oxford Academic, 1 Nov. 2003) <https://doi.org/10.1093/0198247044.003.0004> [accessed 8 Oct. 2023].
[2] Alex Rosenberg and Lee McIntyre, Philosophy of science: a contemporary introduction (Routledge, 2000), p.62.
[3] Gordon E. Moore, “Cramming more components onto integrated circuits”, Electronics, Volume 38, Number 8, April 19, 1965 [Retreived 8th October 2023].
[4] David Lewis, Counterfactuals. (Oxford: Blackwell, 1973), pp. 72-77.
[5] See G. Dan Hutcheson, “Moore's Law 101: The Math and Innovation Economics Behind It” <https://www.chiphistory.org/505-moore-s-law-101-the-math-and-innovation-economics-behind-it> [accessed 8th October 2023].
[6] Lewis, p. 75.
[7] Richard Feynman, The Character of Physical Law (Cambridge, Mass: MIT Press, 1967), p. 13.