Sunday, August 20, 2023

Some Random Thoughts on Scaling Laws (Moore's, Eroom's, Lockheed's, &c)

I enjoyed this recent news story in The Economist on Lockheed's Law ( The article describes an almost inverse scaling behavior where defense and military orders are getting more and more inexpensive, mostly because the allocation of the military budget to manpower is progressively decreasing, and it is possible for manufacturers to make munitions more efficiently. Lockheed's Law is extremely important in terms of how the overall market opportunities (using the language of Kolter et al.) will change in the future. One can imagine that war will become less manpower-intensive and more capital-intensive because of this type of scaling. 

It is interesting to compare the scaling that we see in Lockheed's Law to other famous scaling relationships that have changed markets dramatically. The most famous is Moore's Law, which describes the exponential scaling of computer chips and computation in general over the last couple of decades. This scaling powered the computer and electronics industry. There are several related laws, such as Kryder's Law, which describes the exponential scaling in disk drive capacity. These laws made possible new market opportunities. The extreme case is the handheld or wristwatch computer and the fact that people now carry around computers that are much more powerful than the massive supercomputers of the past.

An associated law describes an opposite trend in the pharmaceutical industry: this "law," dubbed Eroom's Law (i.e., Moore's Law in reverse), states that drugs are becoming exponentially more expensive to put on the market. This is a great comparison to Lockheed's Law. The idea is that it is becoming much more expensive to make pharmaceuticals due to the ever-increasing requirements for research development and larger and more complicated clinical trials. A related scaling law describes the ability to sequence genomic material. This indicates a hyper-exponential increase that, at some points, is even faster than Moore's law. The scaling for DNA sequencing enables very large-scale biomedical research and diagnostic testing, but it hasn't made an impact on new drug discoveries because of the inverse scaling described in Eroom's law. Combined, Eroom's Law and the related law for DNA sequencing are reshaping the biomedical and pharmaceutical industry, making drugs comparatively more expensive but creating new opportunities for diagnostics, which are very cheap. This, in turn, is creating market opportunities for companies that are marketing only drug targets and associated research but don't have the capital to develop a drug themselves.

Altogether, different scaling laws illuminate large-scale trends that are dramatically impacting production as well as market opportunities. What was inconceivable 30 years ago is now trivial because of the exponential scaling in Moore's Law. Perhaps Lockheed's Law will lead to a type of warfare in the future that is so capital-intensive that it will be fundamentally different from the type of engagement we saw in the First and Second World Wars, and this, in turn, will reshape the market for defense products. 


Can the West build up its armed forces on the cheap?

Breaking Eroom’s Law

Moore's Law

DNA Sequencing Costs

Other Stuff Related to Scaling

Nice scaling graph for the size of transformer models