Copyright Protection for Scientific Theories?

An individual (who shall remain nameless so as to prevent the reader’s hapless neocortex from being preempted by hindbrain activation) forbade me to derive a formula for the present value of the Hubble Parameter from the formulas in his theory using only the Gravitational Constant and Cosmic Microwave Background Radiation Temperature as parameters with any uncertainty subsequent to the CODATA 2019 revision relegating other parameters exact, such as speed of light, Stefan–Boltzmann constant (sigma), etc. If he’d explained his rationale for his prohibition in terms other than that he held “copyright” over his formulae, and that he specifically denied me a license to use those formulae, I might have been willing to deny myself the black letter law right to fair use of his theory in doing my own derivation citing his formulae. However, he offered no such rationale. In order to provide myself with a rationale on his behalf that was charitable to him and his related property rights recognized by law, I was forced into various speculative conjectures as to his motives. Moreover, I have, on the basis of my charitable conjectures, altered my behavior to minimize potential damage to his interests that may result from my own, black letter legal, behavior in transgressing his prohibition.

Having said that, there is an argument to be made for extending copyright protection to scientific theories -- not just in their particular form embodied in a published work, and not just when “fair use” standards are violated. This argument is in contradiction to black letter law but that is not the point. People make laws. Laws must be just. If the unnamed individual’s theory turns out to be as revolutionary and free from error as he purports, I can make, I think, a pretty compelling case for him being granted the kind of legal power over the use of his theory that he claims to possess. And this argument is based on two premises, one in the sciences and one in the humanities that I hold dear:

Sciences: While it is true that “laws of nature” are, in some sense, inherently in the public domain, there is another sense in which they are human creations. Specifically, while we might share access to phenomena that anyone can observe, the ability to detect the truth of those phenomena, interpreted as data, is provably beyond the computational capacity of any algorithm. By “truth” I mean that unique observation-driven model (truth functional from theory to reality) that most accurately predicts the not-yet observed phenomena. This proof is part of the theory of Algorithmic Information. Algorithmic Information content of any set of data, encoding a set of observed phenomena, is the shortest program that produces the phenomena as data. Algorithmic Information Theory contains a proof that there is no algorithm that can prove a given program is the shortest program that outputs a given dataset. However, if we are granted, by some oracle, that shortest program, AIT proves it will be the most accurate data-driven model assuming only that observations are of a universe that can be modeled as an algorithm. We’re always uncertain as to the veracity of the claim that we are in possession of the best of all possible models given a standard set of observations. (This is related to The Halting Problem in that some of the programs that you test to see if they, indeed, produce the original data may not halt – leaving one in an indeterminate proof.) Moreover, anyone who has done much work in artificial intelligence knows that the search for merely shorter such programs is exponentially hard. This, in fact, is the basis for The Hutter Prize, the judging committee for which I am on. An advance in scientific theory that reduces even one formula from a formulary that goes into its Algorithmic Information may – particularly in physics – produce profound advances in unification between phenomena with untold benefits to society. Justice then demands that we accord benefits to the discoverer of such a simplified formulary. Justice is usually accorded in terms of awarding property rights.

Humanities: There is something in evolutionary medicine known as “vertical transmission” which contrasts with “horizontal transmission”. This distinction is, according to evolutionary theory, behind the distinction between the evolution of symbiosis and the evolution of virulence. A humane legal system would favor, wherever practical, vertical transmission over horizontal transmission so as to maximize symbiotic relationships within the necessary diversity of interests comprising society. Vertical transmission occurs when what Dawkins calls a “replicator” is transmitted from parent to child – which evolves cooperation between the family lineage and the replicators that lineage embodies. Horizontal transmission occurs when a replicator can transmit outside the lineage. The reason this tends to evolve virulence is that the replicator can decrease the fitness of the lineage, benefiting itself, and then transmit to another lineage to exploit before suffering the consequences of its own exploitation. Think “take the money and run”. Ewald et al hypothesize horizontal transmission between hospital beds in WW I evolved the high virulence of that pandemic’s pathogen: A victim could be near death from exploitation and still be contagious. In the perfect vertical transmission regime of human society, morals, ways of viewing the world, technologies and ideas would be transmitted from parent to child without outside interference. Think homeschooling vs public schools where the public schools are invaded by virulent ideologies/cultures. In this respect, if we don’t protect scientists who make major discoveries in some manner that is just with respect to the benefits accrued by society, it not only will tend to reduce the fitness of those lineages, it will benefit lineages that may be only distantly related if not actively hostile to the creative lineage.

These are not easy issues to deal with in technological civilization, but quite honestly, we must deal with them with a minimum of emotional investment or find our civilization in collapse from demoralization of those we should honor and the empowerment of those who view “honor culture” with contempt.


These are extraordinarily difficult issues and, is so often the case with the law, involve definitions and distinctions which, where they exist, are difficult to justify or explain, and yet cast long shadows on the human project of explaining the phenomena we observe and the human prospect of exploiting that understanding to benefit of ourselves and our progeny.

In my lifetime, I have seen computer programs and algorithms deemed not subject to patent protection because they are “mathematical formulæ”, seen that reversed and a wave of patents granted for things as revolutionary as using XOR to draw non-destructive cursors on raster screens (commonly used in published code a decade or more before the patent was filed on the “invention”), personally signed a US$ 25,000 cheque to a patent troll for said patent who threatened to delay the initial public stock offering of my company by claiming infringement, participated in the Great Patent Orgy of the 1980s and early 1990s where attorneys were advising clients to “patent it all, let God sort it out” by patenting something I’d thought of a couple of decades before (U.S. patent 5,253,193 [PDF]), proposed a “collective defence” against the software patent madness, which by then was escalating toward the level where “business practice” patents would encompass “one click ordering” for on-line commerce, and eventually decided to walk away from the madness, put everything I did in the public domain, and let the mad dogs chew one another’s limbs off in the arena.

How do we decide what can be protected by copyright or patent? For example, a typeface designer cannot copyright a novel font. But the composer of a jingle can copyright its musical notation and assert that copyright over its transformation into many other forms. Over how few notes? What kind of transformation? How complex is a simple tune compared to the equations that define a hinted typeface?

One of the problems with consummating the fiery marriage between science and intellectual property law is that, as the goal of the Hutter Prize demonstrates, science is, in large part, about compressing the vast raw information from observations about the universe we inhabit into concise rules which explain them and make correct (or useful, if not necessarily exact) predictions of what will happen under novel circumstances. Now, from an information theoretic standpoint, one can argue that the novel compression adds no information: it simply encodes observed behaviour more concisely. And if it adds no information, where is the novelty which should be protected and rewarded?

But of course, that compression may enable generations of progress both in further understanding and practical exploitation. What is the discounted future value of \vec {F}=m\vec {a}? How shall the compressor be rewarded, and by whom? And how can a system to provide that reward be created without shackling the process of research and innovation in a tangle of rights negotiation and litigation that causes it to grind to a halt?


To me, a large part or purpose of property rights is to protect a person from harm. There may be a valid argument that the protection benefits society by encouraging a person to reveal their hard earned secrets such that further advancement is possible, but I maintain the intent of this is to encourage the individual to choose this form of protection versus their other options. One of which is secrecy.

Let’s assume I come up with a method to increase crop yield by planting seeds at an optimum distance. This allows my farm to thrive. If everyone can copy my invention, I will experience a tangible loss. If someone applies the same idea in a different domain, I do not have a tangible loss. This is a benefit to society and a benefit to the individual.

Patent protection and copywrite protection are protections. They are not rewards.

If tangible protection was maintained as the key fundamental of IP, many issues would simply disappear.

On a side note. No protection should be provided by individuals, groups or organizations that are funded by the public.


Copyright protects copying, not use. If you have legally obtained a copyrighted work, you may put it to any use whatsoever, as long as you are not copying the work. You can copyright your modifications to that work, creating a derivative work. But you can’t copy the original parts of your derivative work unless you have permission from the copyright holder in the form of a license.

So yes, you can calculate something form somebody’s copyrighted work and publish your calculations. Could you publish the intermediate steps? Possibly not. You certainly could say how you used the original work (presuming someone could obtain a copy) to calculate your result. Copyright doesn’t cover fair use. Fair use can be difficult to determine and you would best know what is all the applicable case law.


E=mc^2 appears in a scientific paper that is copyrighted and I have a copy of that copyrighted paper for which I have paid a subscription to a journal. I do some calculations with that formula. I publish the results and I cite the original author’s paper. Are you saying that the “intermediate steps” I use to do my calculations must not include the original formula because that would violate the copyright? Are you saying if I do algebraic transformations on that formula as part of my “intermediate work” I must not publish those algebraic transformations even though crediting the original formula to the original copyrighted paper and its author?

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That probably falls under fair use, but the thing about fair use is that people’s opinion about what is fair differs. Unless there’s case law around your particular fair use, you’re taking the chance of having to create case law.


The Digital Media Law Project’s document “Works Not Covered By Copyright” uses a closely-related example in the section on “Ideas, concepts, or principles”:

For example, Einstein’s theory of special relativity is not copyrightable because it is an idea (or concept or principle). However, Einstein’s article, “On the Electrodynamics of Moving Bodies,” in which he explained and expressed the theory, was copyrightable.

Legalzoom’s “5 Things You Can’t Copyright” says:

According to the US Copyright Office, Circular 2, this covers quite a few things including:

  • Making, or building things
  • Scientific or technical methods or discoveries;
  • Business operations or procedures
  • Mathematical principles
  • Formulas, algorithms
  • Any other concept, process, or method of operation

But, of course, some of these can be patented.