Nature's Missing Law of Information
This just published monograph reveals the law that governs nature's formational order
The second law of thermodynamics teaches that physical systems left to themselves tend over time to become increasingly disordered. This law, as falling under thermodynamics, understands order as heat energy localized or concentrated to do useful work. The more concentrated this energy, the more useful it is for doing work, and the more ordered it is. The more widely diffused this energy, the less capable it is of doing work, and the more disordered it is.
To appreciate the difference between thermodynamic order and disorder, consider the heat concentrated in a combustion chamber that moves a piston to do mechanical work; and then contrast this with the same heat diffused across a wide area, where it is mechanically useless. The second law rules out spontaneous increases in such concentrations of heat energy. This law is so definitive that patent offices no longer accept applications for perpetual motion machines, which to succeed would require spontaneous increases in such concentrations of energy.
Despite the second law, a tendency also exists for physical systems to become more ordered: cosmic gas clouds form stars and planets, stars as they age form new elements, planets as they congeal form new minerals, and mineralized planets form living things, which then diversify into, as Darwin put it, “endless forms most beautiful and most wonderful.” The order in such cases is not thermal, as in concentrations of heat energy covered by the second law, but formational or configurational, as in arrangements of parts that satisfy some condition or fulfill some role.
Such a tendency toward increasing formational order need not violate the second law. True, if thermal disorder (what physicists call entropy) increases too much, formational order may no longer be sustainable because matter and energy become too diffused to allow for anything other than a formless shmoo (what Aristotle called prime matter). But before a system reaches such a state of maximal thermal disorder (thermal equilibrium or maximal entropy), overall thermal order of a system can decrease even as locales of formational order within it increase.
Thermal order and formational order are therefore distinct. For instance, from the vantage of thermal order, all CDs are equivalent. Yet from the vantage of formational order, two CDs can be quite different. The information in one CD can be random, the information in another nonrandom (as with a CD that encodes random radio noise versus a CD that encodes a Beethoven symphony).
The second law explains why we don’t see certain spontaneous occurrences of thermal order. Moreover, the second law is compatible with occurrences of formational order, neither barring nor necessitating the formational order we find in nature. Yet precisely because of that compatibility, the second law cannot explain formational order.
Over the last few decades, scientists such as Paul Davies, Stuart Kauffman, Leroy Cronin, and Robert Hazen have stressed the need for a new fundamental law of nature to account for increases in formational order. Cronin, for instance, has developed what he calls Assembly Theory, which he contends can explain how complex systems can be formed from simpler parts (as I show, his proposal cannot work). Hazen, in the same spirit, has sketched what he calls the Law of Increasing Functional Information (see his short YouTube video on the topic). For now this law, as Hazen describes it, is more a wish list for what he hopes to see from such a law than a precise and full-orbed formulation of it.
In all such attempts to find a missing law that explains how formational order can arise in nature, the search is for a mechanism or process that will build complex information-rich systems. Invariably, these mechanisms are broadly evolutionary, building systems whose formational order exhibits increasing complexity over time. My recent BIO-Complexity monograph, “The Law of Conservation of Information,” argues that these scientists have identified the right problem but that their proposed solutions are on the wrong track.
Instead, as I argue in this monograph, the missing law that makes sense of the rise of formational order in nature is not a law that shows how such systems can be built but rather a law that explains and measures the obstacles to them being built. This law is therefore in the spirit of the second law. Both are proscriptive generalizations, which is to say general statements of what is proscribed or disallowed.
Consequently, this law’s approach is negative rather than positive, focusing on what can’t be done rather than what can be done under certain preconditions. Nonetheless, knowing what can’t be done is, as this monograph shows, capable of delivering a trove of insights, not least about the ultimate sources of information that build formational order and also about the channels through which such information flows. I call this missing law the Law of Conservation of Information.
My recent BIO-Complexity monograph explains the concept of conservation of information on which this law is based. It lays out what conservation of information is, how it works, why it works, how it underwrites a law of nature, and why it is real and important.
Conservation of information is not just an idea or concept that sits blithely in a world of mathematical abstraction. As a law, it provides a method for measuring information that helps to resolve certain long-standing questions from across the sciences about how to make sense of formational order. In particular, the monograph covers many interesting problems that can be studied with the help of conservation of information, conceived as a method for measuring and tracking information. This monograph explains and justifies the method, indicates the range of problems to which it applies, shows how it can be applied in practice, and addresses attempts to circumvent it.
“The Law of Conservation of Information: Search Processes Only Redistribute Existing Information” is available for free on the BIO-Complexity website (bio-complexity.org), and specifically at the following URL:
bio-complexity.org/ojs/index.php/main/article/view/BIO-C.2025.2/BIO-C.2025.2
Dr. Dembski, you write:
" Instead, as I argue in this monograph, the missing law that makes sense of the rise of formational order in nature is not a law that shows how such systems can be built but rather a law that explains and measures the obstacles to them being built. This law is therefore in the spirit of the second law. Both are proscriptive generalizations, which is to say general statements of what is proscribed or disallowed."
I think this is a very good summary of the LCI paper. In terms of biological evolutionary theory this points to nature on its own as disempowered to create saltations in form ('formational order'). For example the theory of evolution of the eye postulates ('dictates' may be a better word - read any book on eye-evo where 'just-so stories' seem to have become facts) that a single photoreceptor in a flagellated protozoa like Euglena Gracilis could evolve into a sheet of photoreceptors, could evolve into a cupulated eye like that of Nautilus, could evolve a closed vertebrate camera eye with cornea and lens, all on the basis of natural selection (NS). The LCI says 'whoa! wait a minute, formational order doesn't come for free! You can't jump these saltations of form for free, you have to account for 'extra information' in increasing formational order and the accountant (Darwin) has cooked the books with liquid paper on the revenue side. There has to be an outside source of information to bridge these saltations and balance the books of 'existence'.
In metaphysical terms, the LCI proves that biological forms evince a hierarchy of being (existence) and not one of becoming. Aristotle's 'scala natura'. This means information is top-down as a source. Aquinas called it a First Efficient Cause which is not a revelational term but a 'philosophy of nature' term. The LCI proscribes nature generating on its own sufficient power to build 'the greater from the lesser'). All of Aquinas' 5 Ways can be summarized as 'the greater will never come from the lesser'. (Read the great Thomist Garrigou-Lagrange's: 'God , his Existence and his Nature', 1934).
Of course Aquinas used 'existence' pulled 'ex nihilo' to provide formational order. If he were alive today I think he might transcribe his existential metaphysics of a hierarchy of being into an informational metaphysics of a hierarchy of 'informational order', because the amount of existence in any being tracks the amount of information contained in the assembly of its essence (epigenetic yes-no, exist-don't exist decisions). The assembly of a camera eye is vastly more complex and contains vastly more epigenetic yes-no existential decisions than the simple flagellated photoreceptor of Euglena. The camera eye has a much greater existential footprint (informational order) than a photoreceptor.
Think of a Henry Moore sculpture vs Michaelangelo's David. Which has more existence? The David does, because it contains thousands of ordered sequential yes-no, exist-don't exist chisel cuts in its 'ontogeny', compared to a simple Moore sculpture which has maybe a few hundred. You could 'devolve' the David into a Moore if it was outside and exposed to ice, snow, rain and wind over centuries (genetic entropy, like blind cavefish eyes) but you could never turn the Moore into a David without inputting way more existential yes-no chisel cuts coming from the outside, imposed into the more complex 'ontogeny' of David. Think of Moore as Euglena and David as camera eye.
The LCI nicely bridges the Metaphysics of Existence and the Physics of Information. The LCI can be seen as the physical equivalent of a Thomistic 'Law of Conservation of Existence' (LCE) where a physical PSRI (principle of sufficient reason of information) becomes a substitute for the Thomistic PSRE (principle of sufficient reason for existence).
I think people don't yet realize what a seminal paper this is in the philosophy of nature, one that in future hindsight will be looked at as what unlocked information (existence) theory for biology, especially 'proscribing' biological saltations of formational order 'for free' within the 'philosophy of becoming' (evolution).
As a survivalist necessitarian search (NS), the vertebrate camera eye never could have come from a photoreceptor. The LCI and its 'PSRI' prove it. Just read the math. :-)
Marc Mullie MD
Ophthalmologist
Montreal
This is very interesting. As a physicist, I always thought information is more fundamental than energy or momentum, but I had trouble making metrics or finding time to formalize it. It's quite cool that biology is getting hip to this idea.