Tie-ins to Worldviews of Plato, Kant, Spinoza
The EPI approach may remind students of philosophy of the famous adage of “the cave” of the Greek philosopher Plato. A person born and raised in isolation in a cave sees shadows on the wall cast by people outside the cave. From these he concludes that the shadows ARE the people. Here is an example where the acquired information level I is much less than the intrinsic level J defining the people outside. That is, the information efficiency constant obeys κ<<1.
This has a parallel in the philosophy of the German philosopher Immanuel Kant  :
Man observes a phenomenon that is only a sensory version of the “true” effect, the latter called a noumenon. Hence the noumenon is some unknown, perhaps unknowable, absolute statement of the nature of the effect. Man cannot know the absolute noumenon, and so contents himself with merely observing it as a phenomenon, within the limited dimensionality of some sensory framework. Various frameworks have been used for this purpose through the ages: witchcraft, astrology, religion or (most recently) differential equations! How does EPI fit within this scheme, and can it perhaps provide an absolute framework for defining the noumenon?
The framework is in fact provided by the notion of observation. A noumenon is an unknown physical process. To be identified as a noumenon, it must first be observed. (There might be unobservable noumena, such as possible parallel universes, but we will not consider these here.) The observation is an absolute truth about the noumenon. This is in the sense that it is known to exist (but not that the observation is totally accurate, by the way).
The observation is thus an absolute description of a noumenon. This despite being a generally inaccurate description. To exist, it must be observed.
Hence the observation unties a philosophical Gordian knot. It provides a tangible, absolute means for addressing or analyzing the noumenon without getting into its a priori unknown details (such as whether it is composed of “strings,” or “Cooper pair particles,” etc.) Indeed, it allows us, via EPI, to find these details.
With this absolute so identified, we turn next to a choice of description for the observation and the noumenon. Owing to its unparalleled success in describing physical effects , this is by the use of mathematics. This is even despite Goedel’s incompleteness theorem. Other possible choices such as religious insight pale by comparison in their proven effectiveness. Hence the observation is expressed, as well, by the use of mathematics, specifically numbers. These numbered observations are what are commonly called measurements.
To review, one absolute aspect of a noumenon is afforded by its measurement. We now proceed to show how EPI can quantify the noumenon theoretically.
The EPI view of knowledge acquisition regards information level J as the absolute level of information that is provided by “the source space.” We have associated the latter with the noumenon. Hence, within the dimensionality of the given measurement space (see above) J is also regarded as the information level of the noumenon. Note that this identification can be made without knowing in detail what the noumenon is. (Indeed, our aim is to reconstruct it.) Correspondingly, I is that of the phenomenon. Thus, the information difference I – J, previously called the “physical information” K, also measures the loss of information about the absolute truth that is suffered by the observer. (On this basis it might be called the “Kantian” as well.) For example, an observer who views the positions of particles on a macroscopic level ignores valuable information on the microlevel, and thereby loses exactly κ=1/2 of their pre-existing information about position. Here the lost information is that due to uncertainty on the unseen quantum level.
(There is also lost information due to use of too few dimensions, as discussed above, so that this discussion holds for only within the given measurement space. For example, although four-space may only be a projection of some physically meaningful higher-dimensioned space, as far as we know the Klein-Gordon equation is fully the correct wave equation within four-space. Thus, within four-space, phenomenon equals noumenon.)
The Cramer-Rao inequality eq. (6a) was discovered by Professor C.R. Rao (left). (The author is on the right.) The C-R inequality states that the ability to know any measured quantity is strictly limited by the amount of Fisher information that is available. A consequence is that the Fisher information becomes the basis for deriving laws of science via EPI principle (14). This is not unexpected since scientific laws are intrinsically tied into measurements: the laws both theoretically define measurements and (as we found) are created in response to measurements.
Wheeler’s “participatory” universe – turning lemons into lemonade
Over 300 years ago the philosopher B. Spinoza postulated that man is an integral part of nature, as opposed to distinct and separate from it as Descartes had postulated. This can be taken to mean that when man “observes” nature it is not in a fully passive way. He might, for example, be participating in the very effect that he is observing. Spinoza further postulated that knowledge of observations (“sensory” knowledge), in being transient and contingent upon the observations, is a lower form of knowledge than is “reason.” The aim of “reason” is to know how and why the particular observations arose, and, “It is of the nature of Reason to regard things as necessary, not as contingent.” Indeed, Spinoza – unique among all philosophers – claimed that reason could ultimately lead to a complete understanding of nature (or, by his philosophy, “God” ). That is, scenarios where I – J = 0, the absolute minimum, could be attained. But, what form should this “reason” take?
A few years ago  the celebrated physicist John Wheeler continued this chain of ideas about man-the-observer and his relation to nature, ingeniously predicting that information forms a bridge between man and nature:
“All things physical are information-theoretic in origin and this is a participatory universe… Observer participancy gives rise to information; and information gives rise to physics.”
The information mentioned here was not specified by Wheeler to be explicitly Fisher’s. Nevertheless, in hindsight, the correspondences of these ideas to the Fisher-based EPI model of past sections are amazingly direct (italicized words in the following correspond to those in Wheeler’s above statement):
The information theory is that of Fisher, since the observer participancy is the operation of measurement for the purpose of estimating and gaining knowledge. (Note that measurement provides in fact the absolute representation of noumena that Kant sought; see above.) The measurement gives rise to a flow of information J → I [eq. (2)]; this sets off the perturbations obeying eq. (11); the latter gives rise to the EPI variational principle [eq. (1) or (14)]; and this gives rise to physics in the form of the differential equations obeyed by the output PDFs pn(x) of the EPI principle. Many of these differential equations are the famous wave equations of physics (of Schrodinger, Klein-Gordon, Dirac, etc.).
The EPI principle therefore is a representation of Spinoza’s Reason, i.e., it is a means of generalizing from sensory, or lower, knowledge to a higher form that addresses questions of how and why (as discussed above) the data arose.
It should be emphasized that we interpret Wheeler’s above statements as describing how the laws of mathematical physics are discovered, and not how physical “things” such as mass, energy, etc., and physical “effects” such as Coulomb’s law, are created. These are presumed to exist in definite (but unknown) forms prior to the measurement (see discussion a few sections back).
These ideas can be briefly summarized as follows:
Descartes formed the famous adage :
(i) I think, therefore I am
as a proof that we (as thinkers) exist. Descartes believed in a fundamental separation of mind from matter. Spinoza, by comparison, made no such distinction in postulating that man (as a total brain-body) is part of nature. Further, as if logically following this chain of ideas, Wheeler’s ideas suggest the adage :
(ii) I observe, therefore I create.
Or, combining these adages of Descartes and Wheeler,
(iii) I exist, but not merely like a rock or a tree, rather as a creative observer of the laws of nature around me.
Finally, (Spinoza above)
(iv) These laws can be known perfectly.
In effect, Wheeler’s ideas offer a definitive route to turning lemons into lemonade. They are a positive addition to basically negative ideas about the incompleteness of simple observation as enounced by Plato and Spinoza, and then taken up by Kant and Schopenhauer. To summarize, although observation is incomplete and a lower form of knowledge (Spinoza), it can be used creatively as part of an understanding of information (Wheeler); the creativity occurs in the observer’s mind by the exercise of his reason (Spinoza), and the result can be a full understanding (again, Spinoza) of how and why the observation arises.
The EPI contribution to this chain of philosophies is to
(i) identify measurement as providing one absolute basis for defining noumena;
(ii) identify Wheeler’s “information” as specifically that of Fisher (notably, not of Shannon but perhaps of Bohm and Hiley ); and
(iii) show that two such informations I,J, rather than one, are needed in order to provide a quantitative framework for the Spinoza-Wheeler edifice.