A “Cooperative” Universe – beyond the Participatory
Some followers of Kant, notably Schopenhauer, were struck by the largely negative nature of his philosophy. They became despaired of the fact that we never directly “see” the noumenon . Furthermore, as discussed above, we often do not see the full information level of the noumenon, since generally I≤J. In fact Kant thought that we could never attain full information I=J about the noumenon (see above). However, EPI (and, equivalently, the philosopher B. Spinoza) indicates that he was incorrect in this regard. Cases I=J exist. For example, I=J holds for all unitary phenomena, including quantum mechanics. Thus, EPI turns the apparent disadvantage around: It shows that although “the truth” (the mathematical law of physics at the source) may not usually be directly observable; it can, anyhow, be inferred. This is by using EPI, i.e., either by extremizing the difference |I-J| of information or by inferring that I=J in quantum cases and other unitary cases, and in Boltzmann thermodynamics.
As we see below in Sec. 1.6, the extremum is often a minimum. For these noumena EPI accomplishes a minimizing of the loss I-J of the absolute truth in observations of them. Thus, it achieves a level of information I in the data that obeys I≈J, i.e. contains a maximal level of truth about the source. In fact most fundamentally, on the quantum level, EPI accomplishes I = J, i.e., the maximum possible level of truth in the observations. This is comforting, since it satisfies what a measurement is meant to accomplish, and might likewise have lifted Schopenhauer’s spirits.
It should be noted that to accomplish a quantum measurement for which I=J the object must be in a coherent state. In practice this can only be accomplished when viewing microscopic objects, since a loss of coherence, i.e., decoherence, occurs for macroscopic objects. Therefore, in principle, the potential for observing an absolute maximum level I=J of truth is always present.
In the preceding, Wheeler called our universe “participatory.” However, it’s really more than that. By the participatory use of EPI, we infer its laws. However, since in fact the resulting information levels I are close to being their maximum possible, or noumenal, level J, this universe cooperates maximally with our objective of understanding it through observation. Hence, it might be further described as cooperative.
The degree of cooperation is actually of three types:
(1) Since the data contain a maximum of information I about the parameter under measurement, this allows us to optimally estimate it.
(2) By using EPI, we can infer the laws of physics that gave rise to the data. That is, we optimally learn the laws that govern the universe.
(3) Finally, by telling us that I=J nature lets us know that there is nothing more to be learned about the observed effect (at the given scale of observation). Thus the EPI-based observer (at least) is saved from embarking on wild-goose chases. The level of cooperation provided by the universe is so strong that it ought not only be regarded as our school, but also our playground.
In fact this cooperative property is a very special one. Before it was tried (first by Maupertuis and Lagrange as an ‘action’ principle), there was no guarantee that EPI would give rise to correct laws. Certainly the weak form of the anthropic principle does not imply it. That is, our mere existence as a carbon-based life form does not imply an optimum ability to understand the universe. For example, other life forms, such as apes, do not have this ability. Rather, it is our existence as obsessively curious and thinking creatures that permits it, as discussed next.
The cosmologist E. R. Harrison has proposed that universes such as ours evolve specifically to nurture intelligent life forms. Presumably, these life forms play an active role in the evolution of their universe. And information-oriented creatures like us can only do this if we first learn how it works. Of course, the learning process is most effective if I ≈ J, and there we have the EPI principle.
Thus, Harrison’s is a kind of “strong interpretation” of the anthropic principle that leads to a cooperative universe and to EPI. In summary, any Harrison-type universe that forms and nurtures intelligent life must be cooperative in imparting information to such life.
This begs the question of what active role intelligent life will play in the evolution of such a universe. The EPI approach in fact logically supplies us with one. As we saw, this is an information-dominated universe that cooperates by allowing us maximum information gain at each observation. Therefore, assuming that we want to maintain this universe, our ultimate role is to preserve these maximal gains of information. Certainly our invention of libraries and the internet, not to mention secure encoding devices, are concrete steps in this direction.
However, of course natural effects exist that tend to thwart such activities. The Second law of thermodynamics is one well- known example. Its goal, after all, is a “heat death” for the universe, when asymptotically zero information would be gained at each observation. On this basis, then, our goal is straightforwardly to effect a reversal of the Second law within this universe. A first thought is to use other universes or dimensions as depositories for our excess entropy, analogous to the way life processes locally gain order (lose entropy) by dumping waste entropy into their surroundings.
A digression: Deriving so-called “ultimate goals” for mankind, as in the preceding, are not the usual consequences of a physical theory. EPI is notable in being a quantitative approach to physics that also has metaphysical implications. A clarification, however, is in order: This ultimate goal of reversing the Second law is not something that we ought to do but, rather, is something that we will automatically do, as a natural effect of living in a Harrison universe.
The Inevitability of Intelligent Life in this Universe
As is abundantly clear, the laws of nature in our universe permit the total existing level of information in a perceived effect to be elicited by the observer, I ≈ J. This gives rise to an “information niche” in evolution, whereby creatures who depend for their survival upon inputs of information have an advantage. Man is the intelligence-gathering animal par excellence only because intelligence gave us an evolutionary advantage, and perhaps (arguably) still does. This is not to say that all animals tend toward intelligence. Some have their evolutionary niche in running speed, others in swimming or flying well. The condition I ≈ J encourages intelligence to develop, but does not demand it.
Furthermore, this ability should also be aided by “Baldwin coevolution”, whereby behavioral learning, say from parents, can reinforce natural selection in the direction of learned traits. For example, the original finches on the Galapagos Islands arrived from South America with relatively small beaks. Only those finches that repeatedly tried feeding from specialized flowers, such as long-necked ones, evolved in the direction of specialized beaks (such as long ones) for purposes of feeding. With such repeated trial feedings, once mutations arose that conferred slightly longer beaks these birds had an immediately realized biological advantage, and hence produced larger and more robust broods. Without such repeated efforts the mutations would not have been utilized to advantage and, hence, would not have conferred biological advantage. Among animals that depend for their survival upon information, learning is the corresponding behavioral trait that confers advantage. The ability to learn directly increases acquired information levels I, and promotes positive feedback for the genetic change so as accelerate its utility and, hence, its propagation to further generations. .
Some predictions of EPI
Any bona fide physical theory should make predictions (C. Popper). To be “beautiful” is not enough: beauty is in the eye of the beholder, and history is rife with outmoded theories that were regarded by many people as “beautiful” (remember Aristotle’s epicycles?). Uses of the EPI approach have resulted in the following predictions (from refs. [1a-c],, and “Recent Papers” listed below):
(1) Free quarks should exist. This was verified — Free-roaming quarks and gluons have apparently been created in a plasma at CERN (2000). Predictions (1)-(4) are from Frieden and Plastino (2001).
(2) The Higgs particle, currently unmeasured, should have a mass of no more than 207 GeV.
(3) The Higgs particle has not been found because it is equally probable to be anywhere over all of space and time. The particle has a flat PDF in space-time. Therefore it may never be detected.
(4) The Higgs mass effect follows completely from considerations of information exchange, and is in no way dependent upon ad hoc models such as the usual Cooper-pair one (altho the latter can of course be alternatively used to derive the effect as in textbooks).
(5) The allowed quark combinations in formation of hadrons are much broader than as given by the “standard model”. For example, the combination qqqqq is allowed, whereas this is forbidden by the standard model. (Ref. Frieden and Plastino, 2000).
(6) Electrons combine in the same combinations as do quarks in formation of electron clusters and composite fermions. (Ref. Frieden and Plastino, 2000)). Such composite electron clusters have been verified experimentally.
(7) The Weinberg- and Cabibbo angles of particle theory obey simple analytical expressions involving their tangents and the Fibonacci golden mean Φ = 1.618… (see ref. [1b]).
(8) An in situ cancer mass has an absolute minimum level of Fisher information. This represents a reversal of evolution from normally functioning cells to cells whose principal remaining activity is that of reproduction. The resulting EPI prediction (via the “game corollary” in (14) below) is that the cancer mass grows on average with time t as the simple power law tΦ with Φ the Fibonacci golden mean 1.618… Use of this law in the Cramer-Rao inequality eq. (6a) shows that a physician errs, on average, by close to 30% in estimating the onset time of a diagnosed cancer (see Gatenby and Frieden, 2002; or ref. [1b])
(9) Economic valuation PDFs governing price fluctuations for stocks, bonds, etc., follow the use of Fisher information and EPI. This is under the “technical viewpoint”, which is equivalent to equating J = 0. See ref. [1b,c], or paper by Hawkins and Frieden, Physics Letters A 322, p. 126 (2004). The approach regards market dynamics as generally following non equilibrium statistics, as further described in prediction (13) below. Empirical uses of the approach agree with the log-normal nature of the Black-Scholes valuation model.
(10) The EPR-Bohm experiment of two-particle entanglement obeys the predictions of EPI, where J=I connotes the entanglement of realities of the particles (see ref. [1b]). Information J also fills the theoretical requirements of an “active” or “interactive” information” as defined by Bohm and Hiley in . However, it is not active but, rather, merely mathematically expresses a physical law, as do all EPI outputs. See point (h) above.
(11) All transport and population growth phenomena, including the Boltzmann transport equation, the equation of genetic change, and the neutron reactor growth law, may be derived using EPI (see ref. [1b]). EPI thus implies a common basis for both physical and biological growth, including mixtures of the two. Some results of this duality are (a) a template-matching mechanism DNA ↔ TNA for genesis; and (b) a simple rule n ≥ N 1/2 that must be satisfied for a population to be vulnerable to a crash of 20% or more (where n = estimated number of generations since inception, N = present population level).
(12) The speed of light c is, aside from its definition as a speed, a measure of the ability to acquire knowledge. It obeys
c ≥ (dH/dt)/√I
Thus, c is an upper bound to the rate dH/dt at which information about the position of an electron can be learned, relative to the amount √I that is already known (ref. [1b]).
(13) Equilibrium- and non-equilibrium statistical mechanics, as well as economic valuation and non-relativistic quantum mechanics, can be derived using an EPI output in the mathematical form of a constrained Schrodinger wave equation. Also, equilibrium (in particular) thermodynamics can be derived using Fisher I in place of entropy H. (see select papers with Plastino, Soffer and/or Flego under Recent Papers listing below).
(14) Unitless universal constants can be analytically determined as those that minimize I (see [1b], and paper by Gatenby and Frieden listed below). This is a corollary of the knowledge acquisition game mentioned above. This “game corollary” also implies that neutrinos have finite mass (ref. [1b]), as has recently been confirmed.
(15) The entrapment areas of black holes are distributed as approximately an exponential law, but with a much longer tail (see Frieden and Soffer 2002 paper below in “Recent Papers” listing). The extra-long tail enhances the ability of astronomical black holes to entrap neighboring particles. This might provide the currently unknown force that is apparently needed for holding in highly energetic stars that are on the outermost fringes of galaxies. These are moving so fast that their centrifugal forces appear too large to be cancelled by current centripetal force models.
(16) It had long been thought that black holes transmit zero information. By comparison, EPI predicts that a black hole transmits Shannon information at a maximum bit rate (see Frieden and Soffer 2002 paper below). Prof. Stephen Hawking has of late (July, 2004) famously changed his mind on this issue.
(17) The Fisher information of a diffusive system monotonically decreases with time, obeying eq. (5). Or, disorder as measured by Fisher information increases with time (see below eq. (5) ).. This was the first prediction made by EPI . It was subsequently proved . Hence, entropy is not the unique measure of disorder. Statistical mechanics and thermodynamics can be formulated by the alternative use of either entropy or Fisher information [see also prediction (13) preceding]. Moreover, the use of Fisher information allows non-equilibrium thermodynamics to be derived. (See under “Recent Papers” those of S.P. Flego et al. (2003) and B.R. Frieden et al. (2002).)
(18) EPI derives the mechanics of the small, i.e. quantum mechanics, that of macroscopic objects, i.e., Newtonian mechanics, and that of the large, i.e., general relativity theory [1a,b], including the possibility of a finite cosmological constant Λ. The latter naturally emerges as an added constant of integration, and not as an arbitrarily inserted fudge factor (Einstein). It is thought by some to represent the “dark energy” force that operates over astronomical distances. By these derivations, EPI provides a unification of physics over all observable scale sizes. This unification has been a longstanding goal of physical theory. EPI also derives the well-known synthesis of the small and the large called “quantum gravity.” This is in the form of the Wheeler-DeWitt equation [1a,b].
(19) What is the dimensionality of the universe? EPI is consistent with the presence of 3 space dimensions and 1 time dimension. Essentially, only in such a universe can EPI estimates be made and, therefore, can man exist in his current form! (These results are based upon physical analyses due to Tegmark in reference  below.) First, consider the problem of predicting the near-future position of a particle based upon observation of its past positions. With more, or less, than 1 time dimension the problem becomes ill-posed. Therefore the mean-squared error in the predicted position approaches infinity. This is equivalent to zero Fisher information, which means that the received information I is zero, and the estimated position has no validity. If there are more than three space dimensions then neither classical atoms nor planetary orbits can be stable. Hence, the observer cannot make measurements on these, again incurring effectively infinite error and invalidating any estimates of trajectories. Given such inabilities to estimate, man could not exist in his present form. Finally, what if there are less than three space dimensions? This has two untenable results: (a) There can be no gravitational force of general relativity. Hence the attempted measurement of the position of a graviton would give infinite error or zero Fisher I, again giving an invalid estimate. (b) Because of severe topological limitations, all known organisms, including the EPI observer, could not biologically exist (e.g., their arteries could not cross). In summary, man’s existence as an effective observer requires (3+1) dimensions.
(20) EPI derives the dynamics of growth and motion of living nanosystems. This is in the form of a Schrodinger wave equation where the ordinary particle mass is replaced by the mass times the square root of the information efficiency κ, and the potential is purely imaginary. The latter has the simple form i(ħ/2)(gn + dn ) in terms of Lotka-Volterra growth gn and depletion dn coefficients. These are general functions of all the particle populations of the system. In the limit of a system that is spatially homogeneous (well mixed) or has vanishing spatial information (with κ→0), and has either (i) macroscopic masses or (ii) ħ→0 the above SWE becomes the ordinary Lotka-Volterra equation of macroscopic growth. In this way quantum mechanics provides a direct link to biological growth.
(21) The “life conferring” potential V = i(ħ/2)(gn + dn ) mentioned in (20) occurred due to the presence of a special elementary particle. As mass is conferred upon a massless boson by the presence of a Higgs particle, life is conferred upon a lifeless particle by the presence of a special particle.
(22) EPI derives the basic dynamics of human groups (companies, or societies, or countries, or etc). These are the equations of growth over time t describing the group’s relative sub populations and resources pn(t), n=1,…,N. Here informations J and I respectively represent a group’s levels of “ideational” and “sensate” complexity. By definition, the “ideational” level J pertains to ideals, such as the fundamental aims of the group; and the “sensate” level I pertains to the group’s sense-based practiced. The size of I – J therefore represents the degree to which the principles of the group are in fact practiced by its members. Thus, when I – J = 0 is attained this represents a Hegelian alliance between group ideals and practice. Also, the EPI principle I – J = minimum amounts to a prediction that any group tends to (but does not perfectly) live by its ideals. Among the findings are that groups whose constituencies are locked into constant, unregulated growth eventually degenerate into monosocieties. One constituency completely dominates over the other. To avoid this scenario, active steps must be taken to monitor and constantly adjust growth rates in the direction of equality. Thus the need for peacemakers or arbitrators. (See the paper by M. Yolles et al. (2004) under Recent Papers below.)
(23) The manifest success of EPI in providing a framework for physical laws implies that its “knowledge game” aspect is valid. That is, knowledge and Fisher information really are a basis for physics. This, in turn, provides support for the following conjecture
(24) The ultimate precision in determining the position of a photon is a root-mean square uncertainty of 0.113 of its wavelength.
On commercial and defense applications
EPI applies to all problems of science, including problems of engineering and manufacture such as pattern recognition, optimum tolerancing, optimum search and detection, encryption, etc. Such applications of the theory are currently being worked on by various investigators for commercial purposes, military applications, etc., and many are proprietary in nature. I will be happy to connect the reader who is confronting such a problem with an appropriate investigator. Just use my email address at the outset.
It is a great pleasure to acknowledge the numerous conceptual contributions of Bernard H. Soffer in development of the EPI principle. This is principally in emphasizing its epistemic nature, but also in connecting it with the (beautiful and predictive) ideas of John A. Wheeler.