**Abstract**

**Background**

Mere possibility is not an adequate basis for asserting scientific plausibility. A precisely defined universal bound is needed beyond which the assertion of plausibility, particularly in life-origin models, can be considered operationally falsified. But can something so seemingly relative and subjective as plausibility ever be quantified? Amazingly, the answer is, "Yes." A method of objectively measuring the plausibility of any chance hypothesis (The Universal Plausibility Metric [UPM]) is presented. A numerical inequality is also provided whereby any chance hypothesis can be definitively falsified when its UPM metric of ξ is < 1 (The Universal Plausibility Principle [UPP]). Both UPM and UPP pre-exist and are independent of any experimental design and data set.

**Conclusion**

No low-probability hypothetical plausibility assertion should survive peer-review without subjection to the UPP inequality standard of formal falsification (ξ < 1).

The seemingly subjective liquidity of "plausibility"

Are there any objective standards that could be applied to evaluate the seemingly subjective notion of plausibility? Can something so psychologically relative as plausibility ever be quantified?

Our skepticism about defining a precise, objective Universal Plausibility Metric (UPM) stems from a healthy realization of our finiteness [1], subjectivity [2], presuppositional biases [3,4], and epistemological problem [5]. We are rightly wary of absolutism. The very nature of probability theory emphasizes gray-scales more than the black and white extremes of p = 0 or 1.0. Our problem is that extremely low probabilities can only asymptotically approach impossibility. An extremely unlikely event's probability always remains at least slightly > 0. No matter how many orders of magnitude is the negative exponent of an event's probability, that event or scenario technically cannot be considered impossible. Not even a Universal Probability Bound [6-8] seems to establish absolute theoretical impossibility. The fanatical pursuit of absoluteness by finite subjective knowers is considered counterproductive in post modern science. Open-mindedness to all possibilities is encouraged [9].

But at some point our reluctance to exclude any possibility becomes stultifying to operational science [10]. Falsification is critical to narrowing down the list of serious possibilities [11]. Almost all hypotheses are possible. Few of them wind up being helpful and scientifically productive. Just because a hypothesis is possible should not grant that hypothesis scientific respectability. More attention to the concept of "infeasibility" has been suggested [12]. Millions of dollars in astrobiology grant money have been wasted on scenarios that are possible, but plausibly bankrupt. The question for scientific methodology should not be, "Is this scenario possible?" The question should be, "Is this possibility a plausible scientific hypothesis?" One chance in 10^200 is theoretically possible, but given maximum cosmic probabilistic resources, such a possibility is hardly plausible. With funding resources rapidly drying up, science needs a foundational principle by which to falsify a myriad of theoretical possibilities that are not worthy of serious scientific consideration and modeling.

Proving a theory is considered technically unachievable [11]. Few bench scientists realize that falsification has also been shown by philosophers of science to be at best technically suspect [13]. Nevertheless, operational science has no choice but to proceed primarily by a process of elimination through practical falsification of competing models and theories.

Which model or theory best corresponds to the data? [[14] (pg. 32-98)] [8]. Which model or theory best predicts future interactions? Answering these questions is made easier by eliminating implausible possibilities from the list of theoretical possibilities. Great care must be taken at this point, especially given the many non intuitive aspects of scientifically addressable reality. But operational science must proceed on the basis of best-thus-far tentative knowledge. The human epistemological problem is quite real. But we cannot allow it to paralyze scientific inquiry.

If it is true that we cannot know anything for certain, then we have all the more reason to proceed on the basis of the greatest "plausibility of belief" [15-19]. If human mental constructions cannot be equated with objective reality, we are all the more justified in pursuing the greatest likelihood of correspondence of our knowledge to the object of that knowledge--presumed ontological being itself. Can we prove that objectivity exists outside of our minds? No. Does that establish that objectivity does not exist outside of our minds? No again. Science makes its best progress based on the axioms that 1) an objective reality independent of our minds does exist, and 2) scientists' collective knowledge can progressively correspond to that objective reality. The human epistemological problem is kept in its proper place through a) double-blind studies, b ) groups of independent investigators all repeating the same experiment, c) prediction fulfillments, and d) the application of pristine logic (taking linguistic fuzziness into account), and e) the competition of various human ideas for best correspondence to repeated independent observations.

The physical law equations and the deductive system of mathematical rules that govern the manipulations of those equations are all formally absolute. But the axioms from which formal logic theory flows, and the decision of when to consider mathematical equations universal "laws" are not absolute. Acceptance of mathematical axioms is hypothetico-deductively relative. Acceptance of physical laws is inductively relative. The pursuit of correspondence between presumed objective reality and our knowledge of objective reality is laudable in science. But not even the axioms of mathematics or the laws of physics can be viewed as absolute. Science of necessity proceeds tentatively on the basis of best-thus-far subjective knowledge. At some admittedly relative point, the scientific community agrees by consensus to declare certain formal equations to be reliable descriptors and predictors of future physicodynamic interactions. Eventually the correspondence level between our knowledge and our repeated observations of presumed objective reality is considered adequate to make a tentative commitment to the veracity of an axiom or universal law until they are proven otherwise.

The same standard should apply in falsifying ridiculously implausible life-origin assertions. Combinatorial imaginings and hypothetical scenarios can be endlessly argued simply on the grounds that they are theoretically possible. But there is a point beyond which arguing the plausibility of an absurdly low probability becomes operationally counterproductive. That point can actually be quantified for universal application to all fields of science, not just astrobiology. Quantification of a UPM and application of the UPP inequality test to that specific UPM provides for definitive, unequivocal falsification of scientifically unhelpful and functionally useless hypotheses. When the UPP is violated, declaring falsification of that highly implausible notion is just as justified as the firm commitment we make to any mathematical axiom or physical "law" of motion.

**Universal Probability Bounds**

"Statistical prohibitiveness" in probability theory and the physical sciences has remained a nebulous concept for far too long. The importance of probabilistic resources as a context for consideration of extremely low probabilities has been previously emphasized [[20] (pg. 13-17)] [6-8,21]. Statistical prohibitiveness cannot be established by an exceedingly low probability alone [6]. Rejection regions and probability bounds need to be established independent of (preferably prior to) experimentation in any experimental design. But the setting of these zones and bounds is all too relative and variable from one experimental design to the next. In the end, however, probability is not the critical issue. The plausibility of hypotheses is the real issue. Even more important is the question of whether we can ever operationally falsify a preposterous but theoretically possible hypothesis.

The Universal Probability Bound (UPB) [6,7] quantifies the maximum cosmic probabilistic resources (Ω, upper case omega) as the context of evaluation of any extremely low probability event. Ω corresponds to the maximum number of possible probabilistic trials (quantum transitions or physicochemical interactions) that could have occurred in cosmic history. The value of Ω is calculated by taking the product of three factors:

1) The number of seconds that have elapsed since the Big Bang (10^17) assumes a cosmic age of around 14 billions years. 60 sec/min Ãƒâ€” 60 min/hr Ãƒâ€” 24 hrs/day Ãƒâ€” 365 days per year Ãƒâ€” 14 billion years = 4.4 Ãƒâ€” 10^17 seconds since the Big Bang.

2) The number of possible quantum events/transitions per second is derived from the amount of time it takes for light to traverse the minimum unit of distance. The minimum unit of distance (a quantum of space) is Planck length (10^-33 centimeters). The minimum amount of time required for light to traverse the Plank length is Plank time (10^-43 seconds) [[6-8], pg 215-217]. Thus a maximum of 10^43 quantum transitions can take place per second. Since 10^17 seconds have elapsed since the Big Bang, the number of possible quantum transitions since the Big Bang would be 10^43 Ãƒâ€” 10^17 = 10^60.

3) Sir Arthur Eddington's estimate of the number of protons, neutrons and electrons in the observable cosmos (10^80) [22] has been widely respected throughout the scientific literature for decades now.

Some estimates of the total number of elementary particles have been slightly higher. The Universe is 95 billion light years (30 gigaparsecs) across. We can convert this to cubic centimeters using the equation for the volume of a sphere (5 Ãƒâ€” 10^86 cc). If we multiply this times 500 particles (100 neutrinos and 400 photons) per cc, we would get 2.5 Ãƒâ€” 10^89 elementary particles in the visible universe.

A Universal Probability Bound could therefore be calculated by the product of these three factors: 10^17 Ãƒâ€” 10^43 Ãƒâ€” 10^80 = 10^140

If the highest estimate of the number of elementary particles in the Universe is used (e.g., 1089), the UPB would be 10149.

The UPB's discussed above are the highest calculated universal probability bounds ever published by many orders of magnitude [7,8,12]. They are the most permissive of (favorable to) extremely low-probability plausibility assertions in print [6] [[8] (pg. 216-217)]. All other proposed metrics of probabilistic resources are far less permissive of low-probability chance-hypothesis plausibility assertions. Emile Borel's limit of cosmic probabilistic resources was only 1050 [[23] (pg. 28-30)]. Borel based this probability bound in part on the product of the number of observable stars (109) times the number of possible human observations that could be made on those stars (1020). Physicist Bret Van de Sande at the University of Pittsburgh calculates a UPB of 2.6 Ãƒâ€” 1092 [8,24]. Cryptographers tend to use the figure of 1094 computational steps as the resource limit to any cryptosystem's decryption [25]. MIT's Seth Lloyd has calculated that the universe could not have performed more than 10120 bit operations in its history [26].

Here we must point out that a discussion of the number of cybernetic or cryptographic "operations" is totally inappropriate in determining a prebiotic UPB. Probabilistic combinatorics has nothing to do with "operations." Operations involve choice contingency [27-29]. Bits are "Yes/No" question opportunities [[30] (pg. 66)], each of which could potentially reduce the total number of combinatorial possibilities (2NH possible biopolymers: see Appendix 1) by half. But of course asking the right question and getting an answer is not a spontaneous physicochemical phenomenon describable by mere probabilistic uncertainty measures [31-33]. Any binary "operation" involves a bona fide decision node [34-36]. An operation is a formal choice-based function. Shannon uncertainty measures do not apply to specific choices [37-39]. Bits measure only the number of non distinct, generic, potential binary choices, not actual specific choices [37]. Inanimate nature cannot ask questions, get answers, and exercise choice contingency at decision nodes in response to those answers. Inanimate nature cannot optimize algorithms, compute, pursue formal function, or program configurable switches to achieve integration and shortcuts to formal utility [28]. Cybernetic operations therefore have no bearing whatever in determining universal probability bounds for chance hypotheses.

Agreement on a sensible UPB in advance of (or at least totally independent of) any specific hypothesis, suggested scenario, or theory of mechanism is critical to experimental design. No known empirical or rational considerations exist to preclude acceptance of the above UPB. The only exceptions in print seem to come from investigators who argue that the above UPB is too permissive of the chance hypothesis [8,12]. Faddish acceptance prevails of hypothetical scenarios of extremely low probability simply because they are in vogue and are theoretically possible. Not only a UPB is needed, but a fixed universal mathematical standard of plausibility is needed. This is especially true for complex hypothetical scenarios involving joint and/or conditional probabilities. Many imaginative hypothetical scenarios propose constellations of highly cooperative events that are theorized to self-organize into holistic formal schemes. Whether joint, conditional or independent, multiple probabilities must be factored into an overall plausibility metric. In addition, a universal plausibility bound is needed to eliminate overly imaginative fantasies from consideration for the best inference to causation.

**The Universal Plausibility Metric (UPM)**

To be able to definitively falsify ridiculously implausible hypotheses, we need first a Universal Plausibility Metric (UPM) to assign a numerical plausibility value to each proposed hypothetical scenario. Second, a Universal Plausibility Principle (UPP) inequality is needed as plausibility bound of this measurement for falsification evaluation. We need a cut-off point beyond which no extremely low probability scenario can be considered a "scientifically respectable" possibility. What is needed more than a probability bound is a plausibility bound. Any "possibility" that exceeds the ability of its probabilistic resources to generate should immediately be considered a "functional non possibility," and therefore an implausible scenario. While it may not be a theoretically absolute impossibility, if it exceeds its probabilistic resources, it is a gross understatement to declare that such a proposed scenario is simply not worth the expenditure of serious scientific consideration, pursuit, and resources. Every field of scientific investigation, not just biophysics and life-origin science, needs the application of the same independent test of credibility to judge the plausibility of its hypothetical events and scenarios. The application of this standard should be an integral component of the scientific method itself for all fields of scientific inquiry.

To arrive at the UPM, we begin with the maximum available probabilistic resources discussed above (Ω, upper case Omega) [6,7]. But Ω could be considered from a quantum or a classical molecular/chemical perspective. Thus this paper proposes that the Ω quantification be broken down first according to the Level (L) or perspective of physicodynamic analysis (LΩ), where the perspective at the quantum level is represented by the superscript "q" (qΩ) and the perspective at the classical level is represented by "c" (cΩ). Each represents the maximum probabilistic resources available at each level of physical activity being evaluated, with the total number of quantum transitions being much larger than the total number of "ordinary" chemical reactions since the Big Bang.

Second, the maximum probabilistic resources LΩ (qΩ for the quantum level and cΩ for classical molecular/chemical level) can be broken down even further according to the astronomical subset being addressed using the general subscript "A" for Astronomical: LΩA (representing both qΩA and cΩA). The maximum probabilistic resources can then be measured for each of the four different specific environments of each LΩ, where the general subscript A is specifically enumerated with "u" for universe, "g" for our galaxy, "s" for our solar system, and "e" for earth:

To include meteorite and panspermia inoculations in the earth metrics, we use the Solar System metrics LΩs (qΩs and cΩs).

As examples, for quantification of the maximum probabilistic resources at the quantum level for the astronomical subset of our galactic phase space, we would use the qΩg metric. For quantification of the maximum probabilistic resources at the ordinary classical molecular/chemical reaction level in our solar system, we would use the cΩs metric.

The most permissive UPM possible would employ the probabilistic resources symbolized by qΩu where both the quantum level perspective and the entire universe are considered.

The sub division between the LΩA for the quantum perspective (quantified by qΩA) and that for the classical molecular/chemical perspective (quantified by cΩA), however, is often not as clear and precise as we might wish. Crossovers frequently occur. This is particularly true where quantum events have direct bearing on "ordinary" chemical reactions in the "everyday" classical world. If we are going to err in evaluating the plausibility of any hypothetical scenario, let us err in favor of maximizing the probabilistic resources of LΩA. In cases where quantum factors seem to directly affect chemical reactions, we would want to use the four quantum level metrics of qΩA (qΩu, qΩg, qΩs and qΩe) to preserve the plausibility of the lowest-probability explanations.

**Quantification of the Universal Plausibility Metric (UPM)**

The computed Universal Plausibility Metric (UPM) objectively quantifies the level of plausibility of any chance hypothesis or theory. The UPM employs the symbol ξ (Xi, pronounced zai in American English, sai in UK English, ksi in modern Greek) to represent the computed UPM according to the following equation:

where f represents the number of functional objects/events/scenarios that are known to occur out of all possible combinations (lower case omega, ω) (e.g., the number [f] of functional protein family members of varying sequence known to occur out of sequence space [ω]), and LΩA (upper case Omega, Ω) represents the total probabilistic resources for any particular probabilistic context. The "L" superscript context of Ω describes which perspective of analysis, whether quantum (q) or a classical Ã‚Â©, and the "A" subscript context of Ω enumerates which subset of astronomical phase space is being evaluated: "u" for universe, "g" for our galaxy, "s" for our solar system, and "e" for earth. Note that the basic generic UPM (ξ) equation's form remains constant despite changes in the variables of levels of perspective (L: whether q or c) and astronomic subsets (A: whether u, g, s, or e).

The calculations of probabilistic resources in LΩA can be found in Appendix 2. Note that the upper and lower case omega symbols used in this equation are case sensitive and each represents a completely different phase space.

The UPM from both the quantum (qΩA) and classical molecular/chemical (cΩA) perspectives/levels can be quantified by Equation 1. This equation incorporates the number of possible transitions or physical interactions that could have occurred since the Big Bang. Maximum quantum-perspective probabilistic resources qΩu were enumerated above in the discussion of a UPB [6,7] [[8] (pg. 215-217)]. Here we use basically the same approach with slight modifications to the factored probabilistic resources that comprise Ω.

Let us address the quantum level perspective (q) first for the entire universe (u) followed by three astronomical subsets: our galaxy (g), our solar system (s) and earth (e).

Since approximately 10^17 seconds have elapsed since the Big Bang, we factor that total time into the following calculations of quantum perspective probabilistic resource measures. Note that the difference between the age of the earth and the age of the cosmos is only a factor of 3. A factor of 3 is rather negligible at the high order of magnitude of 10^17 seconds since the Big Bang (versus age of the earth). Thus, 10^17 seconds is used for all three astronomical subsets:

These above limits of probabilistic resources exist within the only known universe that we can repeatedly observe--the only universe that is scientifically addressable. Wild metaphysical claims of an infinite number of cosmoses may be fine for cosmological imagination, religious belief, or superstition. But such conjecturing has no place in hard science. Such claims cannot be empirically investigated, and they certainly cannot be falsified. They violate Ockham's (Occam's) Razor [40]. No prediction fulfillments are realizable. They are therefore nothing more than blind beliefs that are totally inappropriate in peer-reviewed scientific literature. Such cosmological conjectures are far closer to metaphysical or philosophic enterprises than they are to bench science.

From a more classical perspective at the level of ordinary molecular/chemical reactions, we will again provide metrics first for the entire universe (u) followed by three astronomical subsets, our galaxy (g), our solar system (s) and earth (e).

The classical molecular/chemical perspective makes two primary changes from the quantum perspective. With the classical perspective, the number of atoms rather than the number of protons, neutrons and electrons is used. In addition, the total number of classical chemical reactions that could have taken place since the Big Bang is used rather than transitions related to cubic light-Planck's. The shortest time any transition requires before a chemical reaction can take place is 10 femtoseconds [41-46]. A femtosecond is 10^-15 seconds. Complete chemical reactions, however, rarely take place faster than the picosecond range (10^-12 secs). Most biochemical reactions, even with highly sophisticated enzymatic catalysis, take place no faster than the nano (10^-9) and usually the micro (10^-6) range. To be exceedingly generous (perhaps overly permissive of the capabilities of the chance hypothesis), we shall use 100 femtoseconds as the shortest chemical reaction time. 100 femtoseconds is 10^-13 seconds. Thus 10^13 simple and fastest chemical reactions could conceivably take place per second in the best of theoretical pipe-dream scenarios. The four cΩA measures are as follows:

Remember that LΩe excludes meteorite and panspermia inoculations. To include meteorite and panspermia inoculations, we use the metric for our solar system cΩs.

These maximum metrics of the limit of probabilistic resources are based on the best-thus-far estimates of a large body of collective scientific investigations. We can expect slight variations up or down of our best guesses of the number of elementary particles in the universe, for example. But the basic formula presented as the Universal Plausibility Metric (PM) will never change. The Universal Plausibility Principle (UPP) inequality presented below is also immutable and worthy of law-like status. It affords the ability to objectively once and for all falsify not just highly improbable, but ridiculously implausible scenarios. Slight adjustments to the factors that contribute to the value of each LΩA are straightforward and easy for the scientific community to update through time.

Most chemical reactions take longer by many orders of magnitude than what these exceedingly liberal maximum probabilistic resources allow. Biochemical reactions can take years to occur in the absence of highly sophisticated protein enzymes not present in a prebiotic environment. Even humanly engineered ribozymes rarely catalyze reactions by an enhancement rate of more than 105 [47-51]. Thus the use of the fastest rate known for any complete chemical reaction (100 femtoseconds) seems to be the most liberal/forgiving probability bound that could possibly be incorporated into the classical chemical probabilistic resource perspective cΩA. For this reason, we should be all the more ruthless in applying the UPP test of falsification presented below to seemingly "far-out" metaphysical hypotheses that have no place in responsible science.