A linear string of stochastically linked units, the sequencing of which is dynamically inert, statistically unweighted, and is unchosen by agents; a random sequence of independent and equiprobable unit occurrence.

Random sequence complexity can be defined and measured solely in terms of probabilistic combinatorics. Maximum Shannon uncertainty exists when each possibility in a string (each alphabetical symbol) is equiprobable and independent of prior options. When possibilities are not equiprobable, or when possibilities are linked (e.g., paired by association, such as "qu" in the rules of English language), uncertainty decreases. The sequence becomes less complex and more ordered because of redundant patterning, or because of weighted means resulting from relative unit availability. Such would be the case if nucleotides were not equally available in a "primordial soup." This is demonstrated below under the section labeled "Ordered Sequence Complexity (OSC)."

Random sequence complexity (RSC) has four components:

1. The number of "symbols" in the "alphabet" that could potentially occupy each locus of the sequence (bit string)

(e.g., four potential nucleotide "alphabetical symbols" could occupy each monomeric position in a forming polynucleotide. In the English language, there are 26 potential symbols excluding case and punctuation.)

2. Equal probabilistic availability (often confused with post-selection frequency) of each "symbol" to each locus

(e.g., the availability of adenine was probably not the same as that of guanine, cytosine, or uracil to each position in a randomly forming primordial oligoribonucleotide. When each possibility is not equiprobable, weighted means must be used to calculate uncertainty. See equation 1)

3. The number of loci in the sequence

(e.g., the number of ribonucleotides must be adequate for a ribozyme to acquire minimal happenstantial function. A minimum of 30–60 "mers" has been suggested 9798

4. Independence of each option from prior options.

(e.g., in the English language, the letters "qu" appear together with much higher frequency than would be expected from independent letter selections where P = 1/26. Thus, if the generation of the signal were viewed as a stationary Markov process [as Shannon transmission theory does], conditional probabilities would have to be used to calculate the uncertainty of the letter "u".)

The Shannon uncertainty of random alphanumeric symbol sequences can be precisely quantified. No discussions of "aboutness" 121399 or "before and after" differences of "knowledge" 100101102103104 are relevant to a measure of the Shannon uncertainty of RSC. Sequences can be quantitatively compared with respect to syntax alone.

In computer science, "bits" refer generically to "the number of binary switch-setting opportunities" in a computational algorithm. Options are treated as though they were equiprobable and independent combinatorial possibilities. Bits are completely nonspecific about which particular selection is made at any switch. The size of the program is measured in units of RSC. But the programming decisions at each decision node are anything but random.

Providing the information of how each switch is set is the very essence of what we want when we ask for instructions. The number of bits or bytes in a program fails to provide this intuitive meaning of information. The same is true when we are told that a certain gene contains X number of megabytes. Only the specific reference sequences can provide the prescriptive information of that gene's instruction. Measurements of RSC are not relevant to this task.

A linear string of linked units, the sequencing of which is patterned either by the natural regularities described by physical laws (necessity) or by statistically weighted means (e.g., unequal availability of units), but which is not patterned by deliberate choice contingency (agency).

Ordered Sequence Complexity is exampled by a dotted line and by polymers such as polysaccharides. OSC in nature is so ruled by redundant cause-and-effect "necessity" that it affords the least complexity of the three types of sequences. The mantra-like matrix of OSC has little capacity to retain information. OSC would limit so severely information retention that the sequence could not direct the simplest of biochemical pathways, let alone integrated metabolism.

Appealing to "unknown laws" as life-origin explanations is nothing more than an appeal to cause-and-effect necessity. The latter only produces OSC with greater order, less complexity, and less potential for eventual information retention (Figs. 1 and 2).

The Shannon uncertainty equation would apply if forming oligoribonucleotides were stochastic ensembles forming out of sequence space:

where M = 4 ribonucleotides in an imagined "primordial soup." Suppose the prebiotic availability p_i for adenine was 0.46, and the p_i 's for uracil, guanine, and cytosine were 0.40, 0.12, and 0.02 respectively. This is being generous for cytosine, since cytosine would have been extremely difficult to make in a prebiotic environment 62. Using these hypothetical base-availability probabilities, the Shannon uncertainty would have been equal to Table 1

Notice how unequal availability of nucleotides (a form of ordering) greatly reduces Shannon uncertainty (a measure of sequence complexity) at each locus of any biopolymeric stochastic ensemble (Fig. 1). Maximum uncertainty would occur if all four base availability probabilities were 0.25. Under these equally available base conditions, Shannon uncertainty would have equaled 2 bits per independent nucleotide addition to the strand. A stochastic ensemble formed under aqueous conditions of mostly adenine availability, however, would have had little information-retaining ability because of its high order.

Even less information-retaining ability would be found in an oligoribonucleotide adsorbed onto montmorillonite 6097105106107108. Clay surfaces would have been required to align ribonucleotides with 3' 5' linkages. The problem is that only polyadenines or polyuracils tend to form. Using clay adsorption to solve one biochemical problem creates an immense informational problem (e.g., high order, low complexity, low uncertainty, low information retaining ability, see Fig. 1). High order means considerable compressibility. The Kolmogorov 4 algorithmic compression program for clay-adsorbed biopolymers (Fig. 2) would read: "Choose adenine; repeat the same choice fifty times." Such a redundant, highly-ordered sequence could not begin to prescribe even the simplest protometabolism. Such "self-ordering" phenomena would not be the key to life's early algorithmic programming.

In addition to the favored RNA Word model 55109, life origin models include clay life 110111112113; early three-dimensional genomes 114115; "Metabolism/Protein First" 116117118119; "Co-evolution" 120 and "Simultaneous nucleic acid and protein" 121122123; and "Two-Step" models of life-origin 124125126. In all of these models, "self-ordering" is often confused with "self-organizing." All known life depends upon genetic instructions. No hint of metabolism has ever been observed independent of an oversight and management information/instruction system. We use the term "bioengineering" for a good reason. Holistic, sophisticated, integrative processes such as metabolism don't just happen stochastically. Self-ordering in nature does. But the dissipative structures of Prigogine's chaos theory 127 are in a different category from the kind of "self-organization" that would be required to generate genetic instructions or stand-alone homeostatic metabolism. Semantic/semiotic/bioengineering function requires dynamically inert, resortable, physical symbol vehicles that represent time-independent, non-dynamic "meaning." (e.g., codons) 73748687128129130131.

No empirical or rational basis exists for granting to chemistry non-dynamic capabilities of functional sequencing. Naturalistic science has always sought to reduce chemistry to nothing more than dynamics. In such a context, chemistry cannot explain a sequencing phenomenon that is dynamically inert. If, on the other hand, chemistry possesses some metaphysical (beyond physical; beyond dynamics) transcendence over dynamics, then chemistry becomes philosophy/religion rather than naturalistic science. But if chemistry determined functional sequencing dynamically, sequences would have such high order and high redundancy that genes could not begin to carry the extraordinary prescriptive information that they carry.

Bioinformation has been selected algorithmically at the covalently-bound sequence level to instruct eventual three-dimensional shape. The shape is specific for a certain structural, catalytic, or regulatory function. All of these functions must be integrated into a symphony of metabolic functions. Apart from actually producing function, "information" has little or no value. No matter how many "bits" of possible combinations it has, there is no reason to call it "information" if it doesn't at least have the potential of producing something useful. What kind of information produces function? In computer science, we call it a "program." Another name for computer software is an "algorithm." No man-made program comes close to the technical brilliance of even Mycoplasmal genetic algorithms. Mycoplasmas are the simplest known organism with the smallest known genome, to date. How was its genome and other living organisms' genomes programmed?

A linear, digital, cybernetic string of symbols representing syntactic, semantic and pragmatic prescription; each successive sign in the string is a representation of a decision-node configurable switch-setting – a specific selection for function.

FSC is a succession of algorithmic selections leading to function. Selection, specification, or signification of certain "choices" in FSC sequences results only from nonrandom selection. These selections at successive decision nodes cannot be forced by deterministic cause-and-effect necessity. If they were, nearly all decision-node selections would be the same. They would be highly ordered (OSC). And the selections cannot be random (RSC). No sophisticated program has ever been observed to be written by successive coin flips where heads is "1" and tails is "0."

We speak loosely as though "bits" of information in computer programs represented specific integrated binary choice commitments made with intent at successive algorithmic decision nodes. The latter is true of FSC, but technically such an algorithmic process cannot possibly be measured by bits (-log₂ P) except in the sense of transmission engineering. Shannon 23 was interested in signal space, not in particular messages. Shannon mathematics deals only with averaged probabilistic combinatorics. FSC requires a specification of the sequence of FSC choices. They cannot be averaged without loss of prescriptive information (instructions).

Bits in a computer program measure only the number of binary choice opportunities. Bits do not measure or indicate which specific choices are made. Enumerating the specific choices that work is the very essence of gaining information (in the intuitive sense). When we buy a computer program, we are paying for sequences of integrated specific decision-node choice-commitments that we expect to work for us. The essence of the instruction is the enumeration of the sequence of particular choices. This necessity defines the very goal of genome projects.

Algorithms are processes or procedures that produce a needed result, whether it is computation or the end-products of biochemical pathways. Such strings of decision-node selections are anything but random. And they are not "self-ordered" by redundant cause-and-effect necessity. Every successive nucleotide is a quaternary "switch setting." Many nucleotide selections in the string are not critical. But those switch-settings that determine folding, especially, are highly "meaningful." Functional switch-setting sequences are produced only by uncoerced selection pressure. There is a cybernetic aspect of life processes that is directly analogous to that of computer programming. More attention should be focused on the reality and mechanisms of selection at the decision-node level of biological algorithms. This is the level of covalent bonding in primary structure. Environmental selection occurs at the level of post-computational halting. The fittest already-computed phenotype is selected.

We can hypothesize that metabolism "just happened," independent of directions, in a prebiotic environment billions of years ago. But we can hypothesize anything. The question is whether such hypotheses are plausible. Plausibility is often eliminated when probabilities exceed the "universal probability bound" 132. The stochastic "self-organization" of even the simplest biochemical pathways is statistically prohibitive by hundreds of orders of magnitude. Without algorithmic programming to constrain (more properly "control") options, the number of possible paths in sequence space for each needed biopolymer is enormous. 10¹⁵ molecules are often present in one test tube library of stochastic ensembles. But when multiple biopolymers must all converge at the same place at the same time to collectively interact in a controlled biochemically cooperative manner, faith in "self-organization" becomes "blind belief." No empirical data or rational scientific basis exists for such a metaphysical leap. Certainly no prediction of biological self-organization has been realized apart from SELEX-like bioengineering. SELEX is a selection/amplification methodology used in the engineering of new ribozymes 133134135. Such investigator interference hardly qualifies as "self-organization." All of the impressive selection-amplification-derived ribozymes that have been engineered in the last fifteen years have been exercises in artificial selection, not natural selection.

Random sequences are the most complex (the least compressible). Yet empirical evidence of randomness producing sophisticated functionality is virtually nonexistent. Neither RSC nor OSC possesses the characteristics of informing or directing highly integrative metabolism. "Bits" of complexity alone cannot adequately measure or prescribe functional ("meaningful") bioinformation. Shannon information theory does not succeed in quantifying the kind of information on which life depends. It is called "information," but in reality we are quantifying only reduced combinatorial probabilistic uncertainty. This presupposes RSC. It is true that sophisticated bioinformation involves considerable complexity. But complexity is not synonymous with genetic instruction. Bioinformation exists as algorithmic programs, not just random combinations. And these programs require an operating system context along with common syntax and semantic "meanings" shared between source and destination.

The sequence of decision-node selections matters in how the polymer will finally fold. Folding is central to biofunction whether in a cell or a buffer in a test tube. In theory, the same protein can fold and unfold an infinite number of times via an ensemble of folding pathways 136. But its favored minimal-free-energy molecular conformation is sequence dependent in the cell or assay mixture. The molecular memory for the conformation is the translated sequence. This is not to say that multiple sequences out of sequence space cannot assume the same conformation.

Nucleotides are grouped into triplet Hamming block codes 47, each of which represents a certain amino acid. No direct physicochemical causative link exists between codon and its symbolized amino acid in the physical translative machinery. Physics and chemistry do not explain why the "correct" amino acid lies at the opposite end of tRNA from the appropriate anticodon. Physics and chemistry do not explain how the appropriate aminoacyl tRNA synthetase joins a specific amino acid only to a tRNA with the correct anticodon on its opposite end.

Genes are not analogous to messages; genes are messages. Genes are literal programs. They are sent from a source by a transmitter through a channel (Fig. 3) within the context of a viable cell. They are decoded by a receiver and arrive eventually at a final destination. At this destination, the instantiated messages catalyze needed biochemical reactions. Both cellular and extracellular enzyme functions are involved (e.g., extracellular microbial cellulases, proteases, and nucleases). Making the same messages over and over for millions to billions of years (relative constancy of the genome, yet capable of changes) is one of those functions. Ribozymes are also messages, though encryption/decryption coding issues are absent. The message has a destination that is part of a complex integrated loop of information and activities. The loop is mostly constant, but new Shannon information can also be brought into the loop via recombination events and mutations. Mistakes can be repaired, but without the ability to introduce novel combinations over time, evolution could not progress. The cell is viewed as an open system with a semi-permeable membrane. Change or evolution over time cannot occur in a closed system. However, DNA programming instructions may be stored in nature (e.g., in permafrost, bones, fossils, amber) for hundreds to millions of years and be recovered, amplified by the polymerase chain reaction and still act as functional code. The digital message can be preserved even if the cell is absent and non-viable. It all depends on the environmental conditions and the matrix in which the DNA code was embedded. This is truly amazing from an information storage perspective.

A noisy channel is one that produces a high corruption rate of the source's signal (Fig. 3). Signal integrity is greatly compromised during transport by randomizing influences. In molecular biology, various kinds of mutations introduce the equivalent of noise pollution of the original instructive message. Communication theory goes to extraordinary lengths to prevent noise pollution of signals of all kinds. Given this longstanding struggle against noise contamination of meaningful algorithmic messages, it seems curious that the central paradigm of biology today attributes genomic messages themselves solely to "noise."

Selection pressure works only on existing successful messages, and then only at the phenotypic level. Environmental selection does not choose which nucleotide to add next to a forming single-stranded RNA. Environmental selection is always after-the-fact. It could not have programmed primordial RNA genes. Neither could noise. Abel has termed this The GS Principle (Genetic Selection Principle) 137. Differential molecular stability and happenstantial self- or mutual-replication are all that nature had to work with in a prebiotic environment. The environment had no goal or intent with which to "work." Wasted energy was just as good as "energy available for work" in a prebiotic world.

Denaturization factors like hydrolysis in water correspond to normal Second Law deterioration of the physical matrix of information retention. This results in the secondary loss of initial digital algorithmic integrity. This is another form of randomizing noise pollution of the prescriptive information that was instantiated into the physical matrix of nucleotide-selection sequences. But the particular physical matrix of retention should never be confused with abstract prescriptive information itself. The exact same message can be sent using completely different mass/energy instantiations. The Second Law operates on the physical matrix, not on the nonphysical conceptual message itself. The abstract message enjoys formal immunity from dynamic deterioration in the same sense that the mathematical laws of physics transcend the dynamics they model.

The purpose of biomessages is to produce and manage metabolic biofunctions, including the location, specificity, speed, and direction of the biochemical reactions. Any attempt to deny that metabolic pathways lack directionality and purpose is incorrect. Genes have undeniable "meaning" which is shared between source and destination (Fig. 3). Noise pollution of this "meaning" is greatly minimized by ideally optimized redundancy coding 9 and impressive biological repair mechanisms 138139140141142143.

For prescriptive information to be conveyed, the destination must understand what the source meant in order to know what to do with the signal. It is only at that point that a Shannon signal becomes a bona fide message. Only shared meaning is "communication." This shared meaning occurs within the context of a relatively stable cellular environment, unless conditions occur that damage/injure or kill the cells. Considerable universality of "meaning" exists within biology since the Last Universal Common Ancestor (LUCA). For this reason, messages can be retrieved by bacteria even from the DNA of dead cells during genetic transformation 144. The entire message is not saved, but significant "paragraphs" of recipe. The transforming DNA may escape restriction and participate in recombination events in the host bacterial cell. A small part of the entire genome message can be recovered and expressed. Evolution then proceeds without a final destination or direction.

Shannon's uncertainty quantification "H" is maximized when events are equiprobable and independent of each other. Selection is neither. Since choice with intent is fundamentally non probabilistic, each event is certainly not equiprobable. And the successive decision-node choice-commitments of any algorithm are never independent, but integrated with previous and future choices to collectively achieve functional success.

The "uncertainty" ("H") of Shannon is an epistemological term. It is an expression of our "surprisal" 145 or knowledge "uncertainty." But humans can also gain definite after-the-fact empirical knowledge of which specific sequences work. Such knowledge comes closer to "certainty" than "uncertainty." More often than not in everyday life, when we use the term "information," we are referring to a relative certainty of knowledge rather than uncertainty. Shannon equations represent a very limited knowledge system. But functional bioinformation is ontological, not epistemological. Genetic instructions perform their functions in objective reality independent of any knowers.

Stochastic ensembles could happenstantially acquire functional sequence significance. But a stochastic ensemble is more likely by many orders of magnitude to be useless than accidentally functional. Apart from nonrandom selection pressure, we are left with the statistical prohibitiveness of a purely chance metabolism and spontaneous generation. Shannon's uncertainty equations alone will never explain this phenomenon. They lack meaning, choice, and function. FSC, on the other hand, can be counted on to work. FSC becomes the objective object of our relative certainty. Its objective function becomes known empirically. Its specific algorithmic switch-settings are worth enumerating. We do this daily in the form of "reference sequences" in genome projects, applied pharmacology research, and genetic disease mapping. Specifically enumerated sequencing coupled with observed function is regarded as the equivalent of a proven "halting" program. This is the essence of FSC.

Symbols can be instantiated into physical symbol vehicles in order to manipulate dynamics to achieve physical utility. Symbol selections in the string are typically correlated into conceptually coordinated holistic utility by some externally applied operating system or language of arbitrary (dynamically inert) rules. But functional sequence complexity is always mediated through selection of each unit, not through chance or necessity.

The classic example of FSC is the nucleic acid algorithmic prescription of polyamino acid sequencing. Codon sequence determines protein primary structure only in a conceptual operational context. This context cannot be written off as a subjective epistemological mental construction of humans. Transcription, post-transcriptional editing, the translation operational context, and post-translational editing, all produced humans. The standard coding table has been found to be close to conceptually ideal given the relative occurrence of each amino acid in proteins 146. A triplet codon is not a word, but an abstract conceptual block code for a protein letter 47. Block coding is a creative form of redundancy coding used to reduce noise pollution in the channel between source and destination 9.

Stochastic ensembles of physical units cannot program algorithmic/cybernetic function.

Dynamically-ordered sequences of individual physical units (physicality patterned by natural law causation) cannot program algorithmic/cybernetic function.

Statistically weighted means (e.g., increased availability of certain units in the polymerization environment) giving rise to patterned (compressible) sequences of units cannot program algorithmic/cybernetic function.

Computationally successful configurable switches cannot be set by chance, necessity, or any combination of the two, even over large periods of time.

We repeat that a single incident of nontrivial algorithmic programming success achieved without selection for fitness at the decision-node programming level would falsify any of these null hypotheses. This renders each of these hypotheses scientifically testable. We offer the prediction that none of these four hypotheses will be falsified.

The fundamental contention inherent in our three subsets of sequence complexity proposed in this paper is this: without volitional agency assigning meaning to each configurable-switch-position symbol, algorithmic function and language will not occur. The same would be true in assigning meaning to each combinatorial syntax segment (programming module or word). Source and destination on either end of the channel must agree to these assigned meanings in a shared operational context. Chance and necessity cannot establish such a cybernetic coding/decoding scheme 71.

How can one identify Functional Sequence Complexity empirically? FSC can be identified empirically whenever an engineering function results from dynamically inert sequencing of physical symbol vehicles. It could be argued that the engineering function of a folded protein is totally reducible to its physical molecular dynamics. But protein folding cannot be divorced from the causality of critical segments of primary structure sequencing. This sequencing was prescribed by the sequencing of Hamming block codes of nucleotides into triplet codons. This sequencing is largely dynamically inert. Any of the four nucleotides can be covalently bound next in the sequence. A linear digital cybernetic system exists wherein nucleotides function as representative symbols of "meaning." This particular codon "means" that particular amino acid, but not because of dynamical influence. No direct physicochemical forces between nucleotides and amino acids exist.