By Tom Veatch
Logic and Her DaughtersEvolution, Cognition, Emotion.
The Queen of All Knowledge
My phonetics professor Leigh Lisker once told me, the less you say, the less you're going to be wrong. At the time I thought he was telling me to shut up, but later realized it was more than and different from that.
Tautology says nothing, and therefore it cannot be denied.
Logic, math and 1=1 are not functions of time; they are true before and after the big bang, before and after the origin of life, and irrespective of a mind that knows it or doesn't know it. Describe some process today, with truth, irrespective whether an instance of it occurred yesterday, today, or tomorrow your description IS, WAS, WILL BE true; define something today, your definition applies outside time, to things your eyes do see or will see but also to things in the past you can never see again. Tautology is automatically true; and truth is timeless.
For example, consider repeated evolution into an unoccupied niche, as in the Galapagos finches, or post-dinosaur-apocalypse predation, etc. You have a species B that evolves to fill a niche which was previously or elsewhere filled by another species A. Now, did the evolutionary niche exist before B evolved to fill it? Obviously Yes, because A had filled it before or elsewhere, so of course it existed, as a possibility. Well then did that niche exist before A filled the niche? Well there is nothing different from A filling it from B filling it, so if it existed before B filled it it must also have existed before A filled it. Therefore evolutionary niches exist, let's say in possibility or in logic, BEFORE they are occupied.
Does not the same argument apply to life and physics and everything? Was life possible before life happened? Yes it was, otherwise it couldn't have. Do the laws of physics, where they are universal and true, that is, which are merely definitional, describing tautological logic amongst terms, do these laws not apply outside of time itself, and therefore also inside of time and therefore before, during, and after the Big Bang and everywhere in the universe? Yes, that's what universal means.
The relationship between language, or let us reduce it to, abstraction, and reality is the fundamental mystery here. But that's not so complicated. Two things in the real world that are similar share some sameness about them. When multi-use, or shall we say, effective mechanisms (since without their ability to be used consistently or repeatedly or predictably even within slightly-variable circumstances we would hardly call them very effective), when they operate, they obviously operate over the multiple things or circumstances in the real world for each of which they are effective. But this is nothing but abstraction: the class of things picked out by the mechanism over which it can operate is thereby no less than an abstract category of things, an agglomeration of similars into a category each member of which can be treated the same, which is treated the same by that mechanism. If the mechanism is nuclear or electrical or gravitational attraction or repulsion or quark interaction before the big bang, its sameness of input/output relations makes it an abstraction, a thing that applies in a general way.
Okay then, yes, if you have a general mechanism in nature, it IS itself an abstraction, by definition because of its generality. Despite diversity, nature does happen to be full of similars and samenesses, of consistents and repeatables, and those are the parts and aspects that organisms, and we, are interested in and need to know or be able to control, being as we all are indeed organisms with, usefully, a will to power, that is, a will to the control of general mechanisms. So if we humans, as an evolved, social, teamwork type of species, have evolved to control and use an inventory or library of abstractions in a lexicon of signals that we can communicate to each other, that makes a lot of sense. Contemplate the opposite: for us to be unable to detect sameness, in general, would be quite the detriment to our capabilities, or to be unable to communicate them, that would limit our capacities for social achievement as well.
By these links, abstraction connects to reality on the one hand and lexicon on the other hand. I haven't, indeed, derived syntax from first principles, no, but animal cognition, and the cognitive capability to reason tautologically, to apply logic, I think we have enough here to connect them: abstractions, minds, and nature itself, in a tight circle of mutual dependency, if not perfect equivalence.
We happen to have the right kind of minds, we'll get to what that means later, but even alien minds must share logical reasoning.
Let's try an example. Two 90 degree rotations are the same, in a sense, as one 180 degree rotation. Does this depend on human cognition, or the words or sentence in which it is expressed? I say No; rather, cognition itself depends on, itself perceives, logic.
My purpose will be to deconstruct logic into tautology, then expand this zone of perfect understanding out from there.
Formal Logic as TautologyEven so-called rules of formal logic themselves reduce to tautology.
Where THIS and THAT reference the same thing, THIS=THAT both says nothing and is absolutely true: it is tautological. Thus also Definition = Tautology.
Newton's Tautological ReasoningApply definition = tautology to Isaac Newton. We know he knew about the hourglass, the yardstick, and the scale, and that there he was, speculating about the laws of nature, about different physical relationships. Under the mythological apple tree, he considered what he did know, measureable qualities starting with 1) weight (with the scale), 2) change in location (with the yardstick) and 3) time (by the hourglass), therefore in principle he could certainly define and measure change in location divided by time i.e. 4) velocity, therefore also (since you can measure velocity, you can also measure velocity twice, and then find the difference, which is how you measure ...) change in velocity over time i.e. 5) acceleration. So, W for weight, let's say, and A for acceleration. Now the clever bit is, he decided to relate weight (under gravity) to acceleration by a discovered, no, an invented, no, a proposed, a DEFINED scaling he called mass, by saying M≝W/A, where here '≝' sign indicates a DEFINITION, or as we write it W=M*A, where here the '=' sign rather conceals the definition in the equation. So it was already a tautology to start with, the definition of the mass of a thing is its weight divided by its acceleration (under gravity). The idea is, if you take the movement out of the weight, you get a degree of non-movingness, of deadness, or unreactiveness, or uninfluenceability, a quantity of resistance to acceleration, that is its mass. So far so good, so pleasant, so firm: we believe it because you can define anything you want, and it'll always be true by definition, in its imaginary definitional world.
But today we stand in awe of this quite especially useful definition, we call it the amazing universal Second Law of Motion, that miraculously seems to apply equally throughout the universe, not just to an apocryphal apple bonking dear Isaac on the head in about 1666, but also over there, out to our planets, far out to other stars, and down inside here also even to molecules and atoms, and in time from the first beginning to the last end, or beyond. Was Newton's miracle the empirical universality of this law? Or was it just a definition, where as we know a definition is necessarily universal? It is universal because it is a definition, which is to say, a tautology. Because of course M is DEFINED as F/A (in the context of gravity W=F, an object's weight is the force it exerts being pulled down by gravity). A definition holds conceptually, that is, outside of time and the mind that conceived it: as a tautology, it asserts nothing, and saying nothing, it cannot be false, it is everywhere and always undeniable, true. It is like a perspective, come over here and look at it this way, then you'll see how things line up in this view. Every perspective is true; it's not the perspective that can be false but well or ill-observed conclusions of fact that may be drawn from viewing the world from that perspective.
The miracle is not that F=MA is true, but that it is useful. Where gravity is disregardable, mass still is measureable by applying non-gravitational force and seeing how much is needed to push the thing around. Nowadays we think the concept of mass that Newton defined into existence is as real as, or more real than, the measurements he started with to measure and define it. Flip a cognitive switch and mass becomes the primitive characteristic out of which complexities like force under gravity are built up, rather than the other way around. Think of it this way or that, however you find useful, the truth is it is true by tautology, by logic, the queen, the king of science, before and after, outside time itself. Tautologus Rex.
I like to say I'm a lazy boy, very lazy, where a choice exists. So here's a lazy boy trick. When I'm doing math, almost all the work intellectually is writing down what I know as an expression or equation and then thinking about it, primarily by substituting equal things into the expression. You can always substitute equals for equals and the result always is an equivalent expression, equally as true as you started with, because you could in principle substitute backwards, too, and get to the same thing.
Lazy Equals, or H notation
My problem is penmanship. I suck at it, and I hate it. I have to re-write the whole equation all over and then over again when all I did was another tiny substitution of some part of it with something equal to that part of it. Maybe it's a very long equation, and maybe I have three or four parts to substitute, or maybe some parts get substituted time after time. And it makes for a lot of stupid, stupid work doing copying, when the only thing I really need to re-write in full is the last version at the end, when I want to talk about that one. So instead I just use what I call H-notation: It's a Lazy Equals sign (remember "Lazy" applied to a cow brand means a 90 degree rotation), an H.
H-notation is just my way of writing an equals sign vertically. It's not a curly brace! Curly braces suck: they are SO hard to draw attractively when large, or with economy of space on the page. Curly braces have a different, more vague, meaning. Curly braces pick something out for a generic comment, like circling something. The comment might or might not be a substitution of something equal to the marked bit, whereas H-notation means equality. Just because it's Lazy, it's still an equals sign. Just because it's partial, it refers to a part of an expression, it still asserts equality between the above and below subexpressions that it connects.
Here: Draw a super-wide H below the part you want to say something about, and write what is equal to that part below the H.
Thus H-notation lets you substitute equals for equals within any expression or equation.
F = m * a |---| |------------| Fg 32'/sec/secFor example, above, Newton's Law F = m * a, in the context of an object under gravity, becomes the statement that the force of gravity on that object is the mass of that object times 32 feet per second per second.
You can use H-notation as often as you want on either side of the equals sign, and you can do it in columns too.
I find that about half of my math homework problems go away, when I don't do the recopying and just use H notation. Try it, you'll like it!
Incidentally, the way real mathematicians seem to solve this is to skip or hide all the step-by-step reasoning and substitutions, and just write the last equation. If you ask them they say that part is "obvious". Because it's job security for them, you see, the more obscure the reasoning is, then the harder everyone has to work to keep up with them, and then they seem to be so much smarter than everyone else. That method works in a bunch of professions, like law, medicine, and even plumbing. But I think it's obnoxious, especially when you're teaching, and math is (or should be) nothing else but teaching people. Write it down, see what comes out, that's how you actually teach yourself, and that's how you also teach others. Surprise! Language works! Who knew!
Dearie, we never told you this but Grandma Della had a secret baby named Robert with that roughneck Joe Smith before she met and got married to Grandpa Fred and had Helen and Fred Junior and John. But Grandma never told Grandpa she had a boy already, and made Joe raise him on the other side of town. So then Bob grew up and met your Aunt Helen, and fell in love and asked her to marry him. But after we explained the facts, she told him No. Because Bob's your uncle.
Another way to say "H notation" is to say "Tautology". Like A = A is a tautology, you can also say
A |---| ABecause it's the same thing.
Tautologies are statements that are true automatically. If something is true by definition, like The sky is above or The earth is below, then they don't actually say anything. Of course it's true: Duh!
Actually it's not duh!, you can discover things that are very surprising using tautological reasoning, or H notation, or mathematical substitution, for example that those three things are the same thing.
You philosophers will recognize H as a Kantian analytic judgement: the consequent is contained in the antecedent, as contrasted with synthetic judgements in which the consequent contains something more that is added to the antecedent.
So far I haven't actually said anything, but now I want to seem to say some things about life and evolution and organisms, though I will continue to assert that I'm not actually saying anything. Observe whether I do or not.
The logic of biological evolution rests on tautologies.
D'oh! I guess actually I didn't say anything there. Just another tautology.
But tautologies have a peculiar force. You can't deny them, or argue with them; inexorable, they hold us all helpless. Therefore submit, brave heart, and see what you may learn! Here are some, in the world of evolution, where organisms can survive and reproduce.
If an organism survives and reproduces then it survives and reproduces.
If it dies then it dies. (But, why and how death itself evolved sure seems like a non-tautological question. Maybe understanding something means reducing it to tautologies.) Whereas if it dies before it reproduces, then none of its descendants actually descend, nor exist, nor multiply. Its branch in the tree of life is cut off. Does this say anything? No. H. It's just another way of saying the same thing.
If organisms with some feature die out of a species, then that feature has been "selected against". A definition: H. If the organisms carrying a feature reproduce before they die, and their descendants do too, then their branches in the tree of life continue forward generation after generation, and if there are many, then there are many; if these contrast with others in that the others without that feature don't, then the feature is "selected for". Definition. H.
Survival and reproduction are required for past, mortal, life to continue into the future.
When a community with internal relationships has members surviving and reproducing before death and its new young members come to participate in maintaining those relationships, the community itself survives and reproduces. Another definition.
The world in which life exists and continues into the indefinite future is a world of sufficient resources, energy, and time or stability, for life, at least for now.
I still don't think I've said anything yet. Just like 1=1.
So let me continue to elaborate tautological reasoning in the logical structure of evolution and living species. I will tag everything that says nothing with an H, indicating H notation or tautological or definitional reasoning has applied, giving perhaps a new way of looking at something, but not anything truly new.
A species is an environmentally compatible (H), practically self-sustaining (H) community (H) of organism-specifying information, comprising a set of fixed and variable genes, the variable ones comprising a set of mutually substitutable alleles within the gene (H) such that organisms each contain a copy of each fixed gene and a copy of one allele for each variable gene (H). Sexual reproduction mixes randomly-chosen halves of each of two parents, independently functional gene sets, to create each descendant, a new individual, a new functional gene set (H, H, H, H). After a few generations of reproductive mixture along with death of forebears in a living species, the genes are mixed around in different bodies but they are the same total set of genes and alleles modulo mutations (H). These practically useful information units depend on each other to survive into the indefinite future (H). If some combination of genes and alleles happen to systematically interfere with survival of its carriers, then the community will drift in the direction of having fewer of that combination within it (H), eventually none (H).
The fixed genes are like fixed framing sentences in the story, everyone's story has these same bits. The alleles, which substitute in as the values of a gene with variable contents, are like mutually substitutable sentences in a story. Then each organism's information is a single story, with the fixed parts, plus a sequence of selections from the substituteable sets. You might consider a happy ending and a sad ending as two substitutable sentences in a short story, for example. The living population, which embodies the species, is the entire set of life-specifying stories currently selected within all the current living organisms, and the species itself is this sort of abstract pond of information, carried by the group of organisms, each being a bearer of its own copy of shared bits of the story. The fixed bits are shared with all, and the variable bits are shared with some, of the other members of the species. The species itself, you might say, is a kind of abstraction, which includes the happy ending AND the sad ending, both at once. It is the commonality across the set of all those stories or narrative subselections. It is defined in biochemistry by the actual DNA choice points and actual choices chosen there, and is defined in bitter logic by their compatibility with and enhancement of mutual or shared survival. Without successful, survival-and-reproduction-compatible cooperation among these informational units, the many choices cannot individually survive, so mutual compatibility is a filtering requirement on the choices and their interactions.
If a life form does not have systems in it which tend to, nay, which reliably, make it survive and reproduce in its environment, then it won't (H). Therefore effective survival and reproduction mechanisms are necessary for an organism and will be present in any evolved species (H). In general if a species has (a) evolved specialized anatomy for a function, it would seem to have (b) a reliable solution for that problem and to hold it (c) high on the priority list for the species to carry out that function. Thus air, food, and reproduction each have both (a) and (b) and (c).
We are moving in the direction of what you, I, and humans all care about.
Directions and path-sequences being innumerable, and pathways compatible with survival being few and limited in character, it follows that if a living system doesn't prioritize, or shall we say, aim at, its target, then it is not likely to hit it (H). These mechanisms may seem designed for an intended (or logically specifiable) purpose only because the link between mechanism and its associated outcome must be rather tight in order to be functional, that is reliably tending toward survival or reproduction or the observed subsidiary outcome (H). The argument is not teleological evolution, but selection based subject to logical constraints. Of course random mutation may or may not create a particular logically possible useful solution to a problem; only if it happens to do so, can that solution be selected for. "Design" in this context is this combination of random creation and functional selection, not something attributable to a some smart individual with a goal and an idea in mind separate from the creation itself; indeed mutation, survival-filtering, reproduction, and selection, is a process that comes up with amazing results.
Prioritization in Evolution
But it is not a happy story getting there. In cases where a survival-connected outcome is only loosely predictable from a certain variable mechanism (with probability P <<1), the carriers of the mechanism will only loosely survive (with probability P) in one generation, and over a few, or for a subtle effect over many, generations without otherwise increased reproduction, that total probability (Pn) will approach zero (H). Functional logic is harsh and controlling, when the tautologies of evolution impose it on life.
From this follows the prioritization of survival before reproduction where separable: you can reproduce another day if you survive first, but if not, then not (H).
We can generalize over many priorities.
If survival depends on multiple subordinate outcomes, and each subordinate outcome has an evolved, effective mechanism to satisfy it but which cannot operate simultaneously and at equal priority with others, then the competitive prioritization of all the mechanisms (for their respective outcomes) and suppression of alternatives to the chosen priority must be done by a competent meta-mechanism, which is able to make and enforce a detailed rank ordering according to system state or circumstances, so as to orchestrate the few survivable and reproducing outcomes reliably (H).
Maslow's hierarchy of needs, the Hindu chakra system, the Freudian plural id, the hormonally-defined (and -governed) subpersonalities, and the at least hypothalamic system for choosing which subpersonality must be in charge when: these are perhaps expressions or, roughly, homomorphisms of a single, of one and the same, of this functional logic and prioritization constraint set, imposed on complex life by the tautologies of life. Of course survival first. Respiration, temperature, rest/sleep, sustenance, have their nonlinear hierarchy of systemic control, which may derive from the duration of time you can survive without that particular homeostatic requirement being met. The sooner you die without some requirement being met, the higher the priority and the more rigid the enforcement. This seems like raw tautology, but we now have separable mechanisms linking to separable functional outcomes: were it not so, were it instead that mechanisms were not linked to outcomes, then those fatal outcomes would fail to be defended against, and at some greater probability would occur, and over generations those life forms will not last long, as the chances multiply. So long-term evolutionary survival statistically implies (over tens, thousands or millions of generations it more and more categorically implies) strong and reliable, carefully, calibratedly, mutually prioritizing, mechanisms to defend against each of the various standard modes of practical failure, of death or non-reproduction.
Observe: Functional outcomes are categorical and discrete. It can be expressed in hard yeses and noes, binary digits, bits, category-based logics, despite the physical continuity and statistical probabilization of every kind of dimension, measurement, control variable or physical Blob in this world at least at the levels we are talking about, far above the level of quantum chemistry. Because there are Outcomes: simple, discrete, dispositive facts. You live, or you die. You reproduce, or you don't. You turn left or turn right, and thus approach food or flee toxicity. In this way evolutionary outcomes or constraints are isomorphic to what come to us as sets of linguistic categories: discrete, typically binary assertions; thus we may talk about the "choices" and "motivations" of an organism. (*It may be a yeast or paramecium entirely lacking in high level brain structures designed to make choices and implement motivations in the form human organisms might have, but considered from a functional, logical perspective, it can be seen as facing choices and balancing motivations.*) In this way organisms are constrained to survive in a symbolically expressible world: a world of discrete abstractions. Not a world of mere low level, continuous physicality, but a world of choice, decision, and action: of discriminating and motivated frames.
Bits in Evolution
This is so not just at the level of conscious, linguistic, supposedly rational humanity, for which internal symbol representation and manipulation and, for example, discrete planning processes are axiomatic among cognitive scientists. It is even true at the level of paramecia, of single-celled mobile creatures (and in recent news even at the level of groups of mitochondria within a cell).
Because if the life form doesn't have mechanisms that reliably produce surviving, reproducing outcomes, which are discrete outcomes, then it won't continue to evolve, but will drop out even from the very dustbin of history into the vacuum of non-existence, as something that never even needed to have been tried as an experiment.
A scientist's job therefore includes the cognitive scientist's job.
The cognitive scientist, remember, creates categorical, discrete logic systems mapping between discrete informational inputs and outputs, using inferred internal "mental" representations that can be modelled using the computer metaphor with bits and memory and actuators and software objects like goals and control subroutines. These logical machines are asserted to be descriptions at some level of organismal process and constraint. They are called cognitive models because they look a lot like computer programs containing logical representations that purport to model what goes on inside organisms of more or less intelligence: formal psychological models.
Cognitivity of Evolution
Is this just the mental masturbation of overexcited grammarians? Or is it a necessary level of description of the functional logic of what actually ends up happening within the context of discrete, evolutionarily unavoidable and potentially bitter outcomes. I say the latter. Because if you can't get that logical system right in describing a biological system, then you don't understand why the thing is able to actually survive and reproduce, and more fundamentally even if you know the physics, the chemistry, the biochemistry, the cell biology, every detail of every subsystem, you still don't have any handle on WHY it survives or not: you don't understand it. System understanding depends on the cognitive scientist's modelling. H! Just try to prove me wrong.
So, what are these discrete categories and the motivational frames of organismal existence, what is the rank ordering of priority, what is the logic controlling their relations and community of interest, and the communications or interactions they must have, if only in sharing to an internal Master Controller their several concerns and status reports or awarenesses for it to mediate or sort?: A scientist must also describe these discrete, cognitive behaviors within the functional logic that applies to them. For if the organism doesn't follow, doesn't implement, that logic, it will shortly be gone. Thus I make room for, I demand!, cognitive modeling of animal behavior, not just of humans or human language, but at least down to the level of protozoa.
To take it to an extreme, we like to think we have a Soul with a Will, with the uniquely human characteristics of drivenness, attention, spatial awareness, integrated action control. Don't you believe you have those qualities? Aren't they at the heart of what you are? Do you think that makes you special, makes us special? I say the same thing goes all the way down, just follow the logic.
For example, it seems that the driven-personality quality of people, as we are, is a quality equally driven and necessary in the least watery wiggler. If an organism isn't driven, doesn't coalign all its available and useful resources, you might say, with all its might, in circumstances that threaten it, to drive toward whatever motivations can be ascribed to it (cognitively) for its (necessary) survival, then obviously it may fail to survive. The tautologies apply, and bye-bye. Even a slight probabilistic slip between mechanism and the survival it relates to will lead over a million generations to obliteration. 0.9991,000,000 is an excellent approximation of zero.
Consider attention itself, consisting in the continual reassessing of priorities and of situational awareness tending to inform those priorities. Attention would seem to be a highly valued early evolutionary achievement. For otherwise rapidly changing conditions would be fatal, and yes the Tautologies of Evolution apply.
Similarly, integrated behavioral control, whereby a single target of action is aimed at, since one can hardly hit two targets at a time much less more, would also seem highly valued, evolutionary speaking. For if competing incompatible priorities are allowed to remain unresolved in a circumstance of potential action, no target may be obtained, an outcome likely to be, or evidently, evolutionarily inferior to one where the most important single target was actually aimed at and acted towards or into being.
I'm not saying mechanisms are the same between humans and protozoa. Mechanisms might be different for the same functional outcome, if new ones might be evolved that are as good or better, but the functional logic is the same, from paramecia to people. Functionally one could say those mechanisms perform the same task, indeed, are the same system. They live in the same functional box, subject to the same logic. No efficient designer, neither Ockham nor hurried evolution itself, would fail to reuse the contents, by the way, so why we should think we are so different from worms with our special uniquely human characteristics of attention, spatial awareness, integrated action control (a.k.a. Will), I don't know. I don't think we are.
I have argued that the unarguable tautologies and harsh constraints of evolution impose a symbolic, discrete logic on successfully evolved (all living) organisms. From what may evolve, I turn next to when things may evolve, in what order.
Putting changes in sequence
We are given a descendant species with some set of novel characteristics N as compared with the shared set of characteristics Sh among the other species in the genus. Are we perhaps entirely unable to reason about the sequence by which the N characteristics evolved? There may be no archeological or DNA data on the question.
But suppose it can be established that some feature N1 is logically prerequisite for another feature N2, then we can at least provisionally infer that N2 evolved after N1. Agreed? If you logically can't have N2 without N1, then N1 must have preceded N2.
For example, what came first, eyes or blue eyes? Blue eyes couldn't have come first in the sequence of evolution, because you can't have blue eyes without having eyes, whereas you can have eyes and even light sensitive patches without irises entirely, without having blue eyes.
Or, what came first, fingers or fingernails? Perhaps it's a failure of scientific imagination, imagining fingernails on something other than fingers, then growing fingers out underneath them, but that sure doesn't make sense to me.
If you can see two features as logically dependent in this way, it would seem to require the dependent feature to follow, or at least not to separately precede, the independent feature. A fuzzy thinker might propose an argument noticing a dependency where an opposite argument may later be found, in that case logic may seem to waver. But logic is universally reliable, for those that can use it. And true logical dependency requires that one feature not independently precede another, and we can use that to absolutely rule out certain orderings of observed features in the evolution of a species. Such a conclusion is not a matter of observation, of contingency, or of probability, but of Logic itself, which precedes the Big Bang itself and anticipates every true discovery ever made, since each must always be logically possible, though noone may have ever noticed, nor may ever.
Is this the limit of our powers? I don't think so, though my professional evolutionary biologist friends seem to act as though all evolutionary reasoning not conducted by their own PhD students or subject to their PhD defense cross-examinations is intellectually substanceless and can be assumed to be morally perverse. I exaggerate slightly. Job security does not give you the right to shut everyone else up with attacks ad hominem or otherwise than based in reason.
Suppose that N2 is easier to evolve in the circumstance where N1 exists: not impossible, but easier. May we make the parallel inference? Well, yes, I think so. The nature of evolution is such a grand statistical drift that statistical effects are very likely to prevail.
Suppose a certain result associated with N2, such as a measureable average, or a population frequency of some feature, etc., is, say, X% more likely to be reproduced or enhanced with another feature, N1, precedent and present than without. That is,
P(N1<N2) = P(N2<N1) * (100-X)/100.Then what is the likelihood of one ordering N1<N2 versus the other N2<N1? It's not just a single point event in the case of evolutionary time, but an accumulation of more or less probable events across generation after generation for tens and hundreds or thousands of generations. Let AP(o,g) be the accumulated probability of order o across g generations. We have to compare the relative likelihoods of P(N1<N2) occurring g times, versus P(N2<N1) occurring g times. Suppose N2<N1 is taken as the null hypothesis with relative probability 1, then
AP(N1<N2,g) = P(N1<N2)^g / P(N2<N1)^g = P(N1<N2)^g = ((100-X)/100)^g |------| |------| 1 100-X/100Thus, if X is only 5%, meaning that both novel features N1 and N2 could each logically or potentially, precede the other, but there is a 5% advantage in one generation if N1 arrives first, then after only 100 generations,
AP(N1<N2,100) = 0.95^100 = 0.00592, about 1/2 of 1%.In this way, small relative fitness differences may justify strong reasoning about the ordering of novel features in the evolution of a species.
Restating: the full-sequence likelihood of the opposite order is (100%-X%)^G with G the number of generations. If X is 5%, and G is 100 generations, then the likelihood ratio of N1 preceding N2 versus N2 preceding N1 (which we can use as null hypothesis with likelihood 1^100=1) is 0.95^100 / 1 = 0.0059. In short, a small degree of relative ease of one evolutionary path versus another potentially reordered path may be translated to an enormously strong argument, from a statistical perspective, for that sequence being the easy rather than the even ever-so-slightly-more-difficult path.
This actually gives us a lot of leverage on the problem. It's not impossible to find relative ease differences, possibly-small impacts on how one feature supports the functionality of another feature.
Things I think can be ordered in this way are quite a few, in no particular order.
Human evolutionary steps
My favorite, Aquatic Ape features: Bipedality. Voluntary breathing control (necessarily preceding speech). Love or tolerance of swimming. Body Hairlessnes. Long head hair. Control of fire. Diet changes. Long distance running. A huge heel. Body temperature regulation by sweating. Ability to swim. Fear of snakes, of sharks, of the various kinds of unknown. Compared with chimps, more acidic stomachs, more ketotic metabolism, less chimp-like raw-fiber digestion, preference for fatter (large) prey. Changes in disgust sensation; Stench, a.k.a. stinky smell sensitivity. Eclectic carnivory; obesity. Tool use. Conversation. Sign systems. Language. Joketelling. Storytelling. Lying. Theory of mind and emotions. Clothing. Multi-sensory integrated spatial awareness. Bodily Decoration. Art. Religion. Moralizing. The Lecture. Admiration. Scapegoating. Mob violence. Male gang formation, predation, rape, war. Multiplication of dominance hierarchies. Gender contrast in anatomy and strength relating to fight and flight contexts. Oversized male larynx. Lowered larynx such that breathing and swallowing are not simultaneously possible. Female relative lack of sense of direction (?). Female sexual attraction to funny males. Cryptic fertility of females. Female orgasm. Commerce and exchange. Lying. Negotiation. Subpopulation variation in melanin concentration, eye color, height, strength, task endurance. Sexual anatomy & physiology peculiarities: excess size, glans skin furrowing, glans shelf, mobile foreskin, extended duration coitus, semen deposit volume and viscosity and viscosity change over short time periods. Subcutaneous body fat distribution. Literacy. Architecture. Internal storytelling about self as a method for emotional regulation. Various subspeciation changes: more vs less curly hair differences, the Asian epicanthic fold, the northern european adaptations for low-light survival despite metabolic need for light-requiring vitamin D3: translucent skin to make the most of little sunlight and lactose tolerance to get D3 from milk sources.My personality is MB ET, an extrovert thinker: I like to talk and think, which are nearly the same thing for me; I accept that being wrong is part of the process. I'm happy to be wrong! If a logical argument shows a stronger effect in the opposite order, fine. And for two events there can only be only three orderings, before, after, and overlapping, and as I've shown we can legitimately reason from one order being a little easier than the other, already it's a strong argument given the exponential filter of evolution. So it's worth making stabs in the dark, if they seem reasonable, because that starts things off. Stating clearly an initial possibly wrong position allows it to be contradicted by something better and thus can progress be made.
Taking this obnoxious yet humble approach, my own view is: