Of scientist-antics and mad-ematics and delusio-linguistics and logic-ish belief
Leonard R. Jaffee, Copyright © 2021, all rights reserved
FORENOTE This article includes four endnotes. The four endnotes are substantive, not mere citations of sources. The endnotes bear important substantive supplementations of this article’s text. To appreciate this article’s text, you must read the endnotes. PREFACE Courts, government departments, legislative committees, administrative agencies, economists, political survey-takers, pundits, historians, ecologists, sociologists, medical “scientists,” drug-makers.........all try to support their arguments with math (or pseudo-math), whether statistics, the calculus, or aught else quantitative (notwithstanding whether actually non-quantifiable). Math can be beautiful as a leaf unfolding or Johann Sebastian Bach's contrapuntal music or the Krebs cycle or a starfish or snow flake or high Gothic architecture. But, like that nude emperor, Western physics, math and mathematical logic bear critical flaws — inconsistencies, critical insufficiencies, logic-fissures that may be corrigible but persist........ The ultimate problem is that scientific facts and rigors — physics-truths, math-truths, “hard” logic truths, and every other “objective” field's objectivities and precisions — are, at root, emotional — matters of emotional choice. Scientists, mathematicians, and logicians choose premises, theorems, axioms (which bear no premise but desire), definitions, observations........that fit their emotional imperatives. Emotional imperatives? I mean: craving to make a system “symmetrical” or “consistent,” or picturing “the universe” and its phenomena in ways that satisfy a wish of controlling nature or of attaining public acclaim or professional, social, or political power or wealth or financial advantage or......... Witness Western astrophysics's absurd assertion of the Big Bang, which astrophysics has had increasingly to modify, and will continue to need to modify, until the modification-stream shows the theory's absurdity, its delusion. The Big Bang theory's ultimate source is Western science's emotional need of perceiving that the universe had a beginning and has or will have an end: a limitless universe is a concept unbearable to Western science, which cannot fathom the prospect that anything is beyond its comprehension, measurement, and control. Simple logic disproves the Western science perception: If “the” universe suffers limit, either nothing or something is beyond. If something is beyond, limit is illusion. If nothing is beyond, limit is illusion. A nothingness bears no limit — unless a something beyond. Suppose a something beyond. If another nothing is beyond that something, either it is limitless or, if that nothing ends, another something is beyond. And so on, infinitely. Limit is illusion — delusion. This logic works in every real or dreamed direction — for time, too. If “the” universe had “origin,” then earlier “another” universe existed. If “Big Bang” happened, it needed surrounding space — empty till eventually bearing the particles(?) of whatever “banged” (if not also something else). The exploding hyper-dense mass could not materialize magically from naught. Did an earlier contraction occur? Was the explosion the end of just one contraction of many? Did the explosion reverse just one collapse of just one slice of infinity? If time starts or stops, only counting begins or ends, not existence. So, lost, the Western physics asks:
Do black holes lead to other universes? Is “our universe” a black hole of a “meta-universe”? Do many “universes” exist (all born of some number of discrete big bangs)? Is space/time measured by the speed of light? Or does speed have no limit — so that both the specific and general relativity theories are junk? [
endnote 1 ]
See, e.g., this and this and this and this and this and this (the last-linked source useful much for referencing other sources). RE: theories or relativity and speed, see also endnote 1.
Those questions imply not only that the Big Bang theory is false. They imply also that the universe — the one & only universe — had no beginning and has and will have no end: The universe is, has been, and will be always one, same, infinite, eternal. For thorough debunking of the Big Bang theory, see Eric Lerner, “The Big Bang Never Happened: A Startling Refutation of the Dominant Theory of the Origin of the Universe” (1991). Like Western physics, math cannot afford to agree completely with real reality — even the “reality” of “pure” “hard” logic or the “reality” of consistency. Otherwise math would crumble into oblivion. Witness the case of 0 (zero) factorial [“0!”]. Math theory insists that “0! = 1,” despite 0 x N = 0, and 0 x 0 = 0. How very consistent, symmetrical! If zero factorial equaled zero (as consistency insists), the concept “factorial” would fail and, with it, much of math that depends on multiplication-streams. [Some have tried to explain-away this “anomaly.” All have failed, their explanations suffering more flaws born of emotional need of defending “the system,” its religion.] Zero factorial is only one example — just one of many KINDS — of problems of consistency of the operation of multiplication — and of problems of “consistency” of math. Consider, e.g., Gödel’s Incompleteness Theorems. The first incompleteness theorem: In any consistent formal system S within which a certain amount of arithmetic can be operated/effected, S’s language will contain statements that can neither be proved nor disproved within S. The second incompleteness theorem: Such formal system S cannot prove that the system [S] itself is consistent (even if it may be consistent). The proposition “1 + 1 = 2” and many other such “obviously true” propositions are, ultimately, unprovable assertions resting on axioms incapable of proving, e.g., (a) all statements concerning natural numbers or (b) the consistency of a number-system or system of arithmetic. From Gödel’s Incompleteness Theorems, one can extrapolate thus: Anything that is complete is inconsistent; and anything that is consistent is incomplete. I do not mean that Gödel’s proofs involved or showed that extrapolation. I mean that, in any system that depends on axioms, "givens," essential definitions, or other such premises, necessarily some system-essential proposition(s) is/are unprovable or inconsistent (within the system or vis-à-vis a sister system) — a flaw that renders the system dependent on some suspension of disbelief. Nothing can prove itself. And if something proves everything, it proves nothing. One can reduce the matter to this: (a) All thought is only language (even if not of any lexicon); (b) all language is ambiguous — its meaning hopelessly indeterminate. Here below occurs a bit of showing of the indefensibility of just one “truth” of math — an aspect of uncertainty of commutativity, or non-commutativity, of multiplication. The demonstration is just one of myriad available showings of the delusion of objectivity of math, “hard” logic, the “exact” sciences, and “scientific” linguistics. I do not mean that most math and hard-logic propositions are not objective or sound or that most scientific observations or applications are unreliable. I do not mean to attribute to math's, logic's, or science's theories any errors wrought by the theories’ misapplications. My points are only these: (a) Math, logic, and science depend partly on unprovable or untenable premises or suffer unavoidable inconsistencies. (b) Some math, science, or logic is either real-world indefensible or necessarily unreliable in some or all applications. (c) Emotion (if not error) moves mathematicians, scientists, and logicians to deny, delusionally, point (a) or point (b). INCONSISTENCY OF COMMUTATIVITY OF MULTIPLICATION Once, while teaching an Evidence Law class treating the matter of whether the law ought to permit Bayesian probability calculus — the Bayes “rule” — to determine an issue like paternity or identity or projected life-span (of a plaintiff seeking damages for an allegedly life-shortening tort), I asserted the negative (as always I do). Among my many reasons was that statisticians tend to disregard the significance of multiplication-order.[
Side-Note # 1: Bayesian probability calculus is a rather metamorphic, set-theoretic-cognate extension of Pascalian conditional probability calculus. End of Side-Note # 1.]
One student was much math-trained and an actuary. He insisted my argument was wrong because (he insisted) always multiplication is a “commutative operation.” A commutative operation is one in which the operation's order does not affect the outcome. So, if multiplication is commutative, then never can multiplication order affect multiplication product: Always, A x B x C would equal B x C x A or C x A x B or B x A x C or C x B x A or A x C x B. Eventually, I proved to my student that his position was wrong for some (maybe many) cases of Bayesian probability calculus. And I proved so without even mentioning whole math-fields in which multiplication is non-commutative, like matrix multiplication. My student was very resistant — kept posing irrelevant math-demonstrations that seemed pertinent if perceived in a world of superficial analysis. His world treated Bayesian probability as if it were just an alternative of analytic geometry (which not Descartes, but the Chinese invented, and about 400 years before Descartes was born). So, when may multiplication not be commutative where mathematicians — like my student — suppose, or insist religiously, that it is commutative? Consider a rather common real kind of case — Bayesian calculation of the paternity-probability indicated by genetic “evidence.” Take the calculation through ABO blood-type and HLA (human leukocyte antigen) data.[
Side-Note # 2: I exclude DNA evidence only because two variables suffice for this demonstration's purpose, and a third variable would not alter the essence of the case. Still multiplication order would affect the outcome. End of Side-Note # 2]
Assume, for simplicity, that genetic mutation does not occur: So, the true father's and the infant's HLA types must “match”; and the infant's ABO type must be either the true mother's or the true father's.[
Side-Note # 3: Mutation-probability is real, but if the case accounted for mutation-probability the outcome would be essentially the same as if the case did not account for mutation-probability. With or without the accounting, multiplication order would affect the outcome. End of Side-Note # 3]
Suppose both the defendant's and the mother's HLA types “match” the infant's. Infant, mother, and defendant have ABO type O negative. Apply the “principle of indifference.” Near-all statisticians would. Otherwise the operation would be impossible, since a true “prior probability” — in this case, P(F) [see below] — would be incalculable.[
Side-Note 4: The “principle of indifference” is a (false) supposition that if no “prior probability” quantity is obtainable, one may (a) assert, arbitrarily (falsely), that the positive and contrapositive prior probabilities are equal (0.5 each) and (b) hallucinate that the posterior probabilities — e.g., P(A∣F)P(H∣A&F) (see below) — shall have rendered the falsehood “insignificant.” See Leonard R. Jaffee, Of Probativity and Probability: Statistics, Scientific Evidence, and the Calculus of Chance At Trial, 46 University of Pittsburgh Law Review 925 (1985), available at this site for a fee and available in most, if not all, law school libraries and in libraries of most federal courts and state appellate courts; and Leonard R. Jaffee, Prior Probability — A Black Hole in the Mathematician's View of the Sufficiency and Weight of Evidence, 9 Cardozo Law Review 967 (1988), available at this site for a fee and available in most, if not all, law school libraries and in libraries of most federal courts and state appellate courts. See also Side-Note 5, infra. End of Side-Note # 4]
So, per the “principle of indifference,” 0.5 is both (i) the (artificial) prior probability of paternity and (ii) the (artificial) prior probability of non-paternity.[
Side-Note # 5: The principle of indifference is very like the choice of making zero factorial = 1 (0! = 1). The real and logical truth would crash the system, which is, in essence, partly delusional. So, emotionally, the mathematician (or statistician) denies the true truth and supplies a falsehood that “saves” the system. (Side-Note # 5 continues, next ¶.) Not only Bayesian probability calculus suffers the trouble of the principle of indifference. Integral calculus suffers the identical trouble; and that, and other, troubles (like 0! = 1) explain relatively often why bridges & tunnel-ceilings collapse & many transactional outcomes are mis-predicted. (Side-Note # 5 continues, next ¶.) To learn why the principle of indifference cannot save Bayesian probability calculus (or even traditional relative frequency statistics) from being limited to subjective guesses (excluded from the field of determining actualities or even actual probabilities), see Leonard R. Jaffee, Of Probativity and Probability: Statistics, Scientific Evidence, and the Calculus of Chance At Trial, 46 University of PittsburghLaw Review 925 (1985) (supra); and Leonard R. Jaffee, Prior Probability — A Black Hole in the Mathematician's View of the Sufficiency and Weight of Evidence, 9 Cardozo Law Review 967 (1988) (supra) End of Side-Note # 5]
The “matching” HLA type occurs in one of every 1000 men. The ABO type (say, O negative) occurs in thirteen of every 100. Among men who have ABO-type O negative blood, eight of 100 have the matching HLA characteristic. Among men who have the matching HLA characteristic, seven of ten have ABO-type O negative. This is very possible. The O negative male subpopulation is immensely greater than that of men who have the matching HLA type. So, the O negative male subpopulation can include many other HLA types of varying relative frequencies. Yet, an HLA type can be very positively correlated to O negative ABO type. [Reality is like that.] • Let F be paternity. • Let A be ABO-type match of putative father and child. • Let H be HLA “match” of putative father and child. • Let P(F∣A&H) or P(F∣H&A) be probability of paternity given A&H or H&A Some essential definitions: ● “(F∣A&H)” means “F 'given' A&H” ● “(F∣H&A)” means “F 'given' H&A.” ●”Given” equates with set theory's “in the world of” (as in “C in the world of D”), which set theory, too, calls “given” (as in “C given D”). • Let “P(F)” be "prior probability" of paternity. • Let “P(H∣F)” be probability of HLA match given paternity. • Let “P(A∣F)” be probability of ABO match given paternity. • Let “P(H∣A&F)” be probability of HLA match given ABO match and paternity. • Let “P(A∣H&F)” be probability of ABO match given HLA match and paternity. • Let the contrapositive probability symbols be parallel.[
Example: P(not-F)P(A∣not-F)P(H∣A¬-F)]
P(H∣A&F) is 1. Whatever defendant's ABO type, if he is the father, his HLA type must match the infant's. P(A∣H&F) is 0.25. [If defendant is the father, the infant must have an HLA attribute that, alone, would make 70% the chance that she is O negative; but an infant has the mother's ABO type 75% more often, and the infant's whole HLA type also may alter the chance that she is O negative.][
Side-Note # 6: (a) The mother's actual HLA & ABO types would not affect calculation — not yet. (b) I left P(A∣H&F) at 0.25, since that could be right and I want to limit disparity to the not-F field. End of Side-Note # 6]
The conditional contrapositives (the not-F quantities) are governed by random population frequencies. So, e.g., P(A∣not-F) = 0.13 (since 0.13 is the random chance of the ABO type), and P(A∣H & not-F) = 0.08 (since among type O blood men, 8 of 100 have the matching HLA characteristic and that matter equals the random chance of type O given the populational frequency of the HLA characteristic). Likewise, P(H∣A&F) is 0.7 (since among men having the HLA characteristic, 7 of 10 have type O blood). The Bayesian equation is: P(F∣A&H) = P(F)P(A∣F)P(H∣A&F) ÷ [P(F)P(A∣F)P(H∣A&F) + P(not-F)P(A∣not-F)P(H∣A & not-F)]. Or, alternatively, the equation is: P(F∣H&A) = P(F)P(H∣F)P(A∣H&F) ÷ [P(F)P(H∣F)P(A∣H&F) + P(not-F)P(H∣not-F)P(A∣H & not-F)] — which reverses some aspects of the multiplication order of P(F∣A&H) = P(F)P(A∣F)P(H∣A&F) ÷ [P(F)P(A∣F)P(H∣A&F) + P(not-F)P(A∣not-F)P(H∣A & not-F)] [The alternative puts the P(A) aspects second instead of first.] If the statistician accounts for ABO type before HLA type, the Bayesian fraction is: (0.5 x 0.25 x 1) ÷ [(0.5 x 0.25 x 1) + (0.5 x 0.13 x 0.08)] or 0.125 ÷ (0.125 + 0.0052), which equals 96%. But if the statistician accounts for HLA type first, the Bayesian fraction is: (0.5 x 1 x 0.25) ÷ [(0.5 x 1 x 0.25) + (0.5 x 0.001 x 0.7)] or 0.125 ÷ (0.125 + 0.00035), which equals 99.72%. The not-F field condition-order's reversal altered the outcome — from insignificant to significant (or from marginally significant to significant, if, as is uncommon, 95% is at least marginally significant). At one point, my student tried to argue that the multiplication-order-change altered the quantities multiplied, rather than changed the product of multiplication of identical quantities. But — as, eventually, my student conceded — his argument was his wish, not ANY kind of truth. The simple truth is: The multiplied quantities did not change. The multiplication-order’s change altered the quantitative outcome. How so? One “sophisticated” reason — call it “reason # 1" — is that the Bayesian theorem treats P(F∣A&H) as interchangeable with P(F∣H&A), since the theorem holds that H&A = A&H — apparently because (X intersection Y) = (Y intersection X). So, per the theorem, P(F∣A&H) = P(F)P(A∣F)P(H∣A&F) ÷ [P(F)P(A∣F)P(H∣A&F) + P(not-F)P(A∣not-F)P(H∣A & not-F)] is identical to P(F∣H&A) = P(F)P(H∣F)P(A∣H&F) ÷ [P(F)P(H∣F)P(A∣H&F) + P(not-F)P(H∣not-F)P(A∣H & not-F)] — despite P(A∣H & not-F) does not = P(H∣A & not-F). The (supposed) “logic” is that P(F∣A&H) = P(F∣H&A) since H&A = A&H. Another “sophisticated” reason — call it “reason # 2" — is that the things multiplied are not mere “quantities.” They are probability-indicators. One probability-indicator is the paternity-probability-indicating bearing of the ABO type (the A∣F, and the A∣not-F). The other probability-indicator is the paternity-probability-indicating bearing of the HLA-type (the H∣F and the H∣not-F). The multiplication-order change alters only the relative “timing” of integration of the two indicators — the order of the positive or contrapositive indicators' being multiplied with each other and with the relevant prior probability [the P(F) or the P(not-F)]. Still another reason — call it “reason # 3": If the multiplication-order change altered the quantities being multiplied, then, FOR THAT REASON, multiplication is non-commutative in the case hypothesized and any like other case. The root-and-ultimate point is that multiplication-order alters the consequence of multiplication. And such “anomaly” occurs not infrequently in sundry fields of math. Cf. non-commutative multiplication of quaternion scalars and matrices — the problem of (ij = +k) BUT (ji = -k) or per this source ij = k, ji = −k jk = i, kj = −i ki = j, ik = −j Multiplication-order may alter product from positive quantity to negative quantity (and, e.g., -1 is different from or “less” than +1). Cf. this and this and this and this and this and this and this. My student’s difficulty was emotional. He had been imbued with a quasi-religious belief/trust of a standard rule that “algebraic” multiplication is commutative. He was confronted by evidence that the rule suffers fissures or that not all algebraic-seeming operations are “algebraic.” The confrontation threatened him psychically — emotionally. He resisted with emotional force — which displaced his thought into the realm of irrationality. My response forced him to renounce his love of “symmetry” or “consistency” — his actuary/statistician self’s delusional denial of the system's actual inconsistencies, inadequacies, even failures. See, again, Leonard R. Jaffee, Of Probativity and Probability: Statistics, Scientific Evidence, and the Calculus of Chance At Trial, 46 University of Pittsburgh Law Review 925 (1985) (supra), and Leonard R. Jaffee, Prior Probability — A Black Hole in theMathematician's View of the Sufficiency and Weight of Evidence, 9 Cardozo Law Review 967 (1988) (supra). Statisticians (or Bayesianists) feel “consistency” requires that “intersection” mean in Bayesian calculus exactly what it means in set theory [in which (X&Y) = (Y&X) and (X&Y&Z) = (Z&Y&X) = (Z&X&Y) = (Y&X&Z) = (Y&Z&X) = (X&Z&Y)], “because” Bayesian calculus derives from a set-theory-like reasoned extension of conditional probability calculus. In set theory, “intersections” bear the “symmetry” of commutativity. So (per statisticians’ emotional need) Bayesian calculus must follow: P(X&Y) must equal P(Y&X) [since in set theory, (X&Y) = (Y&X)] — despite in set theory (A&B)∣B = (B&A)∣B but may not = (A&B)∣A or (B&A)∣A. Confronted — as was my student — with the core unreliability (“inconsistency”) of statistics-systems, the statistician feels fear of having to choose either intractable deception-device complexity or risibly arbitrary avoidance of real inconsistency. If Bayesian buffs admitted the non-commutativity trouble this article illustrates, Bayesian calculus would need (a) to establish a method that tries to (but cannot) account the often infinite inconsistency of consequences of the non-commutativity my hypothetical illustrates, or (b) to establish an indefensible arbitrary (and invalid, immensely unreliable, and very practically dangerous) rule like “the statistician is stuck with whatever happens to be the statistician's first choice of variables-order (a rule just a little more contemnible than the “principle of indifference” and the indefensible assertion “0! = 1”), or (c) to trash the system (and lose oodles of money-compensation now obtained by estimating outcome odds for big businesses or financial institutions or giving expert testimony in litigations or.......)
[ endnote
2 ]
I do not argue that math, science, and logic are utterly unreliable, that to no extent can mathematical operations be “correct,” that scientific investigations/findings cannot supply real-world-trustworthy, practical indications, or that “hard” logic is actually unreliable, “soft.”
Near-all math questions have right (clear, certain, valid, reliable) answers — answers that can and do support most-often-trustworthy engineering and practical physics works. Most big, long bridges and tunnels and very high buildings survive many decades; and, alas, most rockets hit targets.
My point is only that no human perception is clear, certain, consistent, complete, objective, determinate, valid, or reliable. The root-and-ultimate problem is an incurable trouble:
All thought — hence all conscious perception — is just language;
and all language is ambiguous, uncertain, indeterminate, inconsistent,
incomplete.........spawned and evaluated by unreliable judgment.
[ endnote
3 ]
In the field of math-and-mathematical-logic {
or the fields of [a] math and [b] mathematical logic}
the last-preceding observation’s truth enjoys fascinating illumination in the cloud-forming clarity of Natalie Wolchover’s hopeful-hence-hopeless article How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer, Quanta Magazine (15 July 2021).
I condemn, ferociously, the “woke” and critical-race-theory-premised program of abolishing the math-class and science-class requirement of right answers and substituting an “equity” test of whether a Black student ought pass a math or science course despite the student cannot answer math or science questions correctly.
Most math troubles are human errors of application, or choice, of math — not flaws, insufficiencies, or inconsistencies of a math system. Near-all math is exact, and exacting, objective, precise. If we permit math-incompetents to “graduate” into the math/science professions — or into any employment that requires capacity of thinking hard-logic thoughts reliably — we invite utter, society-wide disaster.
Math is not “racist.” Woke crazies and critical race theory psychopaths confuse “equity” with advancing intellectually weak, marginally competent people’s unearned privileges and benefits and imposing the cost on the whole of society, especially on society’s intelligent, prudent, competent, and conscientious folks. [endnote
4 ]
Are the specific and general relativity theories junk? Since Einstein presented his relativity theories, physicists have operated within the perceptual limit of the theory that nothing can travel faster than the speed of light. Then physicists noticed movement faster than light. See, e.g., (1) this and (2) this and (3) this and (4) this and (5) this and (6) this and (7) this and (8) this. But, since Einstein’s relativity theories are religious “truths,” physicists tend to limit their discoveries with caveats like these: ● (a) Nothing can travel as faster-than-light speed in a vacuum. [See, e.g., (1) this and (2) this and (3) this] or ● (b) Faster-than-light speed is only theoretical (like the two relativity theories?). The general relativity theory is pained by the problem that the universe has been perceived as expanding faster than the speed of light. See, e.g., (1) this and (2) this. The problem arose because of the hallucination that the “Big Bang” occurred. The perceived universe-expansion is expansion of the hallucinated “thing” that “banged” in the Big Bang hallucination. See, e.g., (1) this and (2) this and (3) this and (4) this. The Big Bang hallucination “saves” the theories of relativity by absorbing into the general relativity theory the greater-than-light-speed of the hallucinated "expansion" of the universe. See, e.g., this, which assures us thus [emphases mine, LRJ]: While objects within space cannot travel faster than light, this limitation does not apply to the effects of changes in the metric itself. Objects that recede beyond the cosmic event horizon will eventually become unobservable, as no new light from them will be capable of overcoming the universe's expansion, limiting the size of our observable universe. As an effect of general relativity, the expansion of the universe is different from the expansions and explosions seen in daily life. It is a property of the universe as a whole and occurs throughout the universe, rather than happening just to one part of the universe. Therefore, unlike other expansions and explosions, it cannot be observed from “outside” of it; it is believed that there is no "outside" to observe from. Notice the language “it is believed that there is no ‘outside’ to observe from.” Notice also the language “...limiting the size of our observable universe” and the subsequent paragraph’s apparently mixing “limiting...our observable universe” with “the expansion (etc.) of the universe.” One merely “believes” that nothing is outside “the universe,” which, magically, “expands” though nothing is outside into which it can expand. Yet “no new light...will be capable of...limiting the size of our observable universe” — such universe as we humans can observe — as objects “that recede beyond the cosmic event horizon will eventually become unobservable” to human senses (even if somehow immensely magnified), hence cease being part of “our universe.” The relativity theories, speed-limit theories, and universe-expansion theories are manifestations of anthropocentrism — the human emotional need of being able to govern nature, not be ruled or humbled by it, the human wish that nothing be beyond human comprehension or control. The Universe cannot expand. Its space, time, and substance are infinite. At the universe-level, speed is an hallucination.
Perhaps especially if you have not been a law student, even more especially if you have not been a student of a curmudgeonish law professor like me, you may appreciate observing one of the letters I wrote to the law student for whom I created essentially the demonstration I presented above in this article. The student was very, very bright and an actuary working for the government of one of the states of the U.S. As my letter suggests, I respected, even admired, the student to whom I sent the letter. Eventually, the student apprehended, and acknowledged, the error of his perception of the math matters of the subject of our correspondence. He thanked me, I thanked him for his existence and the honor of my knowing him. We became friends. He became an excellent lawyer, then, himself, a law professor. I deleted from the letter a few portions — where the letter’s observations are essentially identical to observations appearing in this article’s text. Otherwise, the letter is verbatim the letter I sent to my student. Now, the letter: Hello — Your relentlessness has been a joy. And it made me think valuable thoughts I would not have thought without it. Have you considered teaching law? Available time doesn't let me respond quite so much as your efforts deserve. But your observations just will not let me go on without giving some fair answer. Before I comment on your written presentation's central argument, I ought clear away any residue of an item of confusion our first related after-class talk bore. When, in that talk concerning independent probabilities, you began trying to put your position, your language — its express terms — treated the probability P(A&B&C) as if appropriately added to each of the three two-probability joint probabilities — P(A&B), P(A&C), and P(B&C): You did not express the need of subtracting P(A&B&C) from, say, P(B&C) before adding P(A&B&C) to the string of propabilities. You seemed to confuse event with space. Now, having read your presentation and its cover note, I expect you must have meant to add the space P(A&B¬-C) covered with the space covered by P(A&B&C). I do not deny such operation can be sound — if it fits a case. But, I wonder a bit at your cover note's follow-up graphic and algebraic demonstration of the point. Really the demonstration shows simply that if, by bisection, you "divide" a space into two exclusive spaces, the two spaces' union is their sum. That proposition carries nothing necessary, or even particularly pertinent, to your argument's point. And, though you could have made your after-class argument with a calculation that included addition, the calculation would have been painfully inelegant. Now to your demonstrations:* * *
[Text deleted by me, LRJ] Your proof is an algebraic factoring-down of P(X)P(Y∣X)P(Z∣X&Y) — where the likelihoods P(Y∣X) and P(Z∣X&Y) assume that P(X&Y) and P(X&Z) are geometrically "dependent" joint probabilities — to P(X)P(Y)P(Z)— which is the expression of the joint probability of independent probabilities. It "shows" that P(X)P(Y∣X)P(Z∣X&Y) = P(X) x P(X&Y)/P(X) x P(X&Y&Z)/P(X&Y), which — by "cancellations" of the Xs in the first likelihood and of the Xs and Ys in the second — reduces to P(X)P(Y)P(Z). But, by definition, P(X) and P(Y) and P(Z) must be the unconditional probabilities P(X), P(Y), and P(Z)— particularly, in your hypothetical, P(A), P(B), and P(C). Yet the unconditional probability P(A) is .16, the unconditional probability P(B) .1024, and the unconditional probability P(C) .04, and their joint probability is not the .0168 you obtained, but .0006554. Still, though this anomaly impeaches interestingly the mathematical probability system, it does not address directly the matter that concerns you. And, rather than muse about the possibly relevant implications of this anomaly, I'll move on to criticize your demonstrations in ways immediately directed to the matter of your explicit concern. Though your hypothetical case and its calculations are imposing, they carry the inquiry a bit off course. One — slight but possibly significant — misdirection follows from your "rounding off" of the ultimate joint probabilities — like product of P(A)P(B∣A)P(C∣B&A). In the relevant field — Bayesian induction — "little" numbers can do significant things. Consider the comparison of P(C)P(A∣C)P(B∣A&C) and P(C)P(B∣C)P(A∣B&C). You say both equal .0168. Not so. P(C)P(B∣C)P(A∣B&C) equals .016856. If you round off to four decimal places, as you have each of your operation ends, you get .0169. If you complete the Bayesian fraction, you find P(not-C) is 1 - .04. or .96, P(B∣not-C) is 207/2400, or .08625, and P(A∣B¬-C) is 183/207, or .884058. The denominator, then, is .0169 + (.96 x .08625 x .884058), or .0169 + .0732, the sum of which is .0901. The fraction, .0169/.0901 equals .1876. If the joining order is, instead, P(C)P(A∣C)P(B∣A&C), the Bayesian denominator is .0168 + (.96 x 340/2400 x 183/340), which equals .0168 + (.96 x .141667 x .538235), or .0168 + .0732, or .09. And .0168/.09 equals .1867. The difference is .0009. That seems small. But consider a Bayesian inference drawn from a DNA "identification" attempt or a genetic "paternity" test that accounts for five or more blood and tissue types. The likelihoods (conditional probabilities) would number at least five, at least three more than in your experiment. Suppose at the two-likelihood level, as in your experiment, a condition-order difference produces a .0009 outcome disparity, at the three-likelihood level, a second .0009 disparity, at the four-likelihood level, a third .0009 disparity, at the five likelihood level a fourth .0009 disparity, at the sixth, a fifth .0009 disparity. Multiply .0009 by 5, and you get .0045. Round off to .01, and the disparity could make the difference between significance and insignificance (as between 96% and 97%, in a jurisdiction that, like Maine, operates at a 3% confidence limit). Maybe one might argue the 0.45% (not really 1%) makes a poor lever up to significance. But one can find cases where the disparities are greater than .0009. If one finds them where the Bayesian calculation involves even more that six likelihoods, the total disparity might be, say, about 2% — not a weak step from 95% to 97%. Even in the kind of case you hypothesize, one might find greater disparity if one increased the number of probabilities and likelihoods. Here is an example — maybe not the strongest, but the first one I happened, accidentally much as arbitrarily, to pick. Add to your hypothetical case a fourth probability — P(D). Let the D space equal 80. P(D), then, will equal 80/2500, or .032. Let P(D&C) equal 30/2500, P(A&C&D) 18/2500, P(B&C&D) 21/2500, and P(A&B&C&D) 18/2500. This will be true if D is a rectangle 16 squares wide and 5 squares high, the bottom perimeter being the top limit of the horizontal-square-sequence nine levels from the from the bottom perimeter of A (or four from the bottom perimeter of B) and the left-hand perimeter being the right hand limit of the vertical square-sequence twelve vertical-square-sequences from the left hand perimeter of A (or seven from the left-hand perimeter of B). The new conditional probabilities are: P(D∣C) = 30/100 = .3. P(D∣not-C) = 50/2400 = .0208. P(D∣A&C) = 18/60 = .3. P(D∣A¬-C) = 22/340 = .0647. P(D∣B&C) = 21/49 = .4286. P(D∣B¬-C) = 24/207 = .1159. P(D∣A&B&C) = 18/42 = .4286. P(D∣A&B¬-C) = 22/183 = .1202. P(A∣C&D) = 18/30 = .6. P(A∣D¬-C) = 22/50 = .44. P(B∣C&D) = 21/30 = .7. P(B∣D¬-C) = 24/50 = .48. P(A∣B&C&D) = 18/21 = .8571. P(A∣B&D¬-C) = 22/24 = .9167. P(B∣A&C&D) = 18/18 = 1. P(B∣A&D¬-C) = 22/22 = 1. Now compare two Bayesian inferences that begin on the same prior probability: 1. P(C)P(B∣C)P(A∣B&C)P(D∣A&B&C) ÷ [P(C)P(B∣C)P(A∣B&C)P(D∣A&B&C) + P(not-C)P(B∣not-C)P(A∣B¬-C)P(D∣A&B¬-C)], 2. P(C)P(D∣C)P(B∣C&D)P(A∣B&C&D) ÷ [P(C)P(D∣C)P(B∣C&D)P(A∣B&C&D) + P(not-C)P(D∣not-C)P(B∣D¬-C)P(A∣B&D¬-C)]. The first inference is: (.04 x .49 x .86 x .4286) ÷ [(.04 x .49 x .86 x .4286) + (.96 x .08625 x .88406 x .1202)] = .00722/.01602 = .451. The second inference is: (.04 x .3 x .7 x .8571) ÷ [(.04 x .3 x .7 x .8571) + .96 x .0208 x .48 x .9167)] = .00719/.01598 = .45. So, when one adds one variable to the case you hypothesized, the Bayesian posterior probability disparity increases to .001. I must admit the disparity-increase is not much. I must admit too that I can play with the figures so the disparity will disappear or reduce to near zero. But the cause lies in concurrence of two unnecessary, very often unrealistic, events: (a) A case — such as you hypothesize — where "dependencies" really aren't dependencies but just functions of merely making the joint probabilities geometrically different from those they would be were joint-probability geometry the consequence of the unconditional probabilities' being independent. (b) A formula that determines joint conditional probabilities just by this proposition: "For every joint probability of conditional probabilities, the first-calculated conditional probability equals the condition's and conditional event's joint two-dimensional, static field reduced to ("divided" by) the like field of the condition, and each following conditional probability equals the instant conditional event's and next-previously calculated numerator's joint two-dimensional, static field reduced to ("divided" by) the like joint field of the numerator of the next previously calculated conditional probability — a proposition that describes a nice geometric motif where mathematician-comforting symmetry consistently proves itself, but, yet, a proposition that tracks very few real conditionally probable possibilities.* * *
[Text deleted by me, LRJ] ============ Then my letter presented a demonstration essentially the same as this article’s paternity-probability demonstration this endnote supplements — to which demonstration my letter added this observation: Such cases do not follow from Venn diagrams, they dictate them. The matter is how to design a diagram that follows from such a case. The trouble is that conventional diagrams tend to produce results like those your hypothetical Venn diagram produced. Thereafter, my letter continued thus: ============ During our last-previous class-session, a student asked a question that reduces to this: “Why might one measure, logically, a second or a later conditional probability by reference to the union of the joint field in the previous conditional probability?” An example ought to demonstrate. Suppose P(X) and P(Y) are rather small, but P(Z) is large and covers most of the union of P(X) and P(Y), all but part of P(X&Y). If "union P(X) and P(Y)" — "[P(XûY)]" — is the "given," P(Z) increases from something significantly less than 1, to virtually 1. If one does not measure P(Z)'s probability by reference to the union of the other two probabilities, one understates its strength (size). (I symbolize "union" as "û" because my printer will not print the customary symbol.) Suppose the question is the probability that a dead man would have lived years longer had he not got black lung disease and liver cancer and eaten much fatty meat and sugary food and little vegetable matter and drunk no wine but much corn whiskey. The relevant relation is that of longevity (call it "L") and not having black lung disease (call it "B") or liver cancer (call it "C") and not eating the diet (call it "D") the man ate. L does not bear a perfect correlation with not-B, not-C, or not-D. (Some B, C, and D sufferers live much longer than some cancer-free, good-eating people who don't have black lung disease.) But L bears a very strong positive correlation with the union of not-B, not-C, and not-D, and also with their joint probability. Those correlations involve 95% of û(not-B,not-C,not-D) and 75% of (not-B¬-C¬-D). Not-B, not-C, and not-D bear strong positive correlation among each other. Suppose, if a person's case, throughout, includes the latter jointure, adventitiously the person likely will not live long as one whose case consistently includes not-B but not always not-C or not-D. The reason includes the facts that the former kind of person tends not to be so capable of self-defense as, but is more hate-inspiring than, the latter kind of person, and both tend to live in places where social violence is not infrequent. In such state of conditions, the û(not-B,not-C,not-D) certainty makes L more probable than does certainty of the joint probability of those variables — and vice versa. A jury would not act illogically if it found high probability of not-C on the premise of the certainty of not-B or not-D or L or some combination of them at some time. Suppose the first evidence-item is not-B. One could put the question: "What is P(L∣not-B)"? The Bayesian numerator would be P(L)P(not-B∣L). If the next evidence item were not-C, and then the next not-D, the Bayesian numerator could become P(L)P(not-B∣L)P(not-C∣û not-B,L)P(not-D∣û not-B,not-C,L). Maybe you wonder whether this calculation is redundant — because the second likelihood (conditional probability) repeats division by all of L. Maybe also you wonder whether the likelihood's denominator is excessive — because it includes all of not-B except (not-B&L), rather than just the part that shares space with L. The answers are: (a) If the measure is redundant, so is a measure by a denominator includes any L, since L's entirety made the denominator of the first likelihood. (b) If, as is true in the case I hypothesize, not-C's probability depends on most of not-B but not all of P(L¬-B), the alternative measure [a P(L¬-B) denominator] understates not-C's pertinent dependence on not-B (also not-C's dependence on L). (c) The denominator is [L¬-(not-B)] + not-B. If you dispute these answers, is your true reason only that you believe the contrary, and if so, is the cause just that you were taught, and became accustomed to, the contrary's choice of logic or analysis? The contrary's logic and analysis really follow perceptual inclination and philosophic taste, which, somewhat, depend on psychic structure (not intelligence, but character and psychological inclination, like hard attraction to "perfect" mathematic symmetry). An earnest, rational, logical, morally apprehensive person would think a probability greater than otherwise if the probability is more likely on condition of any of two or more other probabilities. As such person sifts through, or is presented, proofs, she may legitimately ask first the probability of the first proof given a certain proposition put to question, next the probability of a second proof given both the first proof and the proposition put to question, and then the probability of a third proof given both the first two proofs and also the proposition put to question. At each step of assessment of proof of the proposition put to question, the person may, properly, want to test each "new" proof against the background of all that is relevant of the whole proposition and of the totality of proofs presented or considered before. If the "new" proof appears more probable because of its relation to part of a preceding proof's implications (and that part's probability), the person would be fair and logical if she evaluated the "new" proof in that relation, despite that relation did not involve another of the preceding proofs. Only one good quandary obtains here: Ought the person consider the relation of each "new" proof and every one of a preceding proof's implications, if any of the preceding proof’s implications cannot converge with the proposition put to question? Though not one your presentation's premises and calculations allows so, a fair, logical answer is: If, in the prior-proof implications, one finds premise for or indication of the "new" proof and if the "new" proof finds some explanation in the proposition put to question, then one can say that the correlation between the proposition and the "new" proof is more likely because of the prior proof implications. The case is like this: If apple is certain, then so is non-desert, temperate-clime fruit-tree and like-environment non-fruit-bearing tree-life. So, though apple does not prove pear or juniper, it makes them more likely, specially because in land and weather that support apples we find land and weather that support juniper and pear. So, too, it makes more likely any non-tree plants and animals that thrive where apple, pear, and juniper live — despite apple, itself, may not converge (or may not converge significantly) with carrot, raspberry, or squirrel. See the matter a general way: If, in the range of probabilities of one thing, one finds, anywhere, another thing's probability (if the two probabilities are not exclusive or utterly independent), the first thing's certainty makes more probable the other thing. For if the first thing is certain, the other can occur, more than otherwise, unless the second thing bears a stronger affinity with a third thing exclusive of the first. Even if two things' probabilities are exclusive, still, in the real world, the certainty of one reduces, but does not preclude, probability of the other. Now, if a likelihood's denominator will be the union of probabilities previously accounted-for, always — except accidentally or empirically otherwise — likelihood-order will matter even if it would not matter were the denominator the joint probability of previously-accounted-for probabilities. In the case you hypothesized, the P(A)P(B∣A)P(C∣BûA) would be .0209 — (BûA) being (A + B¬-A), or 400 + 31, or 431. But the P(A)P(C∣A)P(B∣CûA) would be .0055 — (CûA) being (A + C¬-A), or 400 + 40, or 440.
The immediately following quotation-set is excerpted from Leonard R. Jaffee, “The Cotton Country”: "Actions make self. So, word equals idea, consciousness: self is language, utterly. A wolf's howl is longing, though its curve inspires, by mimicry, the sadness of a lip crescented down. "Actions make self only when they behave as words, even if only to the actor. Speech and thought are action, and conscious action is language, that of manifest judgment — even if a wolf's, even to the wolf." “ * * * “Language doesnot
convey
meaning (as if thoughts played cargo of a ship of syntax). Language constitutes meaning (as lust whelps hunger and hunger lusts). “If you say you did not mean what you have written, you had three thoughts, acted three meanings: You wrote one. You thought ("meant") another. You said a third (that you meant not what you wrote). “As "red ball" is not "red plus ball," it is not a conveyance of an idea of a red ball — or of a proposition "red plus ball." The phrase "red ball " means itself, the special idea it is, including what it takes from, and gives, its setting (shape, color, music, milieu), human and else.” “ * * * “Language constitutes the meaning that is self — conscious being. Self embodies programs of thought, feeling, emotion — spawn of comparative analysis, however quick, secret, precerebral, sublime. Contempt is not beast, but judgment. Judgment aggregates and orders terms to build import — as if "lazy" + "thieving" + "squalid" + "cruel" = "contemnible" (a synergy). Emotion is the outcome of a neural algebra obeying axioms of psychic mold.” “ * * * “Often we say words we "don't mean," blurt sentences we "don't intend," of plural significance we can't explain but surprises us. We blame neglect, fear, drunkenness, anger, even "hearing voices" — maybe wizard codes of microwaves — that force words or phrases irresponsible, or conjure acts, like "devil"-slayings, that play the messages of gods. “But do words clasp your throat, wring themselves from you? In our minds, we hear unflagging songs we can't endure, hold relentless conversations with our thoughts, suffer insights, free associations. Volition fleshes like bone, cached in a sarcophagus. “You may believe — as if beyond question, as if truth exists — that you contrive the plans you would utter. But always something not your art — some beast, its motive, unconscious, or nothing — sets and governs the course of thought, your language. Do the words control themselves — as contracts, those emperors, cause what they will? “You insist: "I can attribute some thought to events outside me — my reaction." But why, truly why, do you react as your words do, if you do? What beneath, subliminal, compels our terms? Do they seethe from the well of making dreams? Do they invade? Just happen?” “ * * * “All conscious sense is language. It occurs just as symbol, even if not of any lexicon. “You recall — in image and feeling — a garden party. You chose, subliminally, to recall one part — the smell of a rose a woman wore, perfume to which you attribute significance, by your choice of that memory. You devise the reminiscence symbol. “You remember another scent you loved in your childhood. Even do you feel you smell it, now, as if actual. Why? Subconsciously you chose it among all odors of your past. You pursue its meaning, what it stands for, what it says — its bell that made Pavlov drool.”[
End of quotation of “The Cotton Country”]
All humans edit and interpolate (interpolate, not interpret) every, or virtually every, utterance they read or hear, including their own. Few humans ever speak or write any utterance they expect, or ought to expect, the recipient will not edit or interpolate, or “need” to edit or interpolate— even if subliminally (or “unconsciously” or “subconsciously,” if you prefer those terms) or negligently or by dint of conscious or subliminal bias applied wilfully or subliminally. Quite so, near-always, near-all humans utter statements or questions markedly imprecisely — and blithely so. Near-always, near-all humans do not struggle rigorously to render utterances that constitute thoughts they hope they intend. Near-always, near-all humans blather slop and expect the slop’s recipient(s) will edit and interpolate the slop to transmute it into some intelligent thought that approaches some thought that they — utterers — (may) believe they uttered. The trouble infests not only ordinary language (Indo-European, Tungusic, Mongolic, Turkic, Finno-Ugric, Semitic, Japonic, Koreanic, Han Chinese......) but also technical language (legal, scientific, medical, mathematic, notation of a music-score.......). Even does the trouble infest perception of “non-verbal” “speech,” like a sigh, moan, grunt, or laugh or shoulder shrug or......or what an animal-behavior psychologist deems the “meaning” of orangutan-conduct.[
Side-Note: Orangutans talk, even lie, create words, form unlearned sentences, even teach themselves to use human-made tools (tool-use being a form of speech). See, e.g., this and this and this and this and this and this and this. End of Side-Note]
Even “scientific” propositions (or questions) or math-statements (or questions) suffer the same editing/interpolation susceptibility — though perhaps much less frequently or not until some, or much, time has passed (before editing or interpolation occurs). “Science” and math “evolve” (endure correction, corrective “adjustment,” corrective “elaboration,” falsification......).[
Side-Note: Sir Karl Raimund Popper insisted — rather influentially — that “science” is not science unless it is “falsifiable.” One trouble, though, is whether each of every falsification is falsifiable or has been tested for falsification or falsifiability and whether every possible falsification has occurred — even every possible falsification of every possible falsification. End of Side-Note]
A music composer may cringe when he hears a performance of his symphony: “I did not mean that sound.” Was the “error” what the composer actually wrote or what she thought she wrote or what the conductor perceived the composer or the music score intended or.......? A computer may not understand the meaning a programer intended for an algorithm because the algorithm did not “state” what the programer thought he stated. Mathematicians debate/correct math theories, even specific math-expressions, even their own. Some math-language emendations may seem to occur glacially — unless one tracks evolution by epochs, rather than days , weeks, or years. See also infra endnote 4. The Following quotation is excerpted from Lewis Carroll, “Alice’s Adventures in Wonderland,” Chapter VII, A Mad Tea-Party: “The [Mad] Hatter opened his eyes very wide on hearing this; but all he said was, “Why is a raven like a writing-desk?” “Come, we shall have some fun now!” thought Alice. “I'm glad they've begun asking riddles. — “I believe I can guess that,” she added aloud. “Do you mean that you think you can find out the answer to it?” said the March Hare. “Exactly so,” said Alice. “Then you should say what you mean,” the March Hare went on. “I do,' Alice hastily replied;” at least — at least I mean what I say — that's the same thing, you know.” “Not the same thing a bit!” said the Hatter. “You might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” “You might just as well say...that ‘I like what I get’ is the same thing as ‘I get what I like’!” “You might just as well say,” added the Dormouse, “that ‘I breathe when I sleep’ is the same thing as ‘I sleep when I breathe’!” [End of quotation of Alice’s Adventures in Wonderland] The following quotation is excerpted from Lewis Carroll, “Through the Looking Glass,” Chapter VI, Humpty Dumpty: Humpty Dumpty took the book, and looked at it carefully. “That seems to be done right—” he began. “You’re holding it upside down!” Alice interrupted. “To be sure I was!” Humpty Dumpty said gaily, as she turned it round for him. “I thought it looked a little queer. As I was saying, that seems to be done right—though I haven’t time to look it over thoroughly just now—and that shows that there are three hundred and sixty-four days when you might get un-birthday presents—” “Certainly,” said Alice. “And only one for birthday presents, you know. There’s glory for you!” “I don’t know what you mean by ‘glory,’” Alice said. Humpty Dumpty smiled contemptuously. “Of course you don’t— till I tell you. I meant ‘there’s a nice knock-down argument for you!’” “But ‘glory’ doesn’t mean ‘a nice knock-down argument,’” Alice objected. “When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”
Math is not “White” or “European.” Much math was created (or invented) by Europeans. But math originated in Asia — mostly East Asia and northwest India, but also Persia and Babylonia (before the advent of the math of ancient Greece). Algebra was invented in northwest India. In the 7th through 6th century BCE, Indian mathematicians determined the general quadratic equation for both positive and negative roots. Around 350 BCE, Jain mathematicians devised notations of simple powers and exponents of numbers (squares, cubes.......), which enabled them to define and operate algebraic equations. In the 8th century BCE, Indian mathematicians determined the square root of 2, two centuries before Pythagorus was born. In the 6th century BCE, 2300 years before George Boole “invented” Boolean logic (Boolean algebra), Pā ini (520–460 BCE) used Boolean logic (Boolean algebra). About 2400 years before the advent of electronic computers, Pā ini used a precursor of Backus–Naur form (used in computer programming languages). The Chinese invented or established much of math markedly before Europeans did. A few (of many) instances: • By 1000 BCE, the Chinese had established a fully developed a decimal system. • The Chinese invented Pascal’s Triangle centuries before Pascal was born. • The Chinese invented algebraic geometry (a.k.a. “analytic geometry”) about 4 centuries before Descartes was born. • Hundreds of years before the Christian Era, the Chinese invented decimal multiplication and negative numbers. • The Chinese invented the Pythagorean theorem about 700 years before Pythagorus was born. • The Chinese invented the rule of double false position (or double false position method) about 200 years before the Christian Era (about 2,000 years before the births of Gauss and Jordan, for whom the method’s European version was named — Gauss-Jordan — in Europe. • The Chinese invented the Horner method of solving higher numerical equations about 600 years before Horner was born. • The Chinese found far the greatest number π (Pi) — until the 20th century. For the past few decades, Chinese — and, though less, Japanese, and though still less, South Asians — have dominated the field of mathematics. See, e.g., here and here. See also here at, e.g., pages 97 & 273. Numerous other math-inventions occurred in ancient Persia and Babylonia. Ancient Persians and Babylonians were surely not European and might not be termed “White” per modern American perceptions. Math is not racist. The racists are “woke” crazies and Critical Race Theorists and BLM members/followers and their Democrat, Mainstream Media, and Tech/Social-Media advocates. Most are either psychopaths or idiots whose socio-political/economic programs will destroy what good and positive achievements American society could yet obtain, quite as they are determined to dismantle European/European-American culture and the many great benefits — art, philosophy, logic, literature, music, math, medicine, science — European/European-American culture has bestowed upon humanity. The evil, racist “woke,” Critical Race Theory, BLM, Democrat Black “equity” program will displace merit and competence with an utterly corrupt “affirmative action” that will endanger American society worse than ever before — likely irreversibly so — by installing incompetent Blacks, and, to a lesser extent, incompetent New World Hispanics, in critically vital government and non-government positions. Blacks have contributed nothing — zero — to mathematics creativity or the advancement of mathematics. Ever! [Distinguish (a) applying existing mathematics from (b) advancing mathematics or creating new math-theory or new math-method.] No Black — not even (clearly part-White) Katherine Johnson — has invented a math, a mathematical logic, or a new math-method. Much the reasons are: (a) Black communities tend not to value math or any other form of abstract thought or rigorous critical thinking; (b) the world’s, and America’s, Black population is intellectually inferior — markedly intellectually inferior — to all other races. The mean sub-Saharan Black IQ is 70; mean American Black IQ is 85; mean (New World) Hispanic IQ is 90; mean European and European-American White IQ is 100; mean East Asian IQ is 106; mean Jewish IQ is 113. See, e.g., here and here and here and here and here and here. See also Charles Murray, Facing Reality: Two Truths About Race in America (2021), ISBN: 1641771976, and Arthur R. Jensen, The g Factor: The Science of Mental Ability at pp.350-530 (Praeger Publishers, Westport, CT 1998). Because the “woke,” Critical Race Theory, BLM, Democrat Black “equity” program denies the intellectual inferiority of the Black race, it does very grievous social harm. In the Carribean region — hugely Black and little mixed-race — the mean IQ was 69 in the year 1959. In Jamaica and St. Lucia, three 60 IQ means (virtually moron level mean scores) occurred. See here at p.141. In 2001, Fernandez found the following mean Standard Progressive Matrices [“SPM”] scores in Brazil: Japanese 99; “European” 95; Mulatto 81; Black 71. See here at p.69. The SPM test is nonverbal — involves nonverbal reasoning problems. So, language differences (language-type differences, language-proficiency-differences, and language-related ethnic or cultural differences) do not influence SPM scores. Surely, many American Blacks are competent, and some are very bright [but if one accounts the mean sub-Saharan Black IQ, one must appreciate that American Black competence is attributable much to Black/White or Black/Asian intermarriage or extramarital Black/non-Black race-mixing. The only rational, socioeconomically utilitarian system is meritocracy; and a Black “equity” preference is evil, disutilitarian, irrationality. Do not delude yourself to believe the dross that IQ testing is not a valid indicator of inherited (inborn) intelligence. Properly designed, properly administered IQ testing — or, the SPM-test alternative — is valid and reliable. Such testing accounts socioeconomic/educational/language differences and calculates into determinations sundry non-test-score considerations that account, further, environmental differences and also anatomic and physiological differences: (1) IQ test score malleability (2) “culture-loaded” versus g-loaded” test data (3) sundry reaction-time measures (4) “within-race heritability” (5) “between-race heritability” (6) trans-racial brain-size differences (7) inter-sex brain-size differences (8) trans-racial adoption study data/indicators (9) racial admixture study data/indicators (10) certain life-history variables that are cross-race or inter-race quantifiable And where age/education/language-adjusted IQ testing and SPM testing are employed together, results are very highly reliable. Compare this and this and this and this and this and this and this (especially, but not only, at pp.350-530). Race must not be a determinant of allocation of employment, government-provided benefits, or political, social, or economic advantage or power. Validly and reliably proven merit must be the sole determinant. If our society operates otherwise, it will be doomed. Millions of innocents will be injured horrendously, more than already so, because of manifest influences of “wokeness,” Critical Race Theory, BLM, and associated Democrat actions and policies and the conduct of Mainstream Media, Social Media, and Big Tech.[Side-Note:
Today, 29 June 2021, several university "professors" (six Black, one apparently a Spaniard, all women) informed us that grammatically correct, elegant English-language usage is "racist." One must wonder why they or other such "professors" have not informed us (a) that wolves are racist because they are efficient predators of non-Canis-lupus beasts, (b) that snowflakes are inherently racist because they are white, or (c) that sickle-cell anemia is racist because it prefers Blacks, Mesoamerican & South American "Hispanics," and certain races or ethnicities of the Middle East, Asia, and the Mediterranean's coasts.End of Side-Note]
I am not a Republican or aligned with any other political party. I am an atheist, religion-contemning, Kropotkinian anarchist. Still, the Republican and Libertarian parties tend, more than not, to support and enable liberty and favor rationality, while Democrats do not, but tend to pursue socio-political/economic insanity and curtailment of individual personal freedom and privacy and the individual’s control of her life and her life-affecting options. Am I a “racist”? Many will answer, irrationally, the affirmative — especially “woke” readers. Still, if you are not fully “woke,” see, e.g., this, and also this and this — especially, but not near-only, subsection B. Disclosure of My “Biases” and endnotes 4 through 7 of section II. PREFACE, of this.