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On the Evolution of Scientific Inquiry.

W. M. Schaffer January 2016

Figure Facing. Theory instructs field work in Re-gency England. "Take a view, my dear Sir, through these glasses,” the caption reads, “and you will see that the whole face of nature is as blue as indigo." Note the field geologist's hammer and collecting bag; likewise, the theoretician's lack thereof, his morning coat, barrister's wig and Theory of the Earth discretely held behind his back. Charles Lyell, the object of the satire, trained as a lawyer, wore glasses and took much from the views of James Hutton, an early uni-formitarian. Cartoon by Henry De la Beche circa 1830. Reproduced from Rudwick (1975).

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On Truth, Self-correction and Progress.

Charles Sanders Peirce. “There are real things, whose characters are entirely independent of our opinions … [and] by taking advantage of the laws of percep-tion, we can ascertain by reasoning how things really are; and any man, if he have sufficient experience and reason enough about it, will be led to the one true conclusion.” [Peirce, 1887, p.10]

Karl Popper. “The idea of approximation to the truth is, in my view, one of the most important ideas in the theory of science. … Einstein … was well aware that his theory … was a provisional attempt at a solution … . But what he claimed … was that it represented a better approx-imation to the sought-after theory than did Newton’s … and there-fore a better approximation to the truth.” [Popper, 1999, p. 18]

Larry Laudan.

“Prepared to concede that the theories of the day might eventually

be refuted … several late 18th century reasoned, [that if] there is

no instant, immediate truth, we can at least hope to reach truth in

the long run. Even if the scientist's methods do not guarantee that

he can get the truth on the first attempt, perhaps he can at least

hope to get ever closer to it. [Laudan, 1981, p. 228]

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Thomas Chamberlin. “The moment one has offered an original explanation for a phenom-enon which seems satisfactory … parental affection takes posses-sion of the mind … There springs up also unwittingly a pressing of the theory to make it fit the facts and a pressing of the facts to make them fit the theory." [Chamberlin, 1897, p. 840]

Thomas Kuhn. “The two-sphere universe provided a fruitful guide to the solution of problems outside as well as inside astronomy. By the end of the fourth century B.C. it had been applied … to terrestrial problems, like the fall of a leaf and the flight of an arrow, and to spiritual prob-lems, like the relation of man to his gods. … Fundamental astro-nomical concepts had become strands in a far larger fabric of thought ... The story of the Copernican revolution is not, therefore, simply a story of astronomers and the skies.” [Kuhn (1957), p. 77]

Richard Somerville. “Science … works by expert scientists doing research and publish-ing it in carefully reviewed research journals. Other scientists exam-ine the research and repeat it and extend it. Valid results are con-firmed, and wrong ones are exposed and abandoned. Science is self-correcting. . [Somerville, 2011]

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John P. A. Ioannidis. ”The ability to self-correct is considered a hallmark of science. How-ever, self-correction does not always happen ... History suggests that major catastrophes in scientific credibility are unfortunately pos-sible.” [Ioannidis, 2012, p. 645]

Paul Feyerabend.

“Scientists are not content with running their own playpens in ac-

cordance with what they regard as the rules of scientific method,

they want to universalize these rules, … and they use every means

at their disposal – argument, propaganda, pressure tactics, intimi-

dation, lobbying – to achieve their aims.” [Paul Feyerabend,

1980, 3rd Verso Impression, p. 220]

Stephen K. Sanderson. “The British sociologists of science and their epigones apparently have failed to see the profound irony and self-contradiction in their work. Here are sociologists who think of themselves, it seems, as scientists, but who are nevertheless committed to the claim that sci-ence cannot lay claim to objective truth. Here are people who are using science to make the claim that scientific ideas are social con-structions rather than objective realities. Apparently it has not oc-curred to these sociologists to ask whether or not these ideas apply to themselves, and, if so, whether or not the ideas might be com-pletely self-refuting…” [Sanderson, 2001, p. 37]

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The Orbit of Mercury.

The oft-asserted claim that science advances conse-quent to hypothesis falsification / revision is not en-tirely accurate.

Orbit of Mercury an inter-esting example.

1. According to the physi-

cist, Richard Feynman (1985, p. 158), Newton “guessed the law of gravitation, calculated all kinds of consequences … , compared them with experi-ment – and it took several hundred years before the slight error of the motion of Mercury was observed. Dur-ing all that time, the theory had not been proved wrong … But it could never be proved right because tomor-row’s experiment might suc-ceed in proving wrong what you thought was right.”

Figure 1. In 1859, the advance of Mercury’s perihelion was re-ported to be ~10% faster than predicted by Newtonian me-chanics. General Relativity pro-vides the required correction consequent to the bending of space by the sun’s gravitation.

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2. The perceived perihe-lion advance is due principally to terrestrial precession. a. ~90% of remainder

explained by Newto-nian mechanics (NM)

b. The rest accounted for by general relativ-ity (GR).

3. But GR proposed 50+

years after the anom-aly’s discovery. a. Immediate reaction

was neither to mod-ify nor abandon NM.

b. Instead, a new plan-

et proposed (Baum and Sheehan, 2003).

c. And why not? Nep-tune’s existence had been conjectured & the planet discovered for similar reasons.

Figure 2. In 1859, Urbain Jo-seph Le Verrier proposed that a small planet inside the orbit of Mercury could account for the latter’s anomalous orbit. Top. In just this way, the existence of Neptune had been discovered in 1846. Bottom. As everyone knows, Vulcan eventually did turn up, albeit in another time and place.

turned up, albeit in another time and place.

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Three Important Points. 1. Established theories do not readily fold.

a. Ad hoc hypothesis adjustment (AHHA) a more

frequent reaction to inconvenient observations. b. When reported sightings of Vulcan proved bogus

(Campbell, 1909; Baum and Sheehan, 1997), ad hoc hypotheses proposed.

i. Circumsolar ring of planetesmals – never

observed1

ii. Inverse square law in error – changing the ex-

ponent from 2 to 2 + 𝛿, where 𝛿 ≪ 1, would have rendered the moon’s motion unaccepta-bly anomalous (Hall, 1894; Doggett, 1997).

2. Wiggling the elephant’s trunk2 generates new hypoth-

eses, nothing more – especially when “computers can be used to give a spurious impression of genuine scientific efficiency” [Masterman, 1970, p. 75].

1 The most common view pre-GR. See Iorio (2012) and Brown (2012). 2 The allusion (Dyson, 2004) is to von Neumann’s famous witticism.

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3. In the case of Vulcan, how to proceed was obvious: Find the planet.

4. In case of “all but the kitchen sink” computer simula-

tions of complex phenomena, demonstrating hypoth-esis-observation concordance arguably impossible. a. Multiple parameters / variables / interactions un-

known / not measurable.

b. Such situations encourage trunk wiggling, which is a Faustian temptation – recall Chamberlain.

c. Especially difficult to resist when extra-scientific considerations enter.

Figure 3. Left. A 2-D elephant can be modelled using four pa-rameters. Right. By varying a 5th parameter, its trunk can be wiggled. From Mayer et al. (2010). To watch the animation, go to https://www.youtube.com/watch?v=w1GU27P_sqA.

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Ptolemaic Astronomy.

Geocentric universe.

Makes use of epicycles and other ad hoc devices.

1. Physical hogwash.

2. Nonetheless accurately predicts planetary mo-tion.

Method of “compounded circles” mathematically

equivalent to approximating a time series, 𝑥𝑡, by sums of sines and cosines, i.e., given a sample of 𝑁 points,

𝑥𝑡 = 𝑎0 + ∑ 𝑎𝑖𝑠𝑖𝑛(2𝜋𝜔𝑖𝑡) +

𝑁/2

𝑖=1

∑ 𝑏𝑖𝑐𝑜𝑠(2𝜋𝜔𝑖𝑡) + 휀𝑡

𝑁/2

𝑛=1

1. New observations could always be accommodated.

2. An emblematic example of trunk-wiggling:

“For its subtlety, flexibility, complexity and power the epicycle deferent technique ... has no parallel in the history of science until quite recent times.” [Kuhn, 1957, pp. 73-74]

Retrograde motion of a planet

according to Ptolemy.

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But he added

“it never quite worked. … No version of the system ever quite withstood the test of additional refined observations …” [loc. cit.]

With each “fix-up”, features that had previously been consistent with the model, became anomalous.

And each observation required its own accommodation.

Contrast with Copernicus’ heliocentric model in which retrograde motion a necessary consequence.

As Toulmin (1976, p. 389) observed,

“Almost without exception, the ‘facts’ that supported Copernicus’

position were not ‘novel’. Rather, his intellectual strategy had the

virtue of connecting together, in an intelligible way,[3] a string of

features of the planetary system that had either been unac-

counted for, or … handled separately and one at a time by Ptol-

emy and his successors. In a word … to explain, by a single treat-

ment, all the phenomena that Ptolemy had treated separately …”

I.e., as emphasized by Herschel and Whewell (e.g.,

Ruse, 1975), the ability to account for divers observa-

tions is strong evidence of a theory’s validity.

3 Compare with Darwin (1863, p. 554)

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Self-Corrective Thesis” (SCT).

“Even if the scientist's methods do not guarantee that he can get the truth on the first attempt, perhaps he can at least hope to get ever closer to it.” [Laudan, 1981, p. 228]

This is what Feynman was talking about.

Decomposable into two assertions:

1. False theories eventually refuted.

2. Given a refuted theory, 𝑇, science

“possesses techniques for finding an alternative theory, 𝑇′, that is closer to the truth than 𝑇, or at least determining unam-biguously whether … 𝑇′ is closer to the truth than …𝑇″ [Lau-dan, loc. cit., pp. 229, 246 (note 9)]

SCT, Laudan tells us, is important because it gives us a reason for preferring “science to quackery” (op. cit., p. 229)” – more politely for distinguishing scientific conclusions from other forms of opinion.4

4 Compare with Popper’s (1999, p. 16) claim that a theory is scientific if and only if it is “in principle falsifiable by experience”.

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And Indeed –

When scientists respond to extra-scientific criticism, SCT consequent to failure to falsify and peer review inevitably comes to the fore.

E.g. Richard Somerville’s (2011) condemnation cum appeal to authority of climate change skeptics:

“Science … works by expert scientists doing research and publish-

ing it in carefully reviewed research journals. Other scientists exam-

ine the research and repeat it and extend it. Valid results are con-

firmed, and wrong ones are exposed and abandoned. Science is

self-correcting.” [p. 514]

Likewise, Ayala (2009) emphased the “severe empirical tests” that novel theories must pass.

The conjunction of hypothesis formulation, the artic-ulation of predictions and Popperian falsification 1. Often referred to as the hypothetico-deductive (H-

D) or “scientific” method (Figure 4a).

2. Advocates of strong inference, e.g., Platt (1964), ar-gue that simultaneous consideration of multiple hy-potheses increases likelihood of self-correction.

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Figure 4a. The “scientific” / hypothetico-deductive method. Observa-tions, along with intuition, experience and God knows what else, in-form hypothesis formulation. Hypothesis-induced predictions are then compared with observations. Falsification (hypothesis-observa-tion mismatch) necessitates hypothesis revision. Scientists disagree as to whether or not falsification leads to hypothesis rejection absent alternatives. For opposing views, see Platt (1964) and O'Donohue and Buchanan (2001).

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Imre Lakatos (1970) called Popper’s criterion of de-marcation “dogmatic falsification” (DF).

1. Not a complement – he deemed Popper’s view simplistic.

2. Nor an accurate description of how science works:

3. According to DF, Vulcan’s apparent non-existence should have led to the immediate overthrow of Newtonian mechanics.

4. But of course it didn’t.

Newtonian mechanics explained far too much to be lightly discarded.

1. What was needed was a correction that a. Accounted for Mercury, while

b. Accommodating all the other cases for which

Newtonian astronomy worked. 2. General Relativity filled the bill – at least to 1st ap-

proximation (Forster, 2002; Feyerabend, 1985, pp.56-58).

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What We Have Learned. Regarding falsification.

1. Even Popper (1999, 16ff) acknowledged that theories

can always be “immunized” against falsification.

2. Lakatos’ solution (1970, 132ff) to distinguish “hard core” of a “research programme” from “protective belts” of auxiliary hypotheses (AHs).5

3. AH revision / replacement permits core survival in face of anomalous observations (Figure 4b).

4. AH formulation / revision “saves the scientist from being confused by the ocean of anom-alies. [I]t sets out a research programme which lists a chain of ever more complicated models simulating reality. … Newton first worked out his programme for a planetary system with a fixed point-like sun and one single point-like planet. It was in this model that he derived his inverse square law for Kepler’s ellipse. But this model was forbidden by Newton’s own third law

5 As discussed below, the hard core of evolutionary biology is common descent (e.g., Darwin, 1863a); the protective belt of AH’s, the mech-anisms successively promoted by Lamarck, Darwin and Wallace, their late 19th century successors, the (now not so) “Modern” Synthesis, most recently by proponents of adaptive epigenetic inheritance.

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of dynamics, therefore the model had to be replaced by one in which the sun and the planet revolved around their common centre of gravity … Then he worked out the programme for more planets as if there were only heliocentric but no interplan-etary forces. Then he worked out the case where the sun and the planets were not mass-points but mass-balls. … Having solved this ‘puzzle’, he started working in spinning balls and their wobbles. Then he admitted interplanetary forces and started working on perturbations. At this point, he started to look more anxiously at the facts. Many of them were beautifully explained (qualitatively) by this model, many were not. It was then that he started to work on bulging planets, rather than round planets, etc.” [Lakatos, op. cit., pp. 135-136]

5. Laudan’s (1977; 1981; Matheson and Dallmann, 2015) more general “research traditions”6 that a. Likewise allow for changing AH’s, but also permit

the core to remake itself – e.g., evolutionary biol-ogy (Ruse, 2012).

b. Offer a more “sociology of science” perspective,

6. Taken together, Kuhn, Lakatos, Laudan, etc., encour-age more frequent and direct juxtaposition of philo-sophical reasoning and historical reality.

6 Just where Research Programs end and Research Traditions begin is arguably a matter of definition.

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Figure 4b. Auxiliary hypothesis formulation / revision and improved data acquisition / analysis (bolded) added to the basic H-D scheme.

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Regarding Observations.

1. “Improved” methods of data acquisition / analysis can

also rescue an endangered core (Figure 4b).

2. This the complement to AH adjustment.

Consilience.

1. Observations initially deemed unrelated to a theory

consilient if they turn out to be predictable therefrom.

a. The term is due to William Whewell (1847).

b. Along with John Herschel, Whewell believed con-

silient inductions7 powerful evidence for theory pro-

bity.

2. Likewise, both Darwin and Wallace argued that com-

mon descent explained a multiplicity of otherwise

seemingly unconnected observations.

7 Whewell’s concept of “induction” involved more, specifically what he called “colligation”, than simply inferring that all ravens are black be-cause ravens of another color have yet to be observed – See Forster and Wolfe (1998); Snyder (2012).

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a. Wallace (Sarawak “Law” paper):

“… the law that "Every species has come into existence co-

incident both in time and space with a pre-existing closely

allied species," connects together and renders intelligible a

vast number of independent and hitherto unexplained facts.

… it not merely explains, but necessitates what exists.

Granted the law, and many of the most important facts in

Nature could not have been otherwise, but are almost as

necessary deductions from it, as are the elliptic orbits of the

planets from the law of gravitation.” [1855, p. 196].

b. Darwin (arguing against “heterogeny”8):

““The view given by me on the origin or derivation of species

… connects … by an intelligible thread of reasoning a multi-

tude of facts: … When the advocate of Heterogeny can thus

connect large classes of facts, and not until then, he will

have respectful and patient listeners.” [CD, 1863, p. 554]

3. Recall Toulmin (above) on Copernicus.

4. Conversely, anti-consilient input necessitates hy-

pothesis revision and so forth (Figure 4c).

8 As used by Darwin, the term referred to evolution by “development,” i.e., to the extension of embryogenesis and the consequent realization higher degrees of animal perfection (Chambers, 1844).

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Figure 4c. Anti-consilient observations necessitate hypothesis core and / or auxiliary hypothesis revision.

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Beyond Hypothesis and Observation.

1. Considerations external to the problem at hand pro-

mote “confirmation bias” (Figure 4d) consequent to

a. Scientific proclivity – “How science should be”

b. Ideological proclivity – “How the world should be

2. Examples:

a. Acceptance (Powell, 2001; below) of Kelvin’s age

of the earth because Lord K was “the highest author-

ity in science now living” [Burchfield, 1990, p. ix]

b. Acceptance of Bathybius and Eozoon because

“early evolutionists thought these imaginary creatures must

exist, so they created them” [Gould, 1980, p. 16].9

c. Rejection of transmutation in England pre-Origin

because everyone knew that “creation by law” was

an existential threat to society – e.g., the universally

condemnatory reaction to Vestiges – see below.

9 Those that demurred, e.g., G. C. Wallich, were ignored (Rupke, 1976).

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Figure 4d. Extra-scientific considerations (ESCs) typically pro-mote core stabilization via the adjustment of auxiliary hypothe-ses and data acquisition, analysis and interpretation.

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The Age of the Earth.

“Geologists set about trying to measure the

length of geologic time by their own meth-

ods, part of a general effort during the sec-

ond half of the nineteenth century to base

their science more on measurement than

description. But after laboriously calculating

the age of the earth by one of their hour-

glass methods, geologists required an ex-

ternal reference to certify their result as rea-

sonable. Yet only one reference existed:

the apparently exquisite mathematical cal-

culation of the leading scientist of the day,

Lord Kelvin, who had determined the age of

the earth to be 100 million years. To use a

geological method and reach the same conclusion as Kelvin not

only validated one's scientific acumen, it confirmed the stature of

the discipline of geology. The combination proved irresistible.

Though not many occupied themselves with the age of the earth,

those who did ‘produced an amazing variety of methods and an

even greater homogeneity of results.’ No matter what assump-

tions and approaches they used, the hourglass calculators wound

up agreeing with Kelvin. [Powell, 2001. Mysteries of Terra

Firma. Ch. 1. Emphasis added]

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Thermodynamics based estimates of geological antiquity necessitated ad hoc hypothesis adjustment to square a newly abbreviated geological time scale with Darwinian gradualism. Current estimate of the earth’s age (dotted blue line) is shown for comparison. Radiometric dating, first employed by Rutherford (1906), suggested a far greater age. See Holmes (1911) for an early effort to resolve dis-crepant estimates. Data from Dalrymple (1991, Table 2.1).

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Geological estimates of earth’s age, while mostly greater than Kelvin’s, were generally far lower than Darwin’s (1859) infamous calculation that overestimated the age of the Weald (lower Cretaceous) by a factor of three. Data from Dalrymple (loc. cit.).

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Bathybius haeckelii.

The urschleim as drawn by Ernst Haeckel. The calcium carbonate inclusions, christined coccoliths by T. H. Huxley, turned out to be the remains of pelagic algae that had drifted to the ocean floor; Bathybius itself, an inorganic precipitate. Reproduced from Rehbock (1975).

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Response to Vestiges (Transmutation).

“The world cannot bear to be turned upside down; and we are

ready to wage an internecine war with any violation of our modest

principles and social manners … If our glorious maidens and ma-

trons may not soil their fingers with the dirty knife of the anatomist,

neither may they poison the springs of joyous thought and modest

feeling, by listening to the seductions of this author … who tells

them — that their Bible is a fable when it teaches them that they

were made in the image of God — that they are the children of

apes and the breeders of monsters … that all the phenomena of

the universe, dead and living, are to be put before the mind in a

new jargon, and as the progression and development of a rank,

unbending, and degrading materialism.” [Adam Sedgwick,

1845, p. 3]

“Vestiges struck a note, which, besides being erroneous, was

‘dangerous’ – a word which creeps into all of the reviews and into

all the correspondence and reflects a state of mind transcending

scientific disapproval.” [G. C. Gillispie, 1951, 162-163.]

“You have read of course the Sequel to the Vestiges … The au-

thor of the Vestiges … has improved his knowledge and his ar-

guments so much since his first edition that his deformities no

longer appear so disgusting. It was well that he began to write in

the fullness of his ignorance and presumption, for had he begun

now he would have been more dangerous” [Letter of 8 Janu-

ary, 1846 from J. D. Forbes to Wm. Whewell. Shairp

et al., 1873, p. 178]

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By the Lethean stream. Toads flee the cave as Truth’s light strikes the mask of Reason from the Jacobin’s hideous face and incinerates his tombs of malevolance: Defamation, Libels, Sedition, Abuse, Ignorance, Anarchy and Atheism. Approving seraphim bear the symbols of the British establishment: cross, crown and the scales of justice. The caption reads “ A peep into the Cave of Jacobinism – Magna eƒt Veritas et Prævalebit” (Great is Truth, and it will Prevail”). Colored etching by James Gillray, (Frontpiece of the Anti-Jacobin Review, 1 September 1798). From the storming of the Bastille onwards, French transformism was associated in the Tory mind with Jacobin excess.

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The Hard Core of Darwinism.

As with Wallace and Lamarck (Gould, 2001), common

descent the hard core of Darwin’s views.

Importance assigned to alternative mechanisms, the

evolving belt of protective auxiliary assumptions.10

10 For analogous contemporary views, see Theobold (1999-2012).

Darwin’s theory of evolution as articulated in The Origin. In response to arguments limiting geological antiquity and the efficacy of selec-tion, Darwin would place increasing emphasis on use and disuse and mass induction by the environment. Likewise, Huxley would abandon the postulate of deep time and, by extension, Lyellian gradualism.

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Buttressing the Protective Belt.

By 1867, Darwin was confronting insufficiencies11 of

1. Time (Wm. Thomson – later Lord Kelvin):

a. A world without beginning or end (Hutton, 1788,

304) denies 2nd Law of which Kelvin co-discoverer.

“To suppose, as Lyell … [that] the chemical action and its

heat continued in an endless cycle, violates the principles of

natural philosophy in exactly the same manner … as to be-

lieve that a clock constructed with a self-winding movement

may fulfil the expectations of its ingenious inventor by going

for ever.” [Thomson, 1864]

b. Kelvin assumed the earth cooled conductively

(England, et al, 2007) from a molten state.

c. Estimated (Thomson, 1864) its habitable age ≤ 100

m.y. – insufficient time for gradual evolution.

d. Had previously obtained similar estimate for age of

the sun (Kelvin, 1862) – a compelling example of

“consilient inductions” – see below. 11 See, for example, Eiseley (1959) and Bowler (1992).

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2. Variation (Fleeming Jenkin, Kelvin’s Edinburgh col-league and business associate):

a. Continuing selection exhausts variability.

b. Likewise blending inheritance destroys variability by -~50% per generation.

c. After a few generations, selection has nothing to work on.

d. Evolution can therefore work if and only if sports breed true – which was not Darwin’s theory: “The appearance of a new specimen capable of perpetuat-ing its peculiarity is precisely what might be termed a crea-tion, the word being used to express our ignorance of how the thing happened. The substitution of the new specimens, descendants from the old species, would then be simply an example of strong race supplanting a weak one, by a pro-cess known long before the term 'natural selection' was in-vented. Perhaps this is the way in which new species are introduced, but it does not express the Darwinian theory of the gradual accumulation of infinitely minute differences of every-day occurrence, and apparently fortuitous in their character.” [Jenkin, 1867, pp. 292-293]

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Additions to The Origin’s 6th Edition.

1. AH Abandoned: “Single” (as opposed to “individ-

ual”) variations12 blended out as Jenkins had argued. “… until reading an able and valuable article in the 'North Brit-

ish Review' (1867), I did not appreciate how rarely single vari-

ations, whether slight or strongly-marked, could be perpetu-

ated … ” [Darwin, 1872, p. 71]

2. New AH: Subdivision of species into local popula-tions nonetheless retards loss of variation via in-breeding – i.e., like mate with like.

“To the effects of intercrossing in eliminating variations … , I

shall have to recur; but … most animals and plants keep to

their proper homes, and do not needlessly wander about; …

Consequently each newly-formed variety would generally be at

first local, …; so that similarly modified individuals would … of-

ten breed together. If the new variety were successful in its bat-

tle for life, it would slowly spread from a central district, com-

peting with and conquering the unchanged individuals on the

margins of an ever-increasing circle.” [op. cit., p. 72. Em-

phasis added]

12 Essentially these terms refer to discontinuous vs. continuous varia-tion. In fact, Jenkins’ argument applies to both kinds of variation.

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3. Another New AH: Direct environmental induction of concordant “individual” variations en masse. “… if the varying individual did not actually transmit to its off-

spring its newly acquired character, it would undoubtedly trans-

mit to them … a still stronger tendency to vary in the same

manner. … [T]he tendency to vary in the same manner has

often been so strong that all the individuals of the same species

have been similarly modified without the aid of any form of se-

lection. … [I]f the variation were of a beneficial nature, the orig-

inal form would soon be supplanted by the modified form.”

[loc. cit. Emphasis added.]

4. Still another New AH: Faster rates of evolution

early in earth’s history.

"It is, however, probable, as Sir William Thompson [sic] insists,

that the world at a very early period was subjected to more

rapid and violent changes in its physical conditions than those

now occurring; and such changes would have tended to induce

changes at a corresponding rate in the organisms which then

existed." [Op cit., p. 286, Emphasis added]

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Complementing Auxiliary Hypothesis Adjustment

was Darwin’s “Provisional Theory of Pangenesis”.

1. Dates to the period pre-Origin when Darwin was

working on Natural Selection, but not published until

1868.

2. Provided a mechanism for the inheritance of acquired

characters.

Pangenesis (left) contrasted with germ plasm theory (right). The for-mer imagined that environmental influences are transmitted to the germ via circulating particles called gemmules; the latter, isolation of the germ.

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Redefining the Core.

Creation by law, i.e., DwM, more important than relative

importance of alternative proximate mechanisms.

“I had not formerly sufficiently considered the existence of many

structures which appear to be … neither beneficial nor injurious;

and this I believe to be one of the greatest oversights … in my

work. I may be permitted to say as some excuse, that I had two

distinct objects in view, firstly, to shew that species had not been

separately created, and secondly, that natural selection had been

the chief agent of change, though largely aided by the inherited

effects of habit, and slightly by the direct action of the surrounding

conditions. … if I have erred … in having exaggerated its [natu-

ral selection’s] power … I have at least, as I hope, done good

service in aiding to overthrow the dogma of separate creations.

[Darwin, 1871, vol. I, pp. 152-153, emphasis added]

A defense previously deployed.

“Whether the naturalist believes in the views given by Lamarck,

or Geoffroy St.-Hilaire, by the author of the 'Vestiges,' by Mr. Wal-

lace and myself, or in any other such view, signifies extremely

little in comparison with the admission that species have de-

scended from other species and have not been created immuta-

ble;” [Darwin, 1868b, p. 617]

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Huxley’s (1869b) reply to Kelvin likewise abandoned

the core presumption of gradualism.13

“Biology takes her time from geology. The only reason we have

for believing in the slow rate of change in living forms is that they

persist through a series of deposits which, geology informs us,

have taken a long while to make. If the geological clock is wrong,

all the naturalist will have to do is to modify his notions of the

rapidity of change accordingly.” [Huxley, 1869b]

Previously regarded by CD as foundational.

“Now suppose there were a being who did not judge by mere exter-nal appearances, but who could study the whole internal organiza-tion, who was never capricious, and should go on selecting for one object during millions of generations; who will say what he might not effect? In nature we have some slight variation occasionally in all parts; … and in nature geology shows us what changes have taken place, and are taking place. We have almost unlimited time; no one but a practical geologist can fully appreciate this. [Letter to Asa Gray, 17 September, 1857 (DCP 2136 reproduced in Darwin and Wallace, 1858].

13 THH had, in fact, long been so disposed, e.g., “I see you are inclined to advocate the possibility of considerable "saltus" on the part of Dame Nature in her variations. I always took the same view, much to Mr. Dar-win's disgust, and we used often to debate it.” [Letter of 20 February, 1894, to William Bateson]

38

In Tres Partes Divisa Est.

Falsifiability a sine qua non of self-correction. 1. Generally attributed to

Popper (1992; 1999).

2. Anticipated by C. S. Peirce’s (1877) tripar-tite decomposition of the scientific method.

a. Abduction: Hypoth-esis formulation in re-sponse to unantici-pated observations.

b. Deduction: Logical derivation of implications.

c. Induction: Testing predictions by broadening orig-inal observations to a larger sample.

3. Peirce claimed the scientific method so defined, is

self-correcting and distinguishable from other forms of reasoning.

Charles Sanders Peirce, 19th century American probabilist and philosopher.

39

4. Laudan (1981, 236ff) maintains that Peirce’s argu-ment for self-correction restricted to the claim that successive estimates of probability converge. “Peirce simply cannot handle a case where an [sic] hypothe-sis (of the form "A is B") is replaced by a conceptually different one (say "A is C”)14. [op. cit., p. 243]

5. A-D-I nonetheless a fair description of Darwin’s activ-ities pre-natural selection. a. Darwin’s unexpected observations: Species dis-

tributions in time and space. b. His abducted hypotheses: Isolation and habit

theories (Grinnell, 1974; 1985).

c. His deductions and inductions: the contents of his “transmutation” notebooks (Barrett et al., 1987; also, Grinnell, 1974; 1985; Eldredge, 2005).

6. Darwin initial evolutionary musings entailed

a. Core retention;

b. AH adjustment.

14 For a broader assessment of Peirce’s philosophy, see Burch (2014).

40

7. E.g., The isolation the-

ory, required dispersal

to remote habitats

where new populations

could differentiate – a

problem for large ani-

mals.

8. Accordingly, Darwin

“began … to speculate on … land bridges … The idea of elevation and subsidence of land masses was pressed into service with mounting vigor until Darwin had the entire earth in motion.” [Grinnell, 1974, p. 266]

9. And when anomalies such as old / new world monkey distribution persisted, he conjured up a mid-Pacific continent formed from the now separate land masses of Asia, Af-rica, Australia, and America and throughout which species had spread prior to the continents’ drifting apart! (loc cit. p. 270].

Darwin notebooks, 1836-1839. The Red Notebook, opened aboard the Beagle, was gen-eral purpose. Notebooks A (geology) and B-E, (transmuta-tion) opened post return. Solid lines represent periods encom-passed by each; dotted lines, uncertainties in dating; dashed lines, division of subject mat-ter. Redrawn from Barrett et al. (1987).

41

Self-Correction and the Sociology of Science.

Scientific progress traditionally attributed to what Pop-per (1999) called “critical discussion”, i.e., to attempted falsification and response thereto, i.e., to doing science.

By way of contrast, David Hull identified social factors as the key to understanding how science works – spe-cifically “competitive cooperation” which he believed

1. An unavoidable consequence of scientific practice.

"Science is a matter of competitive cooperation, and both charac-teristics are important. The most important sort of cooperation that occurs in science is the use of the results of other scientists' research. This use is the most important sort of credit that one scientist can give another. Scientists want their work to be acknowledged as original, but for that it must be acknowledged. Their views must be accepted. For such acceptance, they need the support of other scientists. One way to gain this support is to show that one’s own work rests solidly on preceding research. The desire for credit (i.e. competition) and the need for support (i.e. cooperation) frequently come into conflict. One cannot gain support from a particular work unless one cites it, and this citation automatically confers worth on the work cited and detracts from one's own originality." [Hull, 1988, p. 318]

42

2. The mechanism by which science self-corrects.15 “Scientists are so conscientious about producing dependable work because their allies tend to incorporate that work into their own, usually without testing it, and their opponents are just as likely to expose it to careful scrutiny. Erroneous views are liable to hurt one’s opponents, but they are even more likely to dam-age one’ allies [and oneself]. Prior to publication, scientists expose their manuscripts to their allies. Afterwards critical scru-tiny comes from their opponents. The self-correction so im-portant in science does not depend on scientists presenting to-tally unbiased results but on other scientists, with different bi-ases, checking them,” [op. cit., pp. 320-221, Emphasis]

But Hull’s mechanism breaks down when views are widely shared, especially when reinforced by estab-lishment imprimatur – e.g., Cuvier vs. Lamarck; Ox-bridge vs. Vestiges; Huxley vs. Wallich; … 1. Said views can be

a. Shared scientific opinions (SSOs) or

b. Extra-scientific opinions (ESOs).

15 Sanderson (2001, p. 37) commends Hull’s view of self-correction to those “sociologists who think of themselves, it seems as scientists, but who are nevertheless committed to the claim that that science cannot lay claim to objective truth.”

43

2. SSO’s reflect obeisance to prevailing opinion, e.g., a. Planet Vulcan (or a circumsolar ring of plane-

tesmals) had to be there to square observation with Newtonian mechanics, which had to be right.

b. Geological estimates of the earth’s age had to be

abbreviated to square them with Kelvin’s unas-sailable mathematics.

3. ESOs often reflect ideological proclivity and the soci-

etal milieu in which scientific endeavors take place.

a. In England pre-Darwin, everyone knew that mate-rialism a threat to public order, morality, etc.

b. In Europe and North America pre-WWII, everyone knew that unfettered reproduction by “the moron class” (Sanger, 1922) a dire, but remediable threat.

4. ESO’s also consequent to a. Sociology of science: the ongoing jockeying for

power, conflicts, shifting alliances, competition for grants, … in which scientists engage. Hull (1988).

b. Ambition.

44

5. ESOs can foster Faustian bargains, e.g., a. Silence of scientific establishment, including THH

and CD, when Owen(1849) pilloried for raising the possibility of transmutation (Secord, 2000).

b. Silence of most Mendelian geneticists RE the eu-genics movement and its calls for sterilization pre-WWII (Paul and Spencer, 1995).

c. Overly “optimistic” interpretation of one’s data.

6. ESOs can also promote exuberant advocacy of par-

ticular points of view.

a. Adam Sedgwick’s 85 page denunciation of Creation

by Law as enunciated in Chambers’ Vestiges.

b. Konrad Lorenz’ ethological justification16 for exter-

mination in the name of “racial hygiene” (Deich-

mann, 1996, 185-198; Klopfer, 1994; 1999).

16 Lorenz believed that behaviors benefitting whole populations are maintained in the wild, but lost when group selection is relaxed under domestication, especially when races interbreed. He believed this ap-plied to man as well as animals, the result being degeneration of human populations relocated to cosmopolite cities. These ideas were highly compatible with National Socialism. Disgracefully, Lorenz was later awarded the Nobel Prize in Physiology or Medicine in 1973.

45

“Contrary to Lorenz’s previ-

ous assertions, he did not go

directly to the Eastern front,

but served (1942) in Posen

with an SS unit assigned to

perform tests[17] that would

allow distinctions to be made

between Poles and Polish-

German ‘hybrids.’ He [Lo-

renz] was a member of the

Rassenpolitisches Amt [Of-

fice of Racial Policy], the

‘race’ division of the SS.

“…the ideology of the NS

[National Socialist] state

required biological substanti-

ation, and this Lorenz pro-

vided in greater measure

that most other biologists of note. His motivational model [re-

leasers of instinctive behavior] and its application, I sug-

gest, may have been derived as much from this ideology as it

was from the study of animals.” [Klopfer, 1999, p. 60]

17 Psychological studies designed to distinguish the behavioral manifes-tations of German and Polish “genetic substances”, which were pre-sumed distinct (Deichmann, op. cit.).

Following the occupation of Po-land, the Wartheland Adminis-trative District was “cleansed” of untermenschen so as to make room for half a million German colonists. The “worthiness stud-ies” to which Lorenz lent his name determined which of the district’s residents were added to the Volkliste and allowed to remain and which were marked for deportation (Deichmann, 1996, pp. 194-196).

46

Pauses in the Onward March of Scientific Progress.

Case Duration Presumptive Cause

Earth’s Age ~40 y Scientific Authority (Kelvin)

Bathybius ~20 y Scientific Expectation

(1st Life Undifferentiated Protoplasm)

Planet Vulcan

~50 y Scientific Expectation

(Newtonian Mechanics)

Piltdown Man

~50 y Scientific Expectation

(Big Brains First)

Eugenics 60-70 y Scientific Authority (Genetic Determin-

ism); Ideology (Ethnic Chauvinism)

Fixity of Species1 50 y

Ideology (Maintenance of Prevailing Social and Religious Order)

Lysenkoism 35-40 y Political Authority; Ideology (Stalinism; New Soviet Man)

1. From Philosophie Zoologique (Lamarck, 1809) to The Origin of Species (Dar-

win, 1859).

47

Science as Problem Solving.

SCT related to idea that science progresses.

1. If SCT in doubt, so is progress. Yet …

“At the level of the practical applications of scientific knowledge

it is incontrovertible that the science of the year 2000 has

solved problems not solved by the science of the year 1900…"

[Losee, 2004, p. 158]

2. However, in light of preceding counter-examples, it

may be more useful inquire as to

a. The time scales on which SCT holds.

b. The circumstances that promote self-correction

vs. those that impede.

In which regard, Laudan’s (1977) approach relevant.

1. Equates scientific progress with problem solving

broadly define, thereby setting aside SCT.

2. Along with Lakatos, acknowledges that rates of prob-

lem solving vary with time and circumstance.

48

3. Example: Tyco Brahe’s (post-Copernicus) modified

geocentrism accounted for

a. Absence of stellar parallax without requiring the

assumption of “improbable” distances.

b. The fact that a stone dropped from a tower falls

straight down.

c. The Tychonic research programme nonetheless

stagnated and was eventually replaced.

Left. Tyco’s model of the solar system. Right. The giant sextant built for him by the king of Denmark failed to reveal stellar parallax.

49

Modeling Scientific Investigation.

Presumptions.

1. Science seeks to explain observations: Reducing hy-

pothesis-observation mismatch (HOM) an important

driver of investigatory activity.

2. Science is a social activity

a. Multiple individuals; views; biases.

b. Debate / disagreements, that

i. Play out over time, i.e., ongoing back & forth.

ii. Can involve contending “schools” the mem-

bers of which engage in “critical discussions.”

“… we need to form parties … for and against any the-

ory that is being subjected to serious scrutiny. For we

need to have a rational scientific discussion, and dis-

cussion does not always lead to a clear-cut resolution.”

[Popper, 1999, p. 10]

50

3. A grand examples of Popper’s discussions was trans-

mutation vs. special creation in 19th century Britain.

a. For 50 years, Britain’s scientific elite successfully

kept the transformist fox out of the henhouse.

b. An on-going struggle between defenders of the status quo and those who would change it.

c. Both sides scored points, e.g.,

i. Monotremes did lay eggs – point Transform-ism.

ii. Dinosaurs were more sophisticated than living reptiles – point Special Creation.18

iii. The men who caroused in the mold of the Iguanodon on New Year’s Eve, 1853, cele-brated Owenite idealism because it offered a way: common archetypes not ancestors.

d. The battle was waged in both “scientific” (Bridgewater

Treatises) & popular press (Vestiges), RE which, the Revd. Thomas Pearson actually kept score:

18 Pre-Origin, evolution was widely equated with progress over geologic time, a belief to which the replacement of dinosaurs by contemporary snakes and lizards was an inconvenient exception.

51

“Of religious publications he counted 24.5 million a year. From

the atheistic and corrupting presses the total was 28.5 million.

The devil was winning.” [Brooke, 2001, p. 133]

New Year's Eve in the Iguanodon mold at the relocated

Crystal Palace, 31 December, 1853. As part of the festiv-

ities, the celebrants, Hawkins (the sculptor), Prince Albert

and some twenty of Britain's most distinguished natural-

ists, belted out “The Jolly Old Beast”, a ditty composed for

the occasion by Edward Forbes. Each repetition of the

chorus, per Forbes' instructions, was followed by a re-

sounding roar.

52

4. The sorting of scientists into groups referred to above

partly a consequence of specialization, which reflects

a. Differing interests and abilities including discipli-

nary and methodological affinity among individual

scientists.

b. The investment of time and energy required to be-

come proficient / accepted / established in one’s

field.

5. Members of said groups are further

a. United by intellectual / institutional heritage.

b. More likely to attend to results generated by their

own group.

c. Less likely to attend to results generated by other

groups.

53

6. Other examples:

a. Kelvin’s limitations on the age of the earth, as a

practical matter, ignored by evolutionists pre-radio-

metric dating.

“I will maintain to the death that your case of Fernando Po and Abyssinia[19] is worth ten times more than the belief of a dozen physicists.” [CD to J. D. Hooker, 28 Febru-ary, 1866 DCP 5020]

b. Biogeographers, e.g., Simpson (1940) ignored evi-

dence for continental drift pre-seafloor spreading.

c. Etienne Geoffrey’s claim (Appel, 1987) that inverte-

brates are upside down vertebrates as judged by

the placement of nerve cord and aorta was near

universally ignored pre-Evo-Devo.20

7. It is therefore important to distinguish changes in

HOM consequent to local and external inputs, i.e., to

results generated by one’s own group and those pro-

duced by other groups.

Taken Together, the Preceding Suggests. 19 The reference is to the presence of temperate plants on tropical moun-

tains and cyclic climatic change, e.g. Darwin (1876, pp. 335-342).

20 An historically important exception was enthusiasm, e.g., Desmond, (1989), Seccord (2000), for “Unity of Type” in early 19th century Britain.

54

1. Science is a process (Hull, 1988). Its time evolution

appropriately modelled as a dynamical system.

2. At least one of the state variables, 𝑦(𝑡) = 𝐻𝑂𝑀(𝑡).

Figure 1. A dynamical system and its environment. State variables,

𝒙(𝑡) = 𝑥1(𝑡), 𝑥2(𝑡), … , evolve according to the governing equations,

𝑑𝒙(𝑡)/𝑑𝑡 = 𝒇(𝒙(𝑡), 𝒑(𝑡)). Parameter values, 𝒑(𝑡) = 𝑝1(𝑡), 𝑝2(𝑡), … ,

are one-way, and not necessarily constant, environmental inputs.

55

3. Fundamental Decomposition of �̇�(t)=(dy/dt): Distin-

guish changes in HOM consequent to

a. Local input – investigation of a system of interest

(SOI).

b. External input – investigation of other systems.

4. In sum , we have

a. An SOI that gener-

ates observations rel-

evant to one or more

local hypotheses.

b. Environment con-

sisting of other sys-

tems and associated

hypotheses that gen-

erate findings rele-

vant to the SOI & as-

sociated hypotheses.

5. Thus,

Figure 2. Systems and hypotheses. Associated with a system of interest, 𝑆0, are hypotheses, 𝐻00, 𝐻01, … , that purport to account for its observed properties. Observational input is gen-erated consequent to the study of 𝑆0, and other systems, 𝑆1, 𝑆2, …

56

�̇�(𝑡) = �̇�𝑙𝑜𝑐(𝑡) + �̇�𝑒𝑥𝑡(𝑡) (1)

where

a. �̇�𝑙𝑜𝑐(𝑡) is the rate of

HOM reduction due

to studying the SOI.

b. �̇�𝑒𝑥𝑡(𝑡) is the rate of

HOM increase due

to studying other

systems.

6. “System in a bath”:

i. If total number, 𝑁, of system is large, and

ii. If interactions between systems ≈ equal, then

iii. Summed impact of other systems on the SOI ≫

than the effect of SOI on any one of them.

iv. I.e., other systems the “environment.”

Figure 3. Investigation of an SOI as a dynamical system.

57

7. N.B. Each of the preceding “systems” a coupling of

real world and investigatory subsystems.

Figure 4. Scientific inquiry as a coupling of real world & investigatory systems. As shown here, coupling is one way. There are, however, circumstances in which inquiry affects the system being studied, e.g., animal populations censused by slaughter. Moreover, the Real World – Investigatory system can itself be embedded in a larger system wherein science-based policy prescriptions affect real world subjects of inquiry, thereby affecting subsequent observations and inspiring new prescriptions.

58

Changing Rates of HOM Reduction and Increase.

1. Rate of HOM reduction, �̇�𝑙𝑜𝑐(𝑡), consequent to

studying the SOI.

a. Assume an “up-down” function as shown in Figure 5a.

b. Declines, and can even go negative, as 𝑦(𝑡) → 0 because

i. Little interest in working on a problem already “solved”.

ii. There is likely a limit to what AH adjustment can accomplish given the hard core of the research programme in question, and be-yond which further AH adjustment makes things worse.

c. Declines to 0 as 𝑦(𝑡) → ∞ because little interest in

working on an apparently insoluble problem.

Figure 5a. Rate of HOM reduction. In-vestigatory effort by students of the SOI peaks at intermediate levels of

𝑦 = 𝐻𝑂𝑀 and goes negative for y small. Absent external inputs, the sys-tem equilibrates at 𝑦 = 𝑦∗.

59

2. Rate of HOM increase, �̇�𝑒𝑥𝑡(𝑡), consequent to stud-

ying other systems independent of 𝑦(𝑡).

a. Compatibility of observations consequent to the

study of other systems unaffected by locally engen-

dered reductions in HOM.

b. Example: Fixing up

Ptolemaic astronomy

to accommodate new

observations inevita-

bly made observa-

tions previously com-

patible anomalous.

c. Equilibria: Two (𝑦∗

and 𝑦ⱡ) or none.

d. Dynamics: 𝑦(𝑡) → 𝑦∗

or ∞.

e. Equilibria created / destroyed by tangent bifurca-

tion, i.e., when �̇�𝑒𝑥𝑡 tangent to �̇�𝑙𝑜𝑐.

Figure 5b. HOM time evolution mod-elled according to Equations (2) as a balance between local and external in-puts. In terms of Equations (2) below,

𝑟 = 4.0; 𝑢 = 0.5; 𝑦0 = .45.

60

Figure 6. Time evolution of hypothesis-observation mismatch, 𝑦(𝑡), resolved into local and external inputs. With modest rates of anti-consilient input, the local hy-pothesis can be fixed up, for example, via the adjustment of auxiliary hypotheses, in which case, there are stable and unstable equilibria. With sufficiently high rates of anti-consilient input, the equilibria are destroyed by a tangent bifurcation and the hypothesis becomes untenable.

61

f. Equations:

�̇�𝑙𝑜𝑐(𝑡) = 𝑟[𝑦(𝑡) − 𝑢]𝑒−𝑦(𝑡)

(2)

�̇�𝑒𝑥𝑡(𝑡) = 𝑦0

where

i. 𝑟𝑦(𝑡) is the rate of HOM that would obtain as

𝑦 → 0 in the absence of giving up, i.e., with

𝑢 = 0;

ii. 𝑢 is the “problem solved” giving up threshold;

iii. 𝑦0 is the constant rate of HOM increase con-

sequent to the investigation of other systems.

g. Continuation:

i. Equilibria can be continued, i.e., by varying a

single parameter subject to the requirement

that 𝑦 is an equilibrium point.

ii. Bifurcations can be continued by varying two

parameters subject to the requirement that 𝑦 is

an equilibrium and a bifurcation point.

62

h. Consequences:

i. Whether or not HOM → 𝑦∗ depends on initial

value of HOM, and hence choice of hypothesis.

ii. SSOs and ESOs can stabilize.

Figure 7. Continuation of equilibria (top) and bifurcations (bottom) gen-erated by Eqs (2). Bifurcations (+) mark the paired creation / annihilation of equilibria, one of which is stable, the other, unstable. The existence of two equilibria is favored by increasing the rate, 𝑟, of local hypothesis / data refinement, by reducing the rate, 𝑦0, of incompatible external input,

and by reducing the “problem solved” giving up threshold 𝑢.

63

HOM-Dependent External Input.

1. �̇�𝑒𝑥𝑡(𝑡) decreases with 𝑦(𝑡):

a. Locally engendered reductions in

HOM render observations conse-

quent to the study of other sys-

tems increasingly incompatible.

b. Example: Pre-Origin, distribu-

tional data came into increasing

conflict (Darwin, 1845) with inter-

preting adaption as evidence of

Divine Wisdom and Benefi-

cence even as theological scien-

tists continued to make the case.

2. �̇�𝑒𝑥𝑡(𝑡) increases with 𝑦(𝑡).

a. Locally engendered reductions in HOM render ob-

servations consequent to study of other systems in-

creasingly compatible.

b. Example: Post-plate tectonics, species distributions

increasingly consistent with paleogeography (Fig-

ure 9).

Figure 8. Wm Kirby’s Bridgewater Treatise.

64

c. Conversely, plate tectonics rendered irrelevant argu-

ments, such as that advanced by G. G. Simpson

(1940), against the “Wegener hypothesis”.21

21 “One of the many arguments against the Wegener hypothesis, at least in any application to mammals, is that the connections that it provides are corridors, but the faunal relationships on which it depends for evi-dence would not be produced by corridors” [op. cit., 149]

Figure 9. Previously anomalous distributions of fossil species explained by the existence of a southern supercontinent In during the late Paleo-zoic and early Mesozoic.

65

3. A more general equation for external input.

�̇�𝑒𝑥𝑡(𝑡) = 𝑦0(1 + 𝑎𝑒−𝑐𝑦(𝑡)) (3)

where

𝑦0 is the rate of HOM

increase as 𝑦(𝑡) → ∞.

1 + 𝑎 is the rate of

HOM increase or de-

crease if 𝑦(𝑡) = 0.

𝑐 is the departure of

�̇�𝑒𝑥𝑡(𝑡) from 𝑦0(1 + 𝑎),

i.e., degree of nonline-

arity.

4. If other systems “bat last”, 𝑎 < 0 evidence for hypoth-

esis probity – Whewell’s consilience of inductions.

i. Not always the case.

ii. Example: Early 20th century geneticists inter-

preted their observations as indicating new spe-

cies creation by saltation.

Figure 10. Possible dependencies of �̇�𝑒𝑥𝑡(𝑡)on 𝑦 = 𝐻𝑂𝑀.

66

Figure 11. Top. Equilibria continued against 𝑦0 (left) and 𝑟 (right) for different

values of the verisimilitude parameter, 𝑎 in Eqs (3). Other parameters as follows: 𝑐 = 1.0; 𝑟 = 4.0; 𝑢 = 0.5. Tangent bifurcations marked by (+).Bottom. Bi-

furcations continued in the 𝑎 − 𝑦0 plane with 𝑟 = 4.0 (left) and in the 𝑎 − 𝑟 plane with 𝑦0 = .45 (right). Decreasing values of 𝑎 move the system toward the two equilibria region of parameter space.

67

Investigatory Effort a Variable (OCE Model).

1. Dispense with local–external input distinction.

2. Explicitly model

a. Generation of new observations, 𝑂(𝑡), and their reconciliation with hypothesis.

b. Changing intensities of investigatory effort, 𝐸(𝑡).

3. Analogize hypothesis-observation interaction to Michaelis-Menten ki-netics (Figure 12).

4. Assume 𝑂(𝑡)̇ is

a. Autocatalytic;

b. Declines as O(t) ac-cumulates, i.e., a maximum number of incompatible obser-vations beyond which everyone jumps ship.

c. Promoted by 𝐸, which can do double duty.

Figure 12. Hypothesis-obser-vation interaction modelled as a Michaelis-Menten process. Ob-servations (𝑂) are evaluated (𝐻𝑂 complex) with reference to

hypothesis, 𝐻. The result can be dissolution of the complex back to 𝐻 and O, or demonstra-tion that observation and hy-pothesis are compatible. The latter can involve hypothesis modification from 𝐻 to 𝐻′.

68

5. Assume �̇� a balance between

a. Increases ∝ to rate of reconciliation.

b. Constant loss rate.

c. Decreases when 𝐸 small, i.e., there is a “giving up” threshold because scientists, like non-avian dino-saurs, “move in herds”22 – the force that binds being the “received beliefs” (Kuhn, 1962) that constrain “normal science”.

6. Equations satisfying these requirements as follows:

�̇� = 𝐸[𝐹(𝐸)𝐺(𝑂) − 1] (4)

�̇� = 𝑟(1 + 𝛼𝐸)𝑂(1 − 𝑂) − 𝐺(𝑂)𝐸

where

𝐹(𝐸) = 1 − 𝑐𝑒−𝑑𝐸; 𝐺(𝑂) = 𝑘𝑂

𝜒+𝑂. (5)

22 The humorous reference is to the movie, Jurassic Park.

Figure 23. OCE model.

69

7. A diversity of behaviors can obtain:

a. Boundary and interior equilibria.

b. Cycles.

c. Excitability.

8. Excitability:

a. Large amplitude excursions following returning to

“resting” equilibrium.

b. Reminiscent of Kuhnian (1962) paradigm shifts,

but without the weltanschauung divide.

70

Figure 14. Effect of increasing investigatory proficiency. a. All initial conditions lead to abandoned research programmes. b. Stable equi-librium coexists with abandonment. c. Damped oscillations plus ex-citability. d. Stable cycle + excitability. e., f. unstable cycle plus ex-citability.

71

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