Posts Tagged History of Science

Science, God, and the White House

Back in the 80s I stumbled upon the book, Scientific Proof of the Existence of God Will Soon Be Announced by the White House!, by Franklin Jones, aka Frederick Jenkins, later Da Free John, later Adi Da Samraj. I bought it on the spot. Likely a typical 70s mystic charlatan, Jones nonetheless saw clearly our poor grasp of tools for seeking truth and saw how deep and misguided is our deference to authority. At least that’s how I took it.

Who’d expect a hippie mystic to be a keen philosopher of science. The book’s title, connecting science, church and state, shrewdly wraps four challenging ideas:

  1. That there can be such a thing as scientific proof of anything
  2. That there could be new findings about the existence of God
  3. That evidence for God could be in the realm of science
  4. That government should or could accredit a scientific theory

On the first point, few but the uneducated, TIME magazine, and the FDA think that proof is in the domain of science. Proof is deductive. It belongs to math, logic and analytic philosophy. Science uses evidence and induction to make inferences to the best explanation.

Accepting that strong evidence would suffice as proof, point number 2 is a bit trickier. Evidence of God’s existence can’t be ruled out a priori. God could be observable or detectable; we might see him or his consequences. An almighty god could easily have chosen to regularly show himself or to present unambiguous evidence. But Yahweh, at least in modern times, doesn’t play like that (A wicked and adulterous generation demands a sign but none will be given – Matthew 16:4). While believers often say no evidence would satisfy the atheist, I think a focused team could come up with rules for a demonstration that at least some nonbelievers would accept as sufficient evidence.

Barring any new observations that would constitute evidence, point number 3 is tough to tackle without wading deep into philosophy of science. To see why, consider the theory that God exists. Is it even a candidate for a scientific theory, as one WSJ writer thinks (Science Increasingly Makes the Case for God)? I.e., is it the content of a theory or the way it is handled by its advocates that makes the theory scientific? If the latter, it can be surprisingly hard to draw the line between scientific investigations and philosophical ones. Few scientists admit this line is so blurred, but how do string theorists, who make no confirmable or falsifiable predictions, defend that they are scientists? Their fondness for non-empirical theory confirmation puts them squarely in the ranks of the enlightenment empiricist, Bishop Berkeley of Cloyne (namesake of our fair university) who maintained that matter does not exist. Further, do social scientists make falsifiable predictions, or do they just continually adjust their theory to accommodate disconfirming evidence?

That aside, those who work in the God-theory space somehow just don’t seem to qualify as scientific – even the young-earth creationists trained in biology and geology. Their primary theory doesn’t seem to generate research and secondary theories to confirm or falsify. Their papers are aimed at the public, not peers – and mainly aim at disproving evolution. Can a scientific theory be primarily negative? Could plate-tectonics-is-wrong count as a proper scientific endeavor?

Gould held that God was simply outside the realm of science. But if we accept that the existence of God could be a valid topic of science, is it a good theory? Following Karl Popper, a scientific theory can withstand only a few false predictions. On that view the repeated failures of end-of-days predictions by Harold Camping and Herbert Armstrong might be sufficient to kill the theory of God’s existence. Or does their predictive failures simply exclude them from the community of competent practitioners?

Would NASA engineer, Edgar Whisenant be more credible at making predictions based on the theory of God’s existence? All his predictions of rapture also failed. He was accepted by the relevant community (“…in paradigm choice there is no standard higher than the assent of the relevant community” – Thomas Kuhn) since the Trinity Broadcast Network interrupted its normal programming to help watchers prepare. If a NASA engineer has insufficient scientific clout, how about our first scientist? Isaac Newton predicted, in Observations upon the Prophecies of Daniel and the Apocalypse of St. John, that the end would come in 2000 CE. Maybe Newton’s calculator had the millennium bug.

If we can’t reject the theory for any number of wrong predictions, might there be another basis for rejecting it? Some say absence of a clear mechanism is a good reason to reject theories. In the God theory, no one seems to have proposed a mechanism by which such a God could have arisen. Aquinas’s tortured teleology and Anselm’s ontological arguments still fail on this count. But it seems unfair to dismiss the theory of God’s existence on grounds of no clear mechanism, because we have long tolerated other theories deemed scientific with the same weakness. Gravity, for example.

Does assent of the relevant community grant scientific status to a theory, as Kuhn would have it? If so, who decides which community is the right one? Theologians spend far more time on Armageddon than do biologists and astrophysicists – and theologians are credentialed by their institutions. So why should Hawking and Dawkins get much air time on the matter? Once we’ve identified a relevant community, who gets to participate in its consensus?

This draws in point number 4, above. Should government or the White House have any more claim to a scientific pronouncement than the Council of Bishops? If not, what are we to think of the pronouncements by Al Gore and Jerry Brown that the science of climate is settled? Should they have more clout on the matter than Pope Francis (who, interestingly, has now made similar pronouncements)?

If God is outside the realm of science, should science be outside the jurisdiction of government? What do we make of President Obama’s endorsement of “calling out climate change deniers, one by one”? You don’t have to be Franklin Jones or Da Free John to see signs here of government using the tools of religion (persecution, systematic effort to censure and alienate dissenters) in the name of science. Is it a stretch to see a connection to Jean Bodin, late 16th century French jurist, who argued that only witches deny the existence of witches?

Can you make a meaningful distinction between our government’s pronouncements on the truth or settledness of the climate theory (as opposed to government’s role in addressing it) and the Kremlin’s 1948 pronouncement that only Lamarckian inheritance would be taught, and their call for all geneticists to denounce Mendelian inheritance? Is it scientific behavior for a majority in a relevant community to coerce dissenters?

In trying to draw a distinction between UN and US coercion on climate science and Lysenkoism, some might offer that we (we moderns or we Americans) are somehow different – that only under regimes like Lenin’s and Hitler’s does science get so distorted. In thinking this, it’s probably good to remember that Hitler’s eugenics was born right here, and flourished in the 20th century. It had nearly full academic support in America, including Stanford and Harvard. That is, to use Al Gore’s words, the science was settled. California, always a trendsetter, by the early 1920s, claimed 80% of America’s forced sterilizations. Charles Goethe, founder of Sacramento State University, after visiting Hitler’s Germany in 1934 bragged to a fellow California eugenicist about their program’s influence on Hitler.

If the era of eugenics seems too distant to be relevant to the issue of climate science/politics, consider that living Stanford scientist, Paul Ehrlich, who endorsed compulsory abortion in the 70s, has had a foot in both camps.

As crackpots go, Da Free John was rather harmless.

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“Indeed, it has been concluded that compulsory population-control laws, even including laws requiring compulsory abortion, could be sustained under the existing Constitution if the population crisis became sufficiently severe to endanger the society.” – Ehrlich, Holdren and Ehrlich, EcoScience, 3rd edn, 1977, p. 837

“You will be interested to know that your work has played a powerful part in shaping the opinions of the group of intellectuals who are behind Hitler in this epoch-making program.” – Charles Goethe, letter to Edwin Black, 1934

 

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Galileo, Cantor and the Countably Infinite

I recently found my high school algebra book from the classic Dolciani series. In Chapter 1’s exercises, I stumbled upon this innocent question: Determine whether there exists a one-to-one correspondence between the two sets {natural numbers} and {even natural numbers}. At the end of chapter 1 is a short biography of Georg Cantor (d. 1918), crediting him with inventing set theory, an approach toward dealing with the concept of infinity.

I’m going out on a limb here. I’m not a mathematician. I understand that Cantor is generally accepted as being right about infinity and countable sets in the math world; but I think I think his work on on one-to-one correspondence and the countability of infinite sets is flawed.

First, let’s get back to my high school algebra problem. The answer given is that yes, a one-to-one correspondence does exist between natural number and even numbers, and thus they have the same number of elements. The evidence is that the sets can be paired as shown below:

1 <—> 2
2 <—> 4
3 <—> 6

n <—> 2n

This seems a valid demonstration of one-to-one correspondence. In most of math – where deduction rules – a single case of confirming evidence is assumed to exclude all possibility of disconfirming evidence. But this infinity business is not math of that sort. It employs math and takes the general form of mathematical analysis; but some sleight of hand is surely at work. Cantor, in my view, indulged in something rather close to math, but also having a foot in philosophy, and perhaps several more feet (possibly of an infinite number of them) in language and psychology. One might call it multidisciplinary. Behold.

I can with equal validity show the two sets (natural numbers and even numbers) not to have a one-to-one correspondence but a two-to-one correspondence. I do this with the following pairing. Set 1 on the left is the natural numbers. Set 2 on the right is the even numbers:

1      unpaired
2 <—> 2
3      unpaired
4 <—> 4
5      unpaired

2n -1      unpaired
2n <—> 2n

By removing all the unpaired (odd) elements from the set 1, I pair each  remaining member of set 1 with each element of set 2. It seems arguable that if a one to one correspondence exists between part of set one and all of set two, the two whole sets cannot support a one-to-one correspondence. By inspection, the set of even numbers is included within the set of natural numbers and obviously not coextensive with it. Therefore Cantor’s argument, based solely on correspondence, works only by promoting one fact – pairing of terms – while ignoring an equally obvious fact, the matter of inclusion.  Against my argument Cantor seems to dismiss the obvious difficulty by making a sort of mystery-of-faith argument – his concept of infinity entails that a set and a proper subset of it can be the same size.

Let’s dig a bit deeper. First, Cantor’s usage of the one-to-one concept (often called bijection) is heavy handed. It requires that such correspondence be established by starting with sets having their members placed in increasing order. Then it requires the first members of each set to be paired with one another, and so on. There is nothing particularly natural about this way of doing things; Cantor devised it to suit his needs. It got him into enough logical difficulty that he had to devise the concepts of cardinality and ordinality, with problematic definitions. Gottlob Frege and Bertrand Russell had to patch up his definitions. The notion of equipollent sets fell out of this work, along with complications addressed by mental heavy lifters like von Neumann and Tarski, which are out of scope here. Finally, it seems to me that Cantor implies – but fails to state outright – that the existence of a simultaneous two-to-one correspondence (i.e., group each n and n+1 in set 1 with each 2n in set 2 to get a two-to-one correspondence between the two sets) does no damage to the claims that one-to-one correspondence between the two sets makes them equal in size. In other words, Cantor helped himself to an unnaturally restrictive interpretation (i.e., a matter of language) of one-to-one correspondence – one that favored his agenda. Cantor slips a broader meaning of equality on us than the strict numerical equality that math grew up with. Further, his usage of the term – and concept of – “size” requires a special definition.

Cantor’s rule set for the pairing of terms and his special definitions are perfectly valid axioms for mathematical system, but there is nothing within mathematics that justifies these axioms. Believing that the consequences of a system or theory justify its postulates is exactly the same as believing that the usefulness of Euclidean geometry justifies Euclid’s fifth postulate. Euclid knew this wasn’t so, and Proclus tells us Euclid wasn’t alone in that view.

Galileo, who, like Cantor, hurled some heavy-handed arguments when he was in a jam, seems to have had a more grounded sense of the infinite than Cantor. For Galileo, the concrete concept of equality, even when dressed up in fancy clothes like equipollence, does not reconcile with the abstract concept of infinity. Galileo thought concepts like similarity, countability, size and equality just don’t apply to the infinite. By the time of Leibnitz and Newton, infinity had earned a place in math, but as something that could be only approached, but not reached, equaled, measured or compared.

Cantor’s model of infinity may be interesting and useful, but it is a shame that’s it’s taught and reported as fact, e.g., “infinity comes in infinitely many different sizes – a fact discovered by Georg Cantor” (Science News, Jan 8, 2008).

The under-celebrated WVO Quine comes to mind as bearing on this topic. Quine argued that the distinction between analytic and synthetic statements was  false, and that no claim should be immune to empirical falsification. Armed with that idea, I’ll offer that Cantor’s math is subject to scientific examination. Since confirming evidence is always weaker than disconfirming evidence (i.e., Popperian falsifiability) I’d argue the demonstration of inequality of the sets of natural and even numbers (inclusion of one within the other) trumps the demonstration of equal size by correspondence.

Mathematicians who state the equal-size concept as a fact discovered by Cantor have overstepped the boundaries of their discipline. Galileo regarded the natural-even set problem as a true paradox. I agree. Did Cantor resolve this paradox, or did he merely conceal it with language?

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Marcus Vitruvius’s Science

Science, as an enterprise that acquires knowledge and justified beliefs in the form of testable predictions by systematic iterations of observation and math-based theory, started around the 17th century, somewhere between Copernicus and Newton. That, we learned in school, was the beginning of the scientific revolution. Historians of science tend to regard this great revolution as the one that never happened. That is, as Floris Cohen puts it, the scientific revolution, once an innovative and inspiring concept, has since turned into a straight-jacket. Picking this revolution’s starting point, identifying any cause for it, and deciding what concepts and technological innovations belong to it are problematic.

That said, several writers have made good cases for why the pace of evolution – if not revolution – of modern science accelerated dramatically  in Europe, only when it did, why it has continuously gained steam rather than petering out, its primary driving force, and the associated transformations in our view of how nature works. Some thought the protestant ethic and capitalism set the stage for science. Others thought science couldn’t emerge until the alliance between Christianity and Aristotelianism was dissolved. Moveable type and mass production of books can certainly claim a role, but was it really a prerequisite? Some think a critical mass of ancient Greek writings had to have been transferred to western Europe by the Muslims. The humanist literary critics that enabled repair and reconstruction of ancient texts mangled in translation from Greek to Syriac to Persian to Latin and botched by illiterate medieval scribes certainly played a part. If this sounds like a stretch, note that those critics seem to mark the first occurrence of a collective effort by a group spread across a large geographic space using shared standards to reach a peer-reviewed consensus – a process sharing much with modern science.

But those reasons given for the scientific revolution all have the feel of post hoc theorizing. Might intellectuals of the day, observing these events, have concluded that a resultant scientific revolution was on the horizon? Francis Bacon comes closest to fitting this bill, but his predictions gave little sense that he was envisioning anything like what really happened.

I’ve wondered why the burst of progress in science – as differentiated from plain know-how, nature-knowledge, art, craft, technique, or engineering knowledge – didn’t happen earlier. Why not just after the period of innovation in from about 1100 to 1300 CE in Europe. In this period Jean Buridan invented calculators and almost got the concept of inertia right. Robert Grosseteste hinted at the experiment-theory model of science. Nicole Oresme debunked astrology and gave arguments for a moving earth. But he was the end of this line. After this brief awakening, which also included the invention of banking and the university, progress came to a screeching halt. Some blame the plague, but that can’t be the culprit. Literature of the time barley mentions the plague. Despite the death toll, politics and war went on as usual; but interest in resurrecting ancient Greek knowledge of all sorts tanked.

Why not in the Islamic world in the time of Ali al-Qushji and al-Birjandi? Certainly the mental capacity was there. A layman would have a hard time distinguishing al-Birjandi’s arguments and thought experiments for the earth’s rotation from those of Galileo. But Islamic civilization at the time had plenty of scholars but no institutions for making practical use of such knowledge and its society would not have tolerated displacement of received wisdom by man-made knowledge.

The most compelling case for civilization having been on the brink of science at an earlier time seems to be the late republic or early imperial Rome. This may seem a stretch, since Rome is much more known for brute force than for finesse, despite their flying buttresses, cranes, fire engines, central heating and indoor plumbing.

Consider the writings of one Vitruvius, likely Marcus Vitruvius Pollio, in the early reign of Augustus. Vitruvius wrote De Architectura, a ten volume guide to Roman engineering knowledge. Architecture, in Latin, translates accurately into what we call engineering. Rediscovered and widely published during the European renaissance as a standard text for engineers, Vitruvius’s work contains text that seems to contradict what we were all taught about the emergence of the – or a  – scientific method.

Vitruvius is full of surprises. He acknowledges that he is not a scientist (an anachronistic but fitting term) but a collator of Greek learning from several preceding centuries. He describes vanishing point perspective: “…the method of sketching a front with the sides withdrawing into the background, the lines all meeting in the center of a circle.” (See photo below of a fresco in the Oecus at Villa Poppea, Oplontis showing construction lines for vanishing point perspective.) He covers acoustic considerations for theater design, explains central heating technology, and the Archimedian water screw used to drain mines. He mentions a steam engine, likely that later described by Hero of Alexandria (aeolipile drawing at right), which turns heat into rotational energy. He describes a heliocentric model passed down from ancient Greeks. To be sure, there is also much that Vitruvius gets wrong about physics. But so does Galileo.

Most of De Architectura is not really science; it could more accurately be called know-how, technology, or engineering knowledge. Yet it’s close. Vitruvius explains the difference between mere machines, which let men do work, and engines, which derive from ingenuity and allow storing energy.

What convinces me most that Vitruvius – and he surely could not have been alone – truly had the concept of modern scientific method within his grasp is his understanding that a combination of mathematical proof (“demonstration” in his terms) plus theory, plus hands-on practice are needed for real engineering knowledge. Thus he says that what we call science –  theory plus math (demonstration) plus observation (practice) –  is essential to good engineering.

The engineer should be equipped with knowledge of many branches of study and varied kinds of learning, for it is by his judgement that all work done by the other arts is put to test. This knowledge is the child of practice and theory. Practice is the continuous and regular exercise of employment where manual work is done with any necessary material according to the design of a drawing. Theory, on the other hand, is the ability to demonstrate and explain the productions of dexterity on the principles of proportion.

 It follows, therefore, that engineers who have aimed at acquiring manual skill without scholarship have never been able to reach a position of authority to correspond to their pains, while those who relied only upon theories and scholarship were obviously hunting the shadow, not the substance. But those who have a thorough knowledge of both, like men armed at all points, have the sooner attained their object and carried authority with them.

 It appears, then, that one who professes himself an engineer should be well versed in both directions. He ought, therefore, to be both naturally gifted and amenable to instruction. Neither natural ability without instruction nor instruction without natural ability can make the perfect artist. Let him be educated, skillful with the pencil, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens. – Vitruvius – De Architectura, Book 1

Historians, please correct me if you know otherwise, but I don’t think there’s anything else remotely like this on record before Isaac Newton – anything in writing that comes this close to an understanding of modern scientific method.

So what went wrong in Rome? Many blame Christianity for the demise of knowledge in Rome, but that is not the case here. We can’t know for sure, but the later failure of science in the Islamic world seems to provide a clue. Society simply wasn’t ready. Vitruvius and his ilk may have been ready for science, but after nearly a century of civil war (starting with the Italian social wars), Augustus, the senate, and likely the plebes, had seen too much social innovation that all went bad. The vision of science, so evident during the European Enlightenment, as the primary driver of social change, may have been apparent to influential Romans as well, at a time when social change had lost its luster. As seen in writings of Cicero and the correspondence between Pliny and Trajan, Rome now regarded social innovation with suspicion if not contempt. Roman society, at least its government and aristocracy, simply couldn’t risk the main byproduct of science – progress.

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History is not merely what happened: it is what happened in the context of what might have happened. – Hugh Trevor-Roper – Oxford Valedictorian Address, 1998

The affairs of the Empire of letters are in a situation in which they never were and never will be again; we are passing now from an old world into the new world, and we are working seriously on the first foundation of the sciences. – Robert Desgabets, Oeuvres complètes de Malebranche, 1676

Newton interjected historical remarks which were neither accurate nor fair. These historical lapses are a reminder that history requires every bit as much attention to detail as does science – and the history of science perhaps twice as much. – Carl Benjamin Boyer, The Rainbow: From Myth to Mathematics, 1957

Text and photos  © 2015 William Storage

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Sun Follows the Solar Car

Bill Storage once got an A in high school Physics and suggests no further credentials are needed to evaluate the claims of most eco-fraud.

Once a great debate raged in America over the matter of whether man-mad climate change had occurred. Most Americans believed that it had. There were theories, models, government-sponsored studies, and various factions arguing with religious fervor. The time was 1880 and the subject was whether rain followed the plow – whether the westward expansion of American settlers beyond the 100th meridian had caused an increase in rain that would make agricultural life possible in the west. When the relentless droughts of the 1890s offered conflicting evidence, the belief died off, leavings its adherents embarrassed for having taken part in a mass delusion.

Model TWe now know the dramatic greening of the west from 1845 to 1880 was due to weather, not climate. It was not brought on by Mormon settlements, vigorous tilling, or the vast amounts of dynamite blown off to raise dust around which clouds could form. There was a shred of scientific basis for the belief; but the scale was way off.

It seems that the shred of science was not really a key component of the widespread belief that rain would follow the plow. More important was human myth-making and the madness of crowds. People got swept up in it. As ancient Jewish and Roman writings show, public optimism and pessimism ebbs and flows across decades. People confuse the relationship between man and nature. They either take undue blame or undo credit for processes beyond their influence, or they assign their blunders to implacable cosmic forces. The period of the Western Movement was buoyant, across political views and religions. Some modern writers force-fit the widely held belief about rain following the plow in the 1870s into the doctrine of Manifest Destiny. These embarrassing beliefs were in harmony, but were not tied genetically. In other words, don’t blame the myth that rain followed the plow on the Christian right.

Looking back, one wonders how farmers, investors and politicians, possibly including Abraham Lincoln, could so deeply indulge in belief held on irrational grounds rather than evidence and science. Do modern humans do the same? I’ll vote yes.

Today’s anthropogenic climate theories have a great deal more scientific basis than those of the 1870s. But many of our efforts at climate cure do not. Blame shameless greed for some of the greenwashing; but corporations wouldn’t waste their time if consumers weren’t willing to waste their dollars and hopes.

Take Ford’s solar-powered hybrid car, about which a SmartPlanet writer recently said:

Imagine an electric car that can charge without being plugged into an outlet and without using electricity from dirty energy sources, like coal.

He goes on to report that Ford plans to experiment with such a solar-hybrid concept car having a 620-mile range. I suspect many readers will understand that experimentation to mean experimenting in the science sense rather than in the marketability sense. Likewise I’m guessing many readers will allow themselves to believe that such a car might derive a significant part of the energy used in a 620-mile run from solar cells.

We can be 100% sure that Ford is not now experimenting on – nor will ever experiment on – a solar-powered car that will get a significant portion of its energy from solar cells. It’s impossible now, and always will be. No technology breakthrough can alter the laws of nature. Only so much solar energy hits the top of a car. Even if you collected every photon of it, which is again impossible because of other laws of physics, you couldn’t drive a car very far on it.

Most people – I’d guess – learned as much in high school science. Those who didn’t might ask themselves, based on common sense and perhaps seeing the size of solar panels needed to power a telephone in the desert, if a solar car seems reasonable.

The EPA reports that all-electric cars like the Leaf and Tesla S get about 3 miles per kilowatt-hour of energy. The top of a car is about 25 square feet. At noon on June 21st in Phoenix, a hypothetically perfect, spotless car-top solar panel could in theory generate 30 watts per square foot.  You could therefore power half of a standard 1500 watt toaster with that car-top solar panel. If you drove your car in the summer desert sun for 6 hours and the noon sun magically followed it into the shade and into your garage – like rain following the plow – you could accumulate 4500 watt-hours (4.5 kilowatt hours) of energy, on which you could drive 13.5 miles, using the EPA’s numbers. But experience shows that 30 watts per square foot is ridiculously optimistic. Germany’s famous solar parks, for example, average less than one watt per square foot; their output is a few percent of my perpetual-noon-Arizona example. Where you live, it probably doesn’t stay noon, and you’re likely somewhat north of Phoenix, where the sun is far closer to the horizon, and it’s not June 21st all year (hint: sine of 35 degrees times x, assuming it’s not dark). Oh, and then there’s clouds. If you live in Bavaria or Cleveland, or if your car roof’s dirty – well, your mileage may vary.

Recall that this rather dim picture cannot be made much brighter by technology. Physical limits restrict the size of the car-top solar panel, nature limits the amount of sun that hits it, and the Shockley–Queisser limit caps the conversion efficiency of solar cells.

Curbing CO2 emissions is not a lost cause. We can apply real engineering to the problem. Solar panels on cars isn’t real engineering; it’s pandering to public belief. What would Henry Ford think?

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Tom Hight is my name, an old bachelor I am,
You’ll find me out West in the country of fame,
You’ll find me out West on an elegant plain,
And starving to death on my government claim.

Hurrah for Greer County!
The land of the free,
The land of the bed-bug,
Grass-hopper and flea;
I’ll sing of its praises
And tell of its fame,
While starving to death
On my government claim.

Opening lyrics to a folk song by Daniel Kelley, late 1800s

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Great Innovative Minds: A Discord on Method

Great minds do not think alike. Cognitive diversity has served us well. That’s not news to those who study innovation; but I think you’ll find this to be a different take on the topic, one that gets at its roots.

The two main figures credited with setting the scientific revolution in motion did not agree at all on what the scientific method actually was. It’s not that they differed on the finer points; they disagreed on the most basic aspect of what it meant to do science – though they didn’t yet use that term. At the time of Francis Bacon and Rene Descartes, there were no scientists. There were natural philosophers. This distinction is important for showing just how radical and progressive Descartes and Bacon were.

'Descartes" In Discourse on Method, Descartes argued that philosophers, over thousands of years of study, had achieved absolutely nothing. They pursued knowledge, but they had searched in vain. Descartes shared some views with Aristotle, but denied Aristotelian natural philosophy, which had been woven into Christian beliefs about nature. For Aristotle, rocks fell to earth because the natural order is for rocks to be on the earth, not above it – the Christian version of which was that it was God’s plan. In medieval Europe truths about nature were revealed by divinity or authority, not discovered. Descartes and Bacon were both devout Christians, but believed that Aristotelian philosophy of nature had to go. Observing that there is no real body of knowledge that can be claimed by philosophy, Descartes chose to base his approach to the study of nature on mathematics and reason. A mere 400 years after Descartes, we have trouble grasping just how radical this notion was. Descartes believed that the use of reason could give us knowledge of nature, and thus give us control over nature. His approach was innovative, in the broad sense of that term, which I’ll discuss below. Observation and experience, however, in Descartes’ view, could be deceptive. They had to be subdued by pure reason. His approach can be called rationalism. He sensed that we could use rationalism to develop theories – predictive models – with immense power, which would liberate mankind. He was right. 

Francis Bacon, Descartes slightly older counterpart in the scientific revolution, was a British philosopher and statesman who became attorney general in 1613 under James I. He is now credited with being the father of empiricism, the hands-on, experimental basis for modern science, engineering, and technology. Bacon believed that acquiring knowledge of nature had to be rooted in observation and sensory experience alone. Do experiments and then decide what it means. Infer conclusions from the facts. Bacon argued that we must quiet the mind and apply a humble, mechanistic approach to studying nature and developing theories. Reason biases observation, he said. In this sense, the theory-building models of Bacon and Descartes were almost completely opposite. I’ll return to Bacon after a clarification of terms needed to make a point about him.

Innovation has many meanings. Cicero said he regarded it with great suspicion. He saw innovation as the haphazard application of untested methods to important matters. For Cicero, innovators were prone to understating the risks and overstating the potential gains to the public, while the innovators themselves had a more favorable risk/reward quotient. If innovation meant dictatorship for life for Julius Caesar after 500 years of self-governance by the Roman people, Cicero’s position might be understandable.

Today, innovation usually applies specifically to big changes in commercial products and services, involving better consumer value, whether by new features, reduced prices, reduced operator skill level, or breaking into a new market. Peter Drucker, Clayton Christensen and the tech press use innovation in roughly this sense. It is closely tied to markets, and is differentiated from invention (which may not have market impact), improvement (may be merely marginal), and discovery.

BaconThat business-oriented definition of innovation is clear and useful, but it leaves me with no word for what earlier generations meant by innovation. In a broader sense, it seems fair that innovation also applies to what vanishing point perspective brought to art during the renaissance. John Locke, a follower of both Bacon and Descartes, and later Thomas Jefferson and crew, conceived of the radical idea that a nation could govern itself by the application of reason. Discovery, invention and improvement don’t seem to capture the work of Locke and Jefferson either. Innovation seems the best fit. So for discussion purposes, I’ll call this innovation in the broader sense as opposed to the narrower sense, where it’s tied directly to markets.

In the broader sense, Descartes was the innovator of his century. But in the narrow sense (the business and markets sense), Francis Bacon can rightly be called the father of innovation – and it’s first vocal advocate. Bacon envisioned a future where natural philosophy (later called science) could fuel industry, prosperity and human progress. Again, it’s hard to grasp how radical this was; but in those days the dominant view was that mankind had reached its prime in ancient times, and was on a downhill trajectory. Bacon’s vision was a real departure from the reigning view that philosophy, including natural philosophy, was stuff of the mind and the library, not a call to action or a route to improving life. Historian William Hepworth Dixon wrote in 1862 that everyone who rides in a train, sends a telegram or undergoes a painless surgery owes something to Bacon. In 1620, Bacon made, in The Great Instauration, an unprecedented claim in the post-classical world:

“The explanation of which things, and of the true relation between the nature of things and the nature of the mind … may spring helps to man, and a line and race of inventions that may in some degree subdue and overcome the necessities and miseries of humanity.”

In Bacon’s view, such explanations would stem from a mechanistic approach to investigation; and it must steer clear of four dogmas, which he called idols. Idols of the tribe are the set of ambient cultural prejudices. He cites our tendency to respond more strongly to positive evidence than to negative evidence, even if they are equally present; we leap to conclusions. Idols of the cave are one’s individual preconceptions that must be overcome. Idols of the theater refer to dogmatic academic beliefs and outmoded philosophies; and idols of the marketplace are those prejudices stemming from social interactions, specifically semantic equivocation and terminological disputes.

Descartes realized that if you were to strictly follow Bacon’s method of fact collecting, you’d never get anything done. Without reasoning out some initial theoretical model, you could collect unrelated facts forever with little chance of developing a usable theory. Descartes also saw Bacon’s flaw in logic to be fatal. Bacon’s method (pure empiricism) commits the logical sin of affirming the consequent. That is, the hypothesis, if A then B, is not made true by any number of observations of B.  This is because C, D or E (and infinitely more letters) might also cause B, in the absence of A. This logical fallacy had been well documented by the ancient Greeks, whom Bacon and Descartes had both studied. Descartes pressed on with rationalism, developing tools like analytic geometry and symbolic logic along the way.

Interestingly, both Bacon and Descartes were, from our perspective, rather miserable scientists. Bacon denied Copernicanism, refused to accept Kepler’s conclusion that planet orbits were elliptical, and argued against William Harvey’s conclusion that the heart pumped blood to the brain through a circulatory system. Likewise, by avoiding empiricism, Descartes reached some very wrong conclusions about space, matter, souls and biology, even arguing that non-human animals must be considered machines, not organisms. But their failings were all corrected by time and the approaches to investigation they inaugurated. The tension between their approaches didn’t go unnoticed by their successors. Isaac Newton took a lot from Bacon and a little from Descartes; his rival Gottfried Leibniz took a lot from Descartes and a little from Bacon. Both were wildly successful. Science made the best of it, striving for deductive logic where possible, but accepting the problems of Baconian empiricism. Despite reliance on affirming the consequent, inductive science seems to work rather well, especially if theories remain open to revision.

Bacon’s idols seem to be as relevant to the boardroom as they were to the court of James I. Seekers of innovation, whether in the classroom or in the enterprise, might do well to consider the approaches and virtues of Bacon and Descartes, of contrasting and fusing rationalism and observation. Bacon and Descartes envisioned a brighter future through creative problem-solving. They broke the bonds of dogma and showed that a new route forward was possible. Let’s keep moving, with a diversity of perspectives, interpretations, and predictive models.

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Just a Moment, Galileo

Bruce Vojak’s wonderful piece on innovation and the minds of Newton and Goethe got me thinking about another 17th century innovator. Like Newton, Galileo was a superstar in his day – a status he still holds. He was the consummate innovator and iconoclast. I want to take a quick look at two of Galileo’s errors, one technical and one ethical, not to try to knock the great man down a peg, but to see what lessons they can bring to the innovation, engineering and business of this era.

Less well known than his work with telescopes and astronomy was Galileo’s work in mechanics of solids. He seems to have been the first to explicitly identify that the tensile strength of a beam is proportional to its cross-sectional area, but his theory of bending stress was way off the mark. He applied similar logic to cantilever beam loading, getting very incorrect results. Galileo’s bending stress illustration is shown below (you can skip over the physics details, but they’re not all that heavy).

Galileo's beam bending diagram

For bending, Galileo concluded that the whole cross section was subjected to tension at the time of failure. He judged that point B in the diagram at right served as a hinge point, and that everything above it along the line A-B was uniformly in horizontal tension. Thus he missed what would be elementary to any mechanical engineering sophomore; this view of the situation’s physics results in an unresolved moment (tendency to twist, in engineer-speak). Since the cantilever is at rest and not spinning, we know that this model of reality cannot be right. In Galileo’s defense, Newton’s 3rd law (equal and opposite reaction) had not yet been formulated; Newton was born a year after Galileo died. But Newton’s law was an assumption derived from common sense, not from testing.

It took more than a hundred years (see Bernoulli and Euler) to finally get the full model of beam bending right. But laboratory testing in Galileo’s day could have shown his theory of bending stress to make grossly conservative predictions. And long before Bernuolli and Euler, Edme Mariotte published an article in which he got the bending stress distribution mostly right, identifying that the neutral axis should be down the center of the beam, from top to bottom. A few decades later Antoine Parent polished up Mariotte’s work, arriving at a modern conception of bending stress.

But Mariotte and Parent weren’t superstars. Manuals of structural design continued to publish Galileo’s equation, and trusting builders continued to use them. Beams broke and people died. Deference to Galileo’s authority, universally across his domain of study, not only led to needless deaths but also to the endless but fruitless pursuit of other causes for reality’s disagreement with theory.

So the problem with Galileo’s error in beam bending was not so much the fact that he made this error, but the fact that for a century it was missed largely for social reasons. The second fault I find with Galileo’s method is intimately tied to his large ego, but that too has a social component. This fault is evident in Galileo’s writing of Dialogue on the Two Chief World Systems, the book that got him condemned for heresy.

Galileo did not invent the sun-centered model of our solar system; Copernicus did. Galileo pointed his telescope to the sky, discovered four moons of Jupiter, and named them after influential members of the Medici family, landing himself a job as the world’s highest paid scholar. No problem there; we all need to make a living. He then published Dialogue arguing for Copernican heliocentrism against the earth-centered Ptolemaic model favored by the church. That is, Galileo for the first time claimed that Copernicanism was not only an accurate predictive model, but was true. This was tough for 17th century Italians to swallow, not only their clergy.

For heliocentrism to be true, the earth would have to spin around at about 1000 miles per hour on its surface. Galileo had no good answer for why we don’t all fly off into space. He couldn’t explain why birds aren’t shredded by supersonic winds. He was at a loss to provide rationale for why balls dropped from towers appeared to fall vertically instead of at an angle, as would seem natural if the earth were spinning. And finally, if the earth is in a very different place in June than in December, why do the stars remain in the same pattern year round (why no parallax)? As UC Berkeley philosopher of science Paul Feyerabend so provocatively stated, “The church at the time of Galileo was much more faithful to reason than Galileo himself.”

At that time, Tycho Brahe’s modified geocentric theory of the planetary system (Mercury and Venus go around the sun, which goes around the earth), may have been a better bet given the evidence. Brahe’s theory is empirically indistinguishable from Copernicus’s. Venus goes through phases, like the moon, in Brahe’s model just as it does in Copernicus’s. No experiment or observation of Galileo could refute Brahe.

Here’s the rub. Galileo never mentions Brahe’s model once in Dialogue on the Two Chief World Systems. Galileo knew about Brahe. His title, Two Systems, seems simply a polemic device – at best a rhetorical ploy to eliminate his most worthy opponent by sleight of hand. He’d rather fight Ptolemy than Brahe.

Likewise, Galileo ignored Johannes Kepler in Dialogue. Kepler’s work (Astronomia Nova) was long established at the time Galileo wrote Dialogue. Kepler correctly identified that the planetary orbits were elliptical rather than circular, as Galileo thought. Kepler also modeled the tides correctly where Galileo got them wrong. Kepler wrote congratulatory letters to Galileo; Galileo’s responses were more reserved.

Galileo was probably a better man (or should have been) than his behavior toward Kepler and Brahe reveal. His fans fed his ego liberally, and he got carried away. Galileo, Brahe, Kepler and everyone else would have been better served by less aggrandizing and more humility. The tech press and the venture capital worlds  that fuel what Vivek Wadhwa calls the myth of the 20-year old white male genius CEO should take note.

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Kuhn’s Constructionist Corner

Every sinner has a futureA classic is a book that everyone has an no one reads. Or everyone wants to have read but doesn’t want to read. Or so said Mark Twain. Or so people say he said.

Two friends (count ’em, two!) read my last post on Thomas Kuhn and called me to discuss it. This is unprecedented. I didn’t really expect many people to read my random thoughts on esoterica from a half century ago. Like, geek out already. Actually, my Kuhn coverage has now been viewed 910 times. And I know that at least two of those “views” actually read it. I expect advertisers to be lining up at my door soon. Compare this to I Can Has Cheezburger. That site was getting 1.5 million hits a day in 2007.

One friend said that he had downloaded the Kindle sample of Kuhn’s The Structure of Scientific Revolutions and wasn’t able to get through more than a few pages. I should have warned my large reader base that nobody actually reads Kuhn. At least not much of it at once. Instead you mine Kuhn in the same way you mine other religious texts for statements that can be recontextualized (postmodernists love that word) to support your agenda. Seriously, it is much more fun to read about Kuhn than to read Kuhn. And Kuhn can’t hold a candle to Kuhnians – especially those Kuhnians who are rhetorically shrill. You know, the ones compelled to voice the urgency for society to choose between textual demodernism and subcultural dematerialism through a dialectic praxis paradigm that mandates art as a totality.  I’m kidding.

The other friend (I think I actually have more than two friends, but two of them called to discuss Kuhn) challenged me on my accusing Kuhn of being a constructionist. I’m aware that many Kuhn fans insist that he was nothing of the sort. I’ll accept that Kuhn shares little with many constructionists, but will stick to my guns on the claim that the term accurately describes Kuhn as he presents himself in Structure. I think this despite the fact that Kuhn denied that his remarks on world-change were aligned with constructionism. At the same time Kuhn did, however, acknowledge a parallel between his views and with Kantian idealism. (walks like a duck…). Consider a couple of quotes from Structure:

“knowledge is intrinsically the common property of a group or else nothing at all”

“the proponents of competing paradigms practice their trades in different worlds… Practicing in different worlds, the two groups of scientists see different things when they look from the same point in the same direction”

(As an example of the wide range of use and misuse of Kuhn, this quote from Structure appears in The Politics of Gender in African American Churches by Demetrius K. Williams.)

“The man who premises a paradigm when arguing in its defence can nonetheless provide a clear exhibit of what scientific practice will be like for those who adopt the new view of nature. That exhibit can be immensely persuasive, often compellingly so. Yet, whatever its force, the status of the circular argument is only that of persuasion. It cannot be made logically or even probabilistically compelling for those who refuse to step into the circle. The premises and values shared by the two parties to a debate over paradigms are not sufficiently extensive for that. As in political revolutions, so in paradigm choice – there is no standard higher than the assent of the relevant community. To discover how scientific revolutions are effected, we shall therefore have to examine not only the impact of nature and of logic, but also the techniques of persuasive argumentation effective within the quite special groups that constitute the community of scientists.” – Chapter 9 of Structures, emphasis added.

[The] most fundamental aspect of the incommensurability of competing paradigms… is that “the proponents of competing paradigms practice their trades in different worlds. – as cited in: Scott L. Pratt (2009) Logic: Inquiry, Argument, and Order.

Yes, Kuhn’s constructionism is different from that of the postmodernist moral relativists. Kuhn is complex. He rejects epistemic presumptuousness and epistemic modesty at the same time – and does so rationally. He’s part philosophical realist and part logical positivist. He is not a strong constructionist, but but he’s a constructionist of some sort. Or so thinks this amateur multidisciplinarian.

How many Kuhnian constructionists does it take to change a light bulb?
You’re still thinking in terms of incremental change, but we need a paradigm shift

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