Great moments in scientific reasoning.

@ Pat Calahan re: Math and Science

Dr. John Snow, 1813-1858, father of epidemiology and important pioneer in anesthesiology, established link between cholera and the water supply during the 1854 cholera epidemic in London, voted greatest physician of all time by British doctors.

Eratosthenes's calculation of the earth's circumference. The real breakthrough in reasoning, of course, was the Greek application of geometry to the scientific study of astronomy, and the careful collection of data for that, of which this was a salient example, but that also should include Aristarchus's calculations of the relative sizes and distances of the moon and sun, and all the other work that culminated in the Almagest.

Michelson/Morley for the destruction of the ether - demonstrates the power of negative results.

James Clerk Maxwell. Not only did he supply the term that was missing from what we now call Maxwell's equations, he showed that they implied a wave propagating at the speed of light. He went on to reason that this was not a coincidence: light is an electromagnetic wave.

Darwin (easy)

For Geology I'm torn between:
Hutton - uniformitarianism, (really kicking off Geology as a science in the late 18th century) "we find no vestige of a beginning, no prospect of an end."
and
Agassiz - putting together the story of the Ice Ages in the mid 19th century

Both men carefully constructing their arguments in the face of powerful and intractable opposition.

Thomas Young for hypothesizing trichromatic visual function in humans (even though Helmholtz really nailed it).

Hume for his exploration of inductive vs. deductive reasoning.

Wilhelm Hofmeister, 1824-1877, is considered a genius for his insights into botany, often mentioned along with Mendel and Darwin. His major publication in 1851, 8 years prior to Darwin, concluded in a major biological insight that all land plants had the same alternation of generations life cycle, an understanding that was quite remarkable given how difficult it is to see the oft misinterpreted seed plant life cycle as fundamentally the same as that of ferns, horsetails, and clubmosses. He remains very much less known because very few people have read his big German tome and, of course, he studied plants.

Thomas Morgan's chromosomal basis of heredity. Took something completely abstract (Mendel's genes) and connected them with an observable physical reality.

For more recent geology, the paper by Fred Vine and Drummond Matthews that combined the idea of magnetic reversals with the proposed idea of sea-floor spreading was brilliant, and the correspondence of the results to the theory made plate tectonics convincing.

James Lind, clinical trials of scurvy treatments.

Another vote for Darwin, for his arguments from analogy, his deductive reasoning, and his response to possible counter-arguments in the Origin of Species.

Newton for the idea that the natural state of a body without any external forces was to remain in motion.

Just to be a jerk I'd suggest Kant as a reminder that reason and deduction work more unerringly in matters of mind and the exploration of conceptual objects than they do for he empirical world. Also Albert Hofmann to counter-point as a reminder that luck and chance are big factors for the contingent (this would also give you an excuse to photocopy Doom Patrol v.2 #50 into your course reader).

Albert Michaelson, for one of history's all-time greatest failed experiments. Most of all for recognizing that we can learn more from failure than from success.

I'd suggest Archimedes. Lesson: good scientific reasoning can occur in the tub.

Newton and Leibniz for Calculus

Rutherford realising that the atom was mostly empty space with an incredibly dense and small core from an experiment using gold foil.

John Snow, in addition to cholera, should also get a vote for his anaethesia work. Essentially he provided the seminal works in two branches of medicine.

William Henry Perkin. Invented the first aniline dye (mauve/purple) which sparked off the synthetic dye and pharmaceutical industries.

Crick and Watson. Structure of DNA.

Florey Chain and Heatley for working out how to manufacture in industrial quantities Fleming's Penicillin thus saving who knows how many million lives.

I think Aristarchus, Eratosthenes, and Archimedes are all viable candidates. I would add Democritus and possibly Epicurus (although his work on atomic motion seems mostly derived from Democritus).

The Pre-Socratics always impress the hell out of me. They had no tradition to draw on, no pressing problems in search of a solution; just keen observation and a will to figure things out. Sure, they were wrong a lot, but when they were right, hoo-boy!

How about Einstein's explanation of the photoelectric effect in terms of the quantization of light as photons? I also vote for the trichromatic theory of human vision.

Walter Sutton's realization that genes are situated on chromosomes, published in 1903.

Perhaps a bit esoteric, but Georg Cantor and his diagonal proof showing real numbers not being countable is a very accessible proof that shows how you can reason about mathematics as a system - as an object of study applied to itself.

A more more esoteric example of the same type of proof would be the Halting problem proved by Turing. The most dramatic one (but probably hard to explain in simple terms) is Ernst Gödels proof showing the incompleteness of formal systems by showing how you can encode proofs into the system and applying them to themselves.

Both are examples of "breaking the frame" as it were, and using a system to reason about itself. Gödels theorem does this in a very drastic way - encoding

Lazzaro Spallanzani (1729-1799), Italian Professor of Philosophy (logic and metaphysics) who also carried out many experiments in the natural sciences. Best known for his experiments disproving the theory of spontaneous generation, but also was the first to show that actual contact between egg and semen was necessary for fertilization -- later performing the first artificial inseminations. He also was the first to demonstrate that bats navigate using their sense of hearing.

http://www.whonamedit.com/doctor.cfm/2234.html

Not Turing or Cantor or Newton or Leibniz (at least, not Newton for Calculus); that's all Mathematics... although you could make an argument for Turing as a Computer Scientist, I suppose. If you're going to stretch the contest to include Mathematics, I'd throw in Gödel's incompleteness theorems. But Mathematics ain't Science.

Not Hume or Kant, they're both Philosophy (and Hume's argument against induction only goes to show that Science isn't syllogistic logic). Anybody mention Popper and I'll explode in flames. If you're going to include Phil of Sci people, Kuhn gets the nod before Hume or Kant.

Darwin is the obvious "gotta have" one. Snow and Maxwell are good candidates, I second those. Mendel is such a graspable example that his incomplete understanding of genetics only goes to make him a better candidate for the list. Newton for Principa absolutely, not for Calculus. van Leeuwenhoek is a pretty good candidate, talk about opening a new field of observation!

So, where are the women in this list so far?

No Marie Curie, no Barbara McClintock?

I have other notable women in mind, why don't you all?

I'd like to see an economist up there. I'd say Menger/Jevons/Walras for the Marginal Revolution or Mises/Hayek for the Socialist Calculation Problem.

Grace Hopper's compiler is a pretty landmark moment in Computer Science. Marie Curie is another definite must choice.

Occurs to me I'm critiquing others' picks more than I am offering my own. Will sleep on it.

Crick and Watson got the glory, but Rosalind Franklin provided (inadvertently, via theft of her data) the hint that it was a double helix. So there's a woman for you, Peanut.

At CS school, waaay back, I was taught both the Halting Problem and Godel's Incompleteness Theorem. I have to go with Godel for this list, since it was shown to us then that the Halting Problem is one particular consequence of Godel's work*. As for lateral thinking, Godel had Principia Mathematica against him, and Whitehead and Russel (the establishment of the time) had spent their careers on the assumption of the completeness of Math.

This post is about Scientific Reasoning. Math is too Science. At least, the study of formal logic systems of which Math is a subset is a Science. It just provides its own tools, in a self-referential sort of way. And tools for the rest of us as a spin-off. Without which Science is just Philosophy, un-quantified.

* I guess I can't let that one slide with this audience. A program is equivalently considered as a Theorem in the symbolic set of all strings that are valid programs for the given system (== computer). The Halting problem is expressed by feeding a program (that can determine if any arbitrary program halts or not) to itself, with its result inverted, thus rendering the result undecideable. Which is exactly what Godel described, projected onto a CS substrate.

Realizing that all the symbolic logic I had studied could be rendered - usefully - in the form of a string production system was a fundamental step in my practical CS education. Which let me see that MI !=> MU because all the transforms in the MIU system preserve symbol count parity, therefore only even numbers of U's can be produced. So Godel's Theorem is the example of transformational Scientific Reasoning that most affected my life.

Sturtevant's genetic map.

"Newton for the idea that the natural state of a body without any external forces was to remain in motion."

Let's get the basic history right please! That was not Newton's idea at all. Most of the credit for it actually should actually go to Galileo, who did get there via some pretty nifty reasoning. Unfortunately, though, Galileo had things continuing in circular motion forever, rather than in a straight line. It was Descartes (for rather questionable reasons) who amended this to rectilinear motion, and Newton lifted his First Law from Descartes.

Newton did do quite a few impressive bits of reasoning, but I suspect most of them are too complicated and mathematical for Dr. Free-Ride's purposes.

And Marie Curie? What interesting or impressive scientific reasoning did she come up with? I do not mean to deny that she was a great scientist, but her greatness was more about dogged hard work (and about her courage as one of the first woman scientists making a career in what was then very much more of a man's world than it is today) than any particularly interesting reasoning she did. She used fairly standard purification techniques to extract the tiny trace amounts of radioactive elements from a huge mass of pitchblende. It was tough, dangerous work, but there was nothing particularly clever about it. The relevant clever reasoning, such as it was, came from her boss Becquerel.

Great moments in scientific reasoning is not at all the same thing as great achievements in science. (Especially as what Dr. F-R seems to be looking for is stuff with a nice, clean logical structure. Unfortunately, most of the most brilliant and important moments in scientific thinking were not like that at all. Indeed, it seems to me that even Semmelweis' greatness did not lie in the correct but fairly uninteresting logical structure of his reasoning, but in his skill as an observer: he noticed things, like the fact that women's survival rates were inversely proportional to the amount of medical attention they were getting, that others completely missed.)

My own top nomination would be Galileo, for his thought experiment about tying two different sized weights together. (This was how he really refuted Aristotle's ideas about falling bodies, as opposed to mythical experiments dropping weights from the Leaning Tower of Pisa, which, even if he had done it, would not have proved his point.)

I agree that Darwin was a pretty impressive reasoner, but what about his mentor Charles Lyell: for example for the way inferred the great age of Mount Etna, and then showed that by geological standards Etna must be very young.

@ Gray

Math isn't science, I have this argument all the time. Mathematics is about building logically consistent axiomatic systems, science is about deriving the natural laws of the universe from observation. The methods of investigation are different, the tools are different, the standards of quality are different.

Sure, science uses a proper subset of mathematics as tools itself, but it just uses those logically consistent axiomatic systems that happen to work well inside the natural laws of our particular universe.

Note: I'm not saying one is better than the other, any more than I'd suggest that either is better than philosophy. But they aren't the same.

@ Nigel

Your critique of Newton <- Descartes <- Galileo can be applied to almost any great scientific reasoning "event".

Everybody's work depends on what came before, even if it's just the negative results.

So that leads to the meta question: what's the criteria? Are we considering "great scientific reasoning" events in the context of the beauty of the method, the depth of the field that was exposed to observation via the event, or the significance (paradigm-shifting-wise)? Does philosophy of science count, as it is self-referential?

Barbara McClintock's discovery of transposable genetic elements is a good one.

Ada Lovelace, first computer programmer.

http://scienceblogs.com/ethicsandscience/2009/03/a_tremendous_luddite_c…

Pat, if math is not science, then neither is CS. Computer Science (the discipline, not the vocational training of the same name) is applied mathematics, and in many places was part of the department of mathematics until it got big enough to warrant its own department.

The question wasn't about science in any case, but examples of scientific reasoning. Which can be, and is, applied in mathematics, CS and other fields whether one considers them sciences or not.

> If math is not science, then neither is CS.
> Computer Science ... is applied mathematics

That's an interesting philosophical point; I probably agree, but I'd have to think about it some more. Computer Science can be applied math, computational theory, or even engineering depending upon your particular emphasis, so even as a field it doesn't have high cohesion.

> The question wasn't about science in any case,
> but examples of scientific reasoning.

That's absolutely a fair point, but...

> Which can be, and is, applied in mathematics,
> CS and other fields whether one considers
> them sciences or not.

I'm not so sure I agree with this. I definitely don't agree in the case of pure math; like I said above the methodology and tools are different.

Cosmic Variance explained it pretty well here: http://blogs.discovermagazine.com/cosmicvariance/2007/04/11/what-i-beli…

I wrote about it here:
http://padraic2112.wordpress.com/2007/09/28/mathematics-is-not-a-scienc…

... and it's been bandied about on various other sites.

The entire method of theory building in theoretical mathematics is basically completely different from theory building in science. People who argue that they're the same are usually thinking only of applied mathematics (cryptography and calculus spring to mind).

I agree that deriving a formula is applied math, and the act of derivation from empirical data is science, just like the act of applying statistics is applied math, and applying statistics is usually done in science. Certainly there's historical incidents of people coming up with applied math (again, Calculus springs to mind) years before the mathematical theory existed to explain how it worked, in the axiomatic systems sense. There's a lot of fuzzy boundaries there.

Hm; I'm going around the maypole here, I blame fatigue. I've been sick for a few weeks and I'm not getting enough sleep.

Let me put it this way; I've asked plenty of mathematicians when they thought Calculus was an acceptable theory, and none of them said *anything* about when Newton or Leibnitz wrote it up. They all talked about Weierstrass, Bolzano, and Cauchy (among others)... without whom the entire concept of correctness was completely missing from Calculus.

In other words, mathematicians don't consider things to reach theory stage until they can be quantified somehow inside an axiomatic system. Scientists consider things to be a theory when massively sufficient observational evidence exists that conforms best to that theory rather than some other candidate (without falsification, of course). Popper and Hume both tried to wedge logical truth onto science and came away saying that induction didn't work, instead of realizing that syllogistic logic isn't the right tool to describe the workings of science.

Lots of people will probably regard this is pedantic and an unnecessary distinction, but I disagree.

But then again, I'm a gigantic nerd; and at any rate this is the sort of discussion that is properly executed over beers, wine, or scotch with a bunch of other slightly inebriated and overly opinionated nerds. :)

You really should assign Watson's The Double Helix on your syllabus (perhaps you already do). It can serve double-duty for both your scientific reasoning module as well as your ethics module!

I don't know much about the actual line of reasoning she used in the original derivation, but I'd guess that Emmy Noether would be a good candidate for Noether's theorem.

@ Pat Calahan

I agree that there is a fundamental difference between math and science. however, i think there is due to the work Goedel and Turing on incompleteness and the decision problem that often the methods of mathematics and the methods of science are much closer than they are normally thought of however, mathematics holds a much higher standard of what constitutes proof (there's a good chapter in David Deutsch "the Fabric of Reality" about this)
I think the big difference lies in the standard of a completed idea(I could use Proof or Theorey or Theorem, but I don't want to boggle down this already hazy idea of what I'm trying to say with unintended consequences of those words). in science an idea is complete if it is repeatable and has explanatory power. in mathematics an idea has been completed when it is shown to follow logically from other completed ideas. The big difference is, in math i cant just say "Newton was wrong here and it actually works like this" because Newton's mathematical reasoning is solid and hence the math is objectively true, but thats because it has no meaning to the real world when its just math, it is all about the relationships between objects regardless of the objects themselves. Whereas in science you are forced to be talking about things that exist forcing you into an existential crisis and you are looking for models of behavior. if you find a better model for say "Gravity" then the old one may still be useful in gaining concepts, but it is not "true" anymore, at best it becomes a special case of a more general law, if it is lucky enough not to just get replaced.

but when looking at reasoning, i think the great mathematical minds should stand beside the great scientific minds, and not only because many of them are the same minds but also because the reasoning is similar and complementary. when mathematicians and scientists work together we get both better math and better science.

but thats just my quick late night thoughts on the matter, I think it is certainly a question that needs more thought and discussion on all sides.

@ Galen

> If you find a better model for say "Gravity"
> then the old one may still be useful in
> gaining concepts, but it is not "true" anymore...

But that's (part of) the point; it was never "true" to begin with. It was useful, it was correct inside the boundaries of the model proposed. It still is useful, it still is correct inside the boundaries of the model proposed. The model proposed suffers from a completeness problem, sure, but if there's anything we can state with reasonable certainty when it comes to science... it's that whatever theory we're talking about is going to suffer from a completeness problem.

This is why Popper makes me nuts. "Induction doesn't work, because you don't know for sure that your model is correct! But universal concepts still exist and we should try and find them!"

Induction *does* work (if it didn't, it would be perfectly reasonable for anyone to walk up to Popper and shoot him, 'cause, whoops, we can't say that it will work, we can only say it won't!). Induction only works inside of the model you're talking about, though. When you find a case of induction "not working", it's because *the model* is broken or limited, not induction.

Okay, after musing for a few days I'll admit I'm ignoring Popper's insistence on falsification, and that's worthy of note in and of itself.

Someone asked about _women_ who have contributed significant moments in scientific reasoning, so I'll nominate a few. First I'll nominate Lynn Margulis for reasoning endosymbiosis from direct observations in microbiology and pushing the idea through against repeated overwhelming resistance. Also Candace Pert, for reasoning out the mechanisms of opiate receptors. Elaine Morgan probably should be considered as well, for her ingenious reasoning from evidence, although her Aquatic Ape theory does not enjoy the consensual success that Margulis and Pert's theories have had.

I was most impressed by Mendeleev's leaving gaps in the first editions of the periodic table, and having his reasoning confirmed when the missing elements were later discovered.