"History has many ironies. The time-bomb in Gauss's curve is that after his death we discover that there is no God's eye view. The errors are inextricably bound up with the nature of human knowledge. And the irony is that the discovery was made in Göttingen." (Bronowski, 1973, The Ascent of Man, p. 360)
|Portrait of Bronowski from the back cover of his book.
Right panel shows the front cover.
Biography from Enclopaedia Britannica:
Bronowski, Jacob. b. Jan. 18, 1908, Poland. d. Aug. 22, 1974, East Hampton, N.Y., U.S.
Polish-born British mathematician and man of letters who eloquently presented the case for the humanistic aspects of science.
While Bronowski was still a child, his family immigrated to Germany and then to England, where he became a naturalized British subject. He won a scholarship to the University of Cambridge, where he studied mathematics. He not only achieved high honours in mathematics but also received critical acclaim for his poetry and prose. After receiving his Ph.D. (1933) from Cambridge, he taught mathematics (1934-42) at the University College of Hull. During World War II Bronowski pioneered in a field now known as operational research and worked to increase the effectiveness of Allied bombing. After the war he headed the projects division of UNESCO (1948) and then worked for Britain's National Coal Board (1950-63).
When Bronowski, on a scientific mission to Japan to study the effects of the atomic bombings (1945), saw firsthand the ruins of Nagasaki, he gave up military research. From that time on, he concentrated on the ethical as well as the technological aspects of science, and he shifted his attention from mathematics to the life sciences, the study of human nature, and the evolution of culture.
Among his books are The Common Sense of Science (1951) and the highly praised Science and Human Values (1956; rev. ed. 1965). In these books Bronowski examined aspects of science in nontechnical language and made a case for his view that science needs an ethos in order to function. In The Identity of Man (1965) he sought to present a unifying philosophy of human nature. He also wrote William Blake, 1757-1827: A Man Without a Mask (1943), revised as William Blake and the Age of Revolution (1965), and four radio plays.
From 1964 until his death Bronowski was a resident fellow of the Salk Institute of Biological Sciences (San Diego, Calif.). His last major project was the authorship and narration of the BBC television series The Ascent of Man (1973), a luminous account of science, art, and philosophy in human history.
In Chapter 11 of The Ascent of Man, entitled "Knowledge or Certainty", Jacob Bronowski describes the conflict between dogmatic claims to absolute knowledge, and scientific claims regarding inherently uncertain theory. I first saw this episode of the series on 16mm film at the Summer Science Program in Ojai CA, in 1978, when I was 16. Ojai is not too terribly far from the Salk Institute where Bronowski worked, but 1978 was an eternity from 1974 when Bronowski worked there. This episode was included in the SSP curriculum by the Academic Director, Dr. David Pierce. I've watched the episode many times since, and have shown it to every one of my annual classes on Statistics in Psychology. I feel that my presentations of the film suit Bronowski's legacy, because his message is presented in the context of the "study of human nature" (i.e., psychology), by a professor (me) who turned to cognitive science after an undergraduate career in astronomy, physics and mostly mathematics.
Filming for the BBC production of The Ascent of Man was
finished in 1972; the book was published in 1973. Bronowski died in
1974, when I had not yet turned 13 years old. I never heard him speak
in person, but I heard him speak in his video series, and his words
and expression have resonated in me. Ever since seeing "Knowledge or
Certainty", I have wanted to visit Göttingen, which is where much
of the episode is set. Since then I have discovered professional
colleagues working in Göttingen, further enhancing my desire to
visit. I finally had the opportunity in January, 2001, when I was
invited to speak at the 100th Anniversary Celebration of Humboldt
University in Berlin. I took the train to Göttingen from Berlin,
and back again. The train to Berlin is a thematic device in
Bronowski's presentation, as will be described below.
|The Altes Rathaus.|
The center of Göttingen is the old rathaus (Altes Rathaus), shown in the photograph at the right. (The photo is from a tourism brochure; when I was there in January it was cold and not so sunny.) My hotel, aptly named the "Hotel Central", was only a couple blocks away, in the direction of the lower right in the photograph.
"Ancient university towns are wonderfully alike. Göttingen is like Cambridge in England or Yale in America: very provincial, not on the way to anywhere - no one comes to these backwaters except for the company of professors. And the professors are sure that this is the centre of the world. There is an inscription in the Rathskeller there which reads `Extra Gottingam non est vita', `Outside Göttingen there is no life'. This epigram, or should I call it epitaph, is not taken as seriously by the undergraduates as by the professors." (Bronowski, p. 360)
I had forgotten where Bronowski said this epigram was posted, so I asked my academic colleagues where to find it, but none of them knew. They were amused that such a saying existed, because their own existences are quite different. In these modern times, people commute from city to city much more readily. Perhaps that is why Bronowski called it an epitaph. I called the local tourism bureau, and after pondering for a moment, the woman on the phone told me where to find the inscription, and it turned out to be right where Bronowski reported. The entrance to the Rathskeller is under the awning in the photograph above, on the right end.
|The inscription in the entrace of the Rathskeller.|
The photographs above show that the painted inscription is still
there, almost 30 years later. But Bronowski abbreviated it in his
report! Jörn Dieterich informed me later (in May of 2003 after
we met at the Associative Learning Conference in Gregynog, Wales,
U.K.) that the continuation, "Si est vita, non est ita," means "if
there is life outside, it's not as good." (Jörn also told me that
the author of the phrase is/was named August Ludwig von
"The symbol of the University is the iron statue outside the Rathskeller of a barefoot goosegirl that every student kisses at graduation. The University is a Mecca to which students come with something less than perfect faith. It is important that students bring a certain ragamuffin, barefoot irreverence to their studies; they are not here to worship what is known but to question it." (Bronowski, p. 360)
I'm told by my colleagues that one reason Göttingen became home to so many famous scientists (42 Nobel prize winners have studied or taught here) was that Göttingen was the first university in Germany to have no ties to the Church. The professors were not hindered by restrictions on research imposed by the Church. It wasn't just the students who came with less than perfect faith.
respects to the Goosegirl statue.
(The photo at left is from Bronowski's book, p. 363. The middle two photos are my own, taken about 5pm, after dark.
Because it was so dark at the time, I had to electronically enhance the background to make it visible.
The photo on the right is of an anonymous graduate, from a tourism brochure.)
The goosegirl fountain (Das Gänseliesel) is located in the plaza
in front of the Rathaus (see the photograph of the Rathaus, above). I
paid my respects to the statue and to the great intellects she has
looked down on, although I did not go barefoot (it's cold in January!)
or kiss it (alas, I'm not a graduate). The square is a hangout for
teenagers, and the rim of the fountain is replete with young people
apparently oblivious to the brilliant minds who have passed through
this square. But one young woman was kind enough to interrupt her
conversation and take my picture. "Kein problem", she said, before
getting back to chatting with her friends on the rim of the fountain.
It was tremendously invigorating to "talk shop" with colleagues at the University. Professor Michael Waldmann and his collaborators and students were wonderful hosts, both intellectually and personally (see photograph below).
|Seated at dinner are York Hagmayer, Michael Waldmann, myself, and Michael Hildebrandt.|
The literature is full of debate between the causal model approach, championed by Waldmann, and the associative approach, championed by others (and members of both camps would probably call me an associationist). But I believe that the mind is a busy place, with a variety of representations and processes available for use. I believe that both association building and causal modeling are happening in the mind. The real challenge for cognitive scientists is to determine which processes are used in what situations, and how the processes interact. In particular, I believe that the attentional effects that fascinate me, and which I couch in an associative framework, should have analogous effects within causal models. Perhaps, someday, there will be created a unifying framework in which both the associationist and causal model perspectives are understood as special cases, both obeying the same principles.
Although we work in cognitive science, the exchange of ideas in
physics was largely the same, according to Bronowski's description
(pp. 362-363): "And from all over the world people came to
Göttingen to join in. It is rather strange to talk in these terms
about a subject which, after all, is done by midnight oil. Did physics
in the 1920s really consist of argument, seminar, discussion, dispute?
Yes, it did. Yes, it still does. The people who met here, the people
who meet in laboratories still, only end their work with a
mathematical formulation. They begin it by trying to solve conceptual
riddles. ... Think of the puzzles that the electron was setting just
at that time. The quip among professors was (because of the way
university time tables are laid out) that on Mondays, Wednesdays, and
Fridays the electron would behave like a particle; on Tuesdays,
Thursdays, and Saturdays it would behave like a wave. How could you
match those two aspects, brought from the large-scale world and pushed
into a single entity, into this Lilliput, Gulliver's Travels
world inside the atom? That is what the speculation and argument was
about. And that requires, not calculation, but insight, imagination
--- if you like, metaphysics."
Henning Gibbons also provided some fascinating conversation. He showed me the procedures his lab has used to assess latent inhibition and learned inattention. We might try adapting some of his techniques to the task of assessing learned inattention in blocking and the inverse base rate effect. My goal is to get multiple measurement methods that all converge on the same idea: There is learned (in-)attention in various learning situations. But of course there is no direct way to assess attention, and this problem is also at the core of Bronowski's message (p. 356): "We are here face to face with the crucial paradox of knowledge. Year by year we devise more precise instruments with which to observe nature with more fineness. And when we look at the observations, we are discomfited to see that they are still fuzzy, and we feel that they are as uncertain as ever. We seem to be running after a goal which lurches away from us to infinity every time we come within sight of it."
In the evening, it was fun to see the total lunar eclipse from Göttingen. As the map below shows, if I were home in Indiana, I would not have been able to see the eclipse, as the moon would only be rising at the very end of the eclipse. When we stepped into the restaurant for dinner, the eclipse was about midway between phases marked U1 and U2. When we stepped out of the restaurant after dinner, the eclipse was about midway between U3 and U4.
(Strange how some trips are coincidentally marked by astronomical events. When I was invited to speak in London, on August 11, 1999, there was a total solar eclipse visible from the southwest tip of the UK, almost total from London...)
|Lunar eclipse info.|
Despite the beauty and rarity of a total lunar eclipse, and despite my interest in astronomy (I have wonderful memories of viewing a deep red full moon, in total eclipse near the red star Antares in Scorpio, from my backyard as a child), we did not interrupt our dinner to step outside and view the eclipse at its peak, totality. This inattention reflects our modern times. An event that once inspired deep anxiety or horror (Acts 2:20: The sun shall be turned into darkness, and the moon into blood, before that great and notable day of the Lord come. Revelations 6:12: And I beheld when he had opened the sixth seal, and, lo, there was a great earthquake; and the sun became black as sackcloth of hair, and the moon became as blood.) is now treated as innocuous, largely because of scientists.
And there is another link between astronomical events in
Göttingen and Bronowski:
|Gauss on the 10 DM bill.
Notice the Gaussian curve,
complete with equation,
and the drawing
of the observatory
"The paradox of knowledge is not confined to the small, atomic scale; on the contrary, it is as cogent on the scale of man, and even of the stars. Let me put it in the context of an astronomical observatory. Karl Friedrich Gauss's observatory at Göttingen was built about 1807..." (Bronowski, p. 358)
As a child, my parents indulged my interest in astronomy by taking me to many observatories, such as Palomar observatory in southern California, Lick observatory in northern California, Lowell observatory in Flagstaff Arizona, the Naval Observatory in Washington D.C., among others. I was excited to continue my collection of observatory visits here in Göttingen, by experiencing the one in which Gauss worked.
Gauss is revered in Germany (as elsewhere), to such an extent that his image is on the most exchanged currency, the 10 DM bill (I suppose the rough equivalent is Lincoln on the American $5 bill). The picture at right shows that not only is his portrait on the bill, but so is the observatory and the formula for the Gaussian curve! I doubt there is any other currency in the world that commemorates a mathematical formula.
I had a chance to visit the observatory in the later afternoon, after it was already dark. The gate to the grounds was closed but unlocked, as was the front door to the observatory building itself. I let myself in. There was a light in the small library down the hall, but otherwise only the foyer was dimly illuminated. I crept up the narrow, winding stairway, which got darker and darker. At the top was another closed but unlocked door, with an ancient hand-scrawled note (in German, of course) peeling off the front. The combination of darkness, fading tatters and foreign language made it impossible for me to read. I let myself into a completely invisible room. My hand groped along the wall for a light switch. Finding none, I snapped a picture ("mit blitz") so the flash could reveal what lay hidden in the darkness. Emblazened on my eyes was the telescope and observer's chair, on which Bronowski leaned in his video.
Eventually I found a light switch, and leisurely viewed the room,
although the light was still very dim. The room was in
disrepair. Obviously it had not been used in a long time, either for
research or for tourism. But the fact that the room was preserved in a
state from decades ago made it feel like I had stepped through the
darkness and back in time. I stood there for a while, trying to feel
the faint echoes and wisps of the ghosts of Gauss and Bronowski.
|Street sign encountered on the way to the observatory.|
On the way to the observatory, in front of the Nues Rathaus, I unexpectedly encountered a street named Hiroshimaplatz. I have no idea why the street is so named, but I wouldn't be surprised if there is some connection with Bronowski:
"The first atomic bomb was dropped on Hiroshima in Japan on 6 August 1945 at 8:15 in the morning. I had not been long back from Hiroshima when I heard someone say, in Szilard's presence, that it was the tragedy of scientists that their discoveries were used for destruction. Szilard replied, as he more than anyone else had the right to reply, that it was not the tragedy of scientists: `it is the tragedy of mankind'." (Bronowski, p. 370)
Bronowski changed the setting to another place in Germany, and continued with the following remarks:
It is said that science will dehumanize people and turn them into
numbers. That is false, tragically false. Look for yourself. This is
the concentration camp and crematorium at Auschwitz, this is where
people were turned into numbers. Into this pond were flushed the ashes
of four million people. And that was not done by gas. It was done by
arrogance. It was done by dogma. It was done by ignorance. When people
believe that they have absolute knowledge, with no test in reality,
this is how they behave. This is what men do when they aspire to the
knowledge of gods. ¶ Science is a very human form of
knowledge. We are always at the brink of the known, we always feel
forward for what is to be hoped. Every judgment in science stands on
the edge or error, and is personal. Science is a tribute to what we
can know although we are fallible. In the end the words were said by
Oliver Cromwell: "I beseech you, in the bowels of Christ, think it
possible you may be mistaken." ¶ ... We have to cure ourselves
of the itch for absolute knowledge and power. We have to close the
distance between the push-button order and the human act. We have to
touch people. (p. 374)
|Map of Göttingen.|
So where are all these sites? The Goosegirl (Gänseliesel) fountain and Altes Rathaus are located by the information "i" symbol just below the center of the map. My hotel (Hotel Central, not marked) is located a block to the right of the Rathaus on Jüdenstrasse. The observatory (Sternwarte) is located at the bottom right of the map. The Psychology Department is not marked, but is located near the top right of the map, on Gosslerstrasse across the street from the Blauer Turm.
The train station (Bahnhof), where I arrived and departed on the train connecting with Berlin, is at the middle left.
"The link between Göttingen and the outside world was the railway. That was the way the visitors came from Berlin and abroad, eager to exchange the new ideas that were racing ahead in physics. It was a by-word in Göttingen that science came to life in the train to Berlin, because that is where people argued and contradicted and had new ideas. And had them challenged, too. ... When Hitler arrived in 1933, the tradition of scholarship in Germany was destroyed, almost overnight. Now the train to Berlin was a symbol of flight. Europe was no longer hospitable to the imagination - and not just the scientific imagination. A whole conception of culture was in retreat: the conception that human knowledge is personal and responsible, an unending adventure at the edge of uncertainty." (Bronowski, pp. 362, 367)
Bronowski's point came alive for me in Berlin, when I listened to my scientific colleagues who have experienced the cold war and recent reunification of Germany. I saw the place where, in 1933, books were burned in the midst of Humboldt University. After the war, Humboldt University was behind the wall in East Berlin, and I heard of the restrictions imposed upon faculty by the Soviet regime. I learned of the splintering of Humboldt University into the Free University in West Berlin, and of the current struggles to re-open collaboration between the two.
It was quite a privilege to visit Göttingen and Berlin, and to talk with colleagues about their work. For me the trip was a wonderful combination of prospects for future research and respects for past efforts. It was a reaffirmation that Bronowski's humanistic ideals are thriving, and that they cannot be taken for granted.