Criticism and the Growth of Knowledge. Edited by I. Lakatos and A. Musgrave. Pp. viii, 282. £3·50, paperback £1. 1970. (Cambridge University Press.)

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

'When I was your age,' my father was fond of telling me, 'I used to walk 5 miles through a foot of snow just to go to school.' I was impressed for a while, until I noticed that, as he got older, the distance got longer and the snow got deeper. Eventually, he claimed to have walked 20 miles through 6 feet of snow. I became even more suspicious when I found out from my grandmother that they had lived three blocks from school.

In an age of school buses and car-pooling parents, such stories, whether believable or not, conjure up visions of a world almost beyond the imaginations of today's children. I was reminded of that today by an email from my friend and Brandeis colleague Tom Pochapsky, who directed my attention to a fascinating article on the website of Beloit College (http://www.beloit.edu/mindset/2014.php). Each August since 1998, Beloit College has released the Beloit College Mindset List, which provides a look at the cultural background of the students entering college that fall. The creation of Beloit's Keefer Professor of the Humanities Tom McBride and former Public Affairs Director Ron Nief, it was originally created as a reminder to the Beloit faculty to be aware of dated references. As the website notes, 'it quickly became a catalog of the rapidly changing worldview of each new generation.'

So what's the worldview of the class of 2014? According to the latest list, here are a few of the things these 18-year-olds, born in 1992, have experienced - and not experienced:

• Few in the class know how to write in cursive.

• They find that email is just too slow, and they seldom if ever use snail mail. They text. Oh, God, do they text.

• To them, Clint Eastwood is better known as a sensitive film director than as vigilante cop Dirty Harry.

• For them, Korean cars have always been a staple on American highways.

• They've never recognized that pointing to their wrists was a request for the time of day.

• In their world, Czechoslovakia has never existed. There was no Berlin Wall, the Iron Curtain is a meaningless phrase, and Russia has never had a Communist government.

• There has never been a world without AIDS.

• The Beatles and the Rolling Stones are classical music.

• Toothpaste tubes have always stood up on their caps.

• There have always been women priests in the Anglican Church.

• Having hundreds of cable channels but nothing good to watch has always been the norm.

• The US public has never approved of the job the US Congress is doing.

• Most of them have never seen a long-playing record, or even a tape drive. If they have ever seen a typewriter, it was in a museum, possibly alongside a dial telephone.

• They have never lived in a world without personal computers, the Internet, CD-ROMs or laser printers.

There are, of course, many things they have experienced that we also experienced at the same age. Among these are automobiles, jet airplanes, color television sets, and the Chicago Cubs not having won the World Series. Another commonality has been the enduring hostility between the English and the French.

But they couldn't imagine life without PopTarts, juice boxes, and movies you can have on your home TV, and they have no idea how we could have survived in a world that required carbon paper.

All of which got me wondering: what would the scientific worldview be like for someone, let's say, just starting graduate school today (and therefore about 22 years of age)? Born in 1988, how would their scientific lives differ from the lives of the generations preceding them (including mine, which is the only one I really care about)? It makes for some interesting speculation:

• For today's budding biologists, DNA fingerprinting would have always existed. Actual fingerprinting would have been a recent invention, used primarily to secure laptop computers.

• Protein crystal structure determination would for them never be anything but a routine tool.

• Molecular biology would never have been a discipline in its own right. Instead, it would always have been a set of techniques, introduced to students in better high schools.

• They cannot imagine a world without kits to make experiments virtually automatic.

• Since the first free-living organism had its genome sequenced when they were 7 years old, they have grown up in the age of genomics. They have had access to the complete sequence of the human genome since they were in middle school.

• They have never attended a lecture given with slides from a carousel projector, and they may not have ever seen one given from overhead transparencies either. PowerPoint has been in use for virtually their entire lives.

• In their lifetime, no one has ever pipetted anything by mouth.

• DNA sequencing, peptide synthesis, chemical analysis, and gene synthesis have always been farmed out to specialty companies rather than done in one's own lab.

• They have almost certainly never seen anyone blow glass. In fact, many of them may not know that test tubes were ever made of anything but plastic.

• They have always had the option of going into the biotechnology industry.

• The term 'enzyme' has always referred to both protein and RNA.

• Evolution has always been under attack, and science and religion have largely been seen as incompatible.

• There have always been 'big science' projects in biology.

• Chemistry has always been a declining field in terms of student interest, and physics has always been the province of a small number of practitioners.

• Believe it or not, they have never known a world without cDNA microarrays.

• For them, 'Xerox' is a verb, Polaroid makes LCD TVs, and every piece of equipment is computer-controlled.

• They have never requested a reprint. They probably don't know what one is.

• They believe that no science was done before 2000. Any science not indexed on PubMed was not done either, even if it was done yesterday.

• They cannot imagine that there once was only a single Cell journal, and just one Nature as well.

I'm sure you could think of lots more. I know I could, but we had 10 feet of snow last night, and that 50-mile walk to school is going to take me a while.

The past is a foreign country.

By the author of the acclaimed bestseller 'Benjamin Franklin', this is the first full biography of Albert Einstein since all of his papers have become available. How did his mind work? What made him a genius? Isaacson's biography shows how his scientific imagination sprang from the rebellious nature of his personality. His fascinating story is a testament to the connection between creativity and freedom. Based on newly released personal letters of Einstein, this book explores how an imaginative, impertinent patent clerk - a struggling father in a difficult marriage who couldn't get a teaching job or a doctorate - became the mind reader of the creator of the cosmos, the locksmith of the mysteries of the atom and the universe. His success came from questioning conventional wisdom and marveling at mysteries that struck others as mundane. This led him to embrace a morality and politics based on respect for free minds, free spirits, and free individuals. These traits are just as vital for this new century of globalization, in which our success will depend on our creativity, as they were for the beginning of the last century, when Einstein helped usher in the modern age.

https://physicstoday.scitation.org/doi/pdf/10.1063/1.2812127

Einstein: His life and universe.

The collected papers of Albert Einstein.

This essay takes a close look at specially selected features of the Gottingen mathematical culture during the period 1895–1920. Drawing heavily on personal accounts and archival resources, it describes the changing roles played by Felix Klein and David Hilbert, as Gottingen's two senior mathematicians, within a fast-growing community that attracted an impressive number of young talents. Within the course of these twenty-five years Gottingen exerted a profound impact on mathematics and physics throughout the world. Many factors contributed to the creation of a special atmosphere that served as a model for several other important centers for mathematical research. Gottingen exemplified a dynamic new way of doing mathematics within a highly competitive community in which the spoken word often carried more weight than did information conveyed in written texts. This oral dimension of the Gottingen culture played an important, till now overlooked role in the early development of Einstein's general theory of relativity.

Making Mathematics in an Oral Culture: Göttingen in the Era of Klein and Hilbert

In recent years there has been a growing interest among historians and philosophers of mathematics in the history of logic, set theory, and foundations.1 This trend has led to a major reassessment of early work undertaken in these fields, particularly when seen in the light of motivations that animated the leading actors. The present volume may thus be seen as a reflection of this renewed fascination with the work of Hilbert, Brouwer, Weyl, Bernays, and others, an interest that stems in part from the desire to understand the historical and intellectual context that inspired their investigations. With regard to Hilbert, it has been my contention for some time that his stance in the acrimonious foundations debates of the 1920s has tended to reinforce a quite misleading picture of his actual views on the nature of mathematical knowledge. In particular, I have argued that the main tenets of Hilbert’s “formalist program” of the 1920s represent only a portion of his mature “philosophy” of mathematics, as should be readily apparent from the views Hilbert set forth in his 1919-20 lectures “Natur and mathematisches Erkennen” [Hilbert 1992].2

The Calm Before the Storm: Hilbert’s Early Views on Foundations

Einstein's initial fame came in late 1919 with a dramatic breakthrough in his general theory of relativity. Through a remarkable confluence of events and circumstances, the mass media soon projected an image of the photogenic physicist as a bold new revolutionary thinker. With his theory of relativity Einstein had overthrown outworn ideas about space and time dating back to Newton's day, no small feat. While downplaying his reputation as a revolutionary, Einstein proved he was well cast for the role of mild-mannered scientific genius. Yet fame demanded its price. Surrounded by social and economic unrest in Berlin, he was caught between two worlds, one struggling to be born, another refusing to die. Far from withdrawing, he threw himself into the political fray to become a symbol for international reconciliation during the early Weimar Republic. A decade later, his public image acquired another layer when he re-emerged as a Stoic sage and selfless humanitarian, a quasi-religious figure who saw himself as a modern-day Spinoza. Focusing on events of this period and the role of the German media in portraying them, this essay highlights the scientific and political undercurrents that drew Einstein into the public eye at a critical juncture in European history. Its broader aim is to show the import of these themes within the context of the vast literature on Einstein as well as the larger historiography of science.

Einstein and Relativity: What Price Fame?

One of the most famous episodes in the early history of general relativity involves the “race” in November 1915 between Albert Einstein and David Hilbert to uncover the “correct” form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Gottingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Gottingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.

Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

Already as a student in Bonn, Felix Klein was exposed to model-making through his teacher, Julius Plucker, who used models to visualize the properties of special surfaces that arise in line geometry. Afterward, Klein attended Kummer’s seminar in Berlin, where he began to explore the connections between general Kummer surfaces and so-called complex surfaces, first studied by Plucker. In the late 1870s, Klein and Alexander Brill supervised the work of several students at the Munich Technische Hochschule who designed a large collection of models there. There followed a new era in model production, based in Munich but marketed through the Darmstadt firm owned by Brill’s brother. By 1900 the plaster models of L. Brill could be found at leading universities around the world. Our story here centres on Kummer’s famous models, which began as research artefacts in Berlin, before passing to Munich and then proliferating to points beyond.

David E. Rowe

Papers

Making Mathematics in an Oral Culture: Göttingen in the Era of Klein and Hilbert

The Calm Before the Storm: Hilbert’s Early Views on Foundations

Einstein and Relativity: What Price Fame?

Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

Mathematical models as artefacts for research: Felix Klein and the case of Kummer surfaces