Blogs / Cosmic Variance

Greetings from Down Under! Current at the CosPA conference in Melbourne, after spending a couple of days in Sydney — a brief fling through Adelaide up next.

It’s been a mixed bag so far; while I’ve had great fun interacting with people here in Australia, I’ve also been struggling with a nasty cold I picked up on the flight over. Spent yesterday mostly in bed, too fogged up to even work on my talk for Friday. But when I’ve had the strength to be up and about, it’s been a treat. Here’s an iPhone snap of the University of Sydney; that clocktower in the middle houses, appropriately enough, the Centre for Time.

One of the perks of civilization that hasn’t quite caught on in these parts is affordable internet access in hotel rooms, so don’t expect a lot of blogging over the next week or two. Instead, I can point you to a couple of recent videos. One is an extended interview for Edge, entitled Why Does the Universe Look the Way it Does? It is an interview (presented in text and video), not a carefully pre-planned document, so not all thoughts are arranged as elegantly as one might like. Here is some of the flavor:

We are in a very unusual situation in the history of science where physics has become slightly a victim of its own success. We have theories that fit the data, which is a terrible thing to have when you are a theoretical physicist. You want to be the one who invents those theories, but you don’t want to live in a world where those theories have already been invented because then it becomes harder to improve upon them when they just fit the data. What you want are anomalies given to us by the data that we don’t know how to explain.

The other one is a panel discussion on Time Since Einstein, from the World Science Festival. As the description there says, it features Roger Penrose, David Albert, and some other people it would be too exhausting to list individually. Here’s part 1 of 5:

World Science Festival 2009: Time Since Einstein, Part 1 of 5 from World Science Festival on Vimeo.

Now if only my immune system would finish off the little viral buggers inside me, I could get out and see a bit of this interesting country.

So, a few weeks ago we all got an email here at cosmic variance inviting us to the first ever “NASA tweetup” for the next Shuttle Launch. Sean and Mark are in Australia and JoAnne is in Egypt, and Julianne is a launch veteran… but Daniel and I decided that it was too good of an opportunity to pass up. This is despite the fact that neither of us actually knew what a tweetup was, or had ever tweeted before…

So we rearranged our schedules, met yesterday in Denver, woke up at 6 am this morning, and are now at Kennedy Space Center with 100 space twitterers. They’ve got a full program here with astronauts and a tour today, and the launch of mission STS-129 to the space station at 2:29 pm tomorrow. The event just started… So stay tuned, we’ll keep you posted. We will be blogging as well as loosing our tweeting virginity @cosmicvariance. You can follow the rest of the gang by looking for #nasatweetup.

Later today I hop in an airplane to fly to the antipodes, or at least to Australia. (The actual antipodes would be in the middle of an ocean.) Looking forward to it, as this will mean I’ve visited every non-Antarctic continent at least once.

But the reason I’m blogging about it is because I’ll be giving some public talks, and it would be great if any local CV readers dropped by to say hi. I’ll be hitting three different cities:

• Monday 16 November: Sydney
• Friday 20 November: Melbourne
• Monday 23 November: Adelaide

With all these public talks in a row, you would almost think I’m touring in support of some sort of book. That was part of the original idea, but now the book won’t be officially released until January 7. So instead I’ll just be talking in support of … Science! And trying to stay clear of dangerous creatures.

p.s. Wow, I almost did an incredibly boneheaded thing by showing up at the airport without a visa. Why in the world do you need a visa to go from the USA to Australia? I thought it was like a southern version of Canada. Fortunately, when you check in online you get “reminded” that a visa is required; even more fortunately, there is an online instant-visa service that seems to work. This is why I’m a theoretical physicist and not put in charge of anything important.

As I mentioned in my last post, it has been a busy few weeks. In addition to my citizenship interview, I’ve also been traveling to deliver some talks and attend some meetings, as well as attending to all the usual requirements of my job, such as teaching.

Now that I’m basically settled at Penn, I’ve been focused primarily on working on some exciting new projects, while also trying to bring to completion a lot of different research projects that have been languishing somewhat as I got myself settled. I think most of these are back on track now (although some of my collaborators, whose Skype calls I’ve moved several times, may have a different opinion), which is a nice feeling to have after a few months of concerted effort. I even managed to get a conference proceedings finished. I’ll probably post about some of these projects when they’re done.

But over the last few weeks, I’ve also been traveling a little, starting with a colloquium at the University of Wisconsin, Milwaukee, where I talked about modifying gravity to a very knowledgeable audience, and where I was treated to a wonderful (and very late) Friday night out, courtesy of Luis Anchordoqui and Patrick Brady, to whom I owe many thanks. That trip was followed by a colloquium at NASA Goddard Space Flight Center, which seems to employ an inordinate number of people I went to graduate school with. I certainly enjoyed the talk, but particularly enjoyed the meetings they had set up for me during the day. I learned about the long-term possibility of using observations of gravitational wave sources by the LISA experiment, accompanied by optical follow-ups, as a new way to construct a Hubble diagram to trace the cosmic expansion history. While not feasible right now, I found this a fascinating possibility for the future, and I’m hoping that our resident expert may tell us more about it some time.

My final two trips of the recent period were both to New York, and both to NYU. The first was to deliver a seminar at the Center for Particle Physics and Cosmology. The second was for the first of a set of one day meetings that the Center for Particle Cosmology has begun with the NYU Center. That took place a week ago, and featured talks by my colleagues Justin Khoury and Daniel Wesley, and NYU speakers Neal Weiner and Roman Scoccimarro. This was a very fun intellectual exchange, with talks on modified gravity, cyclic cosmologies, and interacting dark matter. Certainly the NYU people set the hospitality bar pretty high for us for when they visit us at Penn next semester.

However, perhaps the most time consuming activity of the last few weeks, in comparison with the rest of the year, has been writing and editing letters of recommendation. This is something I think everyone realizes professors do, but usually doesn’t realize the amount of time it takes.

I don’t know what it is like for everyone, but the first time I was asked to write a serious letter of recommendation was when I was a postdoc, and one of the graduate students I’d been working with asked me if I’d be one of his letter writers as he applied for his first postdoc. This first letter keeps you up at night. One wants to be enthusiastic about the candidate, while realizing that your letter is supposed to provide a service for your colleagues who will evaluate the application, as well as for the candidate. Thus one gets excessively stressed about painting a balanced picture of the candidate’s strengths and weaknesses, while competing with some of the glowing letters that one knows other people will write for their candidates. Nevertheless, you get over it, and you write the best letter you can and hope that it is helpful.

As a faculty member, one rather rapidly comes to realize that writing letters of recommendation is a crucial and time-consuming part of one’s job. So how does one go about it? Well, suppose that someone has asked you for a letter. They might be an undergraduate, a graduate student or a postdoc, asking for a letter for positions ranging from an REU position to a faculty job. The first thing to decide is whether you are prepared to write for them. For me, I tell a person I will write if I think my letter will leave a better impression than receiving no letter at all. If not, then I turn them down and tell them they would do better asking someone else. I also like to tell people roughly the type of letter they can expect. Obviously I don’t give details, but I don’t want there to be any confusion. They might decide they can get a better letter from someone else, or that they just don’t want me to write, and I like them to have enough information to make that decision.

But assuming you’ve made the decision to write for someone, and that they still want you to write, then you have a lot of work ahead of you. There’s some basic stuff to get out of the way up front – how long have you known the person and in what capacity? This is where you lay out why you have sufficient experience with them to be able to provide a complete and authoritative account of their skills, track record and potential. When one is rather junior and writing, this part is important to demonstrate your qualifications before you discuss the applicant’s. As a physicist becomes more senior and well-known, this part of the letter remains just as important, although now it is more because it reassures the reader that the writer actually does know this person well, as opposed to them just being another of the presumably huge number of people clamoring for letters.

Now one moves on to the meat of the matter – evaluating the technical talents of the applicant. Are they deep, broad, sophisticated, creative, and calculationally skilled? There are many nuances involved in this part. Obviously, one wants to be accurate, while highlighting the skills that have impressed you most about the person. If you have written papers with the candidate, then this is the place you’ll write about some of the details and what the candidate brought to the project. If there are relevant weaknesses, you may want to point them out; but in my case, if I’ve decided to write, then I will typically think that these are outweighed by strengths, and you want to make that clear. Perhaps the most important thing to bear in mind here is that these are just your opinions. Yes, they are informed opinions; and yes, they have been solicited by both the candidate and/or the hiring institution because they feel you are qualified to give them. Nevertheless, there is no way around the fact that there is a significant subjective component to a recommendation letter, and it is important to make sure that you recognize this and consider it carefully before making any strong statements.

This, of course, makes letter writing somewhat terrifying (naturally, having to ask for them is also scary). Of course, one doesn’t resent students, postdocs and colleagues for asking for letters (not least because we have all relied on others to do this for us many times), and you want to see your talented colleagues succeed. It’s just that because of this you owe it to everyone involved to do a good job, and this is what makes for the required time commitment. October and November are the time when most letters are requested, and so if you find yourself writing for many people (ten or more people sometimes, at various levels), then it comprises a significant portion of your work over those weeks. It’s a not-often-mentioned, but important part of an academic’s job.

I’m in the middle of jetting hither and yon, talking to people about the arrow of time. (Wouldn’t it be great if I had a book to sell them?) Right now, as prophesyed, I’m at the Quantum To Cosmos Festival at the Perimeter Institute. They’re extremely on the ball over here, so every event is being recorded by the ultra-professional folks at TVO, and instantly available on the web. So here is the talk I gave on Saturday night — a public-level discussion of entropy and how it connects to the history of our universe.

Yes, that’s a pretty suave picture of me on the image capture. What can I say? I’m just one of those lucky folks with an effortless magic in front of the camera.

If you prefer to get your talks about entropy unadulterated by voice and motion, and don’t mind a more technical presentation, I’ve put the slides from my recent Caltech colloquium online. These are aimed basically at grad students in physics, so there is an equation or two, and the caveats are spelled out more clearly. But the punchline is the same.

Taking off to the Great White North this week, for a couple of fun events. First it’s to the Perimeter Institute in Waterloo, which is hosting the Quantum to Cosmos Festival. It’s ten days of fun and big ideas, and best of all it will all be recorded and streamed live. Check out the program here. I’ll be participating in a panel discussion on big ideas Thursday night, and giving a popular talk on the arrow of time Saturday night. But there’s also a promising panel discussion on cosmology on Sunday (moderated by my favorite science writer), as well as interesting-looking talks by people like Peter Diamandis, Jim Gates, Neil Gershenfeld, Cory Doctorow, and even the other Sean Carroll. Plenty of fun to go around.

Then it’s off to the Francophone sector with me, where I’ll be visiting McGill University in Montreal to give another public talk on Monday night. I don’t know of any recordings there, but the talk won’t be that different from Saturday’s. But if there are any CV readers in Montreal, be sure to say hi!

Back for the third and final day of the Philosophy and Cosmology conference in honor of George Ellis’s birthday. I’ll have great memories of my time in Oxford, almost all of which was spent inside this lecture hall. See previous reports of Day One, Day Two.

It’s become clear along the way that I am not as accurate when I’m trying to represent philosophers as opposed to physicists; the vocabularies and concerns are just slightly different and less familiar to me. So take things with an appropriate grain of salt.

Tuesday morning: The Case for Multiverses

9:00: Bernard Carr, one of the original champions of the anthropic principle, has been instructed to talk on “How we know multiverses exist.” Not necessarily the title he would have chosen. Of course we don’t observe a multiverse directly; but we might observe it indirectly, or infer it theoretically. We should be careful to define “multiverse,” not to mention “exist.”

There certainly has been a change, even just since 2001, in the attitude of the community toward the multiverse. Quotes Frank Wilczek, who tells a parable about how multiverse advocates have gone from voices in the wilderness to prophets. That doesn’t mean the idea is right, of course.

Carr is less interested in insisting that the multiverse does exist, and more interested in defending the proposition that it might exist, and that taking it seriously is perfectly respectable science. Remember history: August Comte in 1859 scoffed at the idea we would ever know what stars were made of. Observational breakthroughs can be hard to predict. Rutherford: “Don’t let me hear anyone use the word `Universe’ in my department!” Cosmology wasn’t respectable. For what it’s worth, the idea that what we currently see is the whole universe has repeatedly been wrong.

So how do we know a multiverse exists? Maybe we could hop in a wormhole or something, but let’s not be so optimistic. There are reasons to think that multiverses exist: for example, if we find ourselves near some anthropic cutoff for certain parameters. More interesting, there could be semi-direct observational evidence — bubble collisions, or perhaps giant voids. Discovering extra dimensions would be good evidence for the theories on which the multiverse is often based.

The only direct observations that currently exists that might bear directly on multiverses is the prediction of giant voids and dark flows by Laura Mersini-Houghton and collaborators.

Carr believes that the indirect evidence from finely-tuned coupling constants is actually stronger. Existence of planets requires a very specific relationship between strength of gravity and electromagnetism, which happens to exist in the real world. There is a similar gravity/weak tuning needed to make supernovae and heavy elements. Admittedly, many physicists dislike the multiverse and find it just as unpalatable as God. But ultimately, multiverse ideas will become normal science by linking up with observations; we just don’t know how long it will take.

9:45: George Ellis follows Carr’s talk with what we’ve been waiting for a while — a strong skeptical take on the multiverse idea.

There are lots of types of multiverses: many-worlds, separated by space or time, or completely disjoint. Anthropic arguments are what make the idea go. The project is to make the apparently improbable become probable.

The very nature of the scientific enterprise is at stake: multiverse proponents are proposing that we weaken the idea of scientific proof. Science is about two things: testability and explanatory power. Is it worth giving up the former to achieve the latter?

The abstract notion of a multiverse doesn’t get you anything; you need a specific model, with a distribution of probabilities. (Does Harry Potter exist somewhere in your multiverse?) But if there is some process that generates universes, how do you test that process? Domains beyond our particle horizon are unobservable. How far should we expect to be able to extrapolate? Into a region which, in principle, we will never be able to observe.

In the good old days we accepted the Cosmological Principle, and assumed things continued uniformly forever beyond our observable horizon. Completely untestable, of course. If all the steps in the extrapolation are perfectly tenable, extrapolations are fine — but that’s not the case here. In particular, the physics of eternal inflation (gravity plus quantum field theory, Coleman-de Luccia tunneling) has never been tested. It’s unknown physics used to infer an unobservable realm. Inflation itself is not yet a well-defined theory, and not all versions of inflation are eternal. We haven’t even found a scalar field!

There is a claim that a multiverse is implied by the fine-tuning of the universe to allow life. At best a weak consistency test. Can never actually do statistical tests on the purported ensemble. Another claim is that the local universe, if it’s inside a bubble, should have a slight negative curvature — but that’s easily avoided by super-Hubble perturbations, so it’s not a strong prediction. We could, however, falsify eternal inflation by observing that we live in a “small” (topologically compact) universe. But if we don’t, it certainly doesn’t prove that eternal inflation is right. Finally, it’s true that we might someday see signatures of bubble collisions in the microwave background. But if we don’t, then what? Again, not a firm prediction.

Ultimately: explanation and testability are both important, but one shouldn’t overwhelm the other. “The multiverse theory can’t make any prediction because it can explain anything at all.” Beware! If we redefine science to accommodate the multiverse, all sorts of pseudo-science might sneak inside the tent.

There are also political/sociological issues. Orthodoxy is based on the beliefs held by elites. Consider the story of Peter Coles, who tried to claim back in the 1990’s that the matter density was only 30% of the critical density. He was threatened by a cosmological bigwig, who told him he’d be regarded as a crank if he kept it up. On a related note, we have to admit that even scientists base beliefs on philosophical agendas and rationalize after the fact. That’s often what’s going on when scientists invoke “beauty” as a criterion.

Multiverse theories invoke “a profligate excess of existential multiplicity” in order to explain a small number of features of the universe we actually see. It’s a possible explanation of fine tuning, but is not uniquely defined, is not scientifically testable, and in the end “simply postpones the ultimate metaphysical question.” Nevertheless — if we accumulated enough consistency tests, he’d be happy to eventually become convinced.

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The previous post on the Philosophy and Cosmology conference in Oxford was growing to unseemly length, so I’ll give each of the three days its separate post.

Monday morning: The Case for Multiverses

9:00: We start today as we ended yesterday: with a talk by Martin Rees, who has done quite a bit to popularize the idea of a multiverse. He wants to argue that thinking about the multiverse doesn’t represent any sort of departure from the usual way we do science.

The Big Bang model, from 1 second to today, is as uncontroversial as anything a geologist does. Easily falsifiable, but it passes all tests. How far does the domain of physical cosmology extend? We only see the universe out to the microwave background, but nothing happens out there — it seems pretty uniform, suggesting that conditions inside extend pretty far outside. Could be very far, but hard to say for sure.

Some people want to talk only about the observable universe. Those folks need aversion therapy. After all, whether a particular distant galaxy eventually becomes observable depends on details of cosmic history. There’s no sharp epistemological distinction between the observable and unobservable parts of the universe. We need to ask whether quantities characterizing our observable part of the universe are truly universal, or merely local.

So: what values of these parameters are consistent with some kind of complexity? (No need to explicitly invoke the “A-word.”) Need gravity, and the weaker the better. Need at least one very large number; in our universe it’s the ratio of gravity to electromagnetic forces between elementary particles. Also need departure from thermodynamic equilibrium. Also: matter/antimatter symmetry, and some kind of non-trivial chemistry. (Tuning between electromagnetic and nuclear forces?) At least one star, arguably a second-generation star so that we have heavy elements. We also need a tuned cosmic expansion rate, to let the universe last long enough without being completely emptied out, and some non-zero fluctuations in density from place to place.

If the amplitude of density perturbations were much smaller, the universe would be anemic: you would have fewer first-generation stars, and perhaps no second-generation stars. If the amplitude were much larger, we would form huge black holes very early, and again we might not get stars. But ten times the observed amplitude would actually be kind of interesting. Given an amplitude of density perturbations, there’s an upper limit on the cosmological constant, so that structure can form. Again, larger perturbations would allow for a significantly larger cosmological constant — why don’t we live in such a universe? Similar arguments can be made about the ratio of dark matter to ordinary matter.

Having said all that, we need a fundamental theory to get anywhere. It should either determine all constants of nature uniquely, in which case anthropic reasoning has no role, or it allows ranges of parameters within the physical universe, in which case anthropics are unavoidable.

10:00: Next up, Philip Candelas to talk about probabilities in the landscape. The title he actually puts on the screen is: “Calabi-Yau Manifolds with Small Hodge Numbers, or A Des Res in the Landscape.”

A Calabi-Yau is the kind of manifold you need in string theory to compactly ten dimensions down to four, picked out among all possible manifolds by the requirement that we preserve supersymmetry. There are many examples, and you can characterize them by topological invariants as well as by continuous parameters. But there is a special corner in the space of Calabi-Yau’s where certain topological invariants (Hodge numbers) are relatively small; these seem like promising places to think about phenomenology — e.g. there are three generations of elementary particles.

Different embeddings lead to different gauge groups in four dimensions: E₆, SO(10), or SU(5). Various models with three generations can be found. Putting flux on the Calabi-Yau can break the gauge group down to the Standard Model, sometimes with additional U(1)’s.

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Greetings from Oxford, a charming little town across the Atlantic with its very own university. It’s in the United Kingdom, a small island nation recognized for its steak and kidney pie and other contributions to world cuisine. What you may not know is that the UK has also produced quite a few influential philosophers and cosmologists, making it an ideal venue for a small conference that aims to bring these two groups together.

The proximate reason for this particular conference is George Ellis’s 70th birthday party. Ellis is of course a well-known general relativist, cosmologist, and author. Although the idea of a birthday conference for respected scientists is quite an established one, Ellis had the idea of a focused and interdisciplinary meeting that might actually be useful, rather than just bringing together all of his friends and collaborators for a big party. It’s to his credit that they invited as many multiverse-boosters as multiverse-skeptics. (I would go for the party, myself.)

George is currently very interested and concerned by the popularity of the multiverse idea in modern cosmology. He’s worried, as many others are (not me, especially), that the idea of a multiverse is intrinsically untestable, and represents a break with the standard idea of what constitutes “science.” So he and the organizing committee have asked a collection of scientists and philosophers with very different perspectives on the idea to come together and hash things out.

It appears as if there is working wireless here in the conference room, so I’ll make some attempt to blog very briefly about what the different speakers are saying. If all goes well, I’ll be updating this post over the next three days. I won’t always agree with everyone, of course, but I’ll try to fairly represent what they are saying.

Saturday night:

Like any good British undertaking, we begin in the pub. I introduce some of the philosophers to Andrei Linde, who entertains us by giving an argument for solipsism based on the Wheeler-deWitt equation. The man can command a room, that’s all I’m saying.

(If you must know the argument: the ordinary Schrodinger equation tells us that the rate of change of the wave function is given by the energy. But for a closed universe in general relativity, the energy is exactly zero — so there is no time evolution, nothing happens. But you can divide the universe into “you” and “the rest.” Your own energy is not zero, so the energy of the rest of the universe is not zero, and therefore it obeys the standard Schrodinger equation with ordinary time evolution. So the only way to make the universe real is to consider yourself separate from it.)

Sunday morning: Cosmology

9:00: Ellis gives the opening remarks. Cosmology is in a fantastic data-rich era, but it is also coming up against the limits of measurement. In the quest for ever deeper explanation, increasingly speculative proposals are being made, which are sometimes untestable even in principle. The multiverse is the most obvious example.

Question: are these proposals science? Or do they attempt to change the definition of what “science” is? Does the search for explanatory power trump testability?

The questions aren’t only relevant to the multiverse. We need to understand the dividing line between science and non-science to properly classify standard cosmology, inflation, natural selection, Intelligent Design, astrology, parapsychology. Which are science?

9:30: Joe Silk gives an introduction to the state of cosmology today. Just to remind us of where we really are, he concentrates on the data-driven parts of the field: dark matter, primordial nucleosynthesis, background radiation, large-scale structure, dark energy, etc.

Silk’s expertise is in galaxy formation, so he naturally spends a good amount of time on that. Theory and numerical simulations are gradually making progress on this tough problem. One outstanding puzzle: why are spiral galaxies so thin? Probably improved simulations will crack this before too long.

10:30: Andrei Linde talks about inflation and the multiverse. The story is laden with irony: inflation was invented to help explain why the universe looks uniform, but taking it seriously leads you to eternal inflation, in which space on extremely large (unobservable) scales is highly non-uniform — the multiverse. The mechanism underlying eternal inflation is just the same quantum fluctuations that give rise to the density fluctuations observed in large-scale structure and the microwave background. The fluctuations we see are small, but at earlier times (and therefore on larger scales) they could easily have been very large — large enough to give rise to different “pocket universes” with different local laws of physics.

Linde represents the strong pro-multiverse view: “An enormously large number of possible types of compactification which exist e.g. in the theory of superstrings should be considered a virtue.” He said that in 1986, and continues to believe it. String theorists were only forced to take all these compactifications seriously by the intervention of a surprising experimental result: the acceleration of the universe, which implied that there was no magic formula that set the vacuum energy exactly to zero. Combining the string theory landscape with eternal inflation gives life to the multiverse, which among other things offers an anthropic solution to the cosmological constant problem.

Still, there are issues, especially the measure problem: how do you compare different quantities when they’re all infinitely big? (E.g. number of different kinds of observers in the multiverse.) Linde doesn’t think any of the currently proposed measures are completely satisfactory, including the ones he’s invented. A big problem with Boltzmann brains.

Another problem is what we mean by “us,” when we’re trying to predict “what observers like us are likely to see.” Are we talking about carbon-based life, or information-processing computers? Help, philosophers!

Linde thinks that the multiverse shows tendencies, although not cut-or-dried predictions. It prefers a cosmological constant to quintessence, and increases the probability that axions rather than WIMPs are the dark matter. Findings to the contrary would be blows to the multiverse idea. Most strongly, without extreme fine-tuning, the multiverse would not be able to simultaneously explain large tensor modes in the CMB and low-energy supersymmetry.

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Travel is broadening, and in particle physics we get to do a lot of it. In July, having temporarily settled my father into a nursing home after being hospitalized (the subject of my last post, Part 1), I was able to meet my commitment to travel to Krakow, Poland, to give a plenary talk on the search for the Higgs boson at the annual Europhysics conferenceheld at the Jagiellonian University there (where Copernicus studied for four years, 1491-1495).

Central Krakow emerged from World War II, which began nearly exactly 70 years ago, nearly unscathed. The central square is one of the more beautiful in Europe, similar in a way to that of Prague. But it was hard to avoid waling there without imagining what it must have looked like during the war, occupied by German soldiers who had made Krakow the center of their regional government during the war.

From the square one can take tours in little golf-cart-like jitneys, and see some of the interesting historical sites, including the Jewish Quarter (Kazimierz) and Schindler’s famous enamelware factory. Some of the apartment buildings in Kazimierz are still in the state they were at the end of the war, a rather grim reminder of the central role Krakow played in the Holocaust.

From Krakow one can take day trips to a number of interesting places, and we visited the spectacular salt mines of Wielicka, a UNESCO World Heritage site, which have amazing, huge rooms carved out of the rock.

But there was another interesting place to tour that we were hesitant about – Auschwitz. Others who took the tour came back saying that it was well worth the journey, over an hour by bus each way, but tended not to say much more about it…hmmm.

So on our last free day we took the plunge, signed up for the tour, and went. The bus traveled through quite rural countryside on two-lane roads, past farms and villages, roughly following the Vistula river, until reaching the town of Oswiecim, which the Germans called Auschwitz.

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