Archive for the 'Science' Category

Happy birthday, General Relativity

November 25, 2015


One hundred years ago today, on 25 November 1915, Einstein first presented the field equations for General Relativity during a lecture in Gottingen. GR is regarded, with justice, as among the most beautiful and creative achievements in the history of science. I know of none greater, and I am thankful to have had the opportunity to spend many happy hours working with the field equations — and some unhappy ones too, of course, because they are fiendishly difficult to solve!

On the same date, 25 November 1915, Einstein’s paper on the perihelion advance of Mercury was published in Königlich Preußische Akademie der Wissenschaften. This was the first, and is still one of the most important, experimental tests of General Relativity.


A wee bit here, a wee bit there

November 20, 2015

A few wee bits of note:

  • The recent Synod on the Family in Rome hasn’t, by and large, been a laughing matter, so this provides welcome comic relief.
  • Fr Longenecker, a long-time blogger at Standing on my Head, has recently launched a new blog: The Suburban Hermit. If you’ve an interest in things Benedictine, or like to look at old abbeys and read old books, it might be for you. Just today he wrote about our sort-of patroness, St Julian of Norwich.
  • Canada has a new Prime Minister, and he’s setting a new tone in international affairs.
  • Janet Cupo is planning to host an online book club during Advent this year; we’ll be reading Caryll Houselander’s The Reed of GodThere’s probably still time to get a copy if you’re interested; mine arrived in the mail today.
  • My day job, in part.
  • Wouldn’t it be great to have a school like this in your neighbourhood?
  • On a similar note: Russell Kirk on why one might want to learn Latin? I studied it for a year. Avis, avis, avis.
  • One possible reason: to realize more clearly that English is not normal.
  • Did you know there is an animal that can survive being dehydrated for 10 years, being kept at 200 degrees below freezing, and going to outer space? Meet the mightiest wee bit of them all: the tardigrade.

The divisibility trick

January 7, 2014

You might have learned the “divisibility trick” in grade school. It says that if you want to know whether a number is divisible by 3, there is a shortcut: if the sum of its digits is divisible by 3 then the number itself is divisible by 3. For example, is 459 divisible by 3? Well, 4 + 5 + 9 = 18, which is divisible by 3, so 459 is divisible by 3 as well.

This trick also works with the number 9. Again, you can try it with 459.

A week or two ago I was reading Anthony Esolen’s “Word of the Day” blog in which he stated a result about the divisibility trick generalized to a base-X number system; namely, in a base-X number system the divisibility trick works for X-1 and its factors. I was intrigued, and, as I had given some thought to the divisibility trick a few years ago and had some notes on it, I sat down last night and came up with what I think is a sound proof of the claim.

I am sure there is a nice way to formulate the argument — my approach leans heavily on modular arithmetic, which is closely related to the elegant theory of cyclic groups — but I went about it in the most simpleminded way imaginable. You can read my argument here:

DivisibilityTrickBaseX [pdf, Updated]

An amusing application of this result is in a binary (base-2) number system. The claim simply says that any binary number for which the sum of its digits is divisible by 1 (which is all of them, since every positive integer is divisible by 1) is itself divisible by 1 (which is all of them, for the same reason). So the claim is almost empty in that case.

Elemental boating

June 18, 2013

The topic this week at the What If? blog is a novel one:

What would it be like to navigate a rowboat through a lake of mercury? What about bromine? Liquid gallium? Liquid tungsten? Liquid nitrogen? Liquid helium?

I spent a few days last week on a boat in a lake of water, and after reading the entertaining and instructive responses to the questions above — not neglecting to watch the illustrative videos — I will say this: thank goodness for water!

Notes on neuroscience

June 6, 2013

I am in no respect an expert in neuroscience, but naturally I am aware of the main technical developments of the past few decades — especially functional MRI — which now provide neuroscientists with amazing imagery related to brain activity. I am also aware of the broad effort in the field to establish correlations between brain activity and mental states.

I will not deny that I am mildly discomfited by this effort, not because there is anything suspect about such correlations but because they are so often conjoined with a strange presumption that somehow brain scans are particularly probative windows on human behaviour, whereas in fact they are usually just fancy proxies for things we already know by other means (as has been convincingly argued). One also routinely runs into a tacit neurological reductionism according to which minds are “really just” brains, and you and I are, at bottom, “really just” fleshy computers processing stimuli. In this view of things, the notion of persons as bearers of freedom, dignity, and moral responsibility tends to become, at best, occluded.

My discomfort is only mild because I am aware that, whatever the merits of any particular scientific study, the minds-are-brains view is plagued by conceptual problems and, at least within the ambit of the reigning philosophy of nature in which matter is defined to be devoid of mental properties, is doomed to failure.

But, quite apart from the question of how we should interpret findings of correlations between mental states and brain activity, there remains the question of whether we should believe that such correlations exist in the first place. It seems that we should, but with reservations, for the evidence is not as strong or as straightforward as one might think.

For instance, a few years ago an important paper identified problems with common analysis techniques in fMRI studies. The authors showed that using such techniques they could produce nice correlations using data that were pure noise. Studies which avoided such confused methods uniformly showed comparatively low correlations. The authors speculated that a significant number of the findings claimed by the field might be illusory. I do not know what revisions resulted when (or if) the data were analyzed again.

And now, in this month’s Nature Reviews, comes another paper that criticizes the results of a wide swath of neuroscience work. The authors argue that a significant fraction of neuroscience studies suffer from low statistical power, meaning that both the sample sizes and the effects being studied are generally small. The problems with low power studies are many: the probability of missing true effects is fairly high, as is the probability of falsely “discovering” something that isn’t there. Even when a finding is true, low power studies tend to exaggerate it. Here is a popular level summary of the paper and the issues at stake.

Obviously it is up to the specialists to sort these issues out, and I have no doubt that they will. But there does seem to be warrant for wariness the next time you hear a claim that the neural correlate of this-or-that aspect of your mental life has been found. Sometimes things are just not that simple.


Planck results

March 21, 2013

Big science news today: the Planck experiment has released a huge raft of results based on cosmological observations made during 2009-10. Planck is a satellite-based experiment that has been making precision measurements of the cosmic microwave background (CMB) radiation, the details of which tell us a great deal about the history and structure of the universe. Planck is a truly spectacular project.

I remember that when I was an undergraduate physics student — which was quite a long time ago now — we heard rumours of this satellite, which was then in the planning stages. The hope was that it, and to a lesser extent its predecessor WMAP, would usher in an era of “precision cosmology”, in which cosmologists would have a wealth of high quality measurements against which to judge their theories about cosmic structure and evolution.

Based on the results published today, I would say that those hopes have been triumphantly vindicated. For instance, consider this paper on cosmological parameters; look at Tables 1 and 2. These are amazing results: baryon density is about 2.2%, cold dark matter density about 12%, dark energy density about 68%, Hubble constant about 67, and the age of the universe about 13.8 billion years (with an uncertainty of only about 100 million years!).

There is a lot here for non-specialists to digest — and I certainly count myself in that group. The BBC is on the case.

Planet Mole

July 24, 2012

There is a new physics blog at xkcd called What If? Each week it discusses a question of pressing scientific interest for a general audience. If one loses the train of thought one can always consult the diverting illustrations, which feature those lovable xkcd stick figures.

The issue this week is particularly pressing — if you’ll forgive the pun — as they take up the question of what would happen if one assembled a planet-sized sphere of moles (or comparable small rodents). It’s pretty awful:

The outer surface of the planet radiates heat into space and freezes. Because the moles form a literal fur coat, when frozen it insulates the interior of the planet and slows the loss of heat to space. However, the flow of heat in the liquid interior is dominated by convection. Plumes of hot meat and bubbles of trapped gases like methane—along with the air from the lungs of the deceased moles—periodically rise through the mole crust and erupt volcanically from the surface, a geyser of death blasting mole bodies free of the planet.

The blog has only been going a month or so; the previous posts (on Star Wars, SATs, and baseball) are also interesting.

Reading Rosenberg (with Feser)

July 13, 2012

A few years ago Alex Rosenberg, a professor of philosophy at Duke, published a short article online called “The Disenchanted Naturalist’s Guide to Reality”. I remember that it attracted a fair bit of attention at the time, for it set forth, briefly, the melancholy implications of philosophical naturalism (or ‘materialism’, or ‘scientism’): namely, that morality is unfounded, purpose illusory, freedom fictional, God non-existent, and even conscious experience a kind of elaborate deception. Rosenberg commented that though the premises of naturalism are widely held, the implications are, more often than not, ignored or denied, and that sooner or later that has to change.

Then last year he published The Atheist’s Guide to Reality, which presents the same argument in more elaborate and detailed form. It too has received a lot of attention — even being named “Worst Book of 2011” by Leon Wieseltier at The New Republic, who evidently took offense at the book’s conclusions.

The problem is that, given its premises, those conclusions actually do follow. The book thus provides us with a welcome opportunity to critically examine the premises of naturalism (and, despite the title of the book, it really is naturalism, rather than atheism per se, that is the problem, even if, in practice, the two tend to go together in our culture). This is just what Edward Feser has done over at his blog, in an ambitious ten-part series of posts. He critiques Rosenberg’s argument for scientism, his framing of the relationship between Darwinism and theism, his (“nice”) moral nihilism, his denial of free will, his denial of the intentionality of thought, and much else besides. Feser typically argues that the radical (and sometimes incoherent) conclusions that Rosenberg believes follow from “the facts” are actually thoroughly entangled with the metaphysical commitments of naturalism (and particularly with the view of the natural world as a kind of machine), and do not follow if those commitments are suspended. In so doing, he has done us a good service. It makes for fascinating reading too.

Feser collected links to the whole series on one page, which makes it easy for me to recommend the whole project.

Higgs week

July 6, 2012

It has been a busy week, but I cannot let it pass without saying a brief word about the Higgs boson discovery at CERN. This is something that everyone has been expecting since the lab was upgraded to higher energies a few years ago. In other words, it is not a surprise — and, in fact, from a certain point of view it would have been more exciting if they had not found it. I will even admit that I was feeling a little blasé as the rumours of the discovery began to circulate in recent months.

That changed, however, when I saw this:

The bit above the dashed line is what the fuss is all about. (Source: CERN)

It is real!

The official scientific paper describing the findings has not been published yet, but CERN is reporting the discovery of a boson (a particle with integer spin) with a mass of about 126 GeV (as in the figure above). The mass is roughly equivalent to that of an iodine atom, making the Higgs boson the second heaviest known elementary particle (after the top quark).

The extent to which the properties of this new particle match those predicted by our theory will take time to sort out. Measuring the spin will be an obvious first step, if it hasn’t been done already. Its couplings to the other particles will have to be measured. In other words, a lot of work will be done to check whether this Higgs boson is the one we expected to find.

Time to shelve this away?

Many physicists are hoping that it is not. The cost to build and run these collider experiments is so enormous that if the current facilities at CERN find the Standard Model Higgs boson, and nothing else, there is considerable worry — well-founded worry, in my opinion — that the era of collider physics, which has taught us so much, will be over. The political will to build another, bigger, more expensive experiment will not exist.

If, on the other hand, there is something odd about this Higgs boson, or if CERN finds something else — something unexpected — in the next few years, then our theory will need revision, and more experimental studies will be needed to sort things out. That is an argument to keep going.

Despite those worries, this is a time for celebration. I think especially of the thousands of people who have worked so hard, for so long, to get to this point. The complexity and scale of these experiments beggars description; they are truly amazing feats of design and engineering, and those responsible for them can be justly proud at a time like this. All that work, and we reap the harvest.


This video gives an accessible but informative introduction to the Higgs boson. It takes a minute or so to really get going, and it looks better when viewed at full-screen.

When I consider the heavens…

May 2, 2012

Our good friend, Adam Hincks, S.J., has an article in the Jesuit weekly America in which he reflects on the relationship between contemporary cosmology and Christian faith:

Through much of Western history, it was thought that the motions of the heavens were regular and unchanging. The Christian notion that the cosmos had a beginning in time had to be accepted as an article of faith. With the advent of the Big Bang theory, it might seem that science corroborates revelation, but it is not that simple.

The article is temporarily available to non-subscribers. Read the whole thing.

(Hat-tip: Ibo et Non Redibo)


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