Archive for Physics

Is there a role for rote learning?

Posted in Education, Maynooth with tags , , , , , , , on May 7, 2019 by telescoper

So here we are, then, back to work here in Maynooth for the last week of teaching. Or, to be precise, the last four days – yesterday was a Bank Holiday. With university and school examinations looming, it is no surprise to find an article griping about the Irish Leaving Certificate examinations and the fact that teachers seem to encourage students to approach them by by rote learning. This is something I’ve complained about before in the context of British A-levels and indeed the system of university examinations.

Over my lifetime the ratio of assessment to education has risen sharply, with the undeniable result that academic standards have fallen – especially in my own discipline of physics. The modular system encourages students to think of modules as little bit-sized bits of education to be consumed and then forgotten. Instead of learning to rely on their brains to solve problems, students tend to approach learning by memorizing chunks of their notes and regurgitating them in the exam. I find it very sad when students ask me what derivations they should memorize to prepare for examinations because that seems to imply that they think their brain is no more than a memory device. It has become very clear to me over the years that school education in the UK does not do enough to encourage students to develop their all-round intellectual potential, which means that very few have confidence in their ability to do anything other than remember things. It seems the same malaise affects the Irish system too.

On the other hand, there’s no question in my mind that a good memory is undoubtedly an extremely important asset in its own right. I went to a traditional Grammar school that I feel provided me with a very good education in which rote learning played a significant part. Learning vocabulary and grammar was an essential part of their approach to foreign languages, for example. How can one learn Latin without knowing the correct declensions for nouns and conjugations for verbs? But although these basic elements are necessary, they are not sufficient. You need other aspects of your mental capacity to comprehend, translate or compose meaningful pieces of text. I’m sure this applies to many other subjects. No doubt a good memory is a great benefit to a budding lawyer, for example,  but the ability to reason logically must surely be necessary too.

The same considerations apply to STEM disciplines. It is important to have a basic knowledge of the essential elements of mathematics and physics as a grounding, but you also need to develop the skill to apply these in unusual settings. I also think it’s simplistic to think of memory and creative intelligence as entirely separate things. I seems to me that the latter feeds off the former in a very complex way. A good memory does give you rapid access to information, which means you can do many things more quickly than if you had to keep looking stuff up, but I think there’s a lot more to it than that. Our memories are an essential part of the overall functioning of our brain, which is not  compartmentalized in  a simple way.  For example, one aspect of problem-solving skill relies on the ability to see hidden connections; the brain’s own filing system plays a key role in this.

Recognizing the importance of memory is not to say that rote learning is necessarily the best way to develop the relevant skills. My own powers of recall are not great – and are certainly not improving with age – but I find I can remember things much better if I find them interesting and/or if I can see the point of remembering them. Remembering things because they’re memorably is far easier than remembering because you need to remember them to pass an examination!

But while rote learning has a role, it should not be all there is and my worry is that the teaching-to-the-test approach is diminishing the ability of educators to develop other aspects of intelligence. There has to be a better way to encourage the development of the creative imagination, especially in the context of problem-solving. Future generations are going to have to face many extremely serious problems in the very near future, and they won’t be able to solve them simply by remembering the past.

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More Order-of-Magnitude Physics

Posted in Cute Problems with tags , , , on April 25, 2019 by telescoper

A very busy day today so I thought I’d just do a quick post to give you a chance to test your brains with some more order-of-magnitude physics problems. I like using these in classes because they get people thinking about the physics behind problems without getting too bogged down in or turned off by complicated mathematics. If there’s any information missing that you need to solve the problem, make an order-of-magnitude estimate!

Give  order of magnitude answers to the following questions:

  1. What is the maximum distance at which it could be possible for a car’s headlights to be resolved by the human eye?
  2. How much would a pendulum clock gain or lose (say which) in a week if moved from a warm room into a cold basement?
  3. What area would be needed for a terrestrial solar power station capable of producing 1GW of power?
  4. What mass of cold water could be brought to the boil using the energy dissipated when a motor car is brought to rest from 100 km/h?
  5. How many visible photons are emitted by a 100W light bulb during its lifetime?

There’s no prize involved, but feel free to post answers through the comments box. It would be helpful if you explained a  bit about how you arrived at your answer!

In Praise of Omnibus Science

Posted in Education, Maynooth with tags , , , on April 16, 2019 by telescoper

I’m taking a few days off at the moment so this morning I had a bit of time to catch up on various things. One news item I stumbled across points out that first-choice applications to study at Maynooth University are the highest ever. Within the overall increase of about 7% there is a growth of 17% in Science subjects, which is very good news for the Department of Theoretical Physics as well as the other Departments in the Faculty of Science and Engineering.

Anyway, this spurred me to comment on what I think is one of the strengths of Maynooth University: the Omnibus Science programme.

Currently, most students doing Science subjects here enter on the Omnibus programme, a four-year science course that involves doing four subjects in the first year, but becoming increasingly specialised thereafter. That’s not unlike the Natural Sciences course I did at Cambridge, except that students at Maynooth can do both Theoretical Physics and Experimental Physics in the first year as separate choices. Other possibilities include Chemistry, Computer Science, Biology, etc.

In Year 1 students do four subjects (one of which is Mathematics). That is narrowed down to three in Year 2 and two in Year 3. In their final year, students can stick with two subjects for a Joint Honours degree, or specialise in one, for Single Honours.

I like this programme because it does not force the students to choose a specialism before they have had a taste of the subject, and that it is flexible enough to accommodate Joint Honours qualifications in, e.g., Theoretical Physics and Mathematics. It also allows us to enrol students onto Physics degrees who have not done Physics as part of the Leaving Certificate.

I think it’s a strength that students take such a broad first year rather than locking themselves into one discipline from the start. Part of the reason is that I went to do my own degree at Cambridge expecting to end up specialising in Chemistry, but enjoyed the physics far more, eventually specialising in Theoretical Physics. I’m sure there were others who went the other way too!

One problem with the Omnibus Science programme is that the range of possible final qualifications is perhaps not as clearly advertised as it could be, so some clearer signposting would do no harm.

Machine Learning in the Physical Sciences

Posted in The Universe and Stuff with tags , , , , , on March 29, 2019 by telescoper

If, like me, you feel a bit left behind by goings-on in the field of Machine Learning and how it impacts on physics then there’s now a very comprehensive review by Carleo et al on the arXiv.

Here is a picture from the paper, which I have included so that this post has a picture in it:

The abstract reads:

Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on the interface between machine learning and physical sciences.This includes conceptual developments in machine learning (ML) motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross-fertilization between the two fields. After giving basic notion of machine learning methods and principles, we describe examples of how statistical physics is used to understand methods in ML. We then move to describe applications of ML methods in particle physics and cosmology, quantum many body physics, quantum computing, and chemical and material physics. We also highlight research and development into novel computing architectures aimed at accelerating ML. In each of the sections we describe recent successes as well as domain-specific methodology and challenges.

The next step after Machine Learning will of course be Machine Teaching…

R. I. P. Wolfgang Rindler (1924-2019)

Posted in Books, Talks and Reviews, Education, The Universe and Stuff with tags , , , , on March 5, 2019 by telescoper

A recent comment on this blog drew my attention to the sad news of the death, at the age of 94, of Wolfgang Rindler. He passed away almost a month ago, in fact, but I have only just heard. My condolences to his family, friends and colleagues.

Wolfgang Rindler was a physicist who specialized in relativity theory and especially its implications for cosmology. Among other things he is attributed with the first use of the phrase `Event Horizon‘ as well as elucidating the nature of horizons in general relativity, both in the context of black holes and in cosmology. I never met him personally but to me, and I think to many other people, Wolfgang Rindler will be familiar through his textbooks on relativity theory. I have two in my collection:

I bought the one on the right on recommendation when I was an undergraduate over thirty years ago and the other (shorter) one I acquired second-hand some years later. Both are still very widely used in undergraduate courses.
I found the first one then (as I do now) rather idiosyncratic in approach and notation but full of deep insights and extremely effective from a pedagogical point of view. I still recommend it to students, to balance more conventional modern texts which tend to be far more conventional. It’s no easy thing to write textbooks and Wolfgang Rindler deserves high praise for having devoted so much of his time, and considerable talent, into writing ones whose impact has been so widespread and lasted so long.

Rest in peace, Wolfgang Rindler (18th May 1924 – 8th February 2019).

Ahead of Teaching

Posted in Biographical, Education, mathematics, Maynooth, Music with tags , , , , on February 3, 2019 by telescoper

It’s 3rd February 2019, which means that today is two days after Imbolc, a Gaelic festival marking the point halfway between the winter solstice and vernal equinox. This either happens 1st or 2nd February, and this year it was former, i.e. last Friday In Ireland this day is sometimes regarded as the first day of spring, as it is roughly the time when the first spring lambs are born. It corresponds to the Welsh Gŵyl Fair y Canhwyllau and is also known as the `Cross Quarter Day’ or (my favourite) `The Quickening of the Year’.

I wrote a post about this time last year, on the day I gave my first ever lecture in Maynooth University, on Computational Physics, in a theatre called Physics Hall. That was on Thursday February 1st 2018. It’s hard to believe that was a full year ago. Time certainly has gone quickly this year.

Owing to the vagaries of the academic calendar we’re a week later getting back to teaching this year than last year so my first Computational Physics lecture won’t be until this Thursday (7th February) at 9am, but sadly it won’t be in Physics Hall, which I rather liked, but in Hall C – a much less atmospheric venue, but one rather closer to my office, which will be handy if I forget anything (which I am prone to do). There are about 25 students taking this module, a few down on last year, which means they should fit comfortably into our computer lab. I’m not surprised they moved the lecture, really. The capacity of Physics Hall is 90, and even last year I only had about 30 students. Still, it did have a piano (which Hall C does not):

Computational Physics doesn’t start until Thursday. Before that I have to start my other module: Engineering Mathematics II. This (what you would probably call a `service course’) covers a mixture of things, mainly Linear Algebra but with some other bits thrown in for fun, such as Laplace transforms. Interestingly I find the Mathematical Physics students do not encounter Laplace Transforms in the first year, but perhaps engineers use them more often than physicists do? I think I’ve written only one paper that made use of a Laplace transform. Anyway, I have to start with this topic as the students need some knowledge of it for some other module they’re taking this semester. I reckon six lectures will be enough to give them what they need. That’s two weeks of lectures, there being three lectures a week for this module.

By coincidence rather than good planning, the timetable for this module is quite nice. I have lectures on Monday, Tuesday and Wednesday and then the students have a choice of tutorial (on either Thursday or Friday). That means I can get through a decent amount of material each week before each tutorial. I don’t do the tutorials, by the way: that’s left to one of our PhD students, who gets paid for doing that and correcting the weekly coursework. There are about 50 students on this module, divided into two courses: Electronic Engineering and Robotics and Intelligent Devices. We don’t have Civil or Mechanical or Chemical Engineering, etc at Maynooth.

Campus has been very quiet for the last week or so. The exam period finished in late January but lectures don’t start until tomorrow morning (Monday 4th February) so there have been few students around. No doubt it will be a different story tomorrow. I’ve done my first week’s notes and compiled my first problem set so I’m more-or-less ready to go. First lecture at 2pm tomorrow in Hall H, which is one of the rooms I taught in last term so at least I know where it is!

 

Fourier, Hamilton and Ptolemy

Posted in History, Poetry, The Universe and Stuff with tags , , , , , , , on December 17, 2018 by telescoper

As we stagger into the last week of term I find myself with just two lectures to give in my second-year module on Vector Calculus and Fourier Series. I didn’t want to present the two topics mentioned in the title as disconnected, so I linked them in a lecture in which I used the divergence theorem of vector calculus to derive the heat equation, the solution of which led Joseph Fourier to devise his series in Mémoire sur la propagation de la chaleur dans les corps solides (1807), a truly remarkable work for its time that inspired so many subsequent developments.

Fourier’s work was so influential and widely admired that it inspired a famous Irish mathematician William Rowan Hamilton to write the following poem:

Hamilton-for Fourier

The serious thing that strikes me is not the quality of the verse, but how many scientists of the 19th Century, Hamilton included, saw their scientific interrogation of Nature as a manifestation of the human condition just as the romantic poets saw their artistic contemplation and how many poets of the time were also interested in science.

Anyway I was looking for nice demonstrations of Fourier series to help my class get to grips with them when I remembered this little video recommended to me some time ago by esteemed Professor George Ellis. It’s a nice illustration of the principles of Fourier series, by which any periodic function can be decomposed into a series of sine and cosine functions.

This reminds me of a point I’ve made a few times in popular talks about Astronomy. It’s a common view that Kepler’s laws of planetary motion according to which which the planets move in elliptical motion around the Sun, is a completely different formulation from the previous Ptolemaic system which involved epicycles and deferents and which is generally held to have been much more complicated.

The video demonstrates however that epicycles and deferents can be viewed as the elements used in the construction of a Fourier series. Since elliptical orbits are periodic, it is perfectly valid to present them in the form a Fourier series. Therefore, in a sense, there’s nothing so very wrong with epicycles. I admit, however, that a closed-form expression for such an orbit is considerably more compact and elegant than a Fourier representation, and also encapsulates a deeper level of physical understanding.