Marking Over

Posted in Artificial Intelligence, Biographical, mathematics, Maynooth with tags , , , , on January 19, 2026 by telescoper

Well, that wasn’t too painful. I’ve completed my marking duties. The fact that it has been pouring with rain most of the day made it easy to concentrate on this task. I was going to have a break for lunch, but I decided to keep on going until I was finished, though I did have to take a break for a telecon this afternoon. I also had to dash out to the shops, primarily to replenish my stock of food for the garden birds but also to get some groceries for myself. Having skipped lunch I bought myself something nice for supper.

Looking at the departmental database I see that I appear to be the first member of staff to have finished and uploaded all their Semester 1 examination marking. Normally I’m just happy if I’m not the last!

It feels good to have finished this task. It’s definitely a weight off my mind. I wouldn’t want to leave any loose ends when Trumpageddon comes.

I can’t say anything about the results of course but the change I made to continuous assessment, from take-home assignments to class tests, does not seem to have had a negative effect on either group of students I have been teaching. The opposite may indeed have been the case, as the class tests perhaps provide better preparation for the final assessment than the previous method. I think some other lecturers might make a similar switch in future. Anyway, I definitely plan to do something similar for my Semester 2 module on Particle Physics.

Now I have a couple of weeks before teaching resumes so I can get on with other things. For the rest of this week my priority is to finish revising a paper that I hoped to do before Christmas. I’ll see how that goes before deciding what to do next.

I’ll also have to prepare teaching for Semester 2. That shouldn’t be too difficult, as I’ve taught both modules before, but I do have to give some thought as to precisely how I’m going to word the instructions on the use of AI for my Computational Physics module. That can wait a little while, though, as it mainly affects the mini-project to be done towards the end of the Semester. In the meantime I’ll be thinking about other things…

Barry Ward’s Letter about Grok/AI

Posted in Artificial Intelligence with tags , , , , on January 19, 2026 by telescoper

TD Barry Ward, who is also a barrister, has written a letter laying out very clearly why X/Grok could and should be prosecuted immediately under existing Irish law. I’m sharing it in full as it is the public interest. I’ll add my own opinion that the X premises should be raided as soon as possible before evidence can be destroyed.

The letter follows

–o–

To:
Detective Superintendent Pat Ryan
Garda National Cyber Crime Bureau

Dear Superintendent,

You will no doubt be aware of the social media company X and its Grok app, which utilises artificial intelligence to generate pictures and videos. I understand you are also aware that, among its capabilities is the generation, by artificial intelligence, of false images of real people either naked or in bikinis, etc. There has been a great deal of controversy recently about the use of this technology and its ability to target people without their knowledge or consent.

Whatever about the sharing of such images being contrary to the provisions of Coco’s Law (sections 2 and 3 of the Harassment, Harmful Communications and Related Offences Act 2020), the Grok app is also capable of generating child sexual abuse material (CSAM) or child pornography as defined by section 2(1) of the Child Trafficking and Pornography Act 1998 (as substituted by section 9(b) of the Criminal Law (Sexual Offences) Act 2017).

In the circumstances, it seems there are reasonable grounds that the corporate entity X, as owner of Grok, or indeed the corporate entity Grok itself, is acting in contravention of a number of provisions of the Child Trafficking and Pornography Act 1998 (as amended). Inter alia, it is my contention that the following offences are being committed by X, Grok, and/or its subsidiaries:

1.⁠ ⁠Possession of child pornography contrary to section 6(1) in that the material generated by the Grok app must be stored on servers owned and/or operated by X and with the company’s knowledge, in this jurisdiction or in the European Union [subsections 6(3) and (4) would not apply in this case];

2.⁠ ⁠Production of child pornography contrary to section 5(1)(a) as substituted by section 12 of the Criminal Law (Sexual Offences) Act 2017, in that material is being generated by the Grok app, which constitutes child sexual abuse material (CSAM) or child pornography as defined by section 2(1), since it constitutes a visual representation that shows person who is depicted as being a child “being engaged in real or simulated sexually explicit activity” (per paragraph (a)(i) of the definition of child pornography in section 2(1) as amended by section 9(b) of the Criminal Law (Sexual Offences) Act 2017);

3.⁠ ⁠Distribution of chiid pornography contrary to section 5(1)(b) as substituted by section 12 of the Criminal Law (Sexual Offences) Act 2017, in that the said images that constitute child pornography are being distributed, transmitted, disseminated or published to the users of the Grok app by X or its subsidiaries;

4.⁠ ⁠Distribution of chiid pornography contrary to section 5(1)(c) as substituted by section 12 of the Criminal Law (Sexual Offences) Act 2017, in that the Child pornography is being sold to the users of the Grok app by X or its subsidiaries, now that the app has been very publically put behind a pay wall;

5.⁠ ⁠Knowing possession any child pornography for the purpose of distributing, transmitting, disseminating, publishing, exporting, selling or showing same, contrary to section 5(1)(g) as substituted by section 12 of the Criminal Law (Sexual Offences) Act 2017.

You will also be aware that, pursuant to section 9(1) of the 1998 Act, a body corporate is equally liable to be proceeded against and punished as if it were an individual.

Given the foregoing, as well as the public outcry against public decency, it is clear to me that X is flagrantly disregarding the laws of this country put in place by the Oireachtas to protect its citizens.

I am formally lodging this criminal complaint in the anticipation that you will investigate it fully and transmit a file to the Director of Public Prosecutions without delay; I would be grateful to hear from you in this regard.

Yours sincerely,

Barry Ward TD
Senior Counsel

Leaving X

Posted in Biographical, Maynooth with tags , , , on January 18, 2026 by telescoper

I posted a couple of weeks ago about why you and your institution should leave X (the platform formerly known as Twitter). A few days ago the Royal Irish Academy used its BlueSky account to remind users that it issued the following statement last year – even before the launch of Grok’s child pornography engine:

Last year, we made the decision to step away from X.

The Royal Irish Academy is committed to creating, convening, and sharing knowledge for the public good and as an organisation we value Independence; Integrity; Curiosity; Openness and Rigour.

In our view, X no longer aligns with these values

This is a correct decision by the RIA, and although I’m no longer a Fellow of either the Royal Astronomical Society or the Institute of Physics, I am glad they came to the same conclusion. On the other hand, the Royal Society (of which the Royal Irish Academy is the Irish equivalent) continues to endorse X and its machineries of abuse; this is unsurprising because Elon Musk, who owns X and actively promotes the generation of images of child sexual abuse, is a member of that particular club.

All academic institutions should close their accounts on X. There is no acceptable justification to contribute to a network that promotes racism, transphobia, misogyny and the manufacture and distribution of child pornography. I would have thought this was obvious, but it seems not to be. My employer, Maynooth University, has not yet made any statement about the situation with X, and continues to post there.

As I wrote in a recent post

If you don’t leave a social media platform when you find out that it endorses and encourages abusive exploitation of children then you are supporting that behaviour and helping to promote it. There is no grey area here in this. If you don’t draw the line here, where will you draw it? Staying on X is morally indefensible. It is the Epstein Island of social media.

I should also point out that Grok is breaking the law in Ireland (which is where the EU operations of Twitter are based). Even that doesn’t seem to matter to those who continue to use the platform.

On Maynooth University’s Equality and Diversity page you will find this:

The Maynooth University Equality and Diversity Policy has been developed therefore, to realise these core values of equality, inclusiveness, social justice, dignity and respect.

I’d like to know how remaining on X aligns with these core values, and by what process Maynooth University came to a different conclusion on this than the Royal Irish Academy and other organizations mentioned above. One might well be tempted to infer that the above statement, like so many others produced by University Management, is mere bullshit. Perhaps “The Leadership” is waiting to see what other higher education institutions do before making a decision. But that wouldn’t be leadership at all, would it?

By way of a postscript to this let me share this petition which aims to discourage the sharing of content on X and replacement with Mastodon.

https://my.uplift.ie/petitions/take-x-icons-off-websites-and-emails-and-replace-with-mastodon-icons

I make no apology for encouraging the use of Mastodon. BlueSky is better than X but Mastodon is much better than BlueSky in terms of both its functionality and its governance. It doesn’t have as much reach as other platforms, though, which is why I want to promote it. If I had my way, Maynooth would set up its own Mastodon instance, as the Dublin Institute for Advanced Studies has done, for example.

I removed the X icons from this blog some time ago. I can’t stop people sharing content from this blog on X, but I certainly don’t want to encourage it.

Boulanger, Shostakovich and Rimsky-Korsakov at the National Concert Hall

Posted in Biographical, Music with tags , , , , , , , , , , , , on January 17, 2026 by telescoper

It was a great pleasure last night to be able to attend my first concert of 2026 at the National Concert Hall. It was a rainy evening in Dublin, but the auditorium was nevertheless packed. The only issue was that so many people were there, mostly with overcoats checked into the cloakroom, that it took a long time to get out at the end!

Before the performance

National Symphony Orchestra Ireland was conducted for the evening by guest conductor Anna Sułkowska-Migoń who directed a fine and varied programme of music.

The first piece (D’un Soir Triste; Of a Sand Evening) was by Lili Boulanger. I’ve heard a few pieces by her and found them all excellent, as was this one which is very atmospheric and packs a lot into the 12 minutes or so it takes to perform. The only reason Lili Boulanger is so much less famous than her older syster Nadia is that Lili suffered from ill health nearly all her life, eventually dying from tuberculosis just a few months after this piece was composed at the age of 24. Inevitably the number of compositions by her is very small, but as I said earlier everything I’ve heard by her is very good indeed. Her premature tragic death was a great loss.

After that piece there was considerable reorganization on the stage. The brass, woodwinds and percussion all left and space was made for the Steinway (between the conductor and the audience). Then we were joined by pianist Barry Douglas and trumpeter Darren Moore. The latter brough two trumpets with him, actually, of which more shortly.

The piece we were about to hear was listed in the programme as Concerto for Piano, Trumpet and String Orchestra (which is a more accurate description than the usual name Piano Concerto No. 1) by Dmitri Shostakovich. It’s quite hard to classify really, perhaps you could call it a Triple Concerto, but that doesn’t matter much. Music is much more important than how it is classified.

Although I admire the music of Shostakovich greatly, and look out for performances whenever I can, I had never heard this piece before. I was delighted by it. Written in 1933 when Shostakovich was only 27, it is instantly recognisable in style although I bit lighter and quirkier than one normally expects from that composer. Shostakovich had a wry sense of humour, but he often concealed his jokes to avoid getting into trouble. Not so in this piece, which is overtly playful and mischievous, rather than crypic

The trumpet plays a modest – indeed muted – part early on but, over the four movements, gradually becomes more prominent and at the end it delivers a series of exuberant fanfare-like figures as the key switches from C minor to close in C major. At this point I should given special mention to Darren Moore, Principal Trumpet of the NSOI, who played beautifully. He swtiched trumpets just before the end, where the trumpet is required to be louder and more assertive. I’m going to hazard a guess that he switched to a C trumpet for the closing stages, perhaps from a standard B♭ trumpet used earlier. I’ve heard it said that a C trumpet produces a brighter and cleaner sound, and it certainly did sound different from the other trumpet. If I am right it means that the piece concluded with none of the instruments on stage being transposing instruments.

Now a couple of questions for my readers. I have known some jazz trumpeters over the years and they all played B♭ trumpets. On this basis I always assumed that trumpets in classical orchestras would be B♭ instruments. Now I’m not sure this is true. Do trumpet players in classical orchestras usually use B♭ instruments, or does practice vary? A follow-up question is whether orchestral parts for trumpets and other transposing instruments are scored differently, or are the musicians required to do any transposition themselves? (If I had to bet I’d wager that professionally-trained classical musicians can transpose on sight.) Answers and comments through the comments box please.

Anyway, the hugely enjoyable performance was greeted with cheers and generous applause not only for the excellent soloists Barry Douglas and Darren Moore but for the whole Orchestra.

After the wine break we had a much more familiar work, the orchestral suite Scheherazade by Nikolai Rimsky-Korsakov. Pieces from this suite – especially the first section, The Sea and Sindbad’s Ship – often find their way into collections of popular classics and it is probably Rimsky Korsakov’s greatest hit. It’s inspired by the One Thousand and One Nights although there are only four movements, not 1001! The composer certainly included something for all sections of the orchestra, but there was especially beautiful playing by Elaine Clark (leader). I enjoyed this performance too, mainly as a bit of colourful escapism as did the audience, who have it another standing ovation.

Then it was into the queue to collect my coat and thence on foot to Pearse station for the train back to Maynooth. The rain had stopped by then.

Weekly Update from the Open Journal of Astrophysics – 17/01/2026

Posted in OJAp Papers, Open Access, The Universe and Stuff with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , on January 17, 2026 by telescoper

It’s Saturday once more so time for another update of activity at the Open Journal of Astrophysics. Since the last update we have published seven papers, bringing the number in Volume 9 (2026) to 11 and the total so far published by OJAp up to 459. This week has been quite busy; for only the second time in recorded history we published at least one paper each working day.

I will continue to include the announcements made on our Mastodon account (on Fediscience) to encourage you to visit it. Mastodon is a really excellent service, and a more than adequate replacement for X/Twitter which nobody should be using.

The first three papers this week were all published on Monday January 12th in the folder Astrophysics of Galaxies.

The first paper to report this week is “Rotational Kinematics in the Globular Cluster System of M31: Insights from Bayesian Inference” by Yuan (Cher) Li & Brendon J. Brewer (U. Auckland, New Zealand), Geraint F. Lewis (U. Sydney, Australia) and Dougal Mackey (independent researcher, Australia). This study uses Bayesian modelling to explore the kinematics of globular clusters in the Andromeda Galaxy, revealing distinct rotation patterns that suggest different subgroups were added at separate times.

The overlay is here:

You can find the officially accepted version on arXiv here and the announcement on Fediverse here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Rotational Kinematics in the Globular Cluster System of M31: Insights from Bayesian Inference" by Yuan (Cher) Li & Brendon J. Brewer (U. Auckland, New Zealand), Geraint F. Lewis (U. Sydney, Australia) and Dougal Mackey

doi.org/10.33232/001c.155259

January 12, 2026, 9:55 am 1 boosts 1 favorites

The second paper is “DESI Data Release 1: Stellar Catalogue” by Sergey Koposov (U. Edinburgh, UK) and an international cast of 67 other authors. This paper introduces and describes the stellar Value-Added Catalogue (VAC) based on DESI Data Release 1, providing measurements for over 4 million stars, including radial velocity, abundance, and stellar parameters.

The overlay for this one is here:

The official version of the paper can be found on arXiv here and the Fediverse announcement here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "DESI Data Release 1: Stellar Catalogue" by Sergey Koposov (U. Edinburgh, UK) and an international cast of 67 other authors.

doi.org/10.33232/001c.155260

January 12, 2026, 10:11 am 2 boosts 1 favorites

Next we have “On the origins of oxygen: ALMA and JWST characterise the multi-phase, metal-enriched, star-bursting medium within a ‘normal’ z>11 galaxy” by Joris Witstok (Cosmic Dawn Centre, Copenhagen, Denmark) and 37 others in locations dotted around the world. This paper presents new ALMA observations of the JADES-GS-z11-0 galaxy confirm the presence of the [O III] 88 µm line, suggesting it consists of two low-mass components undergoing star formation and enriched in metals.

The overlay is here:

The official version can be found on arXiv here and the Fediverse announcement is here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "On the origins of oxygen: ALMA and JWST characterise the multi-phase, metal-enriched, star-bursting medium within a ‘normal’ z>11 galaxy" by Joris Witstok (Cosmic Dawn Centre, Copenhagen, Denmark) and 37 others dotted around the world

doi.org/10.33232/001c.155261

January 12, 2026, 10:30 am 1 boosts 2 favorites

The fourth paper this week is also in the folder Astrophysics of Galaxies. but was published on Tuesday 13th January. It is entitled “Accelerated calibration of semi-analytic galaxy formation models” by Andrew Robertson and Andrew Benson (Carnegie Observatories, USA). This paper presents a faster calibration framework for galaxy formation models, using fewer simulations for each evaluation. However, the model shows discrepancies suggesting the model needs to be made more flexible.

The overlay is here:

You can find the officially accepted version on arXiv here and the Mastodon announcement here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Accelerated calibration of semi-analytic galaxy formation models" by Andrew Robertson and Andrew Benson (Carnegie Observatories, USA)

doi.org/10.33232/001c.155306

January 13, 2026, 9:41 am 1 boosts 1 favorites

Next one up, published on Wednesday 14th January in the folder Cosmology and Nongalactic Astrophysics, is “Constraints from CMB lensing tomography with projected bispectra” by Lea Harscouet & David Alonso (U. Oxford), UK), Andrina Nicola (U. Manchester, UK) and Anže Slosar (Brookhaven National Laboratory, USA). This study presents angular power spectra and bispectra of DESI luminous red galaxies, finding that the galaxy bispectrum can constrain the amplitude of matter fluctuations and the non-relativistic matter fraction. The overlay is here:

You can find the officially accepted paper on arXiv here and the Mastodon announcement here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Constraints from CMB lensing tomography with projected bispectra" by Lea Harscouet & David Alonso (U. Oxford, UK), Andrina Nicola (U. Manchester, UK) and Anže Slosar (Brookhaven National Laboratory, USA)

doi.org/10.33232/001c.155341

January 14, 2026, 2:00 pm 2 boosts 0 favorites

The sixth paper this week is “Universal numerical convergence criteria for subhalo tidal evolution” by Barry T. Chiang & Frank C. van den Bosch (Yale U., USA) and Hsi-Yu Schive (National Taiwan University, Taiwan). This was published on Thursday 15th January in the folder Cosmology and Nongalactic Astrophysics; it presents an analysis of a simulation suite that addresses the ‘overmerging’ problem in cosmological simulations of dark matter subhalos, showing that up to 50% of halos in state-of-the art simulations are unresolved. The overlay is here:

The final accepted version of this paper can be found on arXiv here. The Mastodon announcement follows:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Universal numerical convergence criteria for subhalo tidal evolution" by Barry T. Chiang & Frank C. van den Bosch (Yale U., USA) and Hsi-Yu Schive (National Taiwan University, Taiwan)

doi.org/10.33232/001c.155367

January 15, 2026, 9:11 am 1 boosts 0 favorites

Finally for this week we have “Detectability of dark matter subhalo impacts in Milky Way stellar streams” by Junyang Lu , Tongyan Lin & Mukul Sholapurkar (UCSD, USA) and Ana Bonaca (Carnegie Observatories, USA). This was published on Friday 16th January (i.e. yesterday) in the folder Astrophysics of Galaxies. The study develops a method to estimate the minimum detectable dark matter subhalo mass in stellar streams, ranking them by sensitivity and identifying promising lines for further research.

The overlay is here:

The officially accepted version can be found on arXiv here and the Fediverse announcement here:

Open Journal of Astrophysics

New Publication at the Open Journal of Astrophysics: "Detectability of dark matter subhalo impacts in Milky Way stellar streams" by Junyang Lu , Tongyan Lin & Mukul Sholapurkar (UCSD, USA) and Ana Bonaca (Carnegie Observatories, USA)

doi.org/10.33232/001c.155386

January 16, 2026, 9:32 am 0 boosts 0 favorites

That concludes the update for this week. I will do another next Saturday.

Marking Progress

Posted in Biographical, mathematics, Maynooth with tags , , , on January 16, 2026 by telescoper

The last day of a week dominated by examination marking found me briefly back on campus to return the batch of scripts I have finished corrrecting and collect the next set (which, happily, is much smaller):

There are 14 scripts in the pile for my second paper, for my 4th year Mathematical Physics module on Differential Equations and Complex Analysis, around one-third of those for my Engineering Mathematics module Differentiaol Equations and Transform Methods. Based on the total number of examinations I have to mark I am therefore now 50% complete, but based on the number of scripts I’m about 75% through. I should be able to finish the latest batch in a day, but there’s no desperate rush so I’ll do them on Monday. I’m not going to start them now as I am off a concert – my first of 2026 – this evening and I prefer not to work at weekends unless I absolutely have to.

I finished the first set of marking yesterday, and spent most of this morning uploading and checking the scores and the conflation of exam marks with coursework scores. Satisfied that all is OK, I returned the scripts to the office for storage until our Examination Board meeting in about 10 days. I wasn’t on campus long, but there was a fire alarm in the Science Building while I was there. As usual, it turned out to be a false alarm.

Anyway, I should be finished with examination matters by Monday evening, which gives me four days next week to get on with other things. I’m looking forward to the change.

The Exam Room – Cyril E. Power

Posted in Art with tags , , , , on January 15, 2026 by telescoper

The Exam Room by Cyril E. Power (c. 1934, linocut, 26.6 x 38.2 cm, Metropolitan Museum of Art, New York; not on display)

De-Dah – Elmo Hope Trio

Posted in Jazz with tags , , , , , on January 14, 2026 by telescoper

I’m in the middle of marking examinations so I will only do a brief post, while I take a short break, to follow up on the one about Hampton Hawes I did a couple of days ago. When I wrote that one it struck me that there are rather a lot of great musicians, especially pianists like Hampton Hawes, who were never appreciated as much as they should have been. Another that springs to mind is Elmo Hope, for whom Thelonious Monk seems to have been a great influence and who therefore provides an interesting contrast with Hampton Hawes who was perhaps more influenced by Bud Powell. Elmo Hope died young, largely because of a bad heroin habit, which also affected his career through his erratic behaviour and the criminal record he acquired for narcotics offences. He was a really fine musician and composer, though, with a very original voice and idiosyncratic sense of time. This track was recorded in 1953 with Paul Chambers on bass and Philly Joe Jones on drums, both of whom were to find fame with Miles Davis a few years later.

Marking Time Once More

Posted in Biographical, Education, Maynooth with tags , , , , on January 13, 2026 by telescoper

Lecturers at Maynooth University are supposed to be available on the telephone to deal with queries from students concerning their examinations. And so it came to pass that yesterday I was “on call”. Since I live in Maynooth, I decided to come into campus in case of a query so I could go to the examination venue l to deal with it if required. In the event, however, the examination passed off without incident and nobody called.

I wasn’t twiddling my thumbs all morning though. It seemed a good opportunity to go through the accumulated coursework for this module, applying various exemptions for medical or other reasons, so that when I’ve marked the scripts I can immediately combine the results with the CA component.

The examination venue, incidentally, was not on campus but in the Glenroyal Hotel in Maynooth. The Sports Hall on campus is usually one of the places for examinations to be sat, but it is not available this year due to refurbishment. The other day I was in one of the shops in the shopping centre next to the hotel and there were some complaints about the lack of available car parking spaces owing to so many students parking there for their exams. Anyway, the exam scripts found their way to my office this morning and here I am again, back home with a stack of an examination scripts to mark. The picture shows about 40 papers from my module on Differential Equations and Transform Methods. I want to get them out of the way as quickly as possible as I have another paper coming up on Thursday and have a lot of other things to do before term starts at the beginning of February. All the usual displacement activities having been exahusted, I’ve already made a start. With a bit of luck I’ll complete this task by Thursday.

I’ve often discussed the process of marking examinations with my colleagues and they all have different techniques. What I do is mark one question at a time rather than one script at a time. What I mean by that is that I go through every script marking all the attempts at Question 1, then I start again and do Question 2, etc. I find that this is much quicker and more efficient than marking all the questions in each script then moving onto the next script. The reason for this is that I can upload into my mind the model answer for Question 1 so that it stays there while I mark dozens of attempts at it so I don’t have to keep referring to the marking scheme. Other advantages are that it’s easier to be consistent in giving partial credit when you’re doing the same question over and over again, and that also you spot what the common mistakes are more easily.

Anyway, I’ve decided to take a break for today. I’ll start again tomorrow.

The Unsolved Mysteries of Erich von Däniken 

Posted in The Universe and Stuff with tags , , , on January 12, 2026 by telescoper

News of the death of the notorious charlatan Erich von Däniken reminded me that at one time, when I was about 11 years old, I borrowed his book Chariots of the Gods from the public library. Even at that age I thought it was a load of nonsense, but I have to admit that I was fascinated by the origin of the Nazca Lines in Southern Peru, most of which were created between 500 BC and 500 AD but were probably based on even older structures. An example, depicting a humming bird, is shown here:

Von Däniken claimed that these were landing strips for ancient spacecraft piloted by extraterrestrials, an explanation that can easily be refuted. The actual purpose of these structures is yet to be discerned. I thought it was likely that they had some astronomical significance, but if they do then it has yet to be elucidated. How they were made is less difficult to explain: almost certainly they were made by scaling up smaller drawings. This would have required some mathematical understanding, and perhaps the use of coordinates, but there’s no reason to suppose that the people who created them lacked such knowledge. What they mean is indeed an unsolved mystery.

The other unsolved mystery is why people fall for the sort of nonsense peddled by von Däniken. It seems to me that part of the answer is that modern humans have an almost irresistible tendency to assume that earlier human beings were much less intelligent than us. This is clearly not true. In fact human intelligence has evolved very little over the past few millennia. What has evolved is knowledge (passed on cumulatively through the generations) and the technology created using that knowledge. Erich von Däniken promoted the idea that only extraterrestrials could have created the Nazca lines; he and others have suggested that the pyramids of ancient Egypt were built by aliens too. It’s part of our desire to think of ourselves as being much smarter than our ancestors. You only have to look at the world today to realize that humans aren’t as clever as they think they are. In fact we’re just as dumb as humans have always been; we just have better gadgets (including, unfortunately, weapons).

Another book I got out of the public library at about the same time was Worlds in Collision by Immanuel Velikovsky. As far as I can remember, this book propounded a new theory of the solar system in which the planet Venus was ejected from Jupiter and then went rattling around encountering other planets and causing various catastrophes. This was supposed to have happened around 1500 BC which “explains” various historical events, including many described in the Bible. It is nonsense of course, but some people lapped it up, as some continue to believe that the Earth is flat.

I find it hard to understand why some people persist in denying scientific advances for which there is considerable empirical evidence and prefer instead to believe in nonsense peddled by the likes of Erich von Däniken. If anyone can solve that mystery they will be doing the human race a very big favour.