It was with some relief that I saw that this year WordPress have not sent a summary of the year just past. So I was able to look at the statistics and make my own judgement.

Numbers of visitors and views were down for the second year running, and in fact the decrease was much greater than last year’s. Of course this doesn’t account for email or RSS subscribers; though the statistics give the numbers of subscribers, this is not really comparable. Related to this is the fact that the number of comments is down. I do not know whether subscribers can easily post a comment, not having ever subscribed to a blog myself.

It happened that I had just been reading an article in the *Guardian* by Hossein Derakhshan, the “blogfather of Iran”. Six years ago, the regime regarded his blogging activities as so dangerous that they sent him to prison for 20 years. They have recently (and unexpectedly) released him, and so (comparing himself to the Sleepers of Ephesus) he returns to a world which has changed quite a lot in six years. He says very forcefully that the web “has been stripped of its political power and just streams social trivia”. If the authorities in Iran had noticed the same thing, perhaps that is why they released him.

Derakhshan remarks on two huge changes in six years.

- Since its inception, the web has been based on hyperlinks. In his view, a web page with no hyperlinks is a cul-de-sac, or (in a different metaphor) is blind; but a web page to which no hyperlinks point is dead. However, it seems (I didn’t know this, but I have never visited this site) that Instagram disables web links posted there, so that visitors are unable to escape!
- Most users of the web now go straight to Facebook or something similar. Then “algorithms” (whose operation is never made clear but is somehow dependent on past browsing habits) suggest further reading to them, which they usually accept. He says, “I miss when people took time to be exposed to opinions other than their own, and bothered to read more than a paragraph or 140 characters.”

As a consequence, it is not enough to post an article and put hyperlinks to it. He says, “I miss the days when I could write something on my own blog, publish on my own domain, without taking an equal time to promote it on numerous social networks”.

He says that the main factors influencing the algorithms are novelty and popularity. Old items sink into obscurity, and unless you attract “likes”, nobody will read what you write.

By his standards, I am terribly old-fashioned. (Though I have a confession to make; although I do not spend time promoting my blog, I am very grateful to Olexandr Konovalov, who runs the CIRCA twitter account in St Andrews, for tweeting some of my posts which he thinks may be interesting to CIRCA followers. However, this fact makes the next observation even more surprising.)

I looked at the list of my most-read posts and pages in 2015. The top 18 of these were posted in earlier years! So it seems that, at least among people who read what I write, novelty is not so important. As usual, topics like lecture notes, mathematical typesetting, mathematics and religion, and expositions such as the symmetric group, stay near the top from year to year.

I also noticed that my monthly pictures from my 2015 calendar were right down at the bottom. So I have decided not to continue with this. I have created a calendar each year since 2009, and produced copies for family members. At first they were “walking calendars”, with each month’s picture of a place where I had walked in the same month the previous year. In 2013 I generalised the concept a bit, and produced a calendar with pictures of the Regent’s Canal in London, and the following year of the Fife Coastal Path. 2015 marked a move away from documentary pictures to something more “artistic”.

This year’s calendar is called “Ancient Seats of Learning”, and features pictures of Bologna, Cambridge, Coimbra, Leuven, Oxford, Paris, Prague, and St Andrews. At my sister’s request I produced some notes to go with the calendar. So this year I will simply put the notes here, and forgo the monthly pictures.

A final note. While posting this, I see that the WordPress editor does not know the word “hyperlink”.

Happy ❢❢❢

2016 = 2⁵3²7 = 32 • 63 = 2⁵(2⁶ -1) = 2¹¹ – 2⁵ = 11111100000

Hello Prof. Cameron,

I know this is completely unrelated, but to comment in your latest post seemed the best way to capture your attention. I have been reading one of your old blog posts on “multiply transitive permutation sets” — https://cameroncounts.wordpress.com/2012/04/08/multiply-transitive-permutation-sets/ . My master’s project is on “Multiparty secure computation” and I realized that the existence of a sharply 2-transitive permutation set of order “n” would enable me to build a secure protocol for the computation of “n-ary Equality” function which interestingly meets my information theoretic lower bounds, meaning that such a protocol is optimal! Although constructing such a set for a prime “n” is easy, I am not able to do so for higher powers of primes. Is there any literature with such a construction that you could point me to, I can’t seem to find one online?

I have a conference deadline on Jan. 24 and it would really help my cause if I could say something to the information theory and theoretical CS community about such an optimal protocol, for at least prime powers.

Thanks,

Sundar

(Electrical Engineering,

IIT Madras, India)

The construction is easy. For a prime, you are using the integers mod p; you need to replace this by the finite field (Galois field) of the appropriate order. So, if F is a field of order q, where q is a power of the prime p, then the permutations x -> ax+b (for a, b in F, a not zero) is a sharply 2-transitive permutation set (even a group).

Galois fields exist (and are unique) for all prime powers. Most algebra books will give you a proof of this. I think you can find it in my “Introduction to Algebra” but I don’t have a copy here to check.