We live these days on our inner fat, turning over the souvenirs and trophies we've kept, poking in our library and record collection.

A cocooned Irish friend sent Lise a clip in which the French song La Mer was accompanied by seaside scenes painted by Sorolla.  Our beleaguered friends in Madrid live around the corner from Joaquín Sorolla's former residence, now a fine museum.  I dug out our copy of Begoña Torres González beautiful Vida y Obra Sorolla, 978-84-662-1879-5 and came across this

image of his 1906 Puente de Alcántara. Reminded me of days when we could roam.  In the Summer of 2006, I got the bus to wait, and ran across this very bridge to the city (Toledo) side, to get down the bank and taste the Tagus.

Toledo! What a place!  City of steel, Damascene, El Cid, El Greco, and the main channel through which Moorish civilization enriched Europe.

Tasting great rivers is a habit learned from Belloc.  I liked Belloc a lot in my teens.  Revisiting him, I find his antisemitism repellant.

Tagus is a universe, from the pristine stream of the Alto Tajo in the highlands northeast of Madrid, to the magnificent fortifications of Toledo, all the way down to Lisbon, with its gateway to the whole wide World.

Stephen Buckley: Fractals and Real Dynamical Systems

Second edition on the way.
http://www.logicpress.ie/2020-1/index.html

Des MacHale: 1001 Silly Questions

Another Des MacHale gem on the way.
http://www.logicpress.ie/LS/2020-3/index.html

Why didn't God make women first, while He was fresh?

Lise O'Farrell's second novel, The Tears of God, just done:
http://www.logicpress.ie/LS/2020-2/index.html

Newly-discovered Fergal Anton book on limerucks just done.
http://www.logicpress.ie/LS/2020-1/index.html

Here is a limeruck:

Twain
A raft, on a river so wide,
A boy, and a slave by his side.
They trusted to luck,
Ole Jim, and young Huck,
But they've passed the Ohio! Oh, #*%!

Walter Hayman RIP

Walter died on New Year's Eve. He has been my friend for something over forty years. The world will not be the same without him. RIP.

ebooks

Learned how to make an epub version from a LibreOffice source. Submitted an ebook version of Fergal Anton's Tipperary Tango. This is currently available from Lulu.com, and pending approvals should be up soon on Apple, Amazon, Barnes and Noble, Kook, and the rest. The ISBN is 9780244071684. However, I've not yet found any ready-made way to make an epub from latex source, including properly-formatted mathematics and graphics.

Armagh

On the 19th of June we went with the O'Malleys to Ard Mhacha (Armagh) and Eamhain Mhacha (Navan Fort). We had elevenses at the Mulberry coffee-shop opposite the Cathedral gate, then visited the Cardinal O'Fiaich Memorial Library and Archive (a remarkable resource) and the R.C. Cathedral (dedicated to St Patrick), and Navan Fort (Eamhain Macha).  Finally we toured the Palace.

All recommended. Exceptionally friendly natives. Only 90 minutes from Dublin.

We learned of the Tandragee man, a stone statue said to represent Nuad (formerly known to us as Nuadhat Lámh Airgid, Nu-at of the silver arm), king of the Tuatha Dé Danann, who gave his name to Maynooth (Nu-at's plain). Maynooth's main stream is the Lyreen, named for his little finger, and meets the Rye (presumably Rí = King) river just below the town. Nuad lost his arm at the battle of Má Tuireadh, and as a result had to surrender the kingship. Dían Cecht made him the perfectly-functioning silver arm so that he could resume the kingship from the Bres Mac Elatha, who turned out to be a miserable get. It's in the old C of I cathedral, also dedicated to St. Patrick, of course.

New book: Analysis One

I've put my text Analysis One out there. This is the first course in 'hard analysis', the modern-day pons asinorum. 
The pdf of the text remains freely available.
You can get a copy at logicpress.ie (see the catalogue) or from lulu.com (search for Anthony G. O'Farrell).

The hardcover: 

The pdf:

Cherry Blossoms, thirty-first of March

The clocks have sprung on.
The light beats the dark.
I've reached the bright half of another year.
The Moon waxes, full next Tuesday.
Then we watch for Easter sunrise.
Praise the Lord!

Tim Murphy, RIP

When a man dies, a universe is destroyed, even for realists.
Tim's last post on his amazing blog was on 11 February,
and he joined the majority on the 17th. See

http://timmurphy.org/

In  paradisum deducant te Angeli.

Conference Pair

Love Mathematics

1. Go to
http://sagecell.sagemath.org/

2. Copy and paste the following Sage code into the box:


t = var('t')
parametric_plot( [sqrt(2)*cos(t), sin(t) + (3/4)*sqrt(abs(cos(t)))],
                [t,0,2*pi],aspect_ratio=1,fill=true,axes=false,
                thickness=4, color='red',plot_points=2000,
                fillcolor='pink'
               )


3. Press Evaluate.

4. How can you hate that?

(I'm happy to acknowledge that the idea comes from
an equation in Harun Siljak's book, Murder on the
Einstein Express and Other Stories.)

What shape is the square root of -1?

Yesterday we celebrated Quaternion day again, and the Hamilton Walk.  Since it was Sunday, there were no school groups.  There was a good turn-out of grown-ups, and quite  few very small children, some in back-packs.  The formula rescratching is always done by the youngest person present who understands algebra, and this year it was Caoimhin Malone, the youngest ever.  He was willing to cede to Ferdia O'Cairbre, but F graciously declared that he had already done it, and was happy to let C try.


In view of the maturity of the group, I decided to open the spot quiz (before the song and carving, and usually restricted to children) to the whole assembly, and asked the question: What is the shape of the square root of -1? 

A quaternion a +bi+cj+dk has a scalar part a and a vector part v=bi+cj+dk. We can consider v as a point in three-dimensional space, so if we have a set of pure vector quaternions, then it has a shape.  In the real numbers, there are no square roots of -1. In the complex numbers, there are just two, so the set is snake-eyes.  In the quaternions all the square roots are pure vectors, so what shape do they form?  The prize was taken by Harun Siljak   (or Shiljak -- that S has a v on top), who was first with the correct answer.  Harun is the first known Bosnian participant in the Hamilton walk.

A letter from Don Chesley drew attention to a fine article by
Katharine Merow in the online Slate Magazine 
http://www.slate.com/articles/health_and_science/science/2016/10/we_should_celebrate_hamilton_day_a_mathematical_holiday_on_oct_16.html
in which she proposes a global annual holiday on the 16th of October.

I suppose Harun is the same name as that of Haroun al-Rashid, that enlightened despot and patron of mathematics immortalized in the the tales of Sheherezade from the Thousand-and-one Nights. Reminds me of the trick mentioned by Des MacHale on Saturday, that involves taking a number such as 473473 or 287287, and dividing it in turn by "some random numbers, such as 7, 11 and 13."  Des gave a brilliant acceptance speech when he was awarded the first ever Maths Week trophy to recognize achievements in popularizing mathematics.  By common consent he was the outstanding choice.

Des passed on a very interesting question raised by a little boy in school: Where do the numbers go, when you rub them off the blackboard?

Ben Bulben Hike

My friend and I walked up Ben Bulben on Friday.  I've been up before, but thought it worth checking what information was on the web.  Turns out that the info is misleading, so here is a heads-up if you are thinking of going there.


The nose of Ben Bulben,  and the view back down.


I like to walk -- not climb -- up mountains, and get to the top.

When I google Ben Bulben hike, I get:

1. The Sligo tourism description of the "Ben Bulben Loop".   This is a walk that doesn't go up the mountain at all, but lets you look at it from around the "nose".  It involves about 45m of ascent.  The summit of Ben Bulben is at 526m.

2. A number of descriptions and Youtube videos that describe climbs -- not walks.  Some are described as "easy climbs".  However, all these involve climbing up vertical bits of cliff.  If you are not an experienced climber, they are good ways to lose your life.

3. Some descriptions of walks that involve clambering up rather steep slopes with loose stones on them.   These are ok in good weather, provided you are careful.

I did not see a description of the straightforward way to walk up.  This is steep, but not crazy.  You take the public roads  around the north side and up into the valley (Glendarragh) between Ben Bulben
aka Benbulbin) and Benwiskin.  Park somewhere around the "scary bridge" (an 8-foot-wide slab of reinforced concrete without any parapet), grid G468703.  You walk up by the well-used path that climbs southward up to the plateau.  It runs up to the left of the river that runs down the southern end of the valley.  Once you get up you can do a nice loop out west across the 500m summit and the neck to Ben Bulben (526m), back to the neck and then south-east to King's Mountain (462m) , and back north to the same path back down.  Takes about 4 hours from the bridge.  Bring a compass and the 1:50000 Sheet 16, in case you find yourself in mist.   On Ben Bulben, be sure to keep on west to the nose,  after you reach the summit. Stop when you get to top of the 45 degree slope, since a slip on that will take you over the cliff and end your life.   The view all round and down from the nose is absolutely incomparable.  If the weather is suitable, there is a path running close to the cliff edge on the north side, with spectacular views.










(The path up to the plateau is probably discussed on the web, but since I didn't run across it in a quick search, others might end up doing something they might regret, based on what they find online.  Hence this post.)

 Photographed on our patio this morning. The hose is half-inch diameter (about 12mm).

 He seemed to be lost, or just terrified. I went in, got the camera, and came back out, and he was still trying to hide beside the hose.

Is this a pigmy shrew, or a greater white-toothed shrew?  Or something else?

Amusing Book: Tipperary Tango

Less Serious Books, a new division of Logic Press, is publishing the story Tipperary Tango, by the rather enigmatic Fergal Anton, who vanished in mysterious circumstances about twenty years ago.
See:
Less Serious

Analysis Zero

This is my new book on the foundations of analysis. The hardcover version can be got for half-price at the printer's site: http://www.lulu.com/shop/anthony-g-ofarrell/analysis-zero/hardcover/product-22350069.html

It is a bit expensive.  There will in due course be a paperback that you will be able  get from Lulu.com for about Euro 12.50.

Added 3-10-2015: In fact, the paperback costs just Euro 10.00 from Lulu.  (Recommended Retail Price 19.99).

Little book of lecture notes on Geometric Measure Theory

Logic Press has just published Maria Roginskaya's lecture notes.  The book is called Advanced Basics of Geometric Measure Theory, and is available at
http://www.lulu.com/shop/maria-roginskaya/advanced-basics-of-geometric-measure-theory/paperback/product-22307272.html

Topics covered include the Banach-Tarski paradox, cardinals and ordinals, equivalents of the Axiom of Choice, measure and integral, Hausdorff measures, and a remarkable recent result of Korner's on the Hausdorff dimension of sets of sums.

It will take until November or so before the ISBN registration propagates to the whole system, so if you were thinking of ordering it for your institution, or through a bookseller, you should wait until then. It is available right now direct from the printer, Lulu.com, at half price.

Cyclo-lecteur's blog:

We met Jean-Pierre Brèthes when we sat down on the same bench to watch the Chaban-Delmas bridge open for a cruise ship leaving Bordeaux. He blogs at
http://cyclo-lecteur.blogspot.fr/
and is worth reading.