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Richard Walker

Sonnet 33 - Shakespeare as a Painter

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xxx


This is a very famous sonnet and has attracted a large body of commentary, see here for example. Something that has often struck me about this and several other of Shakespeare's sonnets is the way he paints a scene, with a structure like the classic foreground, middle ground and distant background. This is a formula often discussed in art or photography lessons. Shakespeare however starts his word painting from the top - the background - and moves our mental eyes downwards, ending with the gilded streams at our feet. 

In fact this is the order in which I think I view a landscape painting; my eyes are drawn at first to the distance, and then I gradually focus on the parts of the composition representing the middle and near field.

The text above is based on the 1609 Quarto but I have made the punctuation more consistent. The image was AI generated courtesy of Bing.

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Richard Walker

Stresslessness

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Edited by Richard Walker, Thursday, 17 Oct 2024, 16:11

There really is such a word, it's in the the Oxford English Dictionary.

First recorded in 1881, it is the only words I have come across in the OED that lists a citation from Twitter:

I need one month of stresslessness.

@FKAMcButtz 1 October in twitter.com (accessed 10 Sept. 2021)

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Richard Walker

Chat GPT doesn't get it

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Me: 

What do these words have in common? Grapple, impeach, plump, mangonel, spear, quincenary, gunfighter, outdated, compliment, praising.

Chat GPT4: 

The words you provided do not have a straightforward single grammatical or definitional feature in common. However, one possible connection is that many of these words can be associated with conflict or evaluation in some way:

  1. Grapple – can refer to a physical struggle or dealing with a difficult issue (conflict).
  2. Impeach – involves challenging or accusing a public figure (conflict or evaluation of misconduct).
  3. Plump – though generally referring to being full or rounded, "plump for" can mean choosing or supporting something (evaluation or decision-making).
  4. Mangonel – a medieval siege weapon, clearly tied to conflict.
  5. Spear – a weapon used in battle (conflict).
  6. Quincenary – less related to conflict but could be viewed as an evaluation or marking of a significant anniversary.
  7. Gunfighter – directly related to conflict, especially in historical or cinematic contexts.
  8. Outdated – an evaluation term, indicating something is no longer relevant or current.
  9. Compliment – an expression of praise, thus part of evaluation.
  10. Praising – similarly involves positive evaluation or judgment.

So, the commonality could be that many of the words involve conflict, struggle, or evaluation in different contexts.

4o
You said:
what do these words share? grapple, impeach, plump, mangonel, spear, quincenary, gunfighter, outdated, compliment, praising
ChatGPT said:
ChatGPT

The common trait shared by these words is that they are all related to specific actions or roles (either physical or metaphorical). Here's how:

  1. Grapple – A physical action of struggling or wrestling.
  2. Impeach – A formal action to accuse or challenge someone, usually in a legal or governmental context.
  3. Plump – A descriptive action or state of being full or round.
  4. Mangonel – Refers to an object (a type of catapult), which is used for the action of launching projectiles.
  5. Spear – A physical object, but also involves the action of throwing or stabbing.
  6. Quincenary – Refers to the action of marking a 500-year anniversary.
  7. Gunfighter – A person defined by their role or action in gunfights.
  8. Outdated – A state or evaluation resulting from the passage of time (i.e., an action of becoming irrelevant).
  9. Compliment – The action of expressing admiration or praise.
  10. Praising – The act of offering positive evaluation or approval.

Thus, each word is either an action, involves performing a role, or is descriptive of a state resulting from action.

4o
You said:
what attribute do the words have in common
ChatGPT said:
ChatGPT

The attribute that all these words share is that they are all derived from verbs or related to actions. Here's how this applies:

  1. Grapple – Derived from the verb "grapple," meaning to struggle or wrestle.
  2. Impeach – Derived from the verb "impeach," meaning to accuse or bring charges against.
  3. Plump – Derived from the verb "plump," meaning to make something fuller or rounder.
  4. Mangonel – Relates to the action of launching or hurling objects with a catapult.
  5. Spear – Derived from the verb "spear," meaning to pierce or throw with a spear.
  6. Quincenary – Refers to an action marking a 500-year anniversary.
  7. Gunfighter – Refers to a person defined by the action of engaging in gunfights.
  8. Outdated – Refers to the result of the action of becoming no longer relevant.
  9. Compliment – Derived from the verb "compliment," meaning to express praise or admiration.
  10. Praising – A form of the verb "praise," meaning to express approval or admiration.

So, the common attribute is that they are either verbs or linked to actions in some way.

4o

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Richard Walker

Roger and the Garfish

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Do you know a Hrothgar? I bet you do…

Hrothgar was a semi-mythical Danish king who appears in several places in Old English and Old Norse literature. His name is dithematic – it consists of two elements hroth + gar, meaning ‘famous’ and ‘spear’.

Many Germanic names follow this dithematic pattern and there are hundreds, possibly thousands of examples attested. Many survive in modified form to the present day and are very common and familiar given names, for instance

William - will + helm = ‘wish helmet’

Mathilda -  maht + hild = ‘mighty battle’

Rosamund - hros + mund = ‘horse guardian

Robert -  hroth +  beraht = ‘famous bright’

Several of these elements are easy to recognise – will, maht, hros, beraht - and helm survives as a poetical word for helmet. mund was still found in Middle English but is now obsolete, and hild seems to have disappeared earlier.

As for Hrothgar, it has become Roger, a fact I only realised a couple of days ago. Hroth is an element in several other names: Wikipedia quotes Rudolph, Roderick, and Roland; but seems extinct now except in names.

But gar = ‘pike’ i.e.a long, pointed spear, hangs on. This is a garfish, courtesy of Wikipedia.


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Richard Walker

The old path - A Haiku

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Edited by Richard Walker, Tuesday, 8 Oct 2024, 01:02













After the summer/
The old path became overgrown/ 
And lay neglected.

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Richard Walker

Groaners Old & New

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My daughter sent me a list of "groaners" she found somewhere on the web. 

Here are three I rather liked:

How to Write Big Books, by Warren Peace

Things to Do at a Party, by Bob Frapples

I Was a Cloakroom Attendant, by Mahatma Coate

Stop arguing, by Xavier Breath

I felt it my duty to contribute to this genre, so here are some I came up with:

Quit Smoking Today, by Jackie Tinn

Learning to Subtract, by Myna Sign

What to Put in a Cake, by Inga Reedy-Ens

10 Years On the Run, by Noah Plaistow-Hyde




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Richard Walker

The Making of the English Landscape

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The Making of the English Landscape, by W G Hoskins, taught me to see the landscape through new eyes. The idea that underpins the book is captured well by the cover illustration of the 1970 Penguin edition, pictured. I owned a copy of this edition at one time, but now it's been replaced by the Kindle version.


In this book Hoskins shows us how the landscape has been worked and reworked over the last 2000 or so years, and how what we see today can be understood in terms of its history, once we begin to understand what we are looking at and can peel back the layers.

In a similar way studying the origins of the English we use today helps us understand the history of the language and the influences that shaped it. That's why I find etymology an object of absorbing interest, including the etymology of place-names.

Here's a short extract I particularly like from Hoskins, describing a village some miles from where I live and which I've visited a couple of times because it preserves many features of the original settlement. It is a kind of fossil village.

"It stands in the midst of the 1,620 acres of its territory, just off the Icknield Way which forms the entire southern frontier of the parish. The site of the manor house and the church, which stand on the highest ground in the parish, is enclosed by a moat, and the minute village lies along the street to the west. There is not a single outlying farm in the parish, which looks exactly the same on the map of 1950 as it did on the first edition of the Ordnance Survey map in 1834. It is first recorded in a Saxon charter of 973 – ‘the place by the ditch’ – and it retains all the essential characteristics of a small community founded 1,000 years ago. Even the Saxon open fields of Bygrave disappeared within living memory."

Notice the Old English name - Bygrave means "next to the ditch". The -grave element is from an old Germanic root meaning "to dig" and which is also the origin of groove (via Dutch). In fact several of the canals in Amsterdam have names ending in gracht, from the same root, and which means something like "ditch" in modern Dutch.


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Richard Walker

Am I Trigger's broom?

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There is an Only Fools and Horses episode in which the road sweeper Trigger announces that he has won an award for keeping the same broom for 20 years, and adds that the broom has had 17 new heads and 14 new handles.

I was thinking about this and remembered that all the atoms in our bodies get replaced on a surprisingly small time scale. Reading up on it, I found that, according to Time magazine, the turnover is about 98% per year. To put it differently, only about 1 in 50 of the atoms in your body will still be there in a year's time.

In 20 years that would be 1 in 100,000 billion billion billion, which is much more than the estimated number of atoms in a human body. So more or less all the matter that went to make up your body will have been replaced, and you will resemble Trigger's broom in this respect.

I've always been intrigued by this paradox; if all the constituent parts of something are replace, is its identity still the same? It's an important philosophical question, but until now I didn't realise it goes by the name of Theseus's Paradox. 

Plutarch wrote

"The ship wherein Theseus and the youth of Athens returned from Crete [...] was preserved by the Athenians [...], for they took away the old planks as they decayed, putting in new and strong timber in their places."

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Richard Walker

What English words contain "mimi"?

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Someone asked me how mimic was spelled, and that set me wondering: how many words there are with mimi in. 

I thought there could not be many, and indeed it turns out there are just over a dozen, and they are mostly all related in some way to mime. This word originates in Latin mimus, from ancient Greek μῖμος, which referred to some sort of farcical performance, or the act of performing in one, or the kind of act you might put on in such a performance.

So we have mimic, mimicry, mimicking etc., but also pantomiming, and pantomimic. A pantomime is an "all mime', from Greek παντο = all + mime.

The only unrelated words I found with mimi in were semimicro and semimild, which seem to mean roughly what you might guess. 

To finish, here is a rather jolly quotation I found in the OED:

A witty ayery young Lady, of a great fortune,..persecuted with the love of Crazy, Brisk, and Drybob*, whom she mimicks and abuses.

T. Shadwell, Humorists 1671.

A drybob is a smart repartee, according to Grose's Dictionary of the Vulgar Tongue, 1811.





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Richard Walker

find the missing angle!!

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Edited by Richard Walker, Tuesday, 1 Oct 2024, 18:45

I found this geometry problem posted a few days ago maths YouTuber Michael Penn. It was originally published in 2002 in the Mathematical Gazette. It caught my attention because Penn's solution and the one originally published seemed to use trigonometry and calculation of distances involving square roots, and I felt it should be possible to use a purely geometric approach. 

After a lot of thought, by stepping outside the problem I think I've managed to solve it. Below left is the problem and at right the idea that set me on the right road. Suppose I drew in a square and an equilateral triangle to provide a context for the 45° and 30° angles, would that provide any insight?


This was nearly right, but then after more thought I saw  a better approach was to use a square and an equilateral triangle of equal side length, like this.


We can successively compute the angles marked in the diagram is three stages.

1 (green angles marked by single arcs). At C we an internal angle of the equilateral triangle, which is 60 degrees, and two angles which are each half of a right angle, so they are 45 degrees. The line BG passes through H, the midpoint of CF and from the symmetry of the equilateral triangle we see that it makes a right angle with CF, and that the angle CBF is 30 degrees.

2 (blue angles marked by double arcs). The angles at C must sum to 180 degrees, and so angle DCF must be 30 degrees.

CD = CF, because the square and the equilateral triangle have equal side length, and so triangle CDF is isosceles. Hence the two angles marked at D and C are equal and must both be 75 degrees because the angles of CDF must add up to 180 degrees.

3 (red angle marked triple arcs). From consideration of the angles in triangle CGF the angle marked at G must be 30 degrees.

Moreover, triangle CGE has two angles of 75 degrees and so it is isosceles. Because the line through BH bisects the base of this triangle at right angles, the triangle is symmetrical about the line, and the line must pass through point G.

But where has the original problem gone you may ask? Dot in a line from G to A, and,Hey Presto! there it is in plain sight! The triangle shaded in with dots is the one in our problem.


And now look at the kite AGDC. Can you see? - it is symmetrical about the diagonal CG, and therefore θ, the angle we are asked to find, is equal to angle CGD = 30 degrees. Problem solved.






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Richard Walker

Knock-knock 🚪

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Edited by Richard Walker, Sunday, 29 Sept 2024, 21:28

Knock-knock.

        Who’s there? 

Theodore.

         Theodore who?

Theodore’s locked, let me in!


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Richard Walker

Where Have All The Amn't Gone?

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We have the contractions

is not -> isn't

are not -> aren't

But there is no amn't, at least not in standard English. Where did it go?

The best theory seems to be that it did once exist but became ain't, (maybe via amn't > an't > ain't) and then the latter lost its connection to the first person singular "I" and became an informal contraction that can be used with any person: I ain't, you ain't, it ain't, we ain't, they ain't. See here. I think was at one time fairly common but now has an antique feel, to me at least.

Thinking about such contractions I notice that in a question we can use aren't which is a standard contraction: I'm going to the ball, aren't I?


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Richard Walker

Newt in my garden

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We found this newt in the garden just now.


As far as I can tell it is a Smooth New, AKA as a Common Newt. This individual is unusually dark on its upper side, but I'm pretty confident in my identification. It's a beautiful little creature.


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Richard Walker

Sunrise in Rhodes

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Καλημέρα

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Richard Walker

Tom Swifty

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“What’s that chicken doing in the road?” asked Tom crossly. 

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Richard Walker

A Prime Surprise

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It's quite surprising - to me at any rate - that if we take any positive number whatsoever, there is always a prime number that starts with the digits of the number we picked. In fact there are an infinite number of such primes.

I wrote a Python program that lets us input a number and searches for the first prime beginning with the number we entered.

Say we take Einstein's birthdate, 14/03/1879. Write this as 14031879 (which is not itself prime, it's divisible by 3).

Entering this into the program yields 140318797, which as you see starts with the famous scientist's birthdate, and has no divisors other than itself and 1, so it's prime.

Here's another example, this time a random number (I suppose) - the National Lottery jackpot for 14/09/2024, which was 21 27 38 47 49 55. Running the program and entering 212738474955 we get 2127384749557.

By tweaking the program we can get a list of the first few primes that start with the lottery number.

2127384749557
21273847495583
21273847495591
212738474955233

Fascinating!

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Richard Walker

Olive Trees

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Edited by Richard Walker, Saturday, 21 Sept 2024, 20:28


I'm rather pleased with a couple of little olive trees i've just acquired. They have lots of olives on them, I was surprised. I wondered if we could eat the olives, and it seems the answer is yes, but they will need to ripen a bit more, and then be cured, in water or brine, to stop them tasting bitter. It's a bit fiddly but I think it will be worth the effort.

My trees are very small and only youngsters, and that set me thinking about how old olive trees can live to be. This one from Ano Vouves in Crete is claimed to be 2000 - 4000 years, so it stretches back to antiquity.

You can read more about it, and take a virtual walk round it it, at the web site here that I pulled its picture through from.

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Richard Walker

Proof of interesting geometric fact

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Edited by Richard Walker, Tuesday, 17 Sept 2024, 20:01

This is the proof of the question I posted at https://learn1.open.ac.uk/mod/oublog/viewpost.php?post=285828

Here's a sketch


Chord AB is a typical chord passing through a fixed point P in the interior of a circle. Point M is the midpoint of AB and I have drawn in (shown dotted) the two line segments joining P and M to O, the centre of the circle.

By symmetry, the line MO joining the midpoint of the chord to the centre must be perpendicular to the chord. So triangle MOP is right angled, and PO is its hypotenuse.

By the converse of Thales' theorem the hypotenuse of a right angled triangle is the diameter of a circle passing through the three vertices of the triangle, and the centre of the circle is the midpoint of the hypotenuse, N in the diagram above.

The diameter and centre of this circle are fixed by the position of P and O and midpoint M must be on this circle for any chord through P, which is what we wanted to prove.

For information about Thales (fl. 626/623  – c. 548/545 BCE), who seems to have pursued many scientific, mathematical and philosophical interests see here

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Richard Walker

One Liner

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Escalators. They have their ups and downs.

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Richard Walker

Rhyming Nicknames and the origin of Hobgoblin

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Edited by Richard Walker, Monday, 16 Sept 2024, 11:29

Richards often get called Dick - my father always did - but I never really thought much about how Richard could translate to Dick. But yesterday I was reading about how studying pet names for people can help with etymological research and came across the idea of "rhyming nicknames", the result of a process like this

name -> shortened form -> rhyming nickname

So we get Richard -> Rich -> Dick, it's as simple as that

Obviously I knew about ordinary shortenings and diminutive pet names (e.g. Thomas -> Tom ->Tommy) and I've also been intrigued by the fact that names whose shortened form would end in 'R' are modified to end in 'L', e.g. Terence becomes Tel and Harold becomes Hal (probably because "Ter" and "Har" don't trip off the tongue so easily). Another such is Chas.

We can also shorten names from the other end, so Richard can be Hud and William can become Liam for example.

However I hadn't really twigged about the rhyming nicknames but there are lots of them and they seem to have been popular in Middle English. Here are some common examples:

Richard  (again) -> Rick -> Hick

Edward -> Ed ->Ted (or Ned)

William -> Will -> Bill

Here's a surprising one:

Margaret -> Molly -> Polly

or

Margaret -> Meg -> Peg

Finally we have 

Robert -> Rob (possibly via Robin, a diminutive)  -> Bob (or Hob) and Hob is the first element in Hobgoblin, a kind of mischievous elf. Robin Goodfellow, a kind of goblin and Puck-like character, became Hob the goblin.

Goblin is interesting in itself, it seems to be from the same root as German Kobold,  and became the name of Element 27.  Element 28 another troublemaker.



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Richard Walker

Naughty Sunbeams

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There's an oldish joke, I can't remember where I came across it first, that runs as follows.

Q. What happens to naughty sunbeams?

A. They get sent to prism. But they only get a light sentence.

I was thinking about this joke and the fact that the prism refracts the light, and I wondered about the word origin of the word refraction. I looked it up and was quite surprised. It seems to go back to Latin refractthe stem of the past tense of refringere, 'to break or deflect', and be related to fragment and fraction.

The Online Etymology Dictionary goes further and traces it back to a Proto-Indo-European root *bhreg-, 'to break' and that is also the origin of 'break', which is thus a word that has changed little in more than 5,000 years.

Even more surprisingly the same root is probably connected to 'breach', 'brake' and 'brick', as well as a host of other words, see https://www.etymonline.com/word/frangible#etymonline_v_11872.





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Richard Walker

Interesting Geometrical Fact

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Given a circle centre O and a point P in its interior, the midpoints of all the chords passing through P lie on a circle, which also passes through P and through O.

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Richard Walker

Tom Swifty

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"Mirrors don't lie", said Tom reflectively.

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Richard Walker

Ablaut Reduplication

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Edited by Richard Walker, Sunday, 8 Sept 2024, 23:15

My title describes something most of us have known about all our lives without realising it.

Why do 'hip hop' and 'ding dong' sound right, but 'hop hip' and 'dong ding' sound wrong somehow? It's not just familiarity, there is a rule at work, as we shall seen. If I invented a new expression 'squop-squip' it wouldn't sound as satisfactory as the alternative 'squip-squop', because the first version doesn't follow the rule, whereas the second does.

Reduplication is when a word is repeated two or more times. In English there are several kinds of reduplication, for example it can be used to amplify the sense of a word, so 'very very' is stronger than simple 'very' and 'big big' is stronger than just 'big'.

Rhyming reduplication is also very common: higgledy piggledy, silly billy, willy-nilly, Humpty Dumpty, raggle-taggle, easy-peasy (lemon squeezy), teeny-weeny, fuddy-duddy and so on.

Ablaut reduplication is a form of reduplication following a pattern called ablaut, in which semantically related words coming from the same root keep the same consonants but vary the vowel sounds in a predictable way. A classical example in English is sing, sang, sung. Notice that if you say these words aloud, you say the first at the front of the mouth, the second further back, and the third at the back of the mouth.

We have many expressions like; tip-top, tick tock, flim-flam, pitter-patter, jim-jam, and they pretty well all follow the ablaut pattern, with the first part being a higher vowel from front-of-mouth, and the second a lower vowel from further back. We even have some examples with three elements, such as tic-tac-toe and bish bash bosh.

This ablaut pattern is thought to be inherited from the ancient and lost language that is the ancestor of moist European and West Asian languages today. This language had no written form that we know of, and no longer exists, but has been extensively reconstructed from its more recent descendants.

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Richard Walker

An Interesting Geometrical Construction

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Edited by Richard Walker, Friday, 6 Sept 2024, 14:41

Someone asked on Quora how, given two concentric circles, we can construct a square having two vertices on one circle ands two on the other.  


I think this was answered by the notable Alon Amit, but I deliberately haven't looked at his solution yet. Here is my solution.

Choose a point A on the outer circle c and rotate c through 90 degrees about A, to give circe c', shown fotted.


Because c' is the rotated image of c, any point P' on c' is the image on a point P on c, and any point P on c is the inverse image of a point P' on c'. Angle PAP' is a right angle, from the construction, and length PA = length P'A by the same reasoning. This defines the square PAP'Q with two vertices on c, shown shown shaded.

All we now need to do is choose P' to be the point where the dotted circle c' intersects the inner circle and we obtain the required square, since Q must lie on the inner circle by symmetry.


Of course if the inner circle is too small this doesn't work, because the dotted circle and the small one don't intersect. The limiting case is when the inner radius is ~ 0.414 of the outer one.

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