Personal Blogs

For some reason I wondered about the origins of "go" and when I looked it up found a discussion of why the past tense of "go" is "went" rather than "goed". It is rather strange.

In Old English "go" was gan, the ancestor of the modern word, and it already had an irregular plural eode, a word of unknown origin.

At that time "went" was the past of wendan, connected with modern wind (as in turn). "Wend" has survived into Modern English as "wend", as in wend ones way. Nowadays the word has narrowed its meaning to imply travelling in a circuitous and roundabout way and has a rather archaic ring, but originally seems to have meant wind in the general sense.

"Wend" had a past tense "went" (like spend -> spent; send -> sent; lend -> lent; rend (meaning rip) -> rent and probably others) and for some reason is Early Middle English this started to be used in place of eode, which was eventually replaced, and disappeared from the language.

But why was "goed" not adopted? One possibility could be to avoid confusion with "good" which would at that point have had a vowel sound like that in "oak" and a 'g' like that in "go". Just a theory, I don't really have a grasp on these sound changes.

As a wordplay enthusiast I've often mused over what words can be formed by combining the symbols of the chemical elements.

For example, Actinium-Actinium-Iodine-Arsenic would give "acacias" and Barium-Oxygen-Barium-Boron-Sulphur would give "Baobabs".

A while ago I did try to come up with some  examples by hand but only found a few, so I decided to write a little program in Python.(see below[*]). For simplicity I just used lowercase letters e.g. "h", "he", "li" etc. but putting back the capitals would not be too hard. I also excluded the artificial transuranic elements (26 found to date) but again adding them would be easy enough. My reason for omitting them is that their name and symbols are a bit less familiar.

Also note it uses a "greedy" algorithm and if the first two letters is a valid symbol it chooses that first, so it can't handle "those", because it finds "th" (Thorium), then "os" (Osmium), and now the "e' is orphaned. To overcome this I'd need to add some backtracking capability so the program gets a bit more complex.

I analysed an open-source word list of 113,810 words and found 13,435 - let's call them "elementary" - words, about 12%. We'd expect the chances of a word being elementary to fall off as words gets longer, because only 92 one- or two-letter combinations of letters are symbols of chemical elements but the total number of possible one- or two-letter combination is 702, so only about 1 in 8 correspond to elements.

Nonetheless I found some surprisingly examples, with the champion being the 16-letter "counteraccusations". Here are some other long ones.

acacias
acarpous
accepters
accessions
accountancy
accurateness
accuratenesses
articulatenesses
counteraccusation

"counteraccusations" represents Cobalt Uranium Nitrogen Tellurium Radium Carbon Copper (Cu) Samarium Titanium Oxygen Nitrogen Sulphur; 11 distinct elements which I imagine is a record.

What about whole sentences? It's not easy to make up natural-sounding ones, but here is my attempt at one from a scientific setting. I've added proper punctuation to make it more realistic.

"Pop both new boxes in lab one Gabby, ta."

[*] Program follows: list of symbols, then function to test words  then sample function calls.

elements = [
    "h", "he", "li", "be", "b", "c", "n", "o", "f", "ne",
    "na", "mg", "al", "si", "p", "s", "cl", "ar", "k", "ca",
    "sc", "ti", "v", "cr", "mn", "fe", "co", "ni", "cu", "zn",
    "ga", "ge", "as", "se", "br", "kr", "rb", "sr", "y", "zr",
    "nb", "mo", "tc", "ru", "rh", "pd", "ag", "cd", "in", "sn",
    "sb", "te", "i", "xe", "cs", "ba", "la", "ce", "pr", "nd",
    "pm", "sm", "eu", "gd", "tb", "dy", "ho", "er", "tm", "yb",
    "lu", "hf", "ta", "w", "re", "os", "ir", "pt", "au", "hg",
    "tl", "pb", "bi", "po", "at", "rn", "fr", "ra", "ac", "th",
    "pa", "u"
]

def parse(word):

    result = []

    while len(word) > 0:

        token1 = word[0:1]
        token2 = word[0:2]

        # Look for two-letter symbol first
        if token2 in elements:
            result.append(token2)
            word = word[2:]

        # If not check for 1--letter symbol 
        elif token1 in elements:
            result.append(token1)
            word = word[1:]

        else:
            return 'fail'
        
    return result

print(parse('cream'))
print(parse('scone'))

Equilateral triangles ABC and CDE share a common vertex at C. Prove that AD and BE are equal in length.

Solution tomorrow.

Every now and again someone comes up to me in a pub or a hotel or a classroom and sketches this little picture.

"Can you draw this", they say, "without going over the same bit twice or lifting the pen off the paper?"

"I can", I say, and then I try to explain how I can be so confident without even picking up the pen. Here's how it goes.

First identify each point where two of more lines meet.

Now count how many lines meet at each point.

For it to be possible to trace the figure it's necessary that either:

• All the numbers are even, or;
• Two and only are odd (as is the case here) and you start from one of these and end at the other. 

This is because every time you pass through a point you add 2 to the count. If you start and finish at the same point then an extra 1 is added when start and another 1 again when you finish, so all the counts are even. Otherwise if we start and finish at different points, both get an extra 1, so their final count will be odd but all the other counts even.

Providing one of these holds it can be proved (but I'm not going do so here, it's not that hard but a bit too long) that the figure can be traced. And here's a solution (not the only one). The points with an odd count are highlighted.

These ideas were first articulated by Leonhard Euler in 1736. A problem that must have been going the rounds at the time concerned the seven bridges of Königsberg (in Prussia then; now Kaliningrad in Russia). The puzzle was: is it possible to find a tour that crossed each bridge exactly once.

Here are the bridges as shown in Euler's original paper, which you can find in translation here.

Out of interest I looked for the bridges on Google Earth and as you can see only five are still there; b and d were presumably destroyed in WW II. I hope I have identified the other five correctly.

Now if we take A, B , C and D to be points, and the original seven bridges a - g as lines connecting the points, we get this figure, and the problem of the Königsberg bridges becomes one of tracing the figure without crossing any bridge twice or taking the pen off the paper.

All four of A - D have an odd number of lines meeting at them, so from the discussion given earlier the puzzle of the seven bridges has no solution, although with only the five bridges that have survived it does become possible to make a tour of the desired kind, starting at A and ending at D, or vice versa.

Euler called his paper, which has since become very famous, "SOLUTION OF A PROBLEM IN THE GEOMETRY OF POSITION" and it gave rise to the branch of mathematics now called graph theory: nothing to do with x and y-axes, or plotting lines and parabolas etc., but concerned with the properties of arrangements consisting of points (vertices) connected by lines (edges). As well as being of great intrinsic interest and beauty, graph theory is a vital tool in the design of the algorithms and data structures behind the computer programs that play such an important role in modern life.

My friend heard a song by Duffy and when she sang

what he heard was

"Mercy" makes better sense, people don't often beg for birdseed, but that's not necessarily how Mondegreens work.  In The Language Instinct Steve Pinker mentions Mondegreens and notes that the mishearing is often fits the context less well than the original word and this seems be an example of that.

Yet perhaps a singer begging for birdseed does have some kind of underlying logic, when you think about it.

"AI Overview" in Chrome says a polyhedron is:

"a three-dimensional geometric shape with flat polygonal faces, straight edges, and sharp corners or vertices"

which is not a bad definition in my view. Some of these polyhedra are familiar to us; for example here is a back-of-an-envelope sketch of some with 4, 5 and 6 faces.

Note that we are not concerned here with the particular angles or side lengths, just with the topology: how many faces and vertices there are, how many sides each face has, and what faces fit with what other faces around each vertex. 

The solid with 4 faces - a tetrahedron aka triangular pyramid - is the only possibility for 4 faces, and for 5 faces there are exactly two polyhedra - the pyramid with a quadrilateral base and the triangular prism.

The two hexahedra shown are not the only ones however. There are 7 altogether; can you find some or all of the remaining ones? Solution in the Comments.

As the number of faces grows the number of possible polyhedra climbs exponentially [1].

Numbers up 10 faces are exact, but those from 11 on are only estimated.

Amazingly Steven Dutch has enumerated and classified all 2606 enneahedra, finishing on 2 November 2016 [2].

Here's a quick question to finish - what is a regular hexahedron better known as?

References

[1] https://oeis.org/search?q=A000944&language=english&go=Search

[2] https://stevedutch.net/symmetry/polynum0.htm

Malfatti asked how to find three circles in a given triangle, such that each circle would be tangent to the other two cirrcles, and to two sides of the triangle. It seems to have been thought at one time that this would also be the solution to the (different) problem of packing three (not necessarily equal) circles into a triangle so as maximise the are covered by the circles.

For an equilateral triangle Malfatti's original problem is solved by the arrangement in Figure 1.

Intuitively it seems quite plausible that might at the same time maximise the area covered. There doesn't seem to be any way we can make any of the circles bigger without the others becoming smaller, and we might expect the case when the circles are equal to be optimal.

But it isn't; the arrangement of Figure 2 covers a bigger area.

Rather pleasingly the small circles are one-third the size of the big one, as illustrated by te three dotted circles.

The difference is not great, but after some trigonometry and algebra it emerges that Figure 2 is the clear winner, covering 73.9% as opposed to Figure 1 with only 72.9%. 

This set me thinking: what if we replace the equilateral triangle with a square and asked for four circles that cover as much of the square as possible?

The arrangement analogous to Figure 2 appears in Figure 3.

After a bit of calculation, we find this covers 85.5%, and based on our earlier experiences we'd expect this does better than using four equal triangles.

And indeed it does, and we need no calculations; here is a "look and see" proof.

This just amounts to four half-scale copies of Figure 3, but minus the three small circles. So in each smaller square we are covering less than the 85.5% of Figure 3, and the overall percentage covered must also fall short of this value.

This is not a proof that Figure 3 is the best possible of course; only that it is better than Figure 4. Maybe some other arrangement might achieve more than 85.5%.

My brother snapped this unusual cloud formation.

The Cloud Appreciation Society classified it as "Altocumulus stratiformis radiatus, often seen as a precursor to changing weather patterns" and sure enough the weather did change.

I watched a video on YouTube about a bee expert relocating a swarm of bees. After he'd skilfully coaxed them into a special cardboard box, he was asked how many he thought there were, and he said, by the weight of the box, about 20,000.

This reminded me of an old story about a man who had to transport a large number of canaries on perches in the back of a lorry. But the combined weight of the canaries was more than the lorry's axles could safely bear.

To get round this, he got another man to travel in the back with the canaries and stir them up with a pole at frequent intervals, on the principle that as long as they were flying around they wouldn't put any weight on the lorry's axles.

Would this scheme work?

This charming little tree with its delicate foliage is a silver wattle, Acacia dealbata, and a newcomer in our garden.

A. dealbata is a fast growing evergreen, native to south-east Australia, and can reach 30 m in height, so this little tree will need watching.

The flowers of A. dealbata are a mass of bright yellow, picture in the photo from Wikipedia.

A relative, the golden wattle Acacia pycnantha, also has bright yellow flowers, and is the national flower of Australia. I've read a few stories set in the outback and wattles often got a mention but until now was pretty hazy about what exactly there were.

Acacias belong to the pea family of plants and there about 1,000 different species in Austraila. and Africa. The name acacia and the common name wattle are both interesting words etymologically speaking. Acacia is from the Ancient Greek name for the plant, ἀκακία, "akakia", via Latin. The origins of the Greek name are unclear however; it might be related to PIE *ak-, "sharp", "topmost", as found in words like acute, acid, acropolis, acrobat, acronym.  But other theories suggest it was borrowed into Greek from a pre-Greel language spoken in the region.

Wattle seems to derive from the wattle in the phrase "wattle and daub", a traditional way of constructing walls with a framework of branches roughly plastered with lime plaster or mud, perhaps with horsehair in it. The trees were called wattles in Australia because there they often provided the required branches. Wattle itself comes from a OE word watel, "hurdle", and this may have a connection with weave, but there are different theories and the ultimate origin is unclear.

Image credit: Eugene Zelenko, see here 

Here's a little proverb you surely ought to know,
Horses sweat and men perspire but ladies only glow.

—Traditional

I heard someone say they were "sweating like a pig" and wondered where this expression came from. Pigs don't sweat you see; according to Wikipedia not many kinds of animal do. Dogs and cats can only sweat through their paws but rely a lot on panting to keep cool, especially dogs.

This set me wondering about birds too. The RSPB lists a number of ways they can thermoregulate, including

1. Staying in the shade
2. Panting (I didn't know birds pant but they do)
3. Using birds-baths and fountains
4. Restricting activity to the cooler parts of the day

There have been suggestions that some birds keep cool by flying higher, where the air is cooler, but this is uncertain. There is also something with the exotic name of "gular fluttering", practised by herons and cormorants (for example), which involves the birds fluttering the insides of their throats accompanied by rapid breathing.

And what of sweating like a pig? According to this website the phrase appeared in the Morning Post from Wednesday 10 November 1824, applied to a boxer, but this doesn't cast any light on the origins of the phrase. Many sources seem to link it to pig-iron, which the OED says is

"Cast iron as first obtained from a smelting furnace, in the form of oblong blocks"

and this quote shows why the term pig is applied

1. 1806

   The lateral moulds or channels are called pigs; and hence cast-iron receives the appellation of pig-iron.

The main channel is the sow you see and the side channels the pigs. This seems fairly convincing, but where does sweat come in? The suggestion is that as the iron cooled down condensation formed on it and resembled sweat, but this awakes the sceptic in me, I don't find it very believable. Why would the hot iron cool below the temperature of the surrounding air and condensation form?

I tend to go with the website referred to above, which suggests pigs are often considered dirty (this is, ironically, because they wallow in mud to keep cool) and from that pig has become a pejorative term, which was then attached to something else (sweat) considered disagreeable or nasty.

I left some salad leaves out and they went off a bit. My friend said they were "manky" and put them in the recycling. 

It's a common word but where did "manky" come from? Looking it up, there's a whole raft of theories, with a lot of interconnections between them, and although there's probably no single path we can trace with certainty, the majority view is that it probably derives from Latin mancus = maimed, which is also the root of French manqué = failed.

Manqué is a strong contender to be the immediate source — we can easily imagine someone pronouncing it "manky" — but it could also have come from cognate words found in other languages, such as Italian mancare or Scots mank.

Wiktionary on the other hand suggests an Old English word *mancian with cognates in other Germanic languages and which could have connections with Latin mancus, and it's even possible all these words come from an ancient Proto-Indo-European root *mank, again with the sense of maimed, damaged, deficient.

It's also been suggested that Polari may have played a part in the word becoming more common from about 1960 onwards. Here's the Google ngram

There are also words such as "mangey" and "mangled" which may be connected with manky in some way, or what have an influence on its use. But in the end it is, as the OED puts it. a word of uncertain origin.

My friend was right about the salad though. It was dead manky.