The person who invented momentum (was it Isaac Newton?) was originally going to call it 'moment' but at the very last moment they hesitated.
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If you had to pick a size of spiritualist, what would you go for?

The Art of Uncertainty, by David Spiegelhalter, someone who I have long admired. I watched an Oxford Mathematics Public Lecture Chance, luck, and ignorance on YouTube and really liked the content and the way he presented it.
Early in the talk he quotes an Italian statistician de Finetti who famously declared "probability does not exist". Spiegelhalter goes on the say that after 50 years of mulling things over he has decided that Finetti was right! I don't think he is claiming that we can't attach numbers to whether we think some event will happen or not, only that probability (with the possible exception of subatomic particles) probability is not a property of the world but something humans have made up, a "personal expression of our uncertainty".
By this point he had won me over and I bought the book. The lecture, which I watched right through was fascinating. Towards the end he gave an arresting example using a pack of playing cards as a prop.
Randomly shuffle a pack of cards*. Now the order of cards has almost certainly never, ever happened before in the entire history of humankind. If every person ever born had lived to be 100 and shuffled a pack of cards every second of those 100 years the chance of any of them having generated the same order as the pack you hold in your hands is infinitesimally small. Here are the sums:
Estimated number human who have ever lived 120 billion
Seconds in 100 years about 3 billion
So all those people shuffling away could have produced only(!) 120,000,000,000 x 3,000,000,000
= 360,000,000,000,000,000,000 = 3.6 x 1020Â shuffles. Let's call it 4 x 1020Â to simplify the arithmetic coming in a moment.
But the total number of ways to order the pack is 52 x 51 x 50 x ... x 3 x 2 x 1 = 52 factorial, which my calculator says is about 8 x 1067.
That means the chance that one of those people generated the same order as you is
4 x 1020 á 8 x 1067 which is 1 in 4 with 47 zeros after it
It's theoretically possible but the chances it will are almost unimaginable small.Â
* To do this properly you need to do at least 7 successive riffle shuffles or 1 minute of "smooshing", see the fascinating Numberphile video The Best (and Worst) Ways to Shuffle Cards. Anything less than this the pack is probably not truly randomised.
this winter nightfall
the trees stretch their branches up
reaching for the moon
I came across this crossword clue
It goes round and round again (5)*
So I downloaded a list of 370,105 words from dwyl/english-words on GitHub, and wrote a short Python program to extract all the words that are the same backwards as forwards. My program found 232 reversible words, which appear in the list below. Some of them are rare or debatable â I certainly don't know what most of them mean â but there are plenty of familiar words there.
The longest is 'kinnikinnik', which is in the OED and means
A substance used by some Indigenous peoples of North America as a substitute for tobacco or for mixing with it, typically consisting of dried sumac leaves and the inner bark of willow or dogwood.
a, aa, aaa, aba, abba, acca, ada, adda, addda, adinida, affa, aga, aha, ajaja, aka, akka, ala, alala, alula, ama, amma, ana, anana, anna, apa, ara, arara, asa, ata, atta, ava, awa, b, bab, bb, bib, bob, boob, bub, c, cc, cyc, civic, crc, csc, d, dad, dd, deed, deedeed, degged, deified, deked, deled, denned, dewed, did, divid, dod, dtd, dud, e, ecce, ee, eye, eke, elle, eme, ere, ese, esse, eve, ewe, f, ff, g, gag, gig, gog, goog, h, hagigah, hah, halalah, hallah, heh, huh, i, y, yay, yaray, ihi, ii, iii, imi, immi, yoy, j, k, kaiak, kayak, kakkak, kassak, kazak, keek, kelek, kinnikinnik, kook, l, lemel, level, ll, lwl, m, maam, madam, malayalam, malam, mallam, mam, marram, mem, mesem, mim, mym, minim, mm, mmmm, mom, mum, murdrum, n, nan, neven, non, noon, nun, o, ofo, oho, ono, oooo, oto, ottetto, otto, p, pap, peep, peeweep, pep, pip, poop, pop, pp, prp, ptp, pup, q, r, radar, redder, refer, reifier, renner, repaper, retter, rever, reviver, rotator, rotor, s, sagas, samas, sds, sees, selles, sememes, semes, senones, seres, sexes, shahs, siris, sis, solos, sooloos, sos, sps, ss, stats, stets, succus, sus, t, tat, tebbet, tebet, teet, tenet, terret, tgt, tibbit, tipit, tirrit, tit, tyt, tkt, tnt, toot, tot, trt, tst, tut, txt, u, ulu, ululu, umu, uru, usu, utu, v, vav, vv, w, waw, wow, x, xix, xx, xxx, z.Â
* rotor
The shopkeep said, "I can let you have three. Then that's your lot."
Hail is from OE hagol, which may ultimately be related to Latin calix and Greek κΏĎΝΡΞ, pebble, and so from the same origin as calcium.
enclose : indeterminate number of clothes
It being Burn's Night I had haggis with the neeps and tatties and for afters this cranachan, which was very nice indeed.
The OED defines the name like this
Scottish.
"A dessert typically made with whipped cream, whisky, oatmeal, honey, and berries (esp. raspberries)."
and although it must be traditional the first citation the OED gives is from 1946.
Previously I posted a well known problem which asks: suppose we are on a circular boating lake when fog descends. We know the size and shape of the lake and can travel any distance and in any direction we please, but we don't know where we are on the lake, so we are rowing blind. What is the shortest distance we must be prepared to row to be sure of escaping from the pond. and what path should we follow?
The answer is that you should row in the straight line until you hit the bank and may have to travel a distance equal to the diameter of the pond, and this cannot be improved on. My proof is here. I actually found this for myself some years ago but it turned out to have already been published 40 year before. so I was late to the party.
A follow up question was: what if we are on a pond in the shape of an equilateral triangle? The diameter of an equilateral triangle is just the length of one of its sides and this is the least escape distance if you keep to a straight line. But rather surprisingly (well I think it is) a zig-zag escape path exists which is shorter, at about 0.98198 of the side length.
Here are two pictures of the path in different positions and you can probably see how it manages to always reach the perimeter of the triangle even though it is shorter than the diameter.
abeyance : behave as your parents' sisters tell you to.
đ¨Â Â
Hammer : From OE hamor, Proto-Germanic (PG) *hamaraz and probably from a word that meant "stone"; possibly derived from a PIE root ak- "sharp" or "tip"and if so related to a whole host of words; some surprising examples are acrobat, acronym, acropolis, oxygen, eager and vinegar.Â
đŞ
Saw : From OE saue, PG *säge, from PIE *sek "cut" and related to words such as Saxon, scythe, secateur, section, secant , segment and insect.
đ§
Wrench : From OE wrencan, from PG *wrankjan, from PIE *wer- "turn". Related words include adverse, wrangle, wrap, vertex.
neutron : Ronald the newt
electron : vote for Ron!
boson : ship's officer
quark : duck noise
photon : imitation ton
particle : average tickle
âIâm a bit stretched at the momentâ, said Tom intentionally.
To reiterate this question, imagine we are rowing on a round pond 200 m across when suddenly fog descends and visibility is effectively zero. You are lost and unfortunately the fog fell too quickly for you to have any idea of your location relative to the pond's edge. What is the shortest distance you can row to guarantee reaching the edge of the pond and what path should you follow?
To begin with, any straight path of length 200 m must be a diameter of the pond. Therefore, if we choose an direction at random (we do not know where the shore lies relative to our location so one direction is as good as another) and travel in a straight line, we are certain to reach the bank after at most 200 m. So this is am escape path.
It's natural to wonder if some ingenious non-linear path might guarantee hitting the pond's edge in a shorter distance, but we can show this is impossible.
Here's the proof.
Suppose we can guarantee reach the shore in a distance of less than 200 m by following some path starting at A and ending at M and let M be the point half-way along the path, so the path length for M to A and to B are both less than 100 m.
Consider an arbitrary point X somewhere along the path. The distance along the path from M to X must be less than 100 m and the straight line distance from M to X must therefore also be less than 100 m. Since X was an arbitrary point it follows that every point on the path is less than 100 m from M and we can draw a circle with centre M and radius less than 100 m.
But this is smaller than the pond, which has a radius of 100 m! So it's possible for the whole of AB to lie within the interior of the pond and it therefore cannot form a guaranteed escape path.
What strategy should you follow in order to minimise the distance you must row to be certain of reaching the shore? What is that distance?
2. What if the pond, instead of being circular, is an equilateral triangle of side 250 m? How far might you have to row in this case?
But I hadn't heard it.
âThere's a fairy at the bottom of my garden.â
âReally? Whatâs the fairy called?"
"Nuff. Fairy Nuff."
In a comment, Steven McDonald already gave a nice solution to the puzzle here. My own solution is equivalent but framed a bit differently; I went for a more visual explanation.
Each of the rectangles we want to count is determined by some two rows and two columns of the 10x10 grid, as shown in this example:

For the rows we have 10 choices for the first, which leaves 9 choices for the second, but that will have double-counted each combination, because for example row 5 and row 9 represents the same pair as row 9 and row 5. So we must divide by 2 and there are
(10 x 9) / 2Â = 45
distinct combinations.
Similar reasoning gives 45 of ways to choose two distinct columns and so we find there are 45 x 45 = 2025 different rectangles.
I wrote a program in Python that generates 10,000 (genuinely) random digits 0-9. Then I printed these out as a single long number. It is 375 lines long; here are the first three
831890763767461847514714907504909059910471583635723819115293775185358920959225430857532633499685356491399820546977313764001270746221095521182083788787861672547484439646176036442711628220017949593398149413649851543601589892255388029309553753987882231855967054928709292053025019238151606268592151309301940063808830006628974108
There are 1010,000 such 10,000 digit numbers numbers, and so if you or I run the program again the chances of the same one coming up again are infinitesimally tiny. In fact we can be pretty certain that the same number will never be generated ever again.
So if you ran my program, read the output (takes a while!) and then erased it, you would have seen a number that no-one has seen before or will see again. Your very own number!
This is based on something I saw on YouTube a while ago, I can't recall exactly where.
On this 10 x 10 square grid I have drawn some rectangles with their corners on points of the grid and their sides parallel to the sides of the square. The colours have no particular significance I just used them to make the picture more interesting.

There are obviously many other rectangles that can be drawn on this grid. Can you work out how many there are altogether? Answer on Tuesday.
I didn't know this word but it was the last answer in yesterday's crossword. The cryptic clue wasÂ
Line showing equal water depth is over tub (7)
an imaginary line or a line on a map or chart that connects all points having the same depth below a water surface
As well as this meaning the OED provides a second definition, for a special kind of inkwell:
Trade-name for an inkstand with a float so contrived as to keep the ink in the dipping-well at a constant level
Ingenious but I suppose largely obsolete.Since water is involved is there any connection with baths? Well no, isobath is from Latin and Greek. iso means 'the same', in Latin/Greek as in isobar or isotherm, and the bath element means 'deep' in Greek, as in bathysphere. Bath on the other hand is an English word of Germanic descent and comes from a root that originally had connections with warming, so applying the word bath to hot springs is very appropriate. German Bad meaning bath is essentially the same word.
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