Author Archives: Lise Andreasen

#ThisWeeksFiddler, 20250801

Skriv en kommentar

This week the #puzzle is: Can You Squeeze the Squares? #optimal #placements #packing

There’s a square board with side length A. Your friend cleverly places a unit square on the board and challenges you to place another unit square on the board—without moving the first one—so that it too is entirely on the board and the squares don’t overlap. (The unit squares can touch each other.)
Alas, it’s impossible for you to do so! But there’s some minimum value of A for which you can always place a second unit square on the board, no matter how cleverly your friend places the first one.
What is this minimum value of A?

And for extra credit:

Now there’s another square board with side length B. This time, your friend cleverly places three unit squares (which can touch but not overlap) and issues a similar challenge, asking you to place one more unit square on the board.
Once again, it’s impossible for you to do so! But there’s some minimum value of B for which you can always place a fourth unit square on the board, no matter how cleverly your friend places the first three squares.
What is this minimum value of B?

Can You Squeeze the Squares?

***

“Last Week’s Fiddler. Congratulations to the (randomly selected) winner from last week: 🎻 Lise Andreasen 🎻 from Valby, Copenhagen, Denmark.” 😁😁😁

***

Highlight to reveal (possibly incorrect) solution:

Desmos 1 Desmos pictures 1 and 2.

Some assumptions:

  • The placement of the 1st square has to be symmetrical in some way. It will be in the middle. If it is not in the middle, some corner or side will leave more room for the 2nd square, and of course my friend doesn’t want that.
  • The 1st square will either have sides parallel to the sides of the big square or 45 degrees shifted.

Some experimentation:

  • As picture 1 shows, if the 1st, green square is tilted, A is about 2.7. As picture 2 shows, if the 1st, red square isn’t tilted, A is 3. (This picture also demonstrates, that the 2nd square shouldn’t be tilted.) My friend will choose not to tilt the square. A = 3.
  • If A was slightly smaller, the ring around the 1st square wouldn’t be wide enough for an extra unit square to fit.

And for extra credit:

Desmos 2

Experimentation:

  • A small square in the middle of the big square, aligned with the sides of the big square, dominates all 4 corners of the big square nicely. It’s very hard to come up with something using 2 extra squares, that could dominate a bigger square better. I therefore say as a 1st guess B >= 3.
  • A tilted square might dominate 2 corners. 2 other aligned squares in the 2 other corners handle the rest. (Desmos shows 2 green squares, when there’s room for them.) In that case B = 2 + √2 = 3.4142.

#ThisWeeksFiddler, 20250725

Skriv en kommentar

This week the #puzzle is: Can You Sprint to the Finish? #probabilities #strategy #optimal

… you and a competitor are approaching the finish of a grueling stage of the Tour de Fiddler. One of you will win the stage, the other will come in second. As you approach the finish, each of you will test the feeling of your legs, which will be somewhere between 0 percent (“I can barely go on!”) and 100 percent (“I can do this all day!”). For the purposes of this puzzle, these values are chosen randomly, uniformly, and independently.
Immediately after feeling your legs, you and your opponent each have a decision to make. Do you maintain your current pace, or do you sprint to the finish? Among those who sprint for the finish, whoever’s legs are feeling the best will win the stage. But if no one sprints for the finish, everyone has an equal chance of winning the stage. In the Tour de Fiddler, you must each decide independently whether to sprint for the finish based on your legs—you don’t have time to react to your opponent’s decision.
Normally, teams at the Tour de Fiddler keep their strategy and tactics close to the vest. But earlier today, your opponent’s manager declared on international television that if (and only if) your opponent’s legs were feeling 50 percent or better, they’d sprint for the finish.
As you are about to test your legs for the final sprint and see how they feel, what are your chances of winning the stage, assuming an optimal strategy?

And for extra credit:

Instead of one opponent, now you have two—meaning three riders in total. As luck would have it, the managers for both other riders proclaimed that they’d sprint for the finish if (and only if) their legs were feeling 50 percent or better. Note that your opponents’ feelings are independent of each other.
As the three of you near the finish, your own team manager radios you the following message: “If your legs feel <garbled> percent or better, sprint for the finish!”
You can’t make out what the garbled part of the message is, and you’re too tired to radio back for confirmation. Instead, you somehow muster the energy to randomly, uniformly pick a number between 0 and 100 to fill in the blank from your manager’s message, thereby determining your racing strategy—optimization be damned!
Right before you choose your random strategy and test your legs, what are your chances of winning the stage against both opponents?

Can You Sprint to the Finish?

Highlight to reveal (possibly incorrect) solution:

Formulating what we already know:

  • There are 2 competitors, A (me) and B.
  • There will be 1 winner.
  • legs(X) describes the state of X’s legs, somewhere between 0 and 100 percent.
  • For each competitor these 2 steps will be done in order:
    • Determine legs(X).
    • Decide whether to sprint.
  • If both sprint, winner will have max(legs(X)).
  • If 1 sprint, they will win.
  • If 0 sprint, p(A wins) = p(B wins) = 50%
  • If legs(B) >= 50%, they will sprint.
  • A strategy is a list of values, that will lead to a sprint. For B the strategy is 50-100.

Now lets look at the different situations. Let a = legs(A) and b = legs(B).

Situation 1: a < 50.

A sprints?b < 50b => 50
Yesp(A wins) = 1p(A wins) = 0
Nop(A wins) = 50%p(A wins) = 0

In this situation, the strategy of always sprinting dominates. Situation 2, a = 50.

A sprints?b < 50b => 50
Yesp(A wins) = 1p(A wins) = p(a > b) = 0
Nop(A wins) = p(a > b) = 1p(A wins) = 0

In this situation, all strategies lead to the same results. Finally situation 3, a >= 50.

A sprints?b < 50b => 50
Yesp(A wins) = 1p(A wins) = p(a > b) = 50%
Nop(A wins) = 50%p(A wins) = 0

The dominant strategy in this situation is that A sprints. This leads to an overall strategy of always sprinting. However, that wasn’t the question.

  • p(A wins)
  • = p(a < 50) * (p(b < 50) * 1 + p(b > 50) * 0) + p(a > 50) * (p(b < 50) * 1 + p(b > 50) * 1/2)
  • = 1/2 * (1/2 + 0) + 1/2 * (1/2 + 1/4)
  • = 1/4 + 3/8
  • = 5/8

My result: 5/8 = 0.625 = 62.5%.

And for extra credit:

Program

I couldn’t quite get the math right in my head, so I monte carloed the problem. My result: 0.307 / 30.7%.

Hugo-relateret

Skriv en kommentar

Det er på tide at skæve til Hugo-kategorien Best related. Diverse med andre ord.

“Charting the Cliff: An Investigation into the 2023 Hugo Nomination Statistics” og “The 2023 Hugo Awards: A Report on Censorship and Exclusion” er nyheder. De gav et stort plask, da de var nye, og de har påvirket Worldcon. Specielt den anden.

“The Spectacular Failure of the Star Wars Hotel” er en video på YouTube. Jeg så den faktisk, da den var ny. En yderst grundig analyse. Jeg blev dog lidt irriteret over de jævnlige skift af kostume.

r/Fantasy’s 2024 Bingo Reading Challenge (r/Fantasy on Reddit) er mest af alt et fænomen. Jeg kender ikke så meget til det, men det lyder da interessant.

Jeg har allerede behandlet Speculative Whiteness: Science Fiction and the Alt-Right og Track Changes: Selected Reviews.

ISFDBISFDBKarakter
“Charting the Cliff: An Investigation into the 2023 Hugo Nomination Statistics”Camestros Felapton and Heather Rose Jones👽👽☠️
“The 2023 Hugo Awards: A Report on Censorship and Exclusion”Chris M. Barkley and Jason Sanford👽👽👽
“The Spectacular Failure of the Star Wars Hotel”Jenny Nicholson👽👽☠️
r/Fantasy’s 2024 Bingo Reading Challenge (r/Fantasy on Reddit)(a lot or people)👽👽☠️
Speculative Whiteness: Science Fiction and the Alt-RightJordan S. Carroll👽👽👽
Track Changes: Selected ReviewsAbigail Nussbaum👽👽☠️

Åh, det er svært. Men Hugo-rapporten står mit hjerte nær.

Spor ændringer

Skriv en kommentar

Anmeldelse af Track Changes: Selected Reviews, af #AbigailNussbaum. Bog. 2024. Hugo-finalist.

Skitse: En bog fuld af anmeldelser.

Er det science fiction? Bl.a.

Temaer: Anmeldelser. Ikke min yndlingsgenre. Men hvad jeg lige prøvesmagte virkede velskrevet. Analysen af WandaVision er fx tankevækkende. Også af The City and the City.

Citat: “… what bothered me about Discovery were the obvious limitations in its understanding of the Star Trek franchise, and of what could – and should – be done in it:

Like the reboot movies before it, Discovery seems to think that the most – perhaps the only – interesting question to ask within the Star Trek universe is “should we have a Federation?” […] But the thing is, this is literally the most boring, basic question one can ask about Star Trek. The real challenges posed by a society like the Federation aren’t questions of if, but of how. How do you create a truly just, fair, equal society? How do you balance freedom of conscience and opinion with your core values of tolerance and peace? How do you prevent the exploitation of those who are weaker than you? How do you help people outside your society, and do you have the right to encourage them to be more like you?”

Er det godt? Ja. Men som sagt ikke min yndlingsgenre. 👽👽☠️

Spekulativ hvidhed

Skriv en kommentar

Anmeldelse af Speculative Whiteness: Science Fiction and the Alt-Right (gratis), af #JordanSCarroll. Bog. 2024. Hugo-finalist.

Skitse: Den her ser på forskellige måder, hvorpå fascister bruger science fiction. Hvad der bliver skrevet og filmet, læst og set. Hvilke holdninger det kommunikerer og understøtter. Og hvilke videnskabelige fejl, det er nødt til at begå. Her er en flok citater:

Er det godt? Det virker godt researchet. Jeg er jo ikke den rigtige til at vurdere, om det hele er korrekt. Men det virker godt og sammenhængende. Og naturligvis er det her et godt tidspunkt at skrive den her bog på. 👽👽👽

#ThisWeeksFiddler, 20250718

Skriv en kommentar

This week the #puzzle is: Can You Meet Me at the Mall? #ExpectedValue #average #maximum #probabilities

You and two friends have arranged to meet at a popular downtown mall between 3 p.m. and 4 p.m. one afternoon. However, you neglected to specify a time within that one-hour window. Therefore, the three of you will be arriving at randomly selected times between 3 p.m. and 4 p.m. Once each of you arrives at the mall, you will be there for exactly 15 minutes. When the 15 minutes are up, you leave.
At some point (or points) during the hour, there will be a maximum number of friends at the mall. This maximum could be one (sad!), two, or three. On average, what would you expect this maximum number of friends to be?

And for extra credit:

Instead of three total friends, now suppose there are four total friends (yourself included). As before, you all arrive at random times during the hour and each stay for 15 minutes.
On average, what would you expect the maximum number of friends meeting up to be?

Can You Meet Me at the Mall?

Highlight to reveal (possibly incorrect) solution:

Program 1 Program 2

  • My 1st shot at this was a monte carlo program. It says: 2.03123 friends.
  • My 2nd shot was to try to estimate the value by systematically going through a lot of options. Just like small rectangles estimate an integral. This program says: 2.03222 friends.
  • I therefore say a good guess would be 2.03.

And for extra credit:

  • Using the same programs I get 2.47646 and 2.47802.
  • A good guess seems to be 2.48.

Desmos 1, 2 and 3. Probability of two events occurring at overlapping times. Desmos 4.

I actually tried to get something out of playing with desmos, but didn’t quite get there. I also tried modeling a version of the puzzle with 2 friends. Especially the no. 4 above is nice.

Using the article, I get a general expression. T is the length of the interval. The probability that 2 out of 2 friends are there at the same time is 2T – T2. For T = 1/4, this is 7/16. This fits with my programs and with Desmos.

Hugo-romaner

Skriv en kommentar

Så er vi nået til Hugo-romanerne.

ISFDBISFDBMigKarakter
A Sorceress Comes to CallT. KingfisherEn troldkvinde kalder👽👽👽
Alien ClayAdrian TchaikovskyUdenjordisk ler👽👽☠️
Service ModelAdrian TchaikovskyTjenestetypen👽👽☠️
Someone You Can Build a Nest inJohn WiswellNogen at bygge rede i👽☠️☠️
The Ministry of TimeKaliane BradleyTidsministeriet👽👽👽
The Tainted CupRobert Jackson BennettDen beskidte kop👽👽👽

En god kategori. Men det må blive tidsministeriet, den sad bare.

Den beskidte kop

Skriv en kommentar

Anmeldelse af The Tainted Cup, af #RobertJacksonBennett. Roman. 2024. Hugo-finalist.

Skitse: Kol er assistent for Ana, der efterforsker forbrydelser. I dag besøger Kol et gerningssted for at se det hele. Så rapporterer han senere til Ana. Lige i dag er det hele lidt mere spændende, fordi forbrydelsen er et mord. Afdøde blev gennemboret af et voksende træ.

Er det science fiction? Nix. Absolut fantasy.

Temaer: Kol er som led i sin karriere blevet forbedret, så han husker virkelig godt. Den slags forbedringer er der mange af i imperiet. Basis for den slags forbedringer er, at man tapper døde søuhyrer for væsker og eksperimenterer med dem. Et stort job for imperiet er at forhindre søuhyrerne i at komme på land.

Kol er efter min vurdering ordblind. Og så udtrykker han som regel ikke sine følelser. Og han virker bi. Ana virker autistisk: Hun får nemt for mange stimuli og går aldrig ud. Derudover har vi fat i noget Watson/Holmes-dynamik. Ana har brug for udfordringer, ellers tager hun stoffer.

Jobtitlerne lyder romerske: Kol er signum. Andet lyder Schweizisk: Imperiet er opdelt i kantoner. Atter andre inspirationer kommer fra andre lande. Noget er arabisk?

Citat: “A towering, slategray cliff, running underneath the redstained sky like a frame below a painting, its stone wet and gleaming and crawling with vines and growth; and there, in one long, vertical seam in the cliff, a hint of movement: some insect, I thought, crawling from base to top in a slow, labored procession. My eye trembled as I focused on it. I realized it was not an insect but instead a tiny box, wrought of wood, being hauled up on a set of strings. As it reached another notch in the gray cliffs, the box stopped, and even tinier figures emerged. Horses. Four of them, all hauling a shining steel bombard from the box. I blinked, staring into the spyglass. The tiny box was not tiny at all: it was a lift, made for hauling troops and armaments up the vast expanse of the sea walls.”

Er det godt? Meget sjældent er der en fodfejl. “Finally Ana finished.” Har første og sidste ord ikke samme rod? Det er noget rod (!) at have dem så tæt på hinanden. Men alt overvejende, så virker den her bog bare. 👽👽👽

Tidsministeriet

Skriv en kommentar

Anmeldelse af “The Ministry of Time”, af #KalianeBradley. Roman. 2024. Hugo-finalist.

Skitse: Hovedpersonens job er at være sammen med Graham, der ifølge historiebøgerne døde oppe nordpå i 1847, men altså i virkeligheden blev hentet til vores tid med en tidsmaskine. Der er meget at lære i den situation og mulighed for flere forskellige slags sammenbrud, så det skal også passes og observeres. Jobtitel: bro.

Er det science fiction? Ja.

Temaer: Broen har på egen krop oplevet, at fremmede i UK kan have flere forskellige navne. Er man flygtning? Er en tidsrejsende, der ikke kan tage hjem, flygtning? Bliver man ramt af fordomme? Er det rimeligt, at ens nye hjem kræver 100 % tilpasning? Er det bare professionelt, når de ansatte i ministeriet kalder ham 1847? Kan man være flygtning i sit eget land? Hvad er der med Khmer Rouge? Og Holocaust? Der er mange spørgsmål, og i nogle tilfælde også flere svar.

Graham støder sig selvfølgelig på tiden. Det er fx mirakuløst og meget trygt, at Spotify kan spille klassisk musik. Det er svært at vænne sig til dating og kvinders bare ben. Han rødmer regelmæssigt. Der er andre tidsrejsende, der umiddelbart ikke ønsker at holde op med at bruge diverse ord, der i dag virker voldsomt stødende.

Et biprodukt af situationen er, at Graham ikke rigtig må lave noget og derfor keder sig. Han er også vant til at være sammen med mænd, og den kvindelige bro er ikke helt det samme. Til gengæld tænder hun på en fyr, der virker som en helt.

Graham, broen og forfatteren har humoristisk sans og er ikke bange for at bruge den. Graham kalder dukkerne på Sesame Street for ugudelige vederstyggeligheder. Broen omtaler en pedantisk tirsdag.

På et tidspunkt bliver det hele mere kompliceret. Nogle af de ansatte i ministeriet er spioner og sabotører. Men for hvem? Og kan det virkelig passe, at broens chef, Adela, har et meget foranderligt ansigt?

Er det fair, at ministeriet kræver absolut tilpasning fra Grahams side? I mindre målestok, kan broen 100 % kontrollere, hvordan Graham ser hende? Kan hun også kræve, at deres forhold er på hendes vilkår?

Der er små forvarsler. “Senere tænker jeg meget på dette øjeblik.” Sådan noget. Lidt krydderi.

Er det godt? Den er let læst, jeg strøg lige igennem den, spændt på slutningen, deriblandt om Graham og broen får hinanden. Der er humor og leg med sproget. Der er meget alvorlige spørgsmål. Den ramte godt. 👽👽👽

Nogen at bygge rede i

Skriv en kommentar

Anmeldelse af Someone You Can Build a Nest In, af #JohnWiswell. Roman. 2024. Hugo-finalist.

Skitse: Shesheshen er et monster. Lokalt kalder man hende en wyrm, fordi der ikke rigtig bliver skelnet mellem forskellige slags. Egentlig er hun i vinterhi, men så kommer nogle fjollede fyre for at slå hende ihjel. Suk.

Er det science fiction?. Nix. Masser af magi.

Temaer: Hun tænker jævnligt på sin (klamme) mor og far. Sidstnævnte var hendes første måltid.

Hun kan forklæde sig som menneske, bl.a. ved at absorbere knogler i sit (klamme) kød.

Efter de fjollede fyre så nogenlunde er afværget, så beslutter hun sig for at besøge den nærliggende landsby. Hun er nemlig sulten. På en eller anden måde får hun i stedet en kæreste? Og forstår meget bedre folk omkring sig?

Citat: “Romance was awful. She couldn’t even do something as simple as murdering rude people anymore.”

Er det godt? Ærligt talt stoppede jeg ca. 1/3 inde. Der var ikke rigtig noget her, der for alvor interesserede mig. 👽☠️☠️