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Carry the one

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If you want to compare 2 large numbers, and remember to carry the one(s), this is how you do it.

First row in the table below: Our units. In the middle, there’s a familiar system: 1, 10, 100. This is how our own numbers are constructed. There’s a position for 1s, a position for 10s, etc. To the left and to the right, the units are not the familiar ones, but hopefully we can understand this anyway.

Second row: A sum of a lot of other numbers. The sum hasn’t been normalized to its shortest from yet. We want to normalize and then compare with the last row, another number from the same source.

Normalization example: In the second row, 15 and 15 are bolded. The jump from the first to the second column is to multiply by 2. (1/120 * 2 = 1/60.) So to normalize, we look at the first 15 and divide by 2.

  • a = 1/120, b = 1/60
  • 2a = b
  • 15/2 = 7.5
  • 15 = 1 + 7 * 2
    • 15a + 15b
    • = (1 + 7 * 2)a + 15b
    • = a + 7 * 2a + 15b
    • = a + 7b + 15b
    • = a + 22b

So in the next row, instead of 15 and 15, we have 1 and 22.

Move to the next pair of columns and repeat.

1/1201/601/301/101/5110100300300018000
1515241419263911785
122241419263911785
10351419263911785
1022519263911785
102131263911785
10211323911785
1021124211785
102112215785
102112201285
10211220295
10211220236
10211221136

And yes, the end result is, that the 2 numbers aren’t quite the same.

Background: Recently I read this, in From One to Zero, Georges Ifrah :

Science fiction predictions XXVI

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“The Discovery of the Future” , Robert A. Heinlein.

“Phrases like “There’ll always be an England” are pleasant and inspiring at the present time, but we know better. There won’t always be an England, nor a Germany, nor a United States, a Baptist Church, nor monogamy, nor the Democratic Party, nor the modesty taboo, nor the superiority of the white race, nor airplanes. Nor automobiles. They will go. They will be gone-we’ll see them go. Any custom, institution, belief, or social structure that we see around us today will change, will pass, and most of those we will see change and pass.

In science fiction, we try to envision what those changes might be. Our guesses are usually wrong; they are almost certain to be wrong. Some men, with a greater grasp on data than others, can do remarkably well. H. G. Wells, who probably knows more (on the order of ten times as much, or perhaps higher) than most science fiction writers, has been remarkably successful in some of his predictions. Most of us aren’t that lucky;

I do not expect my so-called History of the Future to come to pass. I think some of the trends in it may show up, but I do not think that my factual predictions as such are going to come to pass, even in their broad outlines.”

“I have never been able to understand quite why it is that the historical novel is the most approved, the most sacred form of literature. The contemporary novel is next so; but the historical novel, if you write an historical novel, that’s literature.

I think that the corniest tripe published in a science fiction magazine (and some of it isn’t too hot, we know that; some of my stuff isn’t so hot) beats all of the Anthony Adverses and Gone With the Winds that were ever published, because at least it does include that one distinctly human-like attempt to predict the future.”

Hvis krop er det egentlig?

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Jeg har læst “0wnz0red”/”Din kr0p er v0res”, #CoryDoctorow. Quick fix. Spoilers.

Nogen har udviklet et stykke software, der via passende kabler kan styre alt muligt i en krop: niveau af serotonin, stofskifte, smertetærskel osv. Med lidt kreativitet kan man også opfinde en kur mod en given sygdom. Og hvad så?

En af hovedpersonerne forestiller sig, at man kan putte en masse af det her software i en virus, der på længere sigt vil smitte alle. Nogle fordele vil indtræffe med det samme, andre kræver en lille computer ved siden af, så man selv kan skrue op og ned for tingene. Igen på længere sigt vil den blive billig, så alle kan få en. Voila! Fysisk og psykisk sundhed til alle, og i forbifarten også en slat penge til vores helt.

Vi ser noget af det virke ret godt hos nogle få personer. Det er ikke klart, hvordan effekten i sidste ende vil være på samfundet, men jeg gætter på positiv.

Scroggs, day 7

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A new December and a new bunch of puzzles from mscroggs.co.uk.

The circle all around is 360°.

The angle to the minute hand, corresponding to 22 minutes is 360 * 22/60 = 132.

The angle to the hour hand, going clockwise, corresponding to 8 hours and 22 minutes is 360 * (8 + 22/60) / 12 = 251.

The angle between the hands is 251 – 132 = 119.

#ThisWeeksFiddler, 20241213

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This week the question is: Can You Survive “The Floor”?

… Let’s consider a slightly simplified version of The Floor with nine contestants on a 3×3 square grid. Each round of the game consists of the following steps:

  • One of the remaining contestants is chosen at random. (Note that each contestant is equally likely to be chosen, regardless of how many squares they currently control.)
  • The set of eligible opponents for this contestant is anyone whose territory shares a common edge with the contestant. One of these eligible opponents is chosen at random. (Again, all eligible opponents are equally likely to be chosen, regardless of how many squares they control or how many edges they have in common with the opponent.)
  • The contestant and their selected opponent have a duel, each with a 50 percent chance of winning. The loser is eliminated, and their territory is added to that of the winner.

These rounds repeat until one contestant remains, and that contestant is the overall winner.

You are a contestant on a new season of this 3×3 version of The Floor. The nine positions on the grid are shown below:

Which position would you choose? That is, which position or positions give you the best chance of being the overall winner?

And for extra credit:

Again, a new season of the 3×3 version of The Floor (as described above) is about to begin.

What is your probability of winning for each of the nine starting positions?

Highlight to reveal (possibly incorrect) solution:

Program. Numbers.

This time I wrote a program to investigate the possibilities. In summation these are the probabilities for a win, rounded:

A, C, G, I (a corner): 13%

B, D, F, H (an edge): 10%

E (the middle): 9%

So I should choose to start in a corner.