Paradox, mathematics, poetry, fiction, speculations in philosophy and politics. Copyright 2024, Nathaniel Hellerstein
Thursday, June 30, 2016
Wednesday, June 29, 2016
Tuesday, June 28, 2016
Monday, June 27, 2016
Friday, June 24, 2016
Wilsonian Quantifier Trilemma: frogs and princes
Wilsonian Quantifier Trilemma: frogs and princes
In
an earlier blog I referred to the “Wilsonian quantifiers”; ‘some but not all’
and ‘all or none’. These are to the ‘all’ and ‘exists’ quantifiers as ‘exclusive
or’ and ‘if and only if’ are to ‘and’ and ‘or’. I have found a troika involving
them.
Moe:
No frogs are princes.
Larry:
Some but not all frogs are princes.
Curly:
All frogs are princes.
Moe,
Larry and Curly all agree that frogs exist.
By
2/3 majorities each:
LK:
Some frogs are princes.
ML:
Some frogs are not princes.
KM:
All or no frogs are princes.
The
last can be read, “All frogs are equally
princes.”
Thursday, June 23, 2016
Non-SETI Earth
Non-SETI Earth
For
decades I have been monitoring portions of Earth’s radio output. During that
time I have yet to detect, within that output, any convincing proof of the
existence of intelligent life on planet Earth.
Wednesday, June 22, 2016
Magic Dice
Magic Dice
Consider these four “non-transitive”
dice:
Red: 4 4
4 4 4 4 Y
Yellow: 3 3 3
3 7 7 < <
Green: 2 2
2 6 6 6 G R
Blue: 1 1
5 5 5 5 > >
B
When you roll two of these dice:
Red loses to Blue 2/3 of the
time;
Blue loses to Green 2/3 of
the time;
Green loses to Yellow 2/3 of
the time;
Yellow loses to Red 2/3 of
the time.
A dominance loop! Also:
Red loses to Green 1/2 of the
time;
Blue loses to Yellow 5/9 of
the time;
These dice are fair, yet they are
rigged. If two players choose dice to roll, then the second to choose has a 2:1
advantage. Whatever color your opponent picks, you should pick the next one on
this cycle;
Blue →
Green → Yellow → Red → Blue
This is the ‘redshift’ strategy;
choose a lower-frequency color (except for the wrap-around red → blue). If you use this color code:
Blue = Winter; Green = Spring; Yellow = Summer; Red = Fall;
then the mnemonic is “next season”.
Here are some games based upon magic
dice:
Double-Cross, Double Roll, Double Bet, White Magic, Black Magic and Black Double-Cross.
In the game Double-Cross, one player
has the red and green dice, and the other player has the blue and yellow dice.
They roll one die each, simultaneously. That way either player can undercut the
other. This game combines choice with rigged chance.
In the game Double-Roll, one player
is the first to choose a die for a round of several rolls, but the second
player must twice as often. For a round of 9 rolls, a score of 3 to 6 is a
draw. In the gambling game Double-Bet, the second player must
bet twice as much. These schemes counter-bias the dice.
In the game White Magic, the winner
of a roll must choose first the next time. White Magic’s winners tend to lose
and its losers tend to win. White Magic smooths out all differences. In the
long run it divides the pot evenly amongst the players. White Magic is very
communal.
“Phooey,” say all real gamblers; they’d
prefer White Magic’s dark shadow, Black Magic. In Black Magic, the loser must choose first
on the next roll. Black Magic’s losers tend to keep losing, and its winners
tend to keep winning. Black Magic accentuates random differences. In the long
run it assigns a big winner. Black Magic is very competitive.
You can combine these games and get
hybrids, like Black Double Cross, which combines Double-Cross and Black
Magic. In this game, one player has red-green, the other has blue-yellow;
whoever loses a roll must roll first next roll.
Care for a few rounds?
Subscribe to:
Posts (Atom)