I've seen some authors refer to positions like the one below as
"simple." But no quiz position is ever simple. Deceptively simple,
perhaps, but not simple.
XGID=-BCBbCB-C-a-----abbcbb----:1:-1:1:62:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O O | | O O O | +---+
| O O | | O O O | | 2 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X X |
| X | | X X O X X X |
| O X | | X X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 65 O: 132 X-O: 0-0
Cube: 2, O own cube
X to play 62
The only alternative is 5/3 but then why would Tim post about that, particularly when there's a shortage
of rigorous beginners' accounts on using forcing to prove independence results in set theory? I'm sure Tim's notes
could be improved. (I'm reading Weaver at the moment (Nik not Tom).)
If a set theorist is selected at random, what is the probability that this mathematician prefers models of ZFC where CH is false
to models of ZFC where CH is true?
XGID=-BCBbCB-C-a-----abbcbb----:1:-1:1:62:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O O | | O O O | +---+
| O O | | O O O | | 2 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X X |
| X | | X X O X X X |
| O X | | X X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 65 O: 132 X-O: 0-0
Cube: 2, O own cube
X to play 62
Ripping up the board with 3/1 just "felt wrong" to me, so I didn't
consider it seriously. But a blot on the 3pt isn't much of a liability;
O isn't going to be breaking anchor any time soon, except to hit, and
in that scenario X is probably doomed anyway. X's main task is just to
move his checkers past O's anchor safely.
It is natural to look first at immediate blotting rolls. Either way,
61 blots. After 8/2 5/3, the only other blotting roll is 64, but it
leaves *two* blots; after 8/2 3/1, 64 leaves just one blot, but 44 also blots. This comparison is perhaps not entirely clear.
I believe that the key point to notice is that 8/2 5/3 leads to more blotting rolls later. For example, suppose X rolls 62 63 52 or 53.
X brings both checkers in safely for now, but has five checkers
somewhat awkwardly placed in front of O's anchor. Similarly if X
blots with 61 and O misses, X's cleanup will tend to be easier with
a spare on his 5pt.
1. Rollout¹ 8/2 3/1 eq:+0.690
Player: 82.86% (G:9.83% B:0.03%)
Opponent: 17.14% (G:2.27% B:0.08%)
Confidence: ±0.004 (+0.686..+0.694) - [100.0%]
2. Rollout¹ 8/2 5/3 eq:+0.648 (-0.042)
Player: 80.38% (G:11.05% B:0.02%)
Opponent: 19.62% (G:2.07% B:0.07%)
Confidence: ±0.004 (+0.644..+0.652) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.207.pre-release
On 1/9/2022 5:50 PM, peps...@gmail.com wrote:
The only alternative is 5/3 but then why would Tim post about that, particularly when there's a shortageIf you're not aware of it, Scott Aaronson made an interesting blog post
of rigorous beginners' accounts on using forcing to prove independence results in set theory? I'm sure Tim's notes
could be improved. (I'm reading Weaver at the moment (Nik not Tom).)
on this topic some time ago.
https://scottaaronson.blog/?p=4974
Unfortunately, despite highly positive feedback from his readers, he has
not been motivated to write any followup posts.
I have thought about writing a sequel to my "beginner's guide," but I
have not yet reached a point where I feel I have enough additional
insights to merit another paper.
If a set theorist is selected at random, what is the probability that this mathematician prefers models of ZFC where CH is falseIn case you don't already know, there was an interesting article in
to models of ZFC where CH is true?
Quanta on this topic last year.
https://www.quantamagazine.org/how-many-numbers-exist-infinity-proof-moves-math-closer-to-an-answer-20210715/
On 1/11/2022 8:50 AM, peps...@gmail.com wrote
As far as I know, Tim and David are the only research maths people
[who have been] involved with rgb.
Note that I'm not saying at all that Tim and David are the only
research maths people involved with rgb.
The "As far as I know" caveat is a crucial qualifier.
Douglas Zare used to be involved in r.g.b. and used to be a research mathematician, but I don't think he does math research any more.
I thought that all knowledgeable people rejected CH and intended the probability to be very close to 1.
After briefly looking through the Quanta magazine article, I'm less sure (about what set theorists think).
As far as I know, Tim and David are the only research maths people [who have been] involved with rgb.
Note that I'm not saying at all that Tim and David are the only research maths people involved with rgb.
The "As far as I know" caveat is a crucial qualifier.
I think the Quanta magazine article is much better than usual for pop maths article, despite the topic being so difficult.
camp agree that either c = aleph_0 or c = aleph_2 but think there are arguments both ways....
On Tuesday, January 11, 2022 at 2:16:30 PM UTC, Tim Chow wrote:
... Most people in this
camp agree that either c = aleph_0 or c = aleph_2 but think there are...
arguments both ways.
Is this a typo? By "aleph_0", do you mean "aleph_1"?
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