# P.J.Traill

__PageType__: HomePage

I registered on 2018-01-28 when playing at about 7 kyu in Venlo, back from 5 kyu many years ago must try to get back to that and further! Also present on Josekipedia/Go problems, Board & Card Games Stack Exchange & Wikimedia projects.

I have some awareness of and interest in CGT.

# Unicode

Checking what is converted to hex in page source:

ίΏ‘£ ←→⇒ίΏ‘ αβπ ± ≈

§ ± Χ √⁰Ή²³⁴⁵⁶⁷⁸⁹⁺ⁿ⁽⁾ ₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎ ∈ ≠ ≡ ⇐ ⇔ ⇒ π ← → ↔ ↑↓ ◦‣∙ sqrt ↑0..9+n() ↓etc. elt neq implies pi ellipsis arrows bullets ≥ ≤ ≈ ΠήȜ πώȝ Ππ ήώ Ȝȝ

Greek ɑ

ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ αβγδεζηθικλμνξοπρςστυφχψω

ἁἑἡἱὁὑὡ

£₯ ί ζ ligatures «» Ώ? ‘! ½ ⅓ Ό Ύ ⅐ ⅑ ⅒ ⅓ ⅔ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅛ ⅜ ⅝ ⅞ ⅟ ° degree ℕ Blackboard ⌊⌋⌈⌉ floor*2 ceil*2 Smiley/grumpy (or vice versa) Ίͺ Masculine/feminine ordinal indicators ▲▼►◄ Black pointing triangles

U+25CB ○ white circle (HTML ○) U+2686 ⚆ white circle with dot right (HTML ⚆)[94] U+2687 ⚇ white circle with two dots (HTML ⚇) U+25CF ● black circle (HTML ●) U+2688 ⚈ black circle with white dot right (HTML ⚈) U+2689 ⚉ black circle with two white dots (HTML ⚉)

Evidently it would not be a good idea to use Greek letters for diagram numbers beyond 9 or 10.

# Eyes

Perhaps I want to weigh in at formal definitions of eye, but for now I shall make a few notes here:

## Objectives

- A definition should make sense of large eye, false eye.
- The definition should be static as far as possible, i.e. not depend on formulations like
*all possible sequences of moves*. - It should be true that
*having two (true) eyes means that a group is alive* i.e. cannot be captured in any rule-set!- The converse is less clear.

- The definition should be independent of the board graph, depending only on which points are connected.

## 2018-09-09 Same conclusions as Benson

Having reflected on the matter I came up with a definition; when I checked Benson's Definition of Unconditional Life I found mine was essentially the same, though of course my terminology was different. I was also thinking in terms of arbitrary graphs; while Benson only speaks of square grids (Pm x Pn) his work also appears general.

It seems fair to point out that, although I think
Robert Jasiek says differently in formal definitions of eye,
Benson's Definition *is* static,
in the sense of not relying on analysing sequences of moves, with backtracking to cover the game tree.
That is indeed the purpose of Benson's Theorem, to optimise the determination of pass-alive stones.
He proves that his static analysis gives the same result, in
Theorems 1 (...) & 2: *Let X ⊆ B(x) be the set of all safe x-blocks. Then X is unconditionally alive.*