Editing Ontology:Q5,38

{{HueCSS}}<ol class="hue clean compound"><li>  {{ArticleTitle|star - STM / S1 / Q5,38|NoContents=y}}
<onlyinclude><dfn class="{{{class|field_geo}}} manual" data-dimension="S1" data-qid="5,38" data-numbersign="404" data-field="" data-object="" data-note="" data-lexeme="">{{IS1/STM}}{{#if: {{{1|}}} | [[E:Q5,38|{{{1}}}]] | [[E:Q5,38|{{TTS|tts=star|<nowiki>*</nowiki>}}]] }}{{#if: {{{3|}}} | {{{3}}} | <ins class="note series_hackenbush"> (unreal number)</ins> }}{{#if: {{{2|}}} | <ins class="edition-sense term"> ([[E:Q55,38/{{{2}}}|{{{2}}}]]<nowiki />)</ins> }}{{WaveScore|sum=1|quilt=1|ply=1|enddfn=1}}{{#switch: {{{C|}}} | L = <span></span> | Q = [[C:Hackenbush ontology]] }}</onlyinclude>
</li></ol><!-- change summary template:  copy or update fake Item from [[Special:PermanentLink/NNNN|Q5,38]] -->

== Core characteristics ==

<dl class="wikitable hue series_hackenbush">
{{HueClaim |P=item type| {{Template:S1}} }}
{{HueRoster|EP=PPPA/L|lang=en| {{E:Q5,38}} | {{TTS|tts=star one|<nowiki>*</nowiki>1}} }}
{{HueClaim |EP=PPPA|lang=en| -- }}
{{HueRoster|EP=P42/BB| -- }}  <!-- en: shares thematic block -->
{{HueRoster|EP=P34| {{E:Q618/STM|combinatorial game theory}} [[Category:Combinatorial game theory ontology]] | {{E:Q618/STM|Hackenbush}} [[Category:Hackenbush ontology]] }}  <!-- en: field -->
{{HueRoster|EP=P3| -- }}  <!-- en: sub-case of -->
{{HueRoster|EP=P4| {{E:Q618/STM|number-like object}} }}  <!-- en: case of -->
{{HueRoster|EP=P5| -- }}  <!-- en: super-case of -->
</dl><!--

=== Components ===

<dl class="wikitable hue series_hackenbush">
{{HueRoster|EP=P6| -- }}
</dl> -->

== {{TTS|tts=Wave-builder|Wavebuilder}} combinations ==

<dl class="wikitable hue data_wavebuild three series_hackenbush">  
{{WaveBuildNone| {{E:Q538}} | {{E:Q618/STM|move in P direction}} | {{E:Q618/STM|exactly 1}} }}  <!-- en: Along With, Produces  ??  ?? -->
{{WaveBuildNone| {{E:Q538}} | {{E:Q618/STM|move in N direction}} | {{E:Q618/STM|exactly -1}} }}
</dl>

== {{TTS|tts=Wave-builder|Wavebuilder}} characterizations ==

<dl class="wikitable hue data_wavebuild three series_hackenbush">  
{{WaveRoute| {{E:Q618/STM|zero game}} | {{E:Q618/STM|space in neutral direction}} | {{E:Q538}} }}  <!-- en: From  ??  ?? -->
</dl>

== [[User:Reversedragon/FirstNineThousand|Prototype]] notes ==

<ol class="hue clean">
</li><li class="field_geo" value="740" data-dimension="M3">What are numbers? / What are integers? / What are real numbers?  ->  has several different technical definitions within mathematics.

</li><li class="field_geo" value="771" data-dimension="S">Dedekind cut / <code>{...|...}</code>  ->  an operator used for defining numbers, whether the real numbers or the surreal numbers. a number or set can be put on each side, and the result of the operation goes in the middle of the cut.
</li><li class="field_geo" value="745" data-dimension="S2">Numbers are whatever is between two sets / Numbers are whatever is in the middle of a Dedekind cut ...

</li><li class="field_geo" value="440" data-dimension="S">zero game [https://en.wikipedia.org/wiki/Zero_game]  ->  a game which essentially is over. neither player has a legal move, and the board may as well be empty.
</li><li class="field_geo" value="443" data-dimension="S">move in N direction / move in negative direction (game theory)  ->  these are the more technical definitions of scoreboard points. you can choose to define scoreboards or game spaces in terms of positive and negative numbers, although it results in the strange artifact of star numbers that act oddly like a new version of zero you can multiply. all of this rests on the assumption of a zero-sum game, akin to tic tac toe or checkers.
</li><li class="field_geo" value="444" data-dimension="S">move in P direction / move in positive direction (game theory)
</li><li class="field_geo" value="445" data-dimension="S">space in neutral direction / playable game space in direction which is neither player N nor player P  ->  while moves in a zero-sum game must go a particular direction, game spaces don't have to. this is part of the definition of "star", although I still don't understand what the full definition is.

</li><li class="field_geo" value="418" data-dimension="S">treed dimensionality  ->  the mathematical definition of "dimensions" as how many levels deep you are in a choice tree, or how many columns deep you are in a table. this is not the only definition of "dimensions" nor the most common one. it's generally preferred to define "dimensions" as things that can create whole fields of numbers like a whole real number line that can be expanded out into a plane and a cube of coordinates. I have no issue with that, of course. but, this is the kind of dimensionality that "Item dimension" or "Item dimensionality" refers to in the context of all these numbered Items. the simple [https://en.wikipedia.org/wiki/Tree_(abstract_data_type)#Terminology depth] of a rooted tree that we are referring to as dimensionality.

</li><li class="field_geo" value="538" data-dimension="S">[[Ontology:Q5,38|star]] (unreal number) / star (number-like object in game theory; number that is neither positive nor negative, cancels out itself, and yet can be multiplied)  ->  this thing is unbelievably interesting to me. it feels strangely like a non-numerical object thrown into the slot of a number. it's like the Missingno of numbers.<br />
let's see... GIGO / undefined behavior + Pokémon = glitch Pokémon. undefined behavior + numbers = abstract algebra. or something.
</li></ol>

== Background ==

{{TTS|tts=star|<nowiki>*</nowiki>}} (or {{TTS|tts=star one|<nowiki>*</nowiki>1}}) is a number-like object used to describe games in combinatorial game theory. It represents a game state where there is at least one space which can be taken by either player and count toward either player winning or losing. A positive number counts a space which will be taken by one player, while a negative number counts a space which will be taken by the other player. A rational number is a combination of spaces that count toward one player averaged against spaces that count toward the other. However, a star number is an un-taken space which genuinely does not count toward either player until a particular player is selected to move first.

(incomplete)

=== {{TTS|tts=star|<nowiki>*</nowiki>}} as matrix ===

Thinking of {{TTS|tts=star|<nowiki>*</nowiki>}} as a number similar to an integer or decimal may be less useful than thinking of it as a composite object containing multiple elements that assemble into a [[E:algebra (data structure)|mathematical data structure]]. Matrices in particular are somewhat similar to game states: any particular vector laid out vertically can be concatenated onto a matrix as a new column through an operation called augmentation. If {{TTS|tts=star|<nowiki>*</nowiki>}} gains its contradictory properties from the internal contents of a vector, then it would make sense that augmenting matrices would combine two sets of contradictory elements into one set of contradictory elements that could resolve into zero. Matrices have interesting capabilities, such as multiplying against themselves to produce -1 or 1 — this has allowed complex numbers to be turned into matrices for some applications. The same thing could apply to {{TTS|tts=star|<nowiki>*</nowiki>}}.

== Usage notes ==


[[Category:S1 Signifier Items]]  <!-- tag to suppress extra spacing. page ends here.
TTS-unfriendly, search-friendly numbers:  Q440 Q538
en-GB words:   (none) -->