Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Wed, 15 Jan 2025 21:25:26 -0800 Received: from [192.168.123.254] (port=40300 helo=jiten.lojban.org) by b32fe687e415 with smtp (Exim 4.96) (envelope-from ) id 1tYINf-0010DF-1h for jbovlaste-admin@lojban.org; Wed, 15 Jan 2025 21:25:26 -0800 Received: by jiten.lojban.org (sSMTP sendmail emulation); Thu, 16 Jan 2025 05:25:23 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word tamseingu -- By krtisfranks Date: Thu, 16 Jan 2025 05:25:23 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: 0.0 (/) X-Spam_score: 0.0 X-Spam_score_int: 0 X-Spam_bar: / In jbovlaste, the user krtisfranks has edited a definition of "tamseingu" in the language "English". Differences: 5,5c5,5 < $x_2$ is a nonnegative integer; $x_3$ is an integer (potentially of any signum a priori). $x_5$ is directed and thus admits descriptions such as "rootward", "parent", "superior"/"ancestor", "leafward", "child", and "descendant"/"subordinate". $x_4 is a node which is identified and singled out as being special in the tree, and thus the relationship is not entirely symmetric under exchange of $x_4$ with any other node. For any target node $v$ in $x_5$, the coördinate label for $v$ is determined as follows: For the sake of ease and uniformity of notation, denote $x_4$ by "$μ$"; likewise denote $x_5$ by "$G$". Let/require/assume that the most-recent common direct ancestor of $μ$ and $v$ in/according to $G$ be essentially-unique and denoted by "mrcda$_{G}(μ, v)$"; let $δ$ be the Kronecker delta function on the nodes of $G$; let $ρ$ be a binary function on the Cartesian square of the set of nodes of $G$ mapped to the nonnegative intergers or positive infinity, and be the undirected graph-geodesic distance between its inputs. Let the coördinate label assigned to $v$ be coörd$_{G, μ}(v) = (ξ_{G, μ}(v), υ_{G, μ}(v)) = (ξ, υ) = ((1 - δ(v, $mrcda$_{G}(μ, v))) ρ(μ, $mrcda$_{G}(μ, v)), ρ(v, $mrcda$_{G}(μ, v)) - ρ(μ, $mrcda$_{G}(μ, v)))$. Under these conditions, unique relations/path-shapes which connect $μ$ to $v$ are bijective with the labels; under these conditions, the mapping from labels to nodes should be injective. For example: Assume that $x_4$ is oneself for simplicity and that $x_5$ is one's family tree under the assumption that it records only human genetic relationships due to binary sexual reproduction/inheritance and excludes incest (regardless of the graph-geodesic distance otherwise between the participants), marriage or similar relationships, co-parenting, in-law relationships, half or other partial family relationships, step-familial relationships, adoptions, cross-generational co-parenting, distinctions according to age alone or comparisons thereof, and distinctions according to gender/sex alone or comparisons thereof. In this case, if oneself is labelled by $(0, 0)$, then: one's children are labelled by $(0, 1)$, one's grandchildren are labelled by $(0, 2)$, one's $n$th-great-grandchildren are labelled by $(0, 2+n)$, one's parents are labelled by $(0, -1)$, one's grandparents are labelled by $(0, -2)$, one's $nth$-great-grandparents are labelled by $(0, -(2 + n))$, one's siblings are labelled by $(1, 0)$, one's niblings (children of siblings) are labelled by $(1, 1)$, one's nibling's children are labelled $(1, 2)$, one's neams (siblings of parents) are labelled by $(2, -1)$, one's 1st cousins 0 times removed (children of neams) are labelled by $(2, 0)$, one's first cousins once removed via neams are labelled by $(2, 1)$, etc. Notice that corporate organization charts, as directed from CEO (root) toward subordinates, can have similar labels. See also: "{tamne}", ".{anseingu}", "{grafnseljimcnkipliiu}". --- > $x_2$ is a nonnegative integer; $x_3$ is an integer (potentially of any signum a priori). $x_5$ is directed and thus admits descriptions such as "rootward", "parent", "superior"/"ancestor", "leafward", "child", and "descendant"/"subordinate". $x_4 is a node which is identified and singled out as being special in the tree, and thus the relationship is not entirely symmetric under exchange of $x_4$ with any other node. For any target node $v$ in $x_5$, the coördinate label for $v$ is determined as follows: For the sake of ease and uniformity of notation, denote $x_4$ by "$μ$"; likewise denote $x_5$ by "$G$". Let/require/assume that the most-recent common direct ancestor of $μ$ and $v$ in/according to $G$ be essentially-unique and denoted by "mrcda$_{G}(μ, v)$"; let $δ$ be the Kronecker delta function on the nodes of $G$; let $ρ$ be a binary function on the Cartesian square of the set of nodes of $G$ mapped to the nonnegative intergers or positive infinity, and be the undirected graph-geodesic distance between its inputs. Old Data: Definition: Target node $x_1$ and primary subject node $x_4$ belong to the same (single) strictly-directed, connected tree graph/network/hierarchy or are related by relation scheme $x_5$ such that $x_1$ has coordinates $(x_2, x_3)$ and $x_4$ has coordinates $(0, 0)$ according to the labelling scheme which is described in the notes hereof. Notes: $x_2$ is a nonnegative integer; $x_3$ is an integer (potentially of any signum a priori). $x_5$ is directed and thus admits descriptions such as "rootward", "parent", "superior"/"ancestor", "leafward", "child", and "descendant"/"subordinate". $x_4 is a node which is identified and singled out as being special in the tree, and thus the relationship is not entirely symmetric under exchange of $x_4$ with any other node. For any target node $v$ in $x_5$, the coördinate label for $v$ is determined as follows: For the sake of ease and uniformity of notation, denote $x_4$ by "$μ$"; likewise denote $x_5$ by "$G$". Let/require/assume that the most-recent common direct ancestor of $μ$ and $v$ in/according to $G$ be essentially-unique and denoted by "mrcda$_{G}(μ, v)$"; let $δ$ be the Kronecker delta function on the nodes of $G$; let $ρ$ be a binary function on the Cartesian square of the set of nodes of $G$ mapped to the nonnegative intergers or positive infinity, and be the undirected graph-geodesic distance between its inputs. Let the coördinate label assigned to $v$ be coörd$_{G, μ}(v) = (ξ_{G, μ}(v), υ_{G, μ}(v)) = (ξ, υ) = ((1 - δ(v, $mrcda$_{G}(μ, v))) ρ(μ, $mrcda$_{G}(μ, v)), ρ(v, $mrcda$_{G}(μ, v)) - ρ(μ, $mrcda$_{G}(μ, v)))$. Under these conditions, unique relations/path-shapes which connect $μ$ to $v$ are bijective with the labels; under these conditions, the mapping from labels to nodes should be injective. For example: Assume that $x_4$ is oneself for simplicity and that $x_5$ is one's family tree under the assumption that it records only human genetic relationships due to binary sexual reproduction/inheritance and excludes incest (regardless of the graph-geodesic distance otherwise between the participants), marriage or similar relationships, co-parenting, in-law relationships, half or other partial family relationships, step-familial relationships, adoptions, cross-generational co-parenting, distinctions according to age alone or comparisons thereof, and distinctions according to gender/sex alone or comparisons thereof. In this case, if oneself is labelled by $(0, 0)$, then: one's children are labelled by $(0, 1)$, one's grandchildren are labelled by $(0, 2)$, one's $n$th-great-grandchildren are labelled by $(0, 2+n)$, one's parents are labelled by $(0, -1)$, one's grandparents are labelled by $(0, -2)$, one's $nth$-great-grandparents are labelled by $(0, -(2 + n))$, one's siblings are labelled by $(1, 0)$, one's niblings (children of siblings) are labelled by $(1, 1)$, one's nibling's children are labelled $(1, 2)$, one's neams (siblings of parents) are labelled by $(2, -1)$, one's 1st cousins 0 times removed (children of neams) are labelled by $(2, 0)$, one's first cousins once removed via neams are labelled by $(2, 1)$, etc. Notice that corporate organization charts, as directed from CEO (root) toward subordinates, can have similar labels. See also: "{tamne}", ".{anseingu}", "{grafnseljimcnkipliiu}". Jargon: Gloss Keywords: Word: canonical marked-quipyew coördinate, In Sense: kinship/cousin labelling system Place Keywords: New Data: Definition: Target node $x_1$ and primary subject node $x_4$ belong to the same (single) strictly-directed, connected tree graph/network/hierarchy or are related by relation scheme $x_5$ such that $x_1$ has coordinates $(x_2, x_3)$ and $x_4$ has coordinates $(0, 0)$ according to the labelling scheme which is described in the notes hereof. Notes: $x_2$ is a nonnegative integer; $x_3$ is an integer (potentially of any signum a priori). $x_5$ is directed and thus admits descriptions such as "rootward", "parent", "superior"/"ancestor", "leafward", "child", and "descendant"/"subordinate". $x_4 is a node which is identified and singled out as being special in the tree, and thus the relationship is not entirely symmetric under exchange of $x_4$ with any other node. For any target node $v$ in $x_5$, the coördinate label for $v$ is determined as follows: For the sake of ease and uniformity of notation, denote $x_4$ by "$μ$"; likewise denote $x_5$ by "$G$". Let/require/assume that the most-recent common direct ancestor of $μ$ and $v$ in/according to $G$ be essentially-unique and denoted by "mrcda$_{G}(μ, v)$"; let $δ$ be the Kronecker delta function on the nodes of $G$; let $ρ$ be a binary function on the Cartesian square of the set of nodes of $G$ mapped to the nonnegative intergers or positive infinity, and be the undirected graph-geodesic distance between its inputs. Jargon: Gloss Keywords: Word: canonical marked-quipyew coördinate, In Sense: kinship/cousin labelling system Place Keywords: You can go to to see it.