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| − | ==Moved==
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| − | I've just moved to the Amazon in Brazil. I suffer from anemic bandwidth, so currently I am a bit handicapped.
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| − | ==To Do== | + | ===How to do graphs and charts in wiki=== |
| − | | + | * what extensions exist? |
| − | ===multilingual wiki===
| + | *http://en.wikipedia.org/wiki/Wikipedia:How_to_create_graphs_for_Wikipedia_articles |
| − | start brainstorming about best structure for multilingual wiki
| + | *http://graphtheoryinlatex.blogspot.com/ & http://graphtheoryinlatex.wordpress.com/ |
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| − | *sisterwiki structure: | |
| − | **en.host.com/wiki/page <-> pt.wiki.host.com/wiki/page
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| − | **one-to-one correspondence among languages via subdomains | |
| − | ::- requires administrator to create subdomain | |
| − | ::+ symmetric and non-biased
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| − | ::+ subpage organization permitted
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| − | ::+ categories, templates, properties can be differentiated and translated
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| − | ::- categories, templates, properties must be duplicated, making administration potentially chaotic
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| − | vs.
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| − | *subpage structure:
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| − | **single domain using subpages: host.com/wiki/page <-> host.com/wiki/page/pt
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| − | **dominated by English hub as default
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| − | ::+ does not require administrator to create language subdomains
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| − | ::- ugly structure with one language at top of hierarchy
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| − | ::- subpage organization not permitted
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| − | ::+ categories, templates, properties are unified into a single hierarchy
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| − | ::- categories, templates, properties become complicated to render in multiple languages, require alternate renderings and additional complexity, possibly many redirects that could introduce chaos into the wiki
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| | ===hosting=== | | ===hosting=== |
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| | * Or use Osirus? | | * Or use Osirus? |
| | * Or what is the status of Diaspora? | | * Or what is the status of Diaspora? |
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| − | ===best practices: user page, user talk===
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| − | My user/talk pages are becoming disorganized and lack direction or standardization. What's the best practice for these pages? seems to me:
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| − | * user page (my page): what I have to say about myself and what I'm doing
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| − | * user talk: discussions and interactions between myself and other users.
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| − | any comments?
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| − | ===2012===
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| − | :[[The Sovereign Individual]] book covers a lot of the foundations of the change to come, my interpretation is that this is about the days of centralisation coming to an end and the new distributed bottom-up paradigm coming about... One of the biggest breakthrough's for this new paradigm to really take off is that we need a secure p2p payment system which is an open standard. There's some notes on that at [[Currency]] and some at [[Human Ecology]] --[[User:Nad|nad]] 00:58, 7 June 2010 (UTC)
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| | ==observations== | | ==observations== |
| − | ====dimensionality of spacetime====
| + | [[Dimensionality of space:time]] |
| − | Observations that support the notion that spacetime in nature does not exceed 3 orthogonal dimensions
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| − | [[category:Articles containing maths]] | |
| − | =====[http://www.lomont.org/Math/GeometricAlgebra/NFMPchapt1%20-%20Hestenes%20-%201998.pdf NFCM (New Foundations for Classical Mechanics) summary - David Hestenes] Ch. 1 =====
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| − | * P. 3 reciprocal identity of k-blade and k-vector only holds for <math>\mathcal{G}_n, n \leq 3</math>
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| − | :"The completely antisymmetrized product of k vectors <math> a_1, a_2 \ldots a_k </math> generates a new entity <math> a_1 \wedge a_2 \wedge \ldots \wedge a_k </math> called a k-blade. The integer k is called the step (or grade of the blade.* A linear combination of blades with the same step is called a k-vector. Therefore, every k-blade is a k-vector. ''The converse that every k-vector is a k-blade holds only in the geometric algebras <math>\mathcal{G}_n</math> with <math>n \leq 3</math>.''" (Italics, mine)
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| − | * P. 8 Special and unique properties of ''i'' in 3-space, as unit pseudoscalar, as dual, as inverse space
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| − | : "The properties of geometric algebra which are peculiar to the three-dimensional case are summarized in this section. They all derive from special properties of the pseudoscalar and duality in <math>\mathcal{G}_3</math>.
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| − | :"The unit pseudoscalar for <math>\mathcal{G}_3</math> is so important that the special symbol <math>i</math> is reserved to denote it. This symbol is particularly apt because <math>i</math> has the algebraic properties of a conventional unit imaginary. Thus, it satisfies the equations
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| − | :(2.1) <math>i^2 = -1 </math>
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| − | :and
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| − | :(2.2) <math>i\mathbf{a} = \mathbf{a}i </math>
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| − | :for any vector <math>\mathbf{a}</math>. According to (2.2), the ''imaginary number'' <math>i</math> commutes with vectors, just like the real numbers (scalars). It follows that <math>i</math> commutes with every multivector in <math>\mathcal{G}_3</math>.
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| − | :The algebraic properties (2.1) and (2.2) allow us to treat <math>i</math> as if it were an imaginary scalar, but <math>i</math> has other properties deriving from the fact that it is the unit pseudoscalar. In particular, <math>i</math> relates scalars and vectors in <math>\mathcal{G}_3</math> to bivectors and pseudoscalars by duality."
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| − | :...
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| − | :(2:4) <math>A = \alpha + \mathbf{a} + i\mathbf{b} + i\beta</math>
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| − | :"This shows that <math>A</math> has the formal algebraic structure of a ''complex scalar'' <math>\alpha + i\beta</math> added to a complex vector <math>\mathbf{a} + i\mathbf{b}</math>. The algebraic advantages of the "complex expanded form" (2.4) are such that we shall use the form often."
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| − | {{to do|task=fix maths formula numbering without using tables}}{{to do|task=fix maths formula size inconsistencies}}
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| − | ----
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| − | * Bott periodicity {{to do|task=find reference}}
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| − | * Ardeshir Mehta on the impossibility of n>3 orthogonal directions {{to do|task=find reference}}
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| − | ====Correlations betweeen [[The two domains]] & [[RST]]====
| + | [[Correlations between The Two Domains and RST]] |
| − | I found [[User:Jack| Jack's]] / [[User:Nad| Nad's]] article on [[The two domains]] and the [[Talk:The two domains |discussion thereof]] concerning the dichotomy of the Nodal model, as well as the notion of Fourier transform relating the space and time domains as inverses, intriguing. I see parallels to the concepts espoused in Dewey Larson's [[Reciprocal system of theory]] (RST).
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| − | {{to do|task=expound}}...
| + | [[Both 3-space and 3-time exist]] |
