 Dec 2023

docdrop.org docdrop.org

history is always the result of a lot of causes coming together you know 00:29:22 you have this metaphor of the chain of events and this is a terrible metaphor for there is no chain of events a chain of events imagines that every event is a link connected to one previous event and 00:29:36 to one subsequent event so there is a war there is one cause for the war and there will be one consequence it's never like that in history every event is more like a tree there is an entire system of 00:29:50 roots that came together to create it and it has a lot of fruits with lots of different influences

for: insight  history  complexity, bad metaphor  chain of events

insight: complexity and history
 chain of events is a bad metaphor for things that occur in history
 the complexity of history is that many causes come together too being about an event
 likewise, when that event occurs, it is the cause of many different consequences
 linear vs systems thinking

adjacency between
 history
 emptiness
 Indra's net
 adjacency statement
 history reflects emptiness
 Indra's net extended into historical events


 Oct 2023


Bill Atkinson had an idea about the freedom to associate knowledge not by what comes next on the list but by the links that are associated with it. This means that information can be organized in a nonlinear fashion, allowing for connections to be made between seemingly unrelated ideas. By expanding on this idea, we can create new and innovative ways of storing and accessing information, potentially leading to breakthroughs in fields such as artificial intelligence and data analysis.

 Jul 2023

www.youtube.com www.youtube.com

GRINDE mapping: 1. Grouped: grouping knowledge together 2. Reflective: reflective of your (nonlinear) thinking 3. Interconnected: making more & distant connections (stronger than the groups) 4. Nonverbal (visuals) 5. Directional: which relations are the strongest, in which order can you sequence them? 6. Emphasise (visually) the most important things (see directional as well)

 Apr 2023

zettelkasten.de zettelkasten.de

The result of working with this technique for a long time is a kind of second memory, an alter ego with which you can always communicate. It has, similar to our own memory, no preplanned comprehensive order, no hierarchy, and surely no linear structure like a book. And by that very fact, it is alive independently of its author. The entire note collection can only be described as a mess, but at least it is a mess with a nonarbitrary internal structure.
Luhmann attributes (an independent) life to his zettelkasten. It is effectuated by internal branching, opportunities for links or connections, and a register as well as lack of preplanned comprehensive order, lack of hierarchy, and lack of linear structure.
Which of these is necessary for other types of "life"? Can any be removed? Compare with other systems.

 Mar 2023

web.archive.org web.archive.org

Die schiere Menge sprengt die Möglichkeiten der Buchpublikation, die komplexe, vieldimensionale Struktur einer vernetzten Informationsbasis ist im Druck nicht nachzubilden, und schließlich fügt sich die Dynamik eines stetig wachsenden und auch stetig zu korrigierenden Materials nicht in den starren Rhythmus der Buchproduktion, in der jede erweiterte und korrigierte Neuauflage mit unübersehbarem Aufwand verbunden ist. Eine Buchpublikation könnte stets nur die Momentaufnahme einer solchen Datenbank, reduziert auf eine bestimmte Perspektive, bieten. Auch das kann hin und wieder sehr nützlich sein, aber dadurch wird das Problem der Publikation des Gesamtmaterials nicht gelöst.
Google translation:
The sheer quantity exceeds the possibilities of book publication, the complex, multidimensional structure of a networked information base cannot be reproduced in print, and finally the dynamic of a constantly growing and constantly correcting material does not fit into the rigid rhythm of book production, in which each expanded and corrected new edition is associated with an incalculable amount of effort. A book publication could only offer a snapshot of such a database, reduced to a specific perspective. This too can be very useful from time to time, but it does not solve the problem of publishing the entire material.
While the writing criticism of "dumping out one's zettelkasten" into a paper, journal article, chapter, book, etc. has been reasonably frequent in the 20th century, often as a means of attempting to create a linear bookbound context in a local neighborhood of ideas, are there other more complex networks of ideas which we're not communicating because they don't neatly fit into linear narrative forms? Is it possible that there is a nonlinear form(s) based on network theory in which more complex ideas ought to better be embedded for understanding?
Some of Niklas Luhmann's writing may show some of this complexity and local or even regional circularity, but perhaps it's a necessary means of communication to get these ideas across as they can't be placed into linear forms.
One can analogize this to Lie groups and algebras in which our reading and thinking experiences are limited only to local regions which appear on smaller scales to be Euclidean, when, in fact, looking at larger portions of the region become dramatically nonEuclidean. How are we to appropriately relate these more complex ideas?
What are the second and third order effects of this phenomenon?
An example of this sort of nonlinear examination can be seen in attempting to translate the complexity inherent in the Wb (Wörterbuch der ägyptischen Sprache) into a simple, linear dictionary of the Egyptian language. While the simplicity can be handy on one level, the complexity of transforming the entirety of the complexity of the network of potential meanings is tremendously difficult.

Die schiere Menge sprengt die Möglichkeiten der Buchpublikation, die komplexe, vieldimensionale Struktur einer vernetzten Informationsbasis ist im Druck nicht nachzubilden, und schließlich fügt sich die Dynamik eines stetig wachsenden und auch stetig zu korrigierenden Materials nicht in den starren Rhythmus der Buchproduktion, in der jede erweiterte und korrigierte Neuauflage mit unübersehbarem Aufwand verbunden ist. Eine Buchpublikation könnte stets nur die Momentaufnahme einer solchen Datenbank, reduziert auf eine bestimmte Perspektive, bieten. Auch das kann hin und wieder sehr nützlich sein, aber dadurch wird das Problem der Publikation des Gesamtmaterials nicht gelöst.
link to https://hypothes.is/a/U95jEs0eEe20EUesAtKcuA
Is this phenomenon of "complex narratives" related to misinformation spread within the larger and more complex social network/online network? At small, local scales, people know how to handle data and information which is locally contextualized for them. On larger internetscale communication social platforms this sort of contextualization breaks down.
For a lack of a better word for this, let's temporarily refer to it as "complex narratives" to get a handle on it.
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 thinking inside of the box
 card index as autobiography
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 insight
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 complex narratives
 Lie theory
 local vs. global
 social media
 media studies
 Wörterbuch der ägyptischen Sprache
 context collapse
 zettelkasten complexity
 experimental nonfiction
 rhetoric
 nonlinear narratives
 network theory
 thinking outside of the box
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datatracker.ietf.org datatracker.ietf.org

Another option would be to implement a delay scheme to avoid a brute force attack. After each failed attempt A, the authentication server would wait for an increased T*A number of seconds, e.g., say T = 5, then after 1 attempt, the server waits for 5 seconds, at the second failed attempt, it waits for 5*2 = 10 seconds, etc.
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nesslabs.com nesslabs.com

Beyond cognitive biases and preconceived opinions, common sense is based on linear thinking. “I experience A, therefore I can directly explain it by B.”

 Dec 2022

www.thenation.com www.thenation.com

At its most tame, Ancient Apocalypse simply reinforces a deeply conservative understanding of human history. Conservative, yes, because despite Hancock’s claim to challenge every orthodoxy going, his ideas—like those of Ignatius Loyola Donnelly, Erich von Däniken, and other socalled “pseudoarchaeologists”—rest on a baseline assumption that technology should always be advancing in linear fashion, from primitive simplicity to modern complexity.
There is a broad, conservative baseline assumption within much of archaeology that technology always proceeds in a linear fashion from primitive simplicity to modern complexity.
Archaeologists and historians need to watch carefully for this cognitive bias.

 Nov 2022

en.wikipedia.org en.wikipedia.org

Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities, such as forces and velocity, that have not only a magnitude, but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix, which allows computing in vector spaces. This provides a concise and synthetic way for manipulating and studying systems of linear equations.
A vector space is a mathematical structure that allows us to work with things that have both a magnitude and a direction. This is useful for studying physical quantities like forces and velocity. The concept of vector spaces is important for linear algebra, which is a way of solving systems of linear equations.

n mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
A vector space is a mathematical structure that allows us to work with things that have both a magnitude and a direction. This is useful for studying physical quantities like forces and velocity. The concept of vector spaces is important for linear algebra, which is a way of solving systems of linear equations.
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 Oct 2022

twitter.com twitter.com

The first demo of TidlyWiki from 2004 took the ideas of wiki and applied them to fragments rather than entire pages. The hypothesis was that it would be easier to write in small interlinked chunks that could be gradually massaged into a linear narrative
<script async src="https://platform.twitter.com/widgets.js" charset="utf8"></script>The first demo of TidlyWiki from 2004 took the ideas of wiki and applied them to fragments rather than entire pages. The hypothesis was that it would be easier to write in small interlinked chunks that could be gradually massaged into a linear narrativehttps://t.co/v2v6dyL3Oy pic.twitter.com/MJO7tyopr2
— TiddlyWiki (@TiddlyWiki) September 20, 2022

 May 2022

via3.hypothes.is via3.hypothes.is

“This technique alsoexplains why I don’t think at all linearly and have trouble finding the right sequence ofchapters when writing a book, because indeed every chapter must reappear in everyother.”22
 Luhmann, Archimedes und wir , 145.
Luhmann indicated that his note taking system made it difficult for him to be a linear thinker. Instead he felt that each chapter he wrote "must reappear in every other."
This seems quite similar to Carl Linnaeus' work which he regularly recycled into future works.

 Mar 2022

nesslabs.com nesslabs.com

Beyond cognitive biases and preconceived opinions, common sense is based on linear thinking. “I experience A, therefore I can directly explain it by B.”
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 Feb 2022

linear.axler.net linear.axler.net

https://linear.axler.net/LADRvideos.html
I've seen Gilbert Strang's excellent lecture series. I'm curious how these rank in relation.


Local file Local file

There is one reliable sign if you managedto structure your workflow according to the fact that writing is not alinear process, but a circular one: the problem of finding a topic isreplaced by the problem of having too many topics to write about.
Writing is a circular generative process and not a finite, linear one.

 Jan 2022

www.nytimes.com www.nytimes.com

“It was kind of fun. Like even though I was green, that doesn’t mean my green tops your yellow right? Whatever I did, I just did it with a lot of energy.”
There's been a normalization of providing exterior indicators of internal ideas and people's mental states. Examples include pins indicating pronouns, arm bracelets indicating social distancing or other social norms.
But why aren't we taking these even farther on the anthropological spectrum? Is one society better or worse than another? One religion, one culture? Certainly not. Just like Leah McGowenHare's green band indicating that she's a hugger isn't any more valuable than someone else's yellow fist bump indicator. We need to do a better job of not putting people into linear relationships which only exist in our minds until we realize how horrific and dehumanizing they are.
Cross reference:

 Oct 2021

www.deeplearningbook.org www.deeplearningbook.org

Writing an expression in terms of the trace operator opens up opportunities tomanipulate the expression using many useful identities.
What does writing an expression using trace operator open up to?

the traceoperator is invariant to the transpose operator:
What is the trace operator invariant for?

What is the Frobenius Norm of a Matrix?

For example, the trace operator providesan alternative way of writing the Frobenius norm of a matrix:
The trace operator provides the alternative way of writing which norm of the matrix?

Some operations that arediﬃcult to specify without resorting to summation notation can be speciﬁed usingmatrix products and the trace operator.
Where the trace operator is useful?


cloud.google.com cloud.google.com

Even with this very primitive single neuron, you can achieve 90% accuracy when recognizing a handwritten text image1. To recognize all the digits from 0 to 9, you would need just ten neurons to recognize them with 92% accuracy.
And here is a Google Colab notebook that demonstrates that

 Jul 2021

delong.typepad.com delong.typepad.com

There is no inactive learning, just as there is no inactive reading.
This underlies the reason why the acceleration of the industrial revolution has applied to so many areas, but doesn't apply to the acceleration of learning.
Learning is a linear process.

 Jun 2021

math.stackexchange.com math.stackexchange.com

This also happens to explain intuitively some facts. For instance, the fact that there is no canonical isomorphism between a vector space and its dual can then be seen as a consequence of the fact that rulers need scaling, and there is no canonical way to provide one scaling for space. However, if we were to measure the measureinstruments, how could we proceed? Is there a canonical way to do so? Well, if we want to measure our measures, why not measure them by how they act on what they are supposed to measure? We need no bases for that. This justifies intuitively why there is a natural embedding of the space on its bidual.

The dual is intuitively the space of "rulers" (or measurementinstruments) of our vector space. Its elements measure vectors. This is what makes the dual space and its relatives so important in Differential Geometry, for instance.
A more intuitive description of why dual spaces are useful or interesting.

 Apr 2021

journals.plos.org journals.plos.org

Sy, Karla Therese L., Laura F. White, and Brooke E. Nichols. ‘Population Density and Basic Reproductive Number of COVID19 across United States Counties’. PLOS ONE 16, no. 4 (21 April 2021): e0249271. https://doi.org/10.1371/journal.pone.0249271.

 Nov 2020

stats.idre.ucla.edu stats.idre.ucla.edu

Linear mixed models are an extension of simple linear models to allow both fixed and random effects, and are particularly used when there is non independence in the data, such as arises from a hierarchical structure

 Aug 2020

arxiv.org arxiv.org

Ran, Y., Deng, X., Wang, X., & Jia, T. (2020). A generalized linear threshold model for an improved description of the spreading dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(8), 083127. https://doi.org/10.1063/5.0011658

 Jul 2020


Knittel, C. R., & Ozaltun, B. (2020). What Does and Does Not Correlate with COVID19 Death Rates (Working Paper No. 27391; Working Paper Series). National Bureau of Economic Research. https://doi.org/10.3386/w27391
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 poverty
 telecommuting
 commute
 African American
 economy
 energy
 Iowa
 Indiana
 Michigan
 Louisiana
 public transport
 obesity
 COVID19
 lang:en
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 is:article
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 ICU
 binomial
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 linear regression
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osf.io osf.io

Sevi, S., Aviña, M. M., PéloquinSkulski, G., Heisbourg, E., Vegas, P., Coulombe, M., ArelBundock, V., Loewen, P. J., & Blais, A. (2020). Logarithmic vs. Linear Visualizations of COVID19 Cases Do Not Affect Citizens’ Support for Confinement [Preprint]. SocArXiv. https://doi.org/10.31235/osf.io/h6z4f

 Jun 2020

bmcmedresmethodol.biomedcentral.com bmcmedresmethodol.biomedcentral.com

Boulesteix, A., Strobl, C. Optimal classifier selection and negative bias in error rate estimation: an empirical study on highdimensional prediction. BMC Med Res Methodol 9, 85 (2009). https://doi.org/10.1186/14712288985

 May 2020

psyarxiv.com psyarxiv.com

Ryan, W., & Evers, E. (2020). Logarithmic Axis Graphs Distort Lay Judgment. https://doi.org/10.31234/osf.io/cwt56

 Apr 2020

psyarxiv.com psyarxiv.com

Romano, A., Sotis, C., Dominioni, G., & Guidi, S. (2020). COVID19 Data: The Logarithmic Scale Misinforms the Public and Affects Policy Preferences [Preprint]. PsyArXiv. https://doi.org/10.31234/osf.io/42xfm

 Jan 2020

quantum.country quantum.country

∣00⟩
Does this just look like
[ 1 1 0 0 ]
as in two 0> smooshed together?

∥U∣ψ⟩∥2=jkl∑Ujk∗ψk∗Ujlψl
Lost me here...

T
Transpose?

What does it mean for a matrix UUU to be unitary? It’s easiest to answer this question algebraically, where it simply means that U†U=IU^\dagger U = IU†U=I, that is, the adjoint of UUU, denoted U†U^\daggerU†, times UUU, is equal to the identity matrix. That adjoint is, recall, the complex transpose of UUU:
Starting to get a little bit more into linear algebra / complex numbers. I'd like to see this happen more gradually as I haven't used any of this since college.

 Dec 2019

www.dougengelbart.org www.dougengelbart.org

"You usually think of an argument as a serial sequence of steps of reason, beginning with known facts, assumptions, etc., and progressing toward a conclusion. Well, we do have to think through these steps serially, and we usually do list the steps serially when we write them out because that is pretty much the way our papers and books have to present them—they are pretty limiting in the symbol structuring they enable us to use. Have you even seen a 'scrambledtext' programmed instruction book? That is an interesting example of a deviation from straight serial presentation of steps.3b6b "Conceptually speaking, however, an argument is not a serial affair. It is sequential, I grant you, because some statements have to follow others, but this doesn't imply that its nature is necessarily serial. We usually string Statement B after Statement A, with Statements C, D, E, F, and so on following in that order—this is a serial structuring of our symbols. Perhaps each statement logically followed from all those which preceded it on the serial list, and if so, then the conceptual structuring would also be serial in nature, and it would be nicely matched for us by the symbol structuring.3b6c "But a more typical case might find A to be an independent statement, B dependent upon A, C and D independent, E depending upon D and B, E dependent upon C, and F dependent upon A, D, and E. See, sequential but not serial? A conceptual network but not a conceptual chain. The old paper and pencil methods of manipulating symbols just weren't very adaptable to making and using symbol structures to match the ways we make and use conceptual structures. With the new symbolmanipulating methods here, we have terrific flexibility for matching the two, and boy, it really pays off in the way you can tie into your work.3b6d This makes you recall dimly the generalizations you had heard previously about process structuring limiting symbol structuring, symbol structuring limiting concept structuring, and concept structuring limiting mental structuring.

 Sep 2019

betterexplained.com betterexplained.com

Time for the red pill. A matrix is a shorthand for our diagrams: A matrix is a single variable representing a spreadsheet of inputs or operations.

 Aug 2019

maxgoldste.in maxgoldste.in

This intentional break from pencilandpaper notation is meant to emphasize how matrices work. To compute the output vector (i.e. to apply the function), multiply each column of the matrix by the input above it, and then add up the columns (think of squishing them together horizontally).
read while playing with this: http://matrixmultiplication.xyz/

After months of using and learning about matrices, this is the best gist I've come across.

 Jul 2019

mmlbook.github.io mmlbook.github.io

One major idea in mathematics is the idea of “closure”. This is the question: What is the set of all things that can result from my proposed operations? In the case of vectors: What is the set of vectors that can result bystarting with a small set of vectors, and adding them to each other andscaling them? This results in a vector space
closure in mathematics. sounds similar to domain of a function
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 Oct 2018

yiddishkop.github.io yiddishkop.github.ioMath3

李宏毅 linear algebra lec7
Textbook: chapter 1.7
前一节课已经介绍了如何判断【有没有解】：很多“换句话说”
有没有解 > 是不是线性组合 > 在不在span中。
现在要解决的是：如果有解，那么会有多少个解！

李宏毅 linear algebra lec6: Having solution or Not?
Textbook: chapter 1.6
\(Ax=b\)
能否找到一个 x 使得 \(Ax=b\) 成立.
 Linear combination
 span
有没有解这个问题非常重要：假设 Linear system 是一个电路，现在老板告诉你这个电路要输出 b 这么大的电流，你能不能找到合适的电压源or电流源，还是根本就找不到？
关于“解”的名词定义
consistent
A system of linear equations is called consistent if it has one or more solutions。
只要有解就叫做 consistent.
inconsistent
A system of linear equations is called inconsistent if its solution set is empty(no solution)
没有解就叫做 inconsistent.
如何确定“解”
Naive 方法：线的交点
把 system of linear equations 的方程都画成直线，如果他们有交点，那么就是有解，否则无解。
General 方法
定义引入：Linear Combination
Given a vector set \(\{u_1,u_2,...,u_k\}\)
The linear combination of the vectors in the set: \(v=c_1u_1+c_2u_2+...+c_ku_k,\ c_1,c_2,...,c_k\ are\ scalars\ coefficients\ of\ linear\ combination\)
linear combination is a vector.
有了 Linear combination 的定义之后，我们再回一下 lec5 篇末讲解的关于 使用 column view of product of matrix and vector 所以我们可以得到的结论是：
\(Ax\) 其本质就是一个 linear combination, 他是
 以 \(x\) 的每一位为 scalar coefficient of linear combination,
 以 columns of \(A\) as vectors 作为 vector set engaged in linear combination, 的一个 linear combination
矩阵与向量的乘法就是对矩阵的列做线性组合。
对于 \(Ax=b\) 是否有解（x是变量）这件事，实际就是在问：b 是否是columns of A的所有可能的线性组合中的一种。
从是否有解到是否是线性组合
如果两个向量不是平行的同时不是0向量，那么他们可以组合出二维空间中所有可能的向量（亦即，线性组合的所有可能性覆盖整个2D空间）。
【判断题】：如上所说，如果非零非平行的两个向量的线性组合可以覆盖整个二维空间的话，那么非零非平行的三个向量的线性组合是否可以覆盖整个三维空间呢？
【答案】：否
引入 independent 向量
在三维空间中对参与线性组合的向量不能仅仅给出【非零】【非平行】两个限制，还得加上一个【不在同一个二维平面】。试想，如果三个向量处在同一平面的话，那么不论如何线性组合都不可能与第三维有任何关系。
引入 反之不反
非零非平行 ===> 有解；有解 ==X==> 非零非平行。
引入 span
vector set 的所有可能的 linear combination （另一个vector set）就是这组 vector set 的 span。
\(v = c_1u_1+c_2u_2+...+c_ku_k\)
\(v\) 毫无疑问是一个向量。
如果我们穷举所有可能的\(c_1,c_2,...,c_k\)，他们所得到的向量的集合（vector set \(V\)）就是\(x_1,x_2,...,x_k\)的span，同时，\(x_1,x_2,...,x_k\) 叫做 vector set \(V\) 的 generating set.
引入 generating set
\(if\ Vector\ set\ V=Span(S),\ then\ V\ is\ Span\ of\ S, also\ S\ is\ a\ generating\ set\ for\ V,\ or\ S\ generates\ V\)
\(S\) 可以作为一种描述 \(V\) 特性的方法。为什么我们需要这种描述方法呢？因为 \(V\) 作为一个 span，他通常都非常非常的大（一般都是无穷多个），如果我们想要描述这种无穷大（“无穷”都意味着抽象）的向量的集合，最好的方法就是找到一个更具体（“有限”意味着具体）的可联想的“指标”  generating set  这个向量集合是由什么样的向量集合生成的。
相同的向量集(span)可能由不同的向量集（generating set）产生：
\(S_1=\begin{vmatrix} 1 \\ 1\end{vmatrix}\)
同
\(S_2=\{\begin{vmatrix}1\\1\end{vmatrix},\begin{vmatrix}2\\2\end{vmatrix}\}\)
产生的向量集是相同的。
引入 span of standard vector
standard vector 其实就是 onehot encoding vector. 可以见下：
\(e_1=\begin{vmatrix}1\\0\\0\end{vmatrix}, e_1=\begin{vmatrix}0\\1\\0\end{vmatrix}, e_1=\begin{vmatrix}0\\0\\1\end{vmatrix}\)
\(span(e_1)=one\ R^1\ in\ R^3\), one axis in 3Dspace \(span(e_1,e_2)=one\ R^2\ in\ R^3\), one 2Dspace in 3Dspace \(span(e_1,e_2,e_3)=R^3\), whole 3Dspace.
其实今天学的东西就是“换句话说”，
 \(Ax=b\) has solution or not?
换句话说
 is \(b\) the linear combination of columns of \(A\)?
换句话说
 is \(b\) in the \(span\) of the columns of \(A\)?

李宏毅 linear algebra lec 5
重新定义线性代数
第三节课讲过，一个线性系统不仅仅是一条“直线”，直线只是一种特殊到不能再特殊的情况。线性系统的本质是：
'>' 以下表示线性系统
符合加法性：x>y ==> x1+x2>y1+y2
符合乘法(scalar)性：x>y ==> x1k>yk
广义向量
再结合一个超级牛逼的观点广义向量  函数也是一种向量。我们就把线性系统是一条直线的观点边界向外扩展了一些：
线性系统是以向量（亦即，包含函数和数字和普通向量）作为输入
现实世界中的很多东西都可以表示为向量，就连函数也不例外。
他可以造就这样的奇迹：
加法性：fn>fc ===> fn1 + fn2> fc1+fc2
乘法性：fn>fc ===> fn1k>fc1k
也就是说，线性系统接收的输入和输出都是一个向量，而数字和函数只是特殊的向量。，满足这一特殊性质的线性系统就是【微分】and【积分】。微分和积分更像是一种【功能】而不是一个【函数】，这也是为什么我们不把系统说成函数的原因，因为他强调功能而不是记号表示性，或者说函数只是功能的一个可记号话的特例
线性代数这门学科研究的主要目标就是线性系统。
于是新的关于线性系统的定义至此形成：
\(vector\ \Rightarrow LinearSystem\ \Rightarrow vector\)
\(domain\ \Rightarrow LinearSystem\ \Rightarrow codomain\)
线性系统与联立线性等式
可以证明的是（in lec3）任何线性系统都可以表示为联立线性等式，也就是说联立等式与线性系统是等价的
Linear system is equal to System of linear equations.
【矩阵，联立方程式，线性系统】其实是一个东西
 矩阵 符合加法/乘法性 所以其为一个线性系统
 联立方程式 符合加法/乘法性 所以其为一个线性系统
因为
矩阵=线性系统，
联立方程=线性系统，
所以
矩阵=联立方程。
lec5: 两种方式理解 matrixvector product
 可以按行看待matrix,正常看法；
 可以按列看待matrix,把整个matrix看成一个row向量;
联立方程式 > 按列看待matrix的 product of matrix and vector > 联立方程式可以写成 Product of matrix and vector. 因为之前说过任何一个线性系统都可以写成联立方程式，那么矩阵就是一个线性系统。
\(Ax=b\) 中的 \(A\) 就是一个线性系统
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192.168.199.102:5000 192.168.199.102:5000

2. 綫性相加（combinations），伸展（span）和單位矢量 l 綫性代數的本質 第二章
本节介绍三个相互依存的概念：单位向量，span，线性无关。
基于单位向量和数字的向量的表示
 basis vector \(\hat{i}\)
 basis vector \(\hat{j}\)
 adding together two scaled vectors
是一种新的看待线性代数的观点，非常重要的三个知识点，至此向量的表示可以变成在各个单位向量做放缩然后取和，或者，单位向量的线性组合：
\((5)\hat{i} + (2)\hat{j}\)
可以表示为：
$$ \begin{vmatrix} 5 \\ 2 \end{vmatrix} $$
what if we choose different basis vectors?
虽然不论使用什么方向的两个单位向量，其线性组合始终可以覆盖全部二维空间，但是我们仍然得到了同一个向量的两个不同的表示：
although \((3.1)\hat{i} + (2.9)\hat{j} = \(0.8)\hat{i}+(1.3)\hat{j}\) 但是该向量的实际表示却完全不同：
$$ \begin{vmatrix} 0.8 \\ 1.3 \end{vmatrix} \neq \begin{vmatrix} 3.1 \\ 2.9 \end{vmatrix} $$
所以这里需要给出一种关于线性代数的数字表示法\([3.1, 2.9]\)的一个基本条件：每当使用这种表示法时都必须明确单位向量是什么。
span of vectors
可以想象的是：
 如果两个单位向量之间存在夹角那么他们的线性组合形成的向量一定可以覆盖整个平面；
 如果两个单位向量处在同一个方向（相同or相反）那么他们的线性组合形成的向量只能覆盖这条直线
 如果两个单位向量都是 \(\vec{0}\)，那么他们的线性组合形成的向量都是\(\vec{0}\)
引入概念span
The "span" of \(\vec{v}\) and \(\vec{w}\) is the set of all their linear combinations:
\(a\vec{v} + b\vec{w}\)
let \(a\) and \(b\) vary over all linear numbers.
两个向量的 span 与另一个表述是等价的，仅仅通过加法和乘法两种操作可以产生的所有向量
Vectors VS. Points
【tips】如果仅仅考虑一个向量，经常将向量想象成带箭头线段；如果考虑一堆向量的集合，经常将向量想象成点。
 那么两个同方向的向量的span就形成一条直线
 那么两个不同方向的向量的span就形成一个平面
 那么三个不同方向的向量的span就形成一个体
Redundant and Linearly dependent
任何时候如果你有多个向量，但是去掉其中一个或几个，前者和后者的span没有减少（span is essencially a set  set of all possible linear combination）
\(span(\vec{v},\vec{w},\vec{u})=span(\vec{v},\vec{w})\)
那么就可以说这个向量与其他向量是 Linear dependent （线性相关）， 或者说这个（可以去掉的）向量可以表示为其他向量的线性组合, 因为这个可以去掉的向量处在其他向量的span中。
\(redundant\ \vec{u} \in span(\vec{v}, \vec{w})\)
或者说，他对扩大span(set of linear combination of vectors)没有作用。
由此衍生出另一个概念：Linearly independent
Linearly independent
\(\vec{u} \neq a\vec{v} + b\vec{w},\ for\ all\ values\ of\ a\ and\ b\)
如果某个单位向量无法通过其他单位向量的任何一种系数的线性组合来得到，那么就说这个向量与其他向量都是线性无关的
basis vector
有了之前的 span linearly dependent 两个概念，下面才能正式定义第三个概念：何为 basis vector ？
The basis of a vector space is a set of linearly independent vectors that span the full space
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 Sep 2018

stackoverflow.com stackoverflow.com

Doublecentering a matrix M

 Aug 2018

wendynorris.com wendynorris.com

Viewed from a practice perspective, the distinction between cyclic and linear time blurs because it depends on the observer's point of view and moment of observation. In particular cases, simply shifting the observer's vantage point (e.g., from the corporate suite to the factory floor) or changing the period of observation (e.g., from a week to a year) may make either the cyclic or the linear aspect of ongoing practices more salient.
Could it be that SBTF volunteers are situating themselves in time as a way to respond to a cyclic/linear tension? or a spatial tension?


wendynorris.com wendynorris.com

Coherent, finalized stories are embedded with alinear structure that aligns with clock time and theGregorian calendar (Gabriel 2000, p. 239). Chronology and objective time implant these stories withan identifiable past, present and future and a linearcausality that provides a temporal structure (a beginning, middle and end with plot and characters).This linearity is tied to the inviolability of sequencedevents that occur within a tensed notion of time where,for example, you cannot have a character seeking revenge before an original insult has occurred, nor canyou have a punishment for a crime that will be committed later.
For Gabriel, stories have a linear temporal structure (beginning, middle, end) driven by past, present and future events.


wendynorris.com wendynorris.com

Another strategy in dealing with sui generis time consists in juxtaposing clock time to the various forms of 'social time' and considers the latter as the more 'natural' ones, i.e. closer to subjective perceptions of time, or to the temporality that results from adaptations to seasons or other kinds of natural (biological, environmental) rhythm. This strategy, often couched also in terms of an opposition between 'linear' clock time and 'cyclical' time of natural and social rhythms devalues, or at least questions, the temporality of formal organizations which rely heavily on clock time in fulfilling their coordinative and integrative and controlling functions (Young, 1988; Elchardus, 1988).
by contrasting social time (as a natural phenomenon) against clock time, allows for a more explicit perspective on linear time (clock) and social rhythms when examining social coordination.

 Jul 2018

wendynorris.com wendynorris.com

Since time elapses in a linear fashion and users may switch between tasks during the course of a day, the “elapsed” marbles roll into a track below the storage cylinders.
This is a Western, industrialized perspective of temporal experience and is not universal.
Wonder how users respond to the marble representation/metaphor  does this intuitively make sense to them?


wendynorris.com wendynorris.com

he two patterns—monochronic and polychronic—form a continuum, because polychronicity is the extent to which people prefer to engage in two or more tasks simultaneously, and the complete absence of any simultaneous involvements, engaging tasks one at a time, is the least polychronic position on the continuum.
Monochronic side of the continuum is linear
Polychronic side of the continuum is cyclical
Could Adam's timescape help to further describe this phenomenon? (see Perspectives on time: Zimabrdo + Adam slidedeck)
linear = spatial, historical, irreversible, tied to a beginning
cyclical = process, rhythmic, seasonal, bounded, sequential, hopeful (past+future+present)


wendynorris.com wendynorris.com

In contrast to the assumption oftime as linear, with ordered chunks progressing ina straightforward manner, people often negotiate time rhythmically, arranging timein patterns and tempos that do not always coexist harmoniously.
Does rhythmic time help to explain some of the tension in crowdsourcing crisis data from nonlinear social media streams?

In contrast to the assumption oftime as linear, with ordered chunks progressing ina straightforward manner, people often negotiate time rhythmically, arranging timein patterns and tempos that do not always coexist harmoniously. In line with earlier CSCW findings [e.g., 4, 9, 45, 46], we term thisrhythmic time, which acknowledges both the rhythmic nature of temporal experience as well a potential disorderliness or ‘dissonance’ when temporal rhythms conflict.Like mosaic time, bringing dissonant rhythms into semialignment requires adaptation, work, and patience.
Rhythmic time definition. Counters the idea of linear time.
How does this fit (or not) with Reddy's notion of temporal rhythms?

We call this prevailing temporal logic ‘circumscribed time.’ We use this label to highlight the underlying orientation to time as a resource that can, and should, be mastered. A circumscribed temporal logic infers that time should be harnessed into ‘productive’ capacity by approaching it as something that can be chunked, allocated to a single use, experienced linearly, and owned. In turn, the norms of society place the burden on individuals to manage and ‘balance’ time as a steward, optimizing this precious resource by way of control and active manipulation.
Description of the elements of circumscribed time.

Thedominant temporal logicalso conceptualizestime aslinear. In other words,one chunk of time leads to another in a straight progression. While chunks of time can be manipulated and reordered in the course of a day (or week, or month), each chunk of time has a limited duration and each activity has a beginning and an end. An hour is an hour is an hour, and in the course of a day (or a lifetime) hours stack up like a vector, moving one forward in a straightforward progression.
Definition of linear time.
WRT to temporal linguistics, linear time drives movingego and movingtime metaphors.

 Feb 2017

www.digitalrhetoriccollaborative.org www.digitalrhetoriccollaborative.org

indissolubility
I'm quite interested in this term, and other contrastructural approaches (such as gutters by, and in, which absence becomes "meaningful"). They as a species suggest something of a "nonlinear" logic in which elements resist isolations performed to offer an analysis or critique.

 May 2016

adamcroom.com adamcroom.com

To me, this is what OER for the web should start to reflect.
You mean it’s not just about the price of textbooks??

 Apr 2016


diverse learning.
interdisciplinary, perhaps?

 Feb 2016

linear.pugetsound.edu linear.pugetsound.edu

A First Course in Linear Algebra, Robert A. Beezer<br> Free as PDF or online.
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 Oct 2015

www.nationalgeographic.com www.nationalgeographic.com

I might use something like it as the basis for an NLP passage but at a much much easier level
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