The Primordial Gound – The Public Domain Review
The piece that follows displays a number of the signature characteristics of the classic nineteenth-century genre known as mystification. We have an author who takes us winningly into his confidence as he discusses an intricate tale of old texts lost and recovered, all the while tipping his hand concerning the ambiguous status of the source material at issue. Kant in Sumatra? The Third Critique and the cosmologies of Melanesia? What is going on? Read on, and make of all of this what you will (or can!). But a quick thought: much philosophy (Justin E. H. Smith’s stock-in-trade), like most argumentative writing in history and every other branch of learned endeavor, seeks to compel assent — to leave the reader as little room as possible for thought-escape. To think well in such a textual ecology demands the cultivation of a capacity to find what we might think of as “worm holes” in the world of learned scholarship: loci that drop open into the infinite space of other possibilities. Sometimes such trapdoors can be opened in a footnote or paratext, or, as here, in a tiny textual emendation, through which we are encouraged to glimpse a thoroughly different fundamental ground for all experience. I am not a Geisterseher, Professor Skrastiņš assures Professor Smith — not a ghost-seer. But is that what we need to be if we are to see clearly through the heavy curtains of erudition?
history  explorations  amusing  to-do  to-write-about  to-follow  paratext 
viXra.org open e-Print archive
An alternative archive of 26146 e-prints in Science and Mathematics serving the whole scientific community
preprints  archive  discovered-in-passing 
An Upper Bound for Lebesgue’s Universal Covering Problem, viXra.org e-Print archive, viXra:1801.0292
The universal covering problem as posed by Henri Lebesgue in 1914 seeks to find the convex planar shape of smallest area that contains a subset congruent to any point set of unit diameter in the Euclidean plane. Methods used previously to construct such a cover can be refined and extended to provide an improved upper bound for the optimal area. An upper bound of 0.8440935944 is found.
plane-geometry  proof  rather-interesting  to-write-about  consider:representation 
Kelsey Brookes at the Jacob Lewis Gallery | fibonaccisusan
Kelsey Brookes current solo exhibition at the Jacob Lewis gallery is titled ” The Mathematics Underlying Art”. I was so happy to see that the Fibonacci Sequence is a major theme for these large scale paintings. Each square canvas is divided into thirteen (13 is a Fibonacci Number) wedges radiating from the center point. Then dots are made along each dividing line at intervals that correspond to the Fibonacci Sequence.
generative-art  rather-interesting  to-follow 
Evolution of metazoan morphological disparity | PNAS
We attempt to quantify animal “bodyplans” and their variation within Metazoa. Our results challenge the view that maximum variation was achieved early in animal evolutionary history by nonuniformitarian mechanisms. Rather, they are compatible with the view that the capacity for fundamental innovation is not limited to the early evolutionary history of clades. We perform quantitative tests of the principal hypotheses of the molecular mechanisms underpinning the establishment of animal bodyplans and corroborate the hypothesis that animal evolution has been permitted or driven by gene regulatory evolution.
developmental-biology  biology  rather-interesting  clustering  looking-to-see  to-write-about  consider:feature-discovery 
2 days ago
net.wars: We know where you should live
John Hancock doesn't mention it, but there are some obvious caveats about these figures. First of all, the program began in 2015. How does the company have data showing its users live so much longer? Doesn't that suggest that these users were living longer *before* they adopted the program? Which leads to the second point: the segment of the population that has wearable fitness trackers and smartphones tends to be more affluent (which tends to favor better health already) and more focused on their health to begin with (ditto). I can see why an insurance company would like me to "engage with" its program twice a day, but I can't see why I would want to. Insurance companies are not my *friends*.
corporatism  privacy  science-fiction  dystopia-is-you-know-just-normal  actuarial-statistics 
2 days ago
Evil Online and the Moral Fog | Practical Ethics
I see Evil Online as in the same tradition as Hannah Arendt’s crucially important book The Banality of Evil, which attempted to explain and characterize the behaviour of apparently ‘ordinary’ people – rather than probable psychopaths like Himmler – in the Holocaust. As Cocking and van den Hoven note, whether their idea of a moral fog is a development of the banality thesis or something entirely new doesn’t matter much, since even if it is a development they are taking it further and using the idea of a moral fog to elucidate the way that the online environment we are in can make us insensitive to moral facts we’re otherwise perfectly capable of recognizing. Certainly the particular mechanisms of totalitarianism identified by Arendt aren’t straightforwardly going to explain evil online, but the general issues at stake do have similarities. How is it that Eichmann and the non-psychopathic perpetrators of evil online come to ignore their duty, or arrive at such a distorted view of what duty requires?

The book is also in some ways analogous to Thomas Hobbes’s Leviathan, first published in 1651, in which Hobbes tries to explain how the natural state of human beings is amoral – a war of all against all – and how morality can be seen as a human creation enabling us to escape that state and build a civilization. The online world is something like a state of nature, but the difference between the Hobbesian situation and our own is that we already have a morality. The puzzle is how to disperse the fog, and it is a puzzle we need urgently to think about before it is too late and the fog begins to thicken and drift even further than it is already doing from the online into the real world.
cultural-dynamics  ethics  internet  politics  to-read 
2 days ago
[1802.06764] Stability of items: an experimental test
The words of a language are randomly replaced in time by new ones, but long since it was observed that words corresponding to some items (meanings) are less frequently replaced then others. Usually, the rate of replacement for a given item is not directly observable, but it is inferred by the estimated stability which, on the contrary, is observable. This idea goes back a long way in the lexicostatistical literature, nevertheless nothing ensures that it gives the correct answer. The family of Romance languages allows for a direct test of the estimated stabilities against the replacement rates since the protolanguage (Latin) is known and the replacement rates can be explicitly computed. The output of the test is threefold: first, we prove that the standard approach which tries to infer the replacement rates trough the estimated stabilities is sound; second, we are able to rewrite the fundamental formula of Glottochronology for a non universal replacement rate (a rate which depends on the item), third, we give indisputable evidence that the stability ranking is far to be the same for different families of languages. This last result is also supported by comparison with the Malagasy family of dialects. As a side result we also provide some evidence that Vulgar Latin and not Late Classical Latin is at the root of modern Romance languages.
linguistics  chronology  rather-interesting  simulation  statistics  heterogeneity  it's-more-complicated-than-you-think  to-write-about  cladistics 
2 days ago
9 Collections
The collection classes form a loosely-defined group of general-purpose subclasses of Collection and Stream. The group of classes that appears in the “Blue Book” 1 contains 17 subclasses of Collection and 9 subclasses of Stream, for a total of 28 classes, and had already been redesigned several times before the Smalltalk-80 system was released. This group of classes is often considered to be a paradigmatic example of object-oriented design.
languages  Smalltalk  classes  computer-science  nudge  consider:robustness  to-write-about 
3 days ago
On civil war – An und für sich
The last time our country was on the brink of civil war, the slavers had a stranglehold on institutional power and the terms of debate and yet continually viewed themselves as oppressed victims — and as soon as an opposition president took office, they decided to blow up the country rather than accept his victory. Like contemporary Democrats, Lincoln was conciliatory to a fault, but the slavers would not take yes for an answer. Lincoln was, of course, actually able to become president in the first place despite the slavers’ opposition. If a Democrat won the 2020 election, would they even be able to take office? Would Republicans control enough state-level governments to steal the Electoral College outright? And then what?
politics  Civil-War 
3 days ago
[1512.04722] Visible lattice points in random walks
We consider the possible visits to visible points of a random walker moving up and right in the integer lattice (with probability α and 1−α, respectively) and starting from the origin.
We show that, almost surely, the asymptotic proportion of strings of k consecutive visible lattice points visited by such an α-random walk is a certain constant ck(α), which is actually an (explicitly calculable) polynomial in α of degree 2⌊(k−1)/2⌋. For k=1, this gives that, almost surely, the asymptotic proportion of time the random walker is visible from the origin is c1(α)=6/π2, independently of α.
random-walks  rather-interesting  combinatorics  probability-theory  simulation  nudge-targets  number-theory  representation  to-simulate  consider:feature-discovery 
3 days ago
[1711.05793] On the proximity of large primes
By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeration basis q, we show that there are infinitely many pairs of primes the base q expansion of which differ in at most two digits. Likewise, for any fixed integer t, there are infinitely many pairs of primes, the first t digits of which are the same. In another direction, we show that, there is a constant c depending on q such that for infinitely many integers m there are at least cloglogm primes which differ from m by at most one base q digit.
number-theory  Hamming-distance  proof  consider:looking-to-see  consider:generative-algorithm  nudge-targets 
3 days ago
[1710.08403] Constrained ternary integers
An integer n is said to be ternary if it is composed of three distinct odd primes. In this paper, we asymptotically count the number of ternary integers n≤x with the constituent primes satisfying various constraints. We apply our results to the study of the simplest class of (inverse) cyclotomic polynomials that can have coefficients that are greater than 1 in absolute value, namely to the nth (inverse) cyclotomic polynomials with ternary n. We show, for example, that the corrected Sister Beiter conjecture is true for a fraction ≥0.925 of ternary integers.
number-theory  cryptography  prime-numbers  elliptic-curves  nudge-targets  to-understand 
3 days ago
[1708.03563] On the discriminator of Lucas sequences
"Thus the situation is more weird than Shallit expected and this is confirmed by Theorem 1."

We consider the family of Lucas sequences uniquely determined by Un+2(k)=(4k+2)Un+1(k)−Un(k), with initial values U0(k)=0 and U1(k)=1 and k≥1 an arbitrary integer. For any integer n≥1 the discriminator function k(n) of Un(k) is defined as the smallest integer m such that U0(k),U1(k),…,Un−1(k) are pairwise incongruent modulo m. Numerical work of Shallit on k(n) suggests that it has a relatively simple characterization. In this paper we will prove that this is indeed the case by showing that for every k≥1 there is a constant nk such that k(n) has a simple characterization for every n≥nk. The case k=1 turns out to be fundamentally different from the case k>1.
number-theory  sequences  conjecture  rather-interesting  nudge-targets  pattern-discovery  to-write-about  consider:looking-to-see 
3 days ago
Slippery Characters | Laura Browder | University of North Carolina Press
In the 1920s, black janitor Sylvester Long reinvented himself as Chief Buffalo Child Long Lance, and Elizabeth Stern, the native-born daughter of a German Lutheran and a Welsh Baptist, authored the immigrant's narrative I Am a Woman--and a Jew; in the 1990s, Asa Carter, George Wallace's former speechwriter, produced the fake Cherokee autobiography, The Education of Little Tree. While striking, these examples of what Laura Browder calls ethnic impersonator autobiographies are by no means singular. Over the past 150 years, a number of American authors have left behind unwanted identities by writing themselves into new ethnicities.
Significantly, notes Browder, these ersatz autobiographies have tended to appear at flashpoints in American history: in the decades before the Civil War, when immigration laws and laws regarding Native Americans were changing in the 1920s, and during the civil rights era, for example. Examining the creation and reception of such works from the 1830s through the 1990s--against a background ranging from the abolition movement and Wild West shows to more recent controversies surrounding blackface performance and jazz music--Browder uncovers their surprising influence in shaping American notions of identity.
forgery  autobiographical  history  rather-interesting  literary-criticism  speaking-as  to-write-about 
4 days ago
CABINET // Deception as a Way of Knowing: A Conversation with Anthony Grafton
Anxiety about deception runs deep in the philosophical and religious traditions of Europe, and new techniques for mastering this fear mark episodes in the history of the modern world. Over the course of the nineteenth century, both the playfulness and the peril of deceit came to be distanced from the sphere of rational inquiry: the sciences ceased to have much use for legerdemain; metaphysicians lost interest in the theater. But it was not always so, as the conversation below with Anthony Grafton suggests. Grafton is the Henry Putnam University Professor of History at Princeton University and the author of a shelf of major works on the­ Renaissance, classical scholarship, ­and the history of science, including Forgers and Critics: Creativity and Duplicity in Western Scholarship (Princeton University Press, 1990).­ ­D. Graham Burnett, editor at Cabinet and also professor of history at Princeton, sat down with Grafton to discuss his work on deception and forgery­.
humanities  history  deception  forgery  rather-interesting  to-think-on  the-mangle-in-practice  mastery  mystery  reconfiguration 
4 days ago
Progressive Labels for Regressive Practices - Alfie Kohn
You see the pattern here. We need to ask what kids are being given to do, and to what end, and within what broader model of learning, and as decided by whom. If we allow ourselves to be distracted from those questions, then even labels with a proud progressive history can be co-opted to the point that they no longer provide reassurance about the practice to which the label refers.
pedagogy  corporatism  normalization  coopting  progressivism  rather-interesting 
4 days ago
[math/0408099] Tropical Mathematics
These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the ``tropical approach'' in mathematics, which has gotten a lot of attention recently in combinatorics, algebraic geometry and related fields. It offers an an elementary introduction to this subject, touching upon Arithmetic, Polynomials, Curves, Phylogenetics and Linear Spaces. Each section ends with a suggestion for further research. The bibliography contains numerousreferences for further reading in this field.
group-theory  mathematics  representation  combinatorics  rather-interesting  to-write-about 
6 days ago
TimeMachineEditor is a software for macOS that lets you change the default one-hour backup interval of Time Machine. You can change the interval or create a more sophisticated scheduling (see screenshots below).

This is useful if you don’t need to backup every hour and don’t want the performance penalty. This is also especially useful if you manipulate lots of data within one hour as you would spend the whole day backing up.
MacOS  utility  backup  to-do  dammit 
7 days ago
Quickly recognizing primes less than 100 | The Math Less Traveled
Recently, Mark Dominus wrote about trying to memorize all the prime numbers under . This is a cool idea, but it made me start thinking about alternative: instead of memorizing primes, could we memorize a procedure for determining whether a number under is prime or composite? And can we make it clever enough to be done relatively quickly? This does tie into my other recent posts about primality testing, but to be clear, it’s also quite different: I am not talking about a general method for determining primality, but the fastest method we can devise for mentally determining, by hook or by crook, whether a given number under is prime. Hopefully there are rules we can come up with which are valid for numbers less than —and thus make them easier to test—even though they aren’t valid for bigger numbers in general.
mathematical-recreations  number-theory  heuristics  nudge-targets  consider:looking-to-see  to-write-about 
7 days ago
The Policeman’s Beard is Algorithmically Constructed - 3:AM Magazine
The Policeman’s Beard is an aggressively egotistical book. Measuring 22.6 x 20.3 x 1.5 centimetres, it dwarfs many of its neighbours on the shelf. Its paper cover is bright red, with a doctored photograph of a man who occupies a sturdy frame as he glares at prospective readers. The book begs to be handled, while at the same time warning readers to approach with caution.

And caution is indeed warranted, for The Policeman’s Beard and Racter are puzzling. In some ways, Racter does adhere to the modern conception of authorship. As with any human writer, Racter’s code interacts with a world—albeit a limited world that has been consciously created by its programmers—as a source of information, and remixes content to create unique texts. Yet Racter is rigid, using fixed functions to complete a particular task. The program cannot interpret that which it produces and, indeed, not until a human interprets Racter’s output can it be assigned any cultural value.
generative-art  nanohistory  natural-language-processing  I-remember-it-well  the-mangle-in-practice  to-write-about  literary-criticism  computational-criticism  performative-writing 
8 days ago
[1804.03032] k-NN Graph Construction: a Generic Online Approach
Nearest neighbor search and k-nearest neighbor graph construction are two fundamental issues arise from many disciplines such as information retrieval, data-mining, machine learning and computer vision. Despite continuous efforts have been taken in the last several decades, these two issues remain challenging. They become more and more imminent given the big data emerges in various fields and has been expanded significantly over the years. In this paper, a simple but effective solution both for k-nearest neighbor search and k-nearest neighbor graph construction is presented. Namely, these two issues are addressed jointly. On one hand, the k-nearest neighbor graph construction is treated as a nearest neighbor search task. Each data sample along with its k-nearest neighbors are joined into the k-nearest neighbor graph by sequentially performing the nearest neighbor search on the graph under construction. On the other hand, the built k-nearest neighbor graph is used to support k-nearest neighbor search. Since the graph is built online, dynamic updating of the graph, which is not desirable from most of the existing solutions, is supported. Moreover, this solution is feasible for various distance measures. Its effectiveness both as a k-nearest neighbor construction and k-nearest neighbor search approach is verified across various datasets in different scales, various dimensions and under different metrics.
graph-theory  algorithms  to-understand  rather-interesting  computational-complexity  data-structures 
8 days ago
[1804.10962] Stress anisotropy in shear-jammed packings of frictionless disks
We perform computational studies of repulsive, frictionless disks to investigate the development of stress anisotropy in mechanically stable (MS) packings. We focus on two protocols for generating MS packings: 1) isotropic compression and 2) applied simple or pure shear strain γ at fixed packing fraction ϕ. MS packings of frictionless disks occur as geometric families (i.e. parabolic segments with positive curvature) in the ϕ-γ plane. MS packings from protocol 1 populate parabolic segments with both signs of the slope, dϕ/dγ>0 and dϕ/dγ<0. In contrast, MS packings from protocol 2 populate segments with dϕ/dγ<0 only. For both simple and pure shear, we derive a relationship between the stress anisotropy and dilatancy dϕ/dγ obeyed by MS packings along geometrical families. We show that for MS packings prepared using isotropic compression, the stress anisotropy distribution is Gaussian centered at zero with a standard deviation that decreases with increasing system size. For shear jammed MS packings, the stress anisotropy distribution is a convolution of Weibull distributions that depend on strain, which has a nonzero average and standard deviation in the large-system limit. We also develop a framework to calculate the stress anisotropy distribution for packings generated via protocol 2 in terms of the stress anisotropy distribution for packings generated via protocol 1. These results emphasize that for repulsive frictionless disks, different packing-generation protocols give rise to different MS packing probabilities, which lead to differences in macroscopic properties of MS packings.
physics!  sandpiles  materials-science  simulation  rather-interesting  condensed-matter  phase-transitions  looking-to-see 
8 days ago
Tales from Underwater | Status 451
“If you’re wondering whether it feels a little weird to have had someone you don’t clearly remember being make potentially life-altering decisions about you, the answer is yes.”
essay  depression  cognition  the-mangle-is-coming-from-inside-the-house  philosophy  introspection  resonant  identifiable-in-the-extreme 
8 days ago
[1803.10908] Matrix Product Operators for Sequence to Sequence Learning
The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an exponentially large space. It also allows to describe accurately correlations between distant parts of a system, an important ingredient to account for the context in machine learning tasks. Here we introduce a machine learning model in which matrix product operators are trained to implement sequence to sequence prediction, i.e. given a sequence at a time step, it allows one to predict the next sequence. We then apply our algorithm to cellular automata (for which we show exact analytical solutions in terms of matrix product operators), and to nonlinear coupled maps. We show advantages of the proposed algorithm when compared to conditional random fields and bidirectional long short-term memory neural network. To highlight the flexibility of the algorithm, we also show that it can readily perform classification tasks.
representation  machine-learning  to-understand  matrices  quantum-computing  classification  algorithms 
8 days ago
Coder-Physicists Are Simulating the Universe to Unlock Its Secrets | Quanta Magazine
These small, faint galaxies have always presented problems. The “missing satellite problem,” for instance, is the expectation, based on standard cold dark matter models, that hundreds of satellite galaxies should orbit every spiral galaxy. But the Milky Way has just dozens. This has caused some physicists to contemplate more complicated models of dark matter. However, when Hopkins and colleagues incorporated realistic superbubbles into their simulations, they saw many of those excess satellite galaxies go away. Hopkins has also found potential resolutions to two other problems, called “cusp-core” and “too-big-to-fail,” that have troubled the cold dark matter paradigm.
simulation  looking-to-see  astronomy  rather-interesting  to-write-about  the-mangle-in-practice  (totally) 
9 days ago
In Defense of Hoaxes - Justin Erik Halldór Smith
Whatever. Everyone's playing their assigned roles. But what I wanted to speak to here is the question of hoaxes in general. Quite apart from whether I think “Sokal Squared” has accomplished what its authors claim, I confess I am astounded, though I really should not be by now, by the moralism and the piety about rules and procedures that so many academics are expressing, as if hoaxing were always unethical and lacking in any potential salutary effects. These academics seem entirely unaware of the distinguished history of hoaxing, and to assume that it dates back no earlier than Sokal. They seem never to have read, e.g., Anthony Grafton on the importance of playful deception in the learned culture of Italian humanism. They seem unaware of the rich and fascinating 19th-century genre of the “mystification.” They seem unaware of the often high-minded theoretical ambitions of documentary metafiction and of the vague gradations between this broad genre of writing and outright fraud. They do not know about the French fraudster Denis Vrain-Lucas, who was eventually arrested, in 1869, for having passed off numerous falsified letters as authentic documents. Vrain-Lucas continued to defend himself, from prison, on the grounds that he had breathed new life into the carcass of history by making past characters, including Newton, Galileo, Vercingétorix, and Jesus Christ, more interesting than they actually were. They do not know about Ken Alder's ingenious piece in Critical Inquiry in 2004, which was a purported translation from the French of a prison letter by Vrain-Lucas. I learned more about the history and historiography of science from Alder's piece than from any other single text I could cite. 
hoaxes  academic-culture  politics  history-is-a-feature-not-a-bug  to-write-about  metafiction  paratexts 
14 days ago
Myth & Moor: I Shall Go Into a Hare....
The creativity produced by this team could, I swear, power the lights of the city. Our days in Sheffield fairly crackle with energy, with ideas emerging, shape-shifting, coalescing into song, art, and story. I find that I keep turning to my companions to say: I don't want the week to end.

But it does end, of course. On the final eve, we share some of our work-in-progress with a small audience in a Spiegeltent at The Festival of the Mind...and this is a bit nerve-wracking too. We're all used to presenting work in completed form: a book, CD, a canvas or show, honed and polished. A work-in-progress is a rough, raw thing. What on earth would an audience make of it all?

The fairies are clearly with us that night, and every one of them is in Trickster mode: microphones don't work, other tech goes wrong...but none of that matters in the end. When Ewan sings of fairy shadows, and Lucy of the shifting properties of time, and Marry of the Green Children legend, and Fay of turning from woman to hare, the old stories come to life again. Perhaps they had never really died.
making  workshop  the-experience-of-craft  the-mangle-in-practice  plus-one 
14 days ago
The Kolakoski Sequence - Futility Closet
This is a fractal, a mathematical object that encodes its own representation. It was described by William Kolakoski in 1965, and before him by Rufus Oldenburger in 1939. University of Evansville mathematician Clark Kimberling is offering a reward of $200 for the solution to five problems associated with the sequence:

Is there a formula for the nth term?
If a string occurs in the sequence, must it occur again?
If a string occurs, must its reversal also occur?
If a string occurs, and all its 1s and 2s are swapped, must the new string occur?
Does the limiting frequency of 1s exist, and is it 1/2?

So far, no one has found the answers.
mathematical-recreations  self-reference  fractals  open-questions  nudge-targets  consider:looking-to-see 
14 days ago
Tiling with TriCurves
There are a number of ways one can define a tricurve, the one used here is to start with an arc of some angle, replicate two identical curves ard rotate each about some angle about the ends of the arc. The Tricurve is the enclosed area.
plane-geometry  tiling  rather-interesting  define-your-terms  representation  to-write-about  mathematical-recreations 
14 days ago
Tiling with One Arc-Sided Shape | Math ∞ Blog
A flat puzzle (tiling) with dozens or hundreds of identical pieces may sound a little dull and predictable. But what is the most interesting shape we can use, to get the most unusual designs and the most variety? To make it more visually interesting, let’s say we want a shape with no straight edges—only curves. The following guidelines should help us get started.
plane-geometry  representation  tiling  rather-interesting  mathematical-recreations  to-write-about 
14 days ago
The propagation of error in classical geometry constructions | Joel David Hamkins
I’d like to discuss the issue of error and error propagation in the constructions of classical geometry. How does error propagate in these constructions? How sensitive are the familiar classical constructions to small errors in the use of the straightedge or compass?
plane-geometry  con  structions  robustness  rather-interesting  to-write-about  nudge-targets  consider:multiobjective-selection 
15 days ago
[1801.08003] Threadable Curves
We define a plane curve to be threadable if it can rigidly pass through a point-hole in a line L without otherwise touching L. Threadable curves are in a sense generalizations of monotone curves. We have two main results. The first is a linear-time algorithm for deciding whether a polygonal curve is threadable---O(n) for a curve of n vertices---and if threadable, finding a sequence of rigid motions to thread it through a hole. We also sketch an argument that shows that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve. The second main result is an O(n polylog n)-time algorithm for deciding whether a 3D polygonal curve can thread through hole in a plane in R^3, and if so, providing a description of the rigid motions that achieve the threading.
computational-geometry  geometry  rather-interesting  definition  nudge-targets  consider:feature-discovery  to-write-about  consider:algorithms 
15 days ago
Efficiency of repeated squaring | The Math Less Traveled
Claim: the binary algorithm is the most efficient way to build using only doubling and incrementing steps. That is, any other way to build by doubling and incrementing uses an equal or greater number of steps than the binary algorithm.
algorithms  mathematical-recreations  nudge-targets  consider:looking-to-see  to-write-about 
15 days ago
Kiwi Hellenist: The citation problem
Let me re-state the problem. It didn’t occur to anyone, at any stage, that a research paper ought to look at research on the thing that the article is about. Why not?
science-and-humanities-sittin-in-a-tree  annexation-by-physics  digital-humanities  network-theory  le-sigh  academic-culture 
15 days ago
[1808.02841] On divergent Series
This is the translation of Leonhard Euler's paper "De Seriebus divergentibus" written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example 1!−2!+3!−etc. and uses different methods to sum it. He finds a value of about 0.59....
mathematics  history  translation  series  to-write-about  rather-interesting 
15 days ago
[1808.07006] Observations on continued fractions
This is a translation of Euler's Latin paper "De fractionibus continuis observationes" into English. In this paper Euler describes his theory of continued fractions. He teaches, how to transform series into continued fractions, solves the Riccati-Differential equation by means of continued fractions and finds many other interesting formulas and results (e.g, the continued fraction for the quotient of two hypergeometric series usually attributed to Gau{\ss})
continued-fractions  translation  mathematics  history  rather-interesting  to-write-about 
15 days ago
[1810.00173] On solids whose (entire) surface can be unfolded onto a plane
This is the English translation of Leonhard Euler's Latin paper "De solidis quorum superficiem in planum explicare licet". Euler explains several methods to obtain equations for developable surfaces. Therefore, this paper might be interesting for anyone studying the history of Differential Geometry.
geometry  history  mathematics  translation  rather-interesting 
15 days ago
cooperation for the network era
Organizations need to extend the notion of work beyond collaboration, beyond teams, and beyond the corporate fire wall. They need to make social networks, communities of practice, and narrative part of the work. It’s a big leap but we need to change the business conversation away from confident military terms (target market, strategic plan, marketing campaign) and instead talk in terms of complexity, wicked problems, and cooperation.

We are moving from a market economy to a network economy and the level of complexity is increasing with this hyper-connectedness. Managing in complex adaptive systems means influencing possibilities rather than striving for predictability (good or best practices). Cooperation in our work is needed so that we can continuously develop emergent practices demanded by this complexity. What worked yesterday won’t work today. No one has the definitive answer any more, but we can use the intelligence of our networks to make sense together and see how we can influence desired results. This is cooperation and this is the future, which is already here, albeit unevenly distributed.
organizational-behavior  collective-behavior  collaboration  cooperation  thinking-about-being  to-write-about 
18 days ago
Inside “3-adica” – From Earth to the Stars
Why can’t there be a square root of 2, though? Surely we can at least get close? Can’t we just copy what we saw with 7, and find a number that is (A) an integer squared, and (B) differs from 2 by a (3-adically) “small” quantity that is divisible by a large power of 3?

The problem is, if you square any integer at all, its remainder after you divide by 3 will either be zero (when the number you squared was exactly divisible by 3), or 1, in every other case. If you then subtract 2, the result can’t possibly be divisible by even a single power of 3. So any number squared will lie at a 3-adic distance of at least 1 from 2.

This peculiar way of measuring the distance between numbers turns out to be much more than a game. Everything we’ve done with the number 3 can be generalized to any other prime number, p, to create what are known as the p-adic numbers. Working with this kind of number lets you combine different aspects of mathematics in a very fruitful manner, and even the famous proof by Andrew Wiles of Fermat’s Last Theorem employed techniques that used p-adic numbers.
mathematical-recreations  number-theory  representation  to-write-about 
18 days ago
Why Love Generative Art? — Artnome
Over the last 50 years, our world has turned digital at breakneck speed. No art form has captured this transitional time period - our time period - better than generative art. Generative art takes full advantage of everything that computing has to offer, producing elegant and compelling artworks that extend the same principles and goals artists have pursued from the inception of modern art.
generative-art  criticism  have-read  to-write-about  aesthetics  philosophy-of-art  posthumanism-and-responsibility 
18 days ago
DRM-free Bookshops
A regularly updated list of online shops that sell e-books without DRM.
books  shopping  DRM  copyright  rather-interesting  publishing 
18 days ago
[1712.05630] Sparse principal component analysis via random projections
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so is not vulnerable to a bad choice of initialisation. Our theory provides great detail on the statistical and computational trade-off in our procedure, revealing a subtle interplay between the effective sample size and the number of random projections that are required to achieve the minimax optimal rate. Numerical studies provide further insight into the procedure and confirm its highly competitive finite-sample performance.
dimension-reduction  statistics  data-analysis  algorithms  performance-measure  consider:lexicase  sparseness 
18 days ago
Understanding Society: Patient safety
Medical accidents commonly demonstrate a complex interaction of factors, from the individual provider to the technologies in use to failures of regulation and oversight. We can look at a hospital as a place where caring professionals do their best to improve the health of their patients while scrupulously avoiding errors. Or we can look at it as an intricate system involving the recording and dissemination of information about patients; the administration of procedures to patients (surgery, medication, radiation therapy). In this sense a hospital is similar to a factory with multiple intersecting locations of activity. Finally, we can look at it as an organization -- a system of division of labor, cooperation, and supervision by large numbers of staff whose joint efforts lead to health and accidents alike. Obviously each of these perspectives is partially correct. Doctors, nurses, and technicians are carefully and extensively trained to diagnose and treat their patients. The technology of the hospital -- the digital patient record system, the devices that administer drugs, the surgical robots -- can be designed better or worse from a safety point of view. And the social organization of the hospital can be effective and safe, or it can be dysfunctional and unsafe. So all three aspects are relevant both to safe operations and the possibility of chronic lack of safety.
organizational-behavior  public-health  medicine  to-write-about  robustness  remembering-our-dead 
19 days ago
1918: The Forgotten Year of Death | The Order of the Good Death
Wartime restrictions on communication had deadly effects, including in the United States. President Wilson’s Committee on Public Information and the Sedition Act passed by Congress both limited writing or publishing anything negative about the country. Federally-issued posters asked the public to “report the man who spreads pessimistic stories.” John M. Barry, author of The Great Influenza: The Story of the Deadliest Pandemic in History, writes in an article for Smithsonian Magazine about a particularly tragic consequence of this militant protection of morale. In Philadelphia, doctors pushed for the Liberty Loan parade on September 28 to be canceled, as they were concerned the concentration of people would spur the disease. “They convinced reporters to write stories about the danger,” Barry writes. “But editors refused to run them, and refused to print letters from doctors. The largest parade in Philadelphia’s history proceeded on schedule.” Two days later, the epidemic had indeed spread, and over just six weeks, more than 12,000 citizens of Philadelphia died.
epidemiology  influenza  propaganda  social-dynamics  politics  public-health  history 
19 days ago
Adam Kotsko The Political Theology of Neoliberalism - state of nature
Neoliberals do rely on libertarian rhetoric, but libertarianism is basically neoliberalism for fools. When neoliberals are talking amongst themselves, they always acknowledge that a strong state is absolutely necessary to their agenda. This is because markets do not spontaneously arise in the absence of state interference, or in other words, markets are not natural. They must be artificially constructed, and so one way of defining neoliberalism is as a project to use state power to cultivate or create markets so that people will be forced to be free in the neoliberal sense.
neoliberalism  interview  quotes  hey-I-know-this-guy  to-write-about  fascism  political-economy  financial-crisis  capitalism  worldview 
21 days ago
THE EXTENDED EVOLUTIONARY SYNTHESIS | Proceedings of the Royal Society of London B: Biological Sciences
Scientific activities take place within the structured sets of ideas and assumptions that define a field and its practices. The conceptual framework of evolutionary biology emerged with the Modern Synthesis in the early twentieth century and has since expanded into a highly successful research program to explore the processes of diversification and adaptation. Nonetheless, the ability of that framework satisfactorily to accommodate the rapid advances in developmental biology, genomics and ecology has been questioned. We review some of these arguments, focusing on literatures (evo-devo, developmental plasticity, inclusive inheritance and niche construction) whose implications for evolution can be interpreted in two ways—one that preserves the internal structure of contemporary evolutionary theory and one that points towards an alternative conceptual framework. The latter, which we label the ‘extended evolutionary synthesis' (EES), retains the fundaments of evolutionary theory, but differs in its emphasis on the role of constructive processes in development and evolution, and reciprocal portrayals of causation. In the EES, developmental processes, operating through developmental bias, inclusive inheritance and niche construction, share responsibility for the direction and rate of evolution, the origin of character variation and organism–environment complementarity. We spell out the structure, core assumptions and novel predictions of the EES, and show how it can be deployed to stimulate and advance research in those fields that study or use evolutionary biology.
evolutionary-biology  academic-culture  models-and-modes  theoretical-biology  define-your-terms  rather-interesting  to-write-about 
21 days ago
[1809.10756] An Introduction to Probabilistic Programming
This document is designed to be a first-year graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build these systems. It is aimed at people who have an undergraduate-level understanding of either or, ideally, both probabilistic machine learning and programming languages.
We start with a discussion of model-based reasoning and explain why conditioning as a foundational computation is central to the fields of probabilistic machine learning and artificial intelligence. We then introduce a simple first-order probabilistic programming language (PPL) whose programs define static-computation-graph, finite-variable-cardinality models. In the context of this restricted PPL we introduce fundamental inference algorithms and describe how they can be implemented in the context of models denoted by probabilistic programs.
In the second part of this document, we introduce a higher-order probabilistic programming language, with a functionality analogous to that of established programming languages. This affords the opportunity to define models with dynamic computation graphs, at the cost of requiring inference methods that generate samples by repeatedly executing the program. Foundational inference algorithms for this kind of probabilistic programming language are explained in the context of an interface between program executions and an inference controller.
This document closes with a chapter on advanced topics which we believe to be, at the time of writing, interesting directions for probabilistic programming research; directions that point towards a tight integration with deep neural network research and the development of systems for next-generation artificial intelligence applications.
via:jar  programming-language  representation  probability-theory  models-and-modes  semantics  syntax  pragmatics  to-write-about 
21 days ago
[1602.06208] Every positive integer is a sum of three palindromes
For integer g≥5, we prove that any positive integer can be written as a sum of three palindromes in base g.
number-theory  proof  nudge-targets  consider:algorithms  consider:looking-to-see 
22 days ago
Same-different problems strain convolutional neural networks | the morning paper
Digging deeper, when learning did occur in SD, increasing item size never strained performance. But increasing the overall image size, or increasing the number of items did. (Gray bars in the above figures indicate the number of trials in which learning failed). The results suggest that straining is not simply a direct outcome of an increase in image variability. Using CNNs with more than twice the number of kernels (wide), or twice as many layers (deep) did not change the observed trend.
neural-networks  representation  problem-solving  rather-interesting  ontology  generalization  to-write-about  nudge-targets  consider:feature-discovery 
23 days ago
Treating The Prodrome | Slate Star Codex
I think what they are saying is that, as the world becomes even more random and confusing, the brain very slowly adjusts its highest level parameters. It concludes, on a level much deeper than consciousness, that the world does not make sense, that it’s not really useful to act because it’s impossible to predict the consequences of actions, and that it’s not worth drawing on prior knowledge because anything could happen at any time. It gets a sort of learned helplessness about cognition, where since it never works it’s not even worth trying. The onslaught of random evidence slowly twists the highest-level beliefs into whatever form best explains random evidence (usually: that there’s a conspiracy to do random things), and twists the fundamental parameters into a form where they expect evidence to be mostly random and aren’t going to really care about it one way or the other.
psychology  rather-interesting  consider:what-are-we-doing-to-our-machines?  emergence  to-write-about 
23 days ago
[Essay] The Printed World in Peril | Harper's Magazine
At the end of Bradbury’s Fahrenheit 451, the exiled hoboes return to the cities, which have been destroyed by the nuclear conflicts of the illiterate, bringing with them their head-borne texts, ready to restart civilization. And it’s this that seems to me the most prescient part of Bradbury’s menacing vision. For I see no future for the words printed on paper, or the art forms they enacted, if our civilization continues on this digital trajectory: there’s no way back to the future—especially not through the portal of a printed text.
via:mymarkup  publishing  literary-criticism  media  book-culture  cultural-dynamics  nostalgia  the-many-discomforts-of-change 
28 days ago
[1806.03346] Some Continued Fractions for $pi$ AND $G$
We present here two classes of infinite series and the associated continued fractions involving π and Catalan's constant G based on the work of Euler and Ramanujan. A few sundry continued fractions are also given.
continued-fractions  representation  nudge-targets  to-write-about 
4 weeks ago
[1712.08175] Conversion of Love waves in a forest of trees
We inspect the propagation of shear polarized surface waves akin to Love waves through a forest of trees of same height atop a guiding layer on a soil substrate. We discover that the foliage of trees { brings a radical change in} the nature of the dispersion relation of these surface waves, which behave like spoof plasmons in the limit of a vanishing guiding layer, and like Love waves in the limit of trees with a vanishing height. When we consider a forest with trees of increasing or decreasing height, this hybrid "Spoof Love" wave is either reflected backwards or converted into a downward propagating bulk wave. An asymptotic analysis shows the forest behaves like an anisotropic wedge with effective boundary conditions.
materials-science  simulation  nonlinear-dynamics  rather-interesting  side-effects  consider:pragmatics-of-a-tree  to-write-about 
4 weeks ago
A non-spatial account of place and grid cells based on clustering models of concept learning | bioRxiv
One view is that conceptual knowledge is organized as a "cognitive map" in the brain, using the circuitry in the medial temporal lobe (MTL) that supports spatial navigation. In contrast, we find that a domain-general learning algorithm explains key findings in both spatial and conceptual domains. When the clustering model is applied to spatial navigation tasks, so called place and grid cells emerge because of the relatively uniform sampling of possible inputs in these tasks. The same mechanism applied to conceptual tasks, where the overall space can be higher-dimensional and sampling sparser, leads to representations more aligned with human conceptual knowledge. Although the types of memory supported by the MTL are superficially dissimilar, the information processing steps appear shared.
models-and-modes  emergence  data-analysis  rather-interesting  to-write-about  consider:the-mangle 
4 weeks ago
Morphosis: What is Doctor Who?
All this is a roundabout way of saying: I have some specific hopes for the new female Who. It certainly seems to me that many of the reactionaries who greeted the news of her casting with howls of outrage were only partly motivated by misogyny (though of course they were motivated by that); they were trying, with the hysterical volume of their complaining, to rally to the defence of class itself as a defining feature of British self-identity. It will be interesting to see how Whittaker and her scriptwriters take the character, and to what extent the role can be reconfigured to escape this particular straitjacket.
aesthetics  cultural-norms  fiction  literary-criticism  science-fiction 
4 weeks ago
[1606.03620] Modelling Early Transitions Toward Autonomous Protocells
This thesis broadly concerns the origins of life problem, pursuing a joint approach that combines general philosophical/conceptual reflection on the problem along with more detailed and formal scientific modelling work oriented in the conceptual perspective developed. The central subject matter addressed is the emergence and maintenance of compartmentalised chemistries as precursors of more complex systems with a proper cellular organization. Whereas an evolutionary conception of life dominates prebiotic chemistry research and overflows into the protocells field, this thesis defends that the 'autonomous systems perspective' of living phenomena is a suitable - arguably the most suitable - conceptual framework to serve as a backdrop for protocell research. The autonomy approach allows a careful and thorough reformulation of the origins of cellular life problem as the problem of how integrated autopoietic chemical organisation, present in all full-fledged cells, originated and developed from more simple far-from-equilibrium chemical aggregate systems.
origin-of-life  autopoiesis  self-organization  theoretical-biology  thesis  to-read 
4 weeks ago
Drip - Mike Rugnetta
In part one of this essay, we discussed goods labeled “tactical” and the apparent reference intended by those objects. Our conclusion was, roughly, that tactical objects allow wearers / users to perform an association (a perhaps defensible one) with the armed services and various first responder personnel: police forces, and so on. 

We also uncovered a fundamental tension present in many tactical goods: try as they might to denote a particular lifestyle or occupation, these objects largely connote them. In surveying the array of tactics-based products, one may behold multitudinous visual metaphors for lifestyles focused on service and preparedness but may notice the lack of a material association with those lifestyles, or the people who practice them. In short, we came to understand aspects of tactics-things as pure fashion. 

But the ‘authenticity’ of the objects is not under question here. Rather (or really: in result), we ask how a person may ~become~ “tactical” or “a tactician” through the purchase and use of these items. In this second and final installment of a Half Baked study concerning A Material Semiotics of Tacticality we’ll discuss what tactics are and how the tactical-as-such can be seen in tactical goods. We’ll discuss the ethics of the tactical system of objects, and that system’s seepage into various locales. 
delightful  humor  cultural-norms  aesthetics 
4 weeks ago
#1 Free Web & Mobile Analytics Software
Who uses Matomo?
Individuals, big and small companies all over the world have already liberated their analytics with Matomo.
web-design  tracking  open-source  analytics  to-read 
4 weeks ago
How Channa Horwitz Permeated LA's 1960s Art Scene | AnOther
Who? When an LA Times review of her work referred to contemporary artist Channa Horwitz as a housewife, it epitomised everything art historian Linda Nochlin wrestled with in her pioneering essay in 1971, Why Have There Been No Great Women Artists? Despite studying with James Turrell and Allan Kaprow at CalArts in the 1970s, and exchanging letters with Sol LeWitt, Horwitz remained very much an outlier of the California art world until the last few years of her life.

The Los Angeles native created hand-drawn algorithms combining basic principles and strict geometry to generate measured patterns, many of which resemble Aztec prints from a distance. Like her successful male colleagues, she was interested in bringing together colour, movement, sound and light, and introduced unbendable logic into the realm of west coast minimalism with her synaesthetic compositions. 

Her breakthrough moment in fact grew out of a rejected proposal for an ambitious kinetic sculpture, as part of LACMA’s innovative Art and Technology exhibition in 1968, which infamously featured no female artists. Diagrams she drew detailing the sculpture’s movement went on to inform her work for the next four decades.
abstract-art  artist  exhibition  to-learn-about 
4 weeks ago
MathsJam is a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like. Puzzles, games, problems, or just anything they think is cool or interesting.

We meet on the second-to-last Tuesday of every month, from around 7pm in the evening, in locations around the world.

For more details of local events, choose your region from the menu, or visit the find a jam page.
mathematical-recreations  to-do 
4 weeks ago
No, I Will Not Debate You
There are some stupid mistakes that only very smart people make, and one of them is the notion that a sensible argument seriously presented can compete with a really good piece of theatre.
fascism  social-psychology  media  fucking-rawlsian-veil  debate 
4 weeks ago
The Pinball Problem – Daniel Reynolds – Refractory: a Journal of Entertainment Media
In the forms that play and games have taken over time, from games of “imagination” to formalized sports to more materially mediated forms of gameplay such as boardgames, pinball, and video games, there has been an historical fluctuation in cultural consideration and engagement. Bagatelle, the predecessor to pinball, enjoyed massive popularity among the French aristocracy and subsequently the general populace of that country in the late 18th century. Video games are currently ascendant as a medium for gameplay, and their cultural acceptability as an adult activity has steadily increased in recent decades. Sports were of immense philosophical importance to the ancient Greeks; they have never since enjoyed the same high-cultural esteem, though they have rarely been regarded as wholly trivial, and they enjoy a special cultural status among games in many modern societis. There have been some notable exceptions, however. In 1457, golf was banned in Scotland, ostensibly because it was interfering with the more useful pursuit of archery. In 1491, according to the eleventh edition of the Encyclopedia Britannica, the ban was extended to encompass “fute-ball, golfe, or uther sik unprofitibill sportis.” Profitability, it seems, has always come into consideration in the assessment of games; their less visible benefits tend to be ignored when legislation is involved.
social-norms  games  nanohistory  rather-interesting  the-ludic-in-law  to-write-about 
4 weeks ago
Roto-Tiler – The Inner Frame
Today we look at a puzzle invented by Alan Schoen that he calls Roto-Tiler. He explained this to me a few years ago, and when I showed him notes I made for a class, he denied that this is the puzzle he described. I insist it is, and it is quite certainly not mine.
mathematical-recreations  puzzles  tiling  representation  rather-interesting  to-write-about  nudge-targets 
5 weeks ago
[1808.05845] Popular Products and Continued Fractions
We prove bounds for the popularity of products of sets with weak additive structure, and use these bounds to prove results about continued fractions. Namely, we obtain a nearly sharp upper bound for the cardinality of Zaremba's set modulo p.
continued-fractions  number-theory  to-write-about  nudge-targets  consider:looking-to-see 
5 weeks ago
World without Antibiotics | Public Books
Rather than sealing rifts, progress seems predictably to embolden preexisting fractures across lines of geography, race, class, and gender. In the London of Surgeon X, there are more than a hundred amputations a week, pharmacies are robbed for vital medications, and the poor use second-hand prosthetics that don’t quite fit. The kind of therapy available in the world envisioned by Kenney begins to look an awful lot like battlefield medicine, in which limited time and resources require salvage operations to prevent the loss of limbs or life, but not always both.
biomedicine  futurism  dystopia-is-here-it's-just-not-evenly-distributed  antibiotics 
5 weeks ago
[1808.05587] Deep Convolutional Networks as shallow Gaussian Processes
We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, unlike "deep kernels", has very few parameters: only the hyperparameters of the original CNN. Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass through the original CNN with only one filter per layer. The kernel equivalent to a 32-layer ResNet obtains 0.84% classification error on MNIST, a new record for GPs with a comparable number of parameters.
via:cshalizi  neural-networks  approximation  rather-interesting  representation  deep-learning  algorithms  to-write-about  equivalences-of-motion-over-different-paths 
8 weeks ago
Should Climate Scientists Fly? - Scientific American Blog Network
This is why climate action is about moral courage. Yes, we must have the courage to align our personal actions with our understanding of the science, through decreasing and stopping our flying. But, more importantly, we must have to courage to speak truth to power, despite how this might change our public or professional standing. Climate action is one of the most fundamental social justice movements of our time. No more and no less, our choices now to act as brave stewards of planetary life, despite political realities and institutional denialism, will change the trajectory of the planet forever. It is worth it.
climate-change  politics  activism  neoliberalism  to-write-about  social-justice 
8 weeks ago
The Mathematical Beauty of the Game SET | The Aperiodical
It is my hope that this post has given you some insight into the deep and elegant complexities of the game of SET besides just trying to be the fastest SET-finder in a game. It is miraculous that such a simple game can have such beautiful and joyful connections to some advanced domains of mathematics, even with some open research questions. If interested, the reader is encouraged to explore some of these considerations or generalizations, either playing with finite geometry or doing some combinatorics. The SET community has also developed some other very interesting variations on SET and their connections to other geometries, such as projective geometry, known as ProSet.
mathematical-recreations  games  set-theory  representation  have-explored  nudge-targets  to-write-about 
8 weeks ago
How to use variable fonts in the real world | Clagnut
This article has been updated to reflect pending clarifications and modifications to the CSS Fonts Module Level 4.
A variable font is a single font file which behaves like multiple styles. (I wrote more about them here in an extract from my Web Typography book). There are plenty of sites out there demoing the possibilities of variable fonts and the font variation technology within, but for the new Ampersand conference website I wanted to show variable fonts being using in a real, production context. It might well be the first commercial site ever to do so.
css  web-design  webfonts  typography  to-understand  to-watch 
8 weeks ago
Exploded View Diagrams of Mathematical Surfaces - U.C. Berkeley Computer Graphics Research
We present a technique for visualizing complicated mathematical surfaces that is inspired by hand-designed topological illustrations. Our approach generates exploded views that expose the internal structure of such a surface by partitioning it into parallel slices, which are separated from each other along a single linear explosion axis. Our contributions include a set of simple, prescriptive design rules for choosing an explosion axis and placing cutting planes, as well as automatic algorithms for applying these rules. First we analyze the input shape to select the explosion axis based on the detected rotational and reflective symmetries of the input model. We then partition the shape into slices that are designed to help viewers better understand how the shape of the surface and its cross-sections vary along the explosion axis. Our algorithms work directly on triangle meshes, and do not depend on any specific parameterization of the surface. We generate exploded views for a variety of mathematical surfaces using our system.
visualization  mathematics  topology  rather-interesting  algorithms  to-do 
8 weeks ago
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