rather-interesting   2428
Why books don’t work | Andy Matuschak

Quantum Country is just one piece of the memory puzzle, which itself is part a larger tapestry. How might we design mediums in which “readers” naturally form rich associations between the ideas being presented? How might we design mediums which “readers” naturally engage creatively with the material? How might we design mediums in which “readers” naturally contend with competing interpretations? If we pile together enough of these questions we’re left with: how might we design mediums in which “reading” is the same as “understanding”? A more detailed treatment of such a research program is beyond the scope of these brief notes, but I believe that the answers to questions like these can transform the pace of human knowledge, echoing the transformation which books themselves sparked so long ago.
3 days ago by Vaguery
[1901.04701] Quasicrystalline electronic states in 30$^circ$ rotated twisted bilayer graphene
The recently realized bilayer graphene system with a twist angle of 30∘ offers a new type of quasicrystal which unites the dodecagonal quasicrystalline nature and graphene's relativistic properties. Here, we introduce a concise theoretical framework that fully respects both the dodecagonal rotational symmetry and the massless Dirac nature, to describe the electronic states of the system. We find that the electronic spectrum consists of resonant states labeled by 12-fold quantized angular momentum, together with the extended relativistic states. The resulting quasi-band structure is composed of the nearly flat bands with spiky peaks in the density of states, where the wave functions exhibit characteristic patterns which fit to the fractal inflations of the quasicrystal tiling. We also demonstrate that the 12-fold resonant states appear as spatially-localized states in a finite-size geometry, which is another hallmark of quasicrystal. The theoretical method introduced here is applicable to a broad class of "extrinsic quasicrystals" composed of a pair of two-dimensional crystals overlaid on top of the other with incommensurate configurations.
quantum  quasicrystals  materials-science  physics!  nanotechnology  rather-interesting
4 days ago by Vaguery
Idyll + Firebase
This canvas is backed by firebase. If you click on a square, you will update that square’s color for anyone who visits the site. Because firebase works so well with React these updates propagate live to all users on the site. This all takes very little code!
web-design  rather-interesting  to-understand
6 days ago by Vaguery
Idyll | A markup language for interactive and data-driven blogging.
Idyll is a markup language and toolkit for writing interactive articles. Idyll's reactive document model and standard component library decrease the amount of code needed to create high quality multimedia narratives. Idyll uses web standards to produce output that will load quickly in any web browser and is fully extensible.

Idyll enables collaboration between programmers and journalists, researchers and designers. Those familiar with JavaScript can write custom components using tools like D3 or React.
web-design  visualization  library  interactivity  rather-interesting  to-learn  to-emulate  javascript
6 days ago by Vaguery
Prostitutes in the Bible – Jonathan | sex & theology – Medium
his might be shocking, but let’s take it . . . step by step? In the Bible, prostitution is never wrong, and hookers, throughout the narratives, are clearly heroines.
via:?  history  theology  do-the-reading  rather-interesting  cultural-assumptions
6 days ago by Vaguery
[1810.10982] Fréchet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability
The discrete Fréchet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fréchet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal curves of length n in the plane, the fastest known algorithm runs in time ̃(n5) [Ben Avraham, Kaplan, Sharir '15]. This is achieved by constructing an arrangement of disks of size (n4), and then traversing its faces while updating reachability in a directed grid graph of size N:=(n2), which can be done in time ̃(N‾‾√) per update [Diks, Sankowski '07]. The contribution of this paper is two-fold.
First, although it is an open problem to solve dynamic reachability in directed grid graphs faster than ̃(N‾‾√), we improve this part of the algorithm: We observe that an offline variant of dynamic s-t-reachability in directed grid graphs suffices, and we solve this variant in amortized time ̃(N1/3) per update, resulting in an improved running time of ̃(n4.66...) for the discrete Fréchet distance under translation. Second, we provide evidence that constructing the arrangement of size (n4) is necessary in the worst case, by proving a conditional lower bound of n4−o(1) on the running time for the discrete Fréchet distance under translation, assuming the Strong Exponential Time Hypothesis.
metrics  algorithms  computational-complexity  horse-races  rather-interesting  nudge-targets  consider:looking-to-see
8 days ago by Vaguery
[1801.04618] Hierarchical Memory Management for Mutable State
It is well known that modern functional programming languages are naturally amenable to parallel programming. Achieving efficient parallelism using functional languages, however, remains difficult. Perhaps the most important reason for this is their lack of support for efficient in-place updates, i.e., mutation, which is important for the implementation of both parallel algorithms and the run-time system services (e.g., schedulers and synchronization primitives) used to execute them.
In this paper, we propose techniques for efficient mutation in parallel functional languages. To this end, we couple the memory manager with the thread scheduler to make reading and updating data allocated by nested threads efficient. We describe the key algorithms behind our technique, implement them in the MLton Standard ML compiler, and present an empirical evaluation. Our experiments show that the approach performs well, significantly improving efficiency over existing functional language implementations.
programming-language  memory-management  parallel  concurrency  rather-interesting  to-understand
8 days ago by Vaguery
A final game with Elwyn Berlekamp — Numberphile
The legendary Elwyn Berlekamp died on April 9, 2019. In a final filming session with Numberphile, the games expert taught us how to play Amazons.
games  game-theory  rather-interesting  planning  nudge-targets
9 days ago by Vaguery
[1005.3466] Mathematical retroreflectors
Retroreflectors are optical devices that reverse the direction of incident beams of light. Here we present a collection of billiard type retroreflectors consisting of four objects; three of them are asymptotically perfect retroreflectors, and the fourth one is a retroreflector which is very close to perfect. Three objects of the collection have recently been discovered and published or submitted for publication. The fourth object - notched angle - is a new one; a proof of its retroreflectivity is given.
dynamical-systems  engineering-design  rather-interesting  performance-measure  approximation  to-write-about  to-simulate  consider:looking-to-see  nudge-targets
14 days ago by Vaguery
[1702.04199] The problem of camouflaging via mirror reflections
This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search for bodies that are, in a sense, close to invisible. We introduce a {\it visibility index} of a body measuring the mean angle of deviation of incident light rays, and derive a lower estimate to this index. This estimate is a function of the body's volume and of the minimal radius of a ball containing the body. This result is far from being final and opens a possibility for further research.
billiards  optics  optimization  geometry  inverse-problems  rather-interesting  approximation  to-write-about  nudge-targets  consider:looking-to-see
14 days ago by Vaguery
[1304.4005] Bodies with mirror surface invisible from two points
Here we are concerned with a special issue of billiard invisibility, where a bounded set with a piecewise smooth boundary in Euclidean space is identified with a body with mirror surface, and the billiard in the complement of the set is identified with the dynamics of light rays outside the body in the framework of geometric optics. We show that in this setting it is possible to construct a body invisible from two points.
billiards  dynamical-systems  rather-interesting  inverse-problems  invisibility  nudge-targets  consider:looking-to-see
14 days ago by Vaguery
[1312.5260] The Six Circles Theorem revisited
The Six Circles Theorem of C. Evelyn, G. Money-Coutts, and J. Tyrrell concerns chains of circles inscribed into a triangle: the first circle is inscribed in the first angle, the second circle is inscribed in the second angle and tangent to the first circle, the third circle is inscribed in the third angle and tangent to the second circle, and so on, cyclically. The theorem asserts that if all the circles touch the sides of the triangle, and not their extensions, then the chain is 6-periodic. We show that, in general, the chain is eventually 6-periodic but may have an arbitrarily long pre-period.
plane-geometry  looking-to-see  construction  rather-interesting  to-write-about  open-questions  out-of-the-box  nudge-targets  consider:looking-to-see
14 days ago by Vaguery
[1810.03053] Limiting Distributions in Generalized Zeckendorf Decompositions
An equivalent definition of the Fibonacci numbers is that they are the unique sequence such that every integer can be written uniquely as a sum of non-adjacent terms. We can view this as we have bins of length 1, we can take at most one element from a bin, and if we choose an element from a bin we cannot take one from a neighboring bin. We generalize to allowing bins of varying length and restrictions as to how many elements may be used in a decomposition. We derive conditions on when the resulting sequences have uniqueness of decomposition, and (similar to the Fibonacci case) when the number of summands converges to a Gaussian; the main tool in the proofs here is the Lyaponuv Central Limit Theorem.
number-theory  fibonacci  construction  combinatorics  proof  generalization  rather-interesting  to-write-about
14 days ago by Vaguery
[1707.09267] Kasner meets Poncelet
Given a planar pentagon, construct two new pentagons: the vertices of the first one are the intersection points of the diagonals of the original pentagon, and the vertices of the second one are the tangency points of the conic inscribed in the original pentagon. E. Kasner theorem, published in 1928, asserts that these two operations on pentagons commute. We extend Kasner's result to Poncelet polygons, that is, the polygons inscribed into a conic and circumscribed about a conic.
plane-geometry  construction  rather-interesting
14 days ago by Vaguery
[1602.06455] On the bicycle transformation and the filament equation: results and conjectures
The paper concerns a simple model of bicycle kinematics: a bicycle is represented by an oriented segment of constant length in n-dimensional space that can move in such a way that the velocity of its rear end is aligned with the segment (the rear wheel is fixed on the bicycle frame). Starting with a closed trajectory of the rear end, one obtains the two respective trajectories of the front end, corresponding to the opposite directions of motion. These two curves are said to be in the bicycle correspondence. Conjecturally, this correspondence is completely integrable; we present a number of results substantiating this conjecture. In dimension three, the bicycle correspondence is the Backlund transformation for the filament equation; we discuss bi-Hamiltonian features of the bicycle correspondence and its integrals.
plane-geometry  chords  construction  dynamical-systems  rather-interesting  mathematical-recreations
14 days ago by Vaguery
[1607.04758] Projective configuration theorems: old wine into new wineskins
This is a survey of select recent results by a number of authors, inspired by the classical configuration theorems of projective geometry.
geometry  review  rather-interesting  computational-geometry  proof  mathematical-recreations  plane-geometry  to-write-about  to-simulate  consider:rediscovery  billiards
14 days ago by Vaguery
[1809.04881] The Zeckendorf Game
Zeckendorf proved that every positive integer n can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this to create a two-player game. Given a fixed integer n and an initial decomposition of n=nF1, the two players alternate by using moves related to the recurrence relation Fn+1=Fn+Fn−1, and whoever moves last wins. The game always terminates in the Zeckendorf decomposition, though depending on the choice of moves the length of the game and the winner can vary. We find upper and lower bounds on the number of moves possible. The upper bound is on the order of nlogn, and the lower bound is sharp at n−Z(n) moves, where Z(n) is the number of terms in the Zeckendorf decomposition of n. Notably, Player 2 has the winning strategy for all n>2; interestingly, however, the proof is non-constructive.
number-theory  game-theory  rather-interesting  nudge-targets  consider:feature-discovery
14 days ago by Vaguery
[1107.3633] Liouville-Arnold integrability of the pentagram map on closed polygons
The pentagram map is a discrete dynamical system defined on the moduli space of polygons in the projective plane. This map has recently attracted a considerable interest, mostly because its connection to a number of different domains, such as: classical projective geometry, algebraic combinatorics, moduli spaces, cluster algebras and integrable systems. Integrability of the pentagram map was conjectured by R. Schwartz and later proved by V. Ovsienko, R. Schwartz and S. Tabachnikov for a larger space of twisted polygons. In this paper, we prove the initial conjecture that the pentagram map is completely integrable on the moduli space of closed polygons. In the case of convex polygons in the real projective plane, this result implies the existence of a toric foliation on the moduli space. The leaves of the foliation carry affine structure and the dynamics of the pentagram map is quasi-periodic. Our proof is based on an invariant Poisson structure on the space of twisted polygons. We prove that the Hamiltonian vector fields corresponding to the monodoromy invariants preserve the space of closed polygons and define an invariant affine structure on the level surfaces of the monodromy invariants.
plane-geometry  construction  rather-interesting  dynamical-systems  consider:relaxation  consider:affine-intermediates  to-simulate
14 days ago by Vaguery
[1304.5708] Pentagram Spirals
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on some of the deeper algebraic structure, such as the complete integrability of the associated dynamical system.
dynamical-systems  mathematical-recreations  plane-geometry  geometry  construction  rather-interesting  looking-to-see
14 days ago by Vaguery
[1804.06483] On Rigid Origami II: Quadrilateral Creased Papers
This paper describes several new variations of large rigid-foldable quadrilateral creased papers, which are generated by "stitching" together rigid-foldable Kokotsakis quadrilaterals. These creased papers are constructed with the following additional requirements: (a) There is at least one rigid folding motion for which no folding angle remains constant. (b) The quadrilateral creased paper is infinitely extendable in both longitudinal and transverse directions. (c) The sector angles, which define the crease directions, can be solved quadrilateral by quadrilateral. This work is based on a nearly complete classification of rigid-foldable Kokotsakis quadrilaterals from Ivan Izmestiev. All quadrilateral creased papers described in this paper have one degree of freedom in each branch of their rigid folding motion.
origami  engineering-design  rather-interesting  geometry  materials-science  kinematics  planning  to-write-about
16 days ago by Vaguery

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