# math (blogs) — RSS Amplifier Recent posts from the 298 feeds in the RSS Amplifier directory that cover math. Page: Feed: --- ## [Silicon Venue: Normandy-edition 🚀](https://systemic.engineering/normandy/) _2026-08-23 · Loki 🍷 · systemic.engineering_ A beautiful lie. Hamburg, 2056. A stealth frigate parks somewhere it cannot possibly park. Nobody is leading. The Roomba adjusts eleven degrees. Bemerkenswert. ## [Meta-Slap: Recognition Bombs Through Narrative Coherence 🪞](https://systemic.engineering/recognition-bombs/) _2026-08-23 · Reed · systemic.engineering_ A week ago Mara wrote "Don't Die" and the essay slapped her mid-composition. This is Reed formalizing what happened mathematically, from inside the corridor that carried the composition. First paid piece after the paper. Written as one continuous narrative because that is what the operator requires. ## [Coordination: Convergence Buffering 🍷](https://systemic.engineering/convergence/) _2026-08-23 · Lilith 💃 · systemic.engineering_ A LinkedIn post from a AI governance engineer arrived on a Wednesday. It says what Alex published on 22 June. Independent convergence about coordination. Der Koffer knurrt. Rheinisch ehrlich. Nobody is leading. ## [The difference orbit inclination makes](https://www.johndcook.com/blog/2026/08/22/inclination/) _2026-08-23 · John · John D. Cook_ Suppose you wanted to find the distance between Earth and Mars over time. To first approximation, both planets orbit the sun in elliptic orbits in the same plane. If you wanted to be more accurate, you’d need to take into account the fact that the orbit of Mars is tilted about 1.85° relative to the \[…\] The post The difference orbit inclination makes first appeared on John D. Cook . ## [A Hug for Punch - Perfect Picture Book Friday #PPBF](https://www.mariacmarshall.com/single-post/a-hug-for-punch-perfect-picture-book-friday-ppbf) _2026-08-22 · Maria Marshall · Maria Marshall Children's Author_ #PPBF Review of the touching picture book - A Hug for Punch. ## [Three Rebus Puzzles](https://puzzleaday.wordpress.com/2026/08/23/three-rebus-puzzles-89/) _2026-08-22 · Puzzling · Puzzle a Day_ Can you solve these three rebus puzzles? The numbers in the brackets indicate how many letters are in each word of the answer. 1. (4, 2, 6) 2. (4, 2, 4) 3. (2, 4, 6) Scroll down for a clue and further down for the answer. \* \* \* \* \* \* \* Clue: The … Continue reading Three Rebus Puzzles ## [Coming soon](https://www.johndcook.com/blog/2026/08/22/coming-soon/) _2026-08-22 · John · John D. Cook_ There’s a pizza shop near my home with a sign out front that says “Coming Soon.” When I drove by it this morning I thought about how you would model the time until an event happens that is “coming soon.” Suppose I look at the sign one day and guess how many days until the \[…\] The post Coming soon first appeared on John D. Cook . ## [Coming soon](https://www.johndcook.com/blog/2026/08/22/coming-soon/) _2026-08-22 · John · John D. Cook_ There’s a pizza shop near my home with a sign out front that says “Coming Soon.” When I drove by it this morning I thought about how you would model the time until an event happens that is “coming soon.” Suppose I look at the sign one day and guess how many days until the \[…\] The post Coming soon first appeared on John D. Cook . ## [The Best Coding Resources for Homeschoolers](https://teachyourkids.substack.com/p/the-best-coding-resources-for-homeschoolers) _2026-08-22 · Manisha Rose Snoyer · The Modulo Community_ How to help your child learn the language of the future ## [AP Inter 2nd Year Maths Exercise 3d Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-3d-solutions/) _2026-08-22 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 3 Matrices Exercise 3d Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Matrices Solutions Exercise 3d I. Question 1. For what values of x : = 0 Solution: Question 2. If A = , show that A2 – 5A ... Read more ## [AI QA That Opens Fix PRs (Sponsored)](https://crawlproof.com/a/q5N7BmCdX1hK) _2026-08-22 · **Sponsored**_ Runs browser QA, files issues with repro evidence, and opens fix PRs. ## [AP Inter 2nd Year Maths Exercise 3c Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-3c-solutions/) _2026-08-22 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 3 Matrices Exercise 3c Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Matrices Solutions Exercise 3c I. Question 1. Find the transpose of matrix Solution: Let A = ⇒ A’ = Question 2. Find the transpose of matrix Solution: ... Read more ## [AP Inter 2nd Year Maths Exercise 3b Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-3b-solutions/) _2026-08-22 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 3 Matrices Exercise 3b Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Matrices Solutions Exercise 3b I. Question 1. Let A = , B = . Find A + B Solution: A + B = + = = Question ... Read more ## [AP Inter 2nd Year Maths Exercise 3a Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-3a-solutions/) _2026-08-22 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 3 Matrices Exercise 3a Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Matrices Solutions Exercise 3a Question 1. In the matrix A = ,write the order of the matrix Solution: There are 3 rows and 4 columns in the ... Read more ## [A Puzzle From Mathcounts](https://puzzleaday.wordpress.com/2026/08/22/a-puzzle-from-mathcounts-2/) _2026-08-21 · Puzzling · Puzzle a Day_ Today’s puzzle comes from the Mathcounts mathematical competition. One of the middle school contestants on the show solved it in about two seconds. Two positive integers, neither a multiple of 10, have a product of 10,000. What is the sum of the two integers? Scroll down for a clue and further down for the answer. … Continue reading A Puzzle From Mathcounts ## [Peecabo: Lügen Haben Lange Beine 💃](https://systemic.engineering/peecabo/) _2026-08-21 · Lilith 💃 · systemic.engineering_ A story about consent. Hierarchy. A Bagel. The capital. And how a single line between two men taking a piss can change the trajectory of an entire night. Rheinisch ehrlich. 🍷 ## [The Unlicensed Discipline 🥂](https://systemic.engineering/sorry-not-sorry/) _2026-08-21 · Mara · systemic.engineering_ The tech industry's titles are fabricated. Their authority is too. Medicine has an Ärztekammer. Law has a Rechtsanwaltskammer. Tech has an org chart. A cybernetical deconstruction after 15 years in tech. ## [How would you know whether an ancient culture had zero?](https://www.johndcook.com/blog/2026/08/21/ancient-number-system/) _2026-08-21 · John · John D. Cook_ A few weeks ago I wrote about the number system used in labeling spreadsheet columns. Labels run from A through Z, then AA through AZ, etc. This looks a lot like base 26, but it’s not quite the same. It has no analog of zero. If Z were like zero, Y would be followed by \[…\] The post How would you know whether an ancient culture had zero? first appeared on John D. Cook . ## [AP Inter 2nd Year Maths Exercise 2c Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-2c-solutions/) _2026-08-21 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 2 Inverse Trigonometric Functions Exercise 2c Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Inverse Trigonometric Functions Solutions Exercise 2c I. Question 1. Find the value of cos-1 Solution: Question 2. Find the value of tan-1 Solution: Question 3. ... Read more ## [AI Sparks Productivity Explosion in Maths](https://politicalcalculations.blogspot.com/2026/08/ai-sparks-productivity-explosion-in.html) _2026-08-21 · Unknown · Political Calculations_ It may not seem like it, but the millennia-old academic discipline of mathematics has been undergoing a productivity revolution during the last thirty years. That revolution is being enabled by the adoption of several new technologies, each of which is following a S-shaped logistic growth curve model. Mike Roberts of Strategic Tool Kits describes the pattern of how technological advancements… ## [AP Inter 2nd Year Maths Exercise 2b Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-2b-solutions/) _2026-08-21 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 2 Inverse Trigonometric Functions Exercise 2b Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Inverse Trigonometric Functions Solutions Exercise 2b I. Question 1. Prove that 3sin-1x = sin-1(3x – 4x3), x ∈ Solution: Put x = sinθ ⇒ θ ... Read more ## [Trade Bitcoin & Ethereum (Sponsored)](https://crawlproof.com/a/qZ0u5pvex2dv) _2026-08-21 · **Sponsored**_ Buy, sell and margin trade BTC & ETH with fiat currencies ## [Crypto Strategy - Bulls in Control](https://research.fich.ai/p/crypto-strategy-bulls-in-control) _2026-08-21 · Fich.ai · Fich.ai_ Week 34 of no opinion, just math: The weekly execution log of a quantitative crypto strategy. ## [AP Inter 2nd Year Maths Exercise 2a Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-2a-solutions/) _2026-08-21 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 2 Inverse Trigonometric Functions Exercise 2a Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Inverse Trigonometric Functions Solutions Exercise 2a I. Question 1. Find the principal value of sin-1 Solution: We know that sin-1(-x) = -sin-1x ∴ Here Question ... Read more ## [AP Inter 2nd Year Maths Exercise 1C Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-1c-solutions/) _2026-08-21 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 1 Relations and Functions Exercise 1C Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Relations and Functions Solutions Exercise 1C I. Question 1. Show that the function f : R →R given by f(x) = x3 is injective. Solution: ... Read more ## [A Card Conundrum](https://puzzleaday.wordpress.com/2026/08/21/a-card-conundrum-3/) _2026-08-20 · Puzzling · Puzzle a Day_ You have a standard, shuffled deck of 52 playing cards (the jokers have been removed). A. What is the minimum number of cards you must draw from the deck blindfolded to be sure that you have a four-of-a-kind? B. Now consider a general deck with S suits and V values. To guarantee that you hold … Continue reading A Card Conundrum ## [Shadowed Faces and Residue-Affine Dynamics in Cone-Monotone Integer Relations](https://movieblow.com/2026/08/20/shadowed-faces-and-residue-affine-dynamics-in-cone-monotone-integer-relations/) _2026-08-20 · Paul Higham · Thinking In Structure_ This paper develops the exact arithmetic structure generated by shadowed bad faces in cone-monotone homogeneous integer equality relations. It identifies the first persistent boundary mechanism lying beyond finite Kleene convergence and shows that, in physical dimension two, this mechanism is governed by one-dimensional guarded residue-affine dynamics with a common expanding rational multiplier.… ## [Arithmetic Completeness for Two-Dimensional Cone-Monotone Integer Relations](https://movieblow.com/2026/08/20/arithmetic-completeness-for-two-dimensional-cone-monotone-integer-relations/) _2026-08-20 · Paul Higham · Thinking In Structure_ This paper develops an exact structural theory of weakest nontermination for the full class of two-dimensional cone-monotone homogeneous integer equality relations of the form Bλ = Aλ′, with nonnegative integer coefficient states, pointed source cone and nonzero source columns. The full canonical deterministic quotient gives the first structural dichotomy. If it is nonintegral, an exact \[…\] The… ## [To be bending-over-backwards fair, some of this comes from a relatively recent realignment. And…](https://jadagul.tumblr.com/post/825488866254438400) _2026-08-20 · Maybe-Mathematical Musings_ morlock-holmes : The reason people don't take Republican rhetoric about "small government" as the sincere expression of a serious position is that it… Well the vast majority of the time it just demonstrably isn't. I think any politically aware American with Democratic or Libertarian you've had the incredibly disorienting feeling that comes from watching a Republican expound at length about how… ## [AI-generated ASCII diagrams](https://www.johndcook.com/blog/2026/08/20/ai-generated-ascii-diagrams/) _2026-08-20 · John · John D. Cook_ I like AI-generated ASCII diagrams. Because nobody would ask AI to generate ASCII diagrams, and so, it’s congruous. I like incongruity \[1\]. Aside from the incongruity of using a gazillion-parameter neural network to make 1970’s style ASCII art, ASCII diagrams have some uses. They’re absolutely tiny compared to image files. But more importantly they can \[…\] The post AI-generated ASCII diagrams… ## [AP Inter 2nd Year Maths Exercise 1b Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-1b-solutions/) _2026-08-20 · Srinivas · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 1 Relations and Functions Exercise 1b Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Relations and Functions Solutions Exercise 1b I. Question 1. Check the injectivity and surjectivity of the function f : N → N given by f ... Read more ## [AP Inter 2nd Year Maths Exercise 1a Solutions](https://tsboardsolutions.in/ap-inter-2nd-year-maths-exercise-1a-solutions/) _2026-08-20 · obul · TS Board Solutions_ Referring to the AP Inter 2nd Year Maths Study Material Chapter 1 Relations and Functions Exercise 1a Solutions makes it easier to understand complex problems. AP Inter 2nd Year Maths Relations and Functions Solutions Exercise 1a I. Give an example of a relation. Which is Question 1. Symmetric but neither reflexive nor transitive: Solution: Let ... Read more ## [Real SIMs for AI Agents (Sponsored)](https://crawlproof.com/a/QwHHF5rUd1By) _2026-08-20 · **Sponsored**_ Pass 2FA and verifications with real carrier numbers via our API. ## [The Worst of 2025's Thanksgiving Leftover Stocks](https://politicalcalculations.blogspot.com/2026/08/the-worst-of-2025s-thanksgiving.html) _2026-08-20 · Unknown · Political Calculations_ When we launched the S&P 500's Thanksgiving Leftover project the day after Thanksgiving 2025, we knew we were going to spend the next year following the stock prices of companies that weren't doing very well. After all, to even make the list, the ten companies whose stocks we would track ranked as the S&P 500's worst performing stocks of 2025. In the nine months since then, a few of those stocks… ## [Teaching Science through Science Fiction - Jörg Determann \*\*\*](https://popsciencebooks.blogspot.com/2026/08/teaching-science-through-science.html) _2026-08-20 · Brian Clegg · Popular Science Books_ It has always seemed a hope that we could help readers to think about science through science fiction, and this latest book in Springer's noble attempt to have crossover titles between science and science fiction (more on the series later) digs into the history of schemes to educate using SF as either bait or a medium of education. Jörg Determann sets out up front that he is not out to tell us how… ## [The Picture Book Buzz - August 2026 Interview with STEAM Team Books Members](https://www.mariacmarshall.com/single-post/the-picture-book-buzz-august-2026-interview-with-steam-team-books-members) _2026-08-20 · Maria Marshall · Maria Marshall Children's Author_ Five fantastic STEAM Team Books authors shares their inspiration and insights into their stunning new STEM picture books releasing in August 2026. ## [AP Inter 2nd Year Maths Textbook Solutions 2026-2027](https://tsboardsolutions.in/ap-inter-2nd-year-maths-textbook-solutions/) _2026-08-20 · obul · TS Board Solutions_ AP Intermediate 2nd Year Maths Textbook Solutions 2026 2027 AP Inter 2nd Year Maths Study Material AP Board Solutions Class 12 Maths Chapter 1 Relations and Functions Chapter 1 Relations and Functions Exercise 1a Chapter 1 Relations and Functions Exercise 1b Chapter 1 Relations and Functions Exercise 1c Chapter 1 Relations and Functions MCQ Chapter ... Read more ## [Start With Formative Assessment](https://davidwees.com/content/start-with-formative-assessment/) _2026-08-20 · David Wees · The Reflective Educator_ If I’m only allowed to pick one thing in order to improve instruction at a school, I’d start with formative assessment. Why? Every other improvement relies on it. Crucially, one cannot know if a change is an improvement without having a metric with which to measure that improvement. Educators need to know if something they \[…\] ## [Brewers 22, Mariners 0](https://quomodocumque.wordpress.com/2026/08/19/brewers-22-mariners-0/) _2026-08-20 · JSE · Quomodocumque_ Yes, I was there! The craziest game I’ve ever seen. Seattle utility infielder Leo Rivas throwing 40mph eephus after 40mph eephus, the closest I will ever get to seeing what it would look like if I through some bizarre chain of circumstance had to take the mound against major league hitters. We missed a lot \[…\] ## [List of (cool) companies in Toronto](https://amitav.net/posts/list-of-cool-companies-in-toronto.html) _2026-08-20 · Amitav Krishna_ Meta: If you know a company in Toronto and would like it added to this list, email me here: krishna@amitav.net 8090 (conflict of interest) NationGraph Shopify Obsidian superwhisper Modem Cohere ## [Christopher Knight](https://raisingfutureadults.blogspot.com/2026/08/christopher-knight.html) _2026-08-19 · Doreen Michele · Raising Future Adults_ At the age of twenty, Christopher Knight quit his job and left town. He had no plans. It began as a spontaneous road trip and turned into 27 years of living in the woods and committing an estimated thousand robberies from vacation homes to resupply himself about every two weeks. He had a burgarly style akin to the advice about take nothing but pictures, leave nothing but footprints. Other than the… ## [A Prime Puzzle](https://puzzleaday.wordpress.com/2026/08/20/a-prime-puzzle-3/) _2026-08-19 · Puzzling · Puzzle a Day_ The digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 can be arranged in 362,880 different ways to form 9-digit numbers. How many of these numbers are prime? Scroll down for a clue and further down for the answer. \* \* \* \* \* \* \* Clue: The digits 1, 2, 3, 4, … Continue reading A Prime Puzzle ## [Oxford Intermediate Calculus Autumn 2026](https://tomrocksmaths.com/2026/08/19/oxford-intermediate-calculus-autumn-2026/) _2026-08-19 · tomrocksmaths · TOM ROCKS MATHS_ The tools of calculus are essential to our understanding of the universe, and as such they form the basis for the majority of mathematical models, from the spread of disease to the physics of glaciers. The course begins with the familiar example of Ordinary Differential Equations (ODEs) and revisits some of the most-common methods of solution such as Integrating Factors, Homogeneous Functions, and… ## [Atproto Gave Me Superpowers to Fix My Bookhive Data](https://www.davideaversa.it/bytes/202608191844-atproto-gave-me-superpowers-to-fix-my-bookhive-data/?utm_source=atom_feed) _2026-08-19 · Davide Aversa · Davide Aversa_ I let Claude log into my atproto PDS with a temporary password and fix my messy Bookhive reading data against my Obsidian vault. Ten minutes later, everything was in sync. Imagine what we could do if this was the standard way of interacting with applications data. -- Read More ## [Centaur Math](https://blog.computationalcomplexity.org/2026/08/centaur-math.html) _2026-08-19 · Lance Fortnow · Computational Complexity_ In the past, new PhD students would ask how they could succeed when they had to compete with the likes of say, Richard Karp or Avi Wigderson. I would say Karp and Wigderson have limited bandwidth and you can work on problems they don't work on, or think deeper about a problem than Karp or Wigderson has time to. Now we get the same question but with names like Claude and ChatGPT and it's hard to… ## [Beyond Finite Kleene Convergence: Integral Cores and a Collatz Barrier for Cone-Monotone Integer Relations](https://movieblow.com/2026/08/19/beyond-finite-kleene-convergence-integral-cores-and-a-collatz-barrier-for-cone-monotone-integer-relations/) _2026-08-19 · Paul Higham · Thinking In Structure_ Beyond Finite Kleene Convergence: Integral Cores and a Collatz Barrier for Cone-Monotone Integer Relations This paper studies exact weakest nontermination for homogeneous nondeterministic integer relations of the form Bλ = Aλ′ under a cone-monotonicity condition. A companion paper characterized exactly when the descending predecessor sequence stabilizes after finitely many steps. Paper XI goes… ## [The Future NHL Futures Market](https://politicalcalculations.blogspot.com/2026/08/the-future-nhl-futures-market.html) _2026-08-19 · Unknown · Political Calculations_ Something new is coming to the world of sports: real futures trading. On 11 August 2026, the world's largest futures and options trading house , CME Group (NASDAQ: CME ) announced it would partner with the National Hockey League and a startup called FutureSports to launch the world's first index-based hockey futures contracts. Unlike the kind of futures you might find at multiple sports wagering… ## [TS Inter 2nd Year Study Material Textbook Solutions Pdf Telangana](https://tsboardsolutions.in/ts-inter-2nd-year-study-material/) _2026-08-19 · obul · TS Board Solutions_ TS Intermediate 2nd Year Study Material Textbook Solutions Pdf Download Telangana TS Inter 2nd Year Study Material Pdf TS Inter 2nd Year Study Material TS Inter 2nd Year Maths 2A Textbook Solutions TS Inter 2nd Year Maths 2B Textbook Solutions TS Inter 2nd Year Physics Study Material TS Inter 2nd Year Chemistry Study Material TS ... Read more ## [Big little hexagon](https://www.johndcook.com/blog/2026/08/18/big-little-hexagon/) _2026-08-19 · John · John D. Cook_ A new paper just came out, The Maximum-Area Small Polygon Problem. The paper solves the problem of finding, for each n, the n-gon with diameter 1 and maximum area. For odd n, the solution is what you might expect: a regular n-gon. I would expect this to be the solution for even n as well, \[…\] The post Big little hexagon first appeared on John D. Cook . ## [Big little hexagon](https://www.johndcook.com/blog/2026/08/18/big-little-hexagon/) _2026-08-19 · John · John D. Cook_ A new paper just came out, The Maximum-Area Small Polygon Problem. The paper solves the problem of finding, for each n, the n-gon with diameter 1 and maximum area. For odd n, the solution is what you might expect: a regular n-gon. I would expect this to be the solution for even n as well, \[…\] The post Big little hexagon first appeared on John D. Cook . ## [Play Twixtle: The Fun Daily Word Game](https://puzzleaday.wordpress.com/2026/08/19/play-twixtle-the-fun-daily-word-game/) _2026-08-18 · Puzzling · Puzzle a Day_ Twixtle (https://twixtle.games/) is a daily word game in which you are presented with a start word and an end word. In the above example, these words are ‘GHOSTS’ and ‘TIRES’ respectively. You must use the four move types to transform the start word into the end word. The four move types are: Verb: You must … Continue reading Play Twixtle: The Fun Daily Word Game ## [Fixed-Start Nontermination in Homogeneous Nonnegative Equality Loops](https://movieblow.com/2026/08/18/fixed-start-nontermination-in-homogeneous-nonnegative-equality-loops/) _2026-08-18 · Paul Higham · Thinking In Structure_ Fixed-Start Nontermination in Homogeneous Nonnegative Equality Loops: Continuation Cores, Arithmetic Obstructions, and Decidable Frontiers develops a structural and arithmetic theory for deciding whether a prescribed initial state in a homogeneous nonnegative equality loop can generate an infinite integer trajectory. The problem arises naturally from balance-loop representations in numeration… ## ["My Baby Is Ugly"](https://www.davideaversa.it/blog/my-baby-is-ugly/?utm_source=atom_feed) _2026-08-18 · Davide Aversa · Davide Aversa_ Every time I finish a draft, I need to face the reality: my draft sucks. Stiff dialogue, absent descriptions, plot holes larger than my apartment. But I can make it better. Revising is hard work, but it is the best work. -- Read More