Essays

2024-06-11 An Almanac, Not An Index
2024-06-10 Take Care of the Conditions
2024-04-30 Identity's Radius
2024-03-29 The Glue
2024-02-29 The Constellation of Progress
2024-01-09 A Lighthouse Cutting Through the Fog of Overwhelm
2023-11-08 Data Has a Friction Problem
2023-11-01 Posthaste
2023-10-25 Infrastructure is the Concealed Wiring of Our Civilization
2023-10-18 Reach Out
2023-10-11 Getting the Conditions Right for Progress in Weather Forecasting
2023-09-25 Vampires
2023-08-25 Teleport With Intention
2023-07-25 Cohorts
2023-06-25 Under the Hood
2023-05-25 When it Clicks
2023-04-25 Fifty Thousand
2023-03-25 On Noticing
2023-02-25 The Educator's Tax
2023-01-25 Tractability and Fidelity
2022-12-25 Finishing is a Superpower
2022-11-25 Consuming and Absorbing
2022-10-25 More
2022-09-25 Daily Anchor
2022-08-25 ComSciCon
2022-07-25 Scientific Contributions
2022-06-25 People
2022-05-25 Do I Understand You?
2022-04-25 Research Collaborations
2022-03-25 Exciting Science
2022-02-25 Timing
2022-01-25 The Journey to Completion
2021-12-25 The Language of Science
2021-11-25 Good Questions
2021-10-25 Finding the Story
2021-09-25 A Quantum Summer
2021-08-25 The SATisfying Physics of Phase Transitions
2021-07-25 The Clarity of Brevity
2021-06-25 Building Blocks
2021-05-25 Code as Knowledge Distilled
2021-04-25 Evolving Qubits With Bits
2021-03-25 The Shattering of SAT
2021-02-25 Absorbers and Explorers
2021-01-25 Virtual CNWW
2020-12-25 Pick a State, Any State
2020-11-25 All in the Corners
2020-10-25 The Curse of Dimensionality
2020-09-25 Physics On A Cube
2020-08-25 A Game of Loops
2020-07-27 PSIon
2020-07-20 Speak For Yourself
2020-07-13 Premature Wielding of Mathematical Tools
2020-07-06 Stating My Ignorance
2020-06-29 Give The Easy Examples
2020-06-22 What Have You Built?
2020-06-15 What Makes Your Work Important?
2020-06-08 The Joy of Repetition
2020-06-01 Giving Good Scientific Presentations
2020-05-25 Take What You Can
2020-05-18 Sharing Your Research
2020-05-11 Beautiful Pictures Stuck in our Heads
2020-05-04 Resolution of Care
2020-04-27 Permission Granted
2020-04-20 You Are Not Your Work
2020-04-13 Dreams and Reality
2020-04-06 Death By A Thousand Cuts
2020-03-30 Trivial
2020-01-27 Something Deeply
2019-12-31 Essays and Explanations
2019-12-30 Holding Everything In Your Head
2019-12-27 What's the Story?
2019-12-23 Active and Passive Notes
2019-12-20 Mathphobia
2019-12-16 Random Rules
2019-12-13 Optimizing Everything
2019-12-09 Enough Is Up To You
2019-12-06 Going On A Journey
2019-12-02 Slow
2019-11-29 Muddled Thinking
2019-11-25 Less Serious
2019-11-22 Fighting Overwhelm
2019-11-18 Endurance
2019-11-15 Projects and Resumes
2019-11-11 Potential
2019-11-08 Teaching is Empathy
2019-11-04 The Two Fears
2019-11-01 The Art of Explanation
2019-10-28 Pedagogical Proofs
2019-10-25 Narrow Paths and Open Forests
2019-10-21 Liking Without Doing
2019-10-18 Learning to Teach Yourself
2019-10-14 Glimpsing Connections
2019-10-11 Defaults
2019-10-07 Carrying
2019-10-04 Academic And Life Plans
2019-09-30 Kindness Is Inexpensive
2019-09-27 Getting to the Essence
2019-09-23 Understanding Is Hard-Won
2019-09-20 Necessary Background
2019-09-16 Path Certainty
2019-09-13 Looking Forward
2019-09-09 Remove the Choice
2019-09-06 Generosity
2019-09-02 Archives and Mass
2019-08-30 Concentrated Work
2019-08-26 Being Good Enough
2019-08-23 Ebb and Flow
2019-08-19 Many Tries
2019-08-16 Daily Questions
2019-08-12 Admiring Is Not Doing
2019-08-09 Change In The Room
2019-08-05 Make, Make, Make
2019-08-02 Stories and Tracks
2019-07-29 Not Everything Has To Be A Business
2019-07-26 The Little Details
2019-07-22 Small Steps
2019-07-19 Nuance and Hidden Details
2019-07-15 Like To
2019-07-12 Academics and Hobbies
2019-07-08 Celebrating Consistency
2019-07-05 Identity, Responsibility, and Failure
2019-07-01 More Than Meets The Eye
2019-06-28 Interior Angles of a Regular Polygon
2019-06-24 Boundaries and Focus
2019-06-21 Augmenting Your Toolkit
2019-06-17 Clutter and Blank Space
2019-06-14 A Different Kind of Final Exam
2019-06-10 Notation and Beginners
2019-06-07 Discounting
2019-06-03 Control of the Future
2019-05-31 Slick Versus Pedagogical Proofs
2019-05-27 Levelling Up
2019-05-24 The Rational Roots Theorem
2019-05-20 Mathematics Isn't Just Numbers
2019-05-17 Degeneracy of the Quantum Harmonic Oscillator
2019-05-13 Being Happy With Being Repetitive
2019-05-10 Peeling Back the Onion
2019-05-06 How Many People Need To Watch?
2019-05-03 Do I Have What It Takes?
2019-04-29 Analogies in Mathematics
2019-04-26 Regurgitating
2019-04-22 Picking Yourself
2019-04-19 Learning Without Excitement
2019-04-15 Heuristics Lead to Rigour
2019-04-12 Knowledge From Repetition
2019-04-08 I Could Be Wrong
2019-04-05 Where Does It Belong In The Web?
2019-04-01 Being Good At Mathematics
2019-03-29 Clarity and Words
2019-03-25 No Final Exam
2019-03-22 Patting Yourself On The Back
2019-03-18 Nudging Along Versus Waiting
2019-03-15 Learning is Offloading
2019-03-11 A Survey Of Homework Strategies
2019-03-08 Just A Blink
2019-03-04 Mathematics for Enjoyment
2019-03-01 Not Everyone Thinks The Same
2019-02-25 End of the Treadmill
2019-02-22 Derailing an Explanation
2019-02-18 Equations as Constraints
2019-02-15 Going After The Average
2019-02-11 The Right Touch Of Novelty
2019-02-08 Safe Questions
2019-02-04 The Right Time
2019-02-01 How Deliberate Are Your Explanations?
2019-01-28 The Whole Ride
2019-01-25 One-Sentence Summary
2019-01-21 Familiar Forms
2019-01-18 Snapping Into Focus
2019-01-14 Escaping the Path
2019-01-11 Give Yourself A Gift
2019-01-07 Not The Usual Outreach
2019-01-04 Chasing The Carrot
2018-12-31 Discovering Mathematics
2018-12-24 Bag of Examples
2018-12-17 Only Numbers and Algebra
2018-12-10 Not Necessary
2018-12-03 Memorization in Education
2018-11-26 What Counts As Cheating?
2018-11-19 Balance As A Student
2018-11-12 The Grit to Push Through
2018-11-05 Behind the Equations
2018-10-29 Quantities in Context
2018-10-22 Black Boxes
2018-10-15 The Priority of Education
2018-10-08 A Splash of Colour
2018-10-01 Outside the Curriculum
2018-09-24 Through the Minefield
2018-09-17 Visuals in Mathematics
2018-09-10 The Necessary Details
2018-09-03 By Convention
2018-08-27 Where's the Surprise?
2018-08-20 Being Second Atop the Mountain
2018-08-13 Where Are Your Weaknesses?
2018-08-06 Pairing Simple Examples With Complex Machinery
2018-07-30 Attempting Problems
2018-07-23 Permission to Learn
2018-07-16 Motivating New Tools
2018-07-09 Do You Understand?
2018-07-02 Act of Translation
2018-06-25 Concepts and Mechanics
2018-06-18 Jumps in Abstraction
2018-06-11 Why Can't We Give An Answer to 0/0?
2018-06-04 The Limits of Life
2018-05-28 Hidden Assumptions
2018-05-21 Misaligned Incentives
2018-05-14 Stating One's Goal Clearly When Solving a Problem
2018-05-07 Peripheral Knowledge
2018-04-30 Estimation, Modeling, and Accuracy
2018-04-23 Why Do We Make a Fuss About Definitions?
2018-04-16 Two Types of Mathematics
2018-04-09 One-to-One and Onto
2018-04-02 Recipes
2018-03-26 Intuition about Ideals
2018-03-19 Why Can't We Reach the Speed of Light By Boosting?
2018-03-12 Intuition and Rigour
2018-03-05 When Are Two Things the Same?
2018-02-26 Scrabble Misfortunes
2018-02-19 What is a Differential Equation?
2018-02-12 What Are Toy Models in Physics?
2018-02-05 A Simple Puzzle
2018-01-29 Dimensions of Objects
2018-01-22 No Magic
2018-01-15 Going to the Extreme
2018-01-08 Overhang
2018-01-01 A Nice Way to See the Identity for Binomial Coefficients
2017-12-25 Guided Learning Through Problems
2017-12-18 Teasing Out One's Reasoning
2017-12-11 Calculating $\pi$ Factorial
2017-12-04 Easy Examples Miss the Point
2017-11-27 Minimization (The Rope Cutting Problem)
2017-11-20 Machines and Processes
2017-11-13 Notation
2017-11-06 The Importance of Factoring
2017-10-30 Serving the Results
2017-10-23 Discovery and Delight
2017-10-16 Integrating the Gaussian Function
2017-10-09 The Sweet Spot
2017-10-02 Linear versus Cyclic Permutations
2017-09-25 Period of a Pendulum
2017-09-18 On Uncertainty in Science
2017-09-11 Mathematical Sophistication
2017-09-04 The Limitations of Models
2017-08-28 Cramer's Rule for Solving Linear Systems
2017-08-21 The Distance Formula (Equation Explainer)
2017-08-14 Examples Before Abstraction
2017-08-07 Contradiction as Zeros
2017-07-31 Conceptual Understanding
2017-07-24 Precision in Language
2017-07-17 Proof that there exists a 3-regular graph for any graph with $k$ vertices, with $k \geq 4$ and $k$ even
2017-07-10 Vertices and Edges (An introduction to graph theory)
2017-07-03 First Principles
2017-06-26 Contrapositive Implications as Dominoes
2017-06-19 Units
2017-06-12 Translation
2017-06-03 Why Can’t I Divide By $\sin$?
2017-05-22 Summer Research
2017-04-08 The Friends/Strangers Problem
2017-03-27 Introduction to Vectors
2017-03-17 Can You Teach What You’ve Learnt?
2017-03-15 Derivations and Feeding
2017-03-13 Flashy
2017-03-10 Integrals, Integrands, and Understanding the Notation
2017-03-08 Understanding Algebra and Balancing Equations
2017-03-06 Can You Explain It?
2017-03-03 Full Explanation
2017-03-01 Taking Out The Pencil
2017-02-27 Alternative Perspectives
2017-02-24 Interconnecting Histories
2017-02-22 Notes
2017-02-20 A Tutor’s Job
2017-02-17 Time For Reflection
2017-02-15 Interdisciplinary
2017-02-13 Playing With An Idea
2017-02-10 Filler
2017-02-08 Going Through The Motions
2017-02-06 Juggling
2017-02-03 Imitation
2017-02-01 Why Do I Need This?
2017-01-30 Within One’s Expertise
2017-01-27 Discovery
2017-01-25 On the Boundary
2017-01-23 Only Part of the Picture
2017-01-20 Relearning
2017-01-18 Above My Level
2017-01-16 Participation
2017-01-13 Variations on Simple Harmonic Motion
2017-01-11 The Least Memorization Possible
2017-01-09 Last-Minute Stuffing
2017-01-06 Confidence
2017-01-04 Participation
2017-01-02 Transforming
2016-12-30 Relating
2016-12-28 Cementing
2016-12-26 Number-Crunching
2016-12-23 Simple Harmonic Motion
2016-12-21 Struggle
2016-12-19 Starting Simple
2016-12-16 The Short Route
2016-12-14 Where to Start
2016-12-12 Over the Hump
2016-12-09 Understanding Graphs
2016-12-07 Understanding Terminology
2016-12-05 Traction
2016-12-02 Lead By Example
2016-11-30 The Spotlight
2016-11-28 All In
2016-11-25 Quick Computation
2016-11-23 Order of Operations
2016-11-21 Appreciating the Why
2016-11-18 Building On Top of Each Other
2016-11-16 The Skill of Spotting
2016-11-14 Slumps
2016-11-11 Masking
2016-11-09 This Isn’t The Forefront
2016-11-07 Testing Terminology
2016-11-04 A Place To Be Wrong
2016-11-02 Competitiveness
2016-10-31 Incompatible Ideas
2016-10-28 Time Remaining
2016-10-26 Proofs Can Be Useful
2016-10-24 Good Enough
2016-10-21 Being Smart Doesn’t Have to be About Mathematics or Science
2016-10-19 Derailed Goals
2016-10-17 The Little Frustrations
2016-10-14 The Last-Minute Rush
2016-10-12 Jolting Your Ego
2016-10-10 Stages of Preparation for an Exam
2016-10-07 Qualifying Language
2016-10-05 The Survivor
2016-10-03 A Sense of Play
2016-09-30 Finishing Sentences
2016-09-28 Reading a Solution
2016-09-26 Expertise Does Not Imply Teaching Skills
2016-09-23 Repeating
2016-09-21 Fluency
2016-09-19 Role Reversal
2016-09-16 Cynical
2016-09-14 Jagged Edges
2016-09-12 Not Just For The Test
2016-09-09 Motivation
2016-09-07 A Bunch Of Formulas
2016-09-05 Logical Implications
2016-09-02 Cardioid
2016-08-31 Qualifying Language
2016-08-29 Changing One Block
2016-08-26 Questioning
2016-08-24 Portrayals
2016-08-22 Overstuffing
2016-08-19 A Needless Goal
2016-08-17 Should I Use A Complicated Word?
2016-08-15 Analogies in Teaching
2016-08-12 Energy In
2016-08-10 Building On Top of Each Other
2016-08-08 Can You Change Your Mind?
2016-08-05 What’s in a Good Question?
2016-08-03 Memory Aids
2016-08-01 Electric Shock
2016-07-29 Science Education and Self Learning
2016-07-27 Base
2016-07-25 Elitist
2016-07-22 Defining
2016-07-20 Are You Sure?
2016-07-18 Fickle
2016-07-15 Elegance
2016-07-13 Are You Willing to be Mediocre?
2016-07-11 Slowly Chipping Away
2016-07-08 These Rules Are Stupid
2016-07-06 Scales
2016-07-04 Showing Up On the Nth Day
2016-07-01 Intuition
2016-06-29 Storyline
2016-06-27 Mountains
2016-06-24 Unconscious Dominoes
2016-06-22 The Kill Shot
2016-06-20 You Don’t Have to Love Every Day
2016-06-17 Transfer Difficulty
2016-06-15 The Unwatched Laboratory
2016-06-13 Those Who Are Left
2016-06-10 Absolutes
2016-06-08 An Informed Decision
2016-06-06 Will You Choose to Act?
2016-06-03 Improvement is Not a Race
2016-06-01 Optimal Configurations
2016-05-30 Balance
2016-05-27 Failure
2016-05-25 Reliance on Motivation
2016-05-23 Framing
2016-05-20 The Great Squeeze
2016-05-18 Nanometres
2016-05-16 Pointing Fingers
2016-05-13 Building up the Work
2016-05-11 Curves
2016-05-09 Defaults
2016-05-06 Avoid the Surges
2016-05-04 False Slopes
2016-05-02 Fun
2016-04-29 Cold-Hearted Science
2016-04-27 Future vs. Present You
2016-04-25 Willing to be Wrong
2016-04-22 Approximation
2016-04-20 Excitement
2016-04-18 Deviation
2016-04-13 What’s Worth Remembering
2016-04-08 He vs. She vs. They
2016-03-28 I Get To
2016-03-25 Autopilot
2016-03-21 A Million Choices
2016-03-16 Big
2016-03-14 Just Take a Step
2016-03-09 Driven by the Process
2016-03-09 You’re Not an Impostor
2016-03-04 Iteration
2016-03-02 What’s Holding You Back?
2016-02-29 Amazing Accomplishments are a Byproduct
2016-02-26 Cherry Picking
2016-02-24 Doubt
2016-02-22 Advice on Advice
2016-02-19 Practice
2016-02-12 Teaching
2016-02-10 Walking in Circles
2016-02-08 Just Give Me the Formula
2016-02-05 The Guarantee
2016-02-03 Closed
2016-02-01 Ion Drives and Rockets
2016-01-29 Patterns
2016-01-27 Area Under the Curve
2016-01-25 Half
2016-01-22 Density
2016-01-20 What Are You Practicing?
2016-01-18 Influence and Leaders
2016-01-15 Binary
2016-01-13 A Little is Worse Than Nothing
2016-01-11 Goals Are Milestones
2016-01-08 Application
2016-01-06 The Long Tail
2016-01-02 Tools
2015-12-21 XC
2015-12-12 Iteration
2015-10-09 The Secret