Experiments, Group, Milestones, Murderous Maths, Physics, Together with sis, Trips

All Nerds Unite: Simon meets Steve Mould and Matt Parker in London

Hilarious, inspirational and loaded with cosmic coincidences, this was one of the best evenings ever! Many of our currently favourite themes were mentioned in the show (such as the controversy of Francis Galton, the BED/ Banana Equivalent Dose, sound wave visualizations, laser, drawing and playing with ellipses, Euler’s formula). Plus Simon got to meet his teachers from several favourite educational YouTube channels, Numberphile, StandUpMaths and Steve Mould.

With Steve Mould
With Matt Parker
Community Projects, Computer Science, Group, Milestones, Murderous Maths, Notes on everyday life

Simon introducing himself for the World Science Scholars program

This is Simon’s introductory video for the World Science Scholars program (initiative of The World Science Festival). In May this year, Simon has been chosen as one of the 30 young students worldwide, joining the 2019 cohort for exceptional talents in mathematics. Most of the other students are 14 to 17 years old, age was not a factor in the selection process. To help the students and their future mentors to get to know one another, every World Science Scholar was asked to record an introductory video, no longer than 3 minutes, answering a few questions such as what is the biggest misconception about math, what your favourite branches of math and science are and who among the living mathematicians you’d like to meet.

Throughout the program, the students are given access to over a dozen unique interdisciplinary online courses and have the option to complete an applied math project, alone or as a team, consulting real experts in the field of their project. Simon has already started the first course module, on Special Relativity by Professor Brian Greene. The course has been specifically recorded for the World Science Scholars and reflects the program’s ethos: it’s self-paced, no grades, it relies on beautiful animations and visualizations, it’s full of subtle humour, is dynamic, thought-provoking and quite advanced (exactly in TheĀ Goldilocks Zone for Simon, as far as I could judge), yet broken up into easy-to-digest pieces. It’s difficult to predict how Simon’s path as a World Science Scholar will unfold (I’m afraid of making any predictions as he is extremely autodidact), but so far we have been very pleased with the nature of this program and it seems to match our non-coercive, self-directed learning style. I have especially liked one of the course’s main postulates: “Simultaneity is in the eye of the beholder”.

Simon watching Brian Greene’s Special Relativity course
Studying light clocks
Light clocks. Does the moving light clock tick slower?
Simon thinking about the question: Does the moving light clock tick slower?
Group, Math Riddles, Murderous Maths, Notes on everyday life

MathsJam 18 June 2019

This was the last MathsJam this academic year and a very social one. Simon has enjoyed the outside setting and mingled with the other mathematicians.
Simon had also contributed two problems (numbers 3 and 5). Unfortunately we haven’t seen anyone solve them (the problems come from the Russian math olympiad published in the magazine Kvantik).
Simon had recognized two problems he knew the answers to. Here he is explaining the persistences problem (number 13).
The smallest number with persistence 5 is 679
Simon trying to prove that the solution to problem number 2 is e.
Coding, Computer Science, Contributing, Group

Example of Simon contributing an issue on GitHub

Below is Simon’s issue/ topic suggestion he contributed to the Coding Train GitHub yesterday, addressed to Daniel Shiffman:

Function Overloading

Nah.

Operator Overloading

OK, first, we have to understand the valueOf() function. valueOf() is a function, that typically performs on a string, that converts it into a “primitive” data type.

A number is a primitive data type, because it’s not an object. And, you can see that by opening a Terminal window, running node and type:

> 2 + 2 // and get
4

Because JS doesn’t have any “real” overloading, you can’t put + in between two objects, in between two objects, and get an answer!

Well, with one slight exception, which is the valueOf() function. It will tell JS how to interpret an instance of an object as a primitive data type, whenever you want to add them together or something. If you put a valueOf() function into the prototype (or class, if you will) of an object, and it converts it into a number, or some other primitive data type, you can suddenly do arithmetic on these objects!

This does have a limitation, though. Say you write a class:

class Vector {
  constructor(x=0, y=0) {
    this.x = x;
    this.y = y;
  }

  // Maybe you want a valueOf() function to add them together
  valueOf() {
    // TL;DR What goes here???
  }
}

Maybe you want to add the individual components of a vector to add two vectors together.
It turns out, the answer is, nothing can go in the place of the question mark!

Here’s why: There’s no real primitive data type, with further components. That’s because that’s what a primitive data type is! It doesn’t have data, it is it’s own data! A Vector does have further components, however, and so we arrive at a contradiction. Because a vector has further components, and valueOf() must return something without further components, this situation is impossible!

String Overloading

Well, it’s really the same as Operator Overloading, except you need to use the toString() function instead of the valueOf() function. It converts it into a string. I don’t really know why you’d want to do this, maybe you would affect how you print it. I actually don’t even know if toString() can do this.

[TL;DR] Overloading

Look at this messy video about Matrix Math that you made: https://www.youtube.com/watch?v=NgZAIkDcPkI, at 23:15.

Guess what, there’s a way to fix that!

I don’t know how this one is called. When you say this, it’s an object. But, because objects are associative arrays, you can actually treat this as an associative array! Something like this:

class Matrix {
  constructor(rows, cols) {
    this.rows = rows;
    this.cols = cols;
    // this.data = []

    for (let i = 0; i < this.rows; i++) {
      this[i] = []; // OMG
      for (let j = 0; j < this.cols; j++) {
        this[i][j] = 0; // OMG
      }
    }
  }
  // .
  // .
  // .
}

It’s as easy as that!
If you want to, you could even add a this.length variable, and suddenly, you would even be able to iterate over it, with a for..of loop!

Coding, Community Projects, Computer Science, Contributing, Geometry Joys, Group, Milestones, Murderous Maths, Notes on everyday life

More examples of Simon’s chat contributions on math and coding

Simon is always extremely active in the discussions about the current projects made by/ lectures given by NYU’s Asdociate Professor Daniel Shiffman during his live sessions on the Coding Train channel. He also enjoys “initiating discussions” among the channel’s patrons (grown-up programmers) and Daniel. “Mom, the discussion I initiated is still going on!” I couldn’t possibly post all the coding and math comments/ suggestions that Simon makes in the chats on YouTube, Slack and GitHub (and I don’t believe I should either), but every now and then, I like collecting samples of Simon’s contributing to the discussion:

Simon contributing to a discussion prior to a live session on ray tracing
Simon contributing to Daniel Shiffman’s tutorial on the computational geometry “minimum spanning tree” problem

The small font above says:

Correction: The MST problem does not allow any loops (like A->B, B->C, C->D, D->A again.) So the solution at 2:30 is wrong! In fact, _no wonder it does that_, because Prim’s Algorithm will never find a loop. Here’s why:

Let’s suppose that it could find a loop (let’s say, a loop of 4, so A->B, B->C, C->D, D->A again, but this argument would work the same each way.) Ok, so it will start from A, and mark it as reached. It will check A against B, C and D, find B, and mark B as reached. Then, it will check A against C and D, and B against C and D. and it will find that it should connect B and C, and mark C as reached. Then, it will check A, B and C all against D, and find that it should connect C and D, and mark D as reached. But now, we reach a problem. It will not connect D and A, because both are already reached!

Why was it designed like that? Because that’s what the problem says! It’s a Minimum Spanning _Tree_, so it can’t have any loops.

So there you go, that’s why Prim’s algorithm will not find a loop.

Coding, Computer Science, Contributing, Group, Milestones

Simon’s Computer Science Algorithm Suggestions

Simon’s suggestion for the Coding Train on GitHub:

Because I like computer science these days, here are some computer science algorithm suggestions:

  • Data Structures
    • Array
    • Linked List
    • Hash Table
    • Stack
    • Queue
    • Priority Queue (Binary heap)
    • Suffix Array
    • Graph Theory
      • Graph (general)
      • Tree
      • Binary Tree
        • Full vs. Complete
        • BST
        • Binary Heap
        • AVL Tree
        • Red-Black Tree
        • Segment Tree
        • DFA
      • Biparite
      • UFDS
      • Fenwick Tree
      • Min Spanning Tree
      • Suffix Tree
    • Computational Geometry
      • Polygon, etc.
  • Algorithms
    • Shuffling
      • Fisher-Yates Algorithm
    • Sorting
      • Bubble Sort
      • Selection Sort
      • Insertion Sort
      • Merge Sort
      • Quicksort
      • Counting Sort
      • Radix Sort
      • More?
      • Even More? (Scroll down to see a GIANT table)
    • Traversal / Pathfinding / SSSP
      • Basic
        • Pre-order
        • In-order
        • Post-order
        • Depth-first
        • Breadth-first
        • More?
      • Shortest Pathfinding
        • Dijkstra’s Shortest Path
        • A*
      • More?
      • Even More?
    • Substring Finding
    • Min Spanning Tree
      • Brute-force
      • Kruskal’s Algorithm
      • Prim’s Algorithm(s)
    • Max-flow
    • Graph Matching
    • Cycle Finding
    • Convex Hull
      • Gift Wrapping
      • Graham Scan
      • Quickhull
      • “The Ultimate Planar Convex Hull Algorithm”
      • More?
    • Min Vertex Cover
      • Brute-force
      • MVC
      • Approximation
    • Traveling Salesman
      • Brute-force
      • Dynamic Programming
      • Approximation
    • Steiner Tree

If you’re brave, Do you want more even after all of this?
One last note: you’re not going to do all of them (probably!).

Crafty, Geometry Joys, Group, Logic, Milestones, Murderous Maths, Notes on everyday life, Together with sis

Vladimir Krasnoukhov at MathsJam Antwerp!

all these beautiful puzzles we have received from Vladimir Krasnoukhov

When we arrived at the MathsJam last Tuesday, we heard a couple of people speak Russian. One of them turned out to be a well known Russian puzzle inventor Vladimir Krasnoukhov, who presented us with one colorful puzzle after another, seemingly producing them out of thin air. What a feast! Simon got extremely excited about several puzzles, especially one elegant three-piece figure (that turned out to have no possible solution, and that’s what Simon found particularly appealing) and a cube that required graph theory to solve it (Simon has tried solving the latter in Wolfram Mathematica after we got home, but hasn’t succeeded so far).

Vladimir told us he had been making puzzles for over 30 years and had more than 4 thousand puzzles at home. Humble and electricized with childlike enthusiasm, he explained every puzzle he gave to Simon, but without imposing questions or overbearing instructions. He didn’t even want a thank-you for all his generosity!

Vladimir Krasnoukhov and Simon

Vladimir also gave us two issues of the Russian kids science magazine Kvantik, with his articles published in them. One of the articles was an April fools joke about trying to construct a Penrose impossible triangle and asked to spot the step where the mistake was hidden:

Simon was very enthusiastic about trying to actually physically follow the steps, even though he realized it would get impossible at some point:

Simon and Neva constructing the shape that “allows” to convert it into Penrose impossible triangle (as seen in the optical illusion in the Kvantik magazine)
the next step was already impossible

Simon’s also working on other math problems from the magazine, so more blog posts about Kvantik will follow. We’re very happy to have discovered the website https://kvantik.com

You can find out more about Vladimir Krasnoukhov’s puzzles on planetagolovolomok.ru