art, Crafty, Geometry Joys, Math and Computer Science Everywhere, Math Riddles, Murderous Maths, Notes on everyday life, Simon makes gamez, Simon teaching, Simon's sketch book, Together with sis

Math puzzles: Is it Possible?

Simon has been fascinated by these possible-impossible puzzles (that he picked up from the MajorPrep channel) for a couple of days. He prepared many paper visuals so that Dad and I could try solving them. This morning he produced this beautiful piece of design:

Simon showing one of the puzzles to another parent while waiting for Neva during her hockey training
Simon’s original drawing of the doors puzzle. The solution of the puzzle is based on graph theory and the Eulerian trail rule that the number of nodes with an odd degree should be either 0 or 2 to be able to draw a shape without lifting your pencil. The number of rooms with an odd number of doors in the puzzle is 4 (including the space surrounding the rectangle), that’s why it’s impossible to close all the doors by walking though each of them only once.
Simon explaining odd degree nodes
Computer Science, Crafty, Logic, Math and Computer Science Everywhere, Murderous Maths, Simon teaching, Simon's sketch book, Together with sis

The Diffe-Hellman key exchange algorithm

This is Simon explaining Diffe-Hellman key exchange (also called DiffeHellman protocol). He first explained the algorithm mixing watercolours (a color representing a key/ number) and then mathematically. The algorithm allows two parties (marked “you” and “your friend” in Simon’s diagram) with no prior knowledge of each other to establish a shared secret key over an insecure channel (a public area or an “eavesdropper”). This key can then be used to encrypt subsequent communications using a symmetric keycipher. Simon calls it “a neat algorithm”). Later the same night, he also gave me a lecture on a similar but more complicated algorithm called the RSA. Simon first learned about this on Computerphile and then also saw a video about the topic on MajorPrep. And here is another MajorPrep video on modular arithmetic.

originally there are two private keys (a and b) and one public key g
Neva helping Simon to mix the colors representing each key
Mixing g and b to create the public key for b
Mixing the public and the private keys to create a unique shared key
Done!Both a and b have a unique shared key (purplish)
Simon now expressed the same in mathematical formulas
Simon explained that the ≡ symbol (three stripes) means congruence in its modular arithmetic meaning (if a and b are congruent modulo n, they have no difference in modular arithmetic under modulo n)
Exercise, Notes on everyday life, Together with sis

Vacation Milestones

A couple more milestones passed! Going on a Ferris wheel after having been afraid of heights for years. “Mom, do you know how many rays there are? I’ll tell you: it’s the only time that exponentiation is commutative!”

Diving deep into the water (after being afraid to put his head underneath the water for years), swimming to the platform in the sea and diving from the platform, using a diving mask.

the platform Simon has been diving from is seen in the background
Milestones, Murderous Maths, Notes on everyday life, Simon teaching, Together with sis

My little pure connections to Simon, now 10 years old

What do I love most about Simon’s learning style and being around him are the precious moments he pulls me out of my regular existence, sits me down next to him and shares a piece of his sharp vision with me. I often take notes to make sure I haven’t missed out on the details. Reading back the notes I am often surprised at the hidden layers in his razor-sharp logic that hadn’t revealed themselves to me at first or had even seemed irrelevant to my journalist mind eager to cramp everything to the size of a cocktail bite. Sometimes, Simon takes over and types the rest of the blog entry himself. Like this time.

Dad says he saw someone by the swimming pool reading the book A Mathematician’s Apology. We google it and find out it’s a 1940 essay by British mathematician G. H. Hardy about the beauty of pure mathematics. Knowing how much Simon is drawn towards pure mathematics and that he, too, prefers pure mathematics to applied mathematics, I tell him about our discovery. Simon replies that it’s a silly question to ask him whether he knows Hardy: Yes, Hardy was actually the one who invited Ramanujan!

Simon pauses his breadboard tutorial, comes to the balcony with the view across the Cote D’Azur, sits down against the wall of bright purple flowers and patiently tells me an interesting fact about Hardy. It’s just a fleeting tiny conversation, but the beauty of Simon’s precise memory, the connection I feel to Simon and the setting is so striking I would rather grab my video camera but I don’t dare move as not to lose momentum. I later ask Simon to repeat the facts he told me so spontaneously.

“Hardy came up with the total number of chess games. Well, Shannon estimated it to be 10^120, however Hardy estimated it to be 10^…, 10^50.

Clarification: the former is:

1 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

(1 with 120 zeros)

And the latter is:

1 with 100 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 zeros

(1 with, a 1 with 50 zeros, zeros)

The picture is taken on August 16 when Simon turned 10
Simon’s age in binary
Exercise, Geography, Notes on everyday life, Physics, Together with sis, Trips

Some more London

Taking the Thames Clipper
At London’s olympic pool: Simon and Neva took part in the Ultimate Aquasplash, an inflatable obstacle course for competent swimmers that involved sliding down a 3-meter high slide into deep water – another personal victory
At the Queen Elizabeth Olympic Park
Generating power on a bicycle (you could see how many watt you generate)
At a 3D film for the first time
Back to the Science Museum
Astronomy, Experiments, Geography, history, Milestones, Notes on everyday life, Physics, Space, Together with sis, Trips

We’ve found the real 0° meridian!

And it turned out to be a that little path next to the Royal Observatory in Greenwich, not the Prime Meridian line. The 0° meridian is what the GPS uses for global navigation, the discrepancy results from the fact that the Prime Meridian was originally measured without taking it into consideration that the Earth isn’t a perfect smooth ball (if the measurements are made inside the UK, as it it was originally done, this does’t lead to as much discrepancy as when vaster areas are included).

Simon standing with one foot in the Western hemisphere and the other one in the Eastern hemisphere
The GPS determines the longitude of the Prime Meridian as 0.0015° W
Simon tried to use JS to program his exact coordinates, but that took a bit too long so we switched to the standard Google Maps instead
The Prime Meridian from inside the Royal Observatory building
Looking for the real 0° meridian: this is an open field next to the Royal Observatory. At this point, the SatNav reads 0.0004° W.
And we finally found the 0° meridian! Some 100 meters to the East of the Prime Meridian
The 0° meridian turned out to intersect the highest point on the path behind Simon’s back!
Simon and Neva running about in between the measurements of longitude
Astronomer Royal Edmond Halley’s scale at the Royal Observatory
Halley’s scale is inscribed by hand
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
art, Coding, Geometry Joys, Murderous Maths, Museum Time, Notes on everyday life, Together with sis, Trips

Back at Stedelijk

As for Morellet’s RGB colored cells, very inspiring for a sandpiles coding project. (The photographs don’t convey half of the effect the original canvasses invoke. Morellet’s cells actually appear to be moving when you gaze at the original).
Installation by Barbara Kruger
Installation by Barbara Kruger
Read this poem from top to bottom and it’s depressing, from bottom to top and it’s empowering.