Map of the piano chords

During his piano lessons, Simon has been working on a diagram that would map all the possible chords on the piano. I gave him a huge roll of paper to draw on that he spread on the floor of his piano teacher’s studio. He said he wanted to create a network of chords and how you go to other chords. “Music is basically like finding a path through the network that you like, messing with but preserving the chords in the network. What do I mean by preserving? There’re 4 things that you can do to a chord to preserve it:

  • move some of the notes in the chord by multiples of an octave (like 1 octave, 2 octaves, 3 octaves, etc);
  • split up or mix some of the notes in the chord (taking one note and splitting it into two copies of the same note you start with but in different octaves or mixing the note from two octaves into one);
  • get rid of some notes in the chord;
  • there are some notes you can add to the chord and preserve it.

So far, Simon has been able to map C Major and A Minor tonalities. He got a little bit stuck, but is determined to continue.

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Simon explaining Interstellar

Simon didn’t want to watch Interstellar (he generally dislikes fiction and often finds it too scary as well), but somehow he did get sucked into the story after his sister and I were watching the movie right next to him for several days in a row and talking about it extensively. It’s one of my favourite films and I so much wanted Simon to see the part about time dilation and the black hole, and hear his thoughts about those scenes. I admit they were quite difficult for me to grasp when watching the film for the first time, especially the scene where the main character finds himself in the tesseract and has multiple visions of his daughter from the past. When we got to the scene, Simon was on fire. He kept walking around the room, euphoric  as he was explaining to me how he understood what was happening on the screen:

“They used the many worlds interpretation! The many worlds interpretation is an interpretation of the collapsing of the wave function. It says that the wave function doesn’t collapse, we just find ourselves in a universe where it collapsed intone particular possibility. And there is theoretically another universe where something else happened and there is another version of us experiencing that. This produces uncontrollably infinitely many universes just to get out of collapsing the wave function. What they use is  a metaverse – the multiverse of the many worlds interpretation!

Those grids of shelves are the multiverses! And then there’s a grid of those grids of shelves and that’s a metaverse. A metaverse of all of the multiverses of the many worlds interpretation at every single point in time!

I know why it’s 5-dimensional! It’s the 3 dimensions of space, the 4th number indicates what universe it is in the multiverse, and the last number is which multiverse it is in the metaverse! Which is a time dimension, because it’s metaverse of all the multiverses of the many worlds interpretation at every single point in time. And notice, these are all real numbers! Even the 4th and the 5th dimension can be any real number because there are only countably infinitely many natural numbers, integers and even rational numbers”.

The Senses: Simulating Taste and Smell

You need 24 bits (8 bytes) to simulate color. That’s 24 ones and zeros. How many bits are necessary to simulate taste? Or smell?

Correction: You would need 584 bits to express smell, not 654 (Simon made a mistake in the original calculation).

The Senses: What color is the dress?

A couple of years ago this dress went viral on the internet as some people argued it was blue and black and others saw white and golden. To this day neuroscientists haven’t found an explanation to this. Simon analysed the actual colors as they appear on the screen using the ShareX app. So what color is the dress?

Serious questions

“Mom, photons violate E = mc²  and gluons violate E = mc²!” – Simon shouts, but what about the w and z bosons? He writes down the masses of the w and z bosons expressed in gigaelectronvolts per speed of light squared. If these bosons don’t violate E = mc², he argues, their energy levels would actually equal their mass, as the speed of light squared would cancel out. “I think my hypothesis is false, because it breaks the law of conservation of energy”, he mumbles. The question remains unanswered.

Correction: the actual mass of a w boson is 80.385±0.015 GeV/c2, Simon made a small mistake, as he found out later.

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“Mom, a neutrino passing by a neutron, in order for the neutron to decay, the neutrino has to be really close to the neutron because the lives of the w and z bosons are only 6 x 10^-25 seconds!” Simon is walking around screaming: “zero, zero,zero,zero”, actually saying the life expectancy of a boson out loud: 0.0000000000000000000000006 seconds.  “And these bosons do have mass! they just wander into the neutron with a very low chance of actually hitting the neutron (they don’t go in a straight line like photons)!”

I believe Simon has started asking serious questions… Thinking maybe it’s about time to sign him up for some online college course in Physics? Any MOOC suggestions?

 

Physics Experiments: Slime for Science

We had such a genuinely rewarding homeschooling experience yesterday when we took up Physics Girl’s challenge to recreate the Weissenberg effect – a phenomenon that occurs when a spinning rod is inserted into a solution of elastic (non-newtonian) liquid.

Our first attempts to make slime following Physics Girl’s recipe (1/2 cup PVA glue, 1/2 water plus 1/4 tsp borax dissolved in another 1/2 warm water) failed so we returned to the department store to get starch, a different type of glue and anything else that might help. Did we use the wrong glue? What is borax (originally, we thought it was the same as the salt used to clean the dishwasher)?

After we started asking around, the shop assistants threw in a couple of handy tips (like getting some fluid used for cleaning your contact lenses as it contains something like borax, borate buffers, and mixing that with glue and shaving cream). At the drug store, we got warned about the dangers of pure borax powder if used in large quantities (skin burns), but did manage to get a tiny bottle of the stuff after we assured that it was for an adult supervised experiment. With all this useful info and terribly tired, but fully equipped we returned home and resumed our attempts at mixing perfect slime. You can see for yourself in this unlisted video how we went about it.

Eventually, we ended up adding twice (in not thrice) the amount of borax to finally froth up the right consistency non-newtonian fluid and it just worked!

https://www.youtube.com/watch?v=p5tA1jd5Byc

(Instead of being thrown outward, the solution is drawn towards the rod and rises up around it. This is a direct consequence of the normal stress that acts like a hoop stress around the rod).

Simon wrote: In this video, I make slime “climb” up! It’s because of the “viscoelasticity” of the slime.

Correction: I’ve made a mistake when I said “times H2O”. The dot in the formula didn’t mean “times”, it meant ion.

The borax formula was indeed what Simon called “a mouthful”: Na2[B4O5(OH)4]·8H2O where the dot refers to the elements in square brackets all forming the [B4O5(OH)4]2− ion.

So what is borax? It’s a mineral, a salt of boric acid, also called (di)sodium tertaborate, usually possessing a crystal water content (although the commercially available borax is partially dehydrated).

Thanks to more borax, check out how high our fluid rose – it came out the other side of the straw!

https://www.youtube.com/watch?v=1AlWfVlBaQU

Chemistry Experiments: Colors (surface active agents and pH indicator)

Our new MEL Chemistry box arrived, containing tons of color fun! We have already tried two experiments. In the Color changing milk experiment, the soap touches the milk creating a very thin film of soap on the milk’s surface and causing the colors to spread along with it, producing a mesmerising effect. Molecules of soap and other similar substances lower the surface tension of different liquids and thus are called surface-active agents (SAA). Simon took it a notch further and created antibubbles that glide on the film of soap:

 

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We thought this one looked like a nuclear explosion:

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The second experiment we did was called Magic Liquid and felt like performing a magic trick: a yellowish liquid poured in five different cups turned five different colors, almost all the colors of the rainbow! The secret was putting a tiny bit of a different chemical substance on the bottom of every cup beforehand. The yellowish stuff was actually Thymol blue, also known as thymolsulfonephthalein (chemical formula C27H30O5S ), a pH indicator, and changed color according the acidity of the substances that were already in the cups. The larger the quantity of protons H+, the higher the acidity of the medium, while the OH ions are responsible for the basic medium:

 

Thymol blue molecule visible on the iPad screen:

We also checked the pH of the substances using indicator standard teststrips:

The pH rainbow:

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Simon had already been busy with colors for a few days, revisiting his Magformers collection to build this gorgeous color wheel:

 

The Sky Track

Simon got a belated birthday present from his Russian grandparents, something he had dreamed about for months: the Magformers Sky Track set, sort of a monorail that allows Simon the shuttle to ride vertically and upside down, seemingly defying gravity:

 

Combining the Sky Track with a domino chain reaction:

Simon building the AND logic gate with dominos:

Simon took the Sky Track along when visiting an older friend in Amsterdam and it had great success. We generally see Simon open up more to playing together and just having genuine childlike fun instead of having continuous scruples about waisting time and the need to be working on his science and programming projects without interruption.

Simon’s whiteboard

The whiteboard always reflects Simon’s current state of mind:

On the left are Simon’s notes after reading Physics Girl’s blog about quarks (the colourful stuff is foam clay):

Simon showed this expression with Phi to his math teacher, who noticed that Simon didn’t apply the quadratic formula (with a discriminant b24ac) in his solution. The teacher wondered if Simon knows the formula. As it turned out, Simon knew the formula very well but preferred to prove the solution on his own, because it was so beautiful in the case of Phi: