Albert Einstein, Physics And Reality [General Consideration Concerning The Method Of Science] (1939),

Basic Math in Japanese

あけましておめでとうございます

I’m sorry for the lack of posts recently, I promise I didn’t forget about this blog.

I hope you all find this useful. I formatted the post this way so you can see the phonetic guide. Let me know if it is hard to read; I can upload it again without the guide.

the limits of the universe

Tesserac t Visio n

Blanet: A new class of planet that could form around black holes

The dust clouds around supermassive black holes are the perfect breeding ground for an exotic new type of planet.

Blanets are fundamentally similar to planets; they have enough mass to be rounded by their own gravity, but are not massive enough to start thermonuclear fusion, just like planets that orbit stars. In 2019, a team of astronomers and exoplanetologists showed that there is a safe zone around a supermassive black hole that could harbor thousands of blanets in orbit around it.

The generally agreed theory of planet formation is that it occurs in the protoplanetary disk of gas and dust around young stars. When dust particles collide, they stick together to form larger clumps that sweep up more dust as they orbit the star. Eventually, these clumps grow large enough to become planets.

A similar process should occur around supermassive black holes. These are surrounded by huge clouds of dust and gas that bear some similarities to the protoplanetary disks around young stars. As the cloud orbits the black hole, dust particles should collide and stick together forming larger clumps that eventually become blanets.

The scale of this process is vast compared to conventional planet formation. Supermassive black holes are huge, at least a hundred thousand times the mass of our Sun. But ice particles can only form where it is cool enough for volatile compounds to condense.

This turns out to be around 100 trillion kilometers from the black hole itself, in an orbit that takes about a million years to complete. Birthdays on blanets would be few and far between!

An important limitation is the relative velocity of the dust particles in the cloud. Slow moving particles can collide and stick together, but fast-moving ones would constantly break apart in high-speed collisions. Wada and co calculated that this critical velocity must be less than about 80 meters per second.

source

I love statues like this. How does someone have so much talent?

An Oxford student looking through a book on sale England, 1950

This is the Maiden of Llullaillaco, an Incredibly Well-Preserved Child Sacrifice from the Incan Empire around 500 years ago. 

The Maiden of Llullaillaco, sacrificed at around the age of 15, was discovered with the other “Children of Llullaillaco” which includes a 6 year old girl and a 7 year old boy.

These mummies are so well preserved due to their position within a tomb atop a mountain within the extremely dry Atacama Desert. They are so well preserved, that their internal organs are intact, individual hairs on the arms can be seen and even one of the heart’s still contains frozen blood.

The deaths of the three children occurred by drugging the children with alcohol and coca, then placing them in the tomb where they eventually died in their sleep. This appears to have been a very well prepared process, as hair samples dictated that the children had extremely rich diets leading up to their deaths. The tombs were also adorned with elaborate dress and trinkets.

The boy however, faced a different death that could’ve indicated struggle or a different burial process. The boy was very tightly bound, and had dislocated hips and ribs and it appears he died under stress as the clothing contains both vomit and blood. Suffocation is the likely cause of his death due to the way he was bound.

Beautiful proofs (#4) - When Gauss was a young child...

The legend goes something like this:

Gauss’s teacher wanted to occupy his students by making them add large sets of numbers and told everyone in class to find the sum of 1+2+3+ …. + 100.

And Gauss, who was a young child (age ~ 10) quickly found the sum by just pairing up numbers:

Using this ingenious method used by Gauss allows us to write a generic formula for the sum of first n positive integers as follows: