LL 12

 This week I had a thought about ecosystems. Image a population of foxes and a poulation of rabits, if you graph the amount of foxes to the amount of rabbits the result on the x-y plane is a counterclockwise circle that repeats over and over. However, in nature there is randommnes on which creatures live and die. Imagine the point is on the bottom portion of the circle, if the point by randomness moves up, the circle will shrink, if it moves down the circle will grow, however if it moves left or right, the circle also grows. This shows that because of chaos it is more likely that the circle will grow than shrink, so over time the circle will grow. The circle will continue to grow until either all the predators die or all the prey die.

LL 11

This week I learned some java, and created some programs! I created a math game, and am trying to make some others. I also learned about celular biology and that trees mostly geth their mass from the air. I also learned about taylor series and how you can use polynomials to create approximations for functions in a certain range!

LL 10

 This week I learned about how holograms are made. It's a very facinating process, I learned about how a 2D peice of film can contain a 3D image. I also learned a lot about the nature and science of light. The most surprising thing I learned is that if you have two light scources both illuminating the same plane, the resulting wave pattern is not just the two light waves added together. They are combined in a different way.

Here's the video:

LL 9

 This week I learned about an interesting function called the ruler function which is the number of ones that you carry when counting in bianary. I tried to see how many digits of the ruler function I could name before I lost track and got to 1,024! I also learned about the USS arizona, a ship that was destroyed in the japenese attack on pearl harbor. Almost half of the casualties from pearl harbor were from the sinking of the USS arizona. I was in Scottsedale, Arizona and was able to see part of the wreckage and learn about the ship and how it worked, it was very interesting.

 I also went on a hike and saw delicate arch which is the arch used on some utah licence plates, it's amazing to see up close!

LL 8

 This week I learned about the three kingdoms era of chinese history. It was very interesting, it was one of the most chaotic war periods in all of history! This is a video I watched about it that I really liked.

https://www.youtube.com/watch?v=26EivpCPHnQ 

I also learned about economics and politics in the book "The end of the world is just the beggining" by Peter Zeihan. He talks about what he thinks will happen to economies and politics in the futire and I think it's facinating. I also learned some python, it's a lot easier than C#. The makers of python made it more efficientfor proggrammers to write but it's not as fast.

LL 7

 This week I learned a little bit of calculus from an interesting video series!

https://www.3blue1brown.com/topics/calculus 

I also learned some algebra from a book we have, I actually kinda liked it! I also reached a new high score on the evolution simulator that I mentioned in a previous blogpost. I got 56% fitness for running!

This week I also learned some grammar and got much more comfortable with a couple different grammar related topics.

LL 6

 This week I learned about the science section of the SAT. I learned more efficient ways of answering the questions and interpreting the graphs quickly. I also Leaqrned about the underground railroad a network of anti-slavery houses that escaping slaves could use to escape, it was facinating! I also learned more english. It's starting to click a little more now, it's starting to make more sense!

LL 5

 This week I did a lot of ACT prep, I took a practice ACT test and got a 23! I worked really hard on english and I got a lot better. I learned about redundancy and how it clogs up the reading. (IM rly, good et; EENGLISH) I also found a really cool evolution simulator. You build a creature and then it uses AI to try to make that creature run as fast as possible. I also learned about logrithms and how exponents have two inverses!

 https://keiwan.itch.io/evolution

LL 3

 I did some prep work for the ACT today.    (learnned grammer--i has; Fun, it wuz, very, good, timee;:,.)     I also did some work on algebra and enjoyed that too! I watched an intereting video about LLM's or large language models (AI's for speech like chatGPT)

https://www.3blue1brown.com/lessons/mlp. 

I also learned about a surprizingly difficult math problem.

The worlds best mathmeticians could't solve this in six hours! Here's a link to the solution if you're interested.

https://artofproblemsolving.com/wiki/index.php?title=1988_IMO_Problems/Problem_6

 I also found this thing called emoji kitchen where you can mix emojis, here are some of my favorites:

https://www.google.com/search?q=emiji+kitchen&oq=emiji+kitchen&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIPCAEQABgKGIMBGLEDGIAEMg8IAhAAGAoYgwEYsQMYgAQyCQgDEAAYChiABDIJCAQQABgKGIAEMg8IBRAAGAoYgwEYsQMYgAQyDwgGEAAYChiDARixAxiABDIGCAcQBRhA0gEIMzEzMmowajeoAgCwAgA&sourceid=chrome&ie=UTF-8

LL1

 This week I learned about C#,  a programming language known for being good for making games. I'm still learning the basics, but it's been a lot of fun! I also learned the basics of EMS (Emergency Medical Response), the ethics and legal issues, how to take pulse and how to take off contaminated gloves. I also learned about polynomial long division which you would use if you had one polynomial that you wanted to divide by another. I also learned a few drumming techniques including rolls, grace notes and accents.

LL40

 I was researching celular atomata and wanted to know what "class" meant because whenever I looked up of the celular atomata is listed them as class 1, 2, 3 or 4. I then researched it and foud out it measured how chaotic it was

I finished making a computer program that generates art.

https://scratch.mit.edu/projects/1016183279/

Here are some of my favorites

The one below kinda looks 3D especially in the blue stripe area

LL39

 This week I learned about a type of AI convolutional neural networks, which are like ordinary neural networks exept each layer is lika a grid instead of a line of neurons and each cell only effects the ones nearby. This is particularly good at recognizing patterns that traditional neural networks can't. There most effective for image proccesing because the data is already in a grid so patters are more likely to appear there.

LL38

 This week I took a course on AI. I learned about how to collect and refine data and how to train a neural network. I also learned about newtons fractal, which uses newtons method for finding roots on the complex plane and coloring each point based on what root it lands up on.

LL36

 I watched a video on the physics of car crashes, it was very interesting. The video talked about the many ways car manufatres protect the people in the car. The goal for the car manufacturer is to make the frontal area crush, but the drivers box stay intact, when the frontal area is crumpled it slows the driver down a lot slower than it would if the frontal area was rigid. 

LL35

 This week I took the ARML math test, I got 2/10 which is decent I guess. One of the problems I got right was a combinatorics problem that no one else got right.

LL 34

 This week I wrote an incomplete essay on the technological singularity, here it is:

The technological singularity is the idea that if humans could build an AI smarter than themselves,

it would be a better designer and hence be able to make an even more intelligent AI. This process would

then continue and possibly produce an infinitely intelligent being.

It would be nearly impossible to predict what life would be like for the average human if a superintelligent

being existed; however if the AI is motivated to create better and better versions of itself, it may try

to take over the world and use the world's resources for more computing power.

A self improving computer does not however necessarily produce a superintelligent being. If, for example,

it becomes harder and harder for the computer to improve itself it may take an ever increasing amount

of time for the computer to double in intelligence.

If the computer takes a fairly consistent amount of time to double in intelligence the graph

would look more like this.

While this would lead to exponential growth it does not approach infinity, if however it takes less and less time to double in intelligence it will in theory reach an infinite amount of intelligence in a finite amount of time.

LL 33

 This week I learned about AI and chat GPT, it uses an algorithm called the backpropogation algorithm to try to build what's called a neural network. The neural network tries to figure out what word it should do next.

https://www.3blue1brown.com/topics/neural-networks

I also found a cool AI based guessing game called akinator. It tries to guess the person you're thinking of, it's been able to guess all of mine. The most guesses it took for me was 50 for Terrence Tao, I haven't won any games yet.

https://en.akinator.com/

LL 32

 This week I learned about tetration, which is repeated exponentiation, wich is repeated multiplication, which is repeated addition. Repeated tetration is called pentation and repeated pentation is called hextation. tetration is so hard to compute that for all we know pi terated to itself could be a whole number.

I also found a cool website called neal.fun, it's got really cool educational games. This is one of them, it's called the size of space.

https://neal.fun/size-of-space/

LL31

This week I learned about quantum mechanics and how light is an occilation in the electro magnetic field, it was very interesting.

I also learned about electrical engeening and kirkoffs law which says that all currents entering a node must have a sum of zero.

LL30

This week I learned about logical fallacies like the strawman fallacy, begging the question, circular reasning, etc. I also started learning python, and that's been fun. I took a social skills course and learned about body language and how to be more confident.

LL 29

This week I attended a BYU math club, the week's lesson was on the pidgeonhole principle. The pidgeonhole principle says that if you have less categories then objects, one or more objects must be in the same category. For example, if you have three gloves you have to have either two left or two right because there are only two categories, left and right.

I got most of the problems from the math club right, here is an example of one of the problems.

Imagine you have six boxes labeled one through six. What is the minimum number of balls you must have so that it's immpossible to not have a box with more than N^2 balls?

LL 28

This week I learned about how membranes are formed, certain molecules are hydrophobic on one side while hydrophilic on the other side so the molecule forms into a sphere with hydrophilic parts touching the water on the outside and inside. And hydrophobic molecules touching each other between the two layers.

I also took the test to get into the mega society called the ultra test, which you have to have a one in a milliion iq to pass. I didn't even get close, but I learned a lot.

https://megasociety.org/admission/ultra/

                                                           Mega society logo

LL27

 This week Michael did his Art of Problem Solving class.  There were several problems giving him trouble but he worked through them patiently.  I think he learned more about perseverance and communicating with the team helping him.  He's been writing in his journal consistently, which makes me so happy. He also enjoyed his BYU math club class even though the problems were too difficult for him.  He took a book from my mom's house and reads a concept each night about how to be better.

LL 26

 This week I solved a difficult math problem that I've been working on for a while.

How many sequences of 15 coin flips have 5 HH 4TH 3HT 2TT for example HHTTTTH has 1 HH 1 TH 1HT and 3 TT.

Solution: Imagine we only cared about the 4TH and 3HT, the only sequence of flips that works is THTHTHTH. To build up to the actual problem we need to add the 5HH and 2TT, there are four different places we can put the HH, they are where the H's are. So it's equivalent to putting 5 balls into four buckets which is 5 choose four or 56 possibilities for H, using a similar argument we can show that there are 10 possibilites for T. And 56*10=560 which is our answer.

(this isn't explained super well, here's the official solution.)

LL 25

 This week I learned about differential equations, differential equations are equations that show how a system will change rather then how it is at any given moment. They're usefull for nearly every field of math and science, especially phicics.

I also made a game called light beam frenzy.

https://scratch.mit.edu/projects/955832773/

https://www.3blue1brown.com/lessons/differential-equations

LL 24

 This week I watched an interesting video on convolutions, a convolution is a way of combining two lists of numbers in which you reverse the order of one list, align the first item of one list with the last of the other, multiply then "slide" one over so that two items now alighn, multiply add the two results then slide again and repeat until the process is complete. It's usefull for probibility and image proccesing.

I'm also reading a book called seven tipping points that saved the world, it's currently talking about the battle of britain and how britain useddeception and exeptional planning to defeat the germans who had more expirience, money, aircraft ect.

LL 23

  This week I learned about the quantum uncertainty principle, the more certain you are about the speed of a quantum particle the less certain you can be about it's position and vice-versa. I also learned about knot theory and the möbius strip, a two dimensional object in three dimensional space with one side! 

I read more of the count of monte Cristo, which I'm having trouble following but the count just saved someone from a horse accident I think he caused.

LL 22

 This week I learned about error correction codes and how they detect errors in data and correct them

https://www.3blue1brown.com/lessons/hamming-codes

I learned about extranious solutions to equations, they happen when you do 

LL19-21

This week I read some of count of monte cristo, it's currently talking about the festival of rome which was a huge festival that took place in ancient times. I am also reading a book called grit, It's about what highly successfull people do different from others. It's talked a lot about passion, succesful people are often very passionate about something.