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Ok

So I’m gonna share something cool as ice. I actually found this 2 years ago but never posted it.


Let me introduce this nice thing

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This sum is actually very nice. He wears a tie.

In fact if you input x=10^{-3}, and you would get this:

0.001002002003002004002004003004002006002004004005002006002006004004002008003004004006002008002006004004004009002004004008002008002006006004002010003006004006002008004008004004002012...

Ok so what’s dis? Notice that the decimals follow some pattern:

00, number, 00, number, 00, number….. And then we have some exceptions where “00” is replaced with “0” or “000”

What’s dis? There must be a pattern to the numbers right?

Let’s list down the number and see:

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12

There doesn’t seem to be a pattern is there?

BUT YOU’RE WRONG THERE IS A PATTERN

Let’s start with the first number:

  • 1: The number 1 has 1 divisor
  • 2: The number 2 has 2 divisor
  • 2: The number 3 has 3 divisor
  • 3: The number 4 has 3 divisor
  • 2: The number 5 has 2 divisor
  • 4: The number 6 has 4 divisor

Turns out that the nth number in the sequence is the number of divisors of n!

Cool right? Now why is dis so? Try to figure it out urselfgdby.

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My Views- Science Communication & Scientific Literacy

Hey Guys!

First of all, I’m sooooooooo sorry for breaking my promise and stuff. I know this is super terrible because yeah (breaking promises is bad). To make up for it, i will (probably) be writing more posts (so as long as Julian continues to pester me ceaselessly). I still want to aim for the 1 post every fortnight goal and i’ll still keep trying to achieve that someday.

Make sure you know what you’re getting yourself into before making a promise to a bunch of people

-Clyde Lhui 2016

Lately i have been getting into a lot of stuff. Stuff like learning Japanese, photography, music, cooking and a bunch of other stuff. I might be writing posts about those in future so yeah (i know i say this a lot and end up not writing but oh wells).

Well as you can probably tell by the title, this post is about science communication and scientific literacy (pretty self explanatory i guess). I feel very strongly about these 2 topics and that’s why I’m writing this post.

So first off, DEFINITIONS!

Science communication generally refers to public communication presenting science-related topics to non-experts. This often involves professional scientists (called “outreach” or “popularization”), but has also evolved into a professional field in its own right. It includes scienceexhibitions, journalism, policy or media production.

-Wikipedia

And…

Scientific literacy is the knowledge and understanding of scientific concepts and processes required for personal decision making, participation in civic and cultural affairs, and economic productivity. It also includes specific types of abilities.

-Literacynet.org

 

I know that you guys could have easily googled that but hey, 10 seconds saved is 10 seconds saved 🙂

So in short, science communication is talking to people who aren’t scientists about science and scientific literacy is knowing enough science to make logical and good decisions.

I think you are beginning to see how these 2 things are linked.

Perhaps i should further explain why i decided to write this post. In my daily life, i spend a lot of time with my friends (who are largely a group of nerds (who mostly take pride in their nerdhood)) and my family. Since i love science and i spend a lot of my time with my friends  (who are nerds), we spend a lot of time talking about science and related topics. As such, when i talk to my family about a ‘science related topic’ (I’ll explain the apostrophe later), i notice whenever something is off.

My aunts and uncles like to send long WhatsApp messages about stuff they hear from their friends and 95% of those messages that i end up reading are wrong in one way or another. My mum once showed me this video:

Well I think most of you can see why this video is wrong.

(In case you didn’t figure it out, your stomach is part of your body which is at 37 degrees Celsius for the most part)

(Also ice water warming up is kind of a thing)

I know some of you must be thinking: “I’m not stupid, i wouldn’t believe things that don’t make sense.”

Well there are quite a lot of things that people misunderstand.

For starters, nuclear power. I am a strong advocate for nuclear power. It’s clean, reliable and fairly safe. Unlike solar panels or wind turbines that stop working once the sun stops shining or the wind stops blowing, nuclear power plants can work 24/7 and supply enough power to support entire power grids. Furthermore, new nuclear plant designs which have improved safety features are constantly being suggested, making future power plants safer than before. Despite this, many people have a very negative impression of nuclear power.

Image result for nuclear power plant cooling tower

Does this look familiar?

Well it should. I have seen countless news reports about climate change showing images or videos these pumping out massive white clouds.

The only thing is these are the cooling towers of nuclear power plants.

Most people see these images and go “OH NO! We are pumping all that carbon dioxide into the atmosphere!?”. However, the white clouds coming out of the cooling towers are literal clouds: clouds of water droplets.

(Hopefully) by now you should understand the fact that we are prone to having a lot of misconceptions. It could be due to the way the media presents facts, the way social media promotes controversial content or any other reason out there. Regardless of the reason, i hope that you understand that this is pretty bad and it’s something that is extremely hard to avoid. I myself cannot claim that all the knowledge i possess is 100% accurate (in fact i do get things wrong pretty often).

What i hope you get out of reading this post is that knowledge is never absolute and that life and learning is all about constantly renewing our knowledge by being sceptical and challenging our own beliefs. We all need to keep reading and keep discussing so as to improve the accuracy of our knowledge. I think it’s also important for us to keep an open mind and not to immediately say “No that’s wrong.” when someone has contrasting beliefs (well you could but remember to provide your reasons and explain your views).

Never stop questioning your beliefs and perhaps one day there won’t be Geography teachers believing that the Earth goes around the sun in a day and rotates once around its axis in a year.

Thanks for reading!

Clyde Lhui 🙂

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Rubix Cube Proof

In this post, we will proof that repeatedly applying any algorithm on a solved Rubixs Cube would cause it to eventually return back to its solved state.

What do I mean by this? Well, supposed your algorithm is to turn the top side once. After repeating this algorithm 4 times, you would return back to the solved state right? In the problem above, “any algorithm” would refer to literally ANY ALGORITHM. For instance, your algorithm might be: R’ D D R D R’ D’ R, and repeating this algorithm a sufficient number of times on a solved cube would make it eventually return to its solved state.

This problem seems impossible right? At the very least, it probably involves some uni graph theory concept and stuff right? Before you close off (pls dont), the solution to this problem requires no prerequisites, just a grasp of logic.


Ok, here comes the solution:

To tackle this problem, I will be using this technique called “Proof by contradiction”.

For instance, if I want to proof that statement A is false, I assume otherwise; that A is true. Then I show that if A is true, absurd shit that doesn’t make sense would happen (ie. we would see a contradiction). Since A being true causes a contradiction, A must be false. Hence proved that A is false.

Got the general gist of this technique? Cause this would be fundamental in our proof.

Alright, the actual proof:

Let’s first assume that there exists an algorithm (Let’s call it “f”) that would not cycle. In other words, repeatedly applying “f” on a cube would cause it to always land in a state that it has not been before:

 

Delete.png

 

However, this would imply that a rubix cube has an INFINITE number of different states! This is a contradiction, since it is well known that a rubix cube has a finite number of states (Left as exercise of reader). Since there is a contradiction, we can safely conclude that after applying “f” sufficiently number of times, it would cause the cube to return to a state it was before.

We are not done however, as this conclusion results in 2 possible cases:

delete

Delete.png

Case 1 is where it returns to the solve state (which we want), and Case 2 is where it returns not to the solved state but to some random state within the cycle (which we want to disprove).

To disprove case 2, we employ prove by contradiction again:

Let’s define “f^{-1}” as the inverse algorithm of “f”. In other words:

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Basically, “f^{-1}” is an algorithm that REVERSES what “f” does.

So now, what happens if we replace all “f” with “f^{-1}” in the picture for Case 2? Well, it becomes this:

Delete.png

Now we will show how absurd this would be. Notice the box for “State n”. Notice how this diagram implies that applying the algorithm “f^{-1}” on state n would result in 2 possible states (State n-1 and State k). This is absurd because we know that applying an algorithm on a rubix cube will result in only 1 possible state (ie. each state should only point to 1 other state). Hence we have reached a conclusion that Case 2 is IMPOSSIBLE. Which leaves us with Case 1 as the only case that is possible.

Hence, proved, that repeatedly applying any algorithm on a solved Rubixs Cube would cause it to eventually return back to its solved state.


 

An update to the previous post: I have played with the simulator and recorded some of the animations

 

Hoped you enjoyed this post!

 

 

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Crudely Animated Cloth

Done during school. I might post more of this since I haven’t got the time to play with the “simulator” much. It might take a long time to load though since it is 50fps

 

cloth-1

Lagged my computer a lot just trying to render it. In fact I wasn’t even able to extract the animation from the school’s computer.

I used Desmos for the animation: https://www.desmos.com/calculator/ycn9inng2a

 

 

 

 

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Random Stuff done during EOY

1. Geometry Dash Effects Idea

6-10-1

Explore here: https://www.desmos.com/calculator/n3iwydn0sa

2. Exploring Ruled Surfaces

6-10-2

Explore here: https://www.desmos.com/calculator/ukty5kjfbq

3. Spu7nix’s effect

6-10-3

Context here: https://www.youtube.com/watch?v=0z1Rp3g8U7c&t=67s

Explore here: https://www.desmos.com/calculator/3wjeuxlwuc

4. Whip Gear

6-10-4

Context here: https://www.youtube.com/watch?v=w-JSWtu1oMU

Explore here: https://www.desmos.com/calculator/u6gfbffvmz

 

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Quick Post

Why is it always at 12am that I am suddenly filled with the desire to do something productive?

Anyway, this is a post regarding a class of functions that are fun (subjective), of which I might make an elaborated post about after I’m done with my Analytic Number Theory post.

I’ve yet to look into this thoroughly since I only started doing so today 1150pm so here is a special case:

 

Delete

 

Yeah, does not look so impressive… YET.

Here’s the cool part: Take out your calculator (preferably a scientific one), and ensure that it is set to Radians.

Now, find “F(1)”. Did you get “F(1) = 1”?

How about “F(2)”? Did you get “F(2)=2”?

Continue to do this until “F(4)”, do you see the pattern?

What about “F(5)”? Oh? It loops back to “F(5)=1″…

How about “F(6)”? How about “F(2015)”?

So here’s it: “F(n)” outputs the remainder when “n” is divided by “4”!

So “F(2015)=3” since “2015” divided by “4” gives a remainder of “3”!

 

Now how did the godly Julia derive such an amazing (actually not so) function?

Sorry not going through how goodnite.


How the function looks like when graphed out:

https://www.desmos.com/calculator/j9ucrkjewc