GA1
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GA3,no SGT
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GA5 - Deponia train
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icaio's contribution, no SGT
another one, no SGT
tidhros's contribution
another contribution of icaio

Hey SG,

I will try to post imho interesting more or less recent science stuff here, accompanied by some GAs one for now during the next weeks.
Why? - Because I enjoy science and you enjoy GAs :D

Read the comments, there are some nice additional information. I try to link them at the appropiate places.

Science stuff #6 Noether's theorem

Emmy Noether was one of the great mathematicians of the 20th century and one of the first women who left their mark in that field.
In theoretical physics the theorem given her name states that a symmetry is connected to a conservation law (conservation of energy/momentum/...).
"So what?" you might ask. That certain physical properties are conserved was known before but Noether was the first to base this on a mathematical base. I am not talking about "potential energy at a high starting point = kinetic energy at the ground level" to compute the velocity of something falling down, but about mathematics that proof you can use that formula.

There is a nice article explaining it with some videos for different levels of scientific background (kindergarten - PhD). If you have no clue what I am talking about, watch the kindergarten one!

The great thing about Noether's theorem is that it spawned a new way of physical thinking. Since the 1920s more and more physicists thought "what would happen if I mirror/rotate/... just one property of my physical system?". That lead to the discoveries of many (sub-)atomic particles, antimatter for example.

But there violations of seemingly fine symmetries, the most well known is the CP violation. In short, matter and antimatter do not act in an exactly mirrored way.

Noether's theorem lead to physicists thinking in symmetries. Violations of those symmetries lead to open problems and potentially to new physics.

Science stuff #5

You all know the number, which was called my favorite number, although it is not.

pi

Probably you all know, that pi relates a circles diameter (d) to its circumfence (u): u = pi * d. I really like the animation on wikipedia.
Today we know pi has an infinite amount of decimal places without periodicity aka an irrational number. But what about the past?

around 2000 BCE

4*(8/9)^2 and 3+1/8. Both approximations are only correct at the first decimal place. Recent scientific paper on the matter.

around 550 BCE

Bible: 3

ca. 250 BCE, Archimedes

223/71 < pi < 22/7; as far as I know the first time someone knew he was wrong and gave an upper and lower limit. Although correct to 2 decimal places (aka 3.14)

263 CE

Liu Hui invented an algorithm and calculated pi to 4 decimal places: 3927/1250 = 3.1416.

480 CE

Zu Chongzhi, 355/113 = 3.141592...

ca. 1400 CE

Now it is getting interesting. Most ways to determine pi so far have been to use a polygon with many corners. Madhava of Sangamagrama (or someone else later on) discovered the infinite power series expansion of pi. If you are not familiar with mathematical series, it might get a little bit difficult here.

1897

pi = 3.2 source Thanks Nimmy for the reminder

1910

Srinivasa Ramanujan found a series that gets close to pi really fast, so that this series is still used today.
Edit: Seems that is not the most recent information anymore: https://www.steamgifts.com/go/comment/BEIGIiD

1949

John Wrench and L. R. Smith were the first to use an electronic computer to compute pi to more than 2000 digits.

1958

Francois Genuys cracks 10,000 digits.

1961

Daniel Shanks and John Wrench, 100,000 digits.

1973

Jean Guilloud and Martin Bouyer, 1,000,000 digits.

...

1989

Gregory V. Chudnovsky & David V. Chudnovsky 10^9 digits.

2002

Yasumasa Kanada et al. 10^12 digits.

2011

Shigeru Kondo 10^13 digits.

There is a paper that discusses the possibility of pi being time-dependent.The paper was published 2 days early, due to technical difficulties.
Another paper explores the connection of pi's digits to the Cosmic Microwave Background.

Kind of science stuff #4

Harry Potter and the Methods of Rationality
Not really science itsself, but HPMOR takes a shot at many scientific fields and methods. In my opinion it is a great way to explain some science stuff to people who usually do not read science. You should have a basic understanding of Harry Potter (Like read a book or saw one movie) to enjoy the pages and pages of text.

Science stuff Three:

So I wanted to write about binary logic and the begining of computer science, but -alas!- I was led astray by wikipedia.

Calculus

Calculus is at the heart of (more or less) every quantitative model in science.

Why?
(Nearly) Every model has to adjust for changes in conditions, e.g. CS GO Keys changing their price shortly before Steam sales. If any quantity changes, you have to think about the time frame you take into account. You can do hourly changes, that might work rather well for CS GO keys, but yields strange results for other processes (e.g. bacteria populations or the velocity of a rollercoaster). You have to change your time frame to a value suitable for the system you are trying to describe. Now let's assume you time frames get smaller and smaller, but you still get results in your calculation that do not match you experiment (e.g. Your model says, that the price of Steam keys should drop to 0.20$ but it is stuck at 2$). At some point your time frame gets infinitesimal. Now classical math fails as you are dividing by zero for classical purposes. That's the point you need calculus.
Same is true if you want to if you want to get areas bordered by mathematical functions. A nice example in my opinion is planetary motion. If you compare the area between the Sun and the planet, the area will be the same for a given time frame, regardless if the planet is near the sun on its elliptical path or far away. This is known as Kepler's 2nd law of planetary motion and says in the end, that planets move faster if the are near the sun and slower if they are far away.

Who invented Calculus?

In other words, who should you be thankful for or who should you curse, depending on your personal relation with calculus
That is a rather difficult question that spawned its own research and is known to some as Prioritätsstreit.
Contenders for the crown are Leibniz and Newton. At least the notation we use today is Leibniz' fault.

Reading about Leibbiz lead me to other maths stuff and I will continue reading after posting this.

Science stuff Two: Fourier analysis

If you add two sine (or cosine) waves of different wavelength, you get a new function that is no "nice" wave anymore but something periodic of different shape. If you add a lot of sine waves, you may get (more or less) every possible wave structure.

Why is this science?

In many fields of science, you want to know if there is an underlying periodic structure. You can try to decompose your data using the Fourier transformation to identify these periodic structures.
Going back to this discussion, you can use Fourier analysis to identify the size of astronomical structures on large (cosmic) scales and compare the frequency of occurrence of those with the same quantity from computer models based on different theories.
In signal processing one often uses time–frequency transforms. If you record any data it is time dependent with no frequency information. If you want to analyse the frequencies, you have to Fourier transform it. Probably the best know example is mp3.
You record a music track - time dependent. You want to make the file smaller, you will have to omit part of the data. To do so, you will have to identify information that a human can't detect (i.e. hear). So you need to Fourier transform the music track. That's quite slow, so mp3 was only possible using an implementation of fast Fourier transform (FFT). See also here
Assuming most of you have used (glasses) or played with (physics class,...) optical lenses at some point in their lifes: You can think of lense optics as Fourier transform -> Fourier optics.

Science stuff One: The MeerKAT radio telescope in South Africa.

Why radio telescopes?

• Electromagnetical waves in the radio window can pass through interstellar dust and thus shows astronomical objects not seen in the visible part of the EM spectrum. Radio waves are emitted by so called non-thermal processes. Those sources often have a high engery output, so shaping their surroundings and influencing galactic and cosmic evolution.

Why an interferometer?

• The resolution of any observer is given by the size of its collecting area. Resolution is the smallest angular distance of two objects so that they can still be told apart. So a telecsope should be as large as possible. Due to technical difficulties (weight!) and too high cost, astronomers build many small telescopes and couple their signals (e.g. VLA, ALMA, IRAM and VLT). The virtual telescope's size is given by the largest distance of two single telescopes, 8km - 20km in MeerKAT's case.

Why look at distant space objects?

• Because it is fun! Because there a nice images (e.g. APOD). And because it is the only way to get information about the history of the Milkyway, galaxies and Universe as a whole. How did the Universe evolved? Were laws of physics and fundamental constants always the same or are they time dependent? Do we have a theory for everything we see? If no - can we develope a working theory? If a theory does not work - why?

Why should you care for fundamental research?

• Because you never know where the path might lead. The most important example (for some of you people here) of a scientific discovery that would not have happend without prior fundamental research: semiconductors and thus all modern IT.

I hope you enjoy a little off topic.
If you are on my naughty list and think you are there by mistake, feel free to contact me.