การแปลงฟูเรียร์ (Fourier Series) | ฟูเรียร์ ทรานฟอร์ม

การแปลงฟูเรียร์ (Fourier Series)


นอกจากการดูบทความนี้แล้ว คุณยังสามารถดูข้อมูลที่เป็นประโยชน์อื่นๆ อีกมากมายที่เราให้ไว้ที่นี่: ดูความรู้เพิ่มเติมที่นี่

สอนโดย
ดร.ประจวบ อินระวงค์

การแปลงฟูเรียร์ (Fourier Series)

Euler’s Identity (Complex Numbers)


How the Fourier Transform Works, Lecture 4 | Euler’s Identity (Complex Numbers)
Next Episode: https://bit.ly/38qm6W7
Course playlist: https://bit.ly/2WyzWD4
http://howthefouriertransformworks.com/
In order to describe the Fourier Transform, we need a language. That language is the language of complex numbers. Complex numbers are a baffling subject but one that it is necessary to master if we are to properly understand how the Fourier Transform works. What is the imaginary number “i” and why it is so useful to us when dealing with the Fourier Transform?
This is the sixth in this series of videos which takes a new and visual look at the maths behind the magic of how the Fourier Transform works.
Please help me finish filming the course by supporting me on Patreon: www.patreon.com/MarkNewman
Click below to subscribe to the Course’s mailing list to receive an update when the next video is available, updates about the course’s production, and a notification of when the full course is available to purchase.
http://eepurl.com/dwgO7D
math mathematics learning
Thanks for watching the video How the Fourier Transform Works, Lecture 4 | Euler’s Identity (Complex Numbers)

Euler's Identity (Complex Numbers)

การแปลงฟูเรียร์


การแปลงฟูเรียร์อันที่จริงแล้วก็เป็นรูปหนึ่งของอนุกรมฟูเรียร์ที่ให้คาบเข้าใกล้อนันต์
วิดีโอนี้อธิบายความเชื่อมโยงระหว่างอนุกรมฟูเรียร์กับการแปลงฟูเรียร์
นักศึกษาสามารถดู Playlist ทั้งหมดได้ที่
https://youtube.com/playlist?list=PL7aElt1k85Ea_Y9SMtDz_WFXwKgvIVKv3

การแปลงฟูเรียร์

Is E8 Lattice the True Nature of Reality? Or Theory of Everything?


E8 image credit: Wikipedia | Title: E8 Petrie projection | Author: Jgmoxness | Source: | License: CC BYSA 3.0 https://commons.wikimedia.org/wiki/File:E8Petrie.svg
E8 Lie group and E8 Lattice has sometimes been called the most beautiful mathematical structure in the world. Is it the theory of everything or the true nature of reality? It even has an entire research company behind it called \”Quantum Gravity Research\”
Note: E8 root system animation provided courtesy of David Madore www.madore.org.
It is a 248 dimensional object, but it can also be thought of as an object that has 8 spatial dimensions, with 248 symmetries.
Why is this structure important? Well, it happens to show up in parts of String Theory. But also in 2007, a theoretical physicist Antony Garrett Lisi published a paper proclaiming that the mathematics of this structure contained all the particles and forces in the universe. He called it the “the exceptionally simple theory of everything” What Lisi did is he found a relationship between this object and all the forces and particles we know about.
According to the standard model, there are 4 fundamental forces in nature, strong force, weak force, electromagnetism and gravity. And there are 12 fundamental particles. In addition, each of these particles has a antiparticle of itself. In total, these make up all the elementary particles, and there are exactly 28 of them. 24 elementary particles, and 4 force carrier particles. Each of these distinct elementary particles has eight quantum numbers assigned to it, based on the charges each particle has.
This brings the number of distinct particles to 224.
Lisi found that he could mathematically equate all of these particles to one of the points in the E8 model.
But the model has 248 points, not 224. So what about the empty 24 extra points? He simply created 24 new theoretical particles.
Notice how the lines radiate from each point: Lisi also found patterns emerging between particles and forces like they happen in actual reality – for example, when photons interact with leptons, they create electrons. The same thing happens in the E8 lattice. The connections shown within points on the E8 match up to real, known connections between particles in our physical world.
One of the particles he assigned to this shape behaves very much like the force carrier for gravity – a graviton. And this is the key to Lisi claiming that this could be the “theory of everything.” – because it combines matter particles and gravity in one framework.
Lisi’s theory does have some problems. One of the biggest problems with the theory is that Lisi combines the force carrying particles, Bosons with the matter particles. String theory does this too, but with the rigorous mathematics to go with it. This math is not present in E8, so Lisi combining these appears to be arbitrary.
In addition, a leading mathematician and expert on Lie groups, Skip Garibaldi wrote a paper in 2010 which mathematically disproved Lisi. But Lisi came back with counter arguments to that.
But the elephant in the room is the 24 new theoretical particles that come out of this theory. So it requires the existence of undiscovered matter. However, since the startup of the Large Hardon Collider, it is possible one of lisi’s 24 new theoretical particles could be found. Lisi himself says, \”I’m the first to admit that it’s a long shot.\”
In fact, I think that even if one of the new theoretical particles is found, it would be a huge breakthrough towards proving this theory is on the right track.
How does this compare to string theory? At least there is a way to prove it, unlike string theory – where we don’t really have a way to prove it.
And although E8 has a vast number of dimensions, the physical universe described by the theory would have only the four dimensions we are familiar with and not the 10 or 11 of string theory.
You may have heard of a research organization called Quantum Gravity Research. This group has built a whole company around the idea of E8 being the theory of everything. They have some really well produced and slick videos on you tube that you can check out for yourself. They are like mini movies with actors, special effects, and animations. So I commend them for making this science approachable to everyday people.
The problem with their videos is they are mixing actual proven concepts in physics with a lot of unproven concepts, including new age mysticism. This really diminishes their credibility in my view because the viewer doesn’t know which part is true and which part is conjecture.
E8 is a real mathematical structure. It has been around for a long time. Quantum Gravity Research people did not come up with it.
And I think it’s an interesting idea. All that needs to be done, is for the large hadron collider to find at least one of 24 theoretical particles, and this theory may get hoards of scientists singing its praises.

Is E8 Lattice the True Nature of Reality? Or Theory of Everything?

รวมเพลงฮิต เพลงเก่า SILLY FOOLS [ซิลลี่ ฟูลส์] l แกล้ง, คิดถึง, ขี้หึง, วัดใจ l


ฟังเพลงยาวจุใจ ฟังได้ 24 ชั่วโมง กด SUBSCRIBE ได้ที่นี่
00:00 แกล้ง
05:10 คนที่ฆ่าฉัน
09:32 คิดถึง
14:13 ผิดที่ไว้ใจ
18:56 ไหนว่าจะไม่หลอกกัน
24:04 อย่าบอกว่ารัก
28:26 ขี้หึง
32:53 น้ำลาย
37:16 บ้าบอ
43:40 ไม่หวั่นแม้วันมามาก
47:15 แล้วแต่แป๊ะ
50:42 จิ๊จ๊ะ
55:07 วัดใจ
59:24 เพลงนี้เกี่ยวกับความรัก
01:04:14 เมื่อรักฉันเกิด

รวมเพลงฮิต เพลงเก่า SILLY FOOLS [ซิลลี่ ฟูลส์] l แกล้ง, คิดถึง, ขี้หึง, วัดใจ l

นอกจากการดูหัวข้อนี้แล้ว คุณยังสามารถเข้าถึงบทวิจารณ์ดีๆ อื่นๆ อีกมากมายได้ที่นี่: ดูบทความเพิ่มเติมในหมวดหมู่Wiki

Leave a Reply

Your email address will not be published. Required fields are marked *