Solving partial differential equations with the Fourier series Updated 2025-03-28 +Created 1970-01-01
See: math.stackexchange.com/questions/579453/real-world-application-of-fourier-series/3729366#3729366 from heat equation solution with Fourier series.
Separation of variables of certain equations like the heat equation and wave equation are solved immediately by calculating the Fourier series of initial conditions!
Other basis besides the Fourier series show up for other equations, e.g.:
Sometimes you get annoyed to death with your bike not breaking or changing gears perfectly as you would like, and the people at the bike shop never do the job well enough.
The problem with bike shops is that the employees are already swamped with work, and they don't get paid any extra for doing more work.
As a result, paradoxically, they are often happier, and respect you more if you are trying to get them to help you to fix your own bike!
Also, for the same reason, they don't have the time to go for a quick test ride after a fix to ensure that the bug was actually fixed.
So they ignore things that would obviously be huge ridability benefits (although they might not be obvious to newbie customers), for which customers would gladly pay more money for.
But you start to learn how to do stuff yourself and it feel amazing when you finally get there (after infinite trial and error).
Ciro dreams of a bike shop that actually calls you for the appointment and then teaches you how to fix the thing.
So the best strategy is to have a backup bicycle, and when your main one breaks, you just try to to the fix yourself. That means:
- identifying the broken piece
- watching YouTube videos of how to do the job
- buying a replacement and any missing tools on Amazon
- giving it a shot
Then, if you fail to do the fix, that is OK, just take it to the bike shop, with the piece you've bought, and ask them to do it for you. At least this way you did not waste a golden opportunity to learn!
Bought December 2023 for 300 pounds, so 15 pounds / TB. Needs power supply unfrotunately besides USB, the largest one without needing power supply was only 5 TB at the time so not worth it, given that my P14s alreay carriers 2 TB. 10x is a must for the external crap.
www.westerndigital.com/en-gb/products/external-drives/wd-elements-desktop-usb-3-0-hdd?sku=WDBWLG0030HBK-EESN (archive)
Noise: it has a constant pleasant hum, with a not so nice click every 5 seconds or so. Reasonable, but not amazingly incredible.
The size is reasonable, not megaportable, but definitely reasonable.
users.physics.ox.ac.uk/~lvovsky/B3/ contain assorted PDFs from between 2015 and 2019
Syllabus reads:
- Multi-electron atoms: central field approximation, electron configurations, shell structure, residual electrostatic interaction, spin orbit coupling (fine structure).
- Spectra and energy levels: Term symbols, selection rules, X-ray notation, Auger transitions.
- Hyperfine structure; effects of magnetic fields on fine and hyperfine structure. Presumably Zeeman effect.
- Two level system in a classical light field: Rabi oscillations and Ramsey fringes, decaying states; Einstein
- A and B coefficients; homogeneous and inhomogeneous broadening of spectral lines; rate equations.
- Optical absorption and gain: population inversion in 3- and 4-level systems; optical gain cross section; saturated absorption and gain.
Professor in 2000s seems to beBut as of 2023 marked emeritus, so who took over?
- en.wikipedia.org/wiki/Paul_Ewart. He actually fought not to be dismissed by age and won!
- www.physics.ox.ac.uk/our-people/ewart
Ewart is actually religious:This dude is pure trouble for Oxford!
- www.youtube.com/watch?v=aulL-Qa65i0 Paul Ewart, Chance, Science and Spirituality by Faraday Institute for Science and Religion. Oh, he is/was actually chairman of that crap
- www.youtube.com/watch?v=PVX2F4XvGYo Chaos and the Character of God by Prof. Paul Ewart
Undated materials Ewart:
- users.physics.ox.ac.uk/~ewart/index.htm
- users.physics.ox.ac.uk/~ewart/Atomic%20Physics%20lecture%20notes%20C%20port.pdf
- slides: users.physics.ox.ac.uk/~ewart/Atomic%20Physics%20Lecture%20PPT%20slides%201_8.pdf. Also under: www2.physics.ox.ac.uk/sites/default/files/2011-10-19/atomic_physics_lectures_1_8_09_pdf_pdf_18283.pdf. The course was previously B1, they just change the IDs randomly from time to time to fit the B1-7 numbering.
The United Kingdom is one big field.
Everything is extremely uniform and fully controlled by humans. Maybe this is partially due to it being an island with extensive flood plains. Loots of white mana floating around there.
Some impressively sounding natural parks look more like cute countryside that is slightly hillier than the surrounding countryside.
This uniformity does however make it quite comfortable for its Hobbit inhabitants.
It also means that whenever slightly out of the ordinary happens, e.g., a bit of slightly heavier rain, everything floods. In some way however, the Brits are very pragmatic, and as long as the flood is not too bad, they just let it be, it might be cheaper.
Decent interactive counties map: help.openstreetmap.org/questions/22603/displaying-uk-ceremonial-counties TODO districts...
Stuff that is beautiful but useless because it does not make food or houses cheaper.
Or from Ciro Santilli's best random thoughts:
Without technology, one cannot survive. Without art, one cannot live.
But that sure enough has a Jesus semi-precursor, and likely many others: man shall not live by bread alone.
There is some art however that lives in the fine intersection between beauty and usefulness:
Maybe those are genial. Maybe not. Nostalgia is just too strong to discern. Ciro still goes back to them for rest.
Quick facts:
- Nationalities: Italian and Brazilian
- Grew up in: Brazil
- Relationship status 2017-: married
- Given name pronunciation: take your pick from Ciro Santilli's given name
- Chinese name: 三西猴, means "three western monkeys". Phonetic approximation to SANtilli CIRO. More info at: Ciro Santilli's Chinese name. Semi-unintentionally reminds Chinese people of Sun Wukong (孙悟空). This association is further slightly strengthened by the phonetic choice of 三 San, which Ciro later noticed matches the middle character of Tang Sanzang (唐三藏), the monk in Journey to the West. The given name 西猴 was given by Ciro Santilli's wife, then recent girlfriend, as a semi-joke, and he took it up because the best way to take a joke is to play along with the joker. 三 was chosen by Ciro himself.
- laptop: high end Lenovo ThinkPad
- distro: latest Ubuntu release
- Vim or Emacs: vi/vim. But for The Love, will someone please make an open source C++ integrated development environment that actually just works?
- tabs or spaces: spaces
- Mailing list or Git(Hub|Lab): Git(Hub|Lab), with passion, see Section "Mailing list"
- system or unit tests: system
- programming languages: Python and C++. He'll learn Rust and Haskell once he's rich. As of the 2020s, Rust was picking up some serious steam, so Ciro might end up eating his own words there.
- musical instruments to listen: Chinese Guqin and electric Jazz-fusion guitar
- metric or imperial: metric, for The Love. Science? Standardization? 21st century anyone?
- QWERTY or Dvorak: QWERTY, alas
- birth name: Ciro Duran Santilli
Other people with the same name are listed at Section "Ciro Santilli's homonyms".
19th century illustration of the Journey to the West protagonist Sun Wukong
. Source. Sun Wukong (孙悟空) is a playful and obscenely powerful monkey Journey to the West. He protects Buddhist monk Tang Sanzang, and likes eating fruit, just like Ciro. Oh, and Goku from Dragon Ball is based on him. His japanese name is "Sun Wukong" (same Chinese characters with different Japanese pronunciation) for the love. His given name "Wukong" means literally "the one who mastered the void", which is clearly a Dharma name and fucking awesome in multiple ways. This is another sad instance of a Chinese thing better known in the West as Japanese.
It is worth noting however that although Wukong is extremely charming, Ciro's favorite novel of the Four Great Classic Novels is Water Margin. Journey to the West is just a monster of the week for kids, but Water Margin is a fight for justice saga. Sorry Wukong!
The photo was taken in an open event organized by the awesome Cambridge Synthetic Biology outreach group, more or less the same people who organize: www.meetup.com/Cambridge-Synthetic-Biology-Meetup/ and who helped organize Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it".
Taking part in such activities is what Ciro tries to do to overcome his lifelong regret of not having done more experimental stuff at university. Would he have had the patience to handle all the bullshit of the physical word without going back to the informational sciences? Maybe, maybe not. But now he will probably never know?!
Notice the orange high visibility cycling jersey under the lab coat, from someone who had just ridden in from work as fast as possible as part of his "lunch break". It is more fun when it is hard.
Scribe Jean Miélot, 15th century
. Ciro Santilli fantasizes that he would have make a good scribe in the middle ages, partly due to his self diagnosed graphomania, but also appreciation for foreign languages, and his mild obsession with the natural sciences.
OurBigBook.com is Ciro's view of a modern day scriptorium, except that now the illuminations are YouTube videos.
Chill and eat your bread in peace comes to mind. A scribe, in a library, reading and writing the entire day in peace and quiet. The life!
The job of a Internet-age scribe is basically that of making knowledge more open, legally extracting it from closed copyrighted sources, and explaining your understanding of it to the wider world under Creative Commons licenses on the web. And in the process of greater openness, given a well organized system, we are able combine the knowledge of many different people, and thus make things more understandable than any single/few creator closed source source could ever achieve.
Ciro once saw some cartoon on Wikipedia help pages of a turtle with a book in one hand, and typing into Wikipedia on its computer, TODO find it. That cartoon summarizes well the modern scribe life.
Another analogous version of this fantasy more in touch with Ciro's sinophily is the ideal of the Chinese scholar, notably including their stereotypical attributes such as mastery of the Four arts.
Ciro Santilli piling boxes as a child
. A natural born engineer.
Ciro Santilli waving hello in infrared.
More info at: Figure "Ciro Santilli waving hello in infrared".The weird one, not directly coded in the genetic code.
Jugalbandi in Chartaal-Ki-Sawari from album Together (1990)
Source. Background?Taal Pancham Sawaari by Zakir Hussain
. Source. The top YouTube commend mentions:This video was made in 1970, on Zakir's first visit to the USA. He and Aashish Khan (keeping taal next to him) had a guest residency at UW Seattle, under the ethnomusicology dept. set up by Robert Garfias.
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