Normalized DFT by Ciro Santilli 37 Updated 2025-07-16
There are actually two possible definitions for the DFT:
Variety Jones by Ciro Santilli 37 Updated 2025-07-16
2015 The Variety Show On the trail of the man believed to be Variety Jones, one of the architects of the defunct drug marketplace Silk Road. www.vice.com/en/article/wnx5qn/the-variety-show
www.justice.gov/usao-sdny/file/797251/download some kind of case file of his trial.
The curious thing about VJ is that he actually has some culture and says cool things, e.g.:
IRL - is there anyone with a clue at all? Girlfriend, boyfriend, bunny you talk to, online buddy's who you've know for years? Gramma, priest, rabbi, stripper?
MRI is using NMR to image inside peoples bodies!
Video 1.
How does an MRI machine work? by Science Museum (2019)
Source. The best one can do in 3 minutes perhaps.
Video 2.
How MRI Works Part 1 by thePIRL (2018)
Source.
Video 3.
What happens behind the scenes of an MRI scan? by Strange Parts (2023)
Source.
Video 4.
Dr Mansfield's MRI MEDICAL MARVEL by BBC
. Source. Broadcast in 1978. Description:
Tomorrow's World gave audiences a true world first as Dr Peter Mansfield of the University of Nottingham demonstrated the first full body prototype device for Magnetic resonance imaging (MRI), allowing us to see inside the human body without the use of X-rays.
Featuring the yet-to-be 2003 Nobel Prize in Physiology and Medicine Dr. Mansfield.
Paul Dirac by Ciro Santilli 37 Updated 2025-07-16
Eccentric nerdy slow speaking physicist mostly based in University of Cambridge.
Created the Dirac equation, what else do you need to know?!
QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 1.3 "P.A.M. Dirac and the Birth of Quantum Electrodynamics" quotes Dirac saying how being at high school during World War I was an advantage, since all slightly older boys were being sent to war, and so the younger kids were made advance as fast as they could through subjects. Exactly the type of thing Ciro Santilli wants to achieve with OurBigBook.com, but without the need for a world war hopefully.
Dirac was a staunch atheist having said during the Fifth Solvay Conference (1927)[ref]:
If we are honest - and scientists have to be - we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards - in heaven if not on earth - all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.
Video 1.
Paul Dirac and the religion of mathematical beauty by Royal Society (2013)
Source.
Ciro Santilli once talked to a man who had been working on high-frequency trading for the last six years.
He was quite nice.
Ciro asked him in what way did he feel his job contributed to the benefit of society.
He replied that it didn't contribute at all. It was completely useless. More than that, it so completely useless, that it was even pure. A bit like advanced mathematics, but not even providing beauty for anybody outside of the company, since everything is a closely guarded trade secret, unlike mathematics which is normally published for the vanity recognition.
A great mind can work in the most useless branches of finance, without the desire to improve the world, nor make it worse. Not to compete, nor be afraid, nor anxious. A sand mandala.
Only being. Being, in the exact fraction of a moment where bid meets ask.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact