ECDH has smaller keys. youtu.be/gAtBM06xwaw?t=634 mentions some interesting downsides:
If you can reduce a mathematical problem to the Halting problem of a specific turing machine, as in the case of a few machines of the Busy beaver scale, then using Turing machine deciders could serve as a method of automated theorem proving.
That feels like it could be an elegant proof method, as you reduce your problem to one of the most well studied representations that exists: a Turing machine.
However it also appears that certain problems cannot be reduced to a halting problem... OMG life sucks (or is awesome?): Section "Turing machine that halts if and only if Collatz conjecture is false".
Like a cycler, but the cycle starts at an offset.
To see infinity, we check that if the machine only goes left N squares until reaching the repetition, then repetition must only be N squares long.
Cycler Turing machine by Ciro Santilli 40 Updated 2025-07-16
These are very simple, they just check for exact state repetitions, which obviously imply that they will run forever.
Unfortunately, cyclers may need to run through an initial setup phase before reaching the initial cycle point, which is not very elegant.
Also, we have no way of knowing the initial setup length of the actual cycle length, so we just need an arbitrary cutoff value.
And unfortunately, this can lead to misses, e.g. Skelet machine #1, a 5 state machine, has a (translated) cycle that starts at around 50-200M steps, and takes 8 trillion steps to repeat.
Oxford Instruments by Ciro Santilli 40 Updated 2025-07-16
They are pioneers in making superconducting magnets, physicist from the university taking obsolete equipment from the uni to his garage and making a startup kind of situation. This was particularly notable for this time and place.
They became a major supplier for magnetic resonance imaging applications.
Plane wave function by Ciro Santilli 40 Updated 2025-07-16
In this solution of the Schrödinger equation, by the uncertainty principle, position is completely unknown (the particle could be anywhere in space), and momentum (and therefore, energy) is perfectly known.
The plane wave function appears for example in the solution of the Schrödinger equation for a free one dimensional particle. This makes sense, because when solving with the time-independent Schrödinger equation, we do separation of variable on fixed energy levels explicitly, and the plane wave solutions are exactly fixed energy level ones.
User mode emulation by Ciro Santilli 40 Updated 2025-07-16
User mode emulation refers to the ability of certain emulators to emulate userland code running on top of a specific operating system, usually Linux.
For example, QEMU allows you to run a variety of userland ELF programs directly on it, without an underlying Linux kernel running.
User mode emulation is achieved by implementing system calls and special filesystems such as /dev manually on the emulator one by one.
The general tradeoff is that simulation is less acurate as it may lack certain highly advanced kernel functionality you haven't implemented yet. But it is much easier to run executables with it, and you don't have to wait for boot to finish before running, you just run executables directly from the command line.
Early Google employee by Ciro Santilli 40 Updated 2025-07-16
ChatGPT produces:
  • Heather Cairns (Employee #4) - Joined in 1998. She handled HR and was one of the earliest administrative hires.
  • Harry Cheung (Employee #5) - Joined in 1999. An early engineer.
  • Gerald Aigner (Employee #6) - Hired in 1999. Worked as a software engineer.
  • Susan Wojcicki (Employee #16) - Joined in 1999. She rented her garage to Larry and Sergey in 1998 and later became an integral part of Google's business and advertising teams.
  • Marissa Mayer (Employee #20) - Hired in 1999. Played a major role in Google Search and design.
Omid Kordestani - Joined in 1999 as Google’s first business hire, focusing on sales and revenue generation.
Step busy beaver by Ciro Santilli 40 Updated 2025-07-16
The step busy beaver is a variant of the busy beaver game counts the number of steps before halt, instead of the number of 1's written to the tape.
As of 2023, it appears that BB(5) the same machine, , will win both for 5 states. But this is not always necessarily the case.
Neil Fernandez by Ciro Santilli 40 Updated 2025-07-16
“Especially my father. He was doing most of it and he is a savoury, strong character. He has strong beliefs about the world and in himself, and he was helping me a lot, even when I was at university as an undergraduate.”
An only child, Arran was born in 1995 in Glasgow, where his parents were studying at the time. His father has Spanish lineage, having a great grandfather who was a sailor who moved from Spain to St Vincent in the Carribean. A son later left the islands for the UK where he married an English woman. Arran’s mother is Norwegian.
“My father was writing and my mother is an economist. They both worked from home which also made things easier,” Arran says.
A bit like what Ciro Santilli feels about himself!
One of the articles says his father has a PhD. TODO where did he work? What's his PhD on? Photo: www.topfoto.co.uk/asset/1357880/
www.thetimes.co.uk/article/the-everyday-genius-pxsq5c50kt9:
Neil, a political economist, attended state and private schools in Hampshire but was also taught for a period at home by his mother.
It’s strange because for most people maths is a real turn-off, yet maths is all about patterns and children of two or three love patterns. It just shows that schools are doing something seriously wrong.”

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