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Ciro Santilli  40 Updated 2025-07-16

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Has some of the best map data available for the United Kingdom, but their data appears to be proprietary?

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Binance by

Ciro Santilli  40 Updated 2025-07-16

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Coinbase by

Ciro Santilli  40 Updated 2025-07-16

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Mt. Gox by

Ciro Santilli  40 Updated 2025-07-16

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The first Bitcoin exchange. Coded as a hack, and they didn't manage to fix the hacks as the site evolved in a major way, which led to massive hacks.

Their creation is clearly visible on the archive history of bitcoin.org: web.archive.org/web/20100701000000*/bitcoin.org which started having massively more archives since Mt. Gox opened.

Video 1.

One Mistake Brought Down This FBI Most Wanted Hacker by Crumb (2023)

. Source. Good overview of Mt. Gox.

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Escherichia coli by

Ciro Santilli  40 Updated 2025-07-16

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www.cell.com/cell/fulltext/S0092-8674(15)00568-1 2015. Using Genome-scale Models to Predict Biological Capabilities. Edward J. O'Brien, Jonathan M. Monk, Bernhard O. Palsson.
www.quora.com/What-are-some-good-books-on-Escherichia-Coli-E-Coli

Size: 1-2 micrometers long and about 0.25 micrometer in diameter, so: 2 * 0.5 * 0.5 * 10e-18 and thus 0.5 micrometer square.

Reference strain: E. Coli K-12 MG1655.

Genome:

4k genes
5 Mbps
www.ncbi.nlm.nih.gov/genome/167
wget ftp://ftp.ncbi.nlm.nih.gov/genomes/all/GCF/000/005/845/GCF_000005845.2_ASM584v2/GCF_000005845.2_ASM584v2_genomic.fna.gz
wget -O NC_000913.3.fasta 'https://www.ncbi.nlm.nih.gov/search/api/sequence/NC_000913.3/?report=fasta'

Synthesis project: www.sciencemag.org/news/2016/08/biologists-are-close-reinventing-genetic-code-life

Omics modeling: www.ncbi.nlm.nih.gov/pmc/articles/PMC5611438/ Tools for Genomic and Transcriptomic Analysis of Microbes at Single-Cell Level Zixi Chen, Lei Chen, Weiwen Zhang.

Bibliography:

ecoliwiki.org/colipedia/index.php/Welcome_to_EcoliWiki

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Mycoplasma by

Ciro Santilli  40 Updated 2025-07-16

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Maybe the most famous one is Mycoplasma genitalium byt there are others, and notably with lower biosafety levels:

Biosafety level 1: www.lgcstandards-atcc.org/Search_Results.aspx?dsNav=Ntk:PrimarySearch%7cmycoplasma%7c3%7c,Ny:True,N:1000552-1000577-4294967226&searchTerms=mycoplasma&redir=1

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Lie algebra of

S L (2)

Ciro Santilli  40 Updated 2025-07-16

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This is a good first concrete example of a Lie algebra. Shown at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" has an example.

We can use use the following parametrization of the special linear group on variables

x

y

and

z

M = [1 + x z y (1 + yz) / (1 + x)]

(1)

Every element with this parametrization has determinant 1:

d e t (M) = (1 + x) (1 + yz) / (1 + x) - yz = 1

(2)

Furthermore, any element can be reached, because by independently settting

x

y

and

z

M_{00}

M_{01}

and

M_{10}

can have any value, and once those three are set,

M_{11}

is fixed by the determinant.

To find the elements of the Lie algebra, we evaluate the derivative on each parameter at 0:

M_{x} M_{y} M_{z} = \frac{d M}{d x}_{(x, y, z) = (0, 0, 0)} = \frac{d M}{d y}_{(x, y, z) = (0, 0, 0)} = \frac{d M}{d z}_{(x, y, z) = (0, 0, 0)} = [10 0 - (1 + yz) / (1 + x)^{2}]_{(x, y, z) = (0, 0, 0)} = [00 1 z / (1 + x)]_{(x, y, z) = (0, 0, 0)} = [01 0 y / (1 + x)]_{(x, y, z) = (0, 0, 0)} = [10 0 - 1] = [0010] = [0100]

(3)

Remembering that the Lie bracket of a matrix Lie group is really simple, we can then observe the following Lie bracket relations between them:

[M_{x}, M_{y}] [M_{x}, M_{z}] [M_{y}, M_{z}] = M_{x} M_{y} - M_{y} M_{x} = M_{x} M_{z} - M_{z} M_{x} = M_{y} M_{z} - M_{z} M_{y} = [0010] = [0 - 1 00] = [1000] - [00 - 1 0] - [0100] - [0001] = [0020] = [0 - 2 00] = [10 0 - 1] = 2 M_{y} = - 2 M_{z} = M_{x}

(4)

One key thing to note is that the specific matrices

M_{x}

M_{y}

and

M_{z}

are not really fundamental: we could easily have had different matrices if we had chosen any other parametrization of the group.

TODO confirm: however, no matter which parametrization we choose, the Lie bracket relations between the three elements would always be the same, since it is the number of elements, and the definition of the Lie bracket, that is truly fundamental.

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" then calculates the exponential map of the vector

x M_{x} + y M_{y} + z M_{z}

as:

I cos h (θ) + M_{x} s inh (θ) / θ

(5)

with:

θ^{2} = x^{2} + b c

(6)

TODO now the natural question is: can we cover the entire Lie group with this exponential? Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation" explains why not.

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Lie bracket of a matrix Lie group by

Ciro Santilli  40 Updated 2025-07-16

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[X, Y] = X Y - Y X

(1)

This makes it clear how the Lie bracket can be seen as a "measure of non-commutativity"

Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.

Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.

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One parameter subgroup by

Ciro Santilli  40 Updated 2025-07-16

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The one parameter subgroup of a Lie group for a given element

M

of its Lie algebra is a subgroup of

G

given by:

e^{tM} \in G ∣ t \in R

(1)

Intuitively,

M

is a direction, and

t

is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of

SO (3)

, the rotation group.

One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.

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A single exponential map is not enough to recover a simple Lie group from its algebra by

Ciro Santilli  40 Updated 2025-07-16

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Example at: Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation".

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The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra by

Ciro Santilli  40 Updated 2025-07-16

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Example at: Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation".

Furthermore, the non-compact part is always isomorphic to

R^{n}

, only the non-compact part can have more interesting structure.

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ThinkPad by

Ciro Santilli  40 Updated 2025-07-16

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This is Ciro Santilli's favorite laptop brand. He's been on it since the early 2010's after he saw his then-girlfriend-later-wife using it.

Ciro doesn't know how to explain it, but ThinkPads just feel... right. The screen, the keyboard, the lid, the touchpad are all exactly what Ciro likes.

The only problem with ThinkPad is that it is owned by Lenovo which is a Chinese company, and that makes Ciro feel bad. But he likes it too much to quit... what to do?

Ciro is also reassured to see that in every enterprise he's been so far as of 2020, ThinkPads are very dominant. And the same when you see internal videos from other big tech enterprises, all those nerds are running... Ubuntu on ThinkPads! And the ISS.

Those nerds like their ThinkPads so much, that Ciro has seen some acquaintances with crazy old ThinkPad machines, missing keyboard buttons or the like. They just like their machines that much.

ThinkPads are are also designed for repairability, and it is easy to buy replacement parts, and there are OEM part replacement video tutorials: www.youtube.com/watch?v=vseFzFFz8lY No visible planned obsolescence here! With the caveat that the official online part stores can be shit as mentioned at Section "Lenovo".

Further more, in 2020 Lenovo is announced full certification for Ubuntu www.forbes.com/sites/jasonevangelho/2020/06/03/lenovos-massive-ubuntu-and-red-hat-announcement-levels-up-linux-in-2020/#28a8fd397ae0 which fantastic news!

The only thing Ciro never understood is the trackpoint: superuser.com/questions/225059/how-to-get-used-of-trackpoint-on-a-thinkpad Why would you use that with such an amazing touchpad? And vimium.

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Meter by

Ciro Santilli  40 Updated 2025-07-16

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Gauge block by

Ciro Santilli  40 Updated 2025-07-16

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Highlighted at the Origins of Precision by Machine Thinking (2017).

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Light year by

Ciro Santilli  40 Updated 2025-07-16

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Markua by

Ciro Santilli  40 Updated 2025-07-16

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In leanpub you write your book in a markdown variant they call Markua, marketed as "markdown for books".

TODO is there a reference implementation that runs locally for HTML output? Or the only reference implementation is closed under leanpub?

Spec: markua.com/

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Cf. by

Ciro Santilli  40 Updated 2025-07-16

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De novo by

Ciro Santilli  40 Updated 2025-07-16

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Et aliī by

Ciro Santilli  40 Updated 2025-07-16

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Id est by

Ciro Santilli  40 Updated 2025-07-16

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 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!

Video 1.

Intro to OurBigBook

. Source.

We have two killer features:

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
Video 2.
OurBigBook Web topics demo
. Source.
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:
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
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 2.
You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
.
Figure 3.
Visual Studio Code extension installation
.
Figure 4.
Visual Studio Code extension tree navigation
.
Figure 5.
Web editor
. 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.
Video 4.
OurBigBook Visual Studio Code extension editing and navigation demo
. Source.
Internal cross file references done right:
Infinitely deep tables of contents:
Figure 6.
Dynamic article tree with infinitely deep table of contents
.
Live URL: ourbigbook.com/cirosantilli/chordate
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

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 Pinned article: Introduction to the OurBigBook Project