Immune system Updated 2025-07-16
A cool thought: bacteria like E. Coli replicate every 20 minutes. A human replicates every 15 years. So how can multicellular beings possibly cope with the speed of evolution of parasites?
The answer is that within us, the adaptive immune system is a population of cells that evolves very quickly. So in a sense, within our bodies there is fast cell-level non-inheritable evolution happening daily!
Image editor Updated 2025-07-16
Lorem ipsum Updated 2025-07-16
Ciro Santilli had once assigned this as one of Ciro Santilli's best random thoughts, but he later found that Wikipedia actually says exactly that: en.wikipedia.org/wiki/Reverse_engineering ("similar to scientific research, the only difference being that scientific research is about a natural phenomenon") so maybe that is where Ciro picked it up unconsciously in the first place.
Finally, there it was: a proper and precise definition of mathematics, including a definition of integers, reals and limits!
Theorems are strings, proofs are string manipulations, and axioms are the initial strings that you can use.
Once proved, press a button on your computer, and the proof is automatically verified. No messy complicated "group of savants" reading it for 4 years and looking for flaws!
There are a few proof assistant systems with several theorems in their Git tracked standard library. The hottest ones circa 2020 are:
And here are some more interesting links:
However, as expressed by the QED manifesto, is unbelievable that there isn't one awesome and dominating website, that hosts all those proofs, possibly an on the browser editor, and which all mathematicians in the world use as the one golden reference of mathematics to rule them all!
Just imagine the impact.
Standard library maintainers don't have to deal with the impossible question of what is "beautiful" or "useful" enough mathematics to deserve merged: users just push content to the online database, and star what they like!
We then just use GitHub-like namespaces for each person's theorem, e.g. "cirosantilli/fundmaental-theorem-of-calculus" or "johndoe/fundmaental-theorem-of-calculus" so that each person owns their own preferred definition IDs, which others can reuse.
No more endless bikeshedding over what insane level of generality do your analysis theorems need to be (Ciro Santilli attended at talk about Lean where the speaker mentioned this was a problem)!
This would move things more out of the "pull request and Git tracked code" approach, into a more "database with entries" version of things.
Furthermore, it is just a matter of time until the "single standard library" approach starts to break down, as the git clone becomes impossibly large. At this point, people have to start publishing separate packages. And when this happens, you would need to retest every package that you add to your project. This is why a centralized database is just inevitable at some point, it just scales better.
Interested in a conjecture? No problem: just subscribe to its formal statement + all known equivalents, and get an email on your inbox when it gets proved!
Are you a garage mathematician and have managed to prove a hard theorem, but no "real" mathematician will read your proof because your unknown? Fuck that, just publish it on the system and let it get auto verified. Overnight fame awaits.
Notation incompatibility hell? A thing of the past, just automatically convert to your preferred representation.
Such a system would be the perfect companion to OurBigBook.com. Just like computer code offers the backbone of Linux Kernel Module Cheat Linux kernel tutorials, a formal proof system website would be the backbone of mathematics tutorials! You know what, if OurBigBook.com becomes insanely successful, Ciro is going to add this to it later on.
Furthermore, it would not be too hard to achieve this system!
All we would need would be something analogous to a package registry like PyPI or NodeJS' registry.
Then, each person can publish packages containing proofs.
Packages can rely on other packages that contain pre-requisites definition or theorem.
Packages are just regular git repos, with some metadata. One notable metadata would be a human readable description of the theorems the package provides.
The package registry would then in addition to most package registries have a CI server in it, that checks the correctness of all proofs, generates a web-page showing each theorem.
All proofs can be conditional: the package registry simply shows clearly what axiom set a theorem is based on.
This is a close as we can get to Erdős' book.
Maybe Ciro will just stuff this into OurBigBook.com once that takes over the world.
This project could be seen as a more automated/less moderated version of ProofWiki.
Bibliography:
Ciro Santilli pinging people:
Aminoacyl tRNA synthetase Updated 2025-07-16
Binds an amino acid to the correct corresponding tRNA sequence. Wikipedia mentions that humans have 20 of them, one for each proteinogenic amino acid.
Amit Singhal Updated 2025-07-16
Pitched OurBigBook.com to him:
Idea: make all Sitare University materials open, and allow students to write the content
Also, allow anyone to take the exams without enrolling (possibly for a fee if they don't have scholarship).
This is the way to go if you really want to increase your impact/dollar and do something truly innovative that ill make a mark. Why just mirror existing university models that haven't yet caught up to the Internet Age?
Amniote Updated 2025-07-16
Name origin: amnion, a pellicle that covers embryos of both eggs and also during pregnancy.
Includes:
Does not include amphibians. If you include them, you have the tetrapods.
Starting in the 2019 redefinition of the SI base units, the elementary charge is assigned a fixed number, and the Ampere is based on it and on the second, which is beautiful.
This choice is not because we attempt to count individual electrons going through a wire, as it would be far too many to count!
Rather, it is because because there are two crazy quantum mechanical effects that give us macroscopic measures that are directly related to the electron charge. www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that the two effects are:
Those effect work because they also involve dividing by the Planck constant, the fundamental constant of quantum mechanics, which is also tiny, and thus brings values into a much more measurable order of size.
Interference pattern Updated 2025-07-16
What you see along a line or plane in a wave interference.
Notably used for the pattern of the double-slit experiment.
Amplifier Updated 2025-07-16
Main implementations: the same as electronic switches: vacuum tubes in the past, and transistors in the second half of the 20th century.
Video 1.
How to make an LM386 audio amplifier circuit by Afrotechmods (2017)
Source. Builds the circuit on a breadboard from minimal components, including one discrete transistor. Then plays music from phone through headset cables into a speaker.
tcpdump Updated 2025-07-16
To test it, let's get two computers on the same local area network, e.g. connected to Wi-Fi on the same home modem router.
On computer A, run on terminal 1:
sudo tcpdump ip src 192.168.1.102 or dst 192.168.1.102
Then on terminal 2 make a test request:
curl 192.168.1.102:8000
Output on terminal 1:
17:14:22.017001 IP ciro-p14s.55798 > 192.168.1.102.8000: Flags [S], seq 2563867413, win 64240, options [mss 1460,sackOK,TS val 303966323 ecr 0,nop,wscale 7], length 0
17:14:22.073957 IP 192.168.1.102.8000 > ciro-p14s.55798: Flags [S.], seq 1371418143, ack 2563867414, win 65160, options [mss 1460,sackOK,TS val 171832817 ecr 303966323,nop,wscale 7], length 0
17:14:22.074002 IP ciro-p14s.55798 > 192.168.1.102.8000: Flags [.], ack 1, win 502, options [nop,nop,TS val 303966380 ecr 171832817], length 0
17:14:22.074195 IP ciro-p14s.55798 > 192.168.1.102.8000: Flags [P.], seq 1:82, ack 1, win 502, options [nop,nop,TS val 303966380 ecr 171832817], length 81
17:14:22.076710 IP 192.168.1.102.8000 > ciro-p14s.55798: Flags [P.], seq 1:80, ack 1, win 510, options [nop,nop,TS val 171832821 ecr 303966380], length 79
17:14:22.076710 IP 192.168.1.102.8000 > ciro-p14s.55798: Flags [.], ack 82, win 510, options [nop,nop,TS val 171832821 ecr 303966380], length 0
17:14:22.076727 IP ciro-p14s.55798 > 192.168.1.102.8000: Flags [.], ack 80, win 502, options [nop,nop,TS val 303966383 ecr 171832821], length 0
17:14:22.077006 IP ciro-p14s.55798 > 192.168.1.102.8000: Flags [F.], seq 82, ack 80, win 502, options [nop,nop,TS val 303966383 ecr 171832821], length 0
17:14:22.077564 IP 192.168.1.102.8000 > ciro-p14s.55798: Flags [F.], seq 80, ack 82, win 510, options [nop,nop,TS val 171832821 ecr 303966380], length 0
17:14:22.077578 IP ciro-p14s.55798 > 192.168.1.102.8000: Flags [.], ack 81, win 502, options [nop,nop,TS val 303966384 ecr 171832821], length 0
17:14:22.079429 IP 192.168.1.102.8000 > ciro-p14s.55798: Flags [.], ack 83, win 510, options [nop,nop,TS val 171832824 ecr 303966383], length 0
TODO understand them all! Possibly correlate with Wireshark, or use -A option to dump content.
Telomere Updated 2025-07-16
grep Updated 2025-07-16
If you are a programmer, grep becomes a verb: "to grep" means "to search text files", much like "to Google" means "to search random stuff online".
Analog computer Updated 2025-07-16
Some of the earlier computers of the 20th centure were analog computers, not digital.
At some point analog died however, and "computer" basically by default started meaning just "digital computer".
As of the 2010's and forward, with the limit of Moore's law and the rise of machine learning, people have started looking again into analog computing as a possile way forward. A key insight is that huge floating point precision is not that crucial in many deep learning applications, e.g. many new digital designs have tried 16-bit floating point as opposed to the more traditional 32-bit minium. Some papers are even looking into 8-bit: dl.acm.org/doi/10.5555/3327757.3327866
As an example, the Lightmatter company was trying to implement silicon photonics-based matrix multiplication.
A general intuition behind this type of development is that the human brain, the holy grail of machine learning, is itself an analog computer.

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