Ciro Santilli @cirosantilli 37

This notation is so confusing! People often don't manage to explain the intuition behind it, why this is an useful notation. When you see Indian university entry exam level memorization classes about this, it makes you want to cry.

The key reason why term symbols matter are Hund's rules, which allow us to predict with some accuracy which electron configurations of those states has more energy than the other.

web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf puts it well: electron configuration notation is not specific enough, as each such notation e.g. 1s2 2s2 2p2 contains several options of spins and z angular momentum. And those affect energy.

This is why those symbols are often used when talking about energy differences: they specify more precisely which levels you are talking about.

Basically, each term symbol appears to represent a group of possible electron configurations with a given quantum angular momentum.

We first fix the energy level by saying at which orbital each electron can be (hyperfine structure is ignored). It doesn't even have to be the ground state: we can make some electrons excited at will.

The best thing to learn this is likely to draw out all the possible configurations explicitly, and then understand what is the term symbol for each possible configuration, see e.g. term symbols for carbon ground state.

It also confusing how uppercase letters S, P and D are used, when they do not refer to orbitals s, p and d, but rather to states which have the same angular momentum as individual electrons in those states.

It is also very confusing how extremelly close it looks to spectroscopic notation!

The form of the term symbol is:

^{2 S + 1} L_{J}

(1)

The

2 S + 1

can be understood directly as the degeneracy, how many configurations we have in that state.

Video 1.

Atomic Term Symbols by TMP Chem (2015)

Source.

Video 2.

Atomic Term Symbols by T. Daniel Crawford (2016)

Source.

youtu.be/DAgEmLWpYjs?t=2675 term symbols for carbon ground state

Bibliography:

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x86 custom instructions Updated 2025-07-16

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Intel is known to have created customized chips for very large clients.

This is mentioned e.g. at: www.theregister.com/2021/03/23/google_to_build_server_socs/

Intel is known to do custom-ish cuts of Xeons for big customers.

Those chips are then used only in large scale server deployments of those very large clients. Google is one of them most likely, given their penchant for Google custom hardware.

TODO better sources.

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ASCII art Updated 2025-07-16

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It should be a crime to automatically generate ASCII art from images.

For some ASCII art in the Bitcoin blockchain see: ASCII art.

Random fun mentions:

en.wiktionary.org/wiki/roflcopter | knowyourmeme.com/memes/roflcopter
www.ludd.ltu.se/~vk/pics/ascii/junkyard/misc/who's_who.txt "Who's who in the ascii art world" contains a list of well known artists with their signatures

        z

        ^
        |    *------*
        |   /|      /
        |  / |     /|
top -------*------* |
        |  | *----|-*
        |  |/     | /
        |  |      |/
bottom ----*------*
        |  |      |
        +--|------|-----> y
       /   |      |
      /    |      |
  x  /     |      |
    v
          left   right

Code 1.

3D cube plot ASCII art by Ciro Santilli (2021)

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CIA 2010 covert communication websites / iranfootballsource.com Updated 2025-07-16

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Classification of 6-transitive groups Updated 2025-07-16

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math.stackexchange.com/questions/700235/is-there-an-easy-proof-for-the-classification-of-6-transitive-finite-groups says there aren't any non-boring ones.

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Conjecture reduction to a halting problem Updated 2025-07-16

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bbchallenge.org/story#what-is-known-about-bb lists some (all?) cool examples,

BB(15): Erdős' conjecture on powers of 2, which has some relation to Collatz conjecture
BB(27): Goldbach's conjecture
BB(744): Riemann hypothesis
BB(748): independent from the Zermelo-Fraenkel axioms
BB(7910): independent from the ZFC

wiki.bbchallenge.org/wiki/Cryptids contains a larger list. In June 2024 it was discovered that BB(6) is hard.

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Cool data embedded in the Bitcoin blockchain / 503: Bitcoin over capacity Updated 2025-07-16

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Starting tx a87d406fae047258a12923b3c11a797a5765bd8f868df5c7e9b1cead0e92c9c1: the message:

503: Bitcoin over capacity!

appears about 13 thousand times. WTF happened?

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Cool data embedded in the Bitcoin blockchain / Illegal content of block 229k Updated 2025-07-16

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These can be viewed at bitcoinstrings.com/blk00052.txt and are mostly commented on the "Wikileaks cablegate data" section of Hidden surprises in the Bitcoin blockchain by Ken Shirriff (2014).

Soon after block 229991 uploaded the Satoshi uploader, several interesting files were added to the blockchain using the uploader, and notably some containing content that might be illegal in certain countries, as a test to see if this type of content would make the Bitcoin blockchain illegal or not:

tx 08654f9dc9d673b3527b48ad06ab1b199ad47b61fd54033af30c2ee975c588bd block 229999 contains a leaked private key and a link to: threatpost.com/en_us/blogs/ami-firmware-source-codAe-private-key-leaked-040513
tx b96af3b69b48a82c5eae3e44ebb6ef93f30d7764b1d5b40243e11b0d374ac1b7 block 230001 contains the link:
en.wikipedia.org/wiki/Illegal_prime
followed presumably by one such prime starting with:
4 85650 78965 73978 29309 84189 46942 86137 70744 20873 51357 92401 96520 73668
The number is quoted e.g. at: www.computerforum.com/threads/illegal-prime-number.67782/
- tx 237783998a6799264983150187a73ab6d116f2ba78d3e1f88529e95229f59d67 block 233620 contains another illegal prime starting with:
49310 83597 02850 19002 75777 67239 07649 57284
This one is quoted in a few places online in blockchain illegality discussions:
- www.reddit.com/r/Bitcoin/comments/1akyy4/comment/c8yel60 "What happens if someone inserts illegal content into the block chain?" (2013-03-19)
- news.ycombinator.com/item?id=8055243 "Filecoin – Data storage network and crypto-currency based on Bitcoin" (2014-07-18)
tx 54e48e5f5c656b26c3bca14a8c95aa583d07ebe84dde3b7dd4a78f4e4186e713 block 230009 contains the Bitcoin white paper: bitcoin.org/bitcoin.pdf More context: bitcoin.stackexchange.com/questions/35959/how-is-the-whitepaper-decoded-from-the-blockchain-tx-with-1000x-m-of-n-multisi
tx 691dd277dc0e90a462a3d652a1171686de49cf19067cd33c7df0392833fb986a block 230203 Cablegate index. The announced filename is cablegate-201012041811.7z. As mentioned in Hidden surprises in the Bitcoin blockchain by Ken Shirriff (2014), it has an ASCII list of several other transactions, which presumably when downloaded with the Satoshi uploader can concatenated lead to the full 7z file. Also as mentioned by Ken, it is infinitely easier for the average user to just access the cables directly on WikiLeaks :-) The data is preceded by the message:
```
sSEXWikileaks Cablegate Backup

cablegate-201012041811.7z

Download the following transactions with Satoshi Nakamoto's download tool which
can be found in transaction 6c53cd987119ef797d5adccd76241247988a0a5ef783572a9972e7371c5fb0cc

Free speech and free enterprise! Thank you Satoshi!
```
tx dde7cd8e8f073a525c16c5ee4e4a254f847b7ad6babef257231813166fbef551 block 230229 and tx 4a0088a249e9099d205fb4760c28275d4b8965ac9fd56f5ddf6771cdb0d94f38 block 230231 contain indexes of pages from The Hidden Wiki. These can be viewed at: bitcoinstrings.com/blk00052.txt. Not reproduced here because we are cowards.

So basically, this was the first obviously illegal block attempt.

None of this content is particularly eye-popping for Ciro Santilli's slightly crazy freedom of speech standards, and as of 2021, the Bitcoin blockchain likely hasn't become illegal anywhere yet due to freedom of speech concerns.

Furthermore, it is likely much easier to find much worse illegal content by browsing any uncensored Onion service search engine for 2 minutes.

Ciro Santilli estimates that perhaps the uploader didn't upload child pornography, which is basically the apex of illegality of this era, because they were afraid that their identities would one day be found.

Bibliography: