This was recently asked on Reddit.

To expand, who are Finney, Szabo, and Wei, and what did they do/contribute to the project that warranted being awarded denominations?

up vote 45 down vote accepted
  • Hal Finney was a cypherpunk activist of note, and the first Bitcoin user after Satoshi Nakamoto. He described his history with Bitcoin in this forum post. From that post:

    When Satoshi announced the first release of the software, I grabbed it right away. I think I was the first person besides Satoshi to run bitcoin. I mined block 70-something, and I was the recipient of the first bitcoin transaction, when Satoshi sent ten coins to me as a test. I carried on an email conversation with Satoshi over the next few days, mostly me reporting bugs and him fixing them.

  • Nick Szabo is a researcher who came up with bit gold and who developed the idea of smart contracts.

  • Wei Dai is a cypherpunk who came up with b-money, a concept which was referenced in section 2 of the Bitcoin paper.

What about an ada, babbage, shannon, grand, and einstein?

See unitMap (taken from https://github.com/ethereum/web3.js/blob/0.15.0/lib/utils/utils.js#L40):

var unitMap = {
    'wei':          '1',
    'kwei':         '1000',
    'ada':          '1000',
    'femtoether':   '1000',
    'mwei':         '1000000',
    'babbage':      '1000000',
    'picoether':    '1000000',
    'gwei':         '1000000000',
    'shannon':      '1000000000',
    'nanoether':    '1000000000',
    'nano':         '1000000000',
    'szabo':        '1000000000000',
    'microether':   '1000000000000',
    'micro':        '1000000000000',
    'finney':       '1000000000000000',
    'milliether':   '1000000000000000',
    'milli':        '1000000000000000',
    'ether':        '1000000000000000000',
    'kether':       '1000000000000000000000',
    'grand':        '1000000000000000000000',
    'einstein':     '1000000000000000000000',
    'mether':       '1000000000000000000000000',
    'gether':       '1000000000000000000000000000',
    'tether':       '1000000000000000000000000000000'
};

And a discussion about unit names here: https://github.com/ethereum/EIPs/issues/33 "ERC: finalise unit names"

The whitepaper only has wei, szabo, finney, ether: https://github.com/ethereum/wiki/wiki/White-Paper

web3.js has shannon etc. https://github.com/ethereum/web3.js/blob/master/lib/utils/utils.js

These other unit names are not popular and cause confusion, recent discussion in top comment: https://www.reddit.com/r/ethereum/comments/3to11c/eip_102_serenity_rename_gas_to_mana_vbuterin/

Is an EIP needed to formalize the unit names in web3.js? (Or remove them from web3.js?)

I would say as a matter of style, stick to using wei, shannon, finney and ether. Ether = main unit. Finney = for micropayments. Shannon = for gas prices. Wei = for discussion around APIs and other use cases where you need to talk about the underlying unit.

https://en.wikipedia.org/wiki/Hal_Finney_%28computer_scientist%29
https://en.wikipedia.org/wiki/Nick_Szabo
https://en.wikipedia.org/wiki/Claude_Shannon
https://en.wikipedia.org/wiki/Charles_Babbage
https://en.wikipedia.org/wiki/Ada_Lovelace
https://en.bitcoin.it/wiki/Wei_Dai

The names aren't all meant to be used at the same time; the goal of specifying suggestions for all of them was to have some schelling point on what to use for smaller denominations so that people could easily talk about varying quantities of ether regardless of whether the ETH price was $0.01, $10 or $100,000. In Bitcoin, the community is finding it hard to agree on a smaller denomination (though I suspect that the choice of 10^8 as the base denomination instead of something 10^3n also wasn't helpful), and so we see people talking about 0.0037 BTC, etc all the time; this was what I wanted to avoid. "Millibitcoin" is hard to pronounce in a way that "finney" isn't (also, do you really want to tell a cashier at a bank that you want to purchase "five hundred mETH"?).

I wrote this a while ago. A light-hearted attempt at an explaination: https://medium.com/@tjayrush/what-the-f-is-a-finney-8e727f29e77f

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