Topic: Reasoning behind arbitrary numbers (Read 605 times)

+1 from OP. Very interesting read.

Also thanks to DannyHamilton for pointing out the degree to which these magic numbers are co-dependent.

And by the way, I also think these numbers matter to an extent, if only psychologically. We're just now in the BTC-vs-mBTC stage, which would have come at another point in time (or not at all) if other numbers were chosen.

Thanks for that link.


If the initial block reward is 128 rather than 50, someone would then ask why not 50 or 100.
I guess many of these numbers were picked without particular reason.

Some of the numbers were arbitrarily chosen by Satoshi simply because he thought they seemed like they'd be reasonable.  Others are the result of mathematics based on the arbitrarily chosen  numbers.

Numbers that appear to have been chosen arbitrarily because Satoshi felt like they were reasonable:

5 000 000 000 integer (no decimals) units rewarded per block in the beginning (these units are now commonly called "satoshis").
1 BTC = 100 000 000 integer units (resulting in the block reward being referred to as "50.00000000 BTC").
Difficulty is adjusted every 2016 blocks to keep the average block creation rate close to 2016 blocks per 2 weeks.
Block reward is divided in half (and any decimal portion is truncated) every 210,000 blocks (approximately every 4 years).


You can see from these arbitrary "rules" that the rest of the numbers you ask about can be calculated.

If you start with a reward of 5 000 000 000 and then cut the reward in half every 210 000 blocks (truncating the decimal portion), then the last 1 unit rewarded will be in block 6 929 999 which at a rate of 210 000 blocks every 4 years will be in the year 2140.  If you add up all the rewards from all 6 929 999 blocks, you find that the total number of integer units that will be created is 2 099 999 997 690 000.  Since 1 BTC = 100 000 000 integer units, this means that the total number of bitcoins that will be created is 20 999 999.97690000 which is close enough to 21 million that most people just say "21 million" instead of trying to remember the exact actual number that will be created.

The smallest unit is 10^-8 because the BTC designation was chosen to be 10⁸ integer units.  This resulted in a "reasonable sounding" 50 BTC for the initial reward.  Satoshi could have just as easily chosen 10⁷ integer units or 10⁹ integer units to be designated as "a BTC", but that would have resulted in either a block reward of 500 BTC or 5 BTC.  Satoshi felt like those numbers sounded too extreme.

I believe they do matter very much. Miner rewards are the key element for the security of the chain.

Except for inflation % over time, nothing really matters and any numbers bitcoin is built on would work in my opinion

We refer to these numbers as "magic numbers" :p

See https://bitcointalksearch.org/topic/bitcoin-protocol-magic-numbers-and-reason-263750 for an example of a discussion about them.

If there was a reason they wouldn't be arbitrary, no?
I don't think there is an official reason. Every alt coin seems to be arbitrarily tweaking those values for no reason either. Of course they provide some non-answer that boils down to "I think x is better than y".

Since I'm a newbie and this has probably been asked before, I thought I'd spam it to the Newbies section. Is there a good text, FAQ or similar on the reasoning behind the choice of the arbitrary numbers bitcoin is built on? Such as… why 21 million BTC rather than 1 or 5000 or 10 trillion? Why are they awarded in chunks of 50 rather than 0.1 or 1 or 210? Why is the smallest unit 10^-8 BTC rather than 10^-6, 10^-9 or 10^-10?