Is there a standard, or widely accepted convention, for magic constants in crypto software? Inspired by Magic "Nothing Up My Sleeve" Numbers - Computerphile - YouTube [5:31]. If you just need a constant to begin your algorithm, and the value of that constant isn't important, why not have a widely known convention to always use the digits of Pi or Phi or other well known constant? It would seem that choosing arbitrary numbers is bad because it causes doubt as to the origin of the numbers which may lead some to suspect they were cherry picked for undisclosed weaknesses.
If you just need a constant to begin your algorithm, and the value of that constant isn't important, why not have a widely known convention to always use the digits of Pi or Phi or other well known constant?


Why not use all zeros or all ones then? Why not use what user provided us with? 

There is a joke: Good thing about standards is that we have so many to choose from.

Often there are some values that are supposed to have specific properties, like being prime numbers. Then you have to use CSPRNG with that constant. Why not use this CSPRNG, why not that one. This one is simple, this one is more secure, this is newer, this is more well-established etc.

In short: because they are used in widely different settings, and we usually have some vague requirements:


Sometimes it has to be of any length and secure (DH safe prime generation)
Sometimes it has to be of any length and just simple constant (HMAC)
Sometimes it has to be specific length and have high entropy (AES)
Sometimes it has to be fairly independent from another constant we used somewhere else


Last requirement is probably worst. There might be interference from two different algorithms that happen to use same constant, and since you have one standard you increase such possibility.

Even if you managed to fulfill that somehow, some values are supposed to have high entropy, and some can be plain anything. Making them meaningful decreases speed your algorithm will work on.

All that and you gain that 1% extra security that nobody did plant bug in algorithm. Sadly IMO this doesn't give us much and prevents smart designs that are faster while retaining security.