Re: On raw strings in <origin> commit field

[Mark H Weaver]

Hi Liliana,

Liliana Marie Prikler <liliana.prikler@gmail.com> writes:
> it ought to have been comparatively easy to infer that I was talking
> about push actions (plural) as sequences, not as individual push
> actions like you've used for your proof.

It makes no difference, because the set of push actions is closed under
sequential composition.  Moreover, the argument in my proof applies to
*any* kind of action that can be communicated over a digital
communications channel in finite time.

> From here on, I will assume that each individual push action is finite
> as you did, but I don't think that using communications of finite
> length are a helpful building block here.

Really?  You don't think communications of finite length are a helpful
building block here?

Note that in the real world, every observable time interval is finite.

> Porting Git to Turing
> Machines would have the effect of allowing an infinite tape shared
> between multiple machines and they could possibly run forever.

I'm sorry, I thought we were talking about "Git" as it exists in the
real world.  Please recall that the motivation for my proof was to
refute the following claim of yours from a few messages ago:

>> How about pointing out what acts as the diagonal in your reasoning?
>
>If you are talking specifically about the uncountability of real
>numbers, that'd be quite deep down (as in an uncountability of push
>actions to a particular Git repo, particularly if we also allow
>reinitialization).

You referred to "Git" here.  That's why my proof was about Git.  You
didn't say that you were talking about some theoretical variant of Git
that supports "push actions" that literally *never* end, and that runs
on a theoretical machine with infinite memory that can never be built.

> As we're trying to generalize your proof for a single push action to
> be chosen among a finite set to all communications to a series of push
> actions, we do encounter a problem if we were to encode this as a mere
> list of push actions.  This can be done by a rather simple Cantor
> proof: The set of lists of a particular type T which admits at least
> two values is uncountable (a list of booleans can be directly mapped
> to a binary number and thus Cantor's original proof applied).

No, that's incorrect.  The set of lists of booleans is countable.
Moreover, for any type T, if the set of objects of type T is countable,
then the set of _lists_ of objects of type T is also countable.

Note that lists are finite, by definition.

If you intend to claim that by "push actions", you meant to include
infinite streams of push actions: this has no relevance to the real
world.

Even if we live in an open universe, the fact remains that at any
arbitrary point in time, the age of any git repository is always finite.
Therefore, no one can ever observe the result of an infinite-length
"push action" in the real world.  They can only ever observe the result
of some finite prefix of that so-called "push action".

* * *

I'm sorry, but I'm growing tired of this discussion.  I suppose you will
want to have the last word.  I'll try to resist the temptation to
correct any errors in it, but my silence should not be interpreted as
acceptance of your future claims.

     Regards,
       Mark

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