asuidyasiud

I understand where you are come from, but you are conflating different meta-levels (external vs. internal language/logic): You are absolutely free to use any formal expression "x" a second time, and - crucially - it will have the same mathematical meaning if you choose to do so, as can be seen by pondering over the tautology "P(x) <-> P(x)". This is not a property of the category that you chose to work with, but rather of the formal language that we use when engaging in mathematics, as you have demonstrated yourself when you had permitted that "psi \otimes \psi" made sense.

The non-existence of a morphism "psi -> psi \otimes psi" and the notion of "destroyed information" that you are discussing in the rest of your post is independent from all of this. If you wish I can elaborate on the "no cloning theorem".

No, applying a map does not mutate or consume the parameters, and therefore no information is destroyed. Function application in mathematics is referentially transparent.

To make this point perfectly clear: Whenever you encounter an expression such as "f(x)", you may freely re-use the expression "x" in a different place. This is a matter independent from the category you choose to work with -- for example, the expression "psi \otimes psi" makes sense in the monoidal category of Hilbert spaces.

There is nothing destructive about the map M: A x A -> A.

Mathematicians arguably do not think of the first example as a loop with a mutating variable, but rather as a short-hand notation for f(m) + ... + f(n) - as a macro, if you wish.

I agree with the second part.

It is completely irrelevant, ecologically speaking.

What is call option?

/s

If a group of people comes together, discusses, and comes by some process to a unanimous decision ("consensus") then it does usually make a lot of sense to regard the outcome as the "will of these people".

The point I am trying to make through the last n posts is that Arrow's theorem does concerns the impossibility of a certain, narrow-minded formalization. It is therefore incorrect to conclude that 'the "will of the people" is a nonsensical concept by Arrow's Impossibility Theorem', which is what you had claimed.

I have nothing to say about the people and churches of England.

You misread, I made the converse claim.

The point is that invoking an impossibility theorem oftentimes - and also in this case - demonstrates that the formalization one has chosen to work with is not a desirable one.

For example, if a group of people by some social process comes to a consensus then arguably this represents the "will of the people". Thus it makes sense to reason about this concept without requiring the existence of ranked preferences.

> It won't necessarily give you a proof that your result...

That is precisely the point.

Re "well within the safety margin":

> EDF was granted permission by the regulator in the summer to relax its graphite weight-loss limit at the Dungeness reactor in Kent from 6.2% to 8% after it came close to breaching the original safety margin.

> Hinkley-B and Hunterston-B are also getting close to their higher 15% limits, too.

You can get a DOI for github.

It's the correct substitute for umlauts if the latter are not available (as opposed to "Sud").