Maybe this will help. Here are two criticisms of comp, and two hypotheses 
which aim for a more mathematical treatment of PIP principles under MSR.
*
Presumption of repeatability* (PR) - By overlooking the possibility of 
absolute uniqueness, comp must conceive of all events as locally documented 
stereotypes of a Platonic template rather than true originals. This 
contradicts our intuitions about the proprietary nature of identity and 
would seem to counterfactually predict a very low interest in qualities 
such as individuality and originality, and identification with trivial 
personal preferences. Of course, what we see the precise opposite, as all 
celebrity it propelled by some suggestion unrepeatability and the fine 
tuning of lifestyle choices is arguably the most prolific and successful 
feature of consumerism. 

*Presumption of finite simplicities* - Because comp provides uniqueness 
only in the form of the relative scarcity of vastly complex numbers, it can 
be said to allow for the possibility of novelty only in one direction; that 
of more quantity. New qualities, by comp, must arise on the event horizons 
of the UD, yet qualia inherently speaks in a language of rich simplicity 
instead of cumbersome computables. With comp, there is no new 'one', but in 
reality, every human experience is exactly that.

Hypothesis:

*Diagonalization of the unique* - Because computation lags behind 
experience, no simulation of a brain can catch up to what a natural person *can 
be*, since the potential for their uniqueness is immeasurable and 
unprecedented. Also, nothing can be copied before it is unique, so PIP 
flips the presumption of repeatability (PR) so that all novelty exists as 
an absolutely new simplicity as well as a relatively new complexity, such 
that the continuum of novelty extends in both directions. 

The false dichotomy posed by comp in which we are forced to choose between 
the truth of Church-Turing and the existence of an infinitely low level of 
substitution for human personhood is exposed because under PIP, computation 
is a public repetition of what is irreducibly unrepeatable and private. 
Computation can never get ahead of experience, because computation is an a 
posteriori measurement of it. 

The computer model of what an athlete will do on the field that is based on 
their past performance will always fail to account for the possibility that 
the next performance will be the first time that athlete does something 
that they never have done before. Natural identities are not only 
self-diagonalizing, natural identity itself is self-diagonalization. The 
emergence of the unique always cheats prediction, since all prediction 
belongs to the measurements of an expired world which did not yet contain 
the next novelty.

*Pushing UD* - My admittedly limited understanding of UDA gives me a 
picture of the UD as a program which pulls the experienced universe behind 
it as it extends the computed realm ahead of local appearances. It assumes 
a priori arithmetic truth which simply 'is' which produces the future from 
a fixed past. All phenomena are built bottom up from generic, 
interchangeable bits. The hypothesis under PIP is that awareness is pushing 
the UD, not being pulled by it. Each new number is the residue of an 
unprecedented experience as it decays from immeasurable private qualia into 
quantifiable public reflections. Every measure requires a ruler. Some 
example which is presented as an index for comparison. A "new Michael 
Jordan". A third world war. The uniqueness comes first, and the 
computability follows - fudging and filling as necessary, including ways 
which could be interpreted as supernatural (retrocausational 
discontinuities, mysterious lucky coincidences, etc).

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