### How a sequence of quantum jumps could give rise to experience about continuous flow of time?

I am trying to improve my understanding about the relationship between subjective and geometric time. Subjective time corresponds to a sequence of quantum jumps at given level of hierarchy of selves having as correlates causal diamonds (CDs). Geometric time is fourth space-time coordinate and has real and p-adic variants. This raises several questions.

- How the subjective times at various levels of hierarchy relate to each other? Should/could one somehow map sequences of quantum jumps at various levels to real or p-adic time values in order to compare them - as quantum classical correspondence indeed suggests?

- Subjective existence corresponds to a sequence of
*moments of consciousness*: state function reductions at opposite boundaries of CDs. State function reduction reduction localizes either boundary but the the second boundary is in a quantum superposition of several locations and size scales for CD. We however experience time as a continuous flow. Is this a problem or not? One could argue that it is not possible to be conscious about being unconscious so that gaps would not be experienced. But is this so simple? We are indeed able to experience the gap in sensory consciousness caused by sleeping over night (this does not mean we have been unconscious: we just do not remember).

- Subjective time is certainly not metricizable whereas geometric time is and defines a continuum. But are moments of consciousness well-ordered as the values of real variant of geometric time are? This relates closely to the relationship of subjective time to geometric time. Certainly subjective time does not allow any continuous measure in real sense as geometric time does. One can however map moments of consciousness to integers.

- It would seem natural to be able to say about two moments of consciousness - call them A and B, - whether A is before B or vice versa. Moments of consciousness would be well-ordered and could be mapped to
*real*integers. But is this the case always? There is experimental evidence for the fact that consciously experience time ordering does not always correspond to the physical one. This was observed already by Libet (I have tried to understand these findings for the first time here).

- What about p-adic integers as labels for moments of consciousness as suggested by the vision about p-adic space-time sheets as correlates for cognition and intention (as time reversal of cognition). Given p-adic integers m and n, one can only say whether the p-adic norm of m is larger than, smaller than, or equal to that of n. One can say that p-adic integers are weakly ordered.

- It would seem natural to be able to say about two moments of consciousness - call them A and B, - whether A is before B or vice versa. Moments of consciousness would be well-ordered and could be mapped to

p-Adic integers form a continuum in p-adic topology. Could one map the infinite sequence of quantum jumps already occurred to p-adic integers and in this manner to p-adic continuum instead of real one? Could the p-adic cognitive representations allow to achieve this? If so, the experience about conscious flow of time could be due to the p-adic topology for cognitive representation for the sequence of quantum jumps!

**Could p-adic integers label moments of consciousness and explain why we experience conscious flow of time?**

Next arguments give a more precise formulation for the idea that p-adic integers might label the sequence of quantum jumps at the level of conscious experience, or rather reflective consciousness involving various representations realized as "Akashic records" and read consciously by interaction free measurements (assuming that they make sense in TGD: NMP considerably modifies the standard quantum measurement theory).

- Most p-adic integers expressible as n= ∑
_{k}n_{k}p^{k}are infinite in real sense and in p-adic topology they form a continuum. Suppose that the infinite sequence of moments of consciousness that have already taken place can be labelled by p-adic integers and look what might be the outcome.

- Sounds very strange in ears of real analyst but is true: the integers n and n+ kp
^{N}, for N large are very near to each other p-adically. In real sense they are very far. This allows to fill the gaps between say integers n=1 and 2 by p-adic integers which are very large in real sense.

- The p-adic correlate of the sequence of discrete quantum jumps/moments of consciousness would define p-adic continuum which in turn can be mapped to real continuum by canonical identification.

This raises two questions.

- p-Adic integers are not well-ordered. Could one induced the well-ordering of real time to p-adic context by mapping p-adic time axis to real one in a continuous manner and in this manner achieving mapping of moments of consciousness to real time axis?

- Could canonical identification ∑
_{k}n_{k}p^{k}→ ∑_{k}n_{k}p^{-k}map (or its appropriate modification) allow to map p-adic integers to real numbers and in this manner induce real well ordering to the p-adic side. The problem is that real number with finite pinary expansion has second infinite expansion (1=.9999... is example using decimal expansion) so that two p-adic time values correspond to any real time value with finite pinary digits. Should one restrict the consideration to integers with finite number of pinary digits (finite measurement resolution) and select either branch? Could the two branches correspond to real time coordinates assignable to the opposite boundaries of CD defining two conscious selves in this scale?

**What happens when I type letters in wrong order?**

One can speak about sensory and cognitive orderings of events corresponding to reals and p-adics (for various values prime p or course). The cognitive ordering of events would not be well-ordering if cognition is p-adic. Is there any empirical support for this besides Libet's mysterious looking findings?

Maybe. For instance, as I am typing text I experience that I am typing the letters of the word in the correct order but now and then it happens that the order is changed, even the order of syllables and sometimes even that of short words can change. It is probably easy to cook up a very mundane explanation in terms of neuroscience or even electric circuits from keyboard to computer memory, or computer itself. One can however also ask whether this could reflect the fact that p-adic ordering of the intentions to type letter is not well-ordering and does not always correspond to the real number based order for what happened ?

In TGD Universe writing process involves a sequence of transformations of p-adically realized intention to type a letter to a real action (doing it). At space-time level it is therefore a map from p-adic realm to real realm by a variant of canonical identification crucial in the definition of p-adic manifold concept assigning to real preferred extremal of Kähler action a p-adic preferred extremal in finite measurement resolution (see this). ´

The variant of canonical identification in question defines chart maps from real to p-adic realm and vice versa, and is defined in such a manner that discrete and rationals in a finite subset of rationals are mapped to themselves and defining intersection of real and p-adic realms.

- In the case of p-adic integers this subset is characterized by a cutoff telling the power of p below which p-adic integers and real integers correspond to each other as such. For the corresponding moments of consciousness (now intentions to type letter) one has same ordering in both realms. For integers containing higher powers of p a variant of canonical identification mapping p-adics to reals continuously is applied. In this case ordering anomalies can appear.

- Another pinary cutoff comes from physics: real preferred extremals are mapped to p-adic preferred extremals and vice versa: without the cutoff the p-adic image of real extremal would be continuous but non-differentiable so that field equations would not make sense. The cutoff tells the largest power of p up to which the variant of canonical identification is performed for p-adic integers. Also now ordering anomalies appear if one regards p-adic integers as ordinary integers.

- For the remaining integers the map is obtained by completing the discrete set of points to a preferred extremal of Kähler action on both real and p-adic sides so that physics enters into the game. This assignment need not be unique and the most natural manner to handle the non-uniqueness is to form quantum superposition of all allowed completions with same amplitude: this effective gauge invariance would be very natural from the point of view of finite resolution and conforms with the vision about inclusions of hyper-finite factors as a representation for finite measurement resolution giving rise to the analog of dynamical gauge symmetry.

Could the strange inconsistencies between cognitive (sequences of intentions) and sensory time orderings (sequence of typed letters) reflect the fact that the ordering of p-adic integers as real integers is not the same as the ordering of their real images under canonical identification? Could it be possible to test this and perhaps deduce the prime p characterizing p-adic topology of cognitive representation in question?