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timpu'i numărabil

Written by Romeo Anghelache no comments

gargariseam p'aci c'am motive să cred că unitatea medie a timpului fizic propriu unui sistem fizic delimitat arbitrar e lineară'n entropia informațională a sistemului, pen'că timpu'i numărare de evenimente.

găsesc acu o lună'n urmă, spre surprinderea mea, în Istoria filosofiei vestice de Bertrand Russell, o chestie interesantă: lui Russell i se părea curios că Aristotel considera că timpu'i numărabil. din perspectiva descrisă mai sus, mie nu mi se pare curios deloc. timpu' nu'i altceva decât numerotare (contorizare a evenimentelor observate), deci orice măsură a timpului trebe să fie numărabilă. mai ciudată, de'a dreptu' nefondată, mi se pare presupunerea că durata i'un interval continuu. la tema asta merg liniștit pe mâna lu' Aristotel.

language and arithmetics

Written by Romeo Anghelache no comments

The fundamental theorem of arithmetics says that every natural number greater than 1 is a unique product of prime numbers.

Numbers are, in fact, words written in a language, and the basic, unambiguous, irreducible, particles of this language are the prime numbers, not the digits, because of the theorem above; this means that factoring a number is equivalent to finding a representation of that number that maximizes its information entropy, or finding its proper time unit as an object.

essay on time, subject and object

Written by Romeo Anghelache no comments

Time is a measure of how many events happen in a given situation, it means noticing (counting) them, it is a measure of the knowledge an observer can gain about the surroundings. This kind of time is not universal, it is proper to the observer(s), to the observed, and, in general, to (de)limited physical systems, that is, different observers have naturally different proper time units, dependent on the contexts of those observers.

We can build a more formal relationship between time and knowledge or information. We'll use two ideal cases to formulate a plausible hypothesis, and then plunge into a more realistic world with it.

An observer immersed in a space with no events, would wait an infinity for an event to happen, in other words, the unit of time proper to the observer would be infinity, the observer can't notice anything happening, cannot use a definite unit of time for itself. There's nothing else the observer can define its unit of time relative to, so we can't speak of an infinity of units, therefore, in this ideal case, it's more reasonable to consider its unit of time as being infinite.

To put it differently: if the probability of an event is equal to zero, the unit of time of the event counter (the observer) is infinite.

An observer who is absolutely sure an event will happen (has total knowledge about it) has a unit of time equivalent with zero, null. Because total knowledge about an event means exactly noticing that event, while it happens (if not being the event itself).

To put it differently: if the probability (p) of an event is equal to one, the unit of time (u) of the event counter (the observer) is equal to zero.

These ideal, extreme, cases, suggest, therefore:

if p=0 then u=∞ if p=1 then u=0

A simple function which maps these two extreme cases onto one another is the natural logarithm, so, we can write:

u=-kln p

This mapping is not unique, just a plausible proposal. k is a dimensional constant.

Now for the real world, where multiple events happen, let's label them with an integer, i. An observer surrounded by a number n of events, each of them happening with a probability pi, where i labels each of those events, can calculate an average unit of time, using the logarithmic relation above:

<u>=-kΣipiln pi.

This relation says that the average unit of time proper to an observer is equal with the quantity of information contained in that part of the environment which interacts with it, the 'noticeable' part).

In other words, any thing's proper unit of time is proportional to the informational entropy of its interacting context.

In the mechanical world, where the Newtonian, or Einsteinian, time is used, anything is bound to happen with absolute certainty, so the average time unit u calculated above, is zero.

However, given the history of our concept of time understanding, we chose a constant unit of time, to use it as a gauge for all the other times we'd like to measure. This mechanical gauge has been chosen because the physical process used in defining it is extremely regular (doesn't bring any new knowledge to the observer: the observer knows already what will happen with this regular system when it notices other, independent, events). So we can come with this constant and add it to the relation above, to accomodate our present, conventional, use of the mechanical, constant, unit of time. Let's name this constant c. It means a conventionally transferred knowledge from a purely mechanical system.

So time and knowledge are the same, and their formal relation is:

<u>=-kΣipiln pi+c.

In other words, any thing's proper unit of time is linearly dependent on the informational entropy of its interacting context (that part of the environment which interacts with it).

Now, if we split conceptually a physical system in two, how can we delimit which one is the observer/subject and which one is the observed/object? Based on this kind of time interpretation (each delimited physical system has a proper unit of time of its own), we can say: that physical region having a smaller characteristic unit of time is the observer, the subject, the rest of it, up to the whole (initially delimited) system in discussion, is the observed/the object.

This delimiting procedure is natural, a subject relies on some object invariants to study it, in other words, the subject's time unit has to be smaller than the object's own time unit (the subject needs at least one event to notice an object's relatively invariant feature).

Let's call it statistical time, if not physical time, shall we?

So, unless you know a way to unknow or uninteract with things, you can't turn back in time. This asymmetry should pervade any self-respecting formalism about the relevant parts of nature.

This is an idea which started to define itself in 1986, and took the present form in 1996. This essay is its first, widely available for public, instance.

Peer review this and don't forget to quote me, maybe somebody will find it useful, check my CV and will offer me a research (programmer) position in a (spanish, optimally) digital library, after all ;).

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