Hi Luis,
O.K.:

"Well, if to "travel through data" doesn't take time, then what is meant by "travel"? "

Point understood, BUT:

I should have made the distinction by using the phrase "random travel through the data".

Sure, even random travel "takes time" you may say; but zapping all over the show "randomly" doesn't exactly differentiate the "random data" as anything other than "random data", one might say. (Caution: I don't guarantee these arguments are right.)

So what I mean is: maybe Dr. D. doesn't want his algorithm to depend on the DIRECTION you travel through the data: he wants the ALGORITHM itself to be sole determinant of that DIRECTION.

So his algorithm will be what "makes time" out of a 'random' collection. (However, there is no such thing as randomness, one may argue).

"That is, remove time and you aren't talking about an algorithm at all." Absolutely true.
His "algorithm" is where "time" comes from.

He looks at data that can be in any order.
He wants an algorithm (rule) to say you have to take A PARTICULAR CONSTRAINED PATH through that data; an ORDERED path.

That means the algorithm itself CREATES "time" by constraining your path through the data to a particular ordering, a certain sequence.

His "algorithm" is only "independent of time" in that IT IS TIME.

Since he makes his algorithm ALL THE TIME THERE IS then there is no time outside of it in his scheme: leave out his algorithm and he might say the data is non-ordered (free to be any order; so unconstrained).

His "algorithm" generates "time" in his data; it constrains the data to a particular sequence, it orders the data. The algorithm is independent of time only in that it does not depend on any other
ordering of the data: it is itself a complete ordering of the data that was otherwise free data.

All his "time" is in the "algorithm" itself; it does not depend on other ordering. He wants his algorithm to be the ONLY CONSTRAINT on his data; he wants it to be the "time" generator for his data.

(That is my somewhat muddly guess).

"No certain measurement we make possesses space, but no time -- or time, but no space." Well it takes "time" to travel down a ruler; it takes "length" to have an atomic vibration, a pendulum path, a clock-hand change in position.

" And anything where our human restrictions cause us to only know one aspect by sacrificing our knowledge of the other is a measurement where it is patently impossible (and dumb) to assign algorithms. "

I'll try this idea:
"know only one aspect": know a bunch of data that is free to be in any order;
"sacrifice our knowledge of the other": sacrifice our knowledge of the other aspect being the (OPTIONAL) CONSTRAINT aspect.

But your data must be free (unconstrained); or constrained. Can't be both (except as two ways of looking at optionally constrained data)

"a measurement that is patently impossible (and dumb) to assign algorithms.":

Is it impossible to assign an algorithm (a rule) to a measurement of something that is EITHER free data (any order allowed) or optionally constrained data (order specified)?

Well, the only rule you could assign will be the actual rule of the algorithm itself; your measurement will be: here is my optional rule that I can constrain this data with if I want to.

Dr. Dick seems to be interested on how do optional constraints on free data; interfere with each other; how does logical consistency keep all yout optional rules tidy so your collection of rules don't contradict each other?

Tiny regions of space-time are called uncertain for I guess whatever reason Alex once said!

Can a thing exist without "space"?

Can a thing exist without "time"?

There is a point here which I have tried to tell Dr. Dick that you may agree with.

That is, he has to give his collection of data some arbitrary "time" structure (thus arbitrary algorithm) to have it exist and deal with it.

But I guess if that starting "data in arbitrary time" is such that from here you are FREE TO CHOOSE any arrangement; then he may claim that for arguments sake he is only interested in the "New time" or "new order of the data" that his proposed "algorithm" will deliver.

So he is not concerned that he might be stuck with data in arbitrary space and time; but just concerned with how new rules for ordering that data might interfere with each other in the maintainance of logical consistency between a bunch of new rules?

All he may be saying is that his "algorithm" MUST BE INDEPENDENT of any particular starting arrangement (starting space-time) of his data.

His algorithm must SOLELY BE RESPONSIBLE FOR generating a new arrangement. His "algorithm" must deliver the "new time" that he is interested in comparing with other "new time" possibilities for the data.

He then finds presumably that the laws of logical consistency between introduced algorithms (that keep re-ordering the data when introduced) allow patterns to be observed (like the "life" computer programme I guess) that mimick the laws of physics.

Where a series of introduced algorithms leave an area of data unchanged; perhaps he calls that area "mass".

Where one of these "masses" is coupled to a particular new algorithm, he might call this "momentum".

All the forces of nature (including gravitation, etc. ) might even be represented by the cellular automata interactions in the computer game "life" refered to in a post I wrote "amazing website".

-dolphin