Actually, they could do just what is suggested, then apply that "random number" to select a pre-defined pattern in a lookup table. So nope, you haven't disproved patterns. Even though I've pretty much given up on the idea of finding the pattern or patterns to unlock, doesn't mean anyone has disproved them.
Oh, and by the way, take a look at my professions. I see a pattern there, do you? I suspect that my last two professions (1 holo, 1 opener) will be Smuggler and Architect. That's based on 3 data points. Guess I'll just have to wait until I grind out BE next week (owie, my wrist) to see if I'm close.
Laeri Tor'Zon 15 Masteries (in order): Marksman, Scout, MCH, Pistoleer, TKA, Fencer(H1), Medic, Combat Medic(H2), Bio-Engineer(H3), Pikeman(H4), Brawler, Entertainer, Dancer, Image Designer, Artisan, (Wrong on two possible pattern guesses for myself so far). Pre-guessing my opener: Swordsman or Weaponsmith.
No there is a different reason for those professions appearing.
What % of players have mastered marksman since the beginning?
What % have mastered chef or pikeman?
The holo will never tell you a profession you mastered. Hence all the unused professions are coming up the most and almost no one has gotten marksman.
Because of this you cannot figure out a pattern based on first, second, ... holo unless you get 4 to tell you something. Your first or second or third may be finished before you use your first holocron. Your second doesn't magically become your first in the pattern, if there is one. You just never know what your first one is.
On computer randomness... true, it will never produce a truly random set of numbers. Take the following example.
A leaf falls from a tree. Given the shape of the leaf, it's weight, the height of the tree, the composition of the air, the air pressure, the friction, the strength of gravity, and all the other variables, you can predict exactly where that leaf will land every time.
The problem is, that the "random" computer number, although not actually random, could be based on any number of variables, none of which we know.
For all we know, the server is running Pi, and takes each set of two numbers as a % of 100, multiplies by 32, and rounds off to find a profession number. Although there is a pattern, you have no idea where you lie, and aren't likely to figure it out.
When I don't have a random function available to me in programming, I often will take the sine or cosine of a number like the primary key of a database table. I get numbers anywhere from -1 to 1, and can normalize that set to any range I like. Then sort, and I get an order that looks random to end users. It isn't, but from the end user perspective, and not knowing what they have as an ID, or what I used, or what all the other people have, they are very unlikely to find a pattern in it.
That would be a very simple way to appear random. With a few more functions, you could make it infinately more complex.
Point is, no, it's not really random, but without a lot more information, and some luck, you aren't going to be able to figure it out. That is, of course, assuming the "random" theory is correct...
Lund0529 does provide a reasonable explanation of computer random numbers. In beginning programming classes the function often used is random(-timer) this means that the current timer tick is used as a "seed" in a random number table. Yes the table is actually a pseudorandom number table but as players of this game we have no way to discern the numbers in the table being used so to us everything appears as random.
I am still on the first holo(Weaponsmith) but my feeling about choosing the profession when a holo goes silent is that the best way would be using a random number. You list all the professions you havent mastered in any order you choose(really it doesn't matter) and then assign a number from 1 to the total number of remaining professions. Then you "roll" a die of the number of sides there are professions and find the result in your list and master it. This takes your personal predjudices about any proffessions out of the equation.
Kartae Master Merchant Master Artisan Bria
Zyra working master weaponsmith for holo, I am using a newer character on a second account to do the holos. She had no mastered professions when she started.
Since we're now on programming stuff by talking about pseudo-random numbers, has anyone put forth a theory involving traversing a graph? This is another very common thing in programming. Has anyone put forth a theory that involves each profession as a node in a graph or a matrix or something similar?
Don't mean to be a party pooper here but once again, there is no such thing as totally random in programming. You may have a vast and complex method of generating an end result, but that end result has a starting point and ending point.
however it is close enough to random to render discerning the generated sequence nearly impossible with out both the parameters and the formula for converting the parameters. So in essence while not total random making pattern guessing equivalent to the door to door hair tonic salesman actually having a viable product.
For example if you were to choose numbers corresponding to creation of a toon, as has been verified by jedi deleting their main and then their jedi and having their fs unlock taken away, you could base this end result on any number of factors involved in creator creation. Things like Station name, Toon name, starting race, starting planet, starting city, starting profession etc etc. As I am sure you can see there is quite alot of things you could use as a begining point. Personally I think the professions are based on a combination of things, like starting planet/city, station name and toon name.
I can not recall the post exactly but there is a post somewhere wherein the devs confirmed your begining city has something to do with it. Which is one of the reasons your datapad has a wp to your starting city, this serves as a place holder in your db record from which to keep track of some of the things you need to do.
actually I thought they stated that deleting your character main or jedi would still keep the slot...would love to see the post where someone disproved it but a risky venture obviously.
its not anywhere close to random. its all based off the image design FCSS theory.
when character is created, the image design selections the user made (or the first random ones picked by the computer) are used in a complicated and boring calculation that determines which professions you will need to master.
and then on top of that
combine that calculation with species selection and starting profession and starting location and then play for a few months and when the Dev's feel the need to let another Jedi into the system they open up their database and select the next winner in the Jedi Lottery system.
Dev Hank - woooo, hey Jim look at this guy!! he still has his original melon from character creation. Dev Jim- HaHa, thats cool. make him the next Jedi. Dev Hank- Ok **Hank changes flag setting in DB**
3 hours later---- Lucky Smo on some unexpecting server logs in **POOF** you have now unlocked your Jedi slot WOOHOO!!!!!
SPACE, GCW, PvP, PvE, DWB runs 
