Stargate
A stargate is composed of 39 chevrons. Locking in 7 chevrons establishes a wormhole to a location within our galaxy. Locking in 8 chevrons establish a wormhole to a different galaxy. Assuming that 9 chevons would link to alternate universe, how many universes would that be?
Labels: funphysics
posted by Ragknot at
12:29 PM
43 Comments:
42
This post has been removed by the author.
Does the order you select the 9 chevrons in matter?
Hi Ragknot. I've posted on What a shot. Only yesterday I found out that you can also delete other people's unwanted "contributions" in your own blog, but you can only do that from the comment screen.
If order unimportant then: 211 915 132 universes.
If order important then: 76 899 763 100 160 universes.
Please tell me I've got the combinatorics right this time ;)
Chris,
I don't want to give it away.
Maybe you've solve it, I have not computed yet.
But how high can you count with 2 digits of hexidecimal numbers.
Ok, I don't think anyone else would try this. I decided to show my solution.
A very simple example
If you could use 2 digits in base ten, you could indicate 100 locations (counting zero as the first. 0 to 99. actually 00, 01, 02, 03,... 99. If two digits in base 16 there would be 256. Anyone with a history of computers
should be familiar with that
Here's a short table
digits..base............max......
2.......2.......................4
3.......8.....................512
4.......10..................10000
5.......16................1048576
6.......16...............16777216
8.......20............25600000000
9.......30.........19683000000000
9.......39........208728361158759
so I calculated
208,728,361,158,759
Not sure what you digits/base stuff is about. I just did:
39!/((39-9)!*9!) = 211 915 132
39!/((39-9)!) = 76 899 763 100 160
I am not sure about your computations. I don't see it as a probability problem. But with 39 different dights, we have to be using base 39.
And 39^9 power is 208728361158759
I think you answer is about 1/3 of mine.
Ragknoot...Are you saying you can lock in the same chevron twice?!
Hi Ragknot. Assuming you can pick any 9 chevrons out of 39, then the number of possible permutations or combinations (nCr=n!/(n-r)! or nPr = n!/((n-r)!r!) depending on whether the order you choose them in matters or not. It's not probability, although such things do turn up in that, quite frequently. e.g. for ABCD taking two at a time, you can have AB, AC, AD, BC, BD or CD. If order matters, then also have BA, CA, DA, CB, DB, DC. That's 4!/((4-2)!2!) = 6 and 4!/(4-2)! = 12 ways.
Unless it's especially called for, it doesn't matter one jot what number base you work with except for solving amusing puzzles and the like. A hundred (base 10) items is a 100 (base 10) itmes even if you express it as A3 (base 12) items.
Coises, I swapped the nCr and nPr formulae.
Our last posts crossed. I don't know the rules of the stargate machine. But I assume that you must choose 9 different chevrons. I don't know if it's possible to select a chevron twice or more. If you can then there's far more arrangements that I calculated.
Assuming you can choose one chevron up to 9 times, then there are 9^39 permutations and less than that combinations (not sure about number - that's quite fiddly to calculate).
I've just taken a look at your table. I really not sure what you mean when you say base 39. You've only used base 10 digits. e.g. for hex you have 0123456789abcdef - 16 digit characters. I wouldn't want to invent another 33 symbols to do base 39.
Ok, the stargate is like a rotary phone, with 39 fingerholes, er, chevrons. If you substituted numerals and letter you could go from 0 to 9 then a to z and have 36 but you would 3 more to get 39.
So the base for that numbering system is 39.
Now look at the table, humans use base 10 because 10 digits, or fingers. using the 10 digits and arranging in a group of 4... and you can make 10,000 unique sets
from 0000 to 9999... and that's 10^4.
Just like with hexidecimals (0 to F) and and 2 places you can only go up FF, which we as 16^2.
So with base 39, and 9 places
= 39^9 = 208,728,361,158,759
Nothing to do with probabilities.
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This post has been removed by the author.
This post has been removed by the author.
I can barely follow my own reasoning anymore. There are so many what-ifs that I'm muddling them up a bit. I've deleted my OCT 4, 3:08 post as it was based on a misunderstanding that each chevron itself had 39 possible states. That gave some truly enormous numbers.
So I'll concentrate on your rotary dial telephone analogy. But note that that implies that each chevron has only one internal state, but it can be used more than once. You then get 39^9 permutations.
I've just spotted Knightmare's post. I suspect that the stargate machine doesn't allow using a chevron more that once. I also guess that the order doesn't matter, all that matters is that you have pre-selected the 9 chevrons (the order you do it in doesn't matter) when you press the go button. In which case it's the 39!/(30!9!) = 211 915 132 universes.
What happens if you select 10 chevrons :)
I deleted more posts (although they weren't technically erroneous) they assumed that there were 39 states per chevron - I'd misinterpreted something.
Also just noticed I'd written 9^39 instead of 39^9 in my OCT 3, 7:43 PM post - a senior moment.
Because of all the deletes, I re-emphasise that talking about base 39 number system is completely irrelevant. I realise you led yourself to that way of thinking because you wanted a unique symbol for each position of your telephone dial analogy. I find it far easier to enter 39 (base 10) rather than 10 (base 39) into a calculator - especially as I don't have a base 39 calculator.
As you seem to think I'm doing probability (I'm not), I'll clarify what I've done. I'm considering how many ways I can select 9 items from 39 (without replacement) and without regard to the order I did it in. Unfortunately I can't get my head around that directly. So I actually assume the order is important, and then note that will give me too many combinations by a factor of 9!. The 9! factor is because ABCDEFGHI is equivalent to BACDEFGHI etc. and there are 9! such permutations. So there are 39 ways I can choose the first chevron, 38 for the second ... 31 ways to choose the ninth chevron. That gives 39!/30!. Now divide by 9!.
Sorry, I'm rattling on a bit (again). Greetz.
Chris,
Thanks for the reply. Maybe some of the confusion comes from my mis-wording,
I gather you aren't a fan of the several Stargate programs,
I went to Stargate on Wikipedia and realized my error. There only Chevrons and they engage 39 symbols. The inter ring has the 39 symbols and it rotates to engage one symbol into a chevron, then rotates again to engage another chevron.
In the beginning, only stargates with 7 chervons were known. Like local phones they could only dial within the milky way. But a few years ago one with eight chevrons was found that earth link up to the Pegasus galaxy.
A new season of Stargate (SGU)began Friday with the finding of a 9-chevron stargate. The ninth chevron has not fully worked yet
so we are not yet aware of what it will do.
edit 3rd paragraph
There only "9" Chevrons
Hi Ragknot. I saw the film and 1 or 2 episodes. But with rare exceptions, I haven't watched the telly for at least 6 years.
No "telly" for 6 years?
For some reason, I just thought of a combination lock as a better analogy than a phone. There are nine triangle shaped chevrons around the outer circle, not just one like a combination lock.
The 39 symbols are rotated then halted on the first chevron- then rotated again to the remaining chevron. The stargate is 22 feet wide and operated by a "push button" device where you push a symbol to register the next symbol, much like a digital phone pad connected to a rotary phone.
You can download and watch Stargate on your PC, but the shows are about the characters and strange things from other planets.
You might not seen a stargate device but once or twice for a brief instance.
I actually watched a dozen Star Trek Next Gens a few months ago. But just can't be bothered with it (TV that is).
i have a feeling i am way off, but 2? if im wrong or u wanna help explain how this problem works, let me know. jesusfreakalloftheway@yahoo.com
Hi jesus.... If you think the answer is 2, then I'm baffled by that.
The answer is 31
The answer is: 39!/(30!9!) = 211 915 132 universes.
How can you think it's 31?
Don't forget that the last chevron has to lock onto the symbol of the stargate of origin.
Hi Cordell. I didn't know that. That means that only 8 of the chevrons are free choices and only 38 can are available for selection. So that changes the number of universes to 38!/((38-8)!8!) = 48903492 if the order doesn't matter or, 38!/(38-8)! = 1971788797440 if the order matters.
... in turn that meanse the stargate coding system isn't likely to be as described as you can't go somewhere which required the current stargate's symbol in the destination code.
Lets think Nine digits the last six fix a point in space. seven marks the origin point. eight marks the galaxy. then nine would be the universe marker. 39 cevrons to choose from.....39 universes.
This problem is a 3D location problem not linear. Correction!!!! 38 universes. 37 galaxies. 35*34*33*32*31*30 locations in each galaxy. One symbol is always your origin!
1,168,675,200 locations in each galaxy. 4.32409824E10 locations per universe.
Thanks for that Scott and Anonymous. Not sure which of you has got the right interpretation of the control system. I'd wondered but didn't follow through with the gaping holes in the description. I was troubled that it's all very well selecting a universe, but not where in that universe you could go.
I'm not familiar with the stargate controls. Do you have to end up near another stargate? If not how you get home again? If so, is that actually specified by at least one of the chevrons?
Only 38 or so universes out of the infinitely many that might exist, what a swizz.
Chris
The stargae is used to make a stable wormhole between two points. the first being your origin. the next set of six points would set a spot in a 3d grid to the exact point you wish to travle.(or call) then add an addtional code (like an area code) and that would move you to a different galaxy. Add the ninth code (country code) and you open a wormhole to a different universe.
Please note. Not all star gates have the same set of codes...My above posts to include annomous would only aply to one stargate with the ability to use nine codes.
to answer you other question if I call you and you do not have a phone I get no connection. The same works for a stargate. need two stable points to hold the wormhole.
Comments to swordmaker1968@yahoo.com if you would like.
Hi Scott. Thanks for the explanation. It seems crazy to have to manually identify the stargate that your phoning from - the whole control system seems crazy come to that, but I suppose it's visually appealing. I expect that your explanation is correct or near enough though. I only saw the original film once or twice, and just don't remember the details. I'm just going to have to suspend my disbelief on this one. Greetz.
PS I recommend that you don't publish your email without at least obfuscating it - there will be spambots trawling for that sort of info, you might get a lot of junk email then.
Thanks Chris
Hte e-mail posted goes directly to junk unless you are listed in my address book. I look in span for those I wish to keep.
guys the answer is so simple. At first i was thinking along the way most of you were thinking 39!/30!, but than I got to thinking:
If the first 7 chevrons represent a particular location in a given galaxy that means that the 8th chevron indicates which galaxy you want the wormhole to reference. that means this particular stargate can only open a wormhole in only 39 different galaxies since it only has 39 different chevrons. Using the same logic, the 9th chevron location indicates which universe you want the wormhole to open to. Therefore this stargate can only reference 39 different universes.
No math just logic.
lol
Hi Johnny. It seems that one of the 39 chevrons is wasted in identifying the stargate that you are using. So that only leaves 38 for the number of universes. Most, if not all, of the answers were based on a logical analysis of the information that was known at the time. That information changed as poster's provided refined rules of how a stargate's controls operated, so the calculations had to be modified in the light of that.
When I saw the film, I thought that they were trying to achieve the effect of a primitive looking very high-tech device. They did that at the expense of having a crazy and limited navigation control system. Some otherwise sensible destinations, simply can't be selected at a given stargate because of the illogical control system.
Chris,
I don't know how a stargate works. I never watched the movies or the television shows. I just assumed that the stargate works like the phone. You dial a number to connect with someone, except you use chevrons not numbers. since there are 39 different chevrons to work with, it is like using a number system in base 39.
In the U.S.A. the phone numbers have 10 digits with the first 3 digits represent the area code. Doing the math on that, you have a maximum of 1000 different area codes that this system can support.
Using this concept with the stargate, I assumed that the first 7 "digits" dials in to a particular location within a given galaxy and universe. Selecting the 8th "digit" would indicate the galaxy and the 9th "digit" selects the universe. I also assumed that each of the 9 different "digits" can lock in any of the 39 available chevrons. Thus this system can only open a gate to 39 different stargates. Since there is only 1 "digit" for universe indicator.
Piece out.
P.S. Ragknot when are you going to post the answer to your brain twister?
Hi Johnny. I certainly don't know the official rules for the stargate. I'm pretty sure that Ragknot doesn't either. Ragknot often posts totally original problems that are just for brain-storming and/or entertainment. He doesn't necessarily know the answer - they don't necessarily even have a unique answer.
As you can see, there are quite a few views on how the control system actually works. I've no idea who is right or wrong. I don't even know if the rules changed as the series progressed. According to http://en.wikipedia.org/wiki/Stargate#Universe a ninth chevron allows you to go to a ship named "[The]Destiny".
When I post this he will have achieved 42 responses to his problem - maybe that's the answer ;). Greetz.
The problem is how many different universes, not how many different locations.
In a normal stargate (with 7 glyph codes), six of those glyphs specify the destination, and the seventh is the origin point.
With an 8 glyph address, the eighth glyph is like an "area code". The other seven glyphs are used to determine the address within that galaxy. So even if you're able to re-use the "origin" glyph as one of these area codes, you can still only reference 39 separate galaxies (other than your own).
Same goes for the "universe" glyph. You're effectively limited to 39 universes, and only 39 of the galaxies in each of those universes.
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