# In Stargate, why does Dr. Daniel Jackson say you need 6 points to define a location in 3 dimensional space

Dr. Daniel Jackson

...seven points to outline a course to a position...to find a destination within any three dimensional space, you need six points to determine the exact location...but to chart a course, you need a point of origin

Why do you need 6? Shouldn't 3 suffice? Was this purely a plot device or the biggest blunder in the history of Hollywood? (I am leaving out the third possibility, that I am missing something entirely)

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Well, isn't a single point already a location? So I guess the terms in this statement are a bit fuzzy, anyway. – Christian Rau Dec 18 '11 at 21:27
@ChristianRau Oh ya that too. I realized that, but then forgot about it in favor of other inconsistencies. – puk Dec 18 '11 at 21:30
Another HUGE plot hole that just occurred to me is the entire premise of the movie --that they can't open the starget without the symbols-- is flawed b/c you'd think after a few hours/days, they would just reopen the stargate back home. – puk Dec 18 '11 at 22:12
@DVK Why should it? Only because it's a Science Fiction movie? Definitely not! – Christian Rau Dec 20 '11 at 13:45
@DVK LOL I could migrate it to the Math section – puk Dec 21 '11 at 19:28

His logic is quite simple really.

The x axis has a start and end point.

The y axis has a start and end point that intercept somewhere along the x axis.

the z axis also has a start and end point, that intercept along the y and x axis.

Making 6 points.

If that makes no sense, this picture may explain it.

To clarify this further, if you have a known axis (i.e the centre of the universe), then you could indeed use a three dimensional axis by using (x, y, z). This would give you the distance from the center of the universe on each axis. This is impractical however, because of the level of precision needed in something as massive as space would require a huge number for each axis...this would be impossible for a symbolic representation.

If however you use objects as reference points, then you need far less precision, as you can use intersection to give you the precision, as shown in the diagram.

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Isn't it overkill though? You only need three points. By your argument you could have as many points as you like as long as each vector pair passes through the same point? – puk Dec 18 '11 at 22:51
yes, but those points constitute stars. if you had a clear centre of the universe, then a 3 point axis would work. But if you haven't, and instead you are using other known objects to determine your axis, then you need those 6 points. – Codemwnci Dec 18 '11 at 23:30
ok that makes more sense, but then wouldn't you need 4 points instead of six? – puk Dec 18 '11 at 23:56
OK lets take a step back, what exactly is a "point"? Each point is a constellation right? So lets give it an (x,y,z). If I give you (0,0,0),(10,0,0) and (5,-5,0),(5,5,0) can't you deduce from that the destination point is the intersection point of those two vectors which is (5,0,0)? – puk Dec 19 '11 at 21:45
@ChrisK Aah! That makes much more sense (I myself wondered about the low chance of an intersection from spatial lines). But how do construct those 3 planes from the 6 points? – Christian Rau Dec 20 '11 at 13:51

Any random point (a location) in space can be defined by a coordinate in any number of coordinate systems. The stargate system uses its own coordinate system based on 39 constellations (for a Milky Way stargate), symbolised by chevrons on the stargate. But whether these chevrons symbolize constellations, or even if there exist dimensions in that specific coordinate system is not relevant to answer your question. Fact is that there are 39 points in space known by the stargate.

Accept that a stargate can only establish a wormhole, or travel path, if it knows an origin and a destination.

Now, the simplest definition of such a path would be just 2 points: the origin and the destination. But how many stargates are there? And how many symbols are on a stargate again? Clearly, two points to define the path isn't going to work.

Somehow the destination point has to be constructed out of the 39 points known to the stargate. For instance, take two points which form the ends of a 'line' and the stargate calculates its middle which would translate to the destination point.

The question then rises: is that enough precision? A combination of 2 out of 39 results in only 741 possibilities. So 2 points are too few to give enough resolution.

One step further: take 3 points to define the destination point. The stargate system would calculate the triangle center from those 3 points to get the destination. Well, 3 out of 39 leaves us with 9,139 possibilities: again not enough.

There is no evidence of the Wilky Way having more then 9,139 stargates (or even more then 741), but note that the destination point does nót point to a stargate, but to a random point in space (a stargate could be anywhere). The stargate system just picks the stargate closest to that destination point. (But that is explained in the series later, not in the original movie.) Clearly, space has more then 9.139 locations.

4 points result in 82,251 possible locations, 5 points in 575,757, and finally 6 points result in 3,262,623 possibilities.

And (apparently, but also kind of obviously) a Milky Way devided in at least 3 million sections guarantees a possible unique location of a nearby stargate. So, only with six defining points there are enough posibilities to define enough destination points.

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For some reason I am just not following you. What is a point to you? (x,y,z)? Or a constellation? Or a symbol on a stargate? – puk Dec 20 '11 at 19:44
@puk I edited my answer to explain my theory. But to answer your question: by point I mean a location in 3D space. – NGLN Dec 20 '11 at 21:51
@NGLN There's 200–400 billion stars in the Milky Way. An estimated 50 billion planets with 500 million in the Goldilocks zone see this article. So you're saying it's obvious that only 3 million of these 500 million viable planets are interesting enough to have a stargate? To further complicate your suggested solution, we know from Stargate Universe that some star systems have multiple stargates... so some of your 3 million sections have to be very small. – Chris K Dec 21 '11 at 5:28
@ChrisK Yes. And then thát would be the plot hole. Note the at least. – NGLN Dec 21 '11 at 6:18
This is the right answer. Think about it this way: If you have streets and house numbers, then to tell someone where you live all you to do is give them your address. If the streets have no names and the houses have no numbers, you instead only have a few landmarks (in this case the 39 constellations) then you need to reference those landmarks to tell someone where you are at (between the clock tower and the old barn). The more landmarks you use in your addressing system, the more possible points you can reference. – Jim McKeeth Sep 21 '12 at 20:16

In geometry, we learn about line sectors: Pieces of lines that have two end points. Each of the six points on the XYZ plane is an endpoint thus lowering the possibility of error. Note how Dr. Daniel Jackson said

...you need six points to determine the exact location...

Six points on the XYZ plane gives the exact Stargate that you will exit. The more points you use, the less results you will get. For example, if you type "Cat" into Google, you will get resulted for all different kinds of cats, but if you type "Long-haired calico cat," then you will get less of the results you didn't want and more of the ones you wanted (provided you were searching for Long-haired calico cats). Obviously, depending on where your destination is in the universe, there will be varying amounts of Stargates. In the vicinity of Earth, there is probably only one with the coordinates to dial Earth's Stargate. In the vicinity of Abydos, there are more Stargates.

This is my first time even thinking about this in depth, and my knowledge of Physics is taking over...

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 IMO that's a bad analogy to use. A google search is inherently ambiguous. It looks for best matches. – puk Jun 20 '12 at 19:19

With the logic in the movie, 4 points are enough, because each line appears to pass through the same point, i.e. you only need 2 lines. Given the random placement of stars, it is extremely unlikely that you will find 6 in just a few constellations that enable 3 lines to intersect at the same point (try it with 3 straws, or pencils, and see that it just won't work). 3 planes could designate a point in XYZ, but 2 points are not enough to define a plane, because the plane can have any orientation. In short, the movie logic is flawed.

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 Thank you, that's what I've been trying to say. One only needs two vectors, with two points defining a vectors hence 4 points, to define a single point at the intersection point of those vectors. – puk Aug 22 '12 at 17:50 Half of this answer is the same as my comment. The other half - stating that 4 points is enough - simply doesn't give enough resolution: only 82251 possible locations can be constructed from 4 points, as explained in my answer. Also: a destination point doesn't have to be exact. As explained in the Stargate series later, the destination is locked to the stargate which is nearest to the destination point. – NGLN Sep 21 '12 at 11:13

The universe is continually expanding. In order to define an intersection point within a moving (expanding) spatial section, two points within the referencing vector are required for each of the three referencing axes keeping in mind the expansion doesn't necessarily occur in a uniform (concentric) form.

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 I don't know anything about astro physics, but I know enough to know that in a randomly-ish expanding universe, coordinates are pretty much useless. – puk Dec 28 '12 at 1:08