47 Reference

So, apparently the Star Trek universe is obsessed with the number 47.  To be honest it's something I never really even noticed until the last year or so; that's how out of touch with numbers I am. But the number 47 appears in most episodes in many ways.  Sometimes as the number 47or sometimes the numbers 4 and 7 said together... as in a log entry. Much of the time it's reversed to 74, sometimes it's simply a visual, as the DS9 weapons locker above, or sometimes it's hidden, like in an episode of Voyager that uses 4G (G being the 7th letter of the alphabet.) Every time I look up tidbits and trivia on the Star Trek episodes I'm reviewing, I usually see a note on where the number 47 reference is in the episode if there is one.  So I decided to find out what it's all about.

One of the writers of TNG, Joe Menosky, went to a university called Pomona College in California. A mathematics professor, Donald Bentley created a mathematical proof that all numbers lead to the number 47.  It was a humorous example and not valid in any way.  He could've used any number for the base line to make the same points. But he used the method to introduce his students to the concept of mathematical proofs. The effect, as with most popular teachers, was that his students latched onto the joke and would join in on any real or imaginary "47" sightings in their research for fun.  Menosky took that fascination with the number 47 and integrated it into many Star Trek scripts. Other writers latched onto it as well continuing into DS9 and Voyager.



This is the formula:

”Why all numbers are equal to 47” (as recalled by David Hart, Pomona ’92)

”Draw an isosceles triangle, with points ABC, with line AC representing the "base" of the triangle. By definition, side AB and side BC are equal length, and angle BAC and angle BCA are equal to each other.”

”Assign the smaller of whatever two numbers you intend to prove to the base, line AC. Let's choose...oh, I don't know, maybe 47. Assign the larger number (let's say 74) to the pathway A-B-C. In other words, divide the larger number by 2 and assign that (37 in our example) to line AB; by definition, line BC is then also 37. So, the distance along line AC is 47. The distance along the path from A to B to C equals 74.

Next, bisect each of the three sides. Assign points D,E,F to the midpoints of lines AB, BC, and AC respectively. Draw lines DF and EF. Now, by definition, line AF and line FC are equal (both equal to 23.5, half of 47). Also by definition, line AD and line EC are equal (both half of 37, therefore 18.5). We already established that angles BAC and BCA are equal to each other, therefore by the geometry rule "side-angle-side", triangles ADF and FEC are congruent triangles. Therefore, line EF and line DF are also congruent, and both are equal to 18.5.

Now, step back and answer the question: What is the total length of the path along the line ADFEC? Well, it's four congruent lines, each equal to 18.5, for a total of 74. This is the same length as the original path along A to B to C.

Now, bisect lines AD, DF, FE, EC, AF, and FC. Label the midpoints as follows: midpoint of AD = G. AF = H. DF = I. FE = J. FC = K. EC = L. Now draw the lines GH, GI, JK, and KL. By the same geometric rules and problem solving, triangles AGH, HIF, FJK, and KLC are all congruent, and every line AG, GH, HI, IF, FJ, JK, KL, and LC is equal to 1/2 of 18.5 = 9.25. Now the total path along the line AGHIFJKLC is still 74.

If you continue this process, making infinitely smaller isosceles triangles, and still calculating the path along the line of these triangles from A to C, you still get 74. Now, here's the crux of the argument: In the *limit*, you arrive at two paths along the route from point A to point C. The original line AC is still 47. But, the path from point A to point C along the other route is always equal to 74. Therefore, 47 and 74 are equal to each other. By the same logic, any number can be shown to be equal to 47 (or any other number).”

This makes absolutely no sense to me, of course, since I still have trouble with long division, but those who have studied the higher maths may find it amusing.  The demonstration I find more useful is this video compilation of "47" references from Star Trek TNG. It's not all of them, by any means.  There's only one in here that gives the inverse (74).  But these are a lot of the solid 4-7 references from many seasons of the show.