# the number 496 **URL:** \ **Category:** Factual Questions\ **Created:** [January 9, 2006, 6:20am UTC](https://boards.straightdope.com/t/the-number-496/339116 "2006-01-09T06:20:33Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [January 9, 2006, 6:20am UTC](https://boards.straightdope.com/t/the-number-496/339116/1 "2006-01-09T06:20:33Z")
In the PBS NOVA special Brian Green’s The Elegant Universe, part of the unification of all four forces relied on an equasion equalling 496. Other than this number being a perfect number, that is, a number that is the sum of its divisors, why is this number critical to unifying gravity with quantum mechanics? ---
**Author:** ![TJdude825](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@TJdude825](https://boards.straightdope.com/u/TJdude825)\ **Post date:** [January 9, 2006, 7:17am UTC](https://boards.straightdope.com/t/the-number-496/339116/2 "2006-01-09T07:17:20Z")
I have no idea, but I found a transcript from the show, so maybe someone else can read that and get a better insight. > **[The Elegant Universe: Pt 2](https://www.pbs.org/wgbh/nova/video/the-elegant-universe-part-2/)** > > String's the Thing: Do miniscule vibrating strands of energy hold the key to a unified theory of physics? Wikipedia also has some (probably useless, but possibly interesting) information about the number, such as the fact that 496 is a nontotient. > **[496 (number)](https://en.wikipedia.org/wiki/496_(number))** > > 496 (four hundred \[and\] ninety-six) is the natural number following 495 and preceding 497. > 496 is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 31, 25 − 1, with 24 (25 − 1) yielding 496. Also related to its being a perfect number, 496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 2... ---
**Author:** ![bonzer](https://avatars.discourse-cdn.com/v4/letter/b/45deac/32.png) [@bonzer](https://boards.straightdope.com/u/bonzer)\ **Post date:** [January 9, 2006, 4:48pm UTC](https://boards.straightdope.com/t/the-number-496/339116/3 "2006-01-09T16:48:44Z")
The short answer is, I suppose, that both the _SO(32)_ and _E[sub]8[/sub]xE[sub]8[/sub]_ Lie groups have 496 generators. The slightly longer answer, while all keeping the technical complications hidden, is that naively there were lots and lots of possible string theories that Green and Schwarz could possibly consider at the time. However, the expectation at the time was that all of these would be inconsistent. In particular, it was already known that string theories suffer from something called _anomalies_. As I briefly explained in [this old thread](http://boards.straightdope.com/sdmb/showthread.php?t=112288), these crop up all the time in quantum field theories and, depending on context, can be a really bad thing, revealing that your theory is internally inconsistent. That was the case in string theory. However, as I’ve said, there was a vast choice of possible particular string theories to consider. One thing you could change to get a different theory was change the Lie group that was involved. There are infinitely many such groups, but there’s a simple standard classification of them. For any particular Lie group, you can think of the elements defining a continuous transformation that depends on _d_ real numbers. The integer _d_ is called the _dimension_ of the group and is the number of _generators_ the group has. What Green and Schwarz were checking was whether there are anomalies in all string theories of a type called _heterotic_, the significance of which we’ll skip over. What their calculation essentially showed was that the anomalies in any such theory were proportional to _d_ - 496. Thus string theories involving groups with _d_ = 496 would have no anomalies. And the two Lie groups that had this property were _SO(32)_ and _E[sub]8[/sub]xE[sub]8[/sub]_ (for reasons related to the fact that 496 = 32 x 31/2). This was big news because, although most possible string theories were still inconsistent, Green and Schwarz could now point to two examples that were anomaly free. That was a huge surprise to most other physicists at the time and singled these particular string theories out as unusual compared to most quantum field theories. Hence the explosion of interest in them when they published this result (the “1st String Theory Revolution”). Other similar examples were then found. As to **why** the number 496 was singled out in this way, that’s a lot murkier. The number emerges from calculating anomalies in a rather opaque way: there’s a specific long calculation they had to do and this happens to be the number that comes out at the end. Furthermore, with the advent of M-theory, the dominant belief amongst the experts has become that there’s nothing that special about the _SO(32)_ and _E[sub]8[/sub]xE[sub]8[/sub]_ string theories. Instead, these are particular manifestations of some deeper M-theory. If that is ever unveiled and understood, then presumably the chain of significance becomes reversed: M-theory will explain why these two examples are special and hence show why anomaly cancellation in heterotic strings requires that _d_ = 496. ---
**Author:** ![JKellyMap](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jkellymap/32/15880_2.png) [@JKellyMap](https://boards.straightdope.com/u/JKellyMap)\ **Post date:** [January 9, 2006, 5:10pm UTC](https://boards.straightdope.com/t/the-number-496/339116/4 "2006-01-09T17:10:01Z")
**Bonzer** : If your post above is typical, you are a terrific writer of difficult subjects for a non-specialist audience. If I had any say in the matter, you’d do a cameo (or more) for the Straight Dope staff. ---
**Author:** ![bonzer](https://avatars.discourse-cdn.com/v4/letter/b/45deac/32.png) [@bonzer](https://boards.straightdope.com/u/bonzer)\ **Post date:** [January 10, 2006, 12:39am UTC](https://boards.straightdope.com/t/the-number-496/339116/5 "2006-01-10T00:39:04Z")
Where’s a modestly blushing smilie when you need one? ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [January 10, 2006, 12:53am UTC](https://boards.straightdope.com/t/the-number-496/339116/6 "2006-01-10T00:53:02Z")
> [@bonzer](#): > > Where’s a modestly blushing smilie when you need one? It’s the one that looks like it’s giving a blowjob: :o Seriously, great post. ---
**Author:** ![Otto](https://avatars.discourse-cdn.com/v4/letter/o/bbe5ce/32.png) [@Otto](https://boards.straightdope.com/u/Otto)\ **Post date:** [January 10, 2006, 2:17am UTC](https://boards.straightdope.com/t/the-number-496/339116/7 "2006-01-10T02:17:48Z")
> [@Derleth](#): > > It’s the one that looks like it’s giving a blowjob Which, if you gave those, might also earn you a cameo (or more) on the Straight Dope staff. ---
**Author:** ![wayward](https://avatars.discourse-cdn.com/v4/letter/w/a87d85/32.png) [@wayward](https://boards.straightdope.com/u/wayward)\ **Post date:** [January 10, 2006, 2:30pm UTC](https://boards.straightdope.com/t/the-number-496/339116/8 "2006-01-10T14:30:14Z")
(42 + 23 + 16 - 15 - 4) x 8 = 496 :eek: ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [January 10, 2006, 3:42pm UTC](https://boards.straightdope.com/t/the-number-496/339116/9 "2006-01-10T15:42:28Z")
I think this may be unrelated (maybe not), but I remember Richard Feynman always contended that an explanation for the number 137 (the fine structure constant) was necessary for any grand unified theory. It is equal to the > [@](#): > > square of the charge of the electron divided by the speed of light times Planck’s constant. The above quote was taken from: [http://www.137.com/137/](http://www.137.com/137/)