Oh So Boring…

If you are anything like me…well, no one is like me. I’m unique. But, if you want to be like me, here is an activity that you can do if you are stuck inside during a blizzard like I am now or want to pretend to be. That activity? Looking at old menus!

I know, I know, not that exciting, but, man, is it fascinating! The object of my focus this afternoon is the LA Public Library’s online Menu Collection. Just give it a whirl and I dare you not to be sucked in.  Marvel at what ten bucks would buy you 30 years ago compared to today.

I’m not the first to find this site, but I’m damn sure not going to be the last!

A while back it was announced that Bing would be using Wolfram|Alpha as their math engine.  Which is cool, because Bing is a pretty interesting engine, and W|A is a very cool one, indeed.

However, there is a bit of an issue with its integration, I believe. Namely: they give different answers!  I know this because I tried out an example in the first link up there, that of 2^2^2^2^2.  It turns out the answer to this is a bit vague, so differing solutions are not unexpected, but still…

Why? Exponentiation is not associative, unlike addition or multiplication (it might satisfy the Lie algebra equivalent of the Jacobi identity, I dunno), so the order matters. A lot.  Thus, while 2+(3+4) = (2+3)+4, and likewise for multiplication, 2^(3^4) !=  (2^3)^4. This being exponentiation, it really doesn’t. The latter is 4096, the former is 2417851639229258349412352. Juuuuuuuuuuuuuuuuuuuuust a bit different. So without parentheses, things are vague.

Now how about the example in the article? We’ll get to that. Let’s start with 3 2′s. (2^2)^2 = 16, 2^(2^2) = 16. Phew safe. So, 2^2^2 is fine.

2^2^2^2? Given that, Bing outputs the “bottom-up” answer: ((2^2)^2)^2 = 256. W|A outputs the “top-down”: 2^(2^(2^2)) = 65536. Ah ha.

The disparity is growing, but not bad. So adding one more ^2 shouldn’t be too horrible, right?

Wrong.

Exponentiation grows quickly so order reaaaaaallly matters.

2^2^2^2^2? As expected from above, Bing should do 256^2=65536 and it does. W|A? Well, it does 2^65536. This is a big number. How big? Well…

20035299304068464649790723515

602557504478254755697514192650

169737108940595563114530895061

308809333481010382343429072631

818229493821188126688695063647…

…8091458852699826141425030123391

That is a 19729 digit number. Big.

Therein lies the difference, but which is right? Hmm. Most mathematicians think of repeated exponentiation as “top-down”. So, my main question is why isn’t Bing using W|A as it says? Or is there some extra option I need to assemble?

Oh well. Just an odd thing I noticed.

Not the Clash song, per se, but the question itself. Should I stay or should I go…from the ACS and APS.

For many moons, I’ve been a member of both the ACS (American Chemical Society) and APS (American Physical Society), the former for ten or more, the latter for a few.  As a theoretical chemist, having a membership to these societies was quite useful. You get a subscription to a very good “popular” magazine, Chemical and Engineering News and Physics Today, discounted registration at conferences, and, perhaps most importantly, access to the respective job banks.

All this, though, comes at a cost. When you are a grad student and recent postdoc, the membership cost isn’t too expensive and the benefits well outweigh the costs.  But once you are a “professional member” the costs double–I think–at least to $140 and $118 per annum.

Okay, that’s not bad, not great, but not horrible. *But*, I am no longer a practicing chemist/physicist. I’m a code monkey. A membership to IEEE or ACM would make more sense, really. Heck, I’m kind of attending SC09, the supercomputing conference, next weekend.

But, but, but. I am a chemist. I am a physicist (according to Feynman, no less). I still think of myself as such and I suppose a part of me thinks one day I might be a practicing chemist/physicist again.

I’m not sure what to do.