They're missing the one feature I found killer: Unit parsing in math. Doing something like "sixteen miles per hour in km/ns * 14 hogsheads per parsec" Just Works in Alpha[1], it fails miserably in Google. Sure you can make it work with parens and careful phrasing but...
I had an ultimate fallback for high school physics. Start putting stuff in likely equations where the units work out to the desired answer. That always worked, save for two or three occasions. Unfortunately, once I figured that out, that let me be lazy and kept me from learning as well as I should have.
When Wolfram Alpha starts solving word problems, time to start worrying. Not about machines rebelling, but about cheating in grade school math classes.
With known equations, then yes, dimensional analysis is essentially just a form of bookkeeping that helps you verify your math as you go.
But once you get into using quantum field theory to study new systems, the standard approach is to concoct a conservation of energy equation by summing terms, where each term is a combination of the system's variables with units of energy.
From there, you can discretize the coordinates and predict the existence of various particles (or pseudo-particles, depending on what kind of system you're describing) and their dynamics.
I've run into some weird bugs trying to perform calculations in Wolfram|Alpha. For example, I cannot come up with any query for the general question "human height vs Empire State Building" that works, even though the separate queries "height Empire State Building" and "height average male" return answers with units of length.
Don't take this the wrong way -- I know where you're coming from, and it's natural to push the boundaries, especially for a hacker. But let's stop to appreciate how hilarious this comment looks to someone who majored in physics in the era just before the web. It's like eavesdropping on the gods as they complain about the quality of this year's batch of ambrosia.
You own a machine that returns a meaningful number for "height Empire State Building" and "height average male". In less than a second. And which will perform floating-point division for you, at the press of a few keys. And you're vaguely unhappy because you can't do it all in one step!
Now I know how Hans Bethe (acknowledged grandmaster of the slide rule, who routinely computed logarithms in his head) must have felt when he heard the young grad students comparing the features on their scientific calculators.
I wonder if tools like Wolfram Alpha will eventually succeed in doing for Fermi problems what Google did for Trivial Pursuit: Turning an activity that was formerly regarded as a touchstone of intelligence into a typing exercise. Estimating the number of piano tuners in Chicago will be a lot less impressive when you can just type "piano tuners in Chicago" into a text box and get the answer back to within a decimal place.
Fortunately, right now typing "piano tuners in Chicago" into Alpha just makes Javascript crash in Safari, so I guess we humans can sleep soundly for a while longer. ;)
"rely on Wolfram Alpha to either give you the right answer (depending, of course, on the accuracy of its own index), or no answer at all."
This is wrong because of weaknesses in query parsing/explaining. I tried out Archimedes's sand-reckoner problem (how many grains of sand it takes to fill the solar system); it rephrased my query as "planets volume / volume of a small grain of sand" (which sounds reasonable) and gave an answer off by 17 orders of magnitude, taking "planets volume" to be the volume of the median-sized planet among all the planets. Its query explanation didn't link to any explanation of "planets volume", so I had to make that a separate query to find that out.
They could solve this problem with a better interface to its understanding of your query.
The volume in question was actually that of the classical "sphere of fixed stars" -- I input it initially as something like "volume of the solar system" and had a brief impulse to accept its rephrasing as "planets volume", especially when I couldn't drill down further into its explanation. It's pretty natural to just assume it knows what you meant.
That query calculates "median planet volume / volume of a small grain of sand", as mentioned by the grandparent poster. I believe it is still an open question how to get Wolfram|Alpha to calculate "total planet volume / volume of a small grain of sand".
The query "total volume planets" yields a reasonable answer for that part of the problem, but I can't convince Wolfram|Alpha to divide it by "volume of a small grain of sand"... :-/
I think once the general public, who generally think of Alpfa as a Google competitor, realize Alpha's strengths and how to use it, it will be come a very powerful and commonly used tool.
I can't wait for the API to be released so that all the Hackers out there can do things Mr. Wolfram hasn't imagined yet.
that made me LOL. An ex-colleague started his own company to increase availability of cheap robotic tools in Indian high-schools. I know this isn't what you meant, but it made me think of him.
WA needs the option of explicit operators, so you can specify your query precisely.
For example, for financial entities, you get a drop-down menu choice of Fundamentals, Ratios, Balance sheet and so on - but you can't specify these in a query. Eg: http://www94.wolframalpha.com/input/?i=nike+Ratios gives you the fundamentals, not the ratios.
The most interesting thing about Alpha so far is the effectiveness of its public relations. A LOT of news organizations are talking about this. I've honestly been trying to ignore it, but that has been hard :)
Very curious how they built that kind of press coverage. I'm sure they hired a good PR firm, but still.
(It's scary how much I've become fascinated by marketing issues lately. Am I turning into a sales/marketing person?! I'll be the only marketer who VCs his emacs extensions in a git repo...)
[1] http://www23.wolframalpha.com/input/?i=sixteen+miles+per+hou...