Monday, May 18, 2009

Wolfram Alpha

Okay, this morning I'm trying out Wolfram Alpha for the first time.

About Alpha

I've read about it already and I've been a Mathematica user over the years.  I've also heard Wolfram speak (I think at Georgia Tech a few years ago), so I already think I get what Alpha is supposed to be.  I think search engine is not the most descriptive name for Alpha.  I notice it calls itself a “computational search engine.”   It's really more like a very intelligent calculator connected to a very specific knowledge base or encyclopedia of sorts.  As I understand it, the Wolfram folks have carefully compiled the knowledge base.

Alpha is to a calculator or computer (in the traditional sense of the word) as Google is to the encyclopedia or library.  That's my first approximation to describing it.  Alpha will be good at answering questions that would, in the past, have been answered by an expert if the expert would probably take out a calculator to answer your question.  That means it should be great for the physicist, astronomer and computer scientist in me.  It will initially be confusing to folks in general, but I think they'll catch on over time.  Students will probably pick up on it's usefulness pretty quickly.  

Any rumours of Alpha replacing Google are simply wrong.  It's a different kind of information from a different source.  Both will be interesting sources of information.

That said, there is some overlap between them.


The first thing I typed in was the name of the city I live in.  That worked well.  It listed the population, showed it as a dot on a world map, listed the current temperature and weather, and the nearest cities.

I tried Macon, GA and it said it's only 77 miles from Atlanta.  That's a surprise.  Having grown up there, Macon was always from 85 to 95 miles to Atlanta, depending on starting points.  I'm surprised at 77.  Maybe that's city limit to city limit and they've changed that much.


The next thing I tried was Saturn.  Good again.  It showed a lot of nice information as well as a solar system diagram (to scale!  Extra points for that!) with the planets in their current positions.  Very nice.

I tried Orion and Ursa Major.  Then I thought I'd pursue a question that's been bothering me.  I'd swear that, when I look up at the Big Dipper, the star Delta Ursae Majoris looks dimmer than I remember.  I recall that it's a variable star  so I wonder what type of variable it is, what it's period is if it's periodic, and where in the period it is.  In other words, is it getting dimmer?

The Ursa Major page on Wolfram Alpha looked nice enough.  But finding out about this individual star was hard.  The star wasn't labeled on the constellation diagram.  The mouse pointer turned in to a hand/finger meaning it was something that could be clicked on, but clicking on it made nothing happen, as far as I could tell.  And I tried it several times because the hand/finger insisted that something would happen.

So there was no way to figure out what the name of that star was.  There were a number of stars listed below, by name, so I thought I'd just click on some of them, guessing, and maybe a diagram would pop up so I could tell when I chose the right one.

But clicking on any star in the list simply popped up a window of selectable text representing the whole list.  That's weird, IMHO, and way less then useful, at least to my current way of thinking.  I certainly wasn't any closer to finding the star.

So I went back to Google which went to Wikipedia which had a better diagram with Delta labeled.  Okay, I went back to Alpha and typed in Delta Ursae Majoris.  That certainly worked and a page with basic star info popped up.  It definitely listed it as a variable and magnitude at about 3.3 I think, and even noted it's the dimmest star in UMa.  However, there was no more detailed information.  Nothing like you might get from the old Burnham's Handbook.

At this point, going back and searching on Google and going to several sources including Wikipedia yielded pretty much the same, in some cases the same verbatim, i.e., from the same source, information.


My next question was a major failure.

I wanted to know how long it would take to travel to Alpha Centauri, in relativistic terms, with an acceleration of one g, one Earth gravity.  What I really meant is that you accelerate for half the distance, then turn around and decelerate the rest of the way.  That's the only practical way we know of to travel to another star system.  That would be for extra credit, but I would have accepted the less sophisticated answer of simply accelerating the whole way and watched Alpha Centari streak past at high speed when you got there.

It's also a perfectly simple problem if you know special relativity and requires little bits of knowledge like the distance to Alpha Centauri, the value of one g, etc.  It should be a perfect problem for Wolfram Alpha to solve.  Alas, I couldn't find any form of my question that Alpha could understand.  I finally resorted to terms like simply “relativity” and “delta-t” but I got no where.  Granted, the problem is hard to express and maybe I just never hit on what Alpha was expecting, but I don't think it should be too hard for Alpha to handle.

So I was hugely disappointed in that failure.  It would have been nice to be able to go on and ask Alpha about how much fuel would have been required for the trip, what percentage of light speed would have been reached at mid-point, etc.  The usual follow up questions for that interesting problem.

It's good at Math

Okay, I have to give Alpha credit for being good at math.  I typed in  “sin(x) / x” and “sin(1/x)” and  it spewed out more than I ever saw about those two expressions.  I'm sure it exceeds my CRC Mathematical Tables book.  Of course Mathematica pretty much already did that.

What about statistics?

Since I've been dealing with them at work lately, I tried “hazard function” and “failure rate” but to no avail.  Alpha didn't understand them.

A better calculator?

So, Google already functions as a calculator (most folks probably don't know that), but where it is less than useful is in building up results.   I'd like to use my previous result in a new computation, and that's hard to do.  The best you can do is to put parens around your previous expression or cut and past the previous answer.

I wondered if Alpha would do better.  So far, it doesn't.  It outputs the results in many different forms, enough to make any math teacher happy, but I don't see a way to get them into the next computation.

Here's my simple example.  What is the period of one rotation for the frequency 33 1/3 RPM?  As weird as it sounds, that was a question on my mind when I woke up this morning.

So, I'd like to take 3 and invert it to get 1/3, then add 33, then invert that.  That's simple and it's easy to do on my RPN caculator (which is now a Python program I wrote).  Alas, I could only do this in Wolfram (like Google) via  (1 / ((1/3) + 33)).