## Friday, May 29, 2009

### The Alpha

"I'm not keen on the hype" says Stephen Wolfram, this from the man whom I once heard exclaim "First there was Euclid. Then there Gödel. Then there was Mathematica". Despite the quote, Mathematica doesn't really help you prove new theorems but I found it quite useful when trying a few simple cases, simplifying messy expressions, optimizing parameters and checking other people's proofs.

But then Wolfram wrote that book that Scott Aaronson read so I didn't have to, and had that silly Turing machine contest. Now he comes out with the modestly named WolframAlpha.

WA is not a search engine, it isn't sure what to do with computational complexity and functionality for P=NP is under development. Good luck with that.

On the other hand it has considerable built in data and calculations. Type in sunset Chicago and I'll get useful information that used to take multiple clicks on Google.

More importantly WA is Mathematica Lite. We have a site license for Mathematica at Northwestern but the convoluted process to download it dominates its value to me. But I can just simplify and maximize directly into WA. solve x=4y^2-7, y=x+5 gives clean solutions. I had a little trouble maximizing probabilities with max p(1-2p) but change p's to x's and everything works fine. It solves all my daughter's homework questions on solving quadratic equations and simplifying radicals (but she's smart enough to know not to use it).

So kudos to Wolfram for producing something useful and free. Hope he keeps it that way.

If you make results from Wolfram|Alpha available to anyone else, or incorporate those results into your own documents or presentations, you must include attribution indicating that the results and/or the presentation of the results came from Wolfram|Alpha.

2. Nah.

Maxima is far more powerful, and it is free (GPL).

http://maxima.sourceforge.net/

It is available for Windows, Linux and MacOS.

While I am sure I have access to Mathematica or Maple somehow through my school, Maxima has been good enough for the papers I write. Ultimately, it is reasonably easy to extend Maxima using Lisp, and there are some extensions out there already.

People have bundled Maxima in other tools, so it is widely available.

I must admit that an online version of Maxima would be very nice, but I guess it is hard to pull off in a scalable way.

3. If you make results from Wolfram|Alpha available to anyone else, or incorporate those results into your own documents or presentations, you must include attribution indicating that the results and/or the presentation of the results came from Wolfram|Alpha.This is actually far worse than it sounds. It would be reasonable for elaborate computed answers, but even for purely factual questions, Wolfram|Alpha is supposed to be cited as the primary source (rather than simply acknowledged for having pointed you to data gathered by some other organization). See the FAQ on the site for details. Furthermore, the Wolfram|Alpha site does its best to obscure its own sources. If you click on the sources button at the bottom of the results page, it tells you Wolfram|Alpha is itself the primary source. Then it lists a bunch of background sources and references, with little indication of which data came from each, and in fact with a note explaining that they don't mean to imply that any listed source was actually used for that query.

Basically, Wolfram|Alpha is a black hole for scholarly credit. Wolfram wants everybody to give him all their data, and he wants anybody who uses it to give him credit, but he's very stingy with giving credit himself. That's not reasonable.

4. Mathematica was Maxima with a prettier interface. Seems like Alpha is Google with a prettier interface. On the other hand, just as Mathematica was Maxima without open source, Alpha is Google without giving you access to the sources of your info. You have no idea where it is getting the data.

Seriously, Wolfram never did anything original in his life.

6. It would be nice to have some kind of documentation... It seems that you can use WA as an LP solver, too. Enter "x+y, x + 5y <= 2, y + 5x <= 2" to maximise x+y s.t. x + 5y <= 2 and y + 5x <= 2. Enter just "x + 5y <= 2, y + 5x <= 2" to visualise the set of feasible solutions.

7. I think we can see copyright infringement lawsuits against Alpha in next months. I am sure they have not gathered all those data themselves, they have used what is available on the web.

8. Wolfram really didn't deserve this space on the blog. that was quite a waste.

on the other hand, seems wolfram's plan of making academia like him is somewat working out well as it seems from this blog post.

9. You can also write max p*(1-2p) and everything goes fine.

10. A couple of mice on my blog post on Alpha have been having fun with its handling of floating point: for instance, 1.0001^5754 = 1.0001^5755 = 2 but 1.0001^5756 = 0.

Strange answers and strange assumptions in how it interprets questions aside, my biggest problem with it is what anon #3 already alluded to: the way it gives authoritative-looking answers with no way of verifying them.

11. my biggest problem with it is what anon #3 already alluded to: the way it gives authoritative-looking answers with no way of verifying them.

It is really quite problematic that there is no way to verify the answers given by most of the major mathematical software packages out there because the code is proprietary. Remedying that problem is one of the motivations behind the SAGE project which is developing a full package of open source mathematical software for algebraic and geometric manipulation. Many parts were already out there in individual pieces but SAGE binds the best of these together via a single interface. (Maxima is just one of the pieces.)