Wolfram Alpha

ExactlySolved

Systematic as in methodical, procedural. A network of facts which is connected by a well-defined method or procedure for moving between them. This is not a mathematical definition, so please don't pick it apart (philosophy teaches us that this is pointless i.e. you could not even define the word 'game' in such a way that I could not pick it apart), the only point is that you get the idea that the phrase was trying to convey.

humanino

Oh that's so impressive !
Can you post your WA request page, so we can understand ?

AUMathTutor

ExactlySolved, I wonder how you feel about my objections to its handling of recurrence relations? Are these not valid concerns?

Is the absence of basic theorems and ideas (pigeonhole principle, etc.) acceptable? Is the lack of proofs, references, or explanations acceptable?

And the argument that it should only be compared to other products is bogus. I could make a wood-fired electric toothbrush that also acts as a universal remote for televisions and garage doors, and you could certainly judge its worth and merits in the context of what it is, without respect to other products. W|A was released early, and it was hyped too much (if this is more or less what we can expect). What I see here isn't revolution, not even evolution, just more of the same tired publicity stunts that confuse people who know enough to have high expectations.

AUMathTutor

"Systematic as in methodical, procedural. A network of facts which is connected by a well-defined method or procedure for moving between them. This is not a mathematical definition, so please don't pick it apart (philosophy teaches us that this is pointless i.e. you could not even define the word 'game' in such a way that I could not pick it apart), the only point is that you get the idea that the phrase was trying to convey."

How are the following things not systematic?
- Theorems, principles, and axioms, laws, etc. from Mathematics, CS, Physics, Chemistry, etc...
- Explanations of how to carry out common computational procedures by hand; or, if you will, listings of algorithms for common computational problems and their uses.

This should be a computational knowledge engine, not a computational fact engine. There is a difference between a collection of random facts and knowledge. If you have knowledge of recurrence relations, you can not only solve them, but explain them and provide references and/or the steps used in solving them, including algorithms and other topics.

humanino

http://www93.wolframalpha.com/input/?i=spinor

humanino

http://www93.wolframalpha.com/input/?i=ising+model
It becomes boring now.Good luck.

waht

There are sources: U235

How was it hyped? It's hardly on any major news outlets. And if it was the article got back up. Even Scientific American doesn't mention it, perhaps not yet.

The only way I found out about it is because of this thread.

waht

It has a limited database to only 10 Terabytes.


Ever since google dominated the market, a new approach is long over due. I believe that this just a first step toward something much bigger that's going to be brewing for decades.

Google is working on "google squared" to catch up, so it's going to be interesting.

humanino

Anybody with just a little knowledge and interest in artificial intelligence has heard about it at the very least since March.

Let us admit that the official launch is the 18th. Until then, full functionality is not supposed to be available. Let Wolfram admit that the expectations are as high as his initial claims led us hope.

AUMathTutor

So references and proof are only needed for some facts, not all? I wish that worked in real life.

waht

So you need a reference for 1 + 1?

AUMathTutor

"Anybody with just a little knowledge and interest in artificial intelligence has heard about it at the very least since March."
At least March. I may be hallucinating, but I thought I knew that it was in the works as early as January of this year.

"Let us admit that the official launch is the 18th. Until then, full functionality is not supposed to be available."
This is fair, fine. I just don't know why they made it available early by a few days... oh well.

"Let Wolfram admit that the expectations are as high as his initial claims led us hope."
That's what I'm saying. The guy talks in such lofty terms that it's hard not to get excited about it. I can promise the moon and deliver a picture of the moon and some dubious-looking moon rocks, but come on.

AUMathTutor

"So you need a reference for 1 + 1?"
No, but then again, that's what calculators are for.

There's a difference between 1+1=2 and solving the recurrence relations

f(0)=0
f(n)=2f(floor(n/2))+n

The former does not require any sophistication beyond counting on your fingers. The recurrence, while being comparatively simple and essential to the study of computer science (show me a CS major who does not know what this might represent or how to solve it, and I'll show you a CS major who's not worth his salt), should come along with some sort of explanation or source. There are steps involved in finding a solution (unless you already know the solution).

waht

What were his initial claims?

One claim was that it could combine data from its database.

I asked it to "convert 630 nm to THz." It figured out that's it's dealing with wavelength, and frequency and so found a link in its database and computed the conversion.

ExactlySolved

I'm not sure if it is that impressive, I just input the commands as Mathematica stadard form. My exact example is at my office, but try either of these inputs to get the idea:

Solve[k == Cos[k],k]

http://www58.wolframalpha.com/input/...%5Bk%5D%2Ck%5D

Or for a symbolic example I also used last night we have:

Solve[E^(2 k) = Tanh[k],k]

http://www58.wolframalpha.com/input/...%5Bk%5D%2Ck%5D

It is possible to make the input more sloppy and still get these results, but why bother?

Explanations of Axioms, Principles, etc are systematic, but they do not clearly satisfy the other main criterion of W|A: they are not computable. The way in which W|A differs from an encyclopedia is its ability to combine data according to commands. For example, the input "saturn in 10 days" adds 10 days to the current time and computes various data about the planet saturn at that time. In contrast, I can't think of any relevant calculations you can do on data consisting of a paragraph definition. If you ask "cheeseburger vs 2 hotdog" W|A can compute a nutrition comparison by doubling the data for 1 hot dog to give a more balanced comparison. If you ask e.g. "definition of eigenvalue vs definition of determinant' no relevant calculations can be done. If there are no calcuations to be done, then W|A is not the best tool for the job. This is why many W|A pages link to Mathworld or Wikipedia for this sort of content.

This is a valid point, but IMO this would just be a duplication of static pages which already exist on the web. The goal of W|A is to generate specific answers dynamically by computation, and you cannot for the most part generate definitions, theorems, principles, etc dynamically by computation.

That's a fair criticism, I'm sure that recurrence solvers use very non-human steps, just like integration.

The same poblem occurs in Mathematica, at least naively. If I input:

RSolve[{f[n] == 2 f[n/2] + n, f[0] == 0}, f[n], n]

I get a solution. If I input:

RSolve[{f[n] == 2 f[Floor[n/2]] + n, f[0] == 0}, f[n], n]

I get an error that I cannot bypass. In Mathematica I can say:

RSolve[{f[n] == 2 f[If[OddQ[n], n/2, (n - 1)/2]] + n, f[0] == 0},
f[n], n]

and get a correct solution, where I have replaced the Floor function with an eqivalent If statement. I never work with RSolve or Floor, but I suspect the problem is with the evaluation sequence inolving Floor; however I just don't know. Either way, the If statement gets rejected by W|A.

As you said, the formulas are equivalent, its just a matter of using input that the computer understands. I find it acceptable to learn what works as input.

OK, but there is no synergy between opening garage doors and brushing teeth. Putting these things together does not open any new significant possibilities. If it would, then even the first primitive but plausible attempts to combine them should be supported.

In particular I don't understand the last phrase. The more you know about the technical details, the more impressive W|A is. It seems to me that people who have more technical knowedge will have the most reasonable expectations, not the highest ones.

AUMathTutor

Of course, when I ask "convert kilograms to joules", it says they're not compatible. But if

wavelength = (speed of light) / frequency

works, why not

energy = mass (speed of light squared)

?

ExactlySolved

The following works: 'kilograms to Joules/c^2'

Compare W|A to Google for the following query:

'GeV/c^2 to kilograms'

Both get the right number, but W|A also puts this mass in perspective in terms of elementary particles e.g. 1.1 proton masses.