WolframAlpha: A Magical Knowledge Engine

[humanino]

Last night I needed to solve a transcendental algebraic equation to find the critical point of an ising-type model, but my Mathematica kernels were busy running a monte caro sim, so I used W|A to compute the answer.

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]

ising-type model

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

Wolfram|Alpha's long-term goal is to make all systematic knowledge immediately computable and accessible to everyone. We aim to collect and curate all objective data; implement every known model

Good luck.

 

[waht]

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

There are sources: U235

Source information

*
Isotope data source information
Primary source:
Wolfram|Alpha curated data, 2009.
Wolfram Mathematica IsotopeData »
Background sources and references:
o Atomic Mass Data Center. "NUBASE." 2003. »
o Firestone, R. B. "The Berkeley Laboratory Isotopes Project's: Exploring the Table of Isotopes." 2000. »
o United States National Institute of Standards and Technology. "Atomic Weights and Isotopic Compositions Elements." Physical Reference Data. 2005. »
o United States National Nuclear Data Center, Brookhaven National Laboratory. "Nuclear Wallet Cards." 2008. »
o United States National Nuclear Data Center, Brookhaven National Laboratory. "NuDat 2.3." 2008. »
o Sansonetti, J. E. and W. C. Martin. "NIST Handbook of Basic Atomic Spectroscopic Data." Physical Reference Data. 2005. »
o Raghavan, P. "Table of Nuclear Moments." Atomic Data and Nuclear Data Tables 42, no. 2 (1989): 189-291.
o Audia, G., O. Bersillonb, J. Blachotb, and A. H. Wapstrac. "The NUBASE evaluation of nuclear and decay properties." Nuclear Physics A 729 (2003): 3–128.

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.

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]

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

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]

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

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

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]

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.

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]

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

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/?i=Solve[k+==+Cos[k],k]

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

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

http://www58.wolframalpha.com/input/?i=Solve[E^(2+k)+=+Tanh[k],k]

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

How are the following things not systematic?- Theorems, principles, and axioms, laws, etc. from Mathematics, CS, Physics, Chemistry, etc...

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.

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.

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.

When it does recurrence relations, something that would actually be useful to me, it doesn't show any steps or explain the derivation of the result, so I have no real reason to trust it.

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

It understands

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

but not

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

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.

Since computer scientists would see no difference whatsoever in these two formulas, and strictly speaking the latter is more technically correct, this is unacceptable.

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.

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.

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.

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.

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.

 

[humanino]

What were his initial claims?

http://blog.wolfram.com/2009/03/05/wolframalpha-is-coming/

Mathematica has been a great success in very broadly handling all kinds of formal technical systems and knowledge.
But what about everything else? What about all other systematic knowledge? All the methods and models, and data, that exists?
[...]
we can only answer questions that have been literally asked before. We can look things up, but we can’t figure anything new out.
So how can we deal with that? Well, some people have thought the way forward must be to somehow automatically understand the natural language that exists on the web. Perhaps getting the web semantically tagged to make that easier.
But armed with Mathematica and NKS I realized there’s another way: explicitly implement methods and models, as algorithms, and explicitly curate all data so that it is immediately computable.
It’s not easy to do this. Every different kind of method and model—and data—has its own special features and character. But with a mixture of Mathematica and NKS automation, and a lot of human experts, I’m happy to say that we’ve gotten a very long way.

I admit that WA does much more than has been done before, in interpreting a question and computing the answer. But

...

I'm disappointed because I feel that most of the task is still on the user to provide the appropriate question that WA can answer. In this regards, there is no substantial difference with merely using Mathematica. At least, not yet. So the product as it performs today was released too early.

It also serves one important purpose : put pressure on everybody to make it come true sooner.

 

[AUMathTutor]

"they are not computable. "

I think you and I have a fundamentally different idea of what "computable" means. For me, computation is not only working out answers to mathematical problems, but also constructing a sentence in the English language, finding information in a database, and really coming up with *any* answer. If I ask you to help me solve

y'' - y' + y = exp(x)

You don't just tell me the answer. You develop an answer which is correct in the sense that it solves my problem (the how, not the what). You have computed the correct result by referening knowledge stored in your brain, making a list of relevant facts, and then constructing an explanation in some human language in such a way that my brain accepts your input string and the "figure out the answer to my question" program terminates.

 

[AUMathTutor]

And as far as it only "computing" things in the restricted sense of the word, why on Earth would it tell me who the twelfth president was? That's not computable in the restricted sense of the word, or any sense of the word, other than my interpretation of it as "finding relevant data".

 

[ExactlySolved]

By computable I mean that the data can be combined by a mathematical algorithm to yield new useful information, to equate the mind and all of its activities with computation is romantic but speculative. I am not speaking about computation in the sense of Von Neumann, Turing, Deijkstra, etc but rather in terms of practical and interesting computations that can be done in 2009.

As for historical names, these are attached to data which is computable, such as dates, physiology, geneaology/succession trees, etc. Honestly I don't know why the 12th president's data would be at all a priority, I'll grant that, but eventually as more data is added perhaps someone will think of something interesting that can be done with it.

I'm disappointed because I feel that most of the task is still on the user to provide the appropriate question that WA can answer. In this regards, there is no substantial difference with merely using Mathematica. At least, not yet. So the product as it performs today was released too early.

It also serves one important purpose : put pressure on everybody to make it come true sooner.

I see things the same way, accept that I agree with your ultimate comment more so than your penultimate one. Furthermore, I also see the benefit of W|A driving Mathematica's data integration e.g. W|A has earthquake data but M7 does not have that yet.

 

[AUMathTutor]

"By computable I mean that the data can be combined by a mathematical algorithm to yield new useful information, to equate the mind and all of its activities with computation is romantic but speculative. I am not speaking about computation in the sense of Von Neumann, Turing, Deijkstra, etc but rather in terms of practical and interesting computations that can be done in 2009. "

If that's how you're looking at it, I can understand your position. Since Wolfram is essentially a physicist, I wouldn't be surprised if this was how he saw things too. I think it's misleading to use such a loaded word as "computation", however, just because it sounds "cool". A much better name for the project, such as "mathematical problem-solving engine" would have been more accurate.

 

[Phrak]

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.

Thank you, that's what I was seeking. If I combine what you have said with a careful rereading of the goal of WolframAlpha, systematic knowledge consists of set of information, and a set of tools: algorithms, models and methods... Applying these tools to known information can obtain other specific information (computation). As it's stated goal, this seems to be the primary information WA intends to provide.

 

[waht]

http://blog.wolfram.com/2009/03/05/wolframalpha-is-coming/

I admit that WA does much more than has been done before, in interpreting a question and computing the answer. ButI'm disappointed because I feel that most of the task is still on the user to provide the appropriate question that WA can answer. In this regards, there is no substantial difference with merely using Mathematica. At least, not yet. So the product as it performs today was released too early.

It also serves one important purpose : put pressure on everybody to make it come true sooner.

It's not a mind reading machine. I guess the biggest challenge WA faces is to distill their algorithms to figure out what the users intended to ask from what they asked.

Here is something cool it did. It's probably a useless fact, but it demonstrates how it combines data to form a new one.

"distance from Mars to saturn in five years"

http://www93.wolframalpha.com/input/?i=distance+from+mars+to+saturn+in+five+years

This is a baby step toward a cloud computing engine that will interact with people, and even by talking to it. It has been written in many Arthur C Clarke's novels.

 

[humanino]

It's not a mind reading machine.

Sure. Even on PF it's harder to understand each other than if we could see each other speak.

 

[Phrak]

Radius of electron in light years.

http://www93.wolframalpha.com/input/?i=radius+of+electron+in+light+years"



speed of light times Planck time over Planck length = 2.507

oops

 

[ExactlySolved]

The Planck units are definitely bugged, and notice that $\sqrt{2 \pi} = 2.50663$, so this may have to do with inconsistent conventions on a Fourier transform.

 

[Moonbear]

It's not a mind reading machine. I guess the biggest challenge WA faces is to distill their algorithms to figure out what the users intended to ask from what they asked.

More importantly, they need to find a way to determine which sources to use. It doesn't seem to discriminate between credible and erroneous sources when finding information for answers. That seems even worse than google or wikipedia, which at least cite the source they're using, so the user can determine if they are credible sources.

 

[ExactlySolved]

Moonbear: most of the cite omissions I have seen so far are about mathematical topics, could you give some examples?

 

[Redbelly98]

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.

There was a feature on it on NPR radio last Friday. Not on a par with Fox News or the major television networks, but nonetheless they were putting the word out.

I say give it a couple of months to see if the bugs get worked out.

 

[Coin]

I can't get the site to respond to any query. I get long pauses and then various "unavailable" error messages.

When I first heard of this site a couple weeks back, and heard that the backend engine is based on Mathematica, one of my first responses was "can Mathematica actually scale to serve this much complex data to a google-like website?". My question stands :|

 

[CRGreathouse]

So you need a reference for 1 + 1?

http://us.metamath.org/mpeuni/1p1e2.html

 

[CRGreathouse]

ExactlySolved, are you a Wolfram employee?

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.

That's pretty impressive, since those are dimensionally incompatible. (check site) It even says they're incompatible and gives its assumptions: "(assuming speed of sound at sea level and 15 deg C ~~ 340.3 m/s)". Nice! I see that it doesn't let you change those, at least not in the obvious way: link.

 

[chroot]

ButI'm disappointed because I feel that most of the task is still on the user to provide the appropriate question that WA can answer.

The same could be said of college professors, could it not?

It appears to be an insanely useful application, even if it is not yet the end-all be-all of artificial intelligence. I'm an integrated circuit designer, and I've used it twice today already, saving me probably an hour of work each time... and it's free! I'm pretty damned pleased!

- Warren

 

[Coin]

I finally get the site to respond. Now that it seems to be working again it is impressively speedy even for computationally intensive inputs.

It seems very limited in that it doesn't seem to be able to do anything that the creators didn't specifically think of ahead of time. I can type in "u.s. unemployment rate" and it finds that? If I ask for the "u.s. underemployment rate" it doesn't know what that is. If I ask for the "u.s. unemployment rate over the last four years" or any alternate phrasing it doesn't know what that means. If I ask it for "dow jones 1900-2000" it can give me a graph of that, because it apparently occurred to them to program in the Dow Jones as something for which data exists over a range of time? But it doesn't know that is the case for the unemployment rate, or the "u.s. population". If I type in "u.s. population 1900-2000" it seems to think I want to multiply the u.s. population by 1900, then subtract 2000.

If you stumble across something the creators had in mind when they designed the site, it is fantastic. I've been just typing arbitrary cellular automata rules into it and it produces these beautiful summary plots of the cellular automata rule applied in various ways, and it reveals the Mathematica statements that produced each plot. Of course, like with the u.s. population thing, I hit a dead end if I want to view the data in a different way than they anticipated. Like, okay, I can get it to generate the output of rule 110 and plot it, but what if I want to take that output and instead use it as the input to some other kind of function? I guess I buy Mathematica?

Hopefully they will be logging the queries people type into it on this first day and use this information to refine the kinds of data their system contains and the way it is fetched. In the meanwhile though it seems more likely that this will be useful as a quickie web frontend to Mathematica than it ever will be as a general collection of knowledge.

Will the engine to the site ever become a part of Mathematica itself, such that people can set up wolfram-alpha-like natural-language web interfaces to Mathematica scripts or knowledge bases they created themselves?

 

[f95toli]

The database is rather odd. I entered the name of the small town where I grew up (north of Sweden) and it returned the location, population and weather (quite impressive).

But when I enter the name of the place where I live now (large suburb of greater London) it does not recognize it and instead suggests a small town in Alabama with a not-so-similar name...