WolframAlpha: A Magical Knowledge Engine

[AUMathTutor]

Seeing as how it's the 18th and nothing is better, I can say with certainty that I'm not impressed. The only thing is it seems a bit speedier now, but that may just be my connection.

*sigh*

 

[qntty]

I found this to be rather amusing.

 

[ExactlySolved]

ExactlySolved, are you a Wolfram employee?

No, I'm an academic physicist. I use Mathematica everyday, and although I rely on the mathematical algorithms, I agree that other packages e.g. MATLAB and maple compare in this area (in fact I sometimes use MATLAB at the university for the excellent curve fitting toolbox).

The thing that I really admire about mathematica, that makes me go on and on about this product, is its structure as a programming language. By structure I mean the kinds of things that are done in an upper division undergraduate CS class "Concepts/Organization of Programming Languages" e.g. a book like this:

https://www.amazon.com/dp/0321330250/?tag=pfamazon01-20

Mathematica is a totally functional language like lisp or Haskell, which means that every expression has the uniform structure of a nested set of functions, and a program consists of a composition a functions applied to input to obtain an output. Mathematica's internal evaluations are ultimately rule-based pattern replacements of these functional expressions, a system which the user has direct access to. Everything in mathematica is an expression, even input and output (arbitrary graphics are expressions, not side effects, even the notebooks themselves are expressions).

So that's it, organization and consistency are why I like Mathematica.

I found this to be rather amusing.

The reason that sum^(-1.5) fails the ratio test, which is a bug, is (I'm guessing) that there is mathematica code which compares 1. === 1 and yields false: the use of a machine number exponent leads to the 1. , and the ratio test fails so the sum is reported as diverging. Using n^(-3/2) works, but sum n^(-2.) fails, I'm pretty sure that the comparison of a machine integer and an exact number is the reason.

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?

Yes, W|A will become part of Mathematica, using internet functionality to reason live results from W|A inside a notebook. Also relevant to your question are the soon to be released W|A APIs, best suited for Mathematica itself but also availible for other major web platforms. I would not suggest, however, being overly optimistic about 'openess' of these APIs.

Also I share your concerns about Mathematica scaling performance-wise to this load. The only reason I still use languages like C for some tasks is speed, and I'll readily admit that Mathematica is 10-1000 times slower, having an interpretive kernel. Hopefully computer performance will increase enough overthe next few years to realize more ambitous uses of W|A.

 

[CRGreathouse]

No, I'm an academic physicist.

OK, just wondering.

The reason that sum^(-1.5) fails the ratio test, which is a bug, is (I'm guessing) that there is mathematica code which compares 1. === 1 and yields false: the use of a machine number exponent leads to the 1. , and the ratio test fails so the sum is reported as diverging. Using n^(-3/2) works, but sum n^(-2.) fails, I'm pretty sure that the comparison of a machine integer and an exact number is the reason.

That seems odd to me, since it's not on the boundary. If it failed with sum n^-1.001 that would be different, but -2.?

Also, shouldn't it be using < rather than ===?

 

[AUMathTutor]

Some of the errors are just silly, as in, if you asked the question to the average person with a background in science/engineering, they would not make the same mistakes or have the same trouble.

I thought the point of W|A was to keep you from having to learn a command-line syntax and from considering machine representation of numbers in calculations.

Rather than a product that can create new knowledge, I see a product that can answer petty questions about existing knowledge.

 

[dx]

Rather than a product that can create new knowledge, I see a product that can answer petty questions about existing knowledge.

W|A is not meant to create new knowledge. It is just an interface to Mathematica connected to a large database of computable knowledge.

 

[AUMathTutor]

What in the world do you guys mean by "computable knowledge"?

Most knowledge is computable in the modern sense of the word. If you mean "mathematical", or perhaps more accurately, "approximate mathematical" knowledge, then I feel like W|A is a better product with an unambiguously misleading name.

Of course I don't mean "new knowledge" as in completely unknown facts. What I mean is a novel synthesis of the facts which links ideas in ways that perhaps people haven't already thought of.

This happens with simple genetic algorithms; they find optimal solutions and strategies for solving problems where human beings do not. An analysis of the answers after the fact can reveal the "why" of it, but I think you get what I'm saying.

I was expecting (or, really, hoping for) this:

<< Q >>
Why are plants green?

<< A >>
Plants contain chlorophyl, and chlorophyl is green.
Would you like to know why plants contain chlorophyl?
Would you like to know why cholorophyl is green?
etc.

 

[Borek]

Interesting information. Someone I know from other place meet with Wolfram 18 months ago and they were talking about chemistry part of the W|A. This is what he told about his impressions:

Anyway, it was clear that Wolfram Research is very Mathematica-centric, and there are *no* chemists in the place. I was working with a physicist who had been at NIST, and they all thought him to be a chemist! He wasn't.

I discussed with Stephen the issue of complexity in chemistry, but the response always seemed to be "we can compute that."

Ignroance can be forgiven, self-conceitedness can't. When calculating pH W|A makes mistakes that HS students should not. And yes, you "can compute that", but you have to know how. Then, there are things that we can't compute yet.

 

[AUMathTutor]

They have a lot of work to do before I use the thing for anything other than entertainment.

We could make a drinking game where we ask W|A a question, and we drink if it (a) has no information on the topic, (b) provides meaningless unrelated information about some random fact, or (c) provides a clearly incorrect result to the inquiry.

I have a feeling that would work out pretty well.

 

[dx]

What in the world do you guys mean by "computable knowledge"?

Basically anything that that Mathematica can do something with.

 

[Moonbear]

So, is it really just a web-based version of Mathematica? If so, what's the big deal about it? It's sounding like it might be a useful thing within a very limited area...something for math specialists perhaps? People seem to be promoting it as the next big challenge to Google or a replacement for Google, and I don't see it as even in the same ballpark, let along a competitor. It seems to do something entirely different and for a much more limited set of information and queries.

Still, even if it's just good for a limited range of information, it really would be useful to have it tell you what its sources are. How does it decide which sources to use? How is it supposed to employ any sort of AI if there is no way for it to get feedback and "learn?" For example, when it gives a wrong answer to something, there is no way that I see to flag it and tell it that it's wrong and should skip that source and look for another.

 

[dx]

So, is it really just a web-based version of Mathematica? If so, what's the big deal about it? It's sounding like it might be a useful thing within a very limited area...something for math specialists perhaps?

It's not just a web-based version of Mathematica. The difference is that W|A has access to a very large amount of data, and that it can understand common language (instead of specialized syntax). For example, since it knows the dates of birth and death of Richard Feynman and Albert Einstein, you can ask it a question like "How old was Richard Feynman when Albert Einstein died?", and it will be able to answer (36 years 11 months 7 days). The answer to this question was not known to W|A, but it was able to compute it using the information in its database. This is obviously a very unimaginative example, but you can see the potential capability of W|A given how powerful Mathematica is (it can do far more than addition and subtraction, which was all it needed to do in this example), and how much data it has access to.

 

[CRGreathouse]

Another oddity: it can recognize (not (P xor Q)) or (R and T) and it uses the text form "implies" in its description, but it can't understand (P xor Q) implies (R and T) or (P xor Q) -> (R and T).

The answer to this question was not known to W|A, but it was able to compute it using the information in its database. This is obviously a very unimaginative example, but you can see the potential capability of W|A given how powerful Mathematica is (it can do far more than addition and subtraction, which was all it needed to do in this example), and how much data it has access to.

I see many nice hand-crafted pages, like comparing (LOCATION 1) to (LOCATION 2). Sites providing services like this already exist (for many various templates, not just this one), but having them together in one place and with one interface is nice. I also see a Mathematica interface, or something like it. This is a nice improvement on integrals.com. Finally, I see a souped-up unit converter that solves more problems but makes more mistakes than Google calculator (which I'm told is basically a front-end for the 'units' utility).

I'd like to see more examples of things that go beyond these, that help me see the "potential capability". Right now it's a slick package but I can't see myself using it regularly.

 

[chroot]

Yeah, it seems to be essentially a very fast "robotic librarian." That's not really a disparaging remark, though. It's still a pretty awesome creation.

- Warren

 

[Coin]

Still, even if it's just good for a limited range of information, it really would be useful to have it tell you what its sources are. How does it decide which sources to use?

There's a leeetle bitty "source information" link at the bottom of the page. It's easy to miss and the results are poorly organized (it gives you a list of sources used to build the page, but there's no way to determine what source any specific piece of information came from).

For example, when it gives a wrong answer to something, there is no way that I see to flag it and tell it that it's wrong and should skip that source and look for another.

There's also a tiny "feedback" form at the bottom of the page. I don't know where the stuff put in the feedback form goes, or if anyone reads it. I haven't used it yet-- I noticed a couple of specific things that needed correcting when I was first messing with it but then forgot what they were before I noticed the feedback form...

Something I am concluding is that the W|A tools have the potential to be useful and very cool, but before this can happen what it really needs is some sort of "wiki" like feature for user-supplied data. The Wolfram employees are simply never going to be able to cover everything that needs to be covered. On the other hand their basic tool set seems surprisingly powerful. In the hands of a wider set of specialists it could be used to provide some very cool services. So I am encouraged by ExactlySolved's comments that the W|A engine will be built into future versions of Mathematica in some form.

Last night I was having a discussion with some coworkers about the California budget issues, and specifically the question of whether the California educational system spends too much money for the level of service it provides. We dug up some spreadsheets the Federal government publishes ranking the states' educational systems in terms of things like budget size or standardized test performance. I wound up spending some time extracting and merging some of that data into another spreadsheet, and in the end wound up with nothing more for my efforts than a single scatter plot of basic standardized testing success vs. amount spent per student. Which was interesting, but there were any number of other things I'd have liked to have compared the data against-- population size? State GDP? Percentage of ESL students?-- but it was just too time-consuming with the tools I had at hand. The entire time though I was thinking, everything I'm doing here by hand is stuff I've basically seen Wolfram|Alpha demonstrate it's powerful enough to do automatically-- store tabular data, cross-reference it, plot it based on natural language queries-- if only it had any idea what a state budget is. But I could easily imagine a world where users are allowed to add information to Alpha's data store, or where it were possible for me to install a copy of the base Alpha engine on my own web server, and with probably about the same amount of effort massaging those spreadsheets into whatever format Alpha uses internally as it took for me to fight past iWork's interface bugs last night I could imagine winding up with something able to plot things like "population vs education budget for all u.s. states" based on just a query-- except that it's missing a couple of vital plot types, this seems realistic based on what I've seen Alpha do so far. And once those spreadsheets had been Alpha-ized, that tool would be around for anyone who might want to investigate similar data later.

So there does seem to be a lot of potential here, but it all depends on what they do with it and especially how open they ultimately make the technology...

 

[OAQfirst]

Groklaw has described a legal issue:

The legalese says that they claim copyright on each results page and require attribution.

http://www.groklaw.net/article.php?story=20090518204959409

 

[Coin]

OAQfirst, wow, that's a bit odd. Especially considering they claim copyright on the plots, but as far as I can tell those plots are just being generated via normal Mathematica. So you type something into Alpha, it spits out a plot, that plot is copyrighted, you copy the Mathematica command Alpha used into Mathematica, the plot is no longer copyrighted? Then again maybe getting you to buy a copy of Mathematica is the point...

 

[Moonbear]

Groklaw has described a legal issue:

http://www.groklaw.net/article.php?story=20090518204959409

Even if they obtained the information from another source?

Oh, and thanks Coin for pointing out the feedback and sources links. They need to make them more prominent.

 

[OAQfirst]

If Groklaw's interpretation of those terms are correct, them Wolfram might be infringing copyright law just by returning some of its results if anything it returns is already copyright-claimed by another party. Still, I don't know how enforceable this is. I don't read copyright law (United States) as usually covering this range of content.

EDIT: Ah, Moonbear- I guess we were on the same page with that.

 

[ExactlySolved]

The last few versions of Mathematica have gone outside the niche of 'math specialists' to provide really useful tools for all kinds of physical and social scientists. They call this 'integrated data' and what it means is that with very simple commands you can import data on astronomy, genetics, geography, economics, weather, etc from Wolfram's internet servers.

So there does seem to be a lot of potential here, but it all depends on what they do with it and especially how open they ultimately make the technology...

It is safe to say that your example about state education budgets etc is 'in the works' for W|A, not only will non-wolfram entities be able to add data, but public data like you describe will also eventually be added by Wolfram Inc itself.

Even if they obtained the information from another source?

It's not that the data that's being copyrighted, it is the text and images that W|A produces --- just as you most likely hold the copyright for any text or diagrams in any scientific publications you've authored.

 

[AUMathTutor]

If you guys want to see what most of the math in Griffiths's QM looks like, try

eigenvalue 3 2 sin(x) differential limit as k goes to 3

On W|A. lol. Obviously, just kidding a little bit. But you get the idea. It obviously has no intelligence at all. This is what happens when you hook up a TI to a database of information.

 

[ExactlySolved]

This is what happens when you hook up a TI to a database of information.

Nice hyperbole, but of course it is literally what you get when you hook up Mathematica to a database and try to accept natural language input.

In 5 minutes I made up the following queries that I liked:

Good facts for students writing social science essays:

'population china vs India vs us'
'gdp africa vs eu vs us'

Good for students in intro physics:

'time to fall'
'diffraction'
'Kepler's third law sun and earth'

Lots of good queries for math students of course.

 

[AUMathTutor]

But not for students of CS. I've tried several CS-related queries, and apparently Wolfram didn't think that was important enough to include in the first release... ironically enough...

 

[BobG]

I don't know how you guys can possibly criticize Wolram Alpha! This is the greatest thing since the invention of single serving pieces of bread containing 133 calories per serving.

I asked it, "What's it all about?" and discovered that 1 Albanian lek is equal to about 1.04 cents in American currency (this is a decrease in value from Jul 08 when 1 lek was equal to about 1.31 cents). I also discoverd that 1 lek is equal to about 1.58 kurus.

Actually, I think this article has some good points. The main impact of Wolfram Alpha will be to make Google searches better as Google has to compete.

When I compare Google and Wolfram alpha, Google has about 460 million daily visitors, while Wolfram Alpha has only about 460,000 daily visitors. That contrasts rather starkly on a graph.

When I ask is google crap (it's hard to format a question so that it's accepted), I find that google is better than CRAP. Google sells for $403.67 a share and CRAP sells for only $60.62 a share. More relevant, Google only dropped in value by about 30% over the past year while CRAP has dropped in value by about %50 over the past year.

Competition in crap stocks seems to have increased over the last year.

 

[ExactlySolved]

From the article linked by BobG:

This is the eternal problem for any wannabe Google competitor. Wolfram Alpha doesn't revolutionize search; at best, it adds a marginally useful new layer on top of it. But Google can easily co-opt such improvements—and suddenly everyone's got a better Google.

If the line in bold were true, then I wouldn't care about W|A at all. But if you look at the technology that drives W|A, you will see that Google is 20 years + 1 super genius behind Wolfram Inc. This means that it will take a long time for google to match even the currently much-critisized performance of W|A. In the mean time W|A will be improving exponentially along with Mathematica, so Google will never really catch up.

In the many articles that compare W|A to google, the authors typically make shallow comparisons based on what someone may type into the engine over the course of a few minutes. A deeper comparison results from looking at the history of these projects and how they are driven by their technological foundations, and to see that W|A is built on a foundation that has been improving for longer than Google has existed.

Perhaps fans of Google should recall how the site began in 1998, what was it like searching for information on a web with far fewer pages, on 1998 hardware? Clearly when it was launched, Google was a product that would not really come into its own until the next decade. Whether this will also happen for W|A as I expect, or whether Google will be able to grow in new ways to stay competitive, only time will tell.

The real google.com in 1998.

Edit:

But not for students of CS. I've tried several CS-related queries, and apparently Wolfram didn't think that was important enough to include in the first release... ironically enough...

It maybe a while before mainstream CS topics appear, because Wolfram's vision of CS has a lot more cellular automata and functional programming then the typical university curriculum. Look at the example page for computational science:

http://www.wolframalpha.com/examples/ComputationalScience.html"

But of course it is only a matter of time until mainstream CS topics are added, since there is nothing inherent about them that does not fit within the project.

 

[BobG]

Except google isn't starting from scratch. They're already part of the way there, even if most users don't use google as effectively as they could (http://www.google.com/intl/en/help/features.html).

The main thing google is missing is a good CAS system. While Mathematica, Maple, and Matlab are the most popular, there's quite a few other programs out there that are competitive in function (the disadvantage being that you wouldn't be able to interact with very many users with the less popular programs). MuPad is a good example. In some ways, it was even better than Matlab (the graphics were better, anyway), but then Mathworks just bought MuPad and eliminated the competition.

I think google could probably buy the CAS system; maybe even buy rights to one of the more popular programs.

I don't think Google could run Mathematica, Maple, and Matlab out of business in any event. I just think they could match whatever the other programs would be willing to put out there for free on the internet.

 

[Phrak]

I don't think Google could run Mathematica, Maple, and Matlab out of business in any event. I just think they could match whatever the other programs would be willing to put out there for free on the internet.

To answer this question, I asked "who's the big Guarilla in the room?" ( I went to Google. It corrected my spelling to 'Guerilla' so I wouldn't look stupid. ) I decided to focus on Net Worth.

A lesson in nontechnical internet information searching, or something like it.

Google directed me to Wikipedia who informed me that Google was worth 18.5G. After learning the ropes WolframAlpha told me Google was worth 29.85G dollars. While there I asked WA the networth of Wolfram Research. WA didn't know what to do with my input. Have I the right corporate name? Is it a corportion? "What is Wolfram Research?" WA wouldn't tell me.

Back to Google; "What is Wolfram Research?" It's a 'company'. OK.. ask about 'Wolfram Research Company'; not 'Corporation'. WA was not forthcoming concerning such a company. Neither was Google.

Confusing Steven Wolfram with Eric Weisstein, I Googled Treasure Trove of Physics and discovered that Eric worked for Wolfram Research Inc., and that it is called WRI. Back to work.

WRI is Weingarten Realty Investors (NYSE)‎. Dead end. Googling Stock Quotes lead to Yahoo Finance. A dead end. Finally, after close reading, Wikipedia tells me WR is privately held. WolframAlpha doesn't know what to do with "what is Wolfram Research Incorporated?" But, as such, questions of worth are probable moot anyway. Oh well.

 

[AUMathTutor]

I don't see any useful information for functional programming here.
definition referential transparency
definition function composition
definition lambda calculus
(lambda x.x y)
S ::= bSb | SaS | c, parse tree bcacb
(define (f g h x) (* (g x) (h x))) (f sin cos 1)

... It's a little arrogant of Wolfram to think that he knows better than the rest of the world what is important enough in CS to include in his "computational knowledge engine".

sort ascending (2 4 1 3 8)

I just don't get it. A precocious 5 year old wouldn't have trouble with this. This is arguably the simplest problem in CS, besides searching.

does ("cat", "squirrel", "tree") contain "squirrel"

Beyond me.

 

[Coin]

AUMathTutor: The weird thing is those are all things Mathematica itself does. Like it's got foldl and composition and a full set of higher-order functions.

Which leads to another odd thing about Wolfram Alpha-- what happens when you type Mathematica statements into the search box. Sometimes it accepts it and sometimes it doesn't.

Interestingly, if you give Wolfram Alpha the input:

Sort[{2,3,1}]

It does the right thing! But the NLP engine doesn't appear to recognize the word "Sort".

 

[JasonRox]

AUMathTutor: The weird thing is those are all things Mathematica itself does. Like it's got foldl and composition and a full set of higher-order functions.

Which leads to another odd thing about Wolfram Alpha-- what happens when you type Mathematica statements into the search box. Sometimes it accepts it and sometimes it doesn't.

Interestingly, if you give Wolfram Alpha the input:

Sort[{2,3,1}]

It does the right thing! But the NLP engine doesn't appear to recognize the word "Sort".

It's weird.

Type in "Find the intersection of 4x+1 and -x+6" and it will solve it.

Type in "Find the intersection of x^2 and x+10" and it recognizes nothing.

 

[Coin]

My nitpick of that sort would be:

One of the first things I wound up doing with Wolfram Alpha, trying to think of things it might respond to, was to type in:

"Finite groups of order 2"

It immediately responded there was 1 finite group of order 2.

Curious, I tried something like:

"Finite groups of order (1..1000)"

And it immediately spit out the count of finite groups for all orders 1..1000. I then got briefly very excited and tried:

"Graph finite groups of order (1..1000)"

...but... at this point it refused. It actually even realized I wanted to plot the results of "finite groups of order (1..1000)", it gave me an "Input interpretation" saying so. But it for some reason refused to actually do it. It knows how to plot "1..1000"? Or "x^2". But not for some reason the results of FiniteGroupCount[1 to 1000]. Bizarre.

 

[ExactlySolved]

The strength of Mathematica, and hence W|A, is not the CAS functionality - there are many other packages that do math - but rather the well-designed programming language.

Everything in mathematica is a computable expression, and every expression has a uniform symbolic structure. Contrast this with the toolkits and such in Matlab/Maple that put functionality in a separate window --- new capabilities must be 'tacked on' rather than fully integrated into the system.

Here is a plot of the growth of the number of functions in Mathematica over the years:

Along with an excerpt from a blog post by Stephen Wolfram upon the release of the latest version of Mathematica November 2008:

Watching our development process from the inside, I’ve definitely had the feeling in the past few years that we’ve been entering a new regime of growth. That everything we’ve integrated into Mathematica is interacting to let us somehow build almost exponentially more.

And the plot above suggests that something like that is really happening.

But what’s perhaps most striking is that even as the number of functions and the breadth of functionality have been growing so dramatically, we’ve succeeded in maintaining the unity of Mathematica—and of making sure that every piece of the system fits together in a coherent way.

That’s not been easy, of course. It’s the result of our long-term company culture and of a lot of systems that we’ve built up over the course of more than 20 years. (As well as thousands of hours of personal work by me.)

It’s very satisfying, though. Because it means that the things we so carefully built five, ten, twenty years ago are still there today, making possible our new achievements.

The strengh of Mathematica for a project like W|A is the uniformity of its design, the standard structure of expressions. This allows for the code to be extremely concise, because there is a minimum of special cases, and one can write functions that are very general and highly automated.

It has been said that W|A is already running over 5 million lines of Mathematica code: if it were even possible to write something like W|A in C++, in my experience it would be larger by a factor of 10, over 50 million lines.

Google uses python, C++, and java, and each function in
http://www.google.com/intl/en/help/features.html is seemingly coded as a special case --- just like adding new toolkits to the next version of Matlab or Maple. It's unlikely that we will ever see Google's weather data be computable against its sports data, but W|A, although it does not yet have sports data, is designed to do this sort of thing.

As Phrak discovered WRI is privately held, and I will be surprised if and when they ever go public --- somethings seem to matter more to Stephen Wolfram than money. Based on what I know about the man, I will be surprised if a big company like Google or MS is ever able to get a piece of Mathematica just by throwing money around, at least during Stephen's lifetime, but that's what everyone says before the cash presses start rolling

Wolfram emphasized from the beginning that private information would not be a part of W|A, and although I find in strange that the engine will not discuss it's creators, this is keeping with that general policy.

For those of you who like 'web 2.0' there is now a Wolfram|Alpha community website which allows posters to provide suggestions, and potentially data, etc:

http://community.wolframalpha.com/

 

[CRGreathouse]

http://www29.wolframalpha.com/input/?i={{0,1},{1,-7}}+*+{{7,1},{1,0}}

 

[rootX]

http://www29.wolframalpha.com/input/?i=female
http://www29.wolframalpha.com/input/?i=male

http://www29.wolframalpha.com/input/?i=women
http://www29.wolframalpha.com/input/?i=men

I found it interesting that it provides men or male definition but not female/women.

 

[fluidistic]

I like very much the "weather nameofthecity" option. It shows predictions more precisely than on the official meteorological website (in Argentina at least).
I've once type "Apex" because my girlfriend works for them, but it pointed a satellite and it's position over the ground. That was nice.
On the other hand it's not complete at all. For example if you type in "water triple point", it shows up some nice things, but if you type any other "liquid triple point", WA will get clueless.