WolframAlpha: A Magical Knowledge Engine

[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.

 

[Blenton]

This wouldve been great a couple of years ago when i was in high school!

 

[Borek]

Interesting:

x'' + a x' + b x = 0

f''(x) + a f'(x) + b f(x) = 0

There are at least two people in the world thinking that Alpha is misunderstanding problem as entered in the first case (that's Junior and me).

 

[Office_Shredder]

That's weird. If you swap the a and the b it still solves for x(b)

 

[waht]

WA does a good job of assuming certain things, like:

http://www.wolframalpha.com/input/?i=x''+++2+x'+-6+x+=+0"

which aides in user laziness,

but if you add a or b without specifying what the independent variable is, you should expect to get three possibilities, a(t), b(t) or x(t) and then it would have to solve all three. But it didn't happen like that, it just looks for an independent variable.

 

[Office_Shredder]

Competition. Find input that makes mathematica assume x is a function of 2

 

[CRGreathouse]

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

W|A can't multiply 2x2 matrices correctly?

 

[Mech_Engineer]

Well I just discovered this website after reading a Popular Science article about it. It's sort of a cool idea, but it's basically useless for anything but an online calculator and fun facts about a limited number of topics. With expansion, I can see it being used for a quick way to look up physical properties and scientific constants, but right now even that capability is limited. Making it an engine that gives you an answer about anything is pretty ambitious IMO, but I suppose anything can be done with enough brainpower and computing power behind it...

All you can really do right now (besides solve mathematical equations which it does a pretty good job of, other than the fact you're not really sure how it was solved or how to get the result in a usable format) are things like type in "http://www.wolframalpha.com/input/?i=United+States"") and get a somewhat simplistic comparison of the three, but it just doesn't give a whole lot of useful of hard to find information... I'm more likely to look something up using Google or Wikipedia honestly.

One thing that did grab my interest at first was their example "http://www.wolframalpha.com/input/?i=steam 400F 60psi"" which looks up thermodynamic properties of steam at that state. Cool idea, but it deosn't give enough useful information right now. This might be a nice quick way to look up thermo values later on, but right now there just isn't enough there. It was able to look up R12, which I found promising, but all it gave were some simple values, nothing useful in a thermodynamics context.

Overall I'll be sticking with my usual sources for now, but this site does seem to have pormise as long as they focus their efforts a bit more on the "scientific," where numbers-based calculations are prolific.

 

[Coin]

Well I just discovered this website after reading a Popular Science article about it. It's sort of a cool idea, but it's basically useless for anything but an online calculator and fun facts about a limited number of topics. With expansion, I can see it being used for a quick way to look up physical properties and scientific constants, but right now even that capability is limited. Making it an engine that gives you an answer about anything is pretty ambitious IMO, but I suppose anything can be done with enough brainpower and computing power behind it...

All you can really do right now (besides solve mathematical equations which it does a pretty good job of, other than the fact you're not really sure how it was solved or how to get the result in a usable format) are things like type in "http://www.wolframalpha.com/input/?i=United+States"") and get a somewhat simplistic comparison of the three, but it just doesn't give a whole lot of useful of hard to find information... I'm more likely to look something up using Google or Wikipedia honestly.

One thing that did grab my interest at first was their example "http://www.wolframalpha.com/input/?i=steam 400F 60psi"" which looks up thermodynamic properties of steam at that state. Cool idea, but it deosn't give enough useful information right now. This might be a nice quick way to look up thermo values late on, but right now there just isn't enough there. It was able to look up R12, which I found promising, but all it gave were some simple values, nothing useful in a thermodynamics context.

Overall I'll be sticking with my usual sources for now, but this site does seem to have pormise as long as they focus their efforts a bit more on the "scientific," where numbers-based calculations are prolific.

That was basically the response I had when I first saw Alpha-- pretty thin stuff, but with the potential to grow into something very useful. However, that was in April. Anyone in a position to say, has Alpha really improved any in the seven or so months it's been up?

 

[Raphie]

Online Math Tool Recommendation: Wolfram Alpha

A Sample Input...

http://www.wolframalpha.com/input/?i=67092479/8191

And, boom, just like that,you can figure out, for instance, the repeating decimal period of 67092479/8191... = 1365.

Want pi to 100 digits? No problem. Just enter into the search box N[Pi, 100] and you'll get the following...

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

More or less, if you play around with it, you'll see that this is the equivalent of the Google Calculator on steroids...

Another example that brings up different info...

http://www.wolframalpha.com/input/?i=e^(-phi^2)Raphie

 

[The legend]

That's true. You can do much with that useful tool...

 

[Raphie]

Although admittedly flawed, as, for instance, you can see if you input the following two queries...

INPUT: multiply 2 * 2 matrices
http://www.wolframalpha.com/input/?i=multiply+2+*+2+matrices

INPUT: multiply 2 * 2 matrix
http://www.wolframalpha.com/input/?i=multiply+2*2+matrix

Not in any manner whatsoever to to be sexist, but I think Wolfram Alpha is a bit like some of my past girlfriiends. "She's" a bit "fickle" and you've got to ask the question in the right way...

- RF

 

[EnumaElish]

In the iphone version (not sure if there's a difference) "int sin x dx x=0 to 1" is recognized as the definite integral of sin x from 0 to 1, but "int f(x) dx x=0 to 1" is not recognized as integration.

 

[Mech_Engineer]

In the iphone version (not sure if there's a difference) "int sin x dx x=0 to 1" is recognized as the definite integral of sin x from 0 to 1, but "int f(x) dx x=0 to 1" is not recognized as integration.

That is not an iPhone only problem, that is incorrect input formatting. If you replace "f(x)" with an actual function (like "sin x" in your first example) then it works fine.

 

[Char. Limit]

That is not an iPhone only problem, that is incorrect input formatting. If you replace "f(x)" with an actual function (like "sin x" in your first example) then it works fine.

Also, if you replace f(x) with f'(x), it gives the correct answer: f(1)-f(0).

 

[Coin]

Wolfram Alpha... [is] a bit "fickle" and you've got to ask the question in the right way...

But that's interesting because it seems to defeat the entire point of Wolfram Alpha, doesn't it? I mean, the point of Wolfram Alpha is something like mathematica or a database engine except it allows you to phrase queries in natural language rather than having to learn some elaborate syntax. But if you have to learn to phrase the question in a particular idiosyncratic way, then we're back to just having a computational engine which can answer queries if you learn the syntax. We already had engines like that; for example, *mathematica*! The difference of course being that the syntax for mathematica is documented and it's possible to learn, whereas the syntax for Alpha is some mysterious hidden thing you can only just sort of guess at with trial and error, sometimes it will pick up what you're trying to say, sometimes it won't, with no clear pattern as to when or why...

Case in point...

That is not an iPhone only problem, that is incorrect input formatting. If you replace "f(x)" with an actual function (like "sin x" in your first example) then it works fine.

I think it is valid formatting, Elish is trying to describe an integral of a function f where f is not presently known. The problem is whether it can interpret what you are trying to say. If you tell it "int f(x) dx" it correctly understands you are trying to describe an integral, it then presents the integral back to you and says "I don't know how to solve this", a totally sensible behavior. If you add the "from 0 to 1" back in though it just doesn't know how to interpret what you're saying at all. It would be unreasonable to expect something like wolfram alpha to be able to figure out any crazy thing you type in, but if "int f(x) dx" is valid syntax and "int sin(x) dx from 0 to 1" is valid syntax then why not "int f(x) dx from 0 to 1"?

 

[Mech_Engineer]

I think it is valid formatting, Elish is trying to describe an integral of a function f where f is not presently known. The problem is whether it can interpret what you are trying to say. If you tell it "int f(x) dx" it correctly understands you are trying to describe an integral, it then presents the integral back to you and says "I don't know how to solve this", a totally sensible behavior. If you add the "from 0 to 1" back in though it just doesn't know how to interpret what you're saying at all. It would be unreasonable to expect something like wolfram alpha to be able to figure out any crazy thing you type in, but if "int f(x) dx" is valid syntax and "int sin(x) dx from 0 to 1" is valid syntax then why not "int f(x) dx from 0 to 1"?

The formatting itself I suppose is valid, but do we really need to ding WA for not properly displaying an input which has no solution?

 

[Borek]

We have been there, even in this thread:

https://www.physicsforums.com/showthread.php?p=2443314#post2443314

 

[Raphie]

But if you have to learn to phrase the question in a particular idiosyncratic way, then we're back to just having a computational engine which can answer queries if you learn the syntax. We already had engines like that; for example, *mathematica*!

I agree with all of your points, in general, Coin, including the above, but one nice thing about Wolfram Alpha is that a) it gives one "contextual clues" along the way about how to "ask it the right way," and b) personally speaking, it is a Godsend for the mathematically curious without proper formal training.

If I were a professional in one of the mathematically oriented sciences, I don't think I would be overly impressed with Wolfram Alpha, but as a non-professional, I view it as a vast improvement over, say, the Google Calculator.

A small case in point: Via trial and error I know that (Golden Ratio)^30 and (phi)^30 bring up very different results. That tells me a lot about "phi" as a "variable" vs. "phi" as a "number." And that's something I can build on.

Another (general) case in point: By presenting mathematical information in many ways of a piece, it gives one several "paths" by which to "connect" to the information presented. e.g. Even if one had never heard of Taylor Series, one could intuitively learn about them in principle just by inputting e^(-phi^2).Raphie