Cactus: Calculator And Computer Technology User Service.

Hyde, Hartley

Stephen Wolfram was born in London in 1959. He was educated at Eton and Oxford He gained a PhD in theoretical physics from Caltech in 1979. He became Director of the Center for Complex Systems Research and Professor of Physics, Mathematics and Computer Science at the University of Illinois. He founded Wolfram Research in 1987. He studied complex systems using computational models called cellular automata. He released Mathematica in 1988. WolframAlpha was released in May 2009 and is one more step along the way toward the computational management of large and complex data structures.

At each step of discovery, it has been much easier to say what WolframAlpha is not rather than what it is. When it was promoted as a search engine, people wondered if it was designed to rival Google--it is not. Although it is built around a Mathematica engine, it is not just a portable form of Mathematica. Although the user is presented with thousands of wonderful examples of what the software can discover, I could find neither a clear statement of what WolframAlpha is, nor what it is designed to do. Part of the problem is that the project is still getting started--a work in progress. To some extent users join a voyage of exploration as Stephen Wolfram continues his research with computational knowledge engines.

Do you remember the enormous improvement in performance when your home computer allowed parallel processing of just two CPUs? The cloud of supercomputers that processes your WolframAlpha requests has more than 10 000 CPUs and is growing. The system consists of a huge amount of organised data, a computer program that is able to interpret your request and search the data bank for relevant information, and, finally, the thousands of individual application programs that are simultaneously communicating with the cloud through various application programming interfaces (API). The most easily available API is provided free at www.wolframalpha.com.

Many readers will have downloaded the WolframAlpha app from the iTunes store. This uses a different API. When the app cost US$50, some reviewers talked about having a graphing calculator on their iPhone. It is worth switching off the WiFi and telephone to see how much the app can do under its own steam. You will see why it now sells for US$2.

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By using two keyboards, the app allows the user to type a wide range of special characters into the command line, So long as the request consists of simple arithmetic, the progressive answer is provided in a pop-up box above the command line. As soon as the user touches the <Go> button, the pop-up disappears and the app attempts to communicate with the cloud. Anything more complex than simple arithmetic requires connection to the cloud--little wonder that the price of the app was reduced.

The Internet version of the API could be made capable of more complex tasks using the JavaScript math object, but it does not. It is assumed that anyone using an Internet browser will be doing so online.

Some of the more spectacular responses are achieved with minimal requests, such as a single word, number, city or date. The responses are divided into pods of information. More specific requests will limit the response to those pods that better fit the request. When I was sitting in a meeting that was organising an outdoor event for a November evening, we needed to know when the event should finish. The request:

sunset Adelaide 11 Nov 2010

gave a very specific answer that included a picture of a clock showing 7.56 pm.

Much of the power of the system can be attributed to the clever parsing of requests and awareness of synonyms and alternative spellings. This is one reason why the system can provide so much detail about individual words. Even if there is an American bias, the system is aware that other spellings exist.

If one types in "colour", it responds with information about "color". If one types in "#CF007C", the system assumes that this is a 24 bit RGB colour code. The response includes a colour swatch, close Pantone equivalents and close equivalents from the limited Internet set. Students love to play with this.

Even more impressive responses can be obtained by entering two numbers, towns or even companies. The system will attempt to provide as many comparison pods as possible. If you type "Sydney Melbourne", the system will compare what data it has about the cities, draw a map showing their location and the distance between them. The task of maintaining such a large data resource is huge and this company is aiming to provide growth--expect more pods as the years pass.

WolframAlpha does provide most of the features of a graphing calculator and much more. If you ask it to graph a function, you are given a "close up" and a more distant version.

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You can test the system with difficult functions like y(x) = 5 sin (1/x) but the graph will be limited by the resolution of the screen rather than the WolframAlpha system.

Students can ask WolframAlpha to solve a quadratic equation:

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After solving y = x^2 - 4x + 3 they can expand the results pod by choosing "Show Steps" and the system will respond with a detailed completion of the square.

However, if they ask the system to solve a quadratic expressed in factor form, the explanatory steps are not so clear.

Possible intermediate steps:

(x+2)(x+3) = 0

Split into 2 equations:

x + 2 = 0 or x + 3 = 0

Subtract 2 from both sides:

x = -2 or x + 3 = 0

Subtract 3 from both sides:

x = -2 or x = -3

A linear regression request takes the form: linear fit (1.3, 2.2),(2.1,5.8),(3.7,10.2),(4.2,11.8)

While small amounts of data are manageable on an iPhone, I would prefer to use a mouse to paste larger data sets to the Web-based version. WolframAlpha also allows more complex regression examples such as:

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WolframAlpha responds in typical detail when asked to describe a 120[degrees] rotation; however, I was disappointed that users cannot apply transformations to simple user-defined shapes. Commands such as

plot triangle (2,3),(5,1), (3,7)

are not yet recognised.

WolframAlpha presents very nice translucent representations of 3D solids such as this dodecahedron, but I was disappointed that it cannot construct the Mathematica logo using an hyperbolised dodecahedron.

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Just suppose that a school advocates that students purchase an iPod or iPhone instead of a graphing calculator. There are graphing calculator emulation apps that are more reliable than the devices they emulate--and then there are so many other educational apps that can be added at a very small cost. WolframAlpha would be an obvious choice. It is a very powerful research tool that has applications far beyond mathematics and science--just spend a few hours exploring the website examples. The ability of WolframAlpha to give multiple meanings of words and suggest synonyms could replace a dictionary and thesaurus. WolframAlpha can also access enormous quantities of geographical, scientific and economic data and present selected data in an organised and informative style.

If students used iPods, they could also send emails to each other through the school WiFi--ideal for quiet group activities. They could use WolframAlpha to look up things they had not learned properly. They might even cheat!

At some stage, applications such as WolframAlpha are going to become so attractive that we will rethink our assessment strategies and our students will use their iPods in class and as homework tools more than they use them for music and games.

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Hartley Hyde cactus.pages@internode.on.net