# Using Links to Dig Deeper in Wolfram|Alpha

December 12, 2011 —

The hyperlink has been one of the most powerful tools of the information age. Links make it easier to navigate the complex web of information online by combining the information itself with the method for retrieving it. Clicking a link means “tell me more about this thing,” which naturally lends itself to “surfing.”

At Wolfram|Alpha, we strive to integrate and leverage technologies to create the most powerful computational capabilities and user experiences possible. In Wolfram|Alpha, the output comes in the form of a “report.” If you want to know more about something in the output of an Wolfram|Alpha query, clicking it as a link will generate another such report. Though we’ve had links in Wolfram|Alpha for a while, we’ve recently taken them to the next (computable) level: Wolfram|Alpha now computes links dynamically based on the output generated by your query.

Clicking a link basically feeds the plaintext of that link back into Wolfram|Alpha, creating new output with new links. Thus the navigational ability of the world wide web and the computational ability of Wolfram|Alpha are now intertwined and can feed off each other. You can now surf Wolfram|Alpha like you can surf the Internet.

In particular, mathematical expressions are linked for the first time. For example, suppose we ask Wolfram|Alpha about the equation “r/1 = (1-r)/r”:

In the Solutions pod are two real numbers which may look familiar. By clicking the second one, we essentially feed it back into Wolfram|Alpha, which produces a new output. The last pod of the new output reveals why we thought those two numbers seemed familiar: they are related to the golden ratio!

Perhaps you are interested in the mathematical theory of knots. Entering “8_1 knot” into Wolfram|Alpha gives you all sorts of knot invariants, one of which is the Alexander polynomial:

Clicking the Alexander polynomial feeds it back into Wolfram|Alpha, giving graphs and more detailed information about this expression:

These are just a few examples of the new links found in Wolfram|Alpha.

Since these mathematical links are computed, we are able to do some processing to increase their accuracy and reliability. To ensure that the vast majority of the links work correctly, we’ve been a bit conservative with our initial launch. You can think of these links as “suggestions” for what to ask Wolfram|Alpha next.