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Wolfram Research finally launched Wolfram|Alpha, the much talked about “computational knowledge engine”. It’s unusual description is justified by the fact that we are not dealing with a search engine in the classic sense of the term, nor with the next Google.

At first glance we’re peering at a service that is able to provide objective information about a wide subset of human knowledge. But the idea behind Wolfram|Alpha is much more ambitious, as demonstrated by the first screencast to have been released (narrated by Stephen Wolfram).

Taking advantage of the popular and powerful mathematical software Wolfram Mathematica, this new engine is able to perform calculations on information requested by its users. Therefore there are three components at work: the ability to correctly interpret queries (in English) from the users, the ability to elaborate on the data source so as to reply with coherent results to somewhat complex questions, and finally the not-so-simple task of maintaining an up-to-date and accurate knowledge base for a very wide spectrum of human knowledge.

This is the theory behind - or at least the ultimate aim of - the service. And as such, unlike what has been reported elsewhere, Wolfram|Alpha should immediately be viewed as an addition to what Google already offers (not as a replacement for it).

As expected, the service is extremely good at mathematical calculations. In this case the only limit is the timeout imposed on each query to exclude those that require far too many resources to complete. An example of a calculation that is executed is “integrate e^-x^2”.

For the record, this service is currently under a fair bit of stress because of the initial curiosity of many worldwide, therefore the calculation of the integral above has shown an error message a couple of times (a tribute to HAL 9000):

All sorts of disciplines are represented by the examples on the site, with a particular focus on scientific and engineering ones. The results are elegantly presented and well organized, often illustrated and shown in table form, particularly when the user is asking for a comparison between different data sets. There are also fun tributes, including those to Monty Python and Douglas Adams. But how well does this system work when we step outside of the predefined examples provided by Stephen Wolfram’s team? The results range from exceptionally good to downright disappointing. Let’s see a few examples.

Let’s compare IBM, Google and Sun. As you can see, the results are definitely excellent. The comparison is almost exclusively numeric in nature, but the answer provided by WA jives with what I was hoping for. The same is true if you look for statistical information on a single large company like Telecom Italia.

Since this is a “computational engine” we can even try to perform a few calculations starting with the data that we found to be available in the comparison tables for the companies above. For example, “employees IBM/Google” will show us the ratio over the last few years between the number of IBM and Google employees (IBM currently hires almost 20 times as many people). We can calculate the revenue for each IBM employee by running “(market cap / employees IBM)”, but the engine fails to compare this parameter between companies: “(market cap / employees IBM) / (market cap / employees Google)”, despite the fact that the data for such a calculation is all there in the knowledge base (and as you can see there was already a revenue/employee row in the initial comparison table).

Moving on to something else, we can try to compare two cities like Toronto and Milan, and obtain very useful details. It’s also possible to calculate only certain attributes by running, for example, “population Toronto/Milan” or “distance Toronto Milan”. In the first case the data was updated to 2004, and is perhaps a little outdated now despite the fact that we are talking about demographic data. But the real problem arises when we try to compare the regions of Ontario and Lombardy. We’d expect to see nice geographical, demographical and economical comparisons between the two, yet instead we get nothing. Wolfram|Alpha will report information about little towns like Unionville (NC), but totally ignores a region like Lombardy or a Canadian province like Ontario (with a population of 13 million people). It would seem that this is a big hole in the knowledge of this service. Sure it’s fairly easy to fix, but it’s a symptomatic weakness nevertheless.

If we consider for a moment searches about famous people, we’ll find an excess of zealousness in trying to be concise and objective. In fact, when searching for Barack Obama, the results are limited to his place and date of birth, and stating that he is a head of state. We may be spoiled by Wikipedia, but a photo or a few more details at least were to be expected. For example, at a bare minimum, it could be indicated that we are reading the page of the 44th President of the United States of America. But Wolfram|Alpha reserves this type of treatment for all famous people, including Stephen Wolfram himself.

In the comparison between “Paul Erdos vs Euler” one would expect a nice parallel between these two great, prolific mathematicians (for example, you might expect comparisons on the number of publications, total number of pages, the most significant discoveries, and so on). Instead, the results are limited to a comparison of births and deaths. This is quite disappointing no matter how you look at it. On a side note however, it must be said that WA is quite good at interpreting misspelled names (e.g., Paul Erddsos).

The Natural Language Processing (NLP) capabilities of Wolfram|Alpha are good enough to use the service without encountering any major frustrations, but it doesn’t appear to be a particular revolution or advancement in the field of artificial intelligence either. It is also clear that we are not dealing with a Google-killer nor a Wikipedia-killer, but rather with an innovative new tool that can be used in addition to the existing ones. That said, elsewhere I mentioned that I personally think that this is a step forward for humanity. It may be a small step, but I stand behind that bold statement.

We are at the forefront of a service that will be useful for research and to anyone with a need for correct data as quickly as possible. The knowledge base will have to grow, some data will have to be updated, and the engine will need to permit more freedom in the kind of calculations that are allowed to be performed. There can be little doubt thought that we are witnesses to the birth of something ambitious that has the potential to accelerate the advancement of our civilization.

An Italian translation of this article is available on Stacktrace.it.

Many math lovers and geeks alike celebrate “Pi Day” on March 14. In fact, when using the American style for dates where the month precedes the day, today is 3/14. The most committed among us will even go so far as to keep an eye on their watch or set an alarm to go off at the Pi Minute, celebrated at 1:59 p.m., or even Pi Second at 1:59:26 p.m.

This tradition started in the late 80s and is now celebrated all over the world, particularly in North America, where parties and free pies are available on many campuses.

This year Pi Day is an ever bigger deal, because it’s no longer just a fun celebration of mathematics observed by a few incorrigible geeks. The US Congress approved the H.RES.224, sponsored by Rep. Bart Gordon and 15 cosponsors, titled “Supporting the designation of Pi Day, and for other purposes.”. Thanks to this, March 14, 2009 is now officially National Pi Day. More importantly the resolution includes the following statement:

Whereas Pi can be approximated as 3.14, and thus March 14, 2009, is an appropriate day for `National Pi Day’: Now, therefore, be it

Resolved, That the House of Representatives–
(1) supports the designation of a `Pi Day’ and its celebration around the world;
(2) recognizes the continuing importance of National Science Foundation’s math and science education programs; and
(3) encourages schools and educators to observe the day with appropriate activities that teach students about Pi and engage them about the study of mathematics.

Math-Blog applauds the sponsors of this resolution, which passed with 391 Yeas and 10 Nays. For once, both parties supported the initiative, and there is no doubt that the sponsors of this resolution will receive a great deal of thank you notes for acknowledging, albeit just symbolically, the importance of mathematics and science in our society. Sadly, 10 representatives felt the need to oppose this acknowledgment, and for those who are curious (without getting too political here) all 10 of them happen to be Republican.

There is now an official Pi Day website with cool merchandise, and a Facebook group you can join. To help you enjoy this day perhaps consider picking up a good book on the history of this fascinating transcendental number. While categorically rejecting any numerological implication regarding Pi Day, it’s a good occasion to celebrate mathematics and talk about it with those who otherwise usually wouldn’t be interested. And that could be the most important aspect to come out of the formal recognition of Pi Day.

Seven years ago Stephen Wolfram published A New Kind of Science. I remember the hype surrounding this book. Journalists jumped at the chance to praise a heavy tome that was too complex for most of them to fully understand, but that shipped with an ambitious title and the implicit guarantee that comes from a genius like Wolfram.

It was “buzz worthy” for sure, and all the attention quickly attracted the interest of numerous scientists from many disciplines. As soon as the mathematicians, and particularly computer scientists, managed to get through its 1000+ pages, the first negative reviews began to pour in. Though, in all fairness, a few scientists had a little too much fun with this book and managed to showcase their comedic abilities by writing some of the most hilarious reviews known to humankind.

In this controversial best-seller, Stephen Wolfram primarily dissects the subject of cellular automata and its relevance to other scientific disciplines, in a systematic manner. It’s a book that covers a lot of ground and is arguably a remarkable piece of writing. Yet, the scientific community greeted the book with a fair dose of criticism.

So what went wrong? The main problem with A New Kind of Science is that it set very high expectations due to its author, title, and the numerous reminders of how important this material is, throughout the book.

The main accusations ranged from the book being called a display of Wolfram’s ego, to having very little “new” content, all the way to the more severe claims of not crediting other people’s work. For example, the idea of the universe as a cellular automaton was first presented by Konrad Zuse, so Wolfram’s “new” idea of a discrete, computable universe was anything but groundbreaking. On top of that, the most remarkable technical achievement revealed in this book was arguably the proof that the rule 110 cellular automaton is Turing complete. While this was conjectured by Wolfram, it was actually proven by his assistant Matthew Cook, who was refrained from publishing his results elsewhere by Wolfram’s lawyers.

It’s important to understand that, while perhaps not accepted as the breakthrough that Wolfram had hoped for, this book - and the methods for studying computational systems illustrated within it - is far from gibberish. Wolfram’s ambitious project failed in the eyes of the community due to the extremely high expectations that were set for this book. When you claim to have something radically new, you must be able to back that claim up in a convincing enough manner or else you’re bound to end up with egg on your face.

To be fair to Wolfram (for the few who are not familiar with his work) NKS is a controversial project, but he was already famous for having created the excellent program Mathematica (whose 7th version was recently released), one of the world’s most complete and advanced mathematical software.

Now Wolfram is at it again. According to his recent announcement, he is about to unleash something called WolframAlpha to the world, which combines both his work with Mathematica and NKS. In Wolfram’s own words:

I had two crucial ingredients: Mathematica and NKS. With Mathematica, I had a symbolic language to represent anything—as well as the algorithmic power to do any kind of computation. And with NKS, I had a paradigm for understanding how all sorts of complexity could arise from simple rules.

The project has been kept on the down-low for the past few years, while some of the brightest mathematicians and engineers employed by Wolfram Research, Inc. worked on it. It’s currently in private beta, but will go live in May of this year. From an initial glance, it would seem to be just another search engine a la Google.com. But is it? Not quite. It’s labeled as a “computational knowledge engine”, whose aim is to compute answers from the human knowledge available on the web. Whereas on Google you can search for strings and the results will be a series of relevant links, WolframAlpha will supposedly be able to parse and “understand” a query that’s inputted in English, and compute an answer based on the extensive knowledge stored in its system (assuming that a univocal answer exists). Conceptually speaking, it’s leaps and bounds more complex to get right than Google, which simply looks for matching strings and orders the results based on the popularity of the given keywords (For more information about the mathematics behind Google, read this book).

According to Nova Spivack, who had a chance to try out WolframAlpha, the service is able to compute factual answers to questions such as “What is the location of Timbuktu?”, “How many protons are in a hydrogen atom?,” “What was the average rainfall in Boston last year?,” “What is the 307th digit of Pi?,” “where is the ISS?” or “When was GOOG worth more than $300?”. This project has the potential to change the world as we know it, just like Google did. Several years ago Altavista was fine for most people’s search needs - or so we thought. It took Google to show us how much better off we could be search-wise, how much we needed Google, and ultimately how inadequate Altavista was. Unlike the case of Google and Altavista though, WolframAlpha would not replace Google, since the two services cover complimentary needs. Having access to a service that’s able to compute answers out of the chaos of the factual information that’s available to man would be a major breakthrough for humanity and computer science. And if an API (Application Programming Interface) were to become available, other developers would be able to tap into that with their applications.

Bold claims, high expectations. You understand why, two months away from experiencing something so potentially revolutionary, there is a lot of hype surrounding this project - but also major skepticism. For many this is A New Kind of Science all over again, especially since natural language processing and “computing knowledge” are extremely ambitious challenges in a realm where many have failed before. Pulling this one off would be a major accomplishment (that would dwarf Wolfram’s past achievements, including Mathematica), and, at long last, it would be the hard earned, practical validation of some of the methods and philosophies expressed in NKS by Wolfram.

I fully expect people to find bugs and have many simple questions, for which we will see bizarre answers. We’ll read blog posts about the whole thing and perhaps have a good laugh. But what interests me the most is whether, as Google did in the past, this new engine will be able to be practical and useful on an everyday level. Bugs are fair play and expected, but what we’re looking for here is a spark of true innovation thanks to the mathematical modelling of human knowledge.

I suspect that this engine will either have us in awe like Mathematica did, or leave us with mixed feelings - if not downright disappointment, like A New Kind of Science did for many. I can’t help but hope for the former, as I wait for my chance to try it out.

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