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23
Rejecta Mathematica goes live
Filed Under Math News, Math Websites | 3 Comments
We first mentioned Rejecta Mathematica almost two years ago. While it did take them a while, the site has finally gone live and they recently announced their inaugural issue, which contains papers that have been rejected by peer reviewed journals on mathematical sciences.
The most interesting feature of this initiative is the open letter that prefixes each paper, in which the author illustrates what they believe is the reason behind their work’s rejection and asserts their paper’s case. Scientific papers, like notorious novels, do sometime get undeservedly rejected before their true value is acknowledged. The hard part is distinguishing the hidden gems.
Contrary to what one may have expected though, this edition clearly debunks the notion that Rejecta Mathematica would be a breeding ground for crackpots. The six papers included in this first edition all appear to be interesting and well researched.
Is it the revenge of the rejected? Perhaps, but this unusual publication will still help to enrich our beloved discipline in its own way.
May
18
An almost convincing start for Wolfram Alpha
Filed Under Math News, Math Websites, Software | 5 Comments
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.
Mar
14
Happy National Pi Day!
Filed Under Math News | 19 Comments
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.