The limits of human mathematical reasoning

January 12th, 2007

Charlie Noback pointed me to an interesting article in the WSJ on the limits of human reasoning in Mathematics, When Number Proofs Are Done by Computer, Mightn’t Some Err?.

“If I have $15 and you have $20, and we keep tossing a coin so that you win $1 from me if it turns up heads and I win $1 from you if it lands tails, you have a reasonable chance of eventually bankrupting me and walking away with the whole $35. But your prospects are not so overwhelmingly great that I refuse to play. In fact, your probability of winning it all equals your $20 divided by the sum of our stakes ($35), or just 57%. The “gambler’s ruin” problem has entranced mathematicians since the 1800s, and at this week’s annual meetings of the American Mathematical Society and the Mathematical Association of America in New Orleans it played another role: “as a case study in the limits of proof and of machine proofs,” says mathematician Doron Zeilberger of Rutgers University. Mathematicians, to their dismay, are the first scientists to face the shattering and humbling prospect that the complexities of nature may be beyond the reach of the human mind.”

Zeilberger’s article Symbol-Crunching With the Gambler’s Ruin Problem is online along with a Maple package that automatically computes, symbolically (and numerically), statistical quantities related to the Gambler’s Ruin problem.

It’s well know that machine generated proofs are hard to understand and to check. The WSJ article has an interesting quote from an AMS article Whither Mathematics? by Brian Davies

If the goal of mathematics is understanding, then one cannot deny that computer-assisted proofs do not supply it in full measure.

An intelligent geospatial reasoning system

January 10th, 2007

The SWIG IRC Scratchpad points out a good example of a working distributed, intelligent geospatial reasoning system. It will be hard to improve on this, especially given the low cost to use it.

US federal science funding down 4% :-(

January 9th, 2007

Among the causalities of the current US political turmoil is federal funding for science research. I’ll be the first to agree that compared to the other problems it is not the most important. Yet, there is no good reason for it and it has its ramifications. The CRA policy blog points out an article in the NY Times on the impact of the continuing resolution on science research, Congressional Budget Delay Stymies Scientific Research.

“The failure of Congress to pass new budgets for the current fiscal year has produced a crisis in science financing that threatens to close major facilities, delay new projects and leave thousands of government scientists out of work, federal and private officials say.”

The NSF, a major source of Computer Science research funding, is one of the affected agencies.

The National Science Foundation, which supports basic research at universities, had expected a $400 million increase over the $5.7 billion budget it received in 2006. Now, the freeze is prompting program cuts, delays and slowdowns. “It’s rather devastating,” said Jeff Nesbit, the foundation’s head of legislative and public affairs. “While $400 million in the grand scheme of things might seem like decimal dust, it’s hugely important for universities that rely on N.S.F. funding.”

It looks like some “big science” projects will suffer the most including “a $50 million plan to build a supercomputer that universities would use to push back frontiers in science and engineering”. But all of NSF will be affected and it’s easy to imagine that all of the NSF programs will tighten up a bit.

Congress passed just two out of eleven major spending bills last year — for military and domestic security. The rest were frozen at 2006 levels, an effective 4% reduction. The current Democratic-led congress has announced plans to extend the continuing resolution through the end of the 2007 fiscal year.

Pew on Social Network Usage

January 7th, 2007

Pew Internet just released a survey on social network usage among American teens. While confirming the known, (i) MySpace is the most visited site (ii) girls are more active than boys, the report goes on to say that “74% of respondents post comments on friend’s blog”. I would have loved to see numbers on “x% of respondents have created or plan to create blog posts”.

MySpace has been a major contributor to the growth of blogs recently, and now forms a major chunk of a blog search result. The last we checked MySpace blogs were contributing 15% to 20% of all pings to, with numbers rising by the day.

Top Viewed Publications at Ebiquity in 2006

January 4th, 2007

Listed below are some of our top viewed papers in 2006:

  1. XPod a human activity and emotion aware mobile music player
  2. Swoogle: A Search and Metadata Engine for the Semantic Web
  3. SOUPA: Standard Ontology for Ubiquitous and Pervasive Applications
  4. SVMs for the Blogosphere: Blog Identification and Splog Detection
  5. Finding and Ranking Knowledge on the Semantic Web
  6. Detecting Spam Blogs: A Machine Learning Approach
  7. Information Retrieval and the Semantic Web
  8. An Intelligent Broker Architecture for Pervasive Context-Aware Systems
  9. Social Networking on the Semantic Web
  10. Secure Routing and Intrusion Detection in Ad Hoc Networks

This maps well into the broad areas we work on. If you are interested, our group website also allows viewing papers by cumulative citations, and downloads.

Wii-Mote mashups

January 3rd, 2007

Wii-mote Harry Chen is building a list of Wii-mote Works — links to projects exploring how the Wii Remote game be used in non-game applications. The Bluetooth-based Wii-Mote will be available separately for about $40 and the nunchuck for an additional $20.

How to get hired by Google

January 3rd, 2007

The secret may be to to be a messy extrovert who had a business catering to dog walkers in high school. Or at least to say you are. The New York Times has an interesting article on how Google evaluates interviewees.

“Have you ever made a profit from a catering business or dog walking? Do you prefer to work alone or in groups? Have you ever set a world record in anything? Examples from the Google application survey. Using such questionnaires is not the norm in Silicon Valley, but Google has had trouble in quickly filling positions when it relies on repeated interviews. The right answers could help get you a job at Google.”

It sounds like Google is doing some datamining on its current employees to help select new ones

“Last summer, Google asked every employee who had been working at the company for at least five months to fill out a 300-question survey. Some questions were factual: What programming languages are you familiar with? What Internet mailing lists do you subscribe to? Some looked for behavior: Is your work space messy or neat? And some looked at personality: Are you an extrovert or an introvert? And some fell into no traditional category in the human resources world: What magazines do you subscribe to? What pets do you have?”

This might be a good approach. It’s probably better than asking “How Would You Move Mount Fuji?”, as described by a book by William Poundstone that I quite enjoyed.

Of course, if Google’s survey questions get out, then we will see many web sites sprout up that offer to teach you how to ace the test.

Looking back at the ebiquity research group in 2006

January 1st, 2007

Maybe it’s a bit of a cliché, but this is the traditional time to look back on the past year and reflect on how things are going. It has been an active productive year. Here’s a rundown Ebiquity in 2006 by the numbers.