Logic Nest

The Pirahã People and Numeracy

Ian Luke Kane — Wed, 16 Jul 2008 23:42:02 +0000

I came across this article today on Science Daily that talks about the Pirahã, which, according to Wikipedia, are “an indigenous hunter-gatherer tribe of Amazon natives, who mainly live on the banks of the Maici River in Brazil”. The Science Daily article introduced me to the fact that this tribe has no concept of precise numbers. While they do use indefinite numerical terms such as “some” and “more”, this group does not seem to have any representation for concepts such as “one” or “two”. As MIT professor Edward Gibson states, “here is a group that does not count. They could learn, but it’s not useful in their culture, so they’ve never picked it up.” Absolutely fascinating. You should certainly check out the two links above, especially the portion in the Science Daily article that describes some of the experiments carried out by Gibson and his MIT team that have further illuminated this portion of the Pirahã culture.

This article intrigued me so much that I dug a bit deeper, and found that Daniel L. Everett, the Chair of Languages, Literatures, and Cultures from Illinois State University, has spent a good portion of his career working with the Pirahã people. He has collaborated in the past with Gibson on various projects in the past. Some info can be found here. There’s a great New Yorker story that was published in April 2007 on Dan here that’s certainly worth a look. Here’s a teaser from this article:

The Pirahã, Everett wrote, have no numbers, no fixed color terms, no perfect tense, no deep memory, no tradition of art or drawing, and no words for “all,” “each,” “every,” “most,” or “few”—terms of quantification believed by some linguists to be among the common building blocks of human cognition.

It’s a very long article, but it paints a beautiful picture of linguistics, cognition, faith, and personal relationships. It’s packed full of great questions. There’s a LOT that’s in these writings I’ve linked to that I haven’t even brought up (including the idea of recursion in linguistics), so I urge you all to read more! There are also some great links for further reading in the Wikipedia article linked to above, including several scholarly papers.

Why Tape Tears

Ian Luke Kane — Wed, 16 Jul 2008 16:33:32 +0000

A friend let me know quite a while ago about this story presented on NPR’s site entitled “Mathematicians Explain Tape’s Tendency to Tear”. It’s an explanation of a recent Pedro Reis article in the journal Nature Materials describing the annoying tendancy of tape to narrow while unpeeling it from the roll. As the article explains, Reis’ work “could help engineers test thin films for strength and reliability” The audo of the story is also available on the NPR site.

I love this story because I can imagine Pedro first thinking about this problem while unpeeling a roll of tape. I don’t know if the inspiration actually came this way, but its a great mental image that conveys the idea that some of the most interesting problems to solve are right under our noses.

Here’s the abstract of the paper from Dr. Reis’s website:

Thin adhesive ﬁlms have become increasingly important in applications involving packaging, coating or for advertising. Once a ﬁlm is adhered to a substrate, ﬂaps can be detached by tearing and peeling, but they narrow and collapse in pointy shapes. Similar geometries are observed when peeling ultrathin ﬁlms grown or deposited on a solid substrate, or skinning the natural protective cover of a ripe fruit. In this work, we have shown that the detached ﬂaps have perfect triangular shapes with a well-deﬁned vertex angle; this is a signature of the conversion of bending energy into surface energy of fracture and adhesion. In particular, this triangular shape of the tear encodes the mechanical parameters related to these three forms of energy and could form the basis of a quantitative assay for the mechanical characterization of thin adhesive ﬁlms, nanoﬁlms deposited on substrates or fruit skin.

LaTeX Render

Ian Luke Kane — Fri, 11 Jul 2008 01:04:58 +0000

I spent some time today reinstalling the LaTex Render plugin for Wordpress. I’ll now be able to put some wonderful looking graphics into the blog. I’d like to thank Steve for spending time both writing and debugging the code. So for the time being here is your mathematical moment of zen, for which I also need to thank Steve:

Feel free to also check out the LaTeX in Wordpress post that I wrote a while ago. It should still be mostly up to date. It’s also possible to leave comments using LaTeX syntax as long as they are wrapped in [ tex ] [ / tex ] tags.

Stuff White People Like: Statistics

Ian Luke Kane — Fri, 27 Jun 2008 00:20:24 +0000

If you haven’t yet been introduced to the Stuff White People Like blog, you’re in for a treat. There is a new article on statistics that you can read here. Basically, the blog is comprised of witty, yet strangely accurate descriptions of…well…things that white people like. It’s truly hilarious. For instance, take the first line of this article, “White people hate math. If you want to befriend white people, mention “that weird Asian calculus teacher who drew perfect circles” and how much you hated his class…” Awesome.

LOLCats + Math = Hilariously Cute

Ian Luke Kane — Wed, 18 Jun 2008 01:20:45 +0000

I mean, how can you resist this? Hilarious, cute, and math oriented. I hope this brings a smile to your face today!

more cat pictures

Another caption given for this picture in the comments is “Delta Kitteh knows the difference”. Hehehe.

Purity of Mathematics: XKCD

Ian Luke Kane — Fri, 13 Jun 2008 16:37:39 +0000

I’m sorry, but this XKCD comic was so wonderful that I simply had to post it. If you don’t read this comic religiously, shame on you. I had to shrink the photo down a bit to make it fit, so feel free to click on the comic to head over to the XKCD page.

The Abacus and Mental Math

Ian Luke Kane — Wed, 30 Apr 2008 23:28:49 +0000

I must confess that I’ve never learned to use an abacus (or a slide rule, for that matter). I came across the following video, and thought that it would act as another great view into the wonderful world of mental math. It’s quite tremendous what the human brain is capable of. Check it out:

Midnight Due Dates

Ian Luke Kane — Sun, 23 Mar 2008 17:04:33 +0000

I’ve always hated when professors have midnight due dates for assignments. This is because there doesn’t seem to be a grand understanding of what a midnight due date actually means. For instance, consider that I’m taking two courses, and that each of them has an assignment due at midnight on April 1. For Professor X, midnight on April 1 actually corresponds to 00:00:01 on April 1, i.e. the very first moment after midnight on April 1. For Professor Z, midnight on April 1 corresponds to 23:59:59 on April 1, i.e. the very last moment before midnight on April 2. This has bothered me so much that I’ve done a small amount of research, and have come to realize that Professor X is actually correct.

From the official Greenwich Mean Time website, “Every day starts precisely at midnight and A.M. starts immediately after that point in time e.g. 00:00:01 A.M.” This may seem to be obvious, but there’s a remarkable amount of confusion over the issue. Professors who understand this call for due dates of 11:59:59 PM on a particular day. The airline industry always rounds similarly so as to not confuse customers. So if you ever have an assignment due at midnight, it may be in your best interest to check with your professor about what she or he really means!

Here are a few links other than the official one above that will give you more information about noon and midnight:

Look Around You - Maths (Hilarious!)

Ian Luke Kane — Thu, 10 Jan 2008 17:12:26 +0000

I hadn’t heard of the “Look Around You” BBC television series before yesterday, but I was nearly on the floor laughing by the end of the following video segment about “Maths”. Read up on the series at their Wikipedia entry. I’m sure the other episodes are equally as hilarious. In my opinion, there are few things better than British humor mixed with math. Enjoy the video!

Point Nine Repeating Equals One

Ian Luke Kane — Thu, 10 Jan 2008 04:07:14 +0000

Let’s be honest…there are certain subjects that a math-ish kind of blog must mention at some point. One of these obligatory topics happens to be the “0.9999999… = 1″ proof. It’s one of those facts that delights the mathematically inclined. It’s sort of like the joke that Grandpa always tells when the family gets together: you know it’s coming, and you know how much pleasure he gets out of relaying the joke, but for goodness sake, this is the 99th time you’ve heard the punchline. At any rate, there is a set of about 15 math facts that people love to talk about simply because they’re all totaling mind-blowing or sound totally nonsensical. I tend to think that the “0.9999999… = 1″ proof belongs in the latter category.

The previous digression leads me to mention the Things of Interest blog, and their absolutely fantastic post on various forms of the “0.9999999… = 1″ proof. You can find that post here. In case one proof doesn’t do it for you, this site offers several, each of which occurs at a various level of mathematical rigor. There will definitely be a proof for you here that you’ll understand.

Mathemagic (Arthur Benjamin at TED)

Ian Luke Kane — Tue, 08 Jan 2008 03:11:55 +0000

This is perhaps one of the most amazing videos I’ve every watched on the Internet. I was literally left speechless. I can accomplish certain small feats of mental math, but this is absolutely unbelievable. Arthur Benjamin shows us some inspiring abilities of the human mind. I’m sure he has spent a fair amount of time learning his methods, and that to him his abilities are perfectly normal (in some sense!), but it’s great to watch someone with this talent. I highly recommend watching the video in its entirety.

Do Humans Differ from Machines?

Ian Luke Kane — Wed, 15 Aug 2007 16:30:13 +0000

Slashdot is linking today to an article that considers the implications of the 10 year anniversary of the defeat of chess grandmaster Gary Kasparov by IBM’s Deep Blue computer. The article (here), written by philosopher Daniel Dennett, considers the possible differences, or lack of differences, between humans and machines. I’ve linked to other pieces considered by Daniel Dennett on this blog, and I consider him to be an articulate and fair judge over matters of this type. It is highly worth your time to read this piece and to think it over a bit.

Predicting War

Ian Luke Kane — Fri, 15 Jun 2007 01:20:20 +0000

A few days ago on Slashdot there was an article about a statistical model that claims to be able to accurately predict the result of a war nearly 4 out of 5 times. Here’s a snippet from the University of Georgia’s press release on Dr. Patricia L. Sullivan’s study: “‘If you know some key variables – like the major objective, the nature of the target, whether there’s going to be another strong state that will intervene on the side of the target and whether you’ll have an ally – you can get a sense of your probability of victory,’ said Sullivan, whose study appears in the June issue of the Journal of Conflict Resolution.” Very interesting. Statistics is a beautiful, and very misunderstood, field. When I hear about claims like this my ears definitely perk up. In general, studies like this propose that particular variables (such as a poor military strategy) are predictive of other events (such as a military victory). There’s obviously a cause/effect chain reflected in this type of idea. And believe it or not, there is a LOT of study in the area of cause/effect relationships. People like Peter Spirtes at Carnegie Mellon University spend a lot of time studying these causal relationships.

So while that claim that a statistical model can predict the outcome of wars should be taken with a grain of salt, everyone should consider the fantastic amount of research (and quality science) that is going into these types of causal models.

Primer on Paradoxes

Ian Luke Kane — Thu, 14 Jun 2007 03:30:40 +0000

I came across this wonderful introduction to several famous paradoxes quite a while ago, but haven’t taken the time to inform you all about it. Daniel Haggard presents a non-technical explanation of five age-old paradoxes that have both delighted and confused humanity. It’s a very accessible read and I recommend it for everyone interested in the strange logical conundrums that surround us. I particularly enjoy his section on Newcomb’s Paradox, which boggles my brain every time I think about it. Honestly, I’m glad that paradoxes exist. I mean, nothing I say is true, right?

The Math of Sudoku

Ian Luke Kane — Mon, 11 Jun 2007 16:11:39 +0000

There’s a wonderful article over at ars technica about the mathematics of sudoku. Agnes M. Herzberg and M. Ram Murty recently wrote an article in which they explain some of the mathematical underpinnings of the popular puzzles. They explore several fundamental questions such as “does a given sudoku have a unique solution?” The link above provides a great introduction to the formal paper, and also includes a link to the PDF version of the paper. Check it out. One of the great tidbits from the article includes the stat that there are over 5.5 BILLION unique sudoku puzzles. Yikes. That’s keep even the most committed addicts busy for a while!