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:

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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:

• NIST
• Wikipedia
• CoolQuiz

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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!

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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.

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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.

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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.

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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.

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