What is Mathematics?

Posted on | November 2, 2012 | No Comments

What is Mathematics?

For more than two thousand years, mathematics has been a part of the human search for understanding. Mathematical discoveries have come both from the attempt to describe the natural world and from the desire to arrive at a form of inescapable truth from careful reasoning. These remain fruitful and important motivations for mathematical thinking, but in the last century mathematics has been successfully applied to many other aspects of the human world: voting trends in politics, the dating of ancient artifacts, the analysis of automobile traffic patterns, and long-term strategies for the sustainable harvest of deciduous forests, to mention a few. Today, mathematics as a mode of thought and expression is more valuable than ever before.

The American Heritage College Dictionary (Costello, Ed, 1993) defines language as “a nonverbal method of communicating ideas, as by a system of signs, symbols, gestures, or rules” (p.763).  By this definition, mathematics is a language. “Mathematical symbols are the means by which we write mathematics and communicate mathematical meaning” (Rubenstein & Thompson, Learning mathematical symbolism: Challenges and instructional strategies, 2001, p.65).  In order for students to begin the process of understanding mathematical concepts, they need a solid comprehension of language of mathematics.   “Learning Mathematics Vocabulary: Potential Pitfalls and Instructional Strategies” by Ruberstein & Thompson (2000) suggest that the mathematical concept and the method by which it is presented to students in terms of mathematical jargon is most important to increase learning.

Hayes (1996) furthers the analogy with the idea that math is a written language first, then a spoken language.  “Speaking of Mathematics” makes an excellent analogy between the difficulties that humans have using the language and the difficulties that arise when a computer tries to decipher mathematical symbols.  For example, for the simple task of creating a math test in a Word document, only a select few math symbols are available.  A special program has to be used in order to make available a larger selection of math symbols that the computer will recognize.

Furthermore, each symbol has a specific meaning and an appropriate time to use each of them.  Symbols are used to “name a concept… state a relationship… indicate an operation or a function with one input… indicate an operation or function with two or more inputs… abbreviate words, units, theorems, and so on… and finally, to indicate grouping…” (Rubenstein, 2001, p.66). The following symbols denote just a portion of what makes up the language of mathematics:

• ·        ·        Contentive symbols: Numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9…

Pro-numerals: a, b,…, x, y, z, a, b, …, q, AB, …

• ·        ·        Operative symbols:  +, -, ¸, ´, Ö, log, ( ), d, ¦, S, Ç, È, sin, …
• ·        ·        Relation symbols:  =, >, <, Ì, É, ¹, …, ®, ^, êê, $, …
• ·        ·        Auxiliary symbols:  : (so that), ” (for all)       (Gupta, 1980, p. 30, 31)

Definition:

• A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

Ø  That science, or class of sciences, which treats of the exact

     relations existing between quantities or magnitudes, and of

     the methods by which, in accordance with these relations,

     quantities sought are deducible from other quantities known

     or supposed; the science of spatial and quantitative

     relations.

     [1913 Webster]

Ø  A science (or group of related sciences) dealing with the

       logic of quantity and shape and arrangement [syn: math, maths]

Feast Your Ears On Fresh Jams From Musicians You Love At Hipset Via YC’s Tracks.by

Posted on | August 18, 2012 | No Comments

Hipset is a music discovery site launching today from Y Combinator’s Tracks.by that makes sure you never miss the hot new songs, videos, and other content from the artists you Like on Facebook — updates which the social network might not show in your feed.

If launched on its own, Hipset would just be a fun site for listeners. But while disarmingly simple, it’s the culmination of Tracks.by’s year-long master plan to shake up the music marketing industry. Here’s how Hipset is going to rock you.

The site launched this morning so you can go check it out Hipset now. Once you auth in with Facebook, you’ll find a single Pinterest-style grid view of all the recent posts by all the musicians you Like. That’s something you can’t get on Facebook, which deems most updates from musicians less critical than those by your friends so they’re filtered out of the feed.

In case you’re looking for a laid-back reel of concert clips and studio performances you can sort Hipset by content type, plus you can view dedicated pages for any artist. There’s also a popular feed where you can see algorithmic and human-curated picks for the best new music. With Spotify putting history’s music catalogue at your fingertips, there’s a big opportunity for Hipset to tell us what we should be listening to.

Yeah, it’s cool, but here’s how it fits into Tracks.by’s grand scheme. For the last year, its ex-Ustream founders Mazy Kazerooni and Matt Schlicht have been signing digital marketing deals to build apps and run the Facebook Pages of top artists like Lil Wayne and Drake. It also scored a seed round from investors like Dave Morin, Greylock’s Josh Elman, Menlo Ventures, and Wayne’s manager Cortez Bryant. But all the while they wanted to launch a destination site.

That’s fortunate, because the Facebook Timeline redesign cutting traffic to tab applications by up to 90%, forcing fellow developers like Bandpage to diversify beyond Facebook. If not for repping big celebrities, getting the standalone site Hipset off the ground might be tough. But Matt and Mazy are friends with all these artists and management companies, and can call in favors. So Tracks.by artists including Wayne (aka Weezy F Baby who has 40 million Facebook Likes) are going to promote their Hipset pages.

Why? Because Hipset is deeply tied into Facebook’s Open Graph. It might be a bit aggressive, but it shares to your friends every time you open a post or view a video. That means it makes artists go viral better than if people watched those same videos on YouTube.com, so thats where they want their fans going. Tracks.by will also help artists send email alerts to their fans when the have big announcements like a new single.

Hipset lets Tracks.by own the marketing channel, sucking up huge data sets and filling in where record labels are failing. With the added email marketing features and the power to massage the Popular feed, Tracks.by has the leverage attract more top-tier artists to its service arm.

And then come the ads. Tracks.by controls the feed and knows what artists you Like, so it could easily inject sponsored blocks into the grid view. If a label wants to promote the new Jay-Z single, it could inject a sponsored block featuring his music video into the feed of anyone who Likes Lil Wayne. And Hipset will let brands sponsor downloads of songs, so you could get the Drake single before its released by Liking Pepsi or watching one of its commercials.

So essentially, Tracks.by uses its connections to promote Hipset that seduces clients to its marketing service that sells ads on Hipset. That’s some evil genius-level business.

In the end, it still comes down to product quality, and the design of Hipset is still v1. If it isn’t sticky and sharable, none of this will pan out. Hipset needs to be more than just a better way to browse Facebook music updates. It needs great discovery of new artists, deals to pull in exclusive content, and viral hooks like stats you can publish about what favorite bands you and your best friends have in common.

Whether you want to be the first person on you block to hear that killer new song, or you want a more intimate connection with the artist who made up, Hipset’s got the hook up.

Prevent Google Chrome from Hijacking RSS Feeds

Posted on | August 18, 2012 | No Comments

If you happen to click an RSS or Atom feed inside the latest version of Google Chrome, the browser won’t display the actual content of the XML file but will instead offer you to open the feed in either Google Reader or one of the Chrome apps. →

XML Feeds are ‘greek’ to most users but for the rest of us, Chrome offers no built-in option to turn off this default behavior. Also, if you using an RSS feed reader that is not available as a Chrome app, like FeedDemon or Microsoft Outlook, there isn’t an easy way to set that external program as the default handler for RSS feeds in Chrome.

Google Chrome offers RSS Reading apps instead of showing the actual XML feed

Some people aren’t very happy with this new “feature” of Google Chrome and the list includes Dave Winer, who is widely known as the “inventor” of RSS feeds.

Here are more online reactions seen on Twitter:

• @extraface: OMG Chrome don’t intercept my click, just show me the RSS address that I asked for. You’re not my feed reader, deal with it (cue sunglasses)
• @SebCorbin : OK Chrome, now it’s not funny: if I can’t view the source of a RSS feed, I’m gonna give up and get this old FF
• @elibtronic: Dear Chrome. Stop being a d-bag and just display my RSS feed links as XML. Don’t shell to a gd feed reader. Thank you.
• @sull: Google Chrome used to leave RSS alone but the latest update brings us the traditional feed hijacking feature. #Pathetic #Obnoxious
• @ghurlman: I can’t view a raw RSS feed in Chrome anymore? I *have* to use some chrome store app feed reader? #fail

How do you override the default behavior? Here are some options:

1. If you would like to force Google Chrome to render the XML feed in the browser itself, install the Feed Intent add-on and set it as the default handler for RSS Feeds.
2. If you would like to subscribe to RSS feeds in another online RSS reader that is not available as a Chrome app, get the RSS Subscription add-on and configure it to use your other reader.
3. If you would like to subscribe to a news feed in a desktop RSS reader, just copy-paste any RSS feed URL in Chrome’s address bar and replace http:// with feed:// – Chrome should now open the feed in the external associated program.

Bonus Tip for FeedBurner Users

This story, Prevent Google Chrome from Hijacking RSS Feeds, was originally published at Digital Inspiration on 18/08/2012 under Google Chrome, Rss, Internet.