Punya Mishra’s Web

Niels Bohr, the 1922 Nobel Laureate in Physics once said:

The opposite of a correct statement is an incorrect statement. The opposite of a profound truth is another profound truth.

I was reminded of this when I saw this TED video. Check it out…

(h/t Andrew Sullivan)

The math-po (and sci-po) stream keeps flowing. Math Mama Writes, who started the whole math-poetry movement has some more on her blog, and here is Erin Nash with some really beautiful biological poetry. And of course, here’s her husband Sean Nash having his students writing poetry too. Of course let’s not forget my daughter Shreya (who sort of started this whole thing) and her sci-po’s at her blog Uniquely Mine.

Below are some thoughts about math-poetry – but you can ignore all that and scroll right down to the poem: The infinity of primes!

Math art by durentu

Through all this I have been plugging away at my math poetry. I know the original challenge was to write something to motivate students to learn math (and I did write one along those lines). But more interesting to me has been this theme I have picked up, which is of writing proofs as poetry. I know many people have described mathematics in poetic terms but I am trying something slightly different here. I am trying to explain theorems (as in these couple of instances, see here, here, here and here) and speficially in the poem included below, I am actually trying to construct a mathematical proof in rhyming verse.

Read the rest of this entry »

The Rethink Scholarship is an scholarship for aspiring art directors and designers to Langara College’s Communication and Ideation Design program. This video is to publicize the program.

I stumbled across this little machine that shuts itself off once it has been switched on! How cool is that. I don’t have an clue whom to credit it to and would appreciate a heads up on that. I was reminded of the myth of Sisyphus which led to a great piece of hand-drawn animation on YouTube. So here they are… somewhat apt images for a dull, dreary day in mid-Michigan.

You can watch the Sisyphus youtube video here. And here is a link to another small animated gif about Sisyphus.

The other day, for one reason or another, I did a Google search for the word “recursion.” According to Wikipedia, recursion

… in mathematics and computer science, is a method of defining functions in which the function being defined is applied within its own definition; specifically it is defining an infinite statement using finite components.

This is a screen shot of what Google gave me as a result of my search: (Click on the image for a larger version).

Look carefully at what Google suggests. It says.

Did you mean: recursion

The exact same word that I had searched for… For a moment or two I thought I had found a glitch in Google’s suggestion mechanism… but it suddenly hit me, that this was exactly what recursion meant! If I clicked on that link I would be taking the first step into an endless cycle, an infinite loop, which would end only when I “got it.”

This has been an inside joke amongst programmers for a while. Wikipeda provides one example from a hypothetical dictionary that goes as follows:

Recursion

If you still don’t get it, see: “Recursion”.

So in some sense Google provides a “working definition” of the word – that explains it better than just reading a definition in a dictionary. How cool is that. I think it is little games like this one that make Google so much fun to use.

(I must add that this is not a new discovery. The Wikipedia page about recursion does mention this Google trick – but it was new to me!)

Ambigram.com is a website about ambigrams and the people who make them. Lots of cool stuff for enthusiasts and novices alike. They often conduct competitions and other fun challenges for readers. One recent one was related to palindromes. In brief, they challenged people to create palindromic ambigrams. This is something I had tried a few time a long time ago – but their challenge pushed me to go back and come up with some solutions.

Well, I ended up with more than I had anticipated. I now have a technique, using which, anybody can create a palindromic ambigram of any length! How cool is that.

What is a palindromic ambigram you ask? A palindrogram? An Ambidrome? Read the rest of this entry »

What do you think this is?

Take a guess…

Well, it is the top half of a lake-reflection ambigram. What this means is that if you reflect what you see along a horizontal line at the bottom of the image, the picture you will then get will spell a word. Can you figure out what it says?

While you think about that, let me tell you about this new group-blog set up by graduate students in our Educational Psychology and Educational Technology Program. The blog is called IdeaPlay and is available at ideaplay.org. So sitting here in India I had a few moments to sketch out some ambigrams for their blog. Here are two…

The first is a rotational ambigram that reads the word “Idea” if you go clockwise and the word “Play” if you go anti-clockwise.

And as for the lake reflection ambigram (half of which you saw up there)… well (no great surprise) it reads IdeaPlay as well, like so..

I hope you liked these new ambigrams, and I hope you will check out the the ideaplay.org blog.

In a couple of previous posts I had talked about the idea of postdiction (see the posts here and here). The argument being that good teaching (among a long list of other good things) is postdictable, i.e. it walks the line between predictability and chaos, and most importantly makes sense post hoc. To make my point I had posted a couple of videos that were good examples of being postdictable.

Closely connected to the idea of postdictable is the idea of creating anticipation and suspense. Once again other artists (particularly those working in temporal media such as film, and advertising) seem to have grasped the importance of this earlier than educators. Good film-makers can create suspense out of pretty much the flimsiest of materials. Think of the first scenes from Tarantino’s Reservoir Dogs. The way the scene builds tension out of a disagreement over whether or not to tip is pitch perfect. There is more tension in that scene than in dozens of other “suspense” thrillers.

However making suspense work is difficult. Navigating this line between predictability and tension over the unknown is a fine art. (This is where, of course, the connection with postdictability becomes most clear.)

Check out the two videos below, which highlight just how fine the line is between succeeding at creating suspense and anticipation and failing to do so. Both of these videos are interesting and well made – both have pace and rhythm but one of them builds anticipation while the other just happens. One tells a story, the other doesn’t.
Read the rest of this entry »

I had written earlier about the idea of “postdictable” which was defined as something that is “surprising initially, but then understandable with a bit of thought.” It lies at the spot between predictability and total chaos. The movie Sixth Sense is postdictable in the best sense of the world. Good teaching I believe needs to be postdictable. That is what keeps us engaged, keeps us waiting for more, the payoff as it were. And best of all, once all the pieces are in, we can’t wait to go back and review everything again, to see just how beautifully the whole thing holds together. There is a strong aesthetic component to this – a sense of wholeness, closure, elegance, and inevitability. Good poems have this quality, as do mathematical theorems. A well crafted lecture or a lesson plan has this quality as well. In my mind these ideas are closely tied to the Dewey’s idea of experience and to the idea of design. Hopefully I will have a chance to explore these connections in a later post but for now, here are a couple of commercials that I think were postdictable in a really cool kind of way.
Read the rest of this entry »

Two robots made entirely using Lego Mindstorms NXT Retail-kit that can solve Sudoku problems and the Rubik’s Cube! How totally cool is that. LEGO Mindstorms is a line of Lego sets combining programmable bricks with electric motors, sensors, Lego bricks, and Lego Technic pieces (such as gears, axles, and beams). See Wikipedia article on Lego Mindstorms

See the videos below, and check out the website for the project: Tilted Twister

Sudoku Solver

---

Rubik’s Cube Solver

This is truly amazing… What is also great is that the designer also include directions for making these robots. I gotta get myself one of these

H/T Geekpress

I had written earlier about the idea of Jugaad, the quintessential Indian idea of situational creativity. One of the masters at this is Arvind Gupta. Check out his website for tons of wonderful science toys and experiments that can be made from stuff we typically throw away. Very cool and a critical part of the kind of repurposing of artifacts we need for creative teaching.

Throwaway Technology, playful Pedagogy and powerful Content… who says TPACK needs hi-tech!

Via Major Fun (aka Bernie DeKoven) comes Arvind Gupta, winner of the Defender of the Playful Award.

I just came across these lovely visual mathematical proofs.

For instance consider the following sequence:
1/2 + 1/4 + 1/8 + 1/16 + … = 1

and then see the following image on the blog!!

How cool is that!!!!

I had posted about something similar earlier (see visualizing mathematics).

Note: Before someone gets technical on me, I should admit that these are not “proofs” in the rigorous mathematical sense of the term, but they do provide visual evidence / explanation that helps us understand the underlying patterns.

I also recommend the blog (http://www.billthelizard.com/) on which these “proofs” appeared for a bunch of other interesting stuff about mathematics and programming.

Christopher Bowhuis (a student in our summer on-campus MAET program) provided me a two minute tutorial on cloning myself, or anybody else for that matter. I had to go home and try it out with my kids (and a few of their friends who just happened to show up). Below are a few of the photos, you can click here to see the entire photo set on Flickr.

Three Shreyas

Soham times three!

Three for tea

Three of me

If you want to learn how to do it check out this tutorial. [Note, this tutorial uses GIMP as a photo-editing tool. I used Photoshop.]

I spent some time last week with each of the MAET cohorts at Plymouth England. I have blogged about my time with Year 1 here and Year 2 here (as well as some other posts here and here). This is about what I did with the Year 3 cohort. As usual, I did my TPACK and creativity routine. Some of the poems and photos taken by the students are archived below.

Here’s a haiku by John Arcay
Many Ideas
Involves tweaking the right Knobs
Creativity

Here’s a song about the new NEW, Novel Effective Whole
(To be sung to the tune of The Beatles’ “I’m Looking Through You”)

I’m looking through you
with new ideas
The Novel remix
is relaxing
Making effective
Integration
Can be the whole
For all we know!

Bindu’s NEW Recipe
(Using the 5 steps of creativity and the criteria for creativity)

Preparation: A trip to the market
Incubation: Marinate!
Insight: Season to taste
Evaluation: Proof of the pudding is in the eating
Elaboration: Invite your friends and have a party
NEW?Novel, Efective, and Whole

And finally the photos from the letter search assignment. Since there were 19 students in the class (one more than the Year 2) I modified the assignment I had given Year 2, and just added an exclamation mark! So in essence, I did the same song and dance routine about the solution to Shulman’s three pathologies of learning being Relax, Repose, Reteach! (note the additional exclamation mark). And of course at the end, all was revealed. As it turns out, what they had been searching for were the letters to the words Explore Create Share! (once again with the “!” mark). Here are the two images.

Relax Repose Reteach!

Explore Create Share

Physics Games – online physics-based games.

Some cool stuff here. For instance check out Demolition City

Those of you who have been following this blog know, over the past few months I have made a few short videos with my kids. The ones I am most proud of are a set of three made around the words Explore, Create, Share (you can see them all here). There were great fun to make, and have turned out pretty nicely, if I say so myself

These videos have a few things in common. First, they are short (the longest is a minute long) and involve minimal post production, if any. Second, they always focus on a specific word and attempt to express the meaning of the word through video. Third, each video ends with that word represented in some creative, interesting way.

The other day, while talking with Leigh Wolf, I realized that there was no reason why we could not share the joy of making something like this with others. Why not solicit similar videos from other people? One thought led to another and this competition is the result. The rules of the competition are simple – building on the similarities described above.

1. Each video MUST have a core theme that can be captured in a word (or two). We recommend choosing evocative words related to learning and technology (like design, innovation, invent and so on).
2. The video MUST be original i.e. don’t just copy someone else’s idea, or footage. This is NOT a mashup of existing video.
3. The video should be short (30 seconds to a minute, no more) with minimal editing or post-production.
4. Each video should end with the thematic word represented in some fashion (see the original videos Explore, Create, Share to see how this works).
5. The video MUST use one of the music clips available for download below. These clips were composed specifically for this competition by Sonny Mishra, a freelance musician from Seattle. [Music Clip 1 | Music Clip 2]
6. Once you have created a video, upload it to the web (say YouTube) and send me the link. Please DO NOT send me actual movie files.
7. All links to movies have to be turned in by Wednesday the 22nd of July, 2009.

A jury consisting of myself, Leigh Wolf, Soham & Shreya (the two people who helped make the first three) and Sonny (the music composer) will judge these movies and nominate the winner. The winner will receive a copy of Robert and Michele Root-Bernstein’s book Sparks Of Genius: The Thirteen Thinking Tools Of The World’s Most Creative People, autographed by the authors. How cool is that!!

Do let me know if you have any questions about this competition. Enjoy!

LET THE GAMES BEGIN!!!

I love how these interconnected pipes called the Intertubes lead to serendipitous discoveries. Here are two videos, the first I went looking for, and the second, fell into my lap, so to speak, due to YouTubes related videos section.

The video I went looking for was based on a delightful book I had picked up at a garage sale a few years ago. “The Dot and the Line: A Romance in Lower Mathematics” is a little book (20 pages or so) with an intriguing story-line and its geometrical illustrations. The main character is a straight line who is in love with a dot – but sadly she is more attracted to a wild, unruly squiggle. How the simple line develops his talents and wins the love of the dot is told through whimsical (and mathematically sound) illustrations.

I learned later that the famous animator Chuck Jones had made this into a short film. Here it is (thanks to YouTube).

This is just a wonderful example of how mathematics and art, perception and recognition, creativity and design can come together. This book (and the movie) speak to me at so many different levels. What is most amazing is the ability we humans have to see purpose and meaning in the simplest of lines and curves. So much of art and science depend on this ability to perceive / construct patterns.

Nowhere is this more beautifully (and humorously) illustrated than in this other video I discovered. Written and narrated by Mel Brooks (yes THE Mel Brooks) this animated short film, The Critic, takes a different interpretive stance (crankier and edgier) than the previous narration. That this short animation captures, powerfully how we as humans both seek, and question, the meanings of the patterns we see around us.

I just finished reading parts of Sheri Turkle’s latest book, Simulation and its discontents, and the parallels to what she is writing about and Mel Brook’s Critic are quite strong. The cranky one man in the short recognizes or “sees” meaning is some of the abstract images he sees on the screen and yet he questions their value. The scientists and designers quoted in Turkle’s book echo some of the same concerns.

What is amazing is that the Mel Brooks short was made in 1963, the Chuck Jones movie was made in 1965 and Turkle’s book was published just this year, in 2009!

Over the past few months I have been working with my kids on creating short thematic videos. The themes we chose were the three words, Explore, Create & Share. Though the videos for Explore and Create got made rather quickly, the video for Share appeared to stump us.

Much to my relief, after weeks of discussion and thinking, we finally have a video for the word share. I am including all three videos here, in sequence, so that you can see just how these three videos work together. All three videos have original music composed by my cousin, Sonny Mishra.

7 tools… one big job: Explore

Emergence: Create

… and finally,
A helping hand: Share

(Other videos created by us can be seen here.)

In this TCRecord piece, Daniel T. WIllingham uses what we know about cognitive psychology to explain  Why students don’t like school. He suggests that

although most people believe that humans are good at thinking, it is actually the weakest of our mental faculties… Our minds are biased against thinking, because thinking is slow and effortful. In addition, it’s error-prone; it may not even produce an answer at all, much less a good one.

What we truly hate, according to him are things that are (a) either too easy; or (b) things that are incomprehensible. What fascinates us are problems that hit the sweet spot, not merely unpredictable but rather postdictable. He defines this as being “initially be surprising, but then be understandable with a bit of thought.”As he says:

… interest is engendered by an appraisal process: that is, a process by which we evaluate the potential interest of something before we delve into it. If we perceive an event to be novel and complex, but also comprehensible, we find it intriguing and worthy of continued thought. Tasks that lack complexity seem too easy. Tasks that lack comprehensibility seem too hard.

Just two points here. First, most of school, it seems to me, lies at these two extremes, either lacking in complexity OR lacking in comprehensibility. Combine this with the diversity of student interests and background it is hardly surprising that even students who like to learn, learn to hate schoo.

Second, I had never heard of this term “postdictable” before but I think it is going to become a part of my vocabulary from now on. It helps me explain and categorize educational activities that work from those that don’t. Additionally it helps me explain movies and books I like – from ones that don’t. I know I hate predictable plots and stories (something I am trying to get my daughter to realize particularly around the typical Disney fare she so seems to love). However, complete unpredictablity is also a pain – a waste of time. Movies I like are postdictable… surprising at first glance but understandable later. Cool.

Yesterday after I had posted my two latest ambigrams (see them here) I got a message on Facebook from my cousin Sonny (the one who composed the cool music for my Explore, Create videos) saying

Big deal. I can make “fact” and “fiction” blur together till they are indistinguishable. Using only my brain! And not much effort, either.

Not to be outdone by a good put-down… I created an ambigram that really makes “fact” and “fiction” blur together… Check it out

A few months ago I had created a video mashup of a commercial (see the original and my mashup here). This video ended with three key words, encouraging people to Explore, Create, Share! I then got the idea for creating short videos to represent these three ideas.

I also set some constraints on myself. First, these videos would be short! This meant each video would be between 30 seconds to a minute in length. Second, these videos would be, as far as possible, one continuous shot with minimal post-production and editing. Third, these videos would always end with a typographical representation of the word. Fourth, and finally, these videos would have some kind of a “surprise” at the end.

I was helped in my task by my kids and my cousin Sonny Mishra who composed three original clips of music for the three videos. Sonny has done an amazing job. All three pieces of music are unique, attempting to express musically the theme of the video. That said, all three pieces have a certain family resemblance, so that they all sound connected somehow, at a deeper level.

I have been working on these videos, off and on, with my kids for the past few weeks. We have created original videos for two of the three themes, Explore and Create. Here is the one on Explore (the video on Create can be seen here).

Though I liked what we had come up with for Explore, I also felt that the video was flawed. Essentially, everything happens so quickly that it is difficult to see, till the end, what the objects are that were picked up from the basket. This I felt, robbed some of the impact of the video. So we decided to shoot it again in a slightly different manner. Did it work? Find out for yourself by seeing 7 tools… one big job!. Another change was that this time my daughter was the performer!

What do you think?

(Other videos created by me, with our without my kids, can be seen here.)

I ended the mashup TPACK commercial with the following words, Explore, Create, Share!

Over the past couple of weeks my kids and I have been working on a series of short videos around these three words. The first one we made was around the idea of “Explore,” titled To see .. or not to see.

We created the second one, around the idea “create” this afternoon. Soham suggested calling it Emergence (the title of a Radio Lab podcast we had been listening to a few days ago).

Original music for this series was created by my cousin, Sonny Mishra.

You may notice a certain level of self-plagiarism going on here. We had created a similar video as a new year’s card (see it here). But the idea worked so beautifully for the theme… it would be a shame not to use it. Imitation as they say, is the sincerest form of self-flattery

(Other videos created by me, with our without my kids, can be seen here.)

Enjoy.

Leigh Wolf just sent me a link to this extremely creative YouTube video. The funny thing is that I had seen this a while ago but I didn’t get it. Of course now that Leigh explained it to me, it seems so obvious. Anyway, the narration is crafted in such a way that it reads the same backwards AND forwards. Now this is cool in and of itself, but the kicker is the manner in which the meaning flips when the reading reverses! Very cool.

Here is another one with the same overall idea though less well designed (and a bit more political)

What is most ironic about my “not getting it till explained” is that many years ago I had gotten bitten by the palindromic poetry bug – and had written a bunch of poems that read the same backwards and forwards. Moreover in these poems I tried hard to create a shift in meaning when you began reading the lines in reverse order. So to not notice this self-same pattern when I saw it in the video seems particularly embarrassing. Read the rest of this entry »

If you love optical illusions you have to see this… just absolutely brilliant. The moment she pulls out the driver’s license is priceless. And of course the face / vase flip-flop at the end is cool too. Read the rest of this entry »

This is an extended piece on the manner in which the web, small pieces loosely joined, can lead to “serendipitous connectabilty” (something I had written about earlier here). All this is situated in a story that connects cognitive scientist Douglas Hofstader, Oriya writer and poet J. P. Das, and the father of non-violence Mahatma Gandhi. This is an interesting story in and of itself, and along the way offers some insights into the nature of the Internet and the psychology of creativity. Quite a lot to fit into on posting but bear with me.

Stumbled upon the creative work of Kumiya Mashita. It is amazing just how much can be created with just light and shadows. Just brilliant. Here are some examples:
Read the rest of this entry »

Here is a cool video about a “a mechanical, binary adding machine that uses marbles to flip the bits” – in other words a computer made of wood, that works at a pace that we can grasp! Marvelous. (HT: Collision Detection). Check out the video:

A fascinating series of illusions to reveal just how complicated a phenomenon perception is. I was particularly impressed by the “rubber hand” illusion.

And then, from Gizmodo, comes the Yoshimoto cube. Words are not enough to describe what this mind-bending object can do, you just have to watch the video.
Read the rest of this entry »

Marco Tempest is magician who loves technology, or a techno-geek who happens to be a good magician. He brings an unique amalgam of high-tech and magic to his shows (see this article for details), but that is not what is most impressive about his work. What is impressive is his relatively low-tech side, the one that loves to puzzle viewers with nothing more than a cell-phone camera. These short videos are always single, extended takes, with no editing or post-production whatsoever!! These videos, many of which are hosted on youtube, have to be seen to be believed. The level of creativity, ingenuity, planning and timing is just amazing. Here is one:
Read the rest of this entry »

A YouTube video of Soham solving the rubic cube blindfolded!

[Thanks for Michael Gondry for the idea.]