A very wonderful holidays and a very happy new year to all of you,
from Shreya, Soham, Smita & Punya

Just a few comments on the making of these videos. First, all our new-year videos are stop-motion videos. That’s how we made the first one and it has stuck. Second, all these videos are somewhat typographical in nature – playing with words and their representation. Third, these videos rarely feature us either individually or as a family. A hand or a still-frame may show up once in a while but for the most part our videos are made with inanimate objects.

This year I tried to change all three of these, suggesting that we make a live action video, with us as actors – and have some kind of a puzzle that was not related to words. After spending days thinking about this, working with various ideas, this whole line of thought was vetoed down by both Soham and Shreya. It was interesting to me that over time we had not only become a family that makes videos but a family that makes stop motion videos! How cool an identity is that! Of course, this meant that we then had to start over from scratch to come up with something that fit what we had done in the past.

Speaking of videos made in the past, you can see them by following the links below:

• Happy 2011 (last year’s stop motion card)
• Happy 2010 (stop motion card made in 2009)
• Happy 2009 (stop motion card made in 2008)
• Explore | Create | Share (3 short videos with typographical twists at the end)
• Finding Nemo, the sea-quel (a stop motion sequel to Finding Nemo)
• Shreya’s friends animate their names
• A commercial mashup
• or, view the complete collection (including the great Hari Puttar trailer)

Many years ago I got bitten by the Ambigram bug and before I knew it I had created hundreds! This was of course long before Dan Brown and Angels and Demons made ambigrams wildly popular. It has been fun to see what was once a fringe activity take on a wider popularity. There was a time that I could actually count the number of ambigram artists on the fingers of my hand, and, in fact, most of us knew each other, either formally or informally. Things are very different today as a Google search will easily reveal, but this also means that keeping track of all that is going on in the ambigram field is extremely difficult.

Over the past few months I have been talking with Mark Hunter a gentleman who is trying to make high quality ambigrams accessible to more people, and to raise awareness of ambigrams worldwide.  He is doing this through two different web sites.

He is also the owner of Ambigram.com, which seeks to be an almost one stop site for all you need to know about ambigrams. He told me about how he spent a considerable sum to purchase the Ambigram.com domain name and has worked hard to grow its membership. He has been quite successful in this and in fact they they recently announced their new Ambigrammy Awards! (How cool is that.) He also maintains a list of artists practicing this craft (your’s truly being one of them).

He also runs FlipScript.com, a site dedicated to creating high quality ambigrams on demand. The results are actually quite good, far better than previous attempts to accomplish this task.  Don’t miss his demonstration short story made up of more than 30 ambigrams.

If you are interested in visual wordplay these sites may be excellent time-sinks!

Dear Mr. Mishra,

I am currently working on a poetry research project for school, and one of the requirements is researching five different poets. While looking for people who wrote palindromic poetry, I found your website and decided to use you in my project. The only problem is that I can’t find much information about you for my research. If you could, please respond to this e-mail with a little information about your history (i.e.-date and place of birth, family relations, etc.) as well as your inspiration for writing your palindromic poems. Thank you for your support!!!!!
Sincerely, Jake

P.S.- I am an eighth grader from Colorado and an aspiring poet.

Now I don’t consider myself a poet in any serious sense of the word (my dabbling in mathematical poetry or palindromic poetry notwithstanding). But it is great feeling when something you create and put out there in the world connects with someone else, someone who you would never otherwise have met or gotten to know. Here is what I wrote back to Jake:

Dear Jake –
Thank you so much for writing to me. I am honored to make it to your list of poets and glad that you are interested in palindromic poetry.

As for my history: I am professor at Michigan State University in East Lansing MI. I am originally from India where I studied engineering and design before coming to the US and getting my PhD. My wife is a graphic designer and I have two kids: my son who is a freshman in high school and my daughter who is in 6th grade.

Ever since I was a kid I have always been interested in puzzles and mathematics and poetry and visual design. That I think led to a habit of playing with words and images… so I do a lot of doodling and sketching (specially when I in meetings). I am fond of asking questions and looking at things around me in new ways. For instance, I love photography, on my Flickr site you will find photos of silly things like finding alphabets in cracks, and faces in everyday things. See this link and this one…

• Alphabets in cracks
• Faces we see

Then there are the videos I make with my kids. For instance see the new year’s card we made recently.

This also led to my creating ambigrams, which are words that are written in a special ways so that they can be read multiple ways. You can find a bunch of such designs on my website.

So I guess, palindromic poetry emerged out this desire or propensity to see the world in weird ways. And the challenge of writing poems that read the same backward and forward was inherently interesting. I particularly enjoyed writing ones that flipped in their meaning when you cross the half-way point. For instance in the poem “Me as I sit” the poem switches from me watching you to you watching me!

Finally, as must have noticed, from the dates, most of these were written a bunch of years ago when I was a graduate student at the University of Illinois. I haven’t written too many recently but the fact that they are on my website leads people to them – and I form all kinds of cool connections – such as the email I just received from you. A year or so ago I heard from someone who uses my poetry to teach poetry to inmates in prison (how cool is that!). You can read about that here.

That’s all for now.. I would love to read any palindromic poetry you may have written, if you are comfortable sharing them with me. Thank you again for your interest in my work. I look forward to hearing from you and let me know if there is anything else you need to know.

take care ~ punya

Note: I got Jake’s (and his parent’s) permission to post our correspondence on this blog under the condition that I not include his email address or other contact information.

Many moons ago I had written about the idea of the web as small pieces loosely connected (read Gandhi, ambigrams, creativity & the power of small pieces loosely joined) that allow people to pursue their passions and share it with the world at large. This is what gives the web its power, and this is also why I am not as comfortable with the barricaded worlds created by Facebook, which would not have allowed someone like Jake to easily find me, (but that is a rant for another day).

Interestingly enough, a few readers questioned the very presence of the pentagon! They saw paws and hands and soccer balls … rather than a simple geometric shape. My first response was, “you must be kidding me, how can you NOT see a pentagon?” But as I thought about it a bit more, I began to “see” their point of view. I think, now, that I was too quick to latch onto the “pentagon” rather than consider other shapes. Whether this is a cultural matter (as some people suggested) or an individual quirk (as some others did), I am not sure.

That said, the fact that some kind of a 5-sided, pointed figure was visible was not in doubt. Whether a pentagon was the best way to label it maybe a fair question to ask. The “fiveness” of it, however, is not really under question here.

So… what caused this “five-based” shape?  To cut a long story short, those of you who predicted this pattern had something to do with the heat source below were right, pretty much. I must add though that the lentils had NOT been stirred, and that this pattern emerged because they had not been stirred. Anyway, here is a photo of the heat source. I tried to take this picture from approximately the same location as the first one…

The first thing you notice are the five prongs that hold the pot up. And these five prongs align quite perfectly with the lines of bubbles that come inwards from the other edge of the vessel. The five prongs that hold the pot up prevent direct heat from hitting the base of the vessel and I suppose lead to less “boiling” activity in these areas, making them ideas spots for the bubbles to collect.

As to why  we get the lines between these prongs (what I called the pentagon) is still not clear to me. My suspicion is that the convection currents that move through the water move the bubbles as they form to points where there is less “bubbling.” That explains the lines coming from the side towards the center – but does not fully, at least to my mind, explain the lines that join these prongs together – the pentagon that I first noticed.

Some more experimentation may be in order… I will keep you posted as and when opportunity arises for me to study this further

Thanks for all those of you who chose to comment.

The almost perfect pentagon that showed up on the surface
of the boiling lentils!

How cool is that. And does it mean something that five is a magical number (see this, this and this). As this page on numerology says

Five is the symbol of human microcosm. The number of the human being. Human forms—the pentagon when arms and legs are out stretched. The pentagon is endless —sharing the symbolism of perfection and power of the circle. Five is a circular number as it produces itself in its last digit when raised to its own power. The pentacle, like the circle symbolizes whole, the quincunx being the number of its center and the meeting point of heaven, earth, and the four cardinal points plus the center point.

Five is also representative of the Godhead – Central Creator of the four fours plus itself equalling five. Five is the marriage of the hieros gamos as combination of feminine and the masculine. Feminine being even, as 2, in frequency and masculine being odd as 3 in frequency = 5.

The number five symbolizes meditation; religion; versatility. It represents the five senses (taste, touch, smell, sight, hearing) everywhere except in the East. In the East there are six—the extra being Mind. We find meanings to five in the five petaled flower, five pointed leaves–especially the ROSE. The Rose has much symbolism, but also the lily, vine, all of which represent the microcosm.

The five pointed star depicts individuality and spiritual aspiration, and education when it points upward. The five pointed star pointing downward represents witchcraft, and it is used in black magic. Noted: There is a very broad difference between witchcraft and black magic.

The number five formed the first counting process from which all else came.

Hmm… so what does this magical appearance of the pentagon mean?

If we believe that every pattern has some underlying explanation, can there be a more mundane explanation? I have a possible hypothesis of what lies behind this phenomena… but what do you think? Where did this pattern come from?

Yesterday I received an email from Alex Ruthman, a self-proclaimed regular reader of this blog who had been inspired to create his own triplet ambigrams. Alex is a music educator and researcher at UMass Lowell with an interest in creativity, music technology, web 2.0 and learner agency (see his home page here). Now, Alex has taken the design of such triplets to their next logical level. He does not just prototype them on paper, he designs them in Google Sketchup and then 3D prints them in plastic! Here is a photo he sent to me…

As you can see this shape casts the shadows of L, P & C (depending on where light shines on it). What is more, Alex does not just do this for fun. He has actually found an use for it in his teaching. As he said in his email:

I use these with my music education methods and research courses illustrating multiple perspectives and three modes of engaging with music: listening, performing and creating.

How cool is that!

]]> http://punya.educ.msu.edu/2010/10/21/new-triplet-ambigram-now-in-3d/feed/ 3 http://punya.educ.msu.edu/2010/09/04/veja-du-all-over-again/ http://punya.educ.msu.edu/2010/09/04/veja-du-all-over-again/#comments Sun, 05 Sep 2010 01:19:06 +0000 Punya Mishra http://punya.educ.msu.edu/?p=1514 A véjà du experience is about looking at a familiar situation but with fresh eyes, as if you’ve never seen it before. It forms the basis of an assignment I give in my CEP818, Creativity in Teaching & Learning course. The assignment is described in greater detail here, but the core idea is to take multiple photographs of some everyday object in such a way that the viewer cannot easily determine what the object is! More here.

Today, I spent some time with my kids re-doing the assignment. My son suggested taking pictures of his X-Box 360 but we finally went with an object selected by my daughter. Here are the pictures. What do you think it is?

Triplet ambigrams are 3-d shapes that cast different shadows depending on where you shine light on it. Now every shape (or most shapes) cast different shadows when light falls on them from different direction – the issue is to make these shadows interesting. In the case of triplet ambigrams, the challenge is constructing the simplest object that can make interesting and different shadows.

Here is what I came up with. This three-d shape casts three different shadows – each of which is a letter-form, in this case the letters A, B & C. How cool is that.

ABC Triplet Ambigram (See large size on Flickr)

I also took a picture of my doodles as I came up with this shape. Here is a small version of that sketch (a larger version is available on Flickr).

(see larger version on Flickr)

I have created a few more of these things before. Here is one for CFT (Cognitive Flexibility Theory). I had posted this triplet earlier in the context of the periodic table of elements here.

And another for Cognitive Technology Society. This logo was selected for use by the organization and then they changed their mind, or the organization vanished (one or the other).

And though I took a picture of just one, I noticed these pixilated, bit-mapped graphics (from some Space Invaders type of game) all over the place. I was intrigued but not enough to research it in any way.

Just a couple of days ago I was reminded of this when I saw some stickers of similar characters on Kristen Kereluik’s laptop and told her about the sightings in France. Well, she did the requisite Google search and sent me a few links. As it turns out these are the artistic creations of an artist named (no surprise here), Invader. As Invader’s wikipedia says:

Invader (born 1969) is a French street artist who pastes up characters from and inspired by the Space Invaders game, made up of small coloured square tiles that form a mosaic. He does this in cities across the world, then documents this as an “Invasion”, with maps of where to find each invader.

Kristen also found a Flickr site devoted to documenting this artwork.

How fun!

Over the past few years I have been thinking quite hard about the idea that creative people are not creative in just one area but rather tend to play within and across multiple disciplines or areas. Robert and Michele Root-Bernstein have in their book Sparks of Genius often talked about how the most creative scientists are polymaths, often having artistic and other interests that go beyond their immediate professional interests. In fact they argue, and I would tend to agree with them, that creativity cannot be forced into one box or domain. Creative individuals are curious about everything and often engage in creative activities in multiple areas, though they may specialize in just one area (usually the domain they are most known for).

This is true for the most creative people I know. For instance, consider Douglas Hofstadter (best known for his book Godel, Escher & Back and is work in Artificial Intelligence) dabbles in everything from mathematics to music, wordplay to art. Similarly Scott Kim (best know as a puzzle game designer) creates ambigrams and composes music, plays the drums and teaches mathematics using dance!

In my own way I have tried to do the same. Everything I do, from creating ambigrams to teaching, from photography to developing keynote presentations, from being a parent to advising students on their research, seems to me to be connected and inter-woven. I think my success as a researcher and scholar (to whatever extent I have been successful) derives from this “dabbling” across disciplines.

What is sad, however, is how much such “dabbling” is frowned upon. Through high-school and college, through graduate school and even as a faculty member, I have been advised, always by by well-meaning people, to focus, to find my niche, to become an expert on one thing. I have resisted it, mainly because knowing just one thing, seems, at least to me, such an impoverished way of being.

And I understand why I have received the advice I have. We live in a specialized world. A world where expertise is valued.  And an expert, after all, is someone who knows more and more about less and less. There is no space for dabbling in this world of.

But I wonder about that. I have a friend who is a successful professor of civil engineering. Turns out, that as he was growing up, what he really wanted to be, was a chef! I haven’t had a chance to talk to him about this but I wonder how his vision of being a chef influences what he does as a researcher and a teacher? Does it contribute (in some subconscious manner) to his work? Or has he suppressed it completely?

Either way I see it as a tragedy, in the first case because we haven’t developed a way of speaking of these influences, and in the second case because a possible, fruitful career was nipped in the bud.

The sad thing is that I am seeing school do the same thing to my kids, in fact to most kids I know. NCLB has not helped either. Don’t get me wrong. This is not an argument for some form of dilletantism (dabbling for the sake of dabbling). Not at all. What I am recommending (thanks to the Roob-Bernstein’s for this term) is polymathy. One of my students, Danah Henriksen, is currently working on a dissertation on looking for polymathy in teachers. As she says:

“Polymathy” may be thought of as an informed enthusiasm for more than one field of knowledge or expertise, or excellence in several realms that might seem distant from each other.  It has been suggested that what makes polymaths so successful and fluidly creative is an ability to cross-pollinate ideas and information.  People who open their minds to, and who learn from, multiple knowledge areas can apply new information and unique ways of thinking from one discipline into another.

This for me is the biggest reason for supporting such playing around in multiple areas. These experiences at the fringes (so to speak) of our professional lives, provide us with newer ways of being in the world. They allow us to see the world in new ways. They allow us to question things the field may have taken for granted. Just as Tufte says at the end of the piece, my goal, is to “make people see a little differently.” Turns out one of the best and easiest ways of doing so is by seeing through different disciplinary eyes.

We need to provide better opportunities for our students to do the same.

Martin Gardner died five days ago. Gardner was an influential writer about mathematics and was one of the greatest influences on me (and my friends) as I was growing up. His recreational mathematics column was the main reason I subscribed to the Scientific American back in high school. A few years ago a couple of my high-school friends wrote a mathematical novel (see my posting about Suri & Bal’s A Mathematical Ambiguity) and the high point for them was the fact that Martin Gardner agreed to write a blurb for the back cover. (My point of pride was that I was thanked in the acknowledgments page, putting me cheek-by-jowl with Martin Gardner!).

More personally, it was through Gardner’s writings that I was introduced to authors like Douglas Hofstadter, Raymond Smullyan, Scott Kim and James Randi — people who in turn ended up becoming immense influences on my thinking and way of looking at the world.

Martin Gardner, through his writing, his sense of humor and playfulness, his emphasis on rationality as a tool for understanding the world, his love of mathematics and learning, will always be with me. I know that in some  powerful, deep and fundamental way, he made me who I am today.

Here are couple of my favorites.

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)

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.

Sean Nash (of Nashworld and speaking in rhymes in biology class fame) in his post speaks of a step by step process that one follows when writing such poems. He writes of science but I think the same argument works for mathematics as well. One of the key things he writes is the value of summarizing, which I take to mean truly understanding something before you can translate it (in this case from prose to poetry). I am doing something similar here, where I take something written in mathematical language and translate it into rhyming verse.

The poem below was my attempt at writing a poetry version of Euclid’s proof that there are an infinite number of primes (see the actual mathematical proof). What was interesting was that I started writing the poem based on my recollection of the proof. Once I had a draft I went off and found some actual proofs to link to – and then while reading them, I realized that I had made some subtle but critical mistakes in my poem. [For instance here is a page that gets it right, and here is another that doesn't.] Which meant that I had to go back to the editing table, and a few surgical strikes later, I had a poem that (at least to my eyes) is mathematically sound (its value as poetry is another matter altogether).

Prime Circle by modern_country

As I was doing this, it struck me that this act of writing poetry actually helped me learn and understand this proof. I can’t wait to get back home and share this understanding with my kids. So this poetry has a educative component, not necessarily for the ones reading it (they may as well read the proof in its mathematical form, it isn’t that hard, it is shorter, and they don’t have to deal with my forced rhymes). But it did help me learn.

So this is a good example of how the process of constructing something (the act of design) can be as important, maybe more so, than the actual product that emerges. So the proof of the pudding is not necessarily in the eating but rather may lie in the cooking. But here the proof of the proof lies in the creating not in the reading, but I include the pudding (er… I mean poem) here anyway, for the record.

The infinity of primes

Over numbers and their combinations if you sit and mull
You will find that not one of them is uninteresting and dull.
But it is a certain class of figures that most attention stirs
Yes, I am speaking of those special ones, the prime numbers.

Prime numbers are interesting, the mathematician posits,
‘Cos they make up all the others, the so-called composites.
Here’s an imperfect analogy, a simple little working rule,
Consider the prime to be an atom, then a composite’s a molecule.

Prime numbers by chrisinplymouth

To carry the chemical analogy completely out of bound,
Consider these atoms (primes) as randomly strewn around
Some here, others there, their patterns concealed
Few sequences stand out, no deep design is revealed.

As the ladder of digits you will climb
Hoping to predict the appearance of a prime
One fact stands out, above all else, as you stare
Prime numbers become more and more rare.

The solitude of primes
from View from Here Magazine

In other words, there are fewer primes the higher you go
Does this heightened rarity mean something, or no?
Is there a prime that is the biggest one?
If there is, finding it could be fun.

Of course, there’s another option, it is clear
Is it that primes get rarer but never disappear.
They get fewer and fewer the further we see
But they never really get done, on to infinity.

Which of these two options is the one that’s true
And how much arithmetic do you have to do
To show whether the primes are finite or not?
Ideally via a nice elegant proof, in one clean shot.

Euclid by waxesstatic on Flickr

Euclid, the geometry guy, comes to the rescue
And produced a cool little proof, whew!
So here’s my attempt to show in rhyme
There’s no such thing as the largest prime.
But don’t take my word for this information
Let us take a moment to look at Euclid’s creation.

Now here’s a critical (and smart) mathematical move
Euclid said, that in order the converse to prove,
Let’s start by assuming there is one (whatever it may be)
Let’s give it a name, this biggest prime, let’s call it p.
This largest prime, (p) when all is said and done
Is divisible just by itself and the number 1.

Now lets multiply together all these primes we have, then
We get a humungous number, we shall, for now, call N.
(This number we shall capitalize
To represent its rather large numerical size.)
Because N is the product of every prime we know,
It is divisible by every one of them, that’s easy to show.

Now take this N and to it, just add 1 (that’s all)
A difference that you may consider as insignificant and small.
But think about it for a moment and you may see
What a difference this addition makes to divisibility.

Divisibility, Image from Math is fun

This new number N + 1 you will soon realize
In the case of divisibility can really surprise.
Take any number on our list including p, our largest prime.
N+1 is not divisible by any of these atoms of the number line.
Whichever way you put N+1 through the division blender
You will always be left behind with one solitary remainder!

Stay with us for a moment, we are almost done
In fact, this is where it gets to be kinda fun.
Notice, there are just two possibilities at this juncture
Let us, in turn, consider each conjecture.

Fork on the road by Jessi Joy

Either N+1 is a prime, or it is not.
If it is a prime, our assumption is shot!
For N+1 is clearly
Much bigger than p!
Something that contradicts what we started with
The idea that p is the largest prime must be a myth

Or, it could be that N+1 is a number composite
Implying there are some primes that can cleanly divide it.
One thing for sure, this divisor cannot be
A prime in our original list we see.
‘cos we just showed that dividing N+1
By primes in the first list just cannot be done!

This just means, there are some primes we missed
When we were building our initial complete list.
And if we missed one, you can sure
There are just an infinity more.
Isn’t it time you said to me
Those magical words, QED.

To sum up, the finite prime set idea is pure fiction
Since assuming it leads to a contradiction.
Primes may be rarer and rarer the higher we go
But they do go on forever, and this Euclid did show.

Infinity by Sven Geier

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