Sunday, April 05, 2009


Ambigram by punyamishra

All Cretans are liars
said Epiminedes,
a Cretan,
a classic Paradox.

If Epiminedes tells the truth
then he must be lying.
And if he is lying,
he is telling the truth.

Saturday, April 04, 2009


Ambigram by punyamishra

Watson and Crick
what fun it is
to be
a scientist.

What fun it is
to discover
something new.

What fun it is
to compete
with the best
and win.

Watson and Crick
the secret of life
GB #30

Friday, February 27, 2009


Ambigram by punyamishra

The Internet
inking pacts
across the world.

and connecting
all humanity.

all the dots
into one
continuous whole.

GB #29

Internet II

Internet II
Ambigram by punyamishra

Small knots
woven together
become a net.
Flexible, stable,
and very strong.

Small computers
become the Net.

the power
of communication,
of creativity,
of community.

Small individuals,
linked together
become the

GB #28

Friday, February 20, 2009

Douglas R Hofstadter

Ambigram by punyamishra

Douglas R Hofstadter
sides reversed is
Retdatsfoh R Salgoud
sides reversed is
Douglas R Hofstadter
is one Strange Loop.

Hofstadter wrote
Godel, Escher and Bach:
An eternal golden braid.

A personal review follows.

Saturday, February 14, 2009


Originally uploaded by punyamishra

A dog,
wags his tail,
seeks attention.
And licks your face,
without asking for
your permission.

Comes up close
and becomes

And becomes
your best friend.

GB #26


Originally uploaded by punyamishra

looks the same
whichever way
you look at it.

Look down from the top
or up from bottom --
and find GOD.

Look in the mirror
and see GOD.

Just like the 0,
symbol for

But still,
to count from
one to infinity.

GB #25

Thursday, February 12, 2009

Math Poettary - Infinite

Check out the post here.

A brief explanation

The post mentions the sphere as a "one-point compactification" of the (complex) plane (by adding a point at infinity). The property of the sphere being compact somehow makes it a little closer to being "finite" and therefore easier to handle. But to understand more precisely what all this means you need to take a good course in Complex Analysis or Topology.

When studying complex analysis, I thought that the theorems are simpler, more beautiful, and closer to the finite case than analogous theorems in Real Analysis. I don't know whether that is due to the relationship with the sphere, but I suspect it is so.

Here is an example: You know that a polynomial p(x) with real coefficients (and a finite degree) can be written as a product of factors of the form (x-a) where a is a zero of the polynomial. (The root a is of-course a complex number). Turns out, under certain conditions, we can write a function (which can be viewed as an infinite series) as an (infinite) product of its zeros. For example, consider this formula:

Euler's Product:

Euler Product

(The formula above taken from Wikipedia's entry on the Wallis Product.)

The formula looks nicer if you replace x by (pi)x. Then the expression on the left has zeros at +1, +2, +3, ... and -1, -2, -3, .... And on the right you get factors of the form (1-x/n)(1+x/n) which is zero for x = +n and -n.
In fact, the way we write the product is something to do with making the product "converge" (or make sense).

This formula is definitely something I will write about one day. I think I need to pick up a complex analysis book again...its been too long...and have almost forgotten the beautiful stuff I used to see everyday.


Ambigram by punyamishra

"Beauty in mathematics,"
says Polya,
"is seeing the truth
without effort."

Polya's dictum applies
to Science
as well.

Darwin explained
nature's bounty --
from simplicity
emerged complexity,
adapting by competing.

Darwin explained
so much, so simply,
so beautifully.

GB #24


Originally uploaded by punyamishra

Infinite plane
made compact
becomes a sphere.

Still infinite,
but compact,
somehow closer to
being finite.

GB # 23 (also Math Poettary)

Look here too.

Monday, February 09, 2009

The Modulus Function

Every differentiable function
is also continuous.
"This does not mean,"
the Modulus Function
points out,
"that every continuous function
is differentiable too."

Math Poettary #5