### Design II

Design II

Ambigram by punyamishra

A great design:

Everything fits in nicely

into one complete whole.

Not a hair out of place,

and not one thing

more

than what is

needed.

The form

and the function,

made for each other.

GB #32

### Paradox

Paradox

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.

### Watson-Crick

Watson-Crick

Ambigram by punyamishra

Watson and Crick

show

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

discovered

the secret of life

itself.

GB #30

### Internet

Internet

Ambigram by punyamishra

The Internet

inking pacts

across the world.

Linking

and connecting

all humanity.

Shakily

connecting

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

inter-connected

become the Net.

Unleashing

the power

of communication,

of creativity,

and

of community.

Small individuals,

linked together

become the

Internet.

GB #28

### Douglas R Hofstadter

Sides-reversed-is

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.

### Dog

Dog

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

personal.

And becomes

your best friend.

GB #26

### God

God

Originally uploaded by punyamishra

GOD

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

nothingness.

But still,

required,

to count from

one to infinity.

GB #25

### 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:

(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.

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:

(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.

### Darwin

Darwin

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

### Infinite

Infinite

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.

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