Non-Linear

Regarding some equations.

On first introduction to the idea of convergence, it is natural to take an optimistic view. However, in certain cases it is clear with moral certainty that whatever else happens, convergence does not.

Consider subharmonics. Proving their bare existence, we begin with a theorem of our own before beginning any proofs.

Suppose a positive constant, some fixed function bounded by a given. From there, find a local maximum. Suppose the velocity of a given around a stationary point, spinning.

Consider any variable whatsoever, and let it be x. It follows immediately that the notation parallel to that for symbol y is denoted by an alternate symbol.

We are always supposing. 

We suppose always,

assume the truth.

***

Today is the anniversary of the death of celebrated British mathematician, Dame Mary Cartwright (1900-1998), who is considered one of the pioneers of what came to be known as chaos theory. This exercise is a collage of phrases found in this paper she published in 1945.

Deep Sky Observing

“We don’t live in a general-purpose universe.”

So you own a star chart. 
There is much more.

What’s wrong?
Not seeing anything.
Try averted vision.

What books? What size? 
How far? How much? 
When? 
How far?
Are we there?

How many inches?
Just wait. I have rid myself 
of rarely used accessories 
in my garage.

For example?
I found out 
that I did not want 
to be a mathematician.

What is the best way?
Look at your maps. Find 
a dark country road. In
hunting season, be careful!

Traveling alone?
You may have to walk. 
Worth the effort, 
for dark skies.

Cloud cover?
Pay attention. 
Conditions repeat 
over time.

How do I––?
Look. Use eyes and 
mind: a technique 
for seeing. Take a break. 
Nap. Wash the mirror 
until the solution 
drains away.

How about something 
–for general purposes?
No.

Why not?
We don’t live 
in a general-purpose universe.

Brand new equipment!
Try it out.

Going all the way!
The new bracket does not fit.
The drive gear needs more lubricant.

Wasting precious dark sky time?
Patience. Try out that new mount 
before you leave. 
Be prepared.

Inspiration (and found words/ phrases) from the opening three chapters of:
Coe, Steven R. Deep Sky Observing: The Astronomical Tourist. Springer, 2000.