Holes

I have found holes in the geometry class at Stanford. My tutor is amazed. They apparently knew there were some proofs that were not quite provable based on the theorems they use in the class (you have to extrapolate conclusions from them) but they did not think anyone would fin the holes. Wow! I am SO pleased.

Autumn Soup

Years ago,the family got together with part of the family who lived near DC. Soup was served that was totally yummy. I asked for the recipe and got it -- go to the store and buy whatever looks good. So I did. Every autumn since, I make a vegetable soup using that recipe. I am making it late this year as it has been so warm outside. Buy whatever looks good... I could not believe the size of the leeks yesterday. And the collard greens were perfect and equally huge! Serve with crusty bread and a variety of chesses and you have a repast filled with tons of healthy vigor!

Contact lenses

Ah-ha. Contact lenses help when you are cutting onions!

Beauty

I think it was about two years ago when I realized that in order to find something satisfying, I needed to be able to find beauty in it. It is probably something different that other people need to find in what they do, but for me it is beauty.

I find tremendous beauty in math. The beauty is not a visual beauty but an intellectual one. Beauty in its simplicity; beauty in its structure.

Art also holds beauty for me. Its beauty is both visual and intellectual. As an artist, I see a different beauty in art than most people; it is one of conception and creation.

I am lucky. People can spend an entire lifetime and never fully understand what the things are that they most greatly prize. Beauty is my key.

Salt Rub

I had a salt rub today. Wow. My skin feels SO refreshed! It was a wonderful experience to have it along with the massage.

Having massages is doing more for my allergies than even allergy shots. Many days, my nose and sinuses feel completely clear which is truly amazing. The only thing that I can figure out is that the massages compensate for my naturally low blood pressure. And circulating fluids is very good for a person's health.

Today's Activities

Beginning last night, I began to run a fever. I really cooked over night and today I am drained.

Maybe Menopause

Well, maybe menopause is finally approaching. I am 55; I am a senior citizen so it dare well should be!

I raised the temperature in the downstairs by one degree (yes, only one degree as it was just a touch chilly), changed the couch covers and I was drenched in sweat! I thought that maybe I should lower the temperature again until I looked at Esh. He had on his red Cornell sweatshirt! I asked the fated question....."Are you hot?" "No." "Oh." (We are sometimes minimalist conversationalists.) Hmmm. Maybe menopause.

Elastic

Well, it is finally time to put the summer whites away and bring out all of the darker colors. Thank goodness, I only have to do this ritual twice a year. These days, especially with the trips to UVA, I go f0r comfort. Elastic is amazing.

The Mayan people noticed that if they left the sap of various plants to dry, it became springy. They even noticed that when various plants were planted close together and the saps combined, the elasticity of the substance changed.

So thanks to the Mayans, we have comfort waistbands for all of the seasons!

Black and White

There is something very peaceful about black and white photography.

I need to take my camera to UVA some day and take some shots.

Amazing

Today, I had one of those amazing moments. I had worked on the same proof for probably 10 hours and had built a monster (my tutor said that is the way it is supposed to be). I was so stuck and completely lost and directionless so I turned to the text. And that is when it occurred. I realized such an easy solution and felt really dumb...again.

Next time I will turn to the text sooner!

But wasn't that what I had said last time?

Perfect Beds

This morning was one of those mornings that when you wake up, the bed is perfect. Perfect crispness to the sheets. Perfect temperatures under the sheets. Perfect quiet. Perfect temperature in the room. Perfect comfortableness. The feeling of a perfect bed will last with me for part of the day.. I remember it still.

Turtles At My Funeral

I know there will be turtles at my funeral. Even if nobody can see them. They will be the ones I have stopped for, gently picked up off of the road, and escorted them to the other side. They will all live longer than I will and they will stop by and say "Thank you." They will know I made it to the other side, too.

Toe Nails

Sometime last spring when I finally succumbed to the fact that I could no longer see my toe nails and kept totally butchering my toes every time I went to trim the nails, I decide to start getting pedicures. It included trimming, scrubbing my feet, a foot massage, and then painting my nails. The first color I tired was bright red. When I got home, one of our dogs must have thought that I had injured my toes as she tried to lick off the polish. I noticed that my feet felt really good! In fact so good, I actually began to have dreams about my toes!

Since my first adventure, I have tried bright orange, "Rio Red", a red with a name that refers to a Chihuahua, beige, and today I went with a deep rust for Autumn. My nails feel strong and my feet feel healthy. It just feels so good to take care of yourself!

Many More Classes

Good news came the other day. I was told by Stanford that I could keep taking classes even after Ian graduates. They have an amazing array of classes, and having them online will lead not only to a huge amount of flexibility, but less time involved in traveling form home to somewhere else. I can also take classes while in Ocracoke or ...anywhere.

The classes they offer at the high school level (yes, I am truly starting over in order to build a good foundation) are: Honors Precalculus, Calculus A, Calculus B, Calculus C.

The University classes they offer online are: Linear Algebra, Multivariate Differential Calculus, Multivariate Integral Calculus, Differential Equations, Complex Analysis, Modern Algebra, Real Analysis, Partial Differential Equations, Point-Set Topology, Number Theory, and Logic.

It is an impressive list. Ian looked over my shoulder yesterday while working on a proof and he told me that even in his current Honors Multivariate class at UVA, they are doing proofs as rigorous as those in the Stanford online high school class I am currently taking!

Dimensions

As some people in my life know, I have been thinking about dimensions now for years. I think we have identified them incorrectly. We give no dimensions to a point; in other words, there is only a specific location in space. One dimension is assigned to a line and this dimension is merely the distance, and hence movement in one direction, between the zero dimensional points. Hmmm. Two dimensions for a place so then you can have more than one line and you get the first ability to move but only in two directions. Three dimensions allows the movement in all directions. So most of the dimensions can be viewed as allowing a point the ability to move. Physicists have added a fourth dimension of time.

But does movement have any meaning or relevance without time and mass? I don't think so. Time can be viewed as representing the changes in matter; at least that is how humans view it. We age therefore time is passing. Does movement have any relevance if there is nothing to move. I do not think with we are living in a four dimensional system but one that actually involves many more. If all movement truly stopped, then there would not be any matter Matter requires the movement of its tiniest particles. Are dreams in a two dimensional space?

Bathroom Graffiti

Years ago there was one piece of bathroom graffiti that has stayed with me:

If you sprinkle
When you tinkle,
Please be neat
And wipe the seat!

Beauty In Math

I keep thinking about the proof I did last night before bed. The lines and justifications flowed from my brain so smoothy. The proof not only worked, it was succinct. It was a piece of beauty.

After the fall down the stairs and suffering the troubling trauma of brain dmage, I have worried about whether I would successfully get my math skills back. Last night I had my answer. The proof was so easy for me. I felt so at home with the work, like putting on an old bathrobe that has brought comfort over many years. Nice.

Proof, Proofs and More Proofs

I have been having so much fun the past couple of days doing proofs. A greater level of understanding of predicate logic has ... just happened. I can now sense more accurately when a step will be proved in ProofEd and when it won't. It feels so good using my math skills. It is so much who I am; combination of logic and creativity.

Blog Posting

Every day I discover something new about Blogger. I just discovered the other night that you can change the color of the top banner! And I had fun changing the family blog to go better with a picture of apples I found out on the web via Google Image. The people at Blogger make it all so easy!

Stomach Sleepers Unite!

The other day when I was with friends, I happened to mention that I was the only person in hubby's family who sleeps on her stomach. To my surprise, two of my friends also sleep on their stomachs! Could it be that the stomach sleepers of this world form natural hidden bonds with each other?