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?

Forgetfulness

I must start writing things down! I have thought of a number of ideas for postings and then.....Exactly what was that one I thought of when I was stripping beds? What was the topic of the one I thought of the other day in the car? Forgetfulness happens. I guess it will be really bad when I have forgotten that I forgot something.

Unexpected Change

The day after I wrote my thoughts about roadkill, I noticed the little fawn carcass again by the side of the road. Later that night, I thought about doing a follow-up article on the body slowly deteriorating over time until it became one with the earth, and peace had settled in. I planned on talking about all of the amazing organism that participated in this "recycling" process and how I am in awe of everything on the world -- how organized and wonderfully structured it is. Our "living" planet is like an living oroganism with its cycles of life and death. Each day, I have watched the fawn carcass go through its various stages of approaching the full reccycling process.

It was gone yesterday. People were walking with bags along the side of the highway picking up litter. Apparently, someone had spotted the tiny carcass and taken it away! Where would it go? Would it be put on a trash heap as if it did not matter? Would it be allowed to recycle and become one with the Earth? And what would I end up writing about? Troubling thoughts.

Then I decided to write about change. One thing anyone can always expect, is change. Change always happens. My thoughts of a calming article discussing the wonders of this Earth where shattered... and probably by someone completely unaware of my plans! Hah! Chaos is terrific.

Stray Hairs Part 2

I found this on a blog: http://qcreport.blogspot.com/

A few months’ back, a friend of mine was trying to describe the degree of closeness she felt for another woman. She flailed a bit, and then said in relief, “Well, she’s my tweezer friend”. I said in a tone which I hope was polite and not just alarmed, “Your what?”

“She and I have an agreement. When we’re old, if one of us is in the hospital and not doing well, the other one will come over and tweeze off the weird facial hairs. Tweezer friend.”

I love the idea!

Too Old? ROFL

The other day when my son and I saw a very funny ad on TV I said "OhEmGe. That was SO funny." I looked at my son and saw a shocked and troubled expression on his face.

"What's wrong?"

"You're too....old to say OMG," he said.

Too old? ROFL. I was five when I collected money for UNICEF. I was eight when I visited the UN building and did a report on LASERs. At sixteen, I took the SAT for the first time. As I got older I found out about the FBI, CIA and the KGB. At 22 I went to work at IBM. AT 28 I said TGIF once a week and had to have work reports finished ASAP so that we CYA'd. People invited me places and I had to RSVP. I have been saving JPEG files for years! LOL. Never too old.

AIUI, BTDTGTTSAWIO. YOYO. TTYL.

Moment of Silence

I must share this. I found this on a blog, Rocks In My Dryer.

May We All Pause For a Moment Of Silence...

...in commemoration of today, National Punctuation Day? May we join together in grief over all the butchered its and it's of the world, and may we mourn for the world's stunning lack of proper hyphenation?
These are dark days, my friends. Go hug a comma.

Sprouting Nuts

My masseuse, K, often talks with me about healthy eating ideas; and believe me, she is a wealth of knowledge. Via her husband's research, she cured herself of debilitating arthritus by changing her eating habits.

During the hot rocks massage, she gave me a great idea. I love salads with no dressing that are sprinkled with dried cranberries and raisins, and sometimes cheese or lean meat. She also suggested that I added sprouted nuts! How you make these is simply by placing walnuts or pecans in water for between 30 minutes to six hours. The nuts begin to sprout and apparently the nutritional value triples. Sounds yummy. I will have to try it soon.

Hot Rock Massage

This past Saturday I had a hot rock massage. Wow. It was terrific. K heated up a bunch of very smooth river rocks. Then she covered them with oil and rubbed them all over me. The feeling was amazing. She also placed some rocks in specific places and just let them sit. I could feel my legs relax with a large hot rock was placed in the middle of my lower back and just allowed to sit. K even put rocks between my toes. I recommend this to everyone! BTW, it takes about 600 hours of training to become a professional, licensed masseuse.

Road Kill

As my son and I drive to Charlottesville every day, we often see deer along the highway. Graceful veggie eaters who are so beautiful with their long necks and legs. Yesterday morning there was a mother deer, and a tiny fawn who still had its spots, grazng near the edge of the highway.

On the way home, there was a dead fawn next to the road, it white ummy facing the orad. I hate to think it was the same fawn I had just seen a few hours earlier. I wanted to stop the car and run over to it and embrace its tiny body. I often wish I had healing and life-giving hands when I see road kill. I wish I could either protect all of the beautiful animals on the Earth or I could bring them back to life once they have died. But what a crowded world this would be!

Game Theory and Driving

The mathematical patterns associated with driving is really beginning to fascinate me. It is so much like Game Theory. I can't wait until I have learned the math to equate all of these thoughts.

When a driver is on a highway alone, it like being the only player on a game board. You have a goal to win or finish the game (reach your destination). You follow the rules but do not have to negotiate with any other players (drivers).

When other players are in the game, then a negotiation process occurs involving various means of communications (blinkers,headlights, etc.). People negotiate for space and safety with each other. And everyone pretty much has the end goal of reaching their destination safely through a cooperative effort.

Of course there are always those drivers who zoom past and follow their own rules!

Driving Pain

My right leg hurts now almost every day. Today, because we had forgotten to fill the car up with gas over the weekend, I had to drive very quickly in order to makeup for the time lost gassing the car this morning. The constant heavy pressure for the hour of driving is now being felt in my right leg with pain and small spasms. But anyone can do anything for a year. i firmly believe this to be true.

Why Don't Computers Know?

I don't understand why computers don't understand what I mean when I type in "soem" or "thy". Why don't they know what I intend my password or screenname to be? So what if I type hooly instead of holly They are almost the same; just one letter difference!

Getting Older and Stray Hairs

Aging is interesting. Strange hairs have appeared in my eyebrows and on my chin. Sometimes the ones in my eyebrows are coarse and curly -- sort of pubic in nature. Very odd experience. These hairs curl under the other eyebrow hairs and work the whole bunch in the opposite way they are supposed to lie. It feels sort of like someone is rubbing your eyebrows the wrong way.

What Does "Natural" Mean?

I have found it fascinating over the years when I hear people use the term "unnatural" when referring to human things. How are they unnatural? Unnatural means that something is not related to Nature. So...how exactly are our things not natural? Are we not a part of Nature? We evolved as a part of this Earth just as the birds and bees. All of our products are made from products of this planet so I must think of them as "natural". Why are our houses less natural than a bird's nest? Both are typicall framed with products from trees. Our glues are similar to bird's saliva products. Both are a reformatting of the Earth's natural resources. Seems natural to me!

Going Green

So there was a several simultaneous "green" concert some months ago. The event was touted as being about reducing global warming which is assumed to result from burning fossil fuels. Fossil fuels are burned in our cars and airplanes; and also, still, in most power plants in the form of coal. So....everyone drove or flew to the concerts. The concerts used huge amounts of electricity in the form of lights, speakers and microphones. Was the concert actually about global warming or was it an effort for Al Gore to look good?

The Problem with Division

There is a problem with our system of division. 1/9 in decimals is .1111..., 2/9 is .2222... all the way up to 9/9 which according to the pattern should be .9999... but 9/9 is 1. Mathematicians consider .9999... to be equal to 1 but I don't. There is a negligible difference but there is a difference.