Life can change in an instant

I sat on the side of the road with the world spinning around my head.  I could not stand.  I had the feeling of impending nausea.  The actual nausea soon followed.  Just moments ago, I had been riding my bicycle, enjoying the sun, the crisp gear changes of a perfectly designed and tuned drive train, and hurrying toward home so as not to be fussed at for being out too long. 

The vertigo, that’s what it’s called, came on suddenly as I was riding.  At first, it felt like the road was moving underneath me, like I was being blown about by a strong wind.  I looked around and I listened. I realized that the wind was not that strong.  The spinning was happening inside my head.  I rode more slowly trying to keep the bike in the bike lane.  It was not working.  I began to be afraid that I would fall or worse yet swerve out in front of a car.  I pulled into a parking lot of empty storefronts to assess and see if it would go away.  I was about eight miles from home.  Janice was at home getting ready to go to the lake house for the evening.  I needed to be home so I got back on the bike and tried to ride.  About a quarter mile or less, I recognized that I had to call Janice to come get me.  So I stopped on the side of the road.  I could not stand on one leg and swing the other over the bike seat like a normal person.  I laid the bike down and tried to step over the bike on the ground and I just tumbled onto the concrete sidewalk.  I sat and called Janice.  I am sure the voice sounded normal but the words could not have made sense to her.  “I can’t make it home.  I need you to come get me.”  I did not say I had a wreck or a flat or anything recognizable.  I could not yet put words to what the problem was.  I did not know.   I told Janice to pick me up from a grocery store parking lot across the street from where I sat.  I thought it would be easier and safer to load the bike in a parking lot than on the side of the street.

Now, as I waited, my head spun.  I wondered what was causing it.  Did I have food poisoning?  I had not changed the water in the water bottle before leaving.  Could the old water be contaminated with bacteria?  Was it a stroke, a tumor?  I then tried to get up to walk across the street.  I could not stand at all.  I leaned against a metal light pole for balance.  The parking lot was as far beyond my ability at the moment as flying to the moon.  I sat and called again.  “Pick me up from the Turnpike,” I said, “across from Bruner’s.  I can’t make it to the parking lot.”  The concern was evident in Janice’s voice but she followed with no questions, no comment.  She said, “I am coming.”

I was no help loading the bike.  Janice put it in the back of the station wagon by herself.  This in itself felt unnatural to sit while Janice took care of my bike.  I sat in the passenger seat feeling very strange.  I soon felt the nausea rising in my throat.  I opened the door and saw my lunch and breakfast spread before me on the curb in a slurry of brown liquid.  “Feeding the birds” was what the coach called it a thousand years ago in track.  I thought of the phrase as a leaned out waiting for the next wave to hit.  Janice waited.  I heaved until there was nothing left but wrenching spasms.  “What can I do?” she asked.  The nausea began to wane.  “I want to go home.”  I asked for a plastic bag to use if the nausea came back on the way. 

As we drove the few miles to the house, I did need the bag several times.  It was the violent kind of sickness that feels as if you are dying even when you are not.  I know that it eventually goes away when the stomach is completely empty.  I am aware that dizziness can cause vomiting and stomach upsets that result in vomiting can cause dizziness.  I was wondering which was the cause and which the effect.

Once back at our house, I staggered in holding onto anything handy and banging from one wall to another.  We had to decide our next move, “wait and see,” “ go to the ER,” or “call the family doctor’s Saturday walk-in clinic,” were on the table.  Janice opted for the last.  After a brief description of symptoms, the response from the doctor’s office was quick and emphatic.  Go to the ER now.  So I changed out of my bike clothes and we went.  I vomited again at the door to the ER.  They brought a wheelchair for me.  I wondered if I would be treated by people in hazmat suits as a potential ebola case.  I was asked if I had been in West Africa and my answer of no was sufficient I suppose.  People treating me just wore normal latex gloves.

We spent most of the afternoon and evening in the ER being evaluated.  I gave my medical history (very limited), allergies (none), and medications (a vitamin) several times.  I got some curious comments that I was the easiest patient all day because the list was so short.  I think the ER doctor came to the correct diagnosis pretty quickly but he still evaluated the other more serious possibilities of stroke and cancer.  I had a CAT scan which came back normal.  The ER doctor described to me what he thought it was.  He said that crystals (called canilyths) had formed in my inner ear and when they broke loose from the upper wall of the cochlea or the vestibule, they came to rest on the sensitive nerves involved in balance and perception of motion.  The dizziness was the manifestation of false signals to the nerves.  The ER doctor said he expected my dizziness to subside rather quickly.  He tried a maneuver of rotating my head from one side to the other.  The objective he said might reposition the crystals into the less sensitive anterior portion of the cochlea.  He said it might help.  We tried a test walk down the hall.  I failed.   He recommended admission for overnight observation and probably an MRI the next day.  This was just good careful medicine I think.  He was pretty sure of the diagnosis, just not too confident in the success of the recommended treatment.  So I spent the night in the hospital.  I had a dose of AntiVert (meclizine) in the ER.  A side effect is drowsiness.  I slept well in the hospital.

I got an IV the next day for hydration.  I thought this was curious.  The nurse’s explanation was not particularly satisfying but eventually it became clear from reading the internet that liquid levels in the ear can be affected by dehydration.  My weight that I reported in giving my medical history was more that 10 pounds greater than what they measured in the hospital.  (It must be the calibration of the scales. My home reading is still read the same.)  Anyway I got a saline drip all day.  There is nothing like being attached to a pole to make you feel seriously ill.  About 11:30, I went for an MRI.  About 1:30 the hospital doctor (different doctor from the ER doctor) came by to tell me I was free to go.  The MRI came back normal.  He gave me a name for the diagnosis, benign paroxysmal positional vertigo or BPPV.  He prescribed AntiVert and physical therapy where presumably they will do the head maneuvers again to help reposition my sloshing crystals.   He told me not to drive.  He recommended a cane to help with balance.

This last is funny because Janice and I have been discussing with our friends how to get parents to agree to stop driving and how we will handle it ourselves.  In those discussions, we have been noble about how well we would handle it.  I envisioned this scene in 20 or so years with my Google self-driving car already in the driveway.  It is ironic, that I am facing the possibility of never driving again at the ripe old age of 62.  The cane is just as ironic.  I pleaded with my mother, whose balance became poor in old age, to use a walker or a can.  Her pride kept her from doing it.  And, she fell repeatedly.  Now, I will be carrying either the cane with me or the hyprocrisy of leaving it behind. 

I had BPPV googled within seconds of the doctor’s departure from the room.  It is common and frequently, as in my case, idiopathic, meaning that there is no obvious cause for the onset of symptoms.  The consequences are wide ranging.  It can be serious enough to be considered a permanent disability.  Sometimes it goes away, sometimes it recurs intermittently, sometimes it is permanent and totally debilitating.  My outcome is still unclear.  My symptoms on day two after onset are not too severe.  I feel some dizziness when standing.  When reading a book or the screen of the computer, the words jiggle.  It is tiring to keep the words in focus.   I have a cane that was used as a decoration in an umbrella stand at my side but I don’t use it.

I am at the point of comparing before and after.  Before, I was aware that my balance and reflexes were good, much better than average.  I was quick, agile, and confident in my sense of balance.   I bought a fine racing bicycle at age 60, a world-class water ski boat at age 62 as a testament to my enjoyment of sports requiring balance, reflexes, and strength.  I climbed ladders, stood on chairs, and generally took risks that would not be wise for a person of less ability of any age.  Now, I am a completely different person.

What will I do now?  As you might guess, there is an online forum for those who have BPPV.  I am a sucker for reading such things.  I will probably waste a few hours a day there for a while until it]the questions and answers become repetitious.  I am wondering what I can do for exercise.  I may be able to walk eventually, possibly jog.  These two activities have been approaching becoming the same exercise for a while now anyway.  My current health issue may bring them closer together.  I am worried about finishing the cabinets in the kitchen.  Shop safety depends on balance too.  I am not sure if I can work safely.   I will have to give it some thought and give my body some time to adapt.  Maybe, I will be one of the lucky ones whose symptoms go away.  I don’t know.

I have a doctor’s appointment at 3:00 with an old friend and physician.  It will be an interesting discussion.

Impact of aging on the abililty to maintain a sufficient mental image of mathematical abstractions while working out solution

Mathematics is largely a process of symbolic abstraction.  That is, we create symbols that abstract a physical thing or process into a character whose properties we can work with on the page.  The mental thing we do with the symbol is to remember on the surface of the brain somehow what the symbol means physically.  That is the abstraction from physical thing to symbol.  At the simplest level, a mathematical symbol represents a single scalar value.  It is either known or unknown.  A physical thing is governed by laws that relate this quantity to other quantities.   Abstraction implies that we know not only what the quantity represents but also all the physical laws that can be applied to it  Abstraction is not fundamentally a difficult concept to grasp but the process of abstraction does scale up to some of the most profound and difficult concepts man has ever recognized.  It was a Newton's profound realization that force and acceleration were proportional to mass and that given a known force over time, a straightforward, purely mathematical operation could predict velocity and position for the same time period.

So what does this have to do with aging?  As I have gotten older, I find that the number of things available for ready recall on the very surface of my brain has gone down a bit.   It is hard to say how much but definitely down and not up.  Solving a mathematical problem, I have to maintain a large number of abstractions and equations to see how they might be manipulated algebraically to effect a solution.  Of course, it is not useful to write down an equation that is more than a few lines long so it is always necessary as problems become more involved to abstract the symbols even further to compress the representation into a manageable size equation. The more complex the problem, the more complex the symbols become, and the more of the problem has to be carried in the head rather than written out on the page.  Herein lies the problem.  There is less space up there than there used to be.   Another problem is that one has to pick a direction to try from the available directions to move the current problem closer to a useful form.  It is like being in a maze and having many directions to choose,  I have to make a good guess since exhaustively trying every possible thing would take far too long.  The instinct for doing this is born of experience which I have but also the ability to play it out a few steps ahead like a chess master does when considering a range of moves.  This takes some serious memory skills to visualize the steps very rapidly without writing anything down.  I am pretty sure I would be a poorer chess player now than when I was younger just as a I am poorer at mathematical problem solving

I used to say my IQ or problem solving ability was limited by the size of the piece of paper I had to work things out on and in fact some of my most useful derivations were written out on blotter size quadrille ruled sheets.  I also said it was related to the size of the desk to open up books I needed for reference.  Now the limitation is similar but is internal.

The same difficulty is not present if I simply read someone else's work.  The author has reduced the solution to a linear, step-by-step process.  New abstractions are generally introduced at the point that are needed with appropriate references and explanations.  One can focus just on a single equation at a time to follow along.  One does not need to have the encyclopedia of mathematics immediately available from within memory to see how a problem has been worked out.  Taking things one item at a time requires less mental surface area.

The wheel problem is getting more complicated with each refinement of the derivation with additional terms in the equations and additional coupling between equations.  I am still able to solve the equations but it goes slowly and I have gone back to discover where I missed something.  I am copying equations over on a new piece of paper to renew the terms in the mental image of the equation.

As some one observed, "Getting old is not for sissies."

The status of the wheel problem

For those who are checking this blog daily, here is the news.  I have not stopped working on the wheel problem but I sort of gave up on the math blog.  Let me offer two reasons.  Blogger is not friendly to equations and I cannot write a math blog without equations.  It is not impossible to include equations in Blogger but it is awkward.  And the second reason, no one is apparently reading the blog so there is little incentive to overcome Blogger's mathematical limitations.  I continue to work on the writeup in Word.  Word is a familiar writing environment for me and, with Mathtype, it is relatively friendly to equations and figures.  If you are interested in seeing the current state of the solution in equation form, leave me a comment and we will work something out.  From now on, I shall just talk about the algorithm in general terms without equations.  Some people may be more comfortable with this approach anyway.

The current state of the wheel model is that I found by comparison to experimental data that the model does not predict actual wheels very closely on the single spoke perturbation test.  Also, as the tension in the spokes increases, the comparison gets worse.  As a first guess, I have added hoop stress to the model following the general approach for including axial buckling in an Euler-Bernoulli beam model to the wheel model.  The result is that the hoop stress term generally improves the axial comparison but has almost no effect on the radial results.  I find this puzzling but have reviewed the equations to the point that I think that they are right.  Right in the sense that they a correctly implement the hoop stress that I intended into the axial and radial displacement.  The problem is not a programming error or error in the algebra but is the actual consequence of the what I set out to do.  So I am looking for a new direction.  I think the problem lies instead with the fundamental equations.  I am current working to add cross-bending stiffnesss to the wheel's stiffness matrix.  I don't have a compelling physical reason for this term.  I argued that it was zero in the original derivation because the rim is a slender beam and that the spokes are thus must be attached fairly near the centroid of bending.  The cross bending stiffness term arises when force is not applied at the centroid.  With a symmetric wheel (symmetric about z=0), these cross bending terms are mathematically zero.  I can argue now that perhaps the spokes are not at the bending centroid and thus the term should be considered.  I have not performed an analysis of the rim to see if this idea has physical merit.  I just observed that the shape of the radial  deflection mirrors the shape of the axial deflection and that the cross-bending stiffness would give a mechanism for that dependence to appear proportionately in the radial bending equation.   I have the algebra roughed out for the solution to this model but have not put it into the Word document.  I have also not programmed the new equations.  The algebra is getting more and more tedious which is the subject of my next post.  I am still making sure it is right.