Carnival Of Math February 2020

A Collection Of Math and Science Blog Posts From Around The World

Final Look at 2019: School, Science and Education
by Frederick Koh
A detailed review of 2019 examining science, school and education related events.

Hypot – A story of a ‘simple’ function
by Mike Croucher
Even the most simple looking mathematical functions can be difficult to implement on computers perfectly.  In this post, I look at an extremely common computation where the mathematics can be understood by children and yet efficient and bug-free implementation is complex and the subject of modern research.

Convergence rate of random walks
by John Cook
In some cases, random walks rapidly become more uniformly distributed, quickly going from obviously not uniform to apparently uniform.

Attracted to Attractors
by Ari Rubinsztejn
In this post 3 different chaotic attractions are visualized.

More Modular Knitting
by Pat Ashforth
Geometry in knitting (even for those who ‘can’t do maths’). How many different shapes can be knitted using only 45, 90 and 135 degree angles?

The Multiples of Me
by Sam Hartburn
The Multiples of Me is a poem about prime numbers, and why they needn’t be sad about having no factors.

Two dimensional tessellations at the Curious Minds Club
by Debbie Pledge
I run a recreational maths after school club in England. The post shows I got the children to explore the regular and semi-regular tessellations.

Australian Mathematicians
by LThMath
At the start of January we wanted to do something on our Facebook page to raise awareness about all the problems Australia has been through in the last period. We were shocked at the situation there.  For 2 weeks we researched and wrote more about Australian mathematicians and their work. In addition, each post has a link where you can donate for different charities and organizations. In this post we want to put together all the information we have discovered in those 2 weeks, including the mathematicians and where you can still donate to help.

Welcome to a Carnival of Mathematics!

This month, I will be hosting the Carnival Of Mathematics blog.

The Carnival of Mathematics is a monthly blogging round up hosted by a different blog each month. The Aperiodical will be taking responsibility for organizing a host each month, and links to the monthly posts will be added here. To volunteer to host a forthcoming Carnival (see below for months needing a host), please contact them on their website.

The Carnival of Mathematics accepts any mathematics-related blog posts, YouTube videos or other online content posted during the month: explanations of serious mathematics, puzzles, writing about mathematics education, mathematical anecdotes, refutations of bad mathematics, applications, reviews, etc. Sufficiently mathematized portions of other disciplines are also acceptable.

A FAQ can be found HERE.

I have the honor of hosting the anniversary Carnival! The Carnival of Mathematics will be 13 years old on February 9th.

If you want to get your math related post submitted, fill out this Google Form for consideration.

Brace yourself, there will be a test later.

A Discovery of Bristlecones

Yesterday, we took a trip to visit the Ancient Bristlecone Pine Forest in the high Sierra mountains, in California. The forest is home to thousands of Great Basin Bristlecone Pines (Pinus longaeva) the oldest living trees on Earth. The oldest, clocking in at 4,851 years old, is named Methuselah. 

The altitude of the forest is high, about 10,120 feet at the beginning of the trail through the grove. It is illegal for pilots to fly much higher without supplemental oxygen. As soon as I got out of the car, I was winded. I didn’t stop feeling winded until I was there for about an hour.

The trail is 4.8 miles long and it took more than 5 hours to walk it. There were a few primary obstacles. One is the fact that I am 57 and I don’t trail run anymore. The other is we were constantly stopped by awesome vistas and spectacular photographic opportunities. I took 353 photos – that is 73 photos for every mile walked. Seventy-three!

At every turn there was a spectacular tree – completely different from the rest. Each tree has a different personality and different shape. And there are thousands of them. And most are thousands of years old. There is one valley where all the bristlecone pines were older than Plato’s Republic.

All of these are older than Plato’s Republic.

A bristlecone pine is shaped and sculpted by environmental and geologic forces. Fire will strip away its bark and then 500-800 years later it will rebud new growth. Wind and fierce winter furies will bend and twist the the trees into alien shapes. The rocky, inhospitable alkaline soil will twist and gnarl the roots into complex spirals. The tree rings are so fine they are about as thick as a human hair and must be counted via a microscope. If you put your ear up to the tree and knock on the wood, the sound is an eerie mixture of echo and underwater acoustics. The feel of the wood is near rock solid – with no discernible give or flexibility. It might as well be rock.

Each tree is a different and amazing, nature-made Bonsai tree on a very large scale. My 73 photos per mile were not enough to document them all.

Lastly, I did find Methuselah, the oldest documented living tree on Earth – and She was glorious. She is the true Goddess of the Grove. For an old Druid like me, it is a wonder to behold. We took a bunch of photos and selfies, tree-hugged a bit, whispered to Her and accepted Her blessings of peace. I will never share these photos or share Her position. Her legacy must continue after me as she has stood the ages as well as Her siblings surrounding her. Because you know, there is always that one asshole.

The above photo is one that we dubbed ‘Butthuselah” for obvious reasons.

Bag End 2

Econ-friendly Home Design Inspired By J.R.R. Tolkien

I have always been interested in bio-friendly housing, specifically designs that approach zero-environmental impact.

After seeing The Fellowship of the Ring, you have probably fantasized about living in a Hobbit Hole and lazing about in the shade. I know I have. The night I walked out of the theater on opening night, my OCD kicked in and I designed a Hobbit Hole.

That is when I started expressing my inner architect and wondering of easy, bio-friendly ways to build a Hobbit Hole. This is what I have come up with.

The largest expenses in building a home (not counting the flat screen tv and indoor lap pool) typically are the walls, exterior and roofing system. Obviously, the roof and exterior are done away with for Hobbit Holes. However you have some staggering stress and loading issues with underground housing. The weight of the soil and flora growing on it can produce tremendous loads on a structure. It is even worse when it rains.

Once you start doing the math for wooden structures, the cost quickly skyrockets. On top of high costs to support such loading, you have yet to deal with the issue of water seepage, insect vulnerabilities (termites) and wood rot.

That leaves us the two building materials. Steel and concrete. With the circular nature of Hobbit Holes, one could use large steel pipe, but no source exists that makes low cost steel structures that I could find. But concrete… yes… concrete is the ticket.

All around the world, companies manufacture pre-formed concrete pipe… LARGE concrete pipe. Concrete pipe has several advantages for making Hobbit Holes. They come with an assortment of flanges, protrusions and options that allows for the creation of windows, skylights, doors, garages, fireplaces and chimneys.

As one can see, using such materials for the construction of a Hobbit Hole would make for a comfy home. Or at least a conversation piece.

Although the elliptical may have some aesthetic advantages, the use of round concrete pipe may be the best choice. The main reason is that you will need to have room to place plumbing, ventilation, electrical and communication hardware though out the Hole.

The best solution for this is the area under your flooring. The best example of this type of construction is in naval architecture with sailboats. Plan all of your plumbing, ventilation and wiring, then figure out how much space you will need, vertically. Maybe the use of multiple styles, circular for halls and elliptical for rooms, is the best idea. The halls would need the most space for plumbing, etc as all rooms connect to it. That is the design philosophy I have used for Bag End 2.

The proper name for this type of home is “earth-sheltered home.”

There are some other similar designs and building strategies for constructing homes of this type.

Rammed Earth” homes are homes that are built using spare tires filled with packed dirt. The upside is that are recycling old tires, glass bottles and other uncommon materials to build a house and low cost for heating and cooling. The down side is the incredible labor involved with packing thousands of tires with dirt. Also, there is some concern with rammed earth homes in areas frequented by earthquakes.

Earth Ship” is another type of house. These may include rammed earth construction, but the main goal is off-grid living. Typically, these homes are found the the American West and are of an adobe design.

A Guide To Getting An A&P

My work experience prior to Baker’s

My father had a unique way to get me to learn about cars. He wouldn’t let me get my driver’s license until I learned how to work on cars. And what better way to achieve that than buy a Triumph TR7 that didn’t run. I remember the day it was TOWED to the house. There was to be no driving in my future until that car was fully repaired. Six months later, after a teardown of the engine to replace the head gasket, replacement of the transmission, the rear end, and the drive shaft. Keeping the Zenith Stromberg updraft crabs synced was an ongoing nightmare and DO NOT get me started on Lucas electrical system, which must have been conceived during a Welsh Demon Summoning ritual that went awry.

At the time all of that turmoil was going on, I was working for the local FBO, getting all of my civil time in for when I go get my A&P. At the same time I earned a 2 year degree in electronics and that helped greatly when it came to take the writtens, oral and practical.

But…. life happened. Those halcyon days of working on airplanes ended 25 years ago. I had my time in but I had forgotten a lot of what I had learned via on-the-job training.

When 2018 rolled around, I wanted to go back and finally get my A&P. I saw two ads for A&P prep schools in Trade-A-Plane. I always grab a copy of TAP whenever I can and one ad was always there; Baker’s School Of Aeronautics. I cut it out and saved it. I remember seeing this ad for YEARS in TAP. When I started asking around, Baker’s kept getting highly recommended, especially by a very good friend of mine that got his A&P from there. For me, his recommendation and the ARMY of other graduates that swear by Baker’s, my decision was finalized – Baker’s it is!

My Baker’s Prep

Since it was such a long time since I have wrenched on a certified aircraft, I went whole hog on training materials. I used the King Schools video course which was excellent for me because it actually shows what the questions are pertaining to visually. I get a lot out of visual presentation.

I also used the test prep apps from Dauntless Aviation. The flash card feature is excellent. The apps have excellent descriptions for those of use that need that visual of “how it works.”

For the King Schools video, I didn’t bother with the sample tests, I only watched the videos. Same with the apps, I only used the flash card feature. As the instructors at Baker’s will tell you, ONLY consume the correct answers. Recognize the correct answers and ignore the wrong ones.

List Of Things Not To Do Before You Arrive At Baker’s

  • Don’t take sample tests or random tests.
  • Don’t use the time before Baker’s to slack off – you study.
  • Don’t think this will be easy, it won’t be.

List Of Things Not To Do After You Arrive At Baker’s

  • Don’t go to Nashville – you study.
  • Don’t take weekends off – you study.
  • Don’t fart around after classes – you study.

The staff is there to help you succeed. They are a great bunch of people who are actually dedicated to getting you an A&P certification (don’t call it a license ffs). Don’t fear the DME’s they are very helpful and are not there to make you fail. 

Study Groups

Once you are into the oral and practical portion of the course, have your ass in a study group every night. EVERY. SINGLE. NIGHT. The act of asking each other questions is VITAL to succeeding with your orals. Nothing, no other study method can replace it. If you want to be the loner and study on your own, make sure you have the time off of work and the cash to stay a few extra weeks in Lebanon.


No matter what you spend getting your certs, it will still be waaaay cheaper than a semester of college. That said, there are loads of ways to lower your costs before you get to Lebanon and while you are there.

Some hotels are more expensive than others. I stayed in both the Hampton Inn and the Holiday Inn Express and they both have their pros and cons. I can only speak about the other ones via word-of-mouth from my fellow students.

Hampton Inn


  • Nice accommodations
  • Big lobby to host study groups
  • Good breakfast
  • Free snack pack during the week (bottle of tea, granola bar, coffee cake and a piece of fruit.
  • Literally next door to the school so you might be able to do away with having a car.


  • It is the most expensive choice of the school’s recommended hotels.

Holiday Inn Express


  • Nice accommodations
  • Big lobby to host study groups
  • GREAT breakfast options – it has a CINNABON bar! 
  • It is very affordable


  • You will probably need to rent a car or budget for a lot of Uber rides.

Love Your Walmart

It will cost you a lot if you eat out for every meal. Go to Walmart and buy food that is easy to prepare with just a small refrigerator and microwave. One of my fellow students ate baloney sandwiches for his entire time there.

Aviation Museums

If you are fortunate to live near an aviation museum, do yourself a favor and get a season pass. I went damn near every week for three months to learn all I could about turbine engines. I took hundreds of reference photos and studied them for hours when I would get home. I never worked on one and had a lot to learn to get through the powerplant written test as well as the oral and practical.

My Tips

If you don’t have any knowledge about electricity or electronics, I suggest getting this, an electronic education kit (Amazon Link). It has 130 different experiments that will teach you everything you will need to know about the fundamentals that you will face on the writtens, the orals and the practicals. For only $35, it is a great deal.

If you are a turbine guy and are unfamiliar with the archaic technology called a carburetor, consider this Army educational film on YouTube. Here are some other helpful videos…

Above and beyond all of the above, there was one thing that made me successful and that was flash cards. Not the flash cards from a software app, but actual notecards.

When I got the Oral and Practical book from Baker’s, I took each question, copied it by hand on the front of a notecard and put the answer in my own words on the back. I did this for most of the book for the questions I didn’t know like the back of my hand. When I wasn’t in group, I was going through this stack of cards, read each card and tried to answer. Once I did, I flipped it over to see if I got it or not. I would then place the card in a pile and move on to the card.

I did this over and over and over. Once I knew the card by heart, I would place it in a different pile and then continue on with the pile that I still didn’t know. I repeated this until I was left with no cards in my hands. I then repeated this up until the day I took my orals.


Of my class, only three zipped through everything on the first try. Most failed something; a written, part of the oral or the practical – me included. The powerplant written was a particular struggle due to my unfamiliarity of turbine engines.

Doing the prep work that I have suggested BEFORE you get to Baker’s will help you find success. If you don’t do the prep work and don’t put in the insane hours required to succeed, you can’t blame Baker’s. You have to do your job before they can do their’s.


Baker’s has a damn fine program to get you your certificate – best in the nation. Listen to your instructors. Work your ass off and you will get there.

My Closest Encounter

It was a September day in 1992 when me and some close friends were camping in Rock Castle Gorge near Floyd, Virginia.

Whenever I go camping I tote along a decent sized pair of binoculars for stargazing. I am not looking at anything particular, just looking. When it comes to stargazing, I am more of a casual tourist.

This Saturday night in September I saw something I had never seen before, something that should not and could not be there.

I first noticed a blinking light, to the north, about 330 degrees. It was high up. Very high up, well above normal commercial aircraft flight levels maybe 100,000 feet AGL. The blinking was maybe less the a one second cycle. The light was stationary relative to my position for about an hour, continuously blinking. At the end of the viewing, the blinking stopped, the object increased luminosity and then moved away astonishingly quick, up from its current position until it faded completely from view. If it had any tint to the color of the light it may have been blue, but I am unsure.

At first I thought maybe a quasar. “Do quasars give off radiation in the visible light band?” I thought to myself.  But the star field moved BEHIND it. The blinking light was holding steady. 

There was no evidence of it being an aircraft. There were no navigation lights and there wasn’t any evidence of a red rotating beacon. If it was a strobe, why were there no other lights? And why was it stationary? And I doubt there was some chucklehead pilot aboard flipping the landing light on and off for over an hour with perfect timing.

It wasn’t a helicopter. They can’t fly that high up. There isn’t enough air for rotor blades to maintain lift that high up. Besides, the object was about 4 times higher than the highest altitude helicopters currently available.

It wasn’t a meteor as it stayed stationary for over an hour.

It wasn’t a satellite. They move unless it is a geosynchronous satellite, those might blink to the observer and would remain in the same position in the sky, but they would only be visible to the south, behind me. I was looking the other direction.

So what was it? Here is what is wasn’t:

  • Quasar
  • Airplane
  • Helicopter
  • Meteor
  • Satellite

This clearly puts it as a UFO and in my opinion an extraterrestrial craft.

I am a big fan of Carl Sagan and he shaped my scientific view tremendously. He was often found to be advocating, “tremendous claims require tremendous evidence.” I totally agree. I am just one guy with one observation. But still, if you apply Occam’s Razor that stipulates all things being equal, the simplest explanation is usually the right one, you end up with an extraterrestrial craft.

If you apply Occam’s Razor to this observation, here are the competing ideas.

Quasar – if a quasar was rotating near Earth, within the orbit of the Moon, none of us would be alive right now.

Aircraft – if it was an airplane, the hovering and subsequent acceleration would have killed all aboard and resulted in a fiery crash.

Meteor – if it was a meteor that could stop and go, it would mean the meteor was under controlled navigation and meteors are just hunks of rock… that don’t blink.

Satellite – these objects move in a predetermined path, they do not hover, nor accelerate in other directions.

That leaves us with something from another world. They could have been scientists, observing mankind, or listening to Blue Oyster Cult’s (Don’t Fear) The Reaper on WROV 96.3 FM, Roanoke’s source for classic rock – The Rock Of Virginia!

But maybe they were just out and about. Maybe they were a lot like me, casual tourists in a very large universe.

The Day I Met Carl Sagan

Carl Sagan

I was born in 1963 and grew up on large doses of Apollo. Anything and everything that revolved around NASA, I consumed it with a hunger only a geek could produce. During the 70s my family lived in West Virginia and we would take these trips to various places in the state; Blackwater Falls, Dolly Sods, Pipestem – just about anyplace where we could hike, do a bit of fishing and pitch a tent.

On one such trip we took a wrong turn and happened upon the Green Bank Radio Observatory. My head exploded. I had no clue such a facility was in my home state.

There was a tour offered so we stopped in and took a short bus tour of the facility – the guide pointing out the frolicking deer, the softball field and the radio dishes as we went.

The last stop on the tour was in a little meeting room where we watched a short film and heard a presentation. The presenter, with a very distinctive voice, introduced a brand new film titled “The Power Of 10.” After the film, he gave us a short introduction to a program called SETI. If my young kid brain wasn’t blown by then it was blown now. I had never even considered that other civilizations could be using radio. At that period in my life I was an avid ham radio nerd and knew it was possible to pick up on interstellar signals. Only in ham radio, we called such signals “noise.” Whoever that guy was on the last stop of the tour gave me a lot to ponder.

A couple years later a new TV show about space titled “Cosmos” was announced and I was thrilled! Like the geek that I was, I actually had a notebook so I could take notes as the show went along. As the narration started I instantly knew the voice. Lo’ and behold, here was that same guy from Green Bank now on television telling us how Earth was the shore of the cosmic ocean.

So, I met Carl Sagan before he was “Carl Sagan.” I remember at the presentation he was enthusiastic and actually engaged with the tourists. Even then, his passion for teaching was memorable.

I really lucked out. I know this was not his day job. I am sure he was just at the observatory and couldn’t pass up a chance to give a new group of people a new insight to the stars.

Obituary Of Andrija Puharich

On January 4, 1995, the following death-notice appeared in the Winston Salem Journal


One of the three scientists ordered to leave the Surry County estate of Richard Joshua Reynolds died last night after suffering a heart attack and falling down a flight of steps.

Dr. Andrija Puharich, aged 76, fell about 7:15 p.m. Puharich was extremely frail and his health had been failing, said Susan Mandell, who took care of Puharich. Mandell said earlier that Puharich would not fight the magistrate’s eviction order, and that he was waiting for his social security check because he couldn’t afford to move.

The other scientists, Elizabeth Rauscher and William Van Bise, are fighting the eviction order, and said that Puharich had changed his mind and had filed to fight the eviction order.

The executor of the estate said that he had recently talked to Surry County Social Services to get Puharich involuntarily committed so he would get some medical help. “I knew he could not continue in that environment without first class medical attention.”

To the people who had known Andrija Puharich, the news of his death came as a shock. Many knew that his health had been failing, but few were aware that, in spite of his frail condition, he was fighting an eviction order. It had all started in June 1994 when Richard Joshua Reynolds died.

In 1980, Josh, as his friends called him, had invited Andrija to the estate to study the effects of electromagnetic field on brain waves.

However, when he died, he had not provided for Andrija in his will. The executor handling the sale of the estate had no alternative than to ask Andrija to vacate the premises. The date was set for September 15, 1994. Andrija was resolved to leave, sadly, but nevertheless with all intent. However, in July 1994, he collapsed and was hospitaised. Examination showed severe diabetes; kidney failure, related to the diabetes; anemia, secondary to the kidney function; high blood pressure; progressive dementia, due to the anemia and lack of blood supply to the brain.

He had sudden violent outbursts, pulled out IV’s and pulled off the telemetry patches. He also had a rash on his leg, a possible onset of gangrene.

The doctors advised Andrija to look for placement in a rest home, but he refused to even consider it. It was then decided to return him to the care of Susan Mandell, but to keep placement in a rest home in mind. On the day of his discharge Andrija was stable, talkative and in good spirits, but on the way home he suddenly developed generaised weakness and was re-hospitaised. A few days later he insisted again on leaving, and Susan signed him out.

If only he had not been so bull-headed he might still be alive.

Andrija Puharich was my former husband, and father of my two children, Yvonne and Andy. We knew that he was seriously ill, and that he had to leave the estate. We had therefore come from Holland – where we have lived since 1965 – for a possible last visit, and to help with the packing and moving. This had been four months ago, in September 1994.

Unfortunately at the last minute Andrija refused to go with Andy to upstate New York, where Andy had rented and furnished a small apartment for his father and Susan, not too far from Maritza, Andrija’s daughter.

It was a sad ending of a difficult, but also wonderful visit. It was a time of lovingness. Danica, also a daughter from Andrija’s first marriage had joined us, and in the evening we would all sit on the porch, enjoying the sound of the rushing stream some yards out in front, and the racket of the crickets. Andrija was like a child, loving every minute of our company. With a happy smile on his face he would look at each of us and say over and over again that we should do this more often. He thought it was Christmas, and he thanked me for getting the whole gang together. “You were always such a great organizer,” he said.

It was wonderful to see how, because of this happiness, his periods of lucidity became longer each day. We acted like the lovebirds we once were, holding hands and chatting away, to the delight of the children. They had never seen their parents that way.

And now, only four months later we are back in North Carolina for the interment.

We sit together quietly as we drive through the rugged countryside in the foothills of the Blue Ridge Mountains towards ‘Devotion’, the Reynold’s estate.

Glancing over my shoulder, I see Yvonne’s hand on the black plastic box that contains her father’s ashes. Her face is pale, her eyes large and dark. The same beautiful blue as her father’s used to be. What is she thinking?

So much has happened since we left the Netherlands three days ago. After the call that Andrija had fallen down the stairs and died, we had taken the next possible flight from Amsterdam to North Carolina. Because none of the other children could come we had taken it upon us to fulfill Andrija’s wish to be cremated.

I shudder as I remember the conversation with the gentleman from the funeral home. To perform an inexpensive cremation – there was no insurance, and no money – he would pick up Andrija’s body at Mt. Airy hospital in Dobson, bring it to Greensboro – the only crematorium for Surry County – and execute the cremation as soon as possible. Thinking of the way it is done in the Netherlands. I had asked if we could be anywhere close by to sit in prayer, and if we could see the body.

“I’m sorry,” he answered, “that’s not customary. Besides, we might do the cremation at night.”

“With nobody present, nobody to say goodbye to him?” I asked.

“I thought you wanted it as inexpensive as possible. If you want another kind of cremation…”

“No, but it sounds so cold and heartless. How will you bring Dr. Puharich to Greensboro?”

“In a body-bag, ma’am.”

I couldn’t believe what I heard.

Andy had handed me a tissue and put his arm around me, “papa taught us that the body is only a place where the soul lives temporarily”, he said, “it is not him in that bag, mama.”

I could tell by his voice that he too was shocked and in the eyes of Yvonne I saw the same.

“He also told us that the body is a temple for the soul. Even in the poorest part of India, they cremate their dead with respect,” I had whispered.

Seeing our distress, the gentleman promised to deliver Andrija’s ashes to the motel, so we could have a private ceremony.

Next to me, handsome in his dark suit, my son looks solemn. I know that he is thinking of how to conduct the ceremony, what to say. I would like to voice my feelings also, but I know that I won’t be able to. Instead I’ll read a last farewell that Phyllis Schlemmer, a long-time friend of Andrija, has given me. It is from Judith Skutch, another friend, and supporter of his work. Unable to come herself, she had faxed the message to Phyllis:

“Beloved teacher… it is with tremendous gratitude that I celebrate your life today. You will never know how profoundly you influenced my life. There must be thousands of others who can say the same thing. Go in peace and watch over us. With love. ”

Judith’ words reflect my own feelings. Andrija had been my teacher also, and he certainly influenced my life profoundly. Although we were together for only seven years, we had known each other for nearly forty.

I had just turned 26 when I met Andrija. I was a happy girl, very much in love with a wonderful boy, with whom I was to go to Holland to visit my parents, and afterwards to India. How differently everything had turned out.

Meeting him after he had just taken his mentally ill wife to a hospital, Andrija -then Dr. Puharich, to me – begged me to take care ‘temporarily’ of his three daughters. When we were “young and foolish” and fell in love, my life changed drastically. Instead of going with my friend to Holland, I became a full-time mother of three little girls, and later of a daughter and son of my own.

After we had signed the papers necessary for the release of Andrija’s body from the hospital the next day, we were surprised when asked if we wanted to see the deceased. Andy and I had said yes. but Yvonne did not feel up to it. The room we were taken to was nothing more than a storage room, a large closet where they, kept mops. pails, and other cleaning paraphernalia. The nursing supervisor, a nice lady, with a kind face and a soft compassionate voice, warned us that the body had not had any cosmetic treatment and was still as it was at the time of death. We nodded our understanding; glad that at least we were able to say goodbye. After she had put on surgical gloves, the supervisor opened a metal door in the corner of the room and pulled back the plastic shield that covered the body. Yvonne was right not to have come with us.

I wonder if I’ll ever be able to erase this last memory of Andrija. His forehead was bruised from the fall down the stairs and under the hairline a wound was visible. His lower denture was gone, receding his lower jar grotesquely. Yet he had a peaceful expression as if he were merely asleep. I kissed his forehead, whispered my thanks for the love we had shared and the children he gave me, and wished him God speed. We were numb with grieve.

Crossing the last of six wooden bridges that span the Mitchell River, we are on the driveway that leads to the big old house. Such sadness, the whole place.

Inside the same filth and stench as in September, with zillion cats scurrying away. I can still hear Andrija’s slippered feet shuffling towards the stairs. We had wondered how he still managed to get up and down, unaided and we had been afraid that one day he would slip.

Quickly I go outside to the porch where he used to sit by the hour, enjoying the sound of the rushing stream. I watch the people assembled talking to the reporter from The Charlotte Observer.

Phyllis, and Henry Belk, a businessman from North Carolina, are the only people I know. Israel Carmel is there too. He is a healer and Phyllis’ husband. Another medium, like Phyllis, is Mary Myer. She has brought a portable cassette player and a bouquet of red roses. Joseph, her husband is an engineer and a psychical researcher. Also Elizabeth Rauscher, the other scientist who faces eviction, is present. We are waiting for Susan.

Off to the side I spot Kenneth, the caretaker of the estate. He is a big, burly, bearded man with the kindest eyes I have ever seen. When I had first met him in September, he wore a cowboy hat and, what looked like a shark-tooth necklace on his hairy chest. He carried a knife and a gun, “to protect me from snakes,” he said. He was at the time with his little daughter, and his tenderness towards her, belied his stern exterior. He and his wife had come to love and respect Andrija.

I touch the small gold wedding band on my right hand ring finger. Not wanting it any longer, I had given it to Yvonne many years ago. “Maybe you want to wear it today,” my thoughtful daughter had said.

When Susan appears, Andy asks us to follow him to the bridge for the scattering of the ashes ceremony. He is hugging a white porcelain urn close to his heart.

“I welcome you all on this sad day to say goodbye to a man who has meant a great deal to each and everyone of us at one point or other during his life on planet Earth. I thank you for coming. Some of my dad’s friends couldn’t be here today, but they have faxed their good-byes. May I ask you to read them, and your own farewells, out loud, please.”

While in the background the music softly plays, I listen to the words of love, admiration, and gratitude for Andrija’s “pioneering spirit; his courage to tread new paths and open new doors through which he guided others with kindness, generosity and humor.”

Although my voice quivers and tears make my vision blurry, I manage to read Judith’ message, adding a few words of love of my own.

When all the good-byes are spoken, we stand in a circle and hold hands. Only the sound of flowing water overruns the silence. My daughter’s hand feels icy, as must mine feel in hers, and we tighten our grip.

After Andy has given us a chance to touch the urn, or the ashes, as most of us do, he tips the urn over the railing of the bridge. “Goodbye daddy,” he whispers, “have a save journey to the other side.”

One by one we drop a red rose into the churning water of the Mitchell River and watch them float away. When everybody leaves, we remain behind for a last farewell of our own. A white patch in the river marks the end of an era,” as Elizabeth Rauscher had poignantly stated.

Back at the motel the topic of conversation is of course Andrija.

“Such a remarkable man.“’ I hear Phyllis say. “It was a joy working with him. I have just rewritten my, book The Only Planet Of Choice. I feel that Andrija as the founder of the original group that worked with the Council of Nine should be in it too.”

Many years ago I had beard about “The Nine” from Andy, who or what they were I had no idea.

With mischievous eyes and his typical southern drawl, Henry Belk remembers the “fun” he had with Andrija. “All those wonderful things we did together forty years ago. Do you remember Peter Hurkos?” he asks me. ‘I brought him to the United States to be studied by André.”

“Sure, I remember!’ ” I wonder if he ever knew how angry I used to be with him when Andrija, on more than one occasion had stayed away most of the night giving demonstrations with the psychic Hurkos in order to get financial support for his research from Henry’s friends.

Listening to the people talk about Andrija, I reaise that I hardly know anything about the work he did for the past twenty years. For a long time after I had left I maintained an interest in his work, but in 1974, I got fed up with him. This was undoubtedly also the reason why his three daughters were not present today. Asked about this by the reporter, who had read somewhere that Dr. Puharich had six children, I had excused their absence as being due to out of state residence, work and family commitments. Besides, I told her, they knew that their father was seriously ill and said goodbye when they visited him in July and September of 1994.

All, except one, I reflect, and I wonder how old Athena now is. Is she fifteen or sixteen? She is Andrija’s youngest daughter from his fourth marriage. Maybe she doesn’t even know that her father died. I hope that one day she’ll believe that he did love her very much, as he did all his children.

Although I too had felt unloved often enough, I always tried to convince them that they were wrong. Socrates, Ghandi, Martin Luther King, and many other great minds weren’t the best of husbands and fathers either. Were they incapable of love?

I remember Andrija telling somebody that the happiest time of his life with me had been when we were together in his study, both reading and studying while his three little girls were safe and snug in their beds. Another time, we had five children by then, he said that when he was away he missed us achingly, but while at home he took us for granted. Many years later he asked me why I had always been so angry with him and why I had left him? He really didn’t know.

To my surprise I hear somebody say: “Andrija was such a spiritual man.

“He must be kidding! Andrija was fascinating and exciting. “Never a dull moment with Puharich,” as a friend of us used to say, but spiritual? To me a spiritual person has overcome the desire for worldly goods or acclaim. The Andrija I knew certainly did not fit that bill. He must have spirituaised later.

“Are you all right, Bep? You’re so quiet”

“I’m sorry, Phyllis. I was thinking of the past.”

“The death of a loved one usually brings that on. I hope you’ll also remember the good things you shared. Andrija was not an easy person to live with. Especially for the women in his life he was difficult. How are his daughters taking the death of their father?”

“I don’t know, I haven’t spoken to them about it.”

‘When are you flying back home?”

“On the twenty-second of January. I’ll spend some time with Maritza and my grandchildren first. Andy, Yvonne and I are driving to New York tomorrow.”

“Please say hello to Maritza.”

“I will.”

‘Well, I’m afraid we have to leave. It was wonderful of you and your beautiful children to have come.”

“Nice seeing you again, Phyllis. Thank you for contacting Andrija’s old friends.”

“You’re welcome, dear. It was the least I could do.”

Later that evening I asked Andy to enlighten me on the “Council of Nine.”

“It’s a long story,” he answered, “but to put it in a nutshell, it’s a circle of universal beings living outside time and space.”

“Oh!” And Phyllis is the medium through which these beings speak` “Don’t sound so skeptical, mama. Phyllis has convinced many scientists that she is a genuine medium.”

“I’m sure she is, but I’m a bit confused. I didn’t reaise that the Nine also have to do with outer-space stuff. Uri Geller was also a medium, wasn’t he?”

“Yes, sort of. An extra-terrestrial, called Hoova spoke through him. They all work towards the same goal.”

‘What goal?”

“To warn us that the earth is in deep shit and about to destroy itself. Have you ever read Uri?”

“I tried to, but it was too much hocus pocus for me. Maybe I’ll try again.”

“You should. By the way, you still have ‘Briefing For the Landing on Planet Earth’ I lent you. Read that too. It’s a very good book, written by an objective observer of the channeling sessions.”

“The what?”

“The sessions when Phyllis is in trance.”

“There’s so much I don’t know! Are you familiar with the Nine, Yvon?”

“Not really, but I hope to be soon. Phyllis has asked me to translate her book. Apparently a Dutch publisher has shown an interest.”

“How wonderful! Just the thing you said you’d like to do, being involved with daddy’s work. Maybe…”

“Hey you guys!” Andy interrupted, “I don’t know about you, but I’m ready for a beer, and some television.”

“One more question and then I’ll leave you two. When you were fourteen, Andy, you told me that you were a space-kid. What did you mean by that?”

“That any minute now my eyes will turn green. Next my antenna will pop out of my head, and I’ll beam you to your room. I’ll tell you another time, mama. Goodnight!”

That night I lay awake long. Could it be true that Andrija had been in contact with space intelligence? Who was this “Maverick,” as he used to call himself?

Was he, to quote Aldous Huxley: “One of the most brilliant minds in parapsychology”? Or had he been a man who was easily misguided by so-called psychics, a man who told tales, or had he been crazy? During my short marriage to him I had often accused him of being too gullible, too naive. I had admired his brilliant mind, and begged him to use it for research that would benefit mankind. For a while he did, when he and a friend worked on a hearing aid that would give sound a new route to the brain – through the teeth and facial nerves. The device, for which a patent was granted, would eventually consist of a miniature microphone and transmitter, to be worn on the wrist, or carried in a pocket, and a miniature receiver to be installed in a hollow false tooth. Through contact with nerve ends in a live tooth next to the false one, electric signals would be transmitted via the dental and facial nerves to the brain. How proud I had been when Andrija told me jubilantly that they had made a deaf person hear. All they had to do from there on was to bring the complex equipment down to portable size.

He had stumbled upon the possibility of nerve conduction as a means of helping the deaf, by accident. When he and his friend Joe Lawrence were both captains at the Army Chemical Center in Edgewood, Md., (Andrija in the Medical Corps and Joe in the Dental Corps) Andrija treated a boy who suffered from hearing voices in his head. When he learned that the boy was a cutter, and that he worked with carborundum stones, he had Joe replace the fillings in his teeth.

His assumption, that if carborundum dust came into contact with amalgam fillings the tooth would operate as a radio receiver, had been correct. The voices in the boy’s head stopped.

Too bad Andrija had not pursued the research. It may have given him the recognition he later on in life felt was withheld from him.

After we had returned to the Netherlands, we received the obituary that a friend of Andrija’s had sent to the N.Y. Times Newspaper and Time Magazine.

She had also faxed it to newspapers in London. Reykjavik. Philadelphia, Miami, Chicago and Los Angels: DIED, ANDRIJA PUHARICH, M.D. LLD. 76 – internationally acclaimed American scientist, inventor, researcher, physicist, theorist, and author – of heart failure, in North Carolina. Editor of “THE ICELAND PAPERS” (Select Papers on Experimental and Theoretical Research on the Physics of Consciousness) 1979.

Dr. Puharich was a leader in the field of psychical research, merging quantum mechanics and relativity into a new scientific world-view to examine the way in which brain/mind function gives rise to a focused consciousness.

Member of many scientific societies and recipient of numerous awards and honors, Dr. Puharich’s many friends and colleagues knew him as a true Renaissance Man. Six children and three grandchildren survive him.

To write an obituary about Andrija must have been difficult. What to put in? He had done so many things. In addition to The Iceland Papers and Uri he wrote The Sacred Mushroom, 1959,and Beyond Telepathy, 1962, both published by Double day & Company, and both reissued in 1974 by Doubleday in paperback editions. He also collaborated on a book by John G. Fuller, Arigo, Surgeon of the Rusty Knife, and published over fifty papers and articles in scientific and professional journals.

Integrating Urban Air Mobility Into Current Infrastructure

City planners have been pushing back on the idea of VTOL, air taxies and urban air mobility in general. There is a general feeling of fear when this new, and destined technology is discussed. 

Over the next 30 years, aviation will change in more fundamental ways than it has since Kitty Hawk. That sounds like a radical statement, but it is true when you consider the impact of new aerospace technologies that are currently being worked on.

Current aviation transportation technologies are all based on fossil fuels and hasn’t seen movement since the development of the jet engine. There are two basic types of aviation fuels – Jet A and Avgas. Jet A is like a highly filtered form of kerosene with various additives, usually to prevent icing. Avgas is leaded gasoline, 100LL being the most common. Even though the “LL” stands for low-lead” it is still heavily leaded.

The future is electrically-powered aircraft, but until the energy density of batteries compare to that of fossil fuels, that future may be far off. Battery powered cars are a lot easier to engineer because the car is always resting on the ground, an aircraft must pull itself, and it’s passengers, and cargo up to operational altitude, transit the distance to the destination, land and still have a 45 minute safety reserve as required by the FAA. There will need to be a breathtaking breakthrough in battery tech before it becomes feasible for use in general aviation.

For aviation, the answer might not be batteries at all. Capacitors are rapidly increasing their energy density when compared to lithium ion. “Super-capacitors” have a lot of benefits over lithium-ion batteries, chiefly rapid charging. They also feature longer lifecycles, their manufacture is more environmentally friendly and theoretically they would be cheaper. That said, they will be probably be seen in automotive use cases before they would appear in aircraft.

A great stop-gap to electrify the current aircraft fleet is hydrogen fuel cells. The technology already exists for use in aircraft. You only need a hydrogen tank, fuel cell and electric motor. The typical aircraft would shed pounds, gain useful load and have a much more extended range due to hydrogen having more energy density than fossil fuels.

Naysayers and Prophets of Doom™ rally against automation in all of its forms. There is no way around the simple logical conclusion that automation will continue to grow until all human toil is eliminated. White collar and blue collar jobs will be changed in ways we cannot currently fathom. Automation will touch every single part of human society and culture; emergency services, transportation and logistics will be the first to feel these effects. Call centers for emergency services can be greatly augmented by the use of AI. Autonomous aviation is an easier problem to solve than automated driving. 

With automobiles, the hazards are mind-bendingly numerous – pedestrians, animals, other cars, drunk drivers, drivers that are texting, drivers that are running red lights – essentially other drivers. Aviation has had a set of well-behaved rules and procedures for operation of aircraft in a complex, shared airspace. And on top of that, there is a robust training program and many levels of certifications and endorsements to access that airspace. So it is a no-brainer that aircraft will probably achieve level 5 automation before ground transportation will. 

Aviation has been at Level 3 since the 50s with radio navigation and autopilot. I remember a pilot, from the 1970s, that would fly his Beechcraft Bonanza cross country using VOR as a navigation guide. He would tune his radios to fly toward a VOR navigation station and then set the autopilot. He would then SLEEP until he got to the VOR. When the Bonanza would fly over the VOR, the autopilot would rock the wings of the aircraft in an attempt to stay on the VOR radial. The closer to the VOR, the more the wings would rock and at some point he would wake up and reset the autopilot for another VOR and back to sleep he would go. And yes, this was illegal and wholly ill-advised, but yet he had the tools to do it.

The FAA has already issued rules for the certification of drone pilots (FAR Part 107) and I feel logistics will be the first part of the aviation industry to be automated. In 2013, Amazon CEO, Jeff Bezos, declared his intentions to design, build and deploy a drone delivery program for the internet giant. UPS, FedEx and DHL have all shown signs of interest in autonomous logistics but I am sure their interest is on a much larger scale than the home delivery functionality Amazon is focused on.

Autonomous passenger flight is a much more problematic issue. Uber seems to be leading the way in land-based urban mobility for passenger service. They have a program in Pennsylvania experimenting with self-driving cars and just last year Uber announced their “elevate” plans for flying cars. Insuring passenger safety during automated flights is the FAA’s primary function. Will Part 135 be greatly changed or will a new regulation part be published to handle all the facets of autonomous flight? Time and technology will tell.

Civil Engineering
As the FAA weighs and ponders autonomous flight and how it will integrate with the current airspace system, municipalities are wondering how all this will fit with their current infrastructure. Some plans I have seen range from building rooftops airports (Roofports? Skyports?) to complex and expensive infrastructure solutions that included purpose-built terminals and waystations. The key to a successful implementation of urban mobility will require inexpensive and non-invasive solutions. With any journey, the last 5% of the journey to the destination can be the most expensive and difficult to implement. 

Applying first principles to the problem can yield some pretty simple solutions. 

The cheapest and most most easily adaptable idea is to use traffic circles (or roundabouts if you are not in the US) for VTOL landing pads. Traffic circles are already in place all around the country, usually in neighborhoods and where none exist, common intersections can easily converted to a traffic circle with an integrated VTOL landing pad in the middle. (see featured image above).

Autonomous VTOL air taxis and manned VTOL aircraft can utilize these pads placed in neighborhoods. VTOL ambulances can access patients much more quickly than if they have to use trucks trying to navigate road traffic. Trips to and from a local airport for a commercial flight will be much more manageable with a VTOL trip from the airport to within a block or two from your home.

Autonomous transportation is coming and there is nothing we can do to stop it. Within 30 years, the use of our national airspace will be unrecognizable when compared to what it is today. But fear shouldn’t win out, we can make these changes inexpensively, improve the quality of life for everyone, clean up the environment and push humanity forwarded. And that is always a good thing.

Crossposted from StormBear.Tumblr.Com.