Our Mathematical Brains

Most of us are aware of the golden ratio, approximately 1.618. A rectangle whose larger side has such a ratio with its smaller size is called a golden rectange. A 5 x 8 picture frame comes close.

This ratio is related to the Fibonacci sequence 1,1,2,3,5,8,. . . where each number is obtained by adding the previous two. The ratios of two adjacent numbers approach the golden ratio, and these numbers are often found in nature.

Now one can find two ratios of  lengths between special points in the human skull are both 1.6.
These special points on the cranium  correspond with important underlying neural structures and junctions in both humans and other animals.


Our brains are even more complex than we imagined and advanced mathematics is being employed to understand what’s going on in that fabulous three pounds of matter. Scientists have long known our skulls contain billions of neurons and that thinking and experiencing involve synapses between them. Now they are finding it useful to study cliques of neurons that interact with each other. A neuron can belong to more than one clique. Imagine for each clique, a neuron is represented by a dot on a sheet of paper and if one neuron can transmit to another, draw an arrow. Such a picture is called a graph and there is an area of mathematics called graph theory, which is a subset of algebraic topology, an area of advanced mathematics. Brain researchers are finding it useful to try to understand the ways our minds work by using this mathematics to study the connections in these cliques. The article that alerted me to this use of algebraic topology made the strange claim that our brains contain structures only realized in eleven dimensions. Thinking of the physicists theory that space may be eleven dimensional and algebraic topology is useful in trying to determine the shape of the universe, I was fascinated. However, digging deeper into the source of the article there seems to be inconsistency on the definition of dimension. In one case it refers to it as the number of neurons in the clique, but then cliques with larger numbers of neurons are discussed so I am confused, but as a retired mathematician, I am always delighted that highly theoretical mathematics turns out to be useful in understanding the world we live in.


Curious Scientific Discoveries

A cure for the common cold may be on the horizon. Medical science has discovered a protein without which the cold virus cannot spread. We’ve always heard that the cure is so difficult because the cold is not a single virus but many different ones even though the miserable symptoms are much the same. By gene editing mice to stop producing the protein. It worked on many viruses including polio, and the mice led healthy lives without the protein. Of course, humans will not undergo gene editing, but scientists plan to work on inventing a drug that will suppress the protein.

There is also a bit of optimism for progress on the more serious disease of Alzheimer’s that affects so many in later years. This time the study was done on human patients, albeit on a very small sample of eight people. The subjects wore a cap twice daily for an hour that emitted electromagnetic waves, and in two months they reversed a year of memory loss. They pleaded to keep the caps after the trial was over. There were no negative side effects. Somehow, the waves break up the amyloid-beta and tau proteins, which clutter brains and are linked with Alzheimer’s.

In a how-did- they ever- think- of-it study, Australian researchers have discovered that a rare weird pink seaweed that when added to cattle feed in very small amounts prevents the bloaters from emitting methane. Unfortunately, the seaweed is rare in nature, but they are working on ways to mass produce it for Australian farmers and perhaps globally. This would be a significant help reducing greenhouse gases although it would not help with the increasing amount of forest that is lost to production of cattle.



My Favorite Kinds of Environmental Actions  


With Earth’s growing population and finite resources, all of us should be concerned about maintaining the livability of our home planet. However, there is evidence that people who have to struggle daily to put food on the table and live where clean water cannot be taken for granted have little time and ways to contribute. It is difficult to think of concern for Earth’s future as a luxury. Some organizations have found means to address both poverty and the environment.

I was amazed at the Nature Conservancy’s Fall 2019 magazine’s descriptions of projects they are undertaking. They are inventive and long lasting. They’ve been known for buying land for parks and wildlife preserves, but they do much more.

The city of Nairobi only has access to 70% of the water that its residents need. Their water comes from the Tana River, and runoff from the hillside farms along the river make filtering and purifying the water difficult and expensive. The Nature Conservancy (TNC) established a water fund, which helped farmers plant thickets of bamboo along the banks of streams that flow into the Tana, which traps the silt. The fund  also paid for 70% of the cost for water pans farmers could install at the tops of their hills that trapped water during heavy rains for use for irrigation during the dry season. Farmers benefited by being able to raise garden vegetables, which garner higher prices at that time of year. Win-win.

Another of TNC’s projects is called Blue Bonds for Conservation. It involves buying back sovereign debt at a discount and restructuring the debt to save countries money. In return the countries pledge to use at least 30% of their savings on protecting the countries’ marine waters. Seychelles was the first project.  Another win-win.

A third project involves rebuilding a reef near Adelaide, Australia. Overfishing had wiped out a once thriving home for marine life. Oysters filter water, which once made the area desirable for fish. Along with a team of marine biologists TNC replanted oysters on 50 acres and one year into the project, native species are returning to the reef. If this continues, sustainable fishing can boost the local economy.

It appears if we take care of the earth, it will take care of us.

Scientific Progress Raises Ethical Questions

This is not new, but I was provoked by recent positions by advice columnists regarding people deserving to know if they have a half sibling. In the case in question, I read about a person who discovered one set of cousins had a half sibling from DNA testing. The columnist opined that the cousins deserved to know. I’ve had my DNA tested twice. One service identified the countries of origin of my ancestors and health characteristics of people who have similar genes. The other merely identified people I was related to in their database. I know there have been happy reunion stories, but the reunions were instigated by the discoverer. I am bothered by the privacy rights of parents and the pain that revealing family secrets may cause. At minimum, DNA services should request permission to share relationships. In my case I learned of some potential fourth cousins, which was of no interest to me, but I was fascinated to learn my German background came from a part of Germany that was also French.

Many ethics issues are related to medical science such as gene editing to ensure the health of the baby. But this capability could mean designer babies for looks, intelligence, and athletic ability.

Other medical discoveries may lead to cures of diseases that plague humans, but come at enormous cost. Can society afford to spend millions per year for every sufferer or will it become another advantage for the wealthy? In our current health care system, we spend disproportionately on the ends of life while young people die for inability to pay for health care.

Scientists are the first to say that they are not the ones to dictate how their discoveries are used and that discussions are needed by the general public. I wish more such conversations were taking place.



A New Crater Lake?


I’ve had the pleasure of peacefully sitting in a deck chair overlooking the placid blue crater lake in Oregon. I’ve also viewed the spectacular red-hot lava pool deep in Halema‘uma‘u from the summit of Kilauea on the big island of Hawaii. Both are marvels of nature.

A New York Times article suggests a new crater lake may be forming. In May of 2018, Kilauea’s  volcano violently erupted, and the lava pool at the bottom, which had been there for ten years began to drain. Within a week it disappeared. Now three small green pools appear to be growing. Scientists don’t believe it is rainwater, because it is 167 feet below the water table and suspect it’s water seeping in from the sides and bottom of the deep cavern. Unfortunately, fumeroles in the crater make it too hot to get near the bottom of the crater. Scooping some up via helicopter would be tricky, but that’s likely the only way they can test the water to be certain.

It would be neat to replicate Oregon’s crater lake, but scientists believe that if formed it will likely not be permanent as the magma underneath will build up again.


Footnote to my last blog: Now scientists believe they’ve found evidence that a tsunami once occurred on Mars.

Our Fascination with Mars

If you haven’t seen news of the recent anniversary of the first man on the moon,you’ve probably been in inensive care. I watched the story of the moon landing on PBS. It was good to review the history of years condensed into a few programs. It was clear that Mars was deemed the next  goal. NASA and the Soviets sent unmanned rockets into space to explore several planets and their moons besides Mars over the years. Such missions almost became routine.

Science fiction creatures from outer space seem inevitably to be Martians. Loss of life probably made NASA more cautious about humans landing on Mars, but the idea lingers. National Geographic ran an excellent series called Mars—a mix of a suspenseful fictional story with a history of efforts to explore Mars. Andy Weir’s novel, The Martian was so popular it was made into a movie. Both the National Geographic series and The Martian gave me a real sense of what the planet must look like.

Elon Musk sent a Tesla roadster to Mars in February 2018. It makes sense since there probably aren’t any gas stations there.

Despite all of what has been said about Mars, I was surprised to watch a Nova program on Mars and learn that scientists think that 4 billion years ago, Mars had tons of water: basins, flowing rivers, a magnificent waterfall, and possibly an ocean. Numerous landings sent back information on the shape of the terrain and the nature of the soil and rocks, providing evidence for water having been there. In fact, it appears that Earth, Mars, and other planets were similarly formed and were much alike originally. Only Earth retained its oceans.

So, what happened to the water on Mars? It turns out that Mars has a thin atmosphere, and is smaller, meaning weaker gravity and magnetic field determined by the size of its  core. Earth’s gravity and magnetic field keep our molecules close to Earth, but Maven, which has orbited Mars in an elliptical orbit so that it varies between 150-6,000 kilometers from Mars, measures the number of molecules in Mars’s atmosphere. It loses two to three kilograms per second.  The water has escaped over time.

If early conditions did match those of Earth, scientists wonder if life also began on Mars. They hope to find out.

An easy way to combat climate change and other fascinating science news

* In general people avoid talking about politics, but it’s only recently that climate change has been considered a hot political potato. It may be in Congress, but studies show that 70% of Americans accept the reality of climate change, and discussion increases awareness among the general public. A Yale social psychologist says such discussion is massively important in increasing awareness, and in turn awareness is critical in getting preventive action. One can begin with talking about the need to keep our air and water free of pollution. Who can disagree with that? Then there’s the tendency to give our friends and some relatives credit for being truthful.

* Artificial intelligence is getting smarter.  Gizmodo taught itself how to solve Rubik’s cube without help from a human, and in fact seems to have discovered a most efficient way given the few number of moves. I am curious about what is meant by no help from a human. I’d like to see the starting directions.  I loved Rubik’s cube and used mathematics to find a solution. I never became a whiz kid. It took me too long to figure out where I wanted what, but it provided a wonderful example for teaching my math classes.

* In addition to the five senses: seeing, hearing, feeling, smelling, and tasting, some scientists call our awareness of particular body parts a sixth sense—not to be confused with extrasensory perception. At the end of my yoga program lying in samadhi pose I am told to relax my toes, my lower legs, on up to my face. There is no movement, only awareness of that body part. Now neuroscientists believe they’ve located the neurons responsible for that sixth sense by studying fruit flies. Coincidentally, a collection of six neurons act together.

*Einstein called something called quantum entanglement “spooky action at a distance.” It is a pair of particles that share experience and state so that what happens to one happens to the other no matter how far apart they are. Further the matching is instantaneous seemingly defying the speed of light as the upper limit if one particle were sending a message to the other. Spooky, indeed. Now scientists claim to have a picture of a pair of entangled particles. Click here.