By the Numbers

    Math has always fascinated me, even if I don't quite "get it" at times.  But one only has to glance at the spans of a bridge or the straight lines of a building to recognize that there must be something to angles and lines and such.  So when I saw a book titled Instant Science with wording underneath saying "explained on a single page," well, I was hooked.   And then I opened it and...yikes!  Perhaps I should start with the author's background which is casually mentioned as: ...a background in physics. Her PhD research explores physical phenomena through craft, including weaving biomedical data, Fourier transforming through weaving, and the co-design and making of MRI and CT phantoms with scientists.  What???   But the cover of the book featured something I had heard about over and over but basically didn't know what it was...The Fibonacci Sequence (& the Golden Ratio it leads to).  What the heck was that??*

    The book itself was actually quite interesting, one which allowed you to pick and choose the areas you perhaps wanted to discover or review (or skip), from technology and geology, to chemistry and biology...and of course, math.  But wait!  Before you decide that this doesn't interest you, author Jennifer Crouch began her book by explaining how we number things...clocks and computers, checkbooks and calendars, our everyday world.  Seems easy, right, the basic 1,2,3 counting system we all learned?  Except it turns out that our classic numbering system is just one of many systems that exist, with some of them going back 6000 years.  A quick primer: the Sumerians and Babylonians based their system on 60 (think our clocks and geographic coordinates), while the Mayans used a "base 20" system (think of our decimal system of .25 and 25%); you likely know the Roman numeral system of Xs and Vs but you can thank Brahmagupta (an Arab from the 6th century BC) and Aryabhata (a Hindu from the 5th century BC) who co-created our current system of numbering that uses the common 1,2,3 mode.  Computers don't use that system but rather a "base 8" system, which sometimes doubles to 16 (bit); there's also a "base 12" system (this can be seen in our inches, feet and hours).  And then there's the "base 2" binary coding system of 0s and 1s, something you've likely seen as computers spit out endless streams of what seems numeric gibberish, a system which she "simply" explains as 0 = zero, 1 = one, 10 = two, 11 = three, 100 = four, 101 = five, 110 = six, 111 = seven...and 1000 = eight.  Puzzled yet?  I certainly was, especially as she calmly notes that one should "notice that at the number 8, the 0's reset...what??.  And those are her opening pages (this binary system was what was sent out on Voyager for other possible alien species to learn about us humans here on Earth...in 1976, no less).  

    I bring this up because let's face it, we're blitzed by numbers: the rising number of people infected with the virus, the growing deficits, the amount in stimulus checks, the increased defense budgets, fluctuating gas prices.  And for at least another month or so, we'll be told to both trust or not trust "the science."  But author Crouch put down her views in a brainy yet casual way: Science is difficult to do.  In practice, it is full of tricky technological challenges, experiments failing, cell cultures dying, magnet cooling systems exploding, and things generally going wrong.  It's complex, fiddly, and confusing at the best times.  In fact, much of the history of science is buried away in its failures but these...are important to acknowledge, rather than perceive of science as a series of seamless, glorious, paradigm-shifting innovations and discoveries.  Much toil goes into creating our descriptions of nature.  In addition to this, the personal challenges encountered by individuals and groups who have been discriminated against and experienced racism, homophobia, sexism, classism, and bullying in these social, albeit scientific spaces must continue to be confronted...Science is powerful and affects us all, from the internet, to the weaponization of science in warfare, to green energy, architecture, engineering, and developments in medicine and surgery.  We all have a stake in it and a right to understand the wonderful things it tells us about our universe so that we can think about and question who it benefits, who it harms, and how it is being used here on Earth.  Wow, sort of throws the whole vaccine thing into perspective...

    If you're somehow still reading and perhaps dreading that I'm about to lead you into some astronomical black hole of math, well, rest easy.  For one, I enjoyed math but was little more than just an average student of it.  In other words, forget any mention of calculus or explaining the uses of "pi" (indeed, my lack of knowing Fibonacci should have been a big hint).  But still, it's one of those background subjects that we all have hidden in some dream life, that of wanting to be a doctor or a star athlete, a humanitarian or an Avenger.  Watching some of these rock stars gaze at tens of thousands of fans gyrating like human waves to their singing is puzzling to me; and yet throw me into that crowd and there I am, bouncing with the best of them.  These are all things that we harbor, perhaps more so as we "hibernate" in our homes and try our best to stay healthy.  With these changing times, one can only be grateful for those who are indeed actual scientists who are using their talents to study our planet and our lives and bodies, as well as those who study all the things we cannot see coming from deep space or microscopic whatevers floating in our bloodstreams (who else would think that there were such things as solar radiation or a variety of light and sound spectrums?).  Consider all of this captured in the field of epistemology, which Oxford Languages defines as: ...the theory of knowledge, especially with regard to its methods, validity, and scope.  Epistemology is the investigation of what distinguishes justified belief from opinion.

   Part of this questioning also emerged from a short piece I read in Popular Mechanics that asked if 2+2 really equals 4?  The article questioned our "learning" numbers in a set way, saying: In general, the idea that we innately learn counting numbers --whole values only, no fractions or decimals-- is a common misconception among people who aren't trained in math or human development.  Young children learn numbers one at a time, by counting, but only begin to learn more sophisticated counting --higher numbers-- once they can recognize quantities quickly, an ability called subitizing (I should note that subitizing is now taught in kindergarten)...Counting is an unnatural, learned skill.  Think of how we "rate" things, the piece asks, the standard "on a scale of 1 to 10" pain question a doctor might ask.  It's hard to rate your feelings when they change so much, or when the minimum of maximum of the scale --is your pain level really a 10, as bad as it could possibly be?-- isn't easily conceived by our experience..."There are a lot of people who seek out math and statistics for a sense of certainty: 'This is the answer,' " he (Kareem Carr, a biostatistician Ph. D. student at Harvard) says.  "And there are people who close their minds.  I'm more on the other side: Is there something else I could discover in this complex of ideas?

    What is everything made of?  Why do the stars disappear during the day? asked the book by Eric Weiner, The Socrates Express: These sort of questions didn't interest Socrates.  They were unanswerable, he thought, and in the end, unimportant..."Every question is a cry to understand the world," said the cosmologist Carl Sagan.  Socrates would agree, up to a point.  Every question is a cry to understand ourselves.  Socrates was interested in "how" questions.  How can I lead a happier, more meaningful life?  How can I practice justice?  How can I know myself?  Socrates couldn't fathom why his fellow Athenians weren't more interested in these kinds of questions, given their zest for improvement, be it a better way of making statues or practicing democracy.  Athenians, it seemed to Socrates, worked tirelessly to improve everything -- except themselves.  That needed to change...

    Amidst our world of rapid change (the new Covid-19 coronavirus is mutating faster than expected), some surprising stories are emerging, one being that of something mentioned in the last post, that of hearing too many numbers, and too many people infected, and too many people dying, and the growing realization that we're shutting it all out.  Except, new studies are showing yet another side to this behavior, at least here in the U.S.  Author Olga Khazan had this subtitle to her article in The Atlantic: One giant psychology experiment explains why many people seem like they don’t care about the deaths of the elderly.  Wait, that's me!  She went on: As I wrote in April, “compassion fade” sets in when victims are no longer individuals but statistics, and few Americans have witnessed something of this scale before.  But there’s an additional explanation for this empathy deficit: Part of the reason this majority-white, majority-non-elderly country has been so blasé about COVID-19 deaths is that mostly Black people and old people are dying.  Eight out of 10 American COVID-19 deaths have been among people older than 65; the rest of the dead are disproportionately Black...Discrimination against the old is perplexing, because age will ultimately catch us all.  Though no white person will ever be a Black person, every person, if all goes well, will get old.  But several studies that forced people to imagine life-and-death decisions hint at how little society values the elderly.  

    The Covid-19 virus just passed its one-year anniversary, said STAT, and now it's out in the wild, said National Geographic.  But back to Socrates, what would he be thinking?  Ponder this from Bloomberg's New Economy Forum: Now, as the first vaccines become available, there’s a chance to salvage what’s left of multilateral cooperation.  A crucial test will be raising funds for a collaborative effort, overseen by the the WHO, to procure tests, therapies and vaccines to fight Covid-19 in the world’s least developed countries...Without the funds, the pandemic will rage on in the world’s poorest countries for years, pooling in reservoirs among unvaccinated populations to one day trigger a new pandemic.  The humanitarian case for giving could hardly be clearer: Underdeveloped countries, through no fault of their own, have been overwhelmed by a pandemic that emerged from the natural world, one which the International Monetary Fund warns could “wipe out a decade of progress reducing poverty.” --  The so-called “Access to Covid-19 Tools (ACT) Accelerator” initiative needs $38 billion.  After a global appeal, it remains short by $28.2 billion.

     The New York Review had a series of blistering reactions to all that was happening here in the U.S., the elections and the pandemic among them; the established writers were from all over the world and brought with them a variety of viewpoints.  But it was Mark Lilia who summed up his op-ed in this fashion: What demons are at work here?  You don't know.  But at least you know you don't know.  That's a start.  That's where doctors begin when trying to diagnose patients with bizarre symptoms that may indicate a fatal disease.  They distrust theories and try to see what they see.  They go slow and keep their wits about them.  That is your most precious possession right now: your wits.  Try not to lose them.  Such words made me think of Rudyard Kipling whose famous poem IF began with this: If you can keep your head when all about you are losing theirs and blaming it on you; If you can trust yourself when all men doubt you, but make allowance for their doubting too.  Added another line: If you can bear to hear the truth you’ve spoken...

    I took heart in reading about Jack Griffin who asked this while still in high school: In March of 2013, I sat down in the family room of my home in Georgia to watch 60 Minutes one night before school (like all the cool kids do).  One of their segments was called Hard Times Generation, and it showed how the economy’s recovery from the financial crisis left the most disadvantaged people behind.  At the story’s center were Arielle and Austin.  They were children who, along with their father, were homeless and lived out of a truck in central Florida.  The father worked as a carpenter but lost his job during the housing crash, and medical bills for their late mother cost them and their family everything.  As I watched the story, I realized that I never had to worry about where my next meal came from or where I went to sleep. Despite their circumstances, Arielle and Austin still went to school, just like me.  Unlike me, they got ready for school in the bathrooms of libraries and gas stations.  Like me, they got breakfast and lunch at school.  Unlike me, all of their food outside of school came from a can with no way to heat it up.  Arielle was 15.  Austin was 13.  I was 14 at the time.  Seeing their struggles lit a fire under me.  It made me want to help kids like that in my community, especially in providing the meals they didn’t have waiting for them after school. I  did a simple online search to try and find places that I could volunteer at or donate to, but then I discovered something—Google is a lot better at pointing you to restaurants than it is to food pantries.  My search was much harder than I expected.  I asked myself, “If I’m having this much trouble finding a place to go as someone wanting to volunteer, what if I was someone who needed the food being offered there?”  The story from The Renewal Project tells of Jack starting FoodFinder while in high school, something he continued all through his college years and continues to this day (his site now has data on over 45,000 free food distribution sites throughout the U.S.).

    By the end of Crouch's science book, I admit that 90% of it sailed over my head, despite such vivid descriptions as: The Mandelbrot set is famous for its hypnotic beauty...a result of complex numbers being used in functions within a defined boundary of the number 2.  Hmm, but I did learn that our universe is vast, as in light from beyond the edge of it will never --as in "not ever"-- reach us because it is too far away.  I also learned that matter (as in atoms and such that we can see) make up just 5% of what's out there, but another 27% is there but invisible and emits no light (called dark matter); but something even stronger is pushing all of this away and it is that which makes up 68% of the universe (and is known as dark energy).  But, and here's where it gets interesting, there are filaments of matter that appear to connect galaxies and form "the cosmic web."  And at the edge of the observable universe (at least for us here on Earth) lies "the cosmic horizon."  What faint light we pick up from just one distant galaxy (and this one is easy to remember, MCS0647-JD...got it?) is so far away from us that those stars we "see" are basically dead, their "fuel" long ago spent.  

Jocelyn Bell Burnell.  Photo: NPR

     Depressed yet?  But among these distant stars and galaxies are quasars and pulsars, said Crouch.  If they happen to be pointing in our direction, we can pick up their steady bursts of radio frequency energy.  In the case of pulsars, it was Cambridge student Jocelyn Bell Burnell who picked up the electromagnetic radiation blips, and despite being dismissed by her supervisor, kept plugging away at the data.  Her determination led to the Nobel Prize in Physics for the discovery of pulsars, a prize awarded not to her, but to her male teacher (yes, the one who initially dismissed her observations and work).  Burnell went on to become the President of the Royal Astronomical Society, and later the Institute of Physics, and was recently awarded the Breakthrough Prize in Fundamental Physics, a $3 million prize which she donated in its entirety "to help women, ethnic minority, and refugee students become physicists."

   Okay, almost done.  I need to point out that this new year is again "dawning" on the Age of Aquarius, a period summed up in the musical Hair.  Here's what the site Well & Good had to say: The Age of Aquarius follows a similar progressive, forward-thinking, “we versus I” mentality of visionary, rebellious, innovative, and eccentric Aquarians.  It focuses on humanitarian pursuits of valuing each person’s individuality, holding and taking care of each other as a unit, and also disrupting the system.  As Adama Sesay, astrologer and creator of Lilith Astrology, points out, there will be a major shift in power dynamics in this era.  “For eons the power has rested in traditional, oppressive hierarchical structures, and their beliefs dictated our reality,” says Sesay.  “[In the Age of Aquarius,] the power is turning over to the individual, and giving the freedom for you to choose your own reality based on what aligns with your soul.”  

    Editor Dan Souza opened the recent issue of Cook's Illustrated with this: ...for most of my life, trees were ubiquitous, ignorable.  Then I learned about a tree whose heart-shaped leaves emit a cotton candy-like aroma as they change from green to yellow in October.  It's called a katsura tree, and when I smelled it firsthand, I realized just how much I was missing.  That experience jump-started a passionate curiosity, and I've been studying and appreciating trees ever since.  (Another favorite of mine is the sweet birch.  Snap a small branch; breathe deep; and you'll be hit with the smell of a freshly opened can of root beer, thanks to a high concentration of wintergreen oil in its inner bark.)

    One thing I've come to realize is that I wouldn't have made it as a physicist, and probably not a rock star or doctor or whatever else I fancied in my younger years.  But I never lost that curiosity and that fascination, and wanting to read about those who dove into and excelled in those fields.  Certainly this period of isolating and having time and slowing down whether we want to or not is a good time to ponder what we what to tell others, things that we have wanted to say for a long time but felt that we didn't have the time or that we could always do it later.  Or maybe we just didn't have the courage to do so, even to ourselves.  But maybe just as with those powerful quasars and pulsars, there is a strong energy within us, still pulsating and emanating ever outward...and inward.  During this strange and very different holiday season, my wish would be for each of us. whatever our ages or beliefs, to discover that unwrapping and opening what's inside us may prove to be the most precious gift of all.  Socrates would likely approve...

P.S. On a side note, may I recommend the oddly true story of love and friendship for your viewing, a movie that stars Sean Penn, Natalie Dormer, and Mel Gibson; based on the best-selling book by Simon Winchester, the Professor and the Madman tells the tale of the struggle to create the Oxford Working Dictionary...not quite a holiday film but one that features forgiveness, giving, and lifelong dedication for the good of all.  Then again, if you'd rather just read the real history of St. Nick (and what are assumed to be his Greek roots), then there this account from National Geographic.

*Okay you math majors, I admit my ignorance, not being able to accurately tell you the difference between Euclid's Elements and non-Euclidian geometry (in my defense, I can't even recall learning about these things, much less about Fibonacci).  And on a side note, most practices today mark the BC time category as BCE, the first typically having a religious connotation and the latter simply referring to the now accepted designation of a "common era."  The author, however, stays with the BC moniker and after glancing through her book, I am not going to attempt to argue with her since she might just throw another equation my way.