Mathematics, Its Contents, Methods and Meaning – A Book Review

Back in the times before the Great Flood, I was a lowly undergraduate student in a public university.  I started out as a chemistry major but credits back then were very cheap, almost free, so I ended up taking an enormous number of credits in mathematics too.  When I reached my senior year, I had taken all the requisite chemistry courses for the BS degree but I also had discovered that I found the lab work extremely tedious.  What was a nerd to do?  Well, I took a few more math courses and got my degree in mathematics instead.  Since I was planning on raising an expensive family with Camera Girl, I decided to get a job as an actuary at one of the many fine insurance companies in Manhattan.  Imagine my embarrassment to find that compared to being an actuary a lab chemist was like being James Bond.  These insurance actuaries were the most boring human beings that walked this green earth.  With two strikes against me I had to be careful what I did next.  I talked to some smart guys and they asked me what I thought of chemical engineering.  I asked them, “What is chemical engineering?”  Well, these wise men told me that it was the golden road to wealth, fame and happiness.  Since I’ve always been gullible, I believed them.  Where things went from there is a story for a long winter evening but suffice it to say that I abandoned science for the greener pastures of the engineering world.  In other words, I sold my soul to the devil.  But I earned enough to raise a family.

But I always hankered for the chance to take more math classes.  While I was taking my engineering courses I had the chance to speak to an old math professor of mine and described my regret that I’d be too busy for the next thirty years or so to take anymore math classes and wondered whether he could recommend a self-study text that covered all the fields of mathematics that I might be interested in.  I knew that this guy was something of a bibliophile and luckily for me he said he had the very thing.  He told me it was a Soviet Russian three volume set published in translation by the MIT Press.  It wasn’t too pricey so I bought it and stuck it in a corner of my bookshelf and there it sat mostly unread for thirty years.

About ten years ago I finally got my last kid out of college and paid off the house and I was looking at cleaning out all the junk I had accumulated over the years when I rediscovered this set of books.  On a lark I started thumbing through it and opened up the section on topology.  And quickly discovered that I still enjoyed mathematics.  Now you may think that engineering was a field where mathematics abounds.  But after almost thirty years in the field the mathematical content of what I did on a daily basis had degenerated from differential equations into spreadsheets to figure out equipment depreciation and maybe the odd pressure drop or heat transfer calculation.  I had become a lapsed mathematician.  So, it was with great pleasure that I scanned the various sections of the set.  Non-Euclidean Geometry, Topology, Prime Numbers and other equally useless but interesting things.  Now whenever I have time I delve into the books and lose myself for a few hours and enjoy the guilty pleasure of contemplating the whichness of what.  Today I was reading what these long dead Russians had to say about the relevance of Non-Euclidean Geometry when considering the details of our actual universe.  When a ray of light can be bent by gravity what exactly is the validity of the concept of the parallel postulate?  With our current understanding of particle/wave duality what exactly can we consider empty space?  These esteemed commies made a statement from what they call dialectic materialism and define space as the form of existence of matter.  Now what the hell does that mean?  From what I read they are saying that the concept of space only has meaning in the contest of matter.  Well does that mean there is no such thing as empty space?

This is great stuff.  It makes me feel young again and inspires me to want to write a science fiction story where everything in the universe is adjacent to everything else and therefore problems like faster than light travel are merely a matter of having the correct mental picture when attempting to go from your leather recliner to, let us say, a planet in the Andromeda galaxy.

Anyway, if you’re ever in need of a general reference on mathematics that might spark your gray matter, I highly recommend Mathematics, Its Contents, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov and M. A. Lavrent’ev.

Scientists Real and Imagined – Part 2

Re-posted from 2017 in honor of Halloween

In the first installment of this post I documented my education into the real world of scientists, how they saved the world from giant mutated insects and invented important stuff like flying cars. That time period was the 1960s. It was a carefree time full of youthful high jinx such as race riots and the Manson Family. Fast forward thirty years to 1993. A little movie came out called Matinee. It was about the 1960s. The movie employs a device that I like to call “a movie within a movie.” It’s called that because within the movie you are watching there is a movie being watched by the characters in the movie! It’s a wild concept.

The name of this internal movie is MANT. That’s a portmanteau for man-ant. The eponymous victim of this movie has been transformed from a man into a hybrid man/ ant creature. Once again radiation is involved and eventually the MANT reaches gigantic proportions. And right on schedule arrives the scientist that has glasses and a beard and explains all the technical jargon about this scientific problem. And by an amazing coincidence it’s our old friend Dr. “You’re Wiser Than We Are” from “The Thing from Another World” (Robert Cornthwaite). I mean, what are the odds? He makes such valuable pronouncements as “human/insect mutations are far from an exact science” and “My friend, you’ve suffered some of the worst that our little friend the atom has to offer. It can power a city or level it!”

I was fascinated by the changes I noted in Cornthwaite between the time he was in “The Thing” and “Mant”. No longer was he sympathetic toward the monsters. His allegiance had shifted back to humanity. I attributed this change to the smoldering resentment he felt after the Thing back-handed him into a wall in the earlier movie. Such ingratitude by the monster pushed our friend back into the Humanity First camp once again. I knew this was valuable information. I wrote it down!
Outside of the movie Mant (but inside of Matinee) a teenage girl (played by Lisa Jakub) is swept up in the drama surrounding the Cuban Missile Crisis (and the premiere of Mant) in the southern Florida town of Key West. This girl is the daughter of beatniks and she has her world view changed by exposure to a young Navy brat who also happens to like horror movies. When the movie ends Lisa has gotten over her prejudices against military families and monster movies. What does this have to do with this post? Well it does link us back to the military but hang in there. I have another half-baked segue coming up.
Fast forward to 1998 and a blockbuster called Independence Day erupts onto the cinematic stage. Now it just so happens that there is an ex-Navy pilot named Russel Kay and by a strange coincidence (or is it) his daughter is played by Lisa Jakub! But her love of a navy brat in the last movie has landed her in this movie in a family headed by a delusional alcoholic ex-military flier. Although it’s not apparent how she feels about horror movies she definitely suffers some of the worst of what our friends the aliens have to offer. In Independence Day, the role of scientist is handled by Jeff Goldblum. He is an environmentalist computer scientist who’s always worried about recycling and is totally opposed to nuking the aliens. He’s worried that fallout is worse than extermination of the entire human race by death rays. But by the end of the movie he comes around and cheerfully nukes the aliens on their home base.
I was thinking of dragging this forward by following President Whitmore forward into Lake Placid (well the crocodile is very large) or following Jeff Goldblum into Jurassic Park and Independence Day 2 which has all kinds of scientific mumbo-jumbo and giant creatures but I’m getting tired.
Suffice it to say that even really stupid people and fat-headed scientists can see reality if monsters and giant insects start slapping them around.
And now my patient readers, the payoff.
All of this research has allowed me to formulate a unified theory of scientific behavior. Apparently all scientists are morons and can only learn about reality by being hit over the head by it. Therefore, I propose a new policy. Whenever a scientist dictates a policy based on fat-headed stupidity he should be forced to endure the solution himself until he either sees the error of his way or dies from the paradox of settled science.
For instance, if a climate scientist declares CO2 the death of the planet then he should not produce any of it himself. Now, I don’t propose that he cease breathing. Even though technically respiration is nothing but exchanging O2 for CO2. Let’s just let him slide on the breathing. But that’s all. No internal combustion engines or heating systems or electricity. In fact, nothing produced by technology supported by the industrial revolution. So that also eliminates batteries and solar cells and everything else made in a factory. And finally, I remind everyone that burning coal or oil or even wood produces CO2. So, this scientist is telling us to give up every bit of science going all the way back to the paleolithic age. So, let us limit our friend the scientist to killing fur-bearing animals and eating their flesh and wearing their pelts for warmth. Of course, he’s probably a vegan but we all have to make compromises when inconsistencies crop up.
That’s my plan in a nutshell. It should be amusing to see Al Gore dressed like Fred Flintstone and trying to catch a squirrel for breakfast.

The Real Tomorrow

The only advantage to getting old is grandkids.  Of course, I’m sure there exist grandkids from hell but as a general concept, grandkids are a great idea.  They allow us to have fun, hang out with young people and then send them back to the people who have the real work of attempting to civilize them.  All plusses.  No minuses.

Every year at about this time the local engineering school, Worcester Polytechnic Institute (WPI) sponsors a science exhibition for kids.  The call it “Touch Tomorrow”

( http://wp.wpi.edu/touchtomorrow/the-festival/wpi-research-exhibits/ ).  WPI is affiliated with NASA and provides robotics and other expertise for Mars rovers and robotic components that dig and manipulate objects and sense light and other functions.  So, there are exhibits and presentations on many subjects involving spaceflight, robots and futuristic technology of all sorts.  For my oldest grandson this is like being in heaven.

And it’s pretty good stuff for me too.  Being an engineer and an inveterate fan of science fiction many of the topics are highly interesting and even answer some of my questions about the whichness of what.  So, this event is an annual win-win for me and my descendant.

But, of course, being in New England and the bluest of blue states, the fair has its share of pc virtue signaling and progressive biases.  I won’t go into all of them but suffice it to say that the celebration of women in science and technology is just a little too loud and a little too shrill.  That being said, I noticed a couple of things that gave me some small reason for optimism.

The first was at the forensic medicine exhibit.  A woman who had worked for the coroner had a table full of bones.  She was explaining to the kids how physical parameters of skeletons could allow a coroner to estimate very accurately the age of a child based on evidence from a skull.  This had to do with the stages of dentition.  Then she had a skull of Neanderthal Man.  She was able to relate the difference between Neanderthal and modern humans based on the differences in skull shape and bone thickness.  Finally, she was able to point to the differences in skulls based on sex and also race.  She had skulls for the three major racial families (Caucasoid, Negroid, Mongoloid) and for men and women.  I was shocked that a pack of screeching SJWs had not driven her out of the hall for espousing these hate crimes.  That not only were there physical differences between the races but that men and women were divided along anatomical lines.  Such an outrage.

The second thing I heard was during a presentation by a physics professor on the Universe.  He described the scientific method and very pointedly declared that no scientific fact was ever settled.  He stated categorically that a theory that was refuted by evidence was false.  And he further stated that a true scientist is always hoping that experiments used to prove a theory refute it in some way because these differences from theory are the basis for an increase in knowledge.  He said that when the Higgs Boson was confirmed last year, the disappointment was that it was exactly as calculated.  Even though the discovery was a great triumph of the standard model, the fact that nothing new was learned was a let-down to those hoping for new information.  I was tempted to ask what he thought of global warming data but I didn’t want to get this faithful acolyte of science burned at the stake by adolescents.

After the presentation, I spoke with this physicist and pinned him down about one particular “fact” that he showed during his presentation.  When describing the size of the universe he stated that the universe was potentially 93 billion light years wide.  I asked him whether the universe is currently believed to be bounded or unbounded.  He stated it was believed to be unbounded.  So, I asked him what the physical reality of this edge of the universe at 93 billion light years was.  He said all that it is, is the current guess at how far we’ll be able to observe based on the light after the big bang.  And he continued, “beyond that be dragons.”  Now that’s my kind of scientific answer.

After this presentation, we were finished with the exhibition and headed to a steakhouse for beef and potatoes.  I went with the ribeye and baked potato while this younger fellow heretically opted for sirloin and french fries.  Youth is wasted on the young.

During dinner, we continued our debate of the impossibility of producing a machine to endlessly produce electric energy from a single input of mechanical energy to a dynamo.  He wasn’t having any of it.  To prove my loyalty to the laws of thermodynamics and electromagnetism I agreed to fund his project and purchased a number of components for his machine on (of course) Amazon.com.  In this way, we could provide evidence to confirm or dispute his law of perpetual motion.

When we got to my house, his grandmother provided ice cream and I provided classic horror movies, specifically, “The Bride of Frankenstein” and “The Creature from the Black Lagoon.”  Being a purist I strongly disapprove of TCFTBL being included in the Universal canon.  But we live in disordered times and allowances must be made.

After I returned him to his parents it occurred to me that the name Touch Tomorrow could also be a description for older people spending time with their grandchildren.  They literally are tomorrow and by influencing them we make probably the most lasting effect we will have on the future.  Considering all the negative influences on our children from the forces of progressivism I thought about how good it is that we can impact them directly and have fun at the same time.  So, family actually is good for something.  Who knew?