MICROWAVE COFFEE

Bevy Mae and me are coffee drinkers. Bevy used to drink a dozen cups of fully caffeinated coffee everyday.  By her third cup she could boogie with the best of them.  But that was a long time ago, before we got old. Now she drinks about two cups, and it’s decaffeinated. Me, on the other hand, well, I still imbibe the high-octane stuff.  I love it.


I drink the high-octane stuff.

If your marriage is anything like ours, you probably own one coffee-maker, but you and your spouse drink different brands, flavors or styles of coffee. For us it means we have to store the contents of at least one of our coffee-pots off-site away from the coffee-maker in containers and carafes; perhaps cups or bowls or glasses or whatever is handy. The coffee gets cold.


69050_Coffee Maker.37173901_std
My wife and I have one coffee maker between us. It’s not enough.

Only one of us at a time can store coffee in the coffee-pot. But since we have two microwave-ovens, we don’t really need to keep our coffee hot. We can turn off the coffee-maker after we brew each pot to save energy.  Everyday we reheat our coffees in the microwaves more than once; thanks to having two of them we don’t wait in line.


We have two microwaves. It is one of the very few things which seem to have made a difference in our marriage.
Two microwaves: they can sometimes save a marriage.

Bevy Mae and I have an eclectic collection of coffee mugs gathered together over decades of marriage. I’ve often wondered: how is it that no matter how big the coffee cup or how tiny; how robust the mug or how dainty; how full or empty we fill — or even which microwave we choose — my wife and I almost never set the timer  to reheat our coffee more than once?

We always seem to set the microwave to exactly the right number of minutes and seconds to heat our coffee to exactly the right temperature.


coffee 4
                She got the calculation right.

Think about it. Can there be any doubt that the mathematics required to accurately set the timer must be beyond the capabilities of 99% of the people who set these timers to reheat their coffee everyday?

The size of the cup, its thickness and material; the amount of coffee in the cup — these are important variables that are required to be taken into account when setting the timer. Not only these variables, but there is the subjective calculation: how hot do I want this coffee to be today? Real hot? Tepid? Mildly warm?

There are many tricky variables to track and put into an equation. And, if we are reheating coffee for our significant others, we have to anticipate their calculation of what the best temperature is for their mood and state of mind.


differential equations EngMath_DifferentialEq_Terminology_02
It takes a matrix of differential and difference equations plus a super computer to get microwave coffee right.

It really takes a sophisticated matrix populated with complex differential and difference equations to work out what the results might be under all the possible scenarios. And it might require a government super-computer to crunch the numbers.

Of course, I’ve never done the actual work of creating the matrix —  or the equations. Even if I had, I would have faced the daunting task of isolating all the relevant variables, the tedium of tracking all the units to make sure I ended up with seconds only in the answer, and the exhaustive testing of results to see if they match up with my expectations and experience.

Successful creation and application of a workable calculus might involve a lot of tweaking.


drinking coffee
He didn’t bother with the calculation.

Come to think of it, why would I do that? Guessing seems to work better and it’s a lot faster. But I wonder. Am I really guessing? Or is my brain, somehow, doing the math in some far away place inside my brain, behind the scenes and beyond my conscious scrutiny?

It’s kind of mysterious, being right all the time, about something as complicated as getting the number of minutes and seconds correct when setting the timer to reheat coffee.

And my wife, who knows no math, is as good at the mental calculation as me. Go figure.

Billy Lee

P.S.  Note to readers: On Valentines Day, 2015, Billy Lee bought a second coffee-maker for his wife, Bevy Mae. Why it took Billy Lee so long to solve his coffee-problem is a mystery even skilled mathematicians can’t solve.
The Editorial Board.


microwave coffee math graphic 6
Don’t try these calculations at home. Seriously. This man tried; his face froze — for. two. hours.

WHAT IS MATH?

 



math with color


People seem to think that mathematics is something special — a kind of magic language that when tinkered with properly makes it possible for mortals to unravel mysteries about the universe hitherto known only by God.

I see it differently. Mathematics isn’t a language per se. Although mathematics can be (and is) explained by language, math itself is a collection of rules and symbols that makes it possible to avoid the encumbrances, flourishes, and ambiguities of language. It accomplishes this feat by defining things and their relationships in strictly limited — but important — ways.


euler formula hatEuler Identity – Khan Academy


Math involves symbols and rules that aren’t explained inside the equations. It is the lack of words that gives math its mysterious and magical reputation. But once everything is defined and understood, applying the contrived but logical rules of mathematics enables folks to manipulate equations to uncover previously hidden and non-intuitive relationships among the things they have defined.

What am I saying exactly? I am saying that it is possible to use words alone to describe the process of solving and manipulating an equation, which can lead to insights into the relationship of the things in the equations. But these words will make the process of computation cumbersome, impractical, and confusing.

Spoken language contains noise and nuances that interfere with the manipulation of carefully defined relationships between narrowly defined variables. Yes, the no-nonsense logic and bare bones precision of mathematics as well as the reduction of things to a few carefully chosen attributes enables mathematicians to apply rules to discover consequences that might otherwise remain undiscovered.

But the tightness of mathematical construction makes it a tool which is almost useless for describing and analyzing many subtle yet vivid experiences of a conscious mind — like beauty, the feel of an orgasm, or the experience of grief. For these realities of conscious experience, mathematics has a reputation for being irrelevant.


euler ring     Euler Identity – Wikipedia


Spoken language gives conscious humans the messy modeling mechanism they need to connect with each other to share and understand the more nuanced experiences of life. The messiness and ambiguity of spoken language makes the unique intimacies of human communication possible. Mathematics, despite its elegance, doesn’t do intimacy well.

The Euler Identity, illustrated above, is sometimes presented as an example of the mysterious power of mathematics. But if anyone takes the time to think about it, what does the equation say?  It says that minus one plus one equals zero.



Complex Plane


The explanation is easy.   -1 can be rewritten as e raised to the power of i times π because of simple rules, which place on a circle of radius 1 all the values of e raised to the ith power times anything.

The number that sits next to i is the angle in radians where the result lies, right?  In this case, an angle of π radians (180°) takes the value 1 (at 0°, or 0 radians) to half-way around the circle to the value -1. 

Easy… , right?

Despite the reputation of equations for precision, it turns out that physicists and other scientists struggle to make mathematics match the results of real-world measurements.  It has to do with the problem of scales, mostly.

The electrical force is a trillion times a trillion times a trillion times greater than the force of gravity at the scale of electrons and protons. At the scale of quarks, it’s one-hundred-thousand times greater still.

It’s one example.

The non-technical public is unaware for the most part that astronomical observations involving the movement of stars, planets, and other celestial bodies — or the results of observations made of the subatomic world (no matter how carefully contrived) — fail as often as not to provide results sufficiently in agreement with mathematics to be of any practical use until they are massaged a little.

Fudge-factors are a big component of doing real science. People have won Nobel prizes for inventing fudge-factor protocols to fix things.

It’s true.

Renormalization, perturbation theory (for phenomenon both small and large), Green’s functions, propagators, Feynman diagrams, and many other adjustments and tweaks make up the contortions and modifications that scientists overlay onto their beautiful equations to make them work.

They claim to have good reasons for all the tinkering; it’s complicated down there among the quarks or up there, among the quasars; there are nuances and messiness and ambiguity in the underlying reality of nature that no one can see or fully understand — not now; not anytime soon; perhaps not ever.

At subatomic scales, a tangled mess of virtual particles — which come into and out of existence more or less spontaneously — often gets the blame for the mismatch between mathematical elegance and the cold reality of experimental results.

On the scale of the universe, dark matter and energy (which have yet to be detected or observed) are sometimes blamed for anomalies. Click on the link in this paragraph to learn more.

It’s possible that no system involving mathematics can be contrived by humans to bring the satisfaction of knowing everything for certain; nothing we are able to invent will bring a tranquil end to the pain of cognitive dissonance that seems to drive our species to wonder and explore to find the satisfying answer.

On the other hand, perhaps mathematics is more complex and goes further than we know. Methods may yet be discovered to make mathematics and physics match-up with better accuracy and precision.

Recent work by Cohl Furey and others on numbers known as octonions is showing tantalizing hints that internal properties like the force and charge of particles and their external manifestations like mass and spin are connected in peculiar ways that might be described by a more fully developed mathematics.

Dixon algebra (a combination of four division algebras) is a tool that people are using to collaborate in the search for a path forward. So far, success eludes them.  Some experts are hopeful, but many express skepticism.

The more deeply people travel into the complexities of mathematics and science the more elusive truth seems to become; perhaps God is not a mathematician; maybe Einstein was right when he said, God does not play at dice.

A die is cast into the lap, yes, but its decision is from the LORD, according to an old proverb of Solomon.

Can it really be true that understanding the world is beyond the limitations of all life on the earth — beyond the abilities of the most brilliant minds that have lived or ever will live?

Is it possible that the universe cannot be understood by any conscious life anywhere in the universe for all time?

If so, it’s time to kneel.

Billy Lee