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.
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.
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.
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.
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 secondsonly 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.
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.
Don’t try these calculations at home. Seriously. This man tried; his face froze — for. two. hours.
The visible universe is big. Most scientists believe the invisible universe — the universe no one can see — is really big.
If the Universe shrunk down to where Earth became the size of a period at the end of a sentence, how big would it be?
When I was a kid, questions like these fascinated me; what harm is there to revisit a few?
About 100 dots the size of the period at the end of this sentence must be strung together to make an inch. We can imagine shrinking Earth to the size of one of these dots, then plugging-in the numbers to calculate the scale of everything else. It turns out that the observable universe shrinks to a diameter of about two light years.
Since a light year is nearly six-trillion miles, the universe is fantastically big. At this reduced scale, the size of the universe remains pretty much incomprehensible.
In this pic, the Sun sits directly behind Saturn, which is backlit by it. Earth is the tiny dot inside the illustrator’s circle to Saturn’s left. Earth is hundreds-of-millions of miles into the page—behind the gas-giant and its rings. Click pic to enlarge in new window.
When Earth becomes a period (or dot), the Sun shrinks to close to an inch in diameter — or 2/3 the diameter of a ping-pong ball. [regulation ping-pong balls are 1.575″ in diameter] The dot-sized Earth orbits 10 feet away. Neptune, the farthest planet, is smaller than a BB — a tiny ball of methane ice almost one football field distant (97 yards).
The distance light travels in a year shrinks to 120 miles — a speed approaching ¼ inch-per-second. The distance to Alpha Centauri, the nearest Sun-like star, shrinks to 500 miles. The star Alpha Centauri shrinks to a ball that is only slightly larger than our under-sized ping-pong ball-sized Sun.
Think about two 1″ diameter ping-pong balls separated by 500 miles. Imagine trying to commute between these balls when the top speed is less than ¼ inch-per-second. Of course, nothing travels at the speed of light. At speeds typical of spacecraft today, it takes 100,000 years to reach Alpha Centauri.
At the scale where Earth is a dot, one might wonder what is the size variation of stars. It turns out that most suns (stars) in the universe range in size from a grapefruit to a pea.
Of course, outliers exist like Deneb, the blue-white supergiant visible in the Summer Triangle. At 203 times the size of the Sun, it shrinks to 17 feet or so in diameter depending on how accurately anyone cares to scale things. Rare super-giants are larger; some are 75 feet or more in diameter at this scale. But in the Milky Way Galaxy, our undersized ping-pong Sun is one of the larger stars.
Is there another way to grasp how large the universe is?
The Milky Way Galaxy — the Sun orbits its center in the space between two of its outermost spiral-arms — is 100,000 light-years across. If the Milky Way was reduced to the dimensions of a coin the size of a quarter, the visible universe (the universe that can be seen with telescopes) would collapse into a sphere of space 15 miles in diameter.
In such a reduced sphere of space, large galaxies become the size of Frisbees but outliers like the mammoth IC1101 are the size of truck tires. The smallest galaxies shrivel into mere grains of sand. Distances between galaxies diminish to 100 feet or so but variations are huge because galaxies tend to cluster together to form groups, which are separated from one another by vast distances.
At this scale, astrophysicists say that the presence of galaxies that cannot be seen (because the distances between our Milky Way Galaxy and the farthest-away galaxies recede faster than the speed-of-light) makes the entire universe, visible and beyond, a minimum of 50 miles in diameter. Light, believe it or not, stands still at this scale. No human observer during their lifetime would notice any movement at all of light or any other phenomenon.
Even the faster-than-light expansion of the universe would be unobservable.
According to physicist, Stephen Hawking, it takes a billion years for the universe to expand by 10%. Five miles (10% of 50) during a period of one billion years is 7 billionths-of-an-inch per day. During a human lifetime the expansion adds to 2 thousandths-of-an-inch (.002″) — less than half the width of a strand of hair.
At the scale where the Milky Way Galaxy is the size of a quarter, the entire universe would appear to be frozen solid during the span of a human lifetime.
Artist’s view of water molecules. Molecules are the smallest structures that can be directly observed (with the help of special sensing instruments and computer generated enhancements). Molecules are the building blocks of all things.
What about tiny things?
To examine the scale of the very small we can imagine enlarging molecules, the building blocks of all things, to the size of the same period-sized dots.
How tall might an average person be? After again plugging in the numbers and calculating, it turns out that a human stretches to a height of 1,000 miles. The eye expands to an orb 15 miles across.
Molecules are small. But at this imagined scale — a scale that requires sophisticated instruments to discern — individual molecules become visible. They grow to look like little dots separated by distances only a bit larger than the dots themselves. Sadly, no one can see the individual atoms that make up the molecules. Even at this enlarged scale, they are too small.
No instruments or microscopes can be constructed to enable anyone to “see” atoms. Physicists believe atoms are real because they see the evidence left behind as their debris moves through the detection mediums of cyclotrons, colliders, and other sensors.
Since 1981 physicists have used scanning tunneling microscopes (STMs) to “feel” the forces of atoms with “nano” probes. A computer algorithm plots the forces and creates pictures of atoms, which with this method look like stacked billiard balls.
Billiard balls is not what quantum objects “look” like because quantum objects can’t be seen using human vision but at least scientists can prove that lumps of energy exist and are arranged in patterns that can be analyzed. It’s a start. It’s something.
Models of atoms studied in science class at universities around the world are contrived to help make sense of the results of many experiments. They are somewhat fanciful.
As for living cells — the basic building blocks of all biology — people are able to observe them under magnification because every cell is built-up from many billions of molecules. Some human cells have trillions. The size of a typical cell at the scale where molecules are expanded to about the size of three-dimensional dots is about 60 feet across.
Artist’s large scale view of the universe.
The gulf between the very large and the very small strains credulity but science says it’s real. When thinking about it, I am overcome by wonder and the despair of not knowing why or how.
Theoretical physicist Nima Arkani-Hamed has said that the gulf between the very large and the very small is required to balance the force of gravity against electrical forces in celestial objects like planets. He has pointed out that the ratio of the surface area of a typical atom and the surface area of a typical planet mirrors the difference between the two forces.
Nima Arkani-Hamed, one of the world’s top theoretical physicists, makes a point.
The huge difference between the force of gravity and the force of electricity makes the gap between the very large and the very small essential in a universe that works like ours; the difference in scale is necessary and inevitable, Nima has said.
If the ratio moves too far from this balance — if the surface area of an object gets too big — gravity will overwhelm the electrical forces that hold the atoms apart to cause the object to light up from a process called fusion, which can leave behind a shining star. A much larger object will collapse to become a black hole.
Why is the gap between the force of gravity and the electrical force as vast as the difference in surface area between a typical planet and a hydrogen atom? How did the ratio get that way?
No one knows. The values of the forces seem as finely tuned as they are arbitrary. Nima Arkani-Hamed and others are working to understand why.
Another mystery: Why is the universe so big?
Even Nima Arkani-Hamed admits he doesn’t have the answer — not yet, anyway. Perhaps the answer lies in the geometry of spheres, which is the basis of the Billy Lee Conjecture discussed in the essay Conscious Life.
Speaking of spheres, everyone knows that billiard balls are polished smooth, right? Earth, after being shrunk to the size of a pool ball, is smoother and less blemished; more perfectly round. Exhale on a pool-ball to create a mist that is 10 times deeper at scale than the deepest ocean on Earth.
Do the math.
It’s true.
As a child my nightmare was of an enormous whale crushing a tiny flower. A psychologist told me that the whale was a parent; I was the flower.
Maybe.
But the universe captures my nightmare. It’s really big and I am so very small, helpless, and lost within its vast expanse.
Sensing involves seeing, hearing, feeling, smelling, and tasting, right? It’s the traditional five senses that most folks learned about in elementary school a long time ago.
Scientists added complexity to the number and capabilities of the senses in modern times to include “modalities” like sense of place, pain, balance, temperature, vibration, and awareness of chemical concentrations — like salt and carbon dioxide— inside the body.
All this complexity pushes readers into deep weeds, which I am going to avoid in this essay. It will work just as well not to needlessly bewilder people.
Never mind that certain life forms like birds can sense the earth’s magnetic field, or that sharks can sense the electrical activity in living prey. Many ways of sensing the universe are possible. This essay deals with those most familiar to humans.
Until humans developed the technologies of modern science, sensing (and making sense of what was sensed through the mental process of reasoning) was how people formed ideas about what the universe is. But there was a big problem.
Senses told us the sun looked yellow, thunder sounded loud, rocks felt hard, roses smelled sweet, and almonds tasted bitter.
The problem should now be obvious.
These qualities don’t exist in the universe. They are hallucinations of brains created when organs like the eye, ear, skin, nose, and tongue interact with elements of the universe which, in themselves, share none of these qualities.
Qualities like these don’t exist in the physical universe. They are hallucinations of living brains.
These hallucinations are inaccessible to all but the living organism who experiences them. They are unique and not detectable by others, in this sense: people can ask others if they see the same yellow color they see. When they say yes, they can decide to take them at their word, or not.
It is not possible to prove that they are telling the truth. In fact it’s not possible for anyone to answer truthfully, because no one can know how anyone but themself experiences the color yellow.
The interaction of sense organs, like eyes, with electromagnetic radiation is selective. Only a limited range of frequencies will stimulate the retina of the eye, for example, to emit the necessary electric and chemical messaging the brain uses to construct the hallucination called vision.
Some of the radiation falling into the eye does not interact with any sensing organ and remains undetected. In fact, the human eye can detect only wavelengths of light between 15 and 35 millionths of an inch long (400 to 900 nanometers).
Note to the non-technical :A nanometer is a billionth of a meter, which is written as a decimal point followed by eight zeroes and a one — i.e. .000000001. In engineering shorthand it’s written as 1E-9 meters. Humans see wavelengths of light that are 400 to 900 times longer. Scientists and engineers usually work in meters, not inches. The Editorial Board.
This narrow range is transformed by structures in the retina into messaging the brain can use. Wavelengths up to a thousand times longer (one thirty-second of an inch) are able to be felt as heat.
To the rest of the light spectrum, humans are completely blind. This spectrum includes light with wavelengths as long as sixty miles (called radio waves) down to wavelengths of light called gamma rays, which are many millions of times smaller than the wavelength of violet, the shortest wavelength human eyes can detect.
One reason people (and other life) see and feel a limited range of frequencies is because the energy of the sun that is able to penetrate Earth’s atmosphere to reach its surface lies in this limited band. The rest is blocked.
Of the sun’s energy that is able to reach Earth’s surface, 43% is in the narrow visible spectrum people can see. 49% is in the form of heat, which can be felt. Ultra-violet light — which some insects see — makes up 7%. Life on Earth evolved to sense light at wavelengths able to reach its surface.
The other parts of the light spectrum — like X-ray and gamma light — are deflected or absorbed by the nitrogen and oxygen in the atmosphere. Only 1% of the sun’s energy that manages to reach Earth’s surface lies in these high frequency bands.
A great deal of the light that reaches Earth from outside the solar system falls into the range of low-energy radio frequencies to which all Earth-life is completely blind. Radio-frequency light-waves are long and fuzzy. The sun produces mostly higher frequency light. Radio-waves seem to be unnecessary to the survival of life on Earth.
An ability to sense radio waves makes no impact on living things; it provides no survival advantages. Yes, on Earth intelligent life-forms (i.e. humans) have learned to amplify and convert radio light into sound to communicate and entertain themselves over large distances.
Scientists continue to search for evidence that far away life, should it exist, might share the same aptitude for communication. So far, the search has found nothing — no evidence for any kind of life whatever.
The image of light formed by the mind is fantastic — which means it is useful to the organism that sees the image, but the image doesn’t contain many (or any) clues about the external physical phenomenon that triggered its creation.
There is nothing even remotely similar between the color yellow (or any other color) and the electromagnetic radiation that oscillates trillions of times per second to ignite the mechanisms of vision.
There is nothing even remotely similar between the color yellow (or any other color) and electromagnetic radiation oscillating trillions of times per second.
The hard solid feeling of rock has nothing in common with the silicon atoms from which rock is made and whose nuclei are separated from one another by spaces many thousands of times their size. Nor does it have anything in common with the hundreds of different molecules which make up the nearby skin and nerve cells — themselves many millions of times larger than silicon atoms and separated from them by large distances.
The feeling of hard solid and the color yellow exist in my mind. I am sure of it. But can I find, for example, the color yellow in your mind?
The answer is no. A brain surgeon might probe a part of someone’s brain, and they report seeing yellow. But if she examines the area of the probe, she has no chance of discovering the color yellow. She will never find it.
My experience with the color yellow is subjective. If you tell me you also experience yellow, I believe you, because you are like me, and it seems reasonable that we will experience things in the same way.
But if you were asked to prove you see yellow the way I see it, you couldn’t do it.
Not only colors, but sounds, feelings, smells and tastes will vanish without a trace once life is gone. So again, the question: What, exactly, is the Universe?
If life disappears from the universe it will take the color yellow with it. Only the electromagnetic radiation that triggered the hallucination of the color yellow will remain.
Since the radiation can no longer be detected, seen, or experienced by any conscious observer, what is it exactly? Not only colors, but sounds, feelings, smells, and tastes will vanish without a trace once life is gone.
So again, I ask: What exactly is the universe?
Gas Sensor
Let’s “look” at scientific inquiry for the answer. What does science do? Science examines the universe quantitatively and avoids the qualitative and subjective attributes the senses provide. Or it at least tries to.
Science designs detectors to find as much discoverable phenomenon as it can — phenomenon human biological senses can’t discern or aren’t sensitive enough to experience.
But someone has to ask: Aren’t these detectors nothing more than enhanced sensors augmented by gauges and dials to increase the precision of measurement? And don’t living, conscious human-beings use their senses and their brains to make sense of the information the detectors provide? What has anyone gained by science?
The scientist’s tool of choice is mathematics, because it dramatically reduces the fuzziness — the subjectivity — of the senses, and replaces qualities like the color yellow and the feeling hard solid with measurables like oscillations per second and pounds per square inch; that is, with attributes that can be measured by all observers and which, presumably, exist independently of a conscious mind.
Mathematics uses logic and simplified representations of objects and forces to create symbolic models. Certain operations can be performed on these models to reveal non-intuitive relationships among the simplified variables.
Ok… again, have we gained anything? Or does mathematics force a sacrifice of information and detail to simplify understanding? Are we closer to knowing what the universe is, or farther away? Can the best sensors and the most sophisticated mathematics really get humans closer to understanding what the universe is?
One surprise that mathematics has revealed: telescopes and other sensors show that too much gravity is at work in the universe for the amount of matter and energy scientists see. 85% of the matter that must be out there can’t be seen.
More shocking: 95% of the energy and matter that the theory of gravity says must be out there, no one has ever observed. Physicists don’t know what this invisible matter and energy is, or even where it is — though some scientists believe it is evenly distributed throughout the cosmos. They call it dark matter and dark energy.
I don’t want to scare anyone, but the universe is mysterious, and no one understands it. Two questions I’m grappling with:
2 – Is Consciousness powerless to interact with the universe in ways that change it?
Consciousness may exist independently of any individual conscious-being.
These are serious questions.
If the answers to these questions are yes, then consciousness is not necessary for the universe to exist, and the understanding of what the universe really is will probably never be complete — certainly not for humans. Consciousness is something that evolved over billions of years and will someday be missing once again.
The universe won’t notice or care. Conscious life — like humans — can think about the universe all they want. They will never change it. This is the current popular view, is it not?
But the answers to these questions could be no. And it might be possible to prove it.
Consciousness might be something human beings plug into and even share.
If the answers turn out to be no, the implications are profound.
No means the physical universe may have evolved from consciousness, not the other way around.
No means conscious humans may have the ability to completely understand the universe and make sense of it someday.
No means that consciousness may exist independently of any individual conscious-being.
No might mean consciousness is something human beings plug into and even share.
No might mean God exists, and — though our bodies die — we never will.
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.
Math involves symbols and rules that aren’t explained inside the equations. It is the lackof 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.
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.
The explanation is easy. -1can be rewritten as eraised to the power of i times π because of simple rules, which place on a circle of radius 1 all the values of eraised to the ith power times anything.
The number that sits next toi 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.
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?
