Is a point as huge as a period—
an ocean of carbon particles mashed into
the warp and weft of cellulose,
crannies, abysses of space separating
their dark, emphatic engagement with paper—
or is a point briefer than a
Planck length, light stopped
before it starts a path through a perfect vacuum?
Why do we concern ourselves with such things
(and by “we,” I mean “I,” unless you too are afflicted)?
Because it is important to ask questions
while remaining skeptical, quizzical
when we get answers back,
an irresolvable game of table tennis
our two selves helming each end
of a curvilinear surface occupying nothing,
while we each give the thing
shuttling between us a good smash
with a paddle of no size or substance,
back and forth, on and on and on…
In a place without time
there is no story to tell,
all persons, places,
firm and free,
transfixed and stubborn
in the silent still.
That which would move
does not flinch a fiber,
those who would try
cannot move a muscle,
particles that spin and bounce
do neither in their torpor,
rusted through the core,
the rust can creep no more.
Motion needs time
to step through its dance.
Time needs motion
until the clock stops.
Think of one,
you’ve set them both
a distant goal.
This thing popped into being while I was reading the sixth “brief lesson” in Carlo Rovelli’s Seven Brief Lessons on Physics. That sixth lesson is titled “Probability, Time, and the Heat of Black Holes.” The tiny thing I’ve presented above addresses the unimaginable and, thus, is a paradox.
Which is briefer – Planck time divided by infinity or its inverse?
As I write this soon-to-be-anachronistic piece, it is already the “new year” in various places around the world. For instance, in Hong Kong it is 12:04 A.M on Sunday while it is only 11:04 AM Saturday here (east coast U.S. time).
The truth is far more complicated and far more interesting to consider.
First of all, there is the notion of sidereal time—time relative to a fixed star‘s position. It is used by astronomers, who cannot rely on our own sun’s position as our positional relationship to it is not fixed. As a matter of fact, starting in the 19th century it was noticed that the “fixed stars” are not fixed either. They are just distant enough that they are far more fixed than our local star seems to be. All sorts of calculations can be sorted out to use a non-fixed distant star or bright astronomical object as relatively fixed, but I neither understand these calculations nor would you (I suspect) find them particularly interesting. So, the bottom line is sidereal time is in constant change here on earth. If I am standing shoulder-to-shoulder with you, we are in different sidereal times. Sidereal time has no respect for time zones. Time zones are useful in that it would be a nightmare to discuss the time it actually is if we were not to bunch time together in chunks like we do.
Second, time is not really measured in chunks like hours, minutes, and seconds. One really has to consider the fastest event in the universe to consider time more accurately, if not more usefully. The shortest time is the calculated Planck time, which is 5.39×10-44 seconds (in other words there are 1.9×1043 tP in one second—roughly 2 followed by 43 “zeros”—an incomprehensibly large number of events on the “standard human time scale (SHTS).” It is the amount of time it takes for a photon in a vacuum to pass through a Planck length, which is also very brief, distance-wise.
The thing about Planck time is that it is a time derived from a physical standard calculated by Planck, so although useful for physicists, there’s something a little incestuous about the whole business. Various elements have layers of electrons probabilistically scooting around their nuclei at mind-bending rates of speed, while also changing their quantum energy levels from their lowest energy levels (aka ground states) to a variety of higher energy levels. These electronic transitions have been studied and are variously known to behave themselves in very dutiful ways. As they are in constant motion between energy levels and motion takes time, even on the atomic scale, the distances and times are very tiny. Cesium atoms, for instance, experiences 9,192,631,770(±some variation) transitions between energy levels per second. The atomic clocks based on this cesium transition are so accurate that they are calculated to lose only 1 second in 100,000,000 years (one hundred million years!) or so.
Part of the work that scientists do is involved in never being satisfied with a “good enough” answer; they are always looking for increased, accuracy, precision, measurement stability, always looking for a more refined “truth” than that which has been understood before. If you were a professional runner, for instance, and you just achieved a personal best, you would not go home, pop open a bucket of ice cream and settle in for the rest of your life. The next time you ran, you would try to better your personal best. Same with scientists, except the standards are set by nature and the tools we have to achieve better outcomes are constantly in the process of improvement.
Cesium has been the standard for measuring seconds for some years now but has just been displaced from its throne by an ytterbium-based atomic clock that “ticks” 518,000,000,000,000 (518 trillion) atomic events per human second. This allows a crazy level of stability that makes the mere 9 billion mark previously set by the cesium atomic clocks seem like sundials. The following video is a National Institute of Standards and Technology scientist discussing this improvement on video, along with explanatory text.
If all of this weren’t disconcerting enough for you, these atomic clock scientists have found that time varies with altitude as well. In experiments using aluminum atom atomic clocks, they have been able to demonstrate that these variations in time have an effect with each foot of elevation, meaning that our feet are in a different time zone that our heads (does this explain clumsiness? it’s at least a better excuse than “I can’t walk and chew gum at the same time!”). Over a 79-year lifespan, the difference would only amount to about 90 billionths of a second, but it is there all the same.
The whole point is that while we usher in the new year, we might give pause to remember that what we are celebrating is a not entirely accurate astronomical event. The earth has orbited around our sun for the past 365 days and will start that process again. In the meantime, sidereal time and atomic time—and Planck time for that matter—are all moving at rates that we can’t even comprehend unless we’re practicing the science of measuring—and improving—on atomic clocks and the electronic quantum transitions that are involved. From a practical standpoint, the next time you look at a second hand on a clock or watch a minute pass, consider the atom and all the changes it has gone through in that time. Consider that, as the earth rotates and precesses on its axis each day, we are each in our very own time zone. In fact, various parts of our bodies are in various time zones, particularly if you’re measuring our relatively enormous selves in Planck lengths.
So, Happy New Year! We have orbited our sun at the rate of 67,000 miles per hour—or if that seems too fast to you, let’s just say 19 miles per second—over the past roughly 365.256 days and yet, knowing these underlying facts, we will all count down to midnight in the enormously large seconds increments “ten-nine-eight-seven-six-five-four-three-two-one-happy-new-year!” and 6.144 hours later, the new orbit of the earth around the sun will start.
I can’t remember exactly when it was or how old I must have been but my mother took me to (I think) the state fair in (probably) Columbia, South Carolina when I was (let’s say) ten. If I’m wrong on any of these, it was either Columbia or Beaufort, either a state or county fair and I was either ten or somewhere in the twelve to fourteen range. Additionally, if I’m wrong it doesn’t matter much or at all. With all of that out of the way (this is a factual bit rather than a bit of fiction or it really wouldn’t matter), I will describe what might have been a pivotal incident in growing up less gullible than I might otherwise have been.
We wandered around the fair, wherever it was and however old I might have been. We might have gone on some fairly tame rides or into the “Fun House” (also known as “House of Mirrors”), perhaps a haunted house. By the way, and as a courtesy service to those who are unaware, these rides are neither in a house nor haunted (inhabited by the ghostly remnants of the previously living). On the other hand, you do get to ride in an uncomfortable cart that jerks back and forth, side-to-side as it makes its way along an electrified track past tableaux vivant that are meant to horrify but are usually just cheesy.
We arrived at the time-honored sideshow area of the fair, a place where P.T. Barnum and other impresarios before him once displayed genetic anomalies as a source of amusement for paying customers. Well, and social anomalies like naked women. This was a fairly tame sideshow area as both the year (the early-to-mid 1960s) and the location made truly tasteless sideshows a bit much for the population.
For some reason, my young eyes were drawn to a sign that said “The Cardiff Giant” and I was instantly intrigued. I can’t tell you why but the sign triggered something in my reptilian brain and said “ooo – a real-life giant! a huge person! I must see this person!”
Some of you know the tale of the Cardiff giant and know what I saw next but don’t whisper it to your friends and neighbors. Let this play out….
It didn’t take much work to get my mother to shell out for two tickets—I think they were a dollar each—and we went into this particular tent. A large, or rather long, plaster figure of a male human was supine in a wooden box just a little below the level of my eyes. The figure was not particularly well wrought, not entirely evocative of something that might have ever been alive, and not so huge, even by the dubious standards of fakery, to result in much other than disappointment from me. I had been duped and had caused good money to be spent for the duping! A dollar apiece was, to my young mind and to the times in which we lived, a good chunk of money. I think it may have been equal to my weekly allowance and might have been more that my parents allowed—I can’t remember.
I probably sounded a little comical in my petulance and disappointment. My mother undoubtedly knew that it was a hoax—a rather famous hoax originating in the mid-19th century—and played along as an object lesson for the young and credulous version of myself. But I was beyond disappointed, I was also pretty furious (in a well-behaved way, of course) and let the barker who had taken our money know that I felt cheated.
“That was fake!” I might have said. I certainly said something equally appropriate to the occasion and I said it a bit loudly too. I think all the response I got from the barker was a grunt of surprise that I was surprised but that annoyed me even further. In some way, it clouded a perfectly good day and cast a pall over me whenever I thought about it for some time afterward.
I never went in a sideshow again. I became less gullible. Eventually, although not immediately. Perhaps I even became somewhat less cruel. After all, a giant is nothing for anyone to ogle, living or dead, factual or concocted by hucksters. Neither is a hirsute woman or an elephant man, a human being dwarfed by genetics or a naked woman disrobing because economics have not been kind.
In a way, the sideshow was nothing more than a house of mirrors. Staring back from the box that contained this poor representation of a 19th-century hoax was an image of my own perverse, albeit immature, interest in oddities, a reflection of my own gullibility, a mirroring of an inner self to learn from and leave behind.
Many of us may have had similar experiences, although not always at the enticement of a sideshow sign or a barker’s call. Some of us learn from our experience. Some of us don’t. Some of us steer away from a cruel interest in “otherness,” some are always intrigued.
When you looked in a box containing a mirror, what stared back at you? Did you learn or did you laugh?
She was just a girl,
just like any other
but in the second class
of the day—English—
we sat at the back wall
in a room like many others,
desks pulled together,
whispering with the
whole class hearing
what we said or
how we said
whatever it was
we deemed so central
to our learning.
“We can hear everything,
young man” said our teacher,
and that stopped us
for the second it took
to realize our volume
but our focus was just
where it belonged,
learning from each other
what it meant to be young
and yearning to be free
in a world that would not
allow it to be.
I am a trusting person. The good news is that there is much to trust in our daily lives.
I trust that sometimes around the time I wake the sun will have risen—or will soon rise—in the east. I trust that the weather will vary during the day and although I may be oblivious to it the weather will vary during the night as well. I trust that a year will pass in a series of days and those days will pass in a series of hours, minutes, and seconds. I trust that time will not reverse in this process and I will become older, not younger. I trust that seasons will bring changes to how the world appears, at least in my part of a large planet full of differences.
I trust that I survive each day because the invisible stuff that surrounds me contains oxygen and that some of this oxygen ends up bound to my hemoglobin and myoglobin proteins and will end up servicing core and peripheral functions of my body. I have never seen an oxygen or any other gas molecule per se but I have seen hemoglobin data modeled out using physical probes and understand that hemoglobin is transported in red blood cells (aka erythrocytes), which I have seen through photomicrography recorded by others. I trust that when I drink and eat a whole series of enzymatic processes will turn the foods and beverages into energy, some used immediately, some stored for a nomadic existence that has long ceased to be relevant for many. Some of what was once delicious will cause me to get up when I don’t want to get up and do things which are among the least dignified activities any of us will perform on a regular basis. On the other hand, we have no choice, so why complain?
I trust that most of the people I see on any given day will behave themselves within acceptable parameters… except when some of them are driving, at which time this subset will take actions that they are told by the motor vehicle and people licensing authority are not acceptable… yet they do these things anyway. You’ve probably seen them do these things wherever you are and you may see them do worse things that I shudder to even imagine. I trust that, while most of the people I see are behaving appropriately somewhere, someone is not doing all that well in this regard. Oh, and that the “someone” to whom I refer is accompanied by others who are also not behaving. These behaviors take place in all towns, cities, and countries and by all people, regardless of wealth (presence or absence thereof), country of origin, employment status, religion, ethnicity, gender. Both well-intentioned behavior and its opposite are aspects of human existence. While other creatures on our planet do violence to each other on occasion, we are the only species that participates in violence and its correlates so pervasively and still find a way to live with each other (for the most part).
Sometimes, I look up a word before starting in on it. It seems to have roots back to the early state of languages called Proto-Indo-European (aka PIE (not π)). For a phenomenal map of what languages are derived from which others, please go to the site provided under the following version:
I’m just going to drag something over from the Wiktionary page to get into how trust is linked to some very fundamental human values:
“Protection,” “confidence,” “help,” “be firm, hard, solid.” This is what we associate with the meaning, although we don’t necessarily think through that the word is from Old Norse and Middle English, or that it is related of “confidence” and thus to the Latin fides, which meant trust, faith, and belief and is responsible for fidelity and bona fides. Interestingly, the Wiktionary page also points the reader to derivation of the words “true” and “tree.” “True” seems explicitly related; one wonders if the concept of trust and truth both came from an appreciation for the confidence, help, protection, firm, hard, solid virtues of houses built from the readily available (far more then than now) tree.
It is also interesting that the ideas of faith and belief are concepts that grew simultaneously with the concept of trust. I wonder, though, whether these meant something far more alike to trust when they were conceived than they do now.
While I trust in all of the experiential, reliable events that I cited in the first couple of paragraphs (with some elaboration from the sciences, admittedly), I do not need to have faith in them or believe them to be true. They simply are trustworthy and true. When I listen to politicians tell us to have faith in them or believe in them, I start wondering where I left my wallet and whether my bank has secured the accounts against hacking. I understand why they want my belief but I will give it when their actions measure up to their words. I will believe them when I trust them but I will not trust them until I believe that they have achieved what they promised.
It is also interesting that the word “truss” meaning a structure that supports or stiffens a building is phonetically related to “trust,” as that is the function it is intended to convey to the building. It makes the building, no longer made of trees, one that you can have confidence in entering. Your faith will not be tested, your belief shattered. Well, unless the weather gets really bad. And I trust that it will on some days.
When did fire become a thing? Poor old Prometheus… Probably not his fault at all….
When did fire become a thing? No one knows the answer to that question. Fusion certainly occurred before fire—it happens in suns, along with nuclear fission (radioisotopes exist in the sun)—but this is not fire. It appears flamey. It is hot. It radiates through varying segments of the electromagnetic spectrum. But I am going to limit the definition of “fire” to “combustion,” if you don’t mind.
The simplest combustion reaction occurs when pure hydrogen (H2(g)) and oxygen (O2(g)) gasses are combined in a 2-to-1 ratio and given a little energetic push called activation energy (i.e. hydrogen and oxygen will hang out with each other unless they are provided this energy). Diagrammatically, the activation energy looks like this:
The reactants (hydrogen and oxygen in our example) start on the left side of the hump, an appropriate (or excess) amount of energy is provided, and products result on the right side of the hump. The “ΔH” thing on the right side is beyond the scope here but represents a positive, negative, or neutral amount of energy released in the reaction.
The amount of activation energy varies widely from very small (e.g. some explosives) to “no reaction will ever happen regardless of energy input.” Here is what the most basic combustion reaction looks like in chemical reaction shorthand called “stoichiometry:”
2H2(g) + O2(g) → 2H2O(g)
And now, an entertainment of limited scientific value:
Combustion is generally thought to involve hydrocarbons (e.g. octane in the “gasoline” or “petrol” you use in automobiles) or their oxygenated friends the carbohydrates (e.g. cellulose, a polymeric carbohydrate used in paper and present in wood). The simplest combustion reaction is between methane (CH4(g)) and oxygen (2(g)), again resulting water but also resulting in carbon dioxide (CO2(g)) when the reaction occurs efficiently. When it does not occur efficiently or when it occurs in the presence of other substances (e.g. most of the time) it produces by-products including carbon (elemental symbol “C” aka “soot”). Here is the stoichiometry of that simple reaction:
Methane is commonly known as natural gas, although natural gas is not pure methane when used as a fuel. What the stoichiometry tells us about this reaction is that each molecule of methane uses two molecules of oxygen and produces one molecule of carbon dioxide and two molecules of water, along with an amount of energy released in the process. The energy is used to heat various processes, including home furnaces and water heaters, and used to drive steam and gas turbines to produce electricity.
When octane is used as the hydrocarbon, the balanced equation is as follows:
2C8H18(g) + 25O2(g) → 16CO2(g) + 18H2O(g)
In common English, this means that each molecule of octane requires 25 molecules of oxygen (and that activation energy thing, typically supplied by spark plugs) and results in 16 molecules of carbon dioxide and 18 molecules of water, along with a good burst of energy that drives the pistons, drive shaft, and wheels; the wheels have tires that turn and exert a force against driveways, roads, dirt, mud, water, etc. and the automobile moves forward—or backward—at various speeds as allowed by the transmission.
Candles (if you were wondering where all this leads) are made from paraffin wax, which is a varying mixture of hydrocarbons typically with between twenty (C20) and forty (C40) carbons in their structures. A C20 hydrocarbon like eicosane can have up to 366,319 isomers (isomers all have the same chemical formula of a chemical compound but differ in physical and some chemical properties), while tetracontane (C40H82) has 62,491,178,805,831 (that’s sixty-two trillion four hundred ninety-one billion one hundred seventy-eight million eight hundred five thousand eight hundred thirty-one) isomers (somehow, it seems like more isomers if you spell the number out). The C(xy) compounds between C20 and C40 have numerous possible isomers as well and they increase logarithmically (see chart below) as the number of carbons increase. Not all of these hydrocarbons are in paraffin but these numbers should give you an idea of how chemically complicated a simple candle may be.
While this already seems like a brain-damaging subclause to our proceedings, the estimates for number of isomers for each number of carbon is actually more complicated than I am representing here. If you have further interest, you can take a look at this discussion. If not, let’s proceed.
There is a standard equation for calculating how much product results from combustion in oxygen of any hydrocarbon; it is:
where z = x + y/4.
This means that in cases where there are 20 carbons as for eicosane, the carbon dioxide and water molecules result in the following way:
2 C20H42(s) + 61 O2(g) → 40 CO2(g) + 42 H2O(g)
or… for each two molecules of n-eicosane (one of about 366 thousand isomers of eicosane) are consumed by combustion, sixty-one molecules of oxygen are consumed, thus producing 40 molecules of carbon dioxide and forty-two molecules of water.
The thing is that it is rare that anyone burns a candle or anything else in pure oxygen. When hydrocarbons are consumed in air, a messier equation obtains to the problem:
Note that carbon monoxide is produced, along with hydrogen gas and the more familiar carbon dioxide and water. This version of the equation is why it is critical to ensure adequate air supply when using a kerosene (or other hydrocarbon-based) space heater in a closed space; the amount of carbon monoxide goes up as the amount of oxygen available goes down. Carbon monoxide, a colorless and odorless gas, causes humans to fall asleep and die due to a special kind of asphyxiation caused by very strong binding of carbon monoxide to the iron atoms in your hemoglobin and myoglobin. Once that happens, those proteins cannot carry oxygen through your arteries and your body is “starved” of oxygen.
Okay, so hydrocarbons burn in air (n.b. there is also lots of nitrogen in air and that produces problematic by-products as well) and that means carbon monoxide, carbon dioxide, water, and hydrogen are produced, along with a substantial amount of particulate matter (e.g. particulate carbon and other solid carbon by-products), which ends up in our shared atmosphere (n.b. there is no “U.S.A. atmosphere” or “China atmosphere,” there is one planetary atmosphere). The most common liquid fuel currently consumed is octane but that is not consumed as pure octane, so there are other hydrocarbons and “stuff” consumed at the same time… in air… which produces problematic by-products.
Here’s a chart of how much world liquid fuel has been consumed and is projected for consumption PER DAY over the listed time period:
Yes, the chart does indicate that we consume between 94 and 96 million barrels of liquid fuel per day. One barrel of liquid fuel is equivalent to 0.1172 metric tons and a metric ton is 2,200 pounds (for the non-metricized readers). One barrel is 257.4 pounds of liquid fuel. If we are consuming (let’s be modest) 94 million barrels of liquid fuel per day (and let’s be factual) there are 365 days in a year, we are consuming 8,846,490,400,000 pounds of fuel per year. If we were to pretend that all of this were octane (which it isn’t) and all of that octane followed the simplest hydrocarbon-to-carbon dioxide equation provided above (which it doesn’t), we say that every two units of octane produces sixteen units of carbon dioxide. These don’t have the same mass, of course.
To make this simple, a gallon of gasoline weighs about 6 pounds. Each gallon of gasoline produces about 18 pounds of carbon dioxide (idealized as stated above). If we divide the number of pounds of liquid fuel consumed annually by 6, we will have an estimate of the number of pounds of carbon dioxide produced. Well, the number is:
(8,846,490,400,000 pounds of fuel per year)/(1 gallon/6 pounds) = 1,474,415,066,666.67 pounds of carbon dioxide/year
To do our numbers-into-language thing, that is one trillion four hundred seventy-four billion four hundred fifteen million sixty-six thousand six hundred sixty-seven (let’s round up, given the decimal figure) pounds of carbon dioxide produced from the aforementioned pounds of liquid fuel. Pretty incredible, right?
The bottom lines are these:
we can’t breathe carbon dioxide (it chokes us)
actual combustion produces lots of other by-products that are also not useful for human respiration and cause various respiratory illnesses (cancer, emphysema, asthma for starters)
these numbers don’t include gaseous fuel like methane, ethane, propane, or butane (starting with pentane and going up to heptadecane (C17), the compounds are liquid at 25°C), which are also used as fuels.
these numbers don’t include non-petroleum fuels such as ethanol, which is an oxygenated hydrocarbon but also produces all the by-products listed for hydrocarbons
Our global economy is heavily dependent on consuming something that
is finite in quantity and
produces harmful by-products
is going to go up in price as the amount available nears complete consumption
We have not solved the equation for producing less carbon dioxide and less harmful by-products while maintaining our current lifestyles.
Okay, end of lesson. Talk amongst yourselves. This all needs to be solved.
Burn a candle while you’re at it. Couldn’t hurt (much).