Some are simple to answer, but people who have missed their opportunity to be broadly educated sometimes can’t separate the simple queries from the hard. I’m in that group, more times than not.
I rummaged through an old safe the other day. I found its key tucked away and forgotten in the back of a drawer in an antique desk. I asked myself: what might be in that old safe? Why not take a look? What harm could there be in searching a dusty safe for forgotten objects?
I found old papers and school reports. I found Christmas and birthday greetings and expired credit cards. I found a rectangular tin-foil-wrapped object pressed flat and smooth and a quarter-inch thick — a pamphlet of some kind, perhaps.
I would unwrap it later.
I reviewed a report card from the seventh grade. It held up well during the past 58 years. My geography teacher wrote a comment that caught me by surprise. “Billy Lee is a thinker,” he wrote next to the “A” he gave me.
I remembered back. Mr. Holden drove a taxi-cab nights to make ends meet. Memories flooded in.
He complained that teachers weren’t paid enough. Between taxi fares, he read books. He recited titles and authors, but I knew I would never read them. The writers’ names were unfamiliar — foreign, some of them, which I couldn’t remember or pronounce; the titles? — incomprehensible.
How could anyone read books whose content was unconnected to anything they knew or were able to understand? I couldn’t. I was sure of it.
I found a letter from a girl I once loved. She explained why we could no longer be together. Despite all my wonderful qualities, I was needy, she explained. I needed to turn my needs into wants by finding others to fill in the gaps she couldn’t.
It was odd, I thought. I didn’t realize how technically expert was her craft the first time I read her note. Who knows? Maybe today she is a famous author who writes under a pen-name. Stranger things have happened in the history of literature, right?
The writer of Jane Eyre comes to mind. Charlotte Brontë published her novel under the name of Currer Bell. I always thought a writer of her depth might have come up with a better name. I did, and I’m not half the writer Charlotte was. People have to admit, Billy Lee has a nice ring, no?
Lately, I’ve been writing answers to questions on Quora to which no one can possibly know the answers. I call them mystery questions.
Many of the questions remind me of the sailor’s dilemma where a seaman finds himself stranded and adrift on a raft in a vast ocean of swells during a raging monsoon. The man clings to a few pieces of wood and prays to God for deliverance.
He asks God why was he born when it is clear that his life is going to end in terror, alone on a raft in a bottomless sea with no chance of rescue. If God by some miracle answers his prayer; if God saves him and the storm clears, the sun will bake him alive; eventually the sharks will eat him.
Why? Why? Why?
What sin did he commit that drove him to his fate? What decisions did he make that were ill-advised and unwise?
What might he have done differently to avoid the horrid end he knows will befall him in the few moments that remain before his strength is sapped and he loses his grip on the last piece of wood, which will disintegrate once he’s sucked beneath the churn.
Well, one answer that comes to mind is this: he didn’t plan for his birth; once born he didn’t plan for his death. He never really believed that he was doomed to a lonely, fearful death — the destiny of all living creatures; humans are no exception.
The answer to his cry for answers is that there are no answers. No one avoids losing everything they love. It is every person’s fate. No scheme, no matter how cleverly constructed, avoids it.
And yet the sailor begs God. He shakes his fist and screams against the gale: God, why did you forget me? Why my pointless life? Why did I suffer to the very end?
Amen.
Here are six mysteries I will struggle to explain.
Mystery 1 — What caused or initiated the Big Bang, if there was nothing before it?
95% of the mass and energy of the universe that theories and observations say must be “out there”, no one has been able to find, right?
Does anyone anywhere know anything at all about what the universe is or how it works?
The big bang is a verbal “analogy” used to help folks visualize what a few theorists have worked out mathematically to explain a lot of observations that otherwise make no sense.
Here is the hard part: the mathematics is also an analogy; it isn’t real; it’s just numbers. Mathematics cannot make a model that reflects fundamental realities without simplifying a lot of important stuff — and no one as yet knows what the missing stuff is that human speculation and observation is overlooking.
We all know it’s true.
Mathematics is a way of reasoning — like language but minus its ambiguities and textures. An argument can be made that mathematics and language are not adequate to the challenge of describing reality.
Humans seem to be lost in a mystery of existence from which they will never be rescued. They lack certain fundamental tools that they must someday discover and develop to give them any chance at all to climb out of a very dark hole of ignorance.
It might be possible to understand the cosmos — if the secrets of consciousness are unraveled. Consciousness is the magic-water in the desert of ignorance which — when found, understood, and imbibed — could quench the thirst-to-know that every thinking person suffers. That is my hope, anyway.
Consciousness might be fundamental and foundational. Most people won’t accept it, but almost every brilliant person who has thought the problem through seems to have written that it must be so.
Mystery 2 — Assuming we can completely separate religion and faith from pure science and fact, then speaking from a purely scientific point-of-view, what form would life after death take?
The consciousness that people experience today is the consciousness they will experience after death if consciousness is the fundamental foundation of all reality.
Conscious life-forms plug into universal consciousness like televisions plug into the cable network. TVs come and go, but the cable network is forever broadcasting. The conscious experience it creates appears in the televisions that are connected to it and can be observed on their screens by independent observers.
The reality of television comes from its fundamental foundation, which is a broadcasting system — in this analogy. As long as a television is plugged in and turned on somewhere, the reality of the cable network will continue.
Consciousness does not belong to the TV, but is experienced by it. When the TV “dies”, this consciousness will continue to be experienced by other TVs. The unplugged television will never miss it, and the consciousness it shared with other televisions will never die.
This view of reality has been described in analogous ways by Erwin Schrödinger, John Von Neumann, John Archibald Wheeler, and other brilliant physicists.
DNA is a reservoir of bases that RNA draws from to build sequences that are processed in RNA-built structures called ribosomes. From them polypeptide “necklaces” are fashioned which are folded by Golgi structures into proteins. Proteins become the tissues of the body and the catalysts of cell metabolism, right?
In humans, 10% of DNA is used to make the templates of proteins (2%) and catalysts called polymerases (8%). The rest (90%) is not used as far as anyone knows today.
A lot of extraneous chemical structures play at the edges of DNA to influence what is expressed and what is suppressed. It’s called epigenetics and is an active field of research.
DNA is neither a code nor a cipher. It’s not that simple. A lot more is going on that scientists know about and which scientists know nothing about. For example, proteins exist in the body for which no DNA sequencing has been found in the genome. It’s called dark DNA.
Mystery 4 — If the expansion of the Universe is accelerating, won’t it reach infinite speeds? What does an expanding universe mean after the heat death of the universe?
The universe is expanding like a balloon that is being inflated by the force of something that exists inside it, which no one understands. I’ve heard mainstream physicists say that they believe this expansion is uniform and accelerating; it will lead to a “Big Rip.”
The Big Rip will tear apart everything — including atoms and parts of atoms. Energy will dissipate and the universe will flat-line and disappear. It will be as if the universe never existed when the process is complete. Space, time, energy, and matter ripped to shreds will leave nothing behind.
I’ve always thought that the accelerated expansion of the universe is caused by the gravitational tug of trillions of parallel universes that surround our own like a swarm of fireflies. Accelerated expansion is evidence for massive parallel universes, it seems to me.
As seductive as this idea is, no one is proposing it as a serious explanation for the observations of expansion. I don’t know why, but suspect that many of the smartest people don’t think the parallel worlds model clears up enough of the mysteries in the cosmos to be worth pursuing.
Neither does the Big Rip model. It can be argued that the “rip” model explains nothing. It describes what happens when everything is driven apart by an unknown force to its logical conclusion. Somehow, the description doesn’t seem helpful. It doesn’t answer the biggest question of all: how did everything start in the first place?
How did we get here? Where are we? Is anyone in charge? Will the universe live and die without the benefit of any living thing — any conscious life, including itself — understanding the why and how of it all?
How can something on the scale of a universe exist and then cease to exist whose mysteries were forever out of reach — impossible for conscious-life to grasp or comprehend?
Mystery 5 — How could the precursors to the origin of life move or assemble with intent? At what point would this intent become actual life?
Anyone who says they understand how the precursors of life assemble is telling fibs, because no one has any idea how life started. I’ve heard convoluted conjectures about how clays, for example, might have got life started, but they are unconvincing and not reproducible, at least to my way of thinking.
Based on evidence in ancient rocks it seems more likely that comets and asteroids carried prokaryotic cells to Earth. These cells are thousands of times smaller than the eukaryotic cells that are the building blocks of all animals and plants.
Because these cells are small and are, internally, a disorganized mess (no organelles, no nuclei, tiny amounts of RNA & DNA mixed together like scrambled eggs along with everything else they contain), it seems reasonable that prokaryotes could be abundant in the universe and have existed since the first generation of stars and planets.
These cell types were firmly established on Earth (a third generation star) by Earth-Year one-billion. Oxygen didn’t exist, nor did oceans. Some geologists believe Earth was bone-dry at its start.
Now comes the really hard part to understand. It took two-billion years for these tiny cells to branch-off into the much larger and more tightly organized cells called eukaryotes. During that time an onslaught of ice-balls from the outer reaches of the solar-system created a deluge of water on both Mars and Earth.
Earth — having 2.65 times the gravity of Mars and a magnetosphere (which Mars lost when its iron-nickel core froze) — was able to hold onto both its atmosphere and its oceans.
Oceans are probably the incubators where highly unlikely events occurred that made humans possible. Cells grew in size and complexity. Some engulfed prokaryotic granules that became the mitochondria that every eukaryotic cell uses like mechanical batteries to add the energy necessary for big cells to survive.
Somehow these big cells learned how to use sunlight for power. Photosynthesis released oxygen, which poisoned almost every other kind of living cell on the planet. The survivors, the remnant, took another billion-and-a-half years to become space-exploring civilizations of highly intelligent animals who call themselves humans.
It’s a process that, because of its duration and a number of sporadic near-extinctions, seems unlikely to have happened at all, but here everyone is on Earth to prove that the impossible is possible.
Although I agree with Freeman Dyson that prokaryotic life is going to be found to be pervasive in the hundreds-of-thousands of methane-and-water ice-balls in the outer reaches of the solar system (called the Kuiper Belt), it seems unlikely that the much larger eukaryotic cells (or the animals and plants that evolved from them) will ever be found anywhere else but on mother Earth.
It’s possible that intelligent life has evolved in some other place, but the odds are small enough that by the time humans suffer their inevitable extinction it seems unlikely that they will have found and identified beyond Earth any non-prokaryotic life at all.
And now, at last, the final mystery. Mystery number six.
Who forgot what it is?
Remember the foil wrapped object found in the old safe? What was inside, anyway?
Any guesses?
I took the shiny object to my wife, Bevy Mae, and we carefully peeled away the foil to reveal the contents within.
And of course, dear reader, you guessed right. A stack of money is a wonder to behold. It makes living feel real good, at least for a while. A sufficiently large amount provides the freedom to buy any old thing at all.
Will we buy a sailboat and take our thrills from a roiling ocean?
I have hope that someday readers will visit Quora.com to look up me — Billy Lee — to read my answers to hundreds — perhaps one day thousands — of questions asked by every kind of curious person from every part of the world.
I love to read and think about questions from unmet others — to encounter oddities that have never occurred to me to ask or answer.
It’s humbling to be confronted by the knowledge that not only do I not know the answers to thousands of questions, but I lack the breadth of mind to even imagine such questions; I am convicted by my own lack of curiosity and inability to think deeply about an almost infinite number of mysteries that other people of all types and backgrounds wonder about and seek to understand.
Hundreds of years ago, polymaths — the smartest and most energetic of them, anyway — could know and understand all that humankind ever dreamed. Today, the world is too complex; the depth of knowledge required to understand a narrow subject — like juice-carton safety-caps (I hold a patent) — takes years, maybe decades, to acquire.
Is it any wonder that smart people give up and go stupid?
No matter how much a Doctor of Philosophy knows about the rules of logic, he’s a dummy to every certified automobile mechanic he will ever meet — and vice-versa, right?
A way out of the dilemma is to practice the art of pontification. I pontificate based on a lifetime of experience; and reading; and wandering the world; and poking around in my backyard — to ponder why things are the way they seem to be.
Je connais beaucoup demerde, and I know a lot of nothing. When I write it down, well, magic happens. Resonate rings of truth rise which when later read render me reeling.
I’m unsure where-from the magic comes. It seems to fall from heaven to light the world. I’m driven to share with souls known only to God, because I have no way to know who reads my blog. I know only that some folks make the time, because WordPress stats say it’s so.
One of the things on Quora.com that seems to confuse a lot of people is the difference between momentum — a measure of the mass of an object multiplied by its velocity in a particular direction — and kinetic energy, which is a measure of the energy of an object that has been accelerated for a period of time in a particular direction, which enables it to do work.
Momentum is an object’s mass times its velocity; it is a measure of its inertia along a defined direction. It is measured in newton-seconds.
Kinetic energy is released by an object in units of acceleration that were initially induced by newtons of force. It is equal to half the quantity that is calculated by multiplying an object’s mass by its velocity squared. It is measured in units called joules, which are newton-meters.
Of course, spinning objects that aren’t moving in any direction have momentum and kinetic energy, too. The two are wrapped together in a concept called, torque.
Dear God, help me.
Now, I’m confused. Somebody, please, explain to me. I thought I understood until I started writing. I did. Really.
Another source of confusion concerns the nature of photons, which are tiny packets of oscillating electric and magnetic energy — from which light is made, right?
Photons seem to have no mass in the vacuum of space. When they pass through a material like glass, they leave a wake of disrupted electrons in the glass which belch out polaritons. These particles add mass to the photons and slow them down by as much as forty percent.
When photons exit the glass and enter the vacuum of space they leave the polaritons behind, lose their acquired mass, and jump to light speed, instantaneously.
Who knows for sure that it’s true?
Who understands why?
Here is an interesting thought: if humans — limited in understanding by language and mathematics — are unable to ever know why photons exist and behave as they appear to do, then who can? Who does understand?
Is all the complexity of the universe understood by no one? Is it possible that an unlikely universe can exist forever whose fundamentals cannot be articulated and which lies outside the experience and ability to comprehend of any sentient life-form whatever, whenever, wherever?
What kind of place do we live in, anyway?
Calm down. Take a breath.
Reality may not be as hopelessly inaccessible as it seems. Can it?
Here are some questions, which I’ve answered as truthfully as I know how. The answers are assertions of truth.
1 – How did a single cell organism eventually lead to complex life on earth, and does that mean that all life has a common ancestor (the single cell)?
This one is the 64-million-dollar question that no one has ever answered convincingly. Prokaryotic cells were established 3.5 billion years ago on the early Earth. They evolved to become the bacteria and archaea branches in the tree of life that exist to this day.
Here is the amazing part, at least for me: Eukaryotic cells, which are the much larger and more tightly organized cells of all animals and plants, did not emerge until two billion years after prokaryotes. It took a long time to evolve cells capable of conjugating into more complex life.
For the past 1.5 billion years eukaryotic cells have evolved into life forms capable of civilization and space exploration. The time frame is amazingly long.
The thought that a lunatic could in a moment of bad judgment start a cascade of events that extinguishes all life is troubling.
When astronomers look into space they see no signatures of life as advanced as ours. Again, this is troubling, because it might be an indicator that the knowledge possessed by advanced life-forms may approach some asymptotic limit where self-annihilation becomes inevitable.
2 -What evidence would falsify the theory of evolution?
No one knows all the myriad ways that life evolves, only that it does. That life evolved from cells that were fully functional 3.5 billion years ago is an established fact, because of evidence found in rocks.
Scientists know that it took two billion years for these ancient cells to evolve into the much larger and more tightly organized eukaryotic cells that today are the foundational structures of all animals and plants.
No one knows how life as complex as cells was established on a hostile planet like the early Earth, but everyone has an opinion; these opinions are called conjectures and theories.
One scientist might say that life started on Mars and was transferred to Earth on space debris uplifted by a cataclysm on Mars. Another says no; all the stuff necessary to make prokaryotic (primitive) cells existed in abundance on a young Earth — perhaps near hot vents in the ocean floor. Other geologists say the earth was bone dry at one billion years. Oceans came later, so just what the heck does anyone know for sure, anyway?
Many conjectures purport to explain how life changed from unicellular eukaryotic forms 1.5 billion years ago into the space-exploring civilizations of today. Every conjecture thus far has already been falsified either by evidence or by competing conjectures that make as much sense but are different.
For example: some say mutations in DNA drive evolution. The problem is that mutations are too rare. Some say an eco-sphere of processes driven by a halo of molecules that cling to DNA drives evolution. They call it epigenetics. Others say, no. RNA drives evolution like colonies of intelligent ants who build hives. There are other explanations.
None are verifiable or generally accepted due to an insufficient body of proof that is able to overcome alternative ideas that are equally compelling.
Another problem is that no one knows if DNA life is all there is. DNA is a molecule that cannot be seen or worked with until it is amplified into a viewable goo.
Are there other undiscovered molecules no one knows how to amplify?
Understanding of the parameters and limits of life is incomplete and may perhaps mislead researchers. Humans might not yet know enough to figure out the dynamics of genomes. More needs to be discovered and understood.
Is there a shadow biosphere that is in a symbiotic relationship with DNA? Where is the dark DNA that biologists can’t find that is necessary to code for many of the proteins they know exist?
How were cells themselves established so quickly on Earth? It’s a question whose answer is discussed by countless experts and non-experts; no answer fully satisfies.
Darwin’s ideas about natural selection and survival of the fittest have their place. But he was just getting started, and he died a long time ago. Scientists have a lot of work left to do.
3 – Which Bible story is most objectionable when looked at in the context of modern morality?
All Scripture is God-breathed. To love and be loved by both God and people is why we were born; it’s what makes life precious and worth living. No one wants to die; no one wants to be hated.
The sad part is that everyone suffers; everyone is hated by someone; everyone hates someone; everyone dies after a life of blunders and sin. Christ Jesus came to save the lost, which by the looks of this thread is pretty much everyone.
We have hope. It’s something to hold onto as we grow weak and find ourselves ruined at the end of our minutes in the sun on our beloved Earth.
Jesus made a path for us. It cost him everything a human can pay. He somehow survived the Roman crucifixion that killed him to show the poor and overly burdened that in his power is the way, the truth, and the life.
There is a path to paradise; we — everyone of us — can find it by surrendering to the God who loved us, gave us life, and suffered to set right what we put wrong.
4 – People say Newton’s third law, “For every action, there is an equal and opposite reaction,” is not accurate. Is it true?
Einstein said that only mass and energy exist; they are in fact equivalent; they are the same thing; two sides of the same coin. Energy gives rise to all other phenomenon and forces that scientists observe.
Stephen Hawking said that when mass (or energy) comes into existence a negative energy must emerge to balance it so that when added up everything in the universe sums to zero. It appears that Newton’s third law, equal and opposite, is not only accurate — it is a fundamental balancing principle that undergirds existence.
Mass is matter, which can be positive or negative and is referred to as matter or anti-matter.
The Billy Lee Conjecture claims that mass is pixelated (quantized) such that in the contest of emergence within the smallest spherical volume, matter or anti-matter (one or the other) will prevail due to a natural truncation of π in the putative spherical volume of the creation space.
An evenly divided ratio of matter and anti-matter within a spherical creation-space is physically impossible if π is truncated by pixelization. Matter and anti-matter will annihilate until a single piece of either matter or anti-matter remains after the creation event.
To maintain a zero-sum, balancing counter-energy will emerge according to speculation by the late Stephen Hawking.
Over long periods it seems that an extraordinary amount of matter has accumulated inside our own universe by surviving the natural annihilation of matter by anti-matter. This matter seems to have generated an enormous amount of counter-balancing energy — some of which Newton called gravity. Most of the energy remains undiscovered and is referred to as “dark.”
In our own universe, π seems to “round-off” near the precision of the Planck constant.
In universes outside our own — some of which seem to be pulling our universe apart in an accelerating expansion caused, perhaps, by their own gravitational forces — π may truncate to different values to generate in some cases a prevailing anti-matter and opposing energies that manifest qualities different from the energies found in our own universe.
If parallel universes disrupt the zero-sum strategy of our own, it may still be true that the principle of zero-sum or equal but opposite is operational, but humans are too small and the distances are too far for anyone to ever know for sure that it is true.
5 – What are the major foreign policy issues that the United States of America is working on in 2018?
I’m writing this answer just after the meeting in Singapore between North Korea and the United States involving the Korean nuclear arsenal.
The Secretary of State, Pompeo, said yesterday that NK has two years to de-nuke. This delay might tempt the Japanese to convert their stockpile of 47 tons of plutonium into bombs. Japan and North Korea have issues related to the Japanese occupation of Korea from 1910 to 1945.
It takes ten pounds to make one bomb. The Japanese can make as many bombs as they want in as little as 24 hours.
A Japan armed with 10,000 nuclear bombs (they already have the missiles to launch them) is a clear and present danger to China, Russia, and Korea — not to mention the United States with whom Japan has a beef that goes all the way back to World War Two when the USA destroyed 67 of their cities with napalm; two cities by atomic bombs.
The USA has occupied Japan ever since. Some of the Japanese probably hate us — who knows for sure?
6 – Can a photon’s speed be slowed down? I have heard that it can be slowed by a medium, but I have also heard that it is just the velocity being slowed as it “bounces” from particle to particle? I am not talking about Bose-Einstein condensation.
The current thinking is this: when a photon leaves the vacuum to enter a material object, it leaves a wake in its path that vibrates electrons in the medium. These oscillating (or disturbed) electrons generate polaritons, which are photon-like objects that can catch and add mass to the photon. With mass added, the photon slows down — as much as 40% in glass, for example, which enables more polaritons to pile on.
When the photon exits into the vacuum of space, it disentangles from the polaritons, and instantly resumes light speed.
I didn’t make this up.
It’s what some physicists are saying, and it explains a lot and leaves a lot unexplained — like all things physics when folks go just a little deeper into the abyss of understanding.
7 – What is the relation between light and darkness? Can one exist without the other?
Light is the action of certain wavelengths of electromagnetic radiation on structures in the eye, which trigger hallucinations in the brain that humans report as “light.”
An infinite range of frequencies are “out there.” Humans are blind to almost all of them. People who are unable to trigger hallucinations induced by electromagnetic radiation say that they are experiencing “darkness.”
Some frequencies of light are experienced as “heat.” Because the sensation is not accompanied by visual cues, people in hot rooms with no windows believe they are experiencing “darkness.”
The experience of heat is caused by the same electromagnetic waves that induce visual experience, but they are a tiny bit longer in length than those which induce the experience of the color “red” in humans.
The longer waves carry less energy and are invisible to people unless they view the ”infra-red” light through high-tech sensors. Local fire-departments use these sensors to identify ”hotspots” where fires might reignite.
8 – Given an opportunity to pass through one or two slits with no detection, will a quantum object always pass through both?
If the slits are in the right position and are cut to the right size and are at the right distance from the source, a pattern on a detector screen will evolve over time to look as if waves are passing through the slits and interfering in a predictable way with each other.
Of course, it’s not true, because the particles are shot one at a time and the duration of the experiment can be hours to weeks long. The shots land one dot at a time. After thousands of shots, a pattern that resembles what one would expect of waves interfering is formed by the particles as they accumulate on the detector backstop.
9 – Is Jesus a hoax? Jesus has not walked on Earth in 2,000 years. How can a man 2,000 years ago save anyone?
I was hungry and you gave me something to eat, I was thirsty and you gave me something to drink, I was a stranger and you invited me in, I needed clothes and you clothed me, I was sick and you looked after me, I was in prison and you came to visit me.
The righteous will say, ‘Lord when did we do these things?’
My answer will be, ‘Everything you did to help suffering people, you did for me.’
The preceding is a paraphrase of part of Matthew 25, a book in the Bible.
Read it. Why not?
The answer is in the sense that it is not a hoax that the “least of these” walk the earth when we do. How we treat unfortunates is, in the view of Jesus, the way we treat him. He will return to us the same courtesies when finally we give GOD an account of our lives.
RNA, in its many forms, behaves like ant colonies which swarm over the DNA pile to do a number of tasks that seem to involve a lot of decision making.
RNA selects out of billions of bases a few thousand which it strings together to make “genes” that it transfers to ribosomes — which are made almost entirely of RNA and are among the oldest structures in cells.
At a ribosome, the genes are coupled to RNA that carries amino acids; the amino acids are then ejected from the ribosome to be strung together like necklace beads; they are transported to Golgi structures where they are folded into proteins.
A process this complex — and it’s actually far more complex than this summary implies — can be orchestrated without intelligence; it’s possible, but without intelligence of some form, the process seems, at least to me, to border on the miraculous.
After all, what is the result?
It is a conscious thinking life-form who can, in cooperation with others, figure out its own origins.
11 – How do Quantum spins get affected by Quantum entanglement?
All atoms with electron shells that are home to more than one electron have entangled electrons. The spins tend to oppose each other. With bosonic particles, down conversion techniques produce photons that have opposite polarization.
Most physicists think that spin is induced during measurement; the spin is transmitted oppositely to the entangled partner instantly — no matter how far separated.
For this reason, a pair of entangled particles can be envisioned as a single particle that behaves as if one of its dimensions (the distance between its endpoints) is missing.
The distance between the entangled pair behaves as if it is zero — when it is known to be non-zero.
12 – What is the viability of colonies on other planets?
The two planets closest to Earth are the most viable places for colonies simply because they are the easiest to resupply. They are Mars and Venus.
Neither can sustain colonies, because they lack magnetospheres, which are essential for deflecting high energy particles emitted by the Sun (called the solar wind). These particles are deadly to life. The molten iron-nickel cores of Mars and Venus froze millions of years ago on both planets, which collapsed their magnetospheres.
Venus has a highly toxic atmosphere, which is another reason to rule out colonization there.
Beyond Mars are gas giants. Only their rocky moons are candidates for human colonies. All the moons appear to be too cold to operate the machinery necessary to sustain human life. Most lack protection from the solar wind.
Bonus Assertion – Does a photon consist of (f) quantized energy packets each of (h) joules?
A photon seems to be a packet of vibrating electric and magnetic energy, each part of which exerts its energy at a right angle to the other. The energy in the packet is proportional to vibrational frequency alone. A photon has no mass or acceleration. It travels along at a constant speed in space-time. The electric portion of the energy is about seven times the energy of the magnetic portion.
Photons can become more intense (that is, brighter) when they pile up. Pile ups don’t happen to electrons, protons, and neutrons because they obey an exclusion principle that forbids them from occupying the same space at the same time.
Photons can pile up, but their intensity (or energy) can only be transferred into electrons that are in an energy state that resonates with the frequency of the incoming photons. Non-resonate electrons ignore un-matched photons, so photons pass through non-resonate electrons unimpeded.
The energy of an individual photon can be expressed as its kinetic energy and shown to equal Planck’s constant times the photon’s frequency, which always results in a very small number.
When expressed in terms of its wavelength (λ), photon energy equals the Planck constant (h) times the speed of light (c) divided by the wavelength (λ) of the photon. Notice that the mass term is missing due to a simple manipulation of the relevant equations — which anyone who is interested can find in the following link.
Momentum might not be an appropriate metric for a force carrying boson like a photon, because momentum is based on mass, which many physicists say photons in a vacuum don’t possess.
Another reason momentum could be an inappropriate metric is that the velocity of photons in a vacuum is independent of any reference frame, right? Momentum is a vector quantity that is always measured in relationship to a particular reference frame or the momentum of another particle.
There is a theory that claims that photons pick up mass when they pass through materials like glass. They seem to leave a wake that shakes up electrons in the material. The vibrating electrons release polaritons, which by a mechanism analogous to superposition add mass to the photon and slow it down. When the photon exits and returns to vacuum, it sheds the polaritons, becomes massless, and returns to light speed instantly.
Perhaps photons in the vacuum of space acquire mass by interacting with virtual particles that emit virtual polaritons. Notions about the nature of the universe would be changed radically if such a notion were confirmed by evidence.
Because h and c are constants, they can be multiplied together to give a constant that is very close to 2E-25. Dividing 2E-25 by the wavelength of a photon will give its energy in joules. Of course, all units are SI, which stands for standard international units, correct?
Since E = hf or (hc / λ) , the energy is always a multiple of h, which is the Planck constant. The word “multiple” is a simple way to say “quantized”.
So, the energy of a photon bunch or pile can be expressed as a multiple of the number of photons of a certain wavelength in that bunch. The energy in each individual photon is its wavelength (or frequency, if you like) multiplied by the Planck number — a constant equal to 6.626E-34.
It takes a pile-up — or bunch — of about 7 photons with wavelengths close to 2.5 one-hundred-thousandths of an inch long (635 nanometers) to carry enough energy to light up the sensors in a human eye.
How much energy is in those seven photons? It is seven times 2E-25 / 635E-9 — in joules, right?
It’s 2.2E-18 joules. Converted to an easier metric befitting its scale, the energy is nearly 14 electron volts, which is equivalent to the energy held in 14 electrons.
People say that photons with wavelengths that measure 635 nanometers create the color yellow-orange in their minds.
A lot of people have been poisoned recently, mostly in Europe by Russians, if overseas media is believed.
Mark Rowley, Britain’s chief police official for counterterrorism and international security, told media that the former British agent and Russian citizen Sergei V. Skripal, 66, and his daughter Yulia Skripal, 33, “were targeted specifically,” — poisoned on 7 March 2018 by a nerve agent.
People familiar with nerve poisons have said that the poison used in this attack is impossible for a “non-state” actor to produce, let alone store and deploy to kill others. The statement by Britain’s top terrorism cop doesn’t leave room for many suspects.
Sergei and his daughter endured the mysterious deaths of several family members over the past many years. Now both lie in hospital in intensive care with Sergei remaining in critical condition as this essay is written. The killers seem to have targeted not only Sergei, but his entire family.
This essay isn’t about intentional assassinations by twisted power-trippers with appetites for terror.
The assassinations by poison in England and elsewhere set the context for something far more pervasive and debilitating — the unleashing of toxins on billions of humans and virtually every animal and plant on the earth and sea by uncaring people motivated not by revenge but by the desire to sequester money for themselves, their families, and their businesses.
A lot of money can be made by people who don’t care who or what they poison. There is no limit to how much money they can keep, either. Read Capitalism and Income Inequality.
In this essay I’m going to write about a dozen or so poisons that people are ingesting in ignorance which destroy their kidneys, their brains, their hearts, their nerves, their stomachs, their muscles, their finger and toenails, and their long beautiful hair. Who will warn people about the dangers if I don’t?
This chart is likely the best interactive periodic table on the web. The Royal Society of Chemistry (in London) provides it free to anyone who wants to use it. Click chart or this link to open it in a new window — and have fun!
Television tells us nothing except that the current president and his thugs are rolling back decades of protections against all kinds of dangerous products; nothing in popular media warns anyone that they are floating in a fog of toxins that is making them sick and killing them unawares. Without regulations, it’s going to get worse.
Dozens of people have dropped dead while using paint-strippers that contain the toxin methylene chloride, according to CBS News. (Click link for video.) Manufacturers say that millions use their products safely. Why ban a substance that only kills a few people per year? Life is cheap in unregulated America. It seems like life is going to get a lot cheaper.
Methylene chloride is used to decaffeinate coffee and tea. No one in authority seems to care. A California judge is ruling whether a law that compels coffee retailers to warn customers about cancer risks can be enforced. The chemical in this case is acrylamide, a known carcinogen, which is produced when coffee is brewed.
Acrylamide contaminates French fries, potato chips, bread, and other foodstuffs. The current leadership at the EPA (Environmental Protection Agency) is laughing at California. EPA execs continue to push for deregulation while they strive to keep the population ignorant about the risks of the products they use and ingest.
What would people think if they learned that only one person in three dies of old age? The two other unfortunates are dying from preventable accidents and diseases caused primarily by the toxins they ingest daily. Think about it.
Does anyone believe it? The punks who seized power last year after a tampered election are planning to deconstruct the United States and its agencies, whose mission was once to make life safer and easier for ordinary people.
The danger is not only inside the USA. Anyone who disagrees that homo sapiens are in danger ought to look to the plant and animal kingdoms around the world. Diversity is collapsing; the health of adult animals is deteriorating; fish and other sea-life contain high levels of toxins that make them unsafe to eat.
Were it not for short life spans, the suffering of animals and plants would be obvious to all but the most willfully ignorant. Testing of animals shows that all adult animals are suffering from contamination by heavy metals and other toxins placed into the environment by guess who? — humans, mostly.
What is manganism, anyway? Yes, it’s the title of my essay, but it’s also a matrix of symptoms induced by the deadly neurotoxin, manganese. Like most of the poisons in this article, it is a fundamental element of the periodic table. I am arguing that a position in the periodic table does not entitle entrepreneurs to extract and market elements in the table that are poisons.
Humans need 5 milligrams of manganese daily to power up the enzymes used in cell catalysis. Double the dose to 10, however, and they develop psychosis — manganese madness. The difference between survival and suffering is razor thin.
Symptoms start as irritability, mood swings, and compulsiveness, which progress to full-fledged Parkinson disease-like pathologies that are often misdiagnosed. Manganism lowers IQ and increases aggression — a dangerous juxtaposition.
With the advent of industrialization and the follow-on of high-technology, manganese has been poured into the environment like rain-water. It’s used everywhere in industry to prevent corrosion in metals.
Most steel contains manganese; some steels have as much as 15%. Construction helmets and military headgear are fabricated from them.
Manganese is a major component of alkaline batteries. It’s found in ground water, gasoline, and fertilizers — it’s used on the plants people eat. It’s concentrated by water-heaters that feed hot water to showers, of all places. Never swish water in your mouth from a shower-head while bathing.
Chronic exposure to air contaminated by manganese dioxide particles can cause manganism. MnO2 is classed as a cumulative neurotoxin according to the MSDS for manganese dioxide. The black powder is used in ”salt water” car batteries, now under development to replace lithium batteries. David Pogue ate the powder during a NOVΛ television broadcast to demonstrate its ”safety.” Don’t do it, Billy Lee advises. He recommends that scientists who plan to remain capable of adding together more than two numbers avoid inhaling manganese dioxide dust. The Editorial Board
The sodium-ion battery (some call it a salt-water battery) is, at this moment, coming on line. It uses manganese-dioxide electrodes. The plan is to use these batteries to power cars by 2020, mainly because the batteries don’t catch fire. The introduction of these batteries into electric cars will add another flood of manganese into the environment where it will — eventually — be ingested by plants, animals, and humans.
Brain damage by manganese is irreversible.
People once wondered why the people of ancient Rome went crazy. Edward Gibbon and other historians attributed it to moral decay and corruption. But the people of ancient Rome added lead to their wine to kill pathogens (like mold and fungus) and to sweeten it. Even on a good day adding highly toxic lead to wine is a bad idea.
Americans — like the ancient Romans — are weird, too. Maybe someday historians and pathologists will note the high levels of manganese in our exhumed bodies and conclude that we also unwittingly destroyed ourselves from a single chemical no one really needed and that no one took the time to forbid.
Amethyst. Natural and manufactured contain manganese, which gives it a purple color.
It takes a lot of effort to isolate manganese. People take the time to produce it for one reason and one reason only — to make money. Manganese is an iron-like metal used to impart the color purple to the gemstone, amethyst. Producers of manganese pay lobbyists to convince congress-people to go easy on them, so they can continue to enrich their families while the planet dies beneath their shuffling feet.
Breathing manganese vapors is the most direct path to poisoning, but manganese is also imbibed by eating too many of the wrong vegetables and not eating enough other vegetables that counter-act the toxin. The balance between enough and too much is that fragile.
Modern technology is tipping the balance into the way-too-much zone. Soon people will be too far gone to notice or care. They will be weak and shaky — unable to save themselves; unable to find refuge from poisons they can’t see, smell, or taste.
Steels rust and corrode. Manganese dust worms its way into soils and floats in the air, carried by the wind. Folks spread manganese-rich fertilizers on their lawns and crops. Inhaling small amounts of dust induces neurological injury.
Introducing tens-of-thousands of tons of manganese into the power plants of electric cars is only going to add to the problems of maintaining a healthy Earth.
There is a good reason why tycoons want to make manganese a staple of the world’s diet of toxins. The supply is inexhaustible. The floors of the Earth’s oceans are covered by 500 billion tons of baseball sized nodules of manganese. When the land-based stuff is gone, profiteers plan to scoop manganese nodules off the ocean floors.
At least 500 billion tons of baseball sized manganese nodules lay on the floor of the world’s oceans. Entrapped within are other elements like the neurotoxin, thallium.
Here’s the problem: these nodules contain an additional neurotoxin called thallium, which was used as a rodent poison in the United States until it was banned in 1972 — accidents killed too many pesticide technicians.
Enough said.
I don’t want to depress or scare anyone, so I’m only going to go into detail on a couple of other poisons that are ruining lives. Then I will list a number of toxins that everyone is ingesting everyday — with links added for anyone who wants to learn more.
To any reader who has read this far — congratulations. You have courage and a high bummer tolerance.
Wall-Mart sold to “juniors” hundreds-of-thousands of Miley Cyrus jewelry accessories coated with high levels of cadmiumin 2010. According to press accounts, they refused to stop selling these poison trinkets for months, because they claimed they lacked the tools to test their products for safety. Cadmium is toxic, even in the smallest amounts. There is no safe level.
Artists discovered cadmium’s toxic effects, when first they mixed it into paints to make vibrant orange, yellow, and red colors during the early 1800s. It’s a heavy metal that when ingested instantly attacks the kidneys (which it eventually destroys), lungs, and bones. It causes cancer. Smoking, welding, painting, metals production, galvanizing, and fertilizers are common sources of human contamination.
Ni-Cad (nickel-cadmium) rechargeable batteries are one of the most pervasive consumer products — used in every kind of electronic gadget, including computers and even children’s toys until banned by many countries a few years ago.
Did anyone properly dispose these batteries when they came to the end of their useful lives? I don’t think so. Most folks tossed them in the trash where over the decades they have been corroding in land-fills to poison everything they touch. There is no safe-level for human exposure.
Ni-Cad batteries are banned for general use by the EU (European Union), but are freely available in the United States and other countries. In the current climate of deregulation, toxins like cadmium are going to be unloaded on our unsuspecting populations for one reason and one reason only; we all know why: money.
Billionaires rule, and none live in the toxic wastelands of ordinary America. Greed thrives on greed while it drives out compassion, common sense, and consumer safety.
Cadmium is pervasive in zinc deposits and is embedded in every galvanized piece of metal you have ever handled. In Japan rice grown in cadmium contaminated irrigation water causes itai-itai disease. It makes bones so weak they fracture spontaneously. Click the link to learn more.
People who work to galvanize steel can develop metal fume fever, a flu-like disease that renders them unconscious should they breathe in the cadmium that always contaminates zinc, which is the galvanizing metal. When ingested in fumes, zinc will by itself make workers sick.
Gun enthusiasts sometimes fall victim to metal fume fever, because bullets can tear away microscopic layers of gun-barrel bores; metal-toxins become an invisible mist they inhale unaware.
Zinc-oxide is the major component of sunscreens. Do sunbathers trust the manufacturers of sunscreen around the world to decontaminate zinc from the cadmium in its ores? There is no safe dose for cadmium. Smearing cadmium into the pores of sweating skin is a bad idea.
Zinc is 97.5% of every U.S. penny minted since the 1980s. The copper cladding is less than three percent. It is impossible to remove all traces of cadmium from zinc. Pennies are poisonous. There is no safe level for cadmium. Handling old pennies with sweaty hands (or swallowing one accidentally) is another bad idea.
To say again: I have compiled a list of about a dozen or so poisons that people are ingesting in ignorance that destroy their kidneys, their brains, their hearts, their nerves, their stomachs, their muscles, their finger and toenails, and their long beautiful hair. Who is going to tell them about the dangers if I don’t?
I see nothing on television; I read nothing in print media that warns the public that they are living in a poison glen of toxins where billionaires make them sick and yes, murder them.
Do these greedy monsters care? If they did, they would provide health care to the miserable people they hurt. The truth is, they could care less. The consensus among billionaires is to ruin health care in the United States and let victims fend for themselves.
The wealthy intend to privatize every government program designed to defend the helpless. Their puppets advocate for privatization and an end to regulations on conservative talk shows all the time, and I for one believe they mean it.
It must be asked again: Does anyone know that only one person in three dies of old age? The two other unfortunates are dying from preventable accidents and diseases caused primarily by the toxins they ingest daily.
Anyone who disagrees that humans are at risk ought to look to the plant and animal kingdoms. As I wrote earlier, diversity is collapsing; the health of adult animals is in a terrible state; sea-creatures are irradiated by the run-off from ruined nuclear power generators like those at Fukushima in Japan and those on sea-going vessels that have sunk like the Thresher and Scorpion submarines; sea-life is radio-active and unsafe to eat. Were it not for short life spans, the suffering of animals and plants would be obvious to all but the most willfully ignorant.
Like manganese, selenium is another element in the periodic table that is required in trace amounts for cell catalysis but is toxic in slightly higher amounts. It is produced by burning coal, among other processes.
Selenium causes garlic breath, intestinal distress, hair loss, fingernail fall-out, and neurological damage. It smells like horse-radish. Who wouldn’t eat horse radish if they smelled it in their food? Cirrhosis of the liver, pulmonary edema, and death are not uncommon.
Selenium is a major component of lithium batteries, photo-copiers, and solar cells. Brazil nuts and peaches, especially those grown in certain soils, are sometimes loaded with selenium.
So far I have mentioned three toxic elements: manganese, cadmium, and selenium. It’s the tip of a ginormous iceberg of poisons.
Does anyone understand that catalytic converters — the five inch diameter by two foot long tubes in exhaust pipes under all cars — have a useful life of only 100,000 miles? A lot of things can wreck converters before a hundred-thousand miles — unburned fuel and leaks of coolant and oil can clog and render useless the pollution reducing power of any converter.
Whether wrecked early or not, a large percentage of cars in cities rely on catalytic converters that are ineffective, because many are old, for one thing. They are supposed to prevent pollutants that induce ADHD, autism, and Alzheimer’s in old folks, babies, children, and the vulnerable — which is everyone who doesn’t wear a face mask.
People in China and Japan wear white face masks. When they blacken, they throw them out and put on new. Who wears face masks in the USA? No one.
Catalytic converters arenot working! Look along the curbs of city streets a few days after a heavy snow. It’s a grey-black mess of God knows what. When the snow melts where do the contaminants go that the innocents trusted catalytic converters to soak up?
Isn’t it obvious? The sludge dries to become dust; it blows in the wind; people and animals breathe it in. Animals eat it, because they don’t wash their food.
Environmental contaminants measure in the millions of tons. Workers produce them in factories where they spend their careers trying to avoid the accidents that will poison them and ruin perhaps the rest of their lives.
Few coal miners avoid the miseries of coal toxins — an example that should by now be obvious to anyone who is paying attention. All the old-timers are sick. Visit coal country. Meet these unfortunates.
Go to farms where the run-off from fertilizers contaminates the wells. Only farmers who drink bottled water avoid disease. Go to farm country and look for old men. Ask them about their health issues, if you can find them.
Undiagnosed (or misdiagnosed) people who are sick from toxins do not understand why they suffer from delusional thinking, mood swings, and PTSD-type symptoms. No general tells his battle-hardened soldiers that poison impregnates their ammunition; it’s loaded with spent uranium to make it heavier and more lethal.
Few soldiers on today’s killing fields escape poisoning by the highly toxic materials in their ammunition and the weapons-exhaust that spreads a smoke of poisons on friendly positions during war.
Some soldiers come home terrorized by a fear whose source is unknown to them. Irrational behavior, aggression, spousal abuse, persistent nightmares, even mass shootings are all behaviors that can sometimes be traced back to battlefield poisons, should anyone be brave enough to do the studies that would confirm what anyone with common sense knows is true.
Now might be the time to admit that I’ve found it best to keep essays from becoming overly long; it would take many books to cover the subject of commercial toxins comprehensively.
What follows is a simple list of a few of the elements from the periodic table that are in common use today which are toxic and will kill or debilitate anyone who ingests them. Click on the links to learn more.
Heavy metals – coal is the biggest source, as well as waste from the mining of less-toxic metals. Toxic heavy metals include lead, arsenic, cadmium, mercury, and chromium. Heavy metals help to populate the list of elements below.
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Beryllium – no safe level. Used in all kinds of spark-proof tools and in the alloyed metals of outer-space and under-sea vehicles.
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Chlorine – once used in trench warfare, because it is heavy and clings to the ground. Highly poisonous.
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Bromine – until recently unregulated, it eats the ozone layer. It can cause psychosis in humans and has other toxic effects. People put it in their swimming pools — and in pesticides, which farmers spray on plants people eat.
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Cobalt – can be used to safely house “dirty” bombs. During an explosion cobalt debris converts into a deadly isotope that poisons land for decades.
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Arsenic – a poison unable to be detected until the mid eighteen-hundreds. Referred to in times past as “inheritance powder.”
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Thallium – another “inheritance powder” that is tasteless and odorless. Before government banned its use in 1972, folks used thallium to poison rats and ants. It contaminates many ores, including zinc. It is a pollutant of cement and coal processing. The skin sucks it into the body like a sponge. Low doses cause hair loss.
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Strontium – bones and teeth suck up radio-active strontium like vinegar to a sponge. It bursts into flame when exposed to air, which is one reason it’s used in fireworks and roadside flares.
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Antimony – used by the ancients to make them vomit. They believed purging was a pathway to better health.
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Tellurium – contact with even the smallest amounts will make a person smell bad for weeks. Miners try to avoid it, often without success.
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Barium – makes rat poison that is fatal in doses as small as one gram.
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Cerium – used in the walls of self-cleaning ovens, in cigarette lighters, and in camping lanterns. Commercial grade cerium always contains radioactive thorium. Civilians have been prosecuted for isolating thorium from cerium in vain attempts (thus far) to make atomic bombs.
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Osmium – an extremely toxic metal that is easily absorbed through the skin when touched. It shreds the lungs and ruins the eyes.
OK. I think this is a list that is sufficient to show that not every naturally occurring element is as safe as, say, nitrogen; probably no element is as safe as nitrogen, which is 78% of the air folks breathe. Of course, anyone who breathes nitrogen without oxygen dies of suffocation in minutes.
Are there other elements in the periodic table that are dangerous to human health? Unfortunately, yes. Most of them are refined in labs and used by the military.
This essay is about elements that the public might encounter at work or from products they buy or use to simply live their lives — like foods or building materials in homes, for example.
The problem is this: thousands of toxic materials are produced from combinations of elements that are sold everywhere to do almost everything. Unless these materials are ruthlessly regulated, pigs who produce and profit by them have proven time and again that they are willing to hurt people — sometime kill them — to get rich.
Whoever heard of a CEO going to prison for poisoning someone? It doesn’t happen.
Some people, after reading an essay like this one, might decide that living is fraught with too many dangers. Life is no longer worth living. Some might ask themselves: is it better to just die and get it over with?
Well, one way that works, I’m told, is to ingest 37 bananas. It’s important to eat the peels as well as the meat. Thirty-seven is apparently the right dose.
Bananas are naturally radioactive; they contain potassium; a lot of people don’t know. Who will tell them? Not only radioactivity, but pesticides like chlorpyrifos coat the peels so that people are less likely to get bit by venomous spiders, which most assuredly would otherwise be hiding in bunches of untreated fruit.
Bananas contain substantial amounts of hydroxytryptamine, a serotonin-like chemical that if improperly dosed or taken with other substances can induce either euphoria or adverse reactions up to and including death.
People hell-bent on successful self-immolation might try eating 38 bananas — one more than necessary — just to be on the safe side.
The practice of blowing oneself up by eating one more banana than necessary is called, bananism. I almost used the term to title this essay.
Billy Lee
Warning by the Editorial Board: Billy Lee recommends that anyone who eats more than twenty bananas a day seek medical attention and psychological counseling. Never eat the peels.
Two months ago, I discovered QUORA. It’s been around since 2009.
Since 2010, Quora has enabled people to ask experts questions about topics they like; even to answer questions on subjects they claim to know something about.
Quora is a site for geeks and nerds, and so far I like it. The people who hang out in the areas I hang out tend to be polite, kind, and smart. If they like someone, they follow them and are notified when they post. So far, ten people have signed on to follow me. It’s a start. I think most are from India.
During the first six weeks, 150 or so of my answers were viewed 35,000 times; I got nearly 175 “upvotes”, which enabled many of the answers to move to the head of the line. I wrote most answers in the wee hours between 2 AM and 7 AM when I couldn’t sleep. Insomnia inspired me.
What follows are 25 of the most popular answers I posted to the first 150 or so questions that caught my interest. They are sequenced by popularity — the most read first .
Why not read a few? How many questions can anyone answer? Not many, I’m thinking.
Who knows what you might learn?
What?
Someone thinks they know better than a pontificator with no bonafides?
I don’t think so.
No way! 😉
1) What are some of the most popular “mathematically impossible questions“?
Freeman Dyson — one of the longest-lived and most influential physicists and mathematicians of all time — argued that it is impossible to find a whole (or exact) number that is a power of two where someone can reverse its digits to create a whole number that becomes a power of 5.
In other words, , right? Reversing the digits to make 8402 does not result in an exact number that is a power of 5.
In this case, plus a lot more decimals. It’s not a whole (or exact) number. Not only that, no matter how many decimal places anyone rounds-off 6.09363… , the rounded number raised to the power of 5 will never return 8402 exactly.
Dyson claimed that this conjecture must be true, but there is nothing in mathematics that enables anyone to write a proof. He claimed that there must be an infinite number of similar statements—-each one true, none provable.
The Snowplow Problem is another “impossible” problem. My differential equations professor assigned it with the promise that anyone who solved it would receive a 4.0 grade, regardless of their performance on tests. I was the only student he ever taught who actually managed it.
The problem goes like this: It is snowing at a constant rate. A snowplow starts plowing snow at noon. By one o’clock the plow has traveled one mile. By two o’clock the plow travels an additional half mile. At what time did it start snowing?
It took me 3 days and two pages of calculations, but I got my 4.0.
Note from the Editorial Board: Over 50 people on Quora submitted answers to Billy Lee’s Snow Plow problem. One person had the right answer, but would not produce his proof. He did point out an unusual feature of the solution that Billy Lee had not noticed before. Billy Lee characterized the feature as ”very surprising.” When pressed Billy Lee refused to reveal the secret.
2) How much force is one Newton?
A newton is the force that an average sized apple makes on your hand when you hold it. No matter where in the universe you are; no matter on what planet you stand or how strong the gravitational field, a newton of force always feels the same.
A newton is one kilogram of mass that is accelerating at one meter per second per second. Gravity on Earth accelerates everything at nearly 10 meters per second per second. A kilogram of mass feels like 2.2 pounds on earth. One tenth of 2.2 pounds is 0.22 pounds or 3.5 ounces, which is the weight of a typical apple. The weight is the force that you feel against your hand. It is one newton.
On the moon, an object with the mass of a large brick would feel as light as an apple on earth due to the moon’s lower gravity. The force of the brick in your hand would feel like one newton.
3) . and .. What are x and y?
The simplest way to solve is to make y = (4-x) and create an equation in terms of x.
An easy version to create and solve is
You can solve it by hand using iteration or throw it into an app like Wolfram Alpha and let them solve it in a few seconds.
Either way, one value for x is .606098…. The other is 3.393901… , which you can assign to y. The two numbers add to 4.000… and when substituted into both initial equations return the right results.
4)If I had 1,000,000,000,000,000 times 1,000,000,000,000,000 hamsters floating in space in close proximity, would gravity turn them into a hamster planet?
Assuming the question is serious, it deserves a serious answer.
A typically fat hamster weighs around one ounce, which is about 0.03 kilograms of mass. The number of hamsters in your question is 10E30.
Multiplying the mass of a single hamster by this large number gives the result of 3E28 kilograms.
To compare, the mass of planet Earth is 6E24 kilograms. The mass of the proposed population of hamsters is 5,000 times the mass of the earth.
The sun contains 67 times more mass than the hamster population. If the hamsters are close enough together to hold paws, a hamster planet is almost certain. I haven’t worked out how long the process to congeal would take, but I can estimate that the hamsters would probably die of starvation before the inexorable forces of gravity completed their work.
The hamster planet would be formed mostly from three elements: hydrogen (64%), oxygen (33%), and carbon (10%). 3% would be trace elements like calcium and maybe lithium.
The most likely outcome, given enough time, is a planet-like object. The hamsters have only one-fifth of the mass to make the smallest of the smallest suns — red dwarfs, which populate 67 to 80 percent of the Milky Way Galaxy.
There are way too many hamsters to make a reasonably sized moon.
Their mass (3E28 kg) happens to fall on the border between the range of masses that are required to form celestial objects known as brown dwarfs and the less massive sub-brown dwarfs — sometimes referred to as free-floating planets.
Brown dwarfs don’t have enough mass to ignite like a star, but they do produce heat and can accept small orbiting planets. The chemistry of brown dwarfs is not well-understood and is a bit controversial.
It’s a toss-up, but my vote goes to the notion that the hamsters will eventually form a very large but ordinary planet — a free-floating planet — which I referred to earlier as a sub-brown dwarf. This hamster planet might wander through space for millions (or even billions) of years before being captured by a massive-enough star to begin to orbit.
Because the elements of hydrogen and oxygen are likely to become the constituents of frozen moisture (or water ice), there is the risk that the ice might melt into oceans and perhaps boil away if the hamster planet approaches too close to a star (or sun). In the case where the planet loses its water, a carbon planet with 50 times the mass of earth would form.
Otherwise, should the planet find itself in a far-distant future orbiting in the “goldilocks” zone around a sufficiently massive star, the water would not evaporate. Life could arise in the planet’s oceans. It’s possible.
Life-forms might very well crawl up out of the water and onto land someday where — over the eons and under ideal conditions — they will evolve into hamsters.
5) Why is evolution a valid scientific theory despite the fact that it can’t be conclusively proven due to the impossibility of simulating the millions-of-years processes that it entails?
Evolution is a fact that is thoroughly established by observations made in many disciplines of science. Changes in species happen fast or slow; in the lab and in the field.
The mystery is how one-celled life got established so quickly — it was solidly established within one billion years of earth’s formation. It’s taken 3.5 billion years to go from one-celled life to what we have now.
Why so fast to get life started; why so slow to get to human intelligence and civilization?
People have a lot of ideas, but no one is sure. Some life forms have orders of magnitude more DNA than humans. Only 2% of human DNA is used to make the proteins that shape us.
6) Why do cosmologists think a multiverse might exist?
Many high-level, theoretical physicists have written about the obvious problem our universe seems to have, which is that it has too many arbitrary constants that are too tightly constrained to be explained by any theory so far. No natural cause has been found for so many constants, so it’s fertile ground for theorists.
Stephen Hawking, among others, has said that the odds of one universe having the physics that ours has is 1E500 against. He is joking in his English way, because such a large number is essentially an infinity. It’s not possible to constrain a universe like ours by chance unless there are an infinity of choices, and we happen to be in the one that supports intelligent, conscious life.
Two ways of getting to infinity are the concepts of multi-verse and the new one proposed by Paul J. Steinhardt of Princeton University in 2013, which is based on data supplied by the Planck Satellite launched in 2003. Paul is the Einstein Professor of Science at Princeton, so his opinion holds a lot of weight.
Steinhardt has proposed that the universe is ekpyrotic, or cyclic. He has asserted that the universe beats like a heart, expanding and contracting in cycles, with each cycle lasting perhaps a trillion years and repeating, on and on, forever. Each cycle produces conditions — some which are ideal for life. This heart has been beating forever and will continue to do so, forever.
7) How will we visit distant galaxies if we cannot travel faster than light?
We will never visit distant galaxies, because they are too far away; most are moving away from us faster than our current technologies can overtake. At huge distances space itself is expanding, which adds to our problems.
The expansion of space is gradually accelerating. Any increase in performance by space vehicles over the next few thousand years is certain to be overwhelmed by the accelerating expansion of the universe.
As time goes on the amount of objects that are reachable (or even viewable) by earthlings will shrink.
On the happy side, our own solar system has at least 165 interesting places to visit that should keep folks fascinated for many thousands of years. A huge cavern has been discovered on Mars, for example, that might make a safe habitat against some forms of radiation dangers; it seems to be a place where a colony of humans might be able to live, work, and survive — perhaps even flourish.
Elon Musk is planning a mission to Mars soon.
8) What is the mathematical proof for a+a = 2a ?
Some things that are true can’t be proved. All math systems are based on axioms, which are statements believed to be true but which, in themselves, are not provable.
9) Can you explain renormalization in physics in simple words?
There is a problem in physics that has to do with the huge variation in scales between the very large and the very small. This problem of scales involves not only the size and mass of things, but also forces and interactions.
Philosopher Robert Pirsig believed that the number of possible explanations that scientists could invent for phenomenon were, in actual fact, unlimited.
Despite all the math and all the convolutions of math, Pirsig believed that something mysterious and intangible like quality or morality guided our explanations of the world. It drove him insane, at least in the years before he wrote his classic book, Zen and the Art of Motorcycle Maintenance.
Anyway, the newest generation of scientists aren’t embarrassed by anomalies. They have taught themselves to “shut up and calculate.” The digital somersaults they must perform to validate their work are impossible for average people to understand, much less perform. Researchers determine scales, introduce “cut-offs“, and extract the appropriate physics to make suitable matches to their experimental results.
The tricks used by physicists to zero in on pieces of a problem where sensible answers can be found have many names, but renormalization is one of the best known.
When physicists renormalize an equation, they cut away infinities and other annoying problems (like dividing by zero). They focus the range of their attention to smaller spaces where the vast differences in scales and forces don’t blow up their formulas and disrupt putative pairings of their carefully crafted mathematics to the world of actual observations.
It’s possible that the brains of humans, which use language and mathematics to ponder and explain the world, are insufficiently structured to model the complexities of the universe. We aren’t hard wired with enough power to create the algorithms for ultimate understanding.
10) If a propeller rotates at the speed of light at half of its length, what happens to the outer parts?
Only the ends of the propeller can rotate at near light speed (in theory). At half lengths the speed of the propellers will be half the speed of their ends, because the circumference of a circle is 2πr. (There is no squared term.)
So the question is: will the propellers deform according to the rules of the Lorentz transformation along their lengths due to the difference in velocity along their lengths?
The answer is, yes.
As you move outward along the propeller, it will become thinner in the direction of rotation, and it will get more massive. A watch will tick more slowly at the end than at the middle.
I am not sure how it would look to an outside observer. Maybe such a propeller would resemble in some ways the spiral galaxies, which don’t rotate the way we think they should. Dark matter and energy are the usual postulates for their anomalous rotations. Maybe their shape and motion is related to relativity in some way. I really don’t know.
In reality, no propeller can be constructed that would survive the experiment you describe. But in theory (and ignoring the physical limitations of materials) there would be consequences.
However, no part of the propeller will move at light speed or higher. Such speeds for objects with mass are impossible.
11) What is the fundamental concept behind logarithms?
The first thing that anyone might try to understand is that the word logarithm means exponent.
Example 1:
log 100 = 2 . What does this expression say? It says that the exponent that makes 100 is 2. What confuses people is this: exponent acting on what number?
The exponent acts on a number called the base. Unfortunately, the base is not written down in the two most common logarithm systems, which are log and ln.
The base for the log system is 10. In the example above, the exponent 2 acts on the base 10, which is not shown. In other words, , right? The exponent that makes 100 from the base 10 (not shown) is (equals) 2.
Example 2:
ln 10 = 2.302585… . What does this expression say? It says that the exponent that makes 10 is 2.302585… . Again, exponent acting on what number?
The base used in the ln system is 2.7182818… ,which is an irrational number that has an infinite number of decimal places. It happens to be a useful number in all branches of science and math including statistics, so mathematicians have decided to represent this difficult-to-write-down number with the letter “e”, which is known as Euler’s number.
The base for the ln system is e . In the example above, the exponent 2.302585… acts on the base e , which is not shown.
In other words, , right?
The exponent on e ( which is 2.7182818… and not shown in the original equation above) that makes 10 is (equals) 2.302585… .
All other logarithmic systems express the base as a subscript to the right of the word log.
Example 3:
This expression says: The exponent on seven that makes 49 equals 2.
12) Why do so many spiritual types have mental blocks about science and mathematics?
Everyone has mental blocks about science and math including scientists and mathematicians. Like the lyrics to the old song — people hear what they want to hear and disregard the rest — Einstein, to cite just one example, never accepted most of quantum physics even after it was well established and no longer controversial.
People don’t like the feeling of “cognitive dissonance”. The tension between strongly held beliefs and objective facts can bring unbearable psychological pain to most people. Someone once said that genius is the ability to hold contradictory ideas inside the mind. Most people don’t do that well; they don’t like contradictions.
Here is a link to an essay called Truth that some will find interesting:
Einstein said that time and space (i.e. space-time) depends on mass and energy, which are equivalent. In the absence of mass and energy, space and time are meaningless.
The most recent experiments by NASA have found no evidence that time is anything but continuous. However, the shortest time possible is the length of time it takes light to move the shortest distance possible, which is called Planck time. It is thought to be 5.39E-44 seconds.
Time can be divided into as many smaller increments as anyone wants, but nothing can happen in fewer than the number of intervals that add to 5.39E-44 seconds. Time is a variable that isn’t fundamental. It expands and shrinks in the presence of mass and energy.
Some physicists of the past suggested that the “chronon” might be the shortest interval of time. It is the time light travels past the radius of a classical (at rest) electron — an interval of 6.27E-24 seconds. Its calculation depends only on mass and charge, which can change if a particle other than an “at rest” electron is measured.
It seems to me that time is probably best thought of as being continuous. That said, it doesn’t mean that mass-energy interplay isn’t pixelated — much like a digital camera image. Pixelation is critical to a conjecture concerning the preponderance of matter over anti-matter — a conjecture described in the essay CONSCIOUS LIFE.
14) Which is bigger: or ?
Think of fractions as pies, which are all the same size. The bottom number is the total number of pieces into which each pie is cut. The first pie was cut into 5 pieces, which are all the same size. The second pie was cut into 9 pieces, which again are all the same size.
The second pie is cut into smaller pieces than the first pie, because there are more pieces. Right?
Mice come along and eat pieces from both pies. The top number is the number of pieces they left behind; the top number is the number of pieces the mice didn’t eat.
So which pie plate has more pie on it? Is it the 5 piece pie that has 3 pieces left or the 9 piece pie that has 1 piece left?
If you think hard you will figure out that it must be the first plate that has the most pie on it. Right?
15) Why is a third of 30 equal to 10 and not 9.999999999, as a third of 10 is 3.33333333?
You can make three piles of ten objects in each pile. When you count the total, it adds to exactly 30 objects. So the answer of “10” is demonstrably true, right? Three piles of ten adds to thirty.
There is no way to make three piles of any identical objects that adds to 10. Three piles of three adds to nine. Four piles of three objects adds to twelve.
We are required to make three piles of three objects and then add a piece of a fourth object to each pile that is smaller than a whole piece.
It turns out that the fourth object is 1/3 of a whole object. When these three piles of three objects plus 1/3 of an object are added up they equal exactly ten.
The problem in understanding comes from trying to grasp that 1/3 — when written as a decimal — is what mathematicians call a repeating decimal. The rules of arithmetic say that the decimal form of 1/3 is calculated by dividing “1” by “3”.
Following the rules of arithmetic when doing the division forces an answer to the problem that results in a repeating decimal — in this case, 0.333333… .
There is no way around these rules that keeps math working right, consistent, and accurate.
Sorry.
16) Will we be able to have life extension through cloning?
Cloning not only doesn’t work, it can’t work.
That said, the idea of cloning is to make a genetic replicant of an existing life-form. Extending life-span would require changes to the genome through other means involving changes to structures called telomeres, probably, which straddle the ends of chromosomes in eukaryotic cells.
A short discussion of cloning is included in the essay at this link: NO CODE
NO CODE is long (11,000 words), but explains in words, pics, graphics, videos, and links some of the complexities, misunderstandings, and dangers of current genetic-engineering at an undergraduate level. It explains basic cell biology, protein production, and much more.
17) Why does time slow down when we are on a massive planet or star like Jupiter?
Gravity is equivalent to acceleration. Accelerating clocks tick slower, according to General Relativity, which has been confirmed by experiments. It has to do with the concept of space-time and the fact that all objects travel through space-time at the same rate.
To understand, it helps to read up on space-time, special relativity, and general relativity. The concepts aren’t easy. The universe is an odd place, but it can be described to a somewhat fair degree by mathematics.
Some of the underlying reasons for why things are the way they are seem to be unknowable.
18) If the ancients had focused on science instead of religion, could we have become immortal by now?
Immortality is not possible due to the odds of accidental death, which at the current rate makes death by age 25,000 a virtual certainty for individuals.
Worse: the odds for extinction of the human species as a whole are much higher — it’s a near statistical certainty for annihilation within the next 10,000 years according to experts. It seems counterintuitive, but it’s true.
19) How do I solve, if the temperature is given by f(x,y,z) = and you are located at and want to get as cool as possible, in which direction should you set out?
You want to establish what the gradient is, establish its direction, then head in the opposite direction, right?
By partial differentiation the gradient is (6x – 10y + 4z), right? You don’t have to take another partial derivative and set it equal to zero to establish a maximum, because all the second derivatives of the variables are equal to one, right? You can drop the variables out and treat them as unit vectors like i, j, & k, correct?
The resulting vector points in the direction of increasing temperature, right?
Changing the signs makes a vector that points in the opposite direction toward cooler temperatures. That vector is (-6, 10, -4).
The polar angle (θ) is 71.068° and the azimuth angle (Φ) is 120.964°. The length (or magnitude) is 12.3288. Right? (We won’t use this information to solve the problem, but I wanted to write it down should I need to refer to it to respond to any comments or to help check my work graphically.)
These directions are from the origin, and you aren’t located at the origin. To determine the direction to travel to get to (-6, 10, -4), you need to subtract your current position. Again, for reference your location is .6333 from the origin at θ = 37.8636° and Φ = 30.9638°. Right?
After subtracting your position vector from the gradient vector, the resulting vector is (-6.333, 9.8, -4.5). Agree?
This vector tells you to travel 12.506 at a polar angle (θ) of 68.9105° and an azimuth angle (Φ) of 122.873° to intersect the gradient vector. At the intersection you must change direction to follow the gradient vector’s direction to move toward cooler temperatures at the fastest rate.
I haven’t graphed out the solution to double-check its accuracy. You might want to do this and let me know if you agree or not.
20) What is equal to?
The answer is zero, of course.
But not really. It only seems that way. Each number has three roots.
Depending on which roots are chosen the result can be one of six different sums (as well as zero if both roots are the same). We have to start somewhere so:
What is ?
i = . Right?
Therefore, a third root of i is . Right? It’s not the only root.
It’s the principal root. There are three third roots, which are equally spaced around the unit circle. Right?
It’s clear by inspection that to be equally distributed around the unit circle the other two roots must be and -i. Right?
Convert the three roots to rectangular coordinates and do the subtractions.
Here are the roots in rectangular form: (.86603 + .50000 i) , (-.86603 + .50000 i) , and (0.00000 -i).
Here are the six answers (in bold type) to the original question with the subtractions shown to the right:
These rectangular coordinates can be converted back to the Euler-form ( ). It’s easy for anyone who knows how to work with complex variables. In Euler-form the angle in radians sits next to i. The angle directs you to where the result lies on a unit circle. Right?
In fact, the six values lie 60 degrees apart on the circumference of a circle whose radius is the square root of 3. I don’t know what to make of it except to say that the result seems unusual and intriguing, at least to me.
As mentioned earlier, if both roots are chosen to be the same, then in that particular case the result is zero.
21) What is tensor analysis and how is it used in physics?
Understanding tensors is crucial to understanding Einstein’s General Theory of Relativity.
This question seems to assume that everyone knows what tensors are and how they are represented symbolically. It’s a good bet that some folks reading this question might want some basics to better understand the explanations of how tensors are used for analysis in physics.
If so, here are links to two videos that together will help with the basics:
22) What is the velocity of an electron?
Electrons can move at any speed less than light depending on the strength of the electro-magnetic field that is acting on them. Inside atoms electrons seem to move around at about one-tenth of the speed of light. You might want to check me on this number. The situation is as complicated as your mind is capable of grasping.
When interacting with photons of light electrons inside atoms seem to jump into higher or lower shells or orbits instantaneously. That said, it is impossible to directly observe electrons inside atoms.
On an electrical conductor like a wire, electrons move very slowly, but they bump into one another like billiard balls or dominoes. The speed of falling dominoes can be very high compared to the speed of an individual domino, right?
So, the answer is: it all depends…
23) What exactly is space-time? Is it something we can touch? How does it bend and interact with mass?
Spacetime, according to Einstein, depends on mass and energy for its existence. In the absence of mass and energy (which are equivalent), space-time disappears.
The energy of things like bosons of light — which seem to have no internal (or intrinsic) mass, right? — is proportional to their electric and magnetic fields. Smallest packets of electromagnetic oscillations are called photons.
Many kinds of oscillating fields, like electromagnetic light, permeate (or fill) the universe. In this sense, there is no such thing as nothing anywhere at any scale.
Instruments and tools of science (including mathematics) can give a misleading impression that at very small scales massive particles exist.
According to the late John Wheeler, mass at small scales is an illusion created by interactions with measuring devices and sensors.
Mass is a macroscopic statistical process created by accumulations of whatever it is that exists near the rock bottom of reality where humans have yet to gain access. These accumulations, some of them, are visible to humans; they seem to span 46 billion light years in all directions from the vantage-point of Earth and are displayed for the most part in as many as two-trillion galaxies according to recent satellite data by NASA.
Mass is thought to interact with everything that can be measured (including everything in the Standard Model) by changing its acceleration (that is, its velocity and/or direction), which is equivalent to changing its momentum.
It is in this sense that mass and energy are equivalent. Spacetime depends on mass and energy. Spacetime does not act on mass and energy; it is its result, its consequence.
Spacetime is a concept (or model) that for Einstein helped to quantify how mass and energy behave on large scales. It helped explain why his idea that the universe looks and behaves differently to observers in different reference frames might be the way the universe on large scales works.
His mathematical description of spacetime helped him build a geometric explanation for gravity that can be described for any observer by using tensor style matrices; many find his approach compelling but difficult computationally.
24) Hypothetically speaking, if one could travel faster than light, would that mean you would always live in the dark?
The space in which objects in the universe swim does expand faster than light when the expansion is measured over very large distances that are measured in light-years. A light year is six trillion miles.
At distances of billions of light years, the expansion of space between objects becomes dramatic enough that light begins to stretch itself out. This stretching lengthens the distance between the peaks and valleys of the electric and magnetic waves that light is made from, so its frequency appears to drop.
The wave lengths of white light can stretch so dramatically that the light begins to appear red. It’s called red shift.
Measuring the red shift of light is a way to tell how far away an object like a star is. As light stretches over farther distances the ability to see it is lost.
The wavelengths of light stretch toward the longer infra-red lengths (called heat waves) and then at even farther distances stretch to very long waves called radio-waves. Special telescopes must be placed into outer space to see these waves of light, because heat and radio waves radiating from the earth will interfere with instruments placed at the surface.
Eventually the distances across space become so great that the amplitudes (or heights) of the waves flat line. They flat-line because space is expanding faster than light can keep up. Light loses its structure. At this distance the galaxies and stars drop out of the sight of our eyes, sensors, and instruments. It’s a horizon beyond which the universe is not observable.
No one knows how big the universe is, because no one can see to its end. The expansion of space — tiny over short distances — starts to get huge at distances over 10 billion light years or so. The simple, uncomplicated answer is that the lights go out at about 14.3 billion light years.
Because there is no upper limit to how fast the universe can expand, and because the objects we see at 14.3 billion light-years have moved away during the time it has taken for their light to reach Earth, astronomers know that the edge of the universe is at least 46 billion light years away in all directions. Common sense suggests the universe might be much larger. No one has proved it, but it seems likely.
Over the next few billion years the universe that can be seen will get smaller, because the expansion of space is accelerating. The sphere of viewable objects is going to shrink. The expansion of space is speeding up.
The problem will be that the nearby stars that should always be viewable (because they are close) are going to burn out over time, so the night sky is going to get darker.
Most (4 out of 5) stars in the galaxy are red dwarfs that will live pretty much forever, but no one can see them now, so no one will see them billions of years from now, either. Red dwarfs radiate in the infra-red, which can only be seen with special instruments from a vantage point above the atmosphere.
Stars like our sun will live another 4 or 5 billion years and then die. The not-too-distant future of the ageless (it seems) universe is going to fall dark to any species that might survive long enough to witness it.
25) What does “e” mean in a calculator?
There are two “e”s on a calculator: little “e” and big “E”.
Little “e” is a number. The number has a lot of decimals places (it has an infinite number of them), so the number is called “e” to make it quick to write down.
The number is 2.71828… . The number is used a lot in mathematics and in every field of science and statistics. One reason it is useful is because derivatives and integrals of functions formed from its powers are easy to compute.
Big “E” is not a number. It stands for the word “exponent”, but it is used to specify how many places to the right to move the decimal point of the number that comes before it.
5E6 is the number 5,000,000, for example. The way to say the number is, “five times ten raised to the sixth power”. It’s basically a form of shorthand that means 5 multiplied by .
Sometimes the number after E can be negative. 5E-6 would then specify how many places to the left to move the decimal point. In this case the number is 0.000005, which is 5 multiplied by .
Bonus Question 1 – What difficulties lie in finding particles smaller than quarks, and in theory, what are possible solutions?
The Standard Model is complete as far as it goes. Unfortunately, it covers only 5% of the matter and energy believed to exist in the universe.
And humans can only see 10% of the 5% that’s out there. We are blind to 99.5% of the universe. We can’t see energy, and we can’t see most stars, because they radiate in the infra-red, which is invisible to us.
The Standard Model doesn’t explain why anti-matter is missing. It doesn’t explain dark matter and energy, which make up the majority of the material and energy in the universe. It doesn’t explain the accelerating expansion of the universe.
Probing matter smaller than quarks may require CERN-like facilities the size of our solar system, or if we’re unlucky, larger still.
We are approaching the edge of what we can explore experimentally at the limits of the very small. Some theorists hope that mathematics will somehow lead to knowledge that can be confirmed by theory alone, without experimental confirmation.
I’m not so sure.
The link below will direct readers to an essay about the problem of the very small.
Bonus Question 2 – What if science and wisdom reached a point of absolute knowledge of everything in the universe, how would this affect humanity?
Humanity has reached a tipping point where more knowledge increases dramatically the odds against species survival. Absolute knowledge will result in absolute assurance of self-destruction.
Astronomers have not yet detected advanced civilizations. The chances are excellent that they never will.
Humans are fast approaching an asymptotic limit to knowledge, which when reached will bring catastrophe — as it apparently has to all life that has gone before in other parts of the universe.
Everywhere we look in the universe the tell-tale signatures of advanced civilizations are missing.
We hope readers enjoyed the answers to these questions. Follow Billy Lee on Quora where you will find answers to thousands of unusual and interesting questions. The Editorial Board
What are complex numbers? What does “i” mean, anyway? How can a number be “imaginary“? What does it mean to multiply “i” exactly “i” times? Why is math hard?
For me, math is difficult because it’s interesting. I learn things from equations that aren’t obvious when I think about the world using words and images. Some things can’t be put into words. Some things can’t be pictured.
It’s true.
What makes interesting is the four real numbers it generates. (The numbers are +.2078… , -.2078… , +4.8104… , and -4.8104… .)
Can anyone give a geometric reason why an imaginary number raised to the power of an imaginary number generates four real numbers and no imaginary ones?
What does even mean? Is there anyone who can visualize a reason why the answers make sense? Are all the answers even correct? Or is only one correct, as any calculator that can do the calculation will tell?
Complex numbers are two-dimensional numbers that are made by raising the number ”e” to the power of an imaginary number — called ”i” — times an angle in radians. Complex numbers lie on a circle in the complex number plane. Unless ”e” is preceded by a number that stretches or shrinks it, the numbers always lie on a unit circle like the one in the picture. Recall that ”i” is the square root of minus one. When ”i” is raised to the power of ”i”, the result collapses onto the real number line — in one of four possible places. Which one? The numbers don’t land on the unit circle. The process can be demonstrated mathematically, but any physical intuition about why imaginary numbers with imaginary exponents behave the way they do can be elusive.
Abstract math that hides no model that anyone can visualize makes results startling, even unnerving. It’s a lot like the quantum mechanics of entanglement or the physical meaning of gravity. They can be mathematically described and their effects accurately predicted, but no one can explain why.
Mathematics alone can sometimes describe (or at least approximate) realities of the universe and how it seems to work, but as often as not when humans dive deep into the abyss of ultimate knowledge, math is unable to provide a picture that anyone can understand.
How can that be? Things seem to happen that cannot be thought about except by playing around with numbers and being taken by surprise. Intuition is difficult, if not impossible.
Here is the solution of . Perhaps clues exist in the math that I’ve overlooked. If a model exists in the mind of a reader somewhere, I hope they will share it with me.
(1) = cos (ln i) + i sin (ln i)
By definition: = i
Also: = ln i
Therefore: ln i = i
It should now be obvious to anyone who has taken a basic course in complex variables that multiplying i by i equals the exponent on e in line (1).
Right?
It’s a real number that returns a real result when used as the exponent of e and plugged into a calculator. The answer is completely abstract, though. We might learn more if we take a different path to the result.
By substitution into line (1): = cos () + i sin ()
By half angle formulas:
Convert 2nd term i to :
(2) Simplify the 2nd term:
Euler’s cosine identity is: cos θ =
Therefore: cos (iπ) =
(3) Simplifying: cos (iπ) =
Substitute line (3) into line (2) and simplify:
Now it’s just a matter of pulling out an old calculator and punching the keys.
= .043214; = 23.140693.
I rounded off both numbers, because they seem to go on forever like π and “e”; they prolly are irrational, because they don’t seem able to be formed from ratios of whole numbers. [In fact, they are transcendental numbers, because they transcend algebra. In addition to being irrational, they are not roots of any finite degree polynomial with rational coefficients. Take my word.] Using these numbers will enable anyone to compute who has a simple calculator with a square root key.
When square roots are calculated the answers can be positive or negative. Two negatives make a positive, right? So do two positives. So doing the math gives four numbers. See if your numbers match mine: .2078… , -.2078… , 4.1084… , and -4.1084… .
I don’t know why. The answers aren’t intuitive. Who would guess that imaginary numbers raised to powers of imaginary numbers yield real numbers? — not a solitary number like anyone might expect, but four. Pick one. In nature a unique answer can be arbitrary — determined by chance, most likely.
In this case, no.
It feels to me like the imaginary fairies flying around in complex space are destined to collapse onto the real number line for no good reason, except that the math says they must collapse (maybe from exhaustion?) in at least one of four places. Can anyone make sense of it?
The ln i is well known. It is — — which equals (1.57078… i ). The ln of — — can be rewritten by the rules of logarithms as i ln i, which is i times (1.57078…i ), which equals -1.57078… (a real number). Right? The ln of the correct answer must equal this number. Only one of the four results listed above has the right ln value: .2078… .
It seems odd that a set of equations I know to be sound should return a set of results from which only one can be validated by back-checking. Maybe there is something esoteric and arcane in the mathematics of logarithms that I missed during my education along the way.
Then again square roots can be messy; there are two square roots in the final equation, each of which can be evaluated as positive or negative. Together they produce four possible answers, but just one result seems to be the right one.
Adding the four numbers is kind of interesting. They sum to zero. That is so like the way the universe seems to work, isn’t it? When everything is added up, physicists like Stephen Hawking claim, there’s really nothing here. Everything is imaginary. Some philosophers agree: everything that is real is at its core imaginary.
Are there clues in the pictures and models of complex number space that would ever make anyone think? Sure, I totally get it. Yeah, I’ve got this. Real numbers cascading out of imaginary powers of imaginary numbers make perfect sense — like snowflakes falling from a dark sky.
A mathematician told me, Rotating and scaling is all it is. The base must be the imaginary ”i” alone; ”i” is the key that unlocks everything. The power of the key can be any imaginary number at all; ”i” is why the result of every imaginary power of ”i” becomes real.
The explanation calms me; but it seems somehow incomplete; it’s missing something; in my gut I feel like it can’t be entirely right, though it purports to persuade what the math insists is truth.
, right? Reversing the digits to make 8402 does not result in an exact number that is a power of 5.
plus a lot more decimals. It’s not a whole (or exact) number. Not only that, no matter how many decimal places anyone rounds-off 6.09363… , the rounded number raised to the power of 5 will never return 8402 exactly.
. and . 
. What are x and y?
, right? The exponent that makes 100 from the base 10 (not shown) is (equals) 2.
, right?
or 
?
and you are located at 
and want to get as cool as possible, in which direction should you set out?![\sqrt[3]{i} - \sqrt[3]{i}](https://www.thebillyleepontificator.com/wp-content/ql-cache/quicklatex.com-1d1f75d0d026c7150eebe5ec9e034c9c_l3.png "Rendered by QuickLaTeX.com")
equal to?
?
. Right?
. Right? It’s not the only root.
and -i. Right?
). It’s easy for anyone who knows how to work with complex variables. In Euler-form the angle in radians sits next to i. The angle directs you to where the result lies on a unit circle. Right?
.
.
interesting is the four real numbers it generates. (The numbers are +.2078… , -.2078… , +4.8104… , and -4.8104… .) 
even mean? Is there anyone who can visualize a reason why the answers make sense? Are all the answers even correct? Or is only one correct, as any calculator that can do the calculation will tell?
= cos (ln i) + i sin (ln i)
= i
= ln i
= cos (
) + i sin (
:
= .043214; 
= 23.140693. 
who has a simple calculator with a square root key.