Flavors of Reality

A rather well-known fact of fundamental physics is that when it comes to explaining what the stuff of our Universe is made of, there are a few different ‘right’ answers that cannot be reconciled with each other. Most non-physicists likely don’t know about these, and likely don’t care. But it really is a fascinating topic to mull over informally over coffee.

Broadly speaking, we have three theoretical frameworks that describe our world very accurately — that is, better than any of their predecessors.

Special Relativity

First, we have special relativity, Einstein’s brainchild of 1905. What this theory postulates is that there is an ultimate ‘speed limit’ that everything in our Universe adheres to, that we’ll call c.

Low Velocity

This runs counter to intuition, because we typically expect the speed of objects along the same axis to be additive: if Tom and Jerry are traveling in opposite directions at 10 m/s, from the perspective of Tom, Jerry is traveling at 20 m/s away from him. It turns out this can’t be true as you approach the speed limit c. For instance, if Tom and Jerry are traveling in opposite directions at 90% of c, then common sense would say that Tom should observe Jerry flying away at 180% of c, but in this case, common sense would be wrong. What actually ends up happening is that Tom still sees Jerry traveling a little over 99% of c, which is certainly faster than 90%, but still less than the speed limit.

The consequences of having this speed limit are huge. We end up with so-called relativistic effects such as the shrinking of space and slowing down of time, as nature assiduously works to enforce the speed limit. These effects combine in just the right ways to make the math work, and they’ve been experimentally verified to a high degree of precision.

Incidentally, light happens to always travel at speed c in empty space. This speed is exactly equal to 299,792,458 m/s, which is pretty fast.

A footnote in the theory of special relativity is the famous equation:

E = mc^2

This equation basically says that the stuff we see around us can be converted into energy, and energy can be converted back into stuff.

General Relativity

Despite the name, it’s best to think of general relativity as a completely different beast. Presented (again) by Einstein in 1915, this theory explains gravity. While Newton’s theory of gravity provided equations that worked quite well, Einstein’s theory went much further, by not only providing more accurate equations, but also explaining gravity as the consequence of the geometry of space-time.

Just like special relativity, there is an element of counterintuitiveness to this idea. For instance, we might normally think of objects interacting with each other in a vast, unbounded, otherwise empty space, an idea that is traditionally called absolute space. Not so, says Einstein — space and time emerge as a consequence of stuff in the Universe. This is pithily explained by the following idea: imagine that you somehow get rid of everything in the Universe — stars, planets, galaxies, dust. Conventional wisdom says you’d be left with vast, empty space, whereas according to Einstein, space and time would disappear with everything else.

This might take a while to sink in, and I find it helpful to visualize it as in the picture below. If our Universe had nothing but the Earth in it, imagine the Earth being surrounded by a ‘halo’ or invisible bubble of space-time. This isn’t part of something larger; this is the Universe. You could travel to anywhere within this bubble, but there are a finite number of places you could go to. As a result, if you picked a direction and kept going, you would eventually end up where you started.

Space-Time

What’s important to note here is that it is meaningless to consider what happens when you step ‘outside’ of the bubble, as the bubble is the entirety of space-time.

Now you can imagine what happens when there’s more stuff in the Universe. Let’s say you have both the Sun and the Earth. Each of these has its own bubble, but these bubbles are also connected to each other. Both the Earth and the Sun warp the shape of the bubble around each other, and this interaction leads to the dynamic motion of these objects. What we observe as a ‘force’ between the Earth and the Sun is really just objects traveling in straight lines through the curved geometry of the bubbles, like a strange pair of yo-yos bouncing around. Of course, there is much more to the geometry of space-time and our Universe may not be finite after all, but this is a good start.

General relativity plays by all the rules set by special relativity. In particular, there is a limit to how fast information can travel through space-time. Say the Sun were to magically disappear tomorrow, general relativity says that it would take us at least 8 minutes to find out that something was wrong, the same as the time it takes for the light of the Sun to reach us every day.

General relativity has one striking limitation: nothing in its equations prevents stuff from getting squeezed into a tiny little point that keeps getting compressed ad infinitum. When you play this out, the equations of general relativity lead to absurd results. Such a tiny, infinitely dense point is called a singularity. Common wisdom is that we end up in this theoretical situation simply because general relativity is incomplete — it doesn’t try to describe what happens at the scale of the very small.

Quantum Physics

From general relativity, we now come to (what we believe) happens at the scale of the very small. Here, we’re talking not just about atoms and molecules that make up the stuff around us, but even smaller particles. For instance, most of the atom is concentrated in its nucleus, which is about a hundred thousand times smaller than the atom itself. That, according to one source, is comparable to a “pea in the middle of a racetrack”. The nucleus, in turn, is enormous compared to some other particles and distances that we end up worrying about in particle physics.

Since the 1920s, there have been a steady set of theories, experiments and interpretations that have emerged that I’ll collectively term “quantum theories”. Unsurprisingly, it was Einstein yet again that kicked off this revolution in 1905, when he published a paper that explained the photoelectric effect. The details of this effect are simple and fascinating, but we will jump right to the conclusion, which is this: light is made up of discrete particles, or small bundles of energy.

This, in itself, may not seem very impressive, but it was revolutionary when you consider that over the previous few decades, scientists had finally reached the conclusion that light behaves like a wave rather than a bunch of particles. A particle moves in straight lines from one point to another; but a wave dissipates through a medium and spreads out. Although Newton had originally propounded the corpuscular theory of light (i.e. light as particles), Thomas Young, in 1801, had experimentally shown that light demonstrated typical wave-like behaviors. With his double-slit experiment, Young showed that light ‘waves’ interfere with each other just like waves you might see in water. Einstein’s explanation, while perhaps obvious in retrospect, upended this established belief.

Double-Slit Experiment

So is light a particle or a wave? Today, more than a hundred years from the early days of the quantum, we have absolutely no idea.

A central pillar of quantum physics is the so-called standard model, which is a model of particle physics that has been refined over the years. The standard model is just as much a theoretical failure as it is an experimental success. I like to think of it as a complex computer program. Given the right inputs, it spits out amazingly accurate answers, but it doesn’t deign to offer any explanations.

For instance, the standard model predicts a variety of particles with specific properties, and almost all of these have been experimentally detected. It tells us what kinds of particle interactions to expect with what likelihood, and again, experiments have verified these predictions.

On the other hand, consider this: we have a law that says that the electron number is conserved across all particle interactions. There are a couple of particles (one of them being the electron) that have a non-zero electron number, and when particles interact, the electron number before and after the interaction always remain the same, even if particles transform from one to another. Why? Nobody knows. Quantum physics is full of many such strange rules that are unsupported by common sense explanations.

Despite all this abstruseness, here’s what we know: most types of quantities in nature are quantized, which means they come in discrete increments just like light. At the same time, the way these quanta propagate and interact with each other resembles the behaviors of waves. Just as a quantum of light (aka, photon) behaves like a wave, so does an elementary particle like the electron. This idea has been enshrined in the notion of wave-particle duality, which asserts that all known matter behaves either like a wave or a particle. Only at the time of measurement (there is much debate on what this actually means), and depending on the kind of measurement being attempted, does the wave-particle duality resolve to either wave-like or particle-like behavior.

It’s worth noting at this point that a lot hinges on the kind of measurement being performed. No one has ever observed an electron (say) ‘smeared’ out across multiple points (that’s not how it works), but the probability of discovering an electron at a particular position is determined by its corresponding wave representation. When you do finally find that electron, it could be at some definitive point with some likelihood. But if you do try to pin down the exact position of that electron, you’ll find that it goes into a frenzied rage (metaphorically) making it harder to perform other kinds of measurements on the same electron. Quantum physics forces you to prioritize the kinds of measurements you truly care about, and correspondingly makes other kinds of measurements harder. The net effect is that there’s always a certain minimum amount of uncertainty across specific related properties such as position and momentum.

From a practical standpoint, you can think of waves as a mathematical tool for figuring out the likelihood or probability of a specific outcome, like finding particle in a particular place. These probabilities have turned out to be experimentally correct, but no one can explain why, or what it actually means.

Collision Course

We now come to the most interesting part of the story, which is the collision — not of particles — but of these theoretical frameworks.

General relativity, as you may recall, doesn’t have a notion of quantized space, that is, some limit of how tiny an increment of space can be. Physicists believe that space must be quantized, but no one really knows how.

Quantum physics has been successfully refined to take special relativity into account. But no one has figured out how to take general relativity into account as well. One problem with quantum theories is that they are currently background-dependent. What this means is that the interaction of particles and forces is assumed to be occurring in the backdrop of absolute space. General relativity successfully did away with absolute space, as you may recall, but only in the context of gravity. One would expect a true description of reality to be self-sufficient in its explanatory power, just like general relativity.

Another unexplained phenomenon is that of non-locality. The gist of this idea is that when particles (or rather, their wave representations) interact, they can get ‘entangled’ with each other according to the rules of quantum physics. When this happens, the measurements performed on one particle influences the measurements performed on the other, even when they are far apart. This effect is instantaneous, and we have no explanation for it. At first glance, one might posit that there is some information hidden away in the particles (or waves) themselves that is revealed only at the time of measurement. But this hypothesis consisting of so-called local hidden variables, has been experimentally disproven through an amazing feat of statistical ingenuity (John Stewart Bell, 1964). The best explanation we can come up with is that somehow, somewhere, the Universe keeps track of the relationships between these entangled particles, no matter where they are.

And finally, we have the problem of probability. Now, one might argue that there is nothing wrong with the Universe being a little random in its tastes, but the problem is even more subtle. If you recall the double-slit experiment, one way it might be conducted is to shine a light through two closely-lined up slits and observe an interference pattern at the screen. This is easily explained by describing light as waves; wherever the waves combine with each other, you get a bright line, and wherever the waves cancel each other out, you get a dark stripe. But here’s the rub: suppose you performed the same experiment while carefully shining a single quantum of light (aka, a photon) at a time, you still end up with an interference pattern.

Double-Slit Experiment (Single Photon)

Each photon, being a discrete particle, lands on exactly one spot on the screen. But the probability of the photon landing on the bright line is much higher than the probability of it landing on the dark stripe. So as you keep sending photons through, you can observe the usual interference pattern build up over time. For this to be possible, though, each photon must somehow ‘be aware’ of where the other photons are going to be found, or have been found. Again, it appears the Universe is keeping track of the overall distribution of these photons over time, but nobody can explain how or why this is the case.

The Story of Human Language

I listened to John McWhorter’s course The Story of Human Language. ‘Language’ primarily refers to spoken communication. Written language is considered a relatively new invention; how people write is quite distinct from how they actually speak, even within the same language. A person who speaks in paragraphs is very odd, suggests McWhorter.

The story of language change is all about how sounds evolve over time. Vowels shift, consonants merge. Sometimes sounds get ‘rebracketed’ — word boundaries of commonly used phrases change. Certain combinations of syllables are simply hard (like trying to pronounce ‘February’) and over generations, they morph into something simpler. Certain sounds are in constant danger of disappearing, like the ‘h’ at the start of a word. Word order occasionally flips from subject-object-verb to subject-verb-object, or the other way around. Grammar is, to a degree, optional — a lot of information is derived from context.

Many modern languages have so-called high and low varieties, the high variety being what is considered ‘proper’, and the low variety being what is normally used by everyone. This phenomenon is called diglossia. A newcomer learning a language may mistakenly learn the high form, use it in ordinary speech, and get laughed at. The high form is what’s taught in schools, the low form is what you pick up through everyday experience. Strangely, the low form is generally not considered fit to be formally taught.

Languages don’t really exist, it turns out. All you have is bundles of dialects, each one a little further removed from the other. Language distinctions are drawn by geopolitics; certain languages are even closer to each other than certain dialects. All you have is a continuous evolution of dialects into others as they get separated by geography. These dialects keep evolving further and further until they start looking quite different from the original.

When people of different tongues are forced to interact with each other on a temporary basis, they may create an ultra-simplified language that enables a minimal degree of communication. Such languages are called pidgins and not expressive enough to be considered full-fledged languages. But when the arrangement becomes more permanent over multiple generations, these stunted languages may then develop into new ones called creoles.

The Story of Human Language is an exciting and beautifully narrated tale; I highly recommend listening to it.

Illusion of Explanatory Depth

“Most people feel they understand the world with far greater detail, coherence, and depth than they really do.” [Rozenblit, L., & Keil, F. (2002)]

The illusion of explanatory depth is a cognitive bias that drives people to believe they understand things in far more depth than they actually do. These things may be familiar devices like toilets or refrigerators, or complex systems like government and healthcare. Rozenblit and Keil found that the “ratio of visible to hidden parts is the best predictor of overconfidence for an item”. What this means is that when a system looks simple on the outside, people tend to assume they understand it on the inside.

“Across three studies, we found that people have unjustified confidence in their understanding of policies. Attempting to generate a mechanistic explanation undermines this illusion of understanding and leads people to endorse more moderate positions.” [Fernbach, P. M., Rogers, T., Fox, C. R., & Sloman, S. A. (2013)] The title of this paper says it all: political extremism is supported by an illusion of understanding.

There is one interesting tidbit in the second paper. “Although these effects occurred when people were asked to generate a mechanistic explanation, they did not occur when people were instead asked to enumerate reasons for their policy preferences […]”. If you want to get people to take a more moderate position, don’t ask them why they support one policy over another. Instead, ask them to explain how things work. That makes them realize how little they actually know, which then leads them to conclusions that are less intolerant of others’ points of view.

On Creativity and Tennis Balls

Of late, I’ve been wondering about the nature of creativity. Is creativity something that is built into your genetic makeup? Is it something learned over time? Or is it, perhaps, acquired through the force of habit? Personally, I lean towards the latter hypothesis, that by intentionally mimicking the superficial effects of creativity over long periods of time, one effectively becomes a creative person. Unfortunately, I have not conducted any experiment that might prove or disprove this hypothesis.

Dreams have long fascinated me for this very reason. You wake up in the morning and marvel at the absurdity of the sequences that you experienced during the night (assuming that you do recall some of it). In my personal experience, it’s not that logic has been suspended in dreams, or that paradoxes are taken for granted. Rather, the contradictions are obvious and even well-understood, but you have no choice but to continue forward, because there is a sense of reality to everything. Evolution has taught us that reality may be worked around or controlled to a degree, but must never be disbelieved, lest it get the better of your gene pool.

Our minds are apparently capable of creating these strange sequences that we wouldn’t normally be able to come up with in our waking hours. Last night, I dreamt that I was going to play tennis, something the real me hasn’t done in ages. I figured I would practice my serves (with a vague sense of awareness that the pandemic made it difficult to find actual opponents to play against). I had an hour to play: a dream storyline always has an element of a time crunch that manifests emphatically. Of course, there was simply no explanation for the odd shapes of some of the tennis balls, as if they were cut from a full loaf of bread. Would they bounce correctly? Was I missing something? Should I try these oddly shaped balls? I didn’t have too much time to ponder though, as I only had ten minutes left of the hour that I had started with.

I hypothesize that to be creative is to posit improbable associations. Start from the absurd idea that tennis balls must come from loaves of bread, and chip away at the absurdity over time, until all you’re left with is a Good Idea™️.

End-of-History Illusion

Apparently, individuals, at all ages, believe that they are unlikely to change much in the future (in terms of personal growth and maturity), even in the face of evidence that they’ve grown in the past. The psychologists who studied this effect gave it a cool name: the end-of-history illusion.

The psychology of your future self by Dan Gilbert on TED

Personally, I am skeptical that this is a problem, even if the bias was shown to be real. There’s a danger to thinking too much about the future: we may forget to live in the now. We might miss the chance to let opportunity and luck take us to all kinds of interesting places.

Lucky Bamboo

I sense the light, although I cannot quite see it. I feel the warmth in my veins, a sense of richness filling my body that contrasts vividly against the coolness at my feet. The light beckons to me from one side, and I reach out longingly. I feel strength growing inside of me, bit by bit, everyday.

I stay very still; I know of no other way. As I am, I meditate upon the world – who am I and why do I exist? I do not know the answers, and I have no one else to ask, but I am in harmony with the world, and the world is in harmony with me; I know of no other way.

I dream sometimes. I don’t always know the difference between what is real and what is dreamt. It is difficult to judge reality harshly when you know so little of it.

I can’t quite see my beginning, and I certainly can’t predict my end, but I am not afraid, for I think I am loved.

Painting “Lucky Bamboo” by Geetha on namelessly.me

A Rant About Physics

Fundamental physics has become complicated over the past century, at least in public perception. With many flashy new ideas like ‘strings’ and ‘multiverses’ being proposed, it is difficult to separate what we think we actually know, from hypotheses, or even conjectures.

Physics is the natural science that seeks to explain our objective reality using a small set of laws that govern it. There is much packed within this pithy definition, that we can go over with a fine-toothed comb.

First and foremost, physics is a study of reality. Its goal is to observe reality very carefully and look for patterns that may be codified into fundamental laws. Its method is experiment — start with a hypothesis of what such a fundamental law might be, design an experiment whose anticipated outcome is best explained by the hypothesis, and then perform the experiment to test the prediction. Good experiments ensure that if they are clearly unsuccessful, the hypothesis may be safely discarded. On the contrary, a successful experiment does not prove the hypothesis, it only increases the likelihood that the hypothesis is correct. The history of science is rife with examples of better explanations superseding good ones.

We seldom know if a particular law is ‘fundamental’. Many laws that we deemed fundamental turned out to be special cases of something even simpler. But the creed of physics is parsimony — to reduce reality into as few laws as possible that merit explanation. We can explain the movements of all the planets in the sky when we understand the laws of gravity. This ‘law of parsimony’ is colloquially known as Occam’s Razor.

Second, the reality studied by physics must objectively exist. Unless we agree that something is real, in the sense that it can be subject to experiment, it doesn’t have a place of study in physics. For instance, hallucinations generated by the human brain are not part of our objective reality, though one is free to study the behavior of the brain (this is neuroscience, not physics). The study of consciousness is not a part of physics, unless there is evidence that the behavior of higher organisms cannot be adequately explained by known physical laws (we have no such evidence).

Occasionally, a theory may predict the existence of hitherto unheard of phenomena as side-effects. If these phenomena are later discovered, they lend further credence to the theory. For instance, black holes were predicted by general relativity, and experimentally detected later on. But for a hypothesis to be scientifically useful, it must be falsifiable — it must offer an experiment whose outcome is capable of refuting the theory.

It’s worth noting at this point that there are several popular science conjectures that are decidedly unscientific. Any variant of the ‘multiverse’ conjecture — the idea that there are other so-called universes that no conceivable experiment can detect — fails the test of falsifiability, and has no place in science. The ‘mathematical universe hypothesis’ — the claim that the universe is mathematics — falls into the same category of pseudoscience, as it doesn’t explain reality as we know it. Yet another idea that is unscientific is the claim that the universe is a gigantic simulation — no experiment has ever been proposed that would distinguish a simulated universe from a real one. If you find people making tall claims that are unsupported by experimental evidence, you would be right to be skeptical.

Finally, a subtle yet important assumption in physics is that our reality is governed by laws that remain the same over time. There is a tenet here that there is order underlying the chaos of reality. The idea that our reality is dictated by these unchanging laws is deeply incompatible with the idea of an omnipresent and omniscient deity making decisions on a whim. If there were experimental evidence of such a deity, the laws governing the deity would then merit further explanation. The laws of physics are all there is to reality, and the quest of physics is to discover them. It’s turtles all the way down.

The static nature of laws is a consequence of the law of parsimony. If a certain law changes over time or is different in different parts of the universe, there must be a higher law that explains the conditions under which it varies. If you keep discovering these higher laws, what you eventually end up with must be permanent and unchanging.

Frozen Lake

We hiked up to Heather Lake on Saturday morning, a 5 mile roundtrip with an elevation of 1,781 feet, according to my fitness tracker. Being one of the easier hikes at driving distance from the city, Heather Lake Trail generally sees a lot of foot traffic. That’s especially so with COVID-19 restrictions in place, as hiking is one of the few outdoor activities still possible when the weather allows it.

Our own plans tend to be created on a whim, of course. When you get up in the morning and discover that it’s not going to rain, you’re forced to think of something to do before the clouds move in again. If you dally, the weather gods may get angry and change their minds.

The trailhead is a little over an hour drive from Seattle. The last mile is on a pothole-ridden road that somebody should really consider fixing. The trail itself is fairly straightforward, and can be tackled at a brisk pace. The path is wooded with tall trees and a few small streams that need to be negotiated.

Heather Lake Trail
The Trail

In a sense, a hike through the woods is a spiritual experience, though you may not always know it at the time. When you spend all of your energy sensing your environment, absorbing the sights and smells, and stepping carefully from one rock to the next, your mind has the opportunity to switch into low gear, hum silently and contemplate the meaning of life.

The meaning of life is not complicated. The mind is usually a jumble of distinct and sometime conflicting motivations crisscrossing through the terrain. To understand the meaning of life is to organize these motivations into an aesthetic, if not simpler, hierarchy. Let the deeper motivations bubble up weightlessly so you can understand them better, and then let them sink back down to the bottom of your mind. Dust off ideas and observe them dispassionately without the constraint of time looming over you. Some ideas become clearer, others become superfluous. The process is automatic, like air rushing to fill a vacuum.

When we reached the lake, we discovered, to our surprise, that it was completely frozen. A few people were brave enough (or stupid enough) to stand on the ice in the middle of the lake and take pictures.

Heather Lake - Frozen
The Lake is Frozen
Heather Lake - People on the Lake
People Standing on the Lake

The Paradox of Tolerance

In a free society, tolerance means that individuals put up with ideas and actions that they don’t necessarily agree with. Evelyn Beatrice Hall famously expressed the Voltairean principle as “I disapprove of what you say, but I will defend to the death your right to say it.” Every free citizen is at liberty to act as they please, as long as they don’t infringe on the freedoms of others.

Tolerance does not imply freedom from consequences. Don’t do stupid things or say hurtful words and expect others to be okay with it. And if you intentionally make false statements that cause harm to others, tort laws may catch up with you.

The ‘paradox of tolerance’ refers to the idea that when a society is tolerant without limit, its ability to be tolerant is eventually destroyed by the intolerant. When ideas of intolerance are given a free rein, these ideas can take root in a critical mass of people with the power to impose their own will on the populace. Moreover, it is only a matter of time before incentives align to make this happen.

According to Karl Popper, this paradox doesn’t imply that ideas of intolerance should not be tolerated at all. Society may continue to tolerate these ideas to the extent that they can be kept in check through rational argument and public opinion — in fact, it is preferable to do so unless force is necessary.

One way to rationalize this paradox is that if you’re a tolerant person in a tolerant society, you’re playing by a set of rules and expect everyone else to do the same. Someone espousing intolerance is effectively trying to change the rules of the game. If they convince enough people to join their cause, you’re at a disadvantage because trying to stop them is against your ethos. If things get out of hand (as they’re bound to eventually, if enough people believe they will benefit), your only option is to break your own rules and shut them down.

Sadly, once you say it’s okay to break your own rules, the intolerant in positions of power will eventually take advantage of this loophole to further their own agendas.

Unusual Numbers

Numbers are a human invention. As intelligent and rational creatures, we have learned to operate effectively in a world of abstract thought, where the concept of numbers goes beyond what we can count. But as humans, we cannot discount the evolutionary basis for how our apparatus works.

It turns out that numbers that are really large or really small are well-nigh impossible for us to comprehend. Upon careful inspection, this is not surprising, as comprehension is simply a form of analogy-making. We understand things when we can compare and contrast them with other things we are already familiar with. When we are presented with numbers that are very different from what we encounter in everyday experience, we have no way to make sense of them. Here are some examples:

Despite the beautiful pictures of galaxies you might have seen, the scale of the Universe is so vast that a galaxy is mostly empty space. For instance, the average density of our Milky Way galaxy — together with all its brilliant stars and planets — is conservatively estimated to be of the order of 1 kilogram over every billion cubic kilometers. If you imagine a box that spans a kilometer across on every side, magnify it a thousand million (1,000,000,000) times, and add a bag of potatoes into this box — that’s how empty our galaxy is. The space between galaxies is far emptier.

sky space dark galaxy
Photo by Pixabay on Pexels.com

We estimate that there are 2 trillion galaxies in the observable universe. A trillion is a million million. To put that in context, a trillion is a number that is so large that removing a few millions doesn’t make much of a difference — you’re still left with about a trillion. Astronomers conservatively estimate that there are about a 100 million stars in the average galaxy, and about 1,000,000,000,000,000,000,000,000 stars in all in the observable universe. That’s one followed by 24 zeros.

Okay, now here’s a fun fact: there are more molecules of water in a few regular-sized drops than the total number of stars in the observable universe. All it takes is about a hundredth of a liter of water.

Molecules are pretty average-sized in the bigger scheme of things. The Planck length is the theoretical minimum limit to distance you can meaningfully speak of. Nothing smaller than the Planck length exists, according to present-day theory. The Planck length is so small that if you were to magnify a particle that spans the width of a human hair (~0.1 mm) to the size of the observable universe, the Planck length would itself be as big as the original size of the particle (~0.1 mm).

And finally, humans have evolved on our planet for millions of years, right? It turns out that if you overlay the Earth’s entire history until today over a 24 hour clock (midnight to midnight), single cell life forms appeared at around 4 am, multicellular organisms appeared at around 5:30 pm, and all of human history spans the last two minutes until midnight.

Life is all about perspective.