The Opening Series: Paradox and the implications, Or How I learned to love the both/and

Author's Note: This is an opening series of 5 newsletters to help define what this whole newsletter is about. If you are here: it is article 3 of 5 and feel free to read the first ones HERE to catch up. This article here is significantly longer than all other newsletters (past, present and future) because it has to be. It’s better if I do this ugly work up front, then we can get to the good stuff soon enough. This is still good….I hope.

If by some reason you’re reading this, I imagine you’ve been forced to learn some Math. I’m not going to get into real math, that’s not for this newsletter, but I do want to jog your memory and have you think about what you get when you multiply any number by zero.

What’s the answer to this question: 1 x 0 = ?

Or this one- one hundred times zero? A thousand times zero, or let’s say 10,000 times 0, what’s the answer to that one? Elementary math tells us, it’s always the same answer - zero.

How about this one, if I drop a single seed of millet (a cereal grain kind of like wheat) does it make a sound?

If you’re like me and opportunities to drop random seeds of millet have missed you throughout your life - you’re not alone.

I wouldn’t know if a single seed of millet, rice, or wheat would innately make a sound if dropped or not (It might make a sound in a cavern, on a tin or wood floor but not outside on dirt, right? Well the context/circumstance conversation is for another newsletter) but for a second let’s imagine we’re outside, on dirt, some seven thousand years ago and we drop a single seed of grain on the ground. Does it make a sound?

My guess is, and maybe it’s yours too, no it does not.

Now imagine I have a bushel of millet seeds (which weighs about fifty pounds). Does that make a sound? It certainly would.

Now, here’s your second math equation: if a single seed of millet doesn't make a sound (1 millet seed = 0 sounds) but a lot of them do make a sound (10,000 millet seeds = 1 sound), and we’re in agreement that the little makes zero sound and the many, many, many more of the same millet seeds then does make a sound? Then doesn’t that math looks like: (1/10,000 x 0 = 0?).

Hmmmmm. One seed that doesn’t make sound, but when comprised with a bunch of their seemingly identical brethren they do. Hmmmmm.

That contortion in your face, the wrinkle in your brow, furl in your lip, or finger scratching on your head is paradox, specifically “The Millet Sound Paradox” and that is courtesy of Zeno of Elea, the “Inadvertent” GodFather of Both/And.

How one person tried to “Joker” the Greek Mathematics Movement

In Greece, in the 7th and 6th century BCE, there was a major movement in Mathematics. Now, this isn’t a history newsletter (or a math one, clearly) so let me say this first- no the Greeks didn’t “invent” Math. However, they did lay claim to many theories that make up what we consider to be “Modern” and hold up to this day. Think Pythagorean’s Theorem for example. These individuals held court all throughout Greece, Italy, Egypt and beyond as they laid bare their attempt to quantify human existence through proofs, formulas, theorems and more.

At the same time, there was a group of philosophers, mathematicians of thought if you will, who were hypothesizing their own theories about human existence but through the medium of spoken word and thought. Their words and ways held capture over individuals they spoke to in a way that would seem almost religion-like.

These philosophers are widely known to this day. Names like Socrates and Plato are synonymous with philosophy. Their aim was simple: to theorize, commentate, romanticize and most of all invoke curiosity through language and thought experiments.

Then there was Zeno of Elea. Zeno was a philosopher of the same era, 5th Century BCE. He resided in Elea, Italy, and traveled often to listen and learn from Parimendes, a famous philosopher of the time who also held the attention of Socrates and Plato alike.

These individuals would gather in classroom-like arenas and “hold court”. Each one rising to verbally joust with the other. Going back and forth, each person having their chance to pique the interest of the audience with theories on the nature of life.

Zeno was in this audience, until he wasn’t. That is to say he decided to speak up and be heard, and his words are known to this day. In fact, it’s his collection of words, in a way only known as Zenoean, that he arguably created the idea of “Paradox” as we know it today.

Zeno of Elea would often defend the theories of Parimendes and his major work. It was through this defense that Zeno would enter into a back-and-forth with the various other audience members through a series of questions designed to illuminate the absurdity of monism or the idea of a “one-and-only true god” while also attempting to poke holes in the Greek Mathematics movement. This is where we ultimately first hear of the Millet seed Paradox, but it’s not the first time we hear from Zeno.

The first time we see the work of Zeno, it’s in a passage in Plato’s work Parimendes (which depicts this moment below and others during Parimendes dissertation):

Once Socrates had heard it, he asked Zeno to read the first hypothesis of the first argument again, and, after it was read, he said: “What do you mean by this, Zeno? ‘If the things that are are many, that then they must be both like and unlike, but this is impossible. For neither can unlike things be like, nor like things unlike’? Is this not what you say?” “Yes,” said Zeno. “Then if it is impossible both for things unlike to be like and for like things to be unlike, then it’s also impossible for there to be many things? For if there were many things, they would incur impossibilities. So is this what your arguments intend, nothing other than to maintain forcibly, contrary to everything normally said, that there are not many things? And do you think that each of your arguments is a proof of this very point, so that you consider yourself to be furnishing just as many proofs that there are not many things as the arguments you have written? Is this what you say, or do I not understand correctly?” “Not at all,” said Zeno, “but you have understood perfectly well what the treatise as a whole intends” (Pl. Prm. 127d6–128a3).

Now, take some time to breathe because, yes, that is a brutal paragraph of words.

Now go back and read it again.

You did? Okay, good (did you?).

In short, Zeno is laying out a series of statements via “antinomies”, a way of constructing a theory by laying out a yin-and-yang style of statements, and Socrates being somewhat confused, asks him clarifying questions to make sense of what seems like nonsense. Same girl, same.

In his statement, Zeno casts doubt on the idea of one thing (a pen, a banana, etc) being finite (having a set amount) and therefore worthy of its own truth. While also casting doubt that the “many '' of those same things could then be infinite and true as its own truth, and that together these two ideas are separately true theories and mathematicians or philosophers alike would have to choose: Either - Or.

Saying it again, for clarity as my eyes are crossed, Zeno’s theory is that if you think “one banana” means “one finite thing” then you can’t believe in the many (potentially infinite) of that same thing.

This makes sense right?

If I have one banana in my hand, I don’t have an infinite amount. But If I theoretically had a tree that created infinite amounts of bananas in my backyard and I could conveniently pluck and eat them at will, then I would no longer have “one” banana. I’d have a problem with radioactivity, but I digress.

His inferred final response to a befuddled Socrates, is that the only option is to hold both theories as true and untrue at the same time.

But why does he do this? My belief, he does it to make mathematics seem futile. Why put into quantifiable terms what is inherently impossible to do (because of these thought experiments).

You’re thinking to yourself, why does this matter? Why do I care that he spent time poking holes in mathematics when modern science, technology, physics and more are all underpinned by mathematics almost alone. It isn’t futile.

This is where I ask you to look at the passage without caring about what’s said.

Did you see it? In plain sight? The first time I read this passage it was there that I felt the reality of what I was seeing. That it was real, it was old, and it was something I must learn more about. It’s not Millet seeds, or things being many being not and many or infinite and not.

What is there, in plain sight, are the words “both” and “and”. It’s that existence in this passage that marks the beginning of understanding exactly what we are embarking on.

It’s here: ‘If the things that are are many, that then they must be both like and unlike, but this is impossible.

And here again: “Then if it is impossible both for things unlike to be like and for like things to be unlike, then it’s…”.

What does this mean? Why is the existence of the two words important? Alone, they aren’t important in this context, and together they carry with them the essence of what we’re getting at, but the idea really begins to make sense when you circle back to a paradox like the Millet Seed Paradox.

Back to that Millet Seed

Remember earlier, I prefaced the Millet Seed Paradox by using elementary multiplication formulas to help contort reality and to make a point. But that’s not fair since using Math to describe a hypothetical word-formula is purposefully confounding and that also happens to be the goal of Zeno of Elea.

It led him to create the Paradox of the MIllet Seed and many others like “Achilles versus the Tortoise” and their impact on society has reverberated throughout history. There is a statue standing in Italy to this day that depicts Achilles racing a turtle.

But something along the way got lost in these paradoxes. They became thought experiments meant to confound and confuse. They became ways for individuals to poke at complex theory with a simple reminder of a millet seed and whether it makes a sound or not. Most of all, paradox became a word meant to confuse more than provide clarity. Distract and move a part more than bring together.

This is why I created this newsletter, because I aim to give clarity (albeit cloudy-clarity) back to the paradox in the spirit Zeno of Elea actually meant but didn’t have the time to worry about.

And what is that clarity you ask?

That while a fallen millet seed makes no sound is probably true, and that dropping a bushel of the same seeds would make a noise is also true, the bigger picture here is that both things can be true at the same time.

This is it, my hypothesis: two (or more) things can be true and untrue at once.

Always.

In almost every scenario of life, death, taxes, love, or hate. All of these complex ideas, feelings, and news stories of the day can all have various shades of black and white and when we come together to understand them it’s always best to aim to agree on a shade of gray instead of whether black or white is true by itself.

When we get lost in the idea of whether a thing can only be one or many and not both, we are distracted from the bigger idea in front of us that pushes us closer to our collective brink. When we get distracted by arguments over having to make a decision on who you support more, either team “Soundless One Millet Seed” or Team “Loud Millet Bushel” we don’t see the common ground.

When we risk life and limb over which side is right, either math and science over feelings and reason, we become entrenched in ideas that mean nothing instead of the ones that do.

That “both/and” is always the better answer instead of “either/or”.

Or maybe not.

On second thought, it’s probably both.