3. Philosophy as… Explosion.

“The Principle Of Explosion” is an overlooked starting point.

Just one point…
The Principle Of Explosion” is not a joke.
Taken seriously, it is a serious and radical premise for inquiry.

The Principle Of Explosion is the alternative to The Law of Non Contradiction. It’s an opposite starting point for philosophy. Most people don’t take it seriously, or aren’t even aware it’s an option.


But before I begin my argument proper, I’m going to loosen you up a bit. Consider it a pre-workout stretch. Let’s begin with a poem. I hope it makes more and more sense as you read on.

It is comfortable with contradiction, open to the kinds of associations that emerge; the multiple-truths that reveal themselves.

What is this?
This.
This is a cup. 
Is the cup half empty, or half full?
It is both. 
It is also not a cup at all. 
Starstuff. A trillion atoms. Ten trillion electrons. 
Frantically dancing an infinity of orbits.
Mostly space. Or mostly time?
Or a spaceship travelling both, from past into future, meeting us presently.
From the perspective of an astronaut, it is just part of Earth.
From the perspective of an ant, it is a mountain to climb.
It is technology. 
It is a museum piece from the future.
Your descendants will marvel that humans endured such inefficiency. 
But your ancestors would have wondered at it, maybe worshiped it.
A marvel of straight lines and modern manufacturing. 
It is cultural, historical artifact. 
Millennia upon millennia of cups. 
It has stories to tell.
It is Swedish design. 
It is somebody’s job. 
It is an economic phenomenon; a market transaction.
It is supply and demand making love. 
It is a weapon. Smash it. Poison with it. 
Or bring healing with it.
It’s a shape-shifting goddess pretending to be a cup.
It’s an alien. 
A musical instrument. A magnifying glass.
A hand-warmer. A guest-impresser. A cheap gift. 
A waker-up’er. An alarm o’clock. A caffeine addiction. A scent. 
It is The New Covenant; My blood, which is poured out for you.
It is poetry, for… 
It came from nothing, it returns to nothing. 
It is you, because without it, you die of thirst. 
And without you, it never would have come to be. 
It is a child of the human mind. 
A reminder of all you Thirst for; 
And a reminder that even after you are quite drunk, 
And all desire is quenched, 
Will come the morning’s headaches, and you will Thirst again.
It is the question you’re asking. 
And the answer you’re looking for. 
And all the Questions and Answers you never thought to ask. 
If only you could fully understand it. 
Mystery incarnate.
It is all of these things. 
And none of these things. 
What is a cup?
This is a cup. 
This.

What is “The Principle Of Explosion”? 
The Principle Of Explosion comes from Logic. 
It states that:

From a contradiction, anything follows.

In other words, 
If A=B is true, and A≠B is also true, then a contradiction is true. 
If a contradiction is true, anything is true. 
If anything is true, we have a magic wand. 
So pigs can fly. 
And unicorns are real. 
And Santa Claus delivers presents on Christmas eve. 
And I’m a whale.

If you’re a well behaved student of Logic, now’s your cue: 
“Oh, I get it! It’s a joke. 
Obviously, contradictions can’t be true. 
Because otherwise, there’d be chaos. 
And logic wouldn’t prove anything.”

For millennia, Philosophy has been so intimidated by contradictions — so horrified at the prospect that they might be true; so traumatized by the memory of what we saw There; in that place, beyond the frontier; visions there were, many visions wondrous fair, yea, visions of realms, heroes, marvels and gleaming gods; but also Titans unleashed, monsters of the deep, Terrors gathering in the dark — that we have erected this huge wall, this mighty shield, this only defense, against them.

The Law of Non-Contradiction is that fortress. 
That fortress adamant. That fortress of adamant mind.
That last noble bastion of classical reason. Keeping watch at dusk. 
Wild, wild the terrors of the night.

Imagination bound. 
The dam fills with water. And poureth over. 
Far below, fertile valleys drink deep. 
Fertile valleys not ocean floor.

Why am I speaking poetically? 
There’s another way to say this.

Saying it directly just hurts, it is so blunt. 
But you want to know. So here:

IF THE LAW OF NON-CONTRADICTION IS WRONG, THEN EVERYTHING YOU KNOW IS WRONG. The world as we know it today is built on this foundation. Above all foundations, this foundation. What we call math, logic, philosophy, science, the humanities — all of it — it’s all based on this premise. Our thinking and our achievements and our civilization all start with this premise: that if something is true, it cannot also be false (in the same sense); that is, that contradictions cannot be true, cannot be real; that reality must be consistent.

Maybe you have already confronted this before, so you are not shocked. But if you have already crossed this threshold, it is good to return to it, and renew your sense of wonder. How can it be? When I first considered this, my reality shattered. It is just that big.

If you are “invested” in The Law of Non-Contradiction, or “Planet NonCon”, as I called it in my last post, then you want to defend “The Law” at all costs. It is your bulwark. All of your systems, all of your names and symbols, all of your truths, all of your meaning — it is all supported by this one thing. Take away that support, and it all just unravels, and you are literally drifting in the void of space.

For the first 24 years of my life, my upbringing, exposure, and education (both formal and informal) was predominantly Western. Western philosophy is stunningly beautiful. It really is. It is a grand tradition, and there is much to explore within it, much debate. But underlying all the seeming diversity is this hidden agreement, this common ground: that there is such a thing as Truth, and such a thing as False, and it can be found. It is a Law of Thought; a “fundamental axiomatic rule”; upon which “rational discourse itself” is based.

You may object. You may argue that Science (be careful with that capital S) does not hold any “truths”, but rather that it operates by negative truth. That is, it disproves hypotheses, and those hypotheses which have not yet been disproven and which we have arrived at some theoretical basis for defending, we treat as truths. Nor is there any illusion that Science will ever arrive at an “end”. That it is an infinite pursuit. That there will always be more to learn.

But even still, Science is based on this premise of Non-Contradiction, just like the other disciplines. If we arrive at a theory, the theory is falsifiable; and it cannot both stand and not stand. It must either stand or not stand.

In the 20th century, this foundation began to crumble. From Gödel’s Incompleteness Theorems in Logic and Mathematics, to Relativity and Quantum Mechanics in Physics, there were these stunning developments that emerged which challenge our notion that there is such a thing as objective reality, such a thing as truth, such a thing as an view of the world that is complete and consistent and achieveable.

Was it merely a poetic coincidence that in the same century in which classical Math, Logic, and Science began to unravel, classical civilization itself began to unravel? The World Wars and The Cold War were deeply traumatizing. In the moment of technology’s greatest triumph, it terrified. And so did ideologies, states, and organizations. These epic achievements of power and scale were destabilizing, even in their most positive dimensions. A bad case of be careful what you wish for. In the Arts and Humanities, there were movements that expressed this disorientation. Everyone was trying desperately to find their way back to the path. To put Humpty Dumpty back together again. To reassemble, to reconstruct, a shattered perspective. To tell an old story that no longer motivated; a used up story. To look in all the old places of joy, comfort and solace, and find only confusion, only despair. This wasn’t just an academic phenomenon. It was a felt cultural experience. What T.S. Elliot called The Waste Land.

So it was that The Law Of Non-Contradiction, that fortress adamant, fell. It came under attack, not from the outside, but from within. “A great civilization is not conquered from without until it has destroyed itself within.” The most convincing argument against “The Law” comes from assuming “The Law”. Taking it as the premise for a grand argument, the kind of Argument that only a Civilization can make, the kind of Argument that takes thousands of years to make. Then, at the end of it, we arrive at a Reductio. The conclusion is absurd. Therefore the premise must be thrown out.

But wait. Perhaps it was just bad luck. Perhaps without those wars, we would have been less traumatized, less prone to extremes. Western civilization has accomplished so much in every discipline. How can we say that The Law Of Non-Contradiction is wrong or has failed?

When they sent the first telegraph across the Atlantic, the message was What hath God wrought? So in awe were we at this device, this marvel, the work of our own hands, that in that moment, we stared in wonder as if it had been made by God. Our technological achievements have always seemed to synthesize our scientific and cultural and economic achievements in a single symbol; they give us the sense that we are still, that Western civilization is still, “made in the image of God”. For what we are really asking ourselves is What hath Man wrought? We are in self-amazement. Brought to a dangerous state of wonder, a state near-worship. So much so that we must direct it outwards. Must direct it up.

And I think that sense is still with us in 2017. What wonders exist. What wonders are being made. As I type, hundreds of billions of dollars of capital are hard at work, enabling some of the most daring experiments mankind has ever financed. There are so many frontiers advancing. It is a very strange world we live in where the zietgeist is that robots will take away our jobs. What hath God wrought?

So clearly The Law Of Non-Contradiction can’t be useless. It works. It demonstrably works. It has accomplished so much. It put a man on the moon. It has Constructive power.

And yet, it is broken. It, and our Civilization, has these deep gashes. These paradoxes, impasses and quandries. It is Dickens. In this one Civilization, there are these two competing narratives. Best of times, worst of times. There is more abundance than ever before. Yet there is famine in the land. Plague in the city. Lethargy, malaise. A sense of purposelessness, directionlessness, and confusion. You can feel it. Peter Thiel is its great prophet. He asks, “What happened to the future?” And he’s right. We’ve lost that virility and confidence, that sense of mandate and destiny, which propels a civilization forward, to new heights — which critics will later say, came with new crimes. But that’s just the point. Florence of the Renaissance was not a peaceful place. It was all turmoil and tumult. It had explosive energy. Greed and ambition were present. Some were trampeled. But Mona Lisa.

A generation ago, Joseph Campbell gave us the same warning, but in different words. As a mythologist, he saw that as a Civilization, we had lost our Myth, our Grand Narrative, our Motive Force. The great achievements of our Civilization cannot be explained by economic phenomenon. If you want Pyramids and Cathedrals, tell them The Great Story. We’ve lost that. So we are in The Waste Land.

One of his peers, Alan Watts, looked East for that story. I like to call him the C.S. Lewis of Buddhism, because he was able to re-iterpret the great scriptures of the Orient (not just Buddhism, but Hindu, Taoist, even Sufi), and breath them again into life in language that made sense to a skeptical modern Western audience.

Philosophy’s story can be summarized thus. 
Two philosophers came to a fork in the road.
To the West was The Law Of Non-Contradiction. 
To the East was The Principle Of Explosion. 
One went West. 
One went East.

What happens when you take The Principle Of Explosion seriously? 
You must accept the implications of valid contradictions. 
Which are staggering.

If contradictions are valid, then you can take any sentence: 
Say, “I am not you”. 
And you can assert the contradiction. 
You can say “I am you.”
You can say both: 
“I am you and I am not you, at the same time, in the same sense.”

At first glance, this seems so ludicrous, that most people go West. Then thousands of years later they eventually run up against contradictions again.

So let’s open this door. Let’s go East. And see what happens.

Our first contradiction was this: 
I am you and I am not you. 
Let’s add some more statements. 
Pigs can’t fly”, you say?
Well, pigs can fly. Pigs both can fly and can’t. 
And we can even one up that statement. 
The statement “Pigs both can and can’t fly” is itself both true and false. 
And so on. 
“Frodo is not real”, you say? 
Well, yes he is. And he isn’t. And he both is and isn’t. 
And that is both true and not.
And that it is true is both true and not.

You see? It is explosive. Contradictions have this explosive quality, because they imply everything. No matter where you start, you somehow seem to move out rapidly in every direction.

You might ask, “Well, how is this useless? How is this not just nonsense?”
Aw, you had to ask the practical question.
Spoil our fun!

Fine. I’ll frame this in Western terms. Which is actually the way I first came to realize this very Eastern understanding.

In the Enlightenment, there were some important Germans, eh? Hegel, Kant and Nietzsche, in particular.

One of Hegel’s big ideas was this Logic concept he called “Dialectic”. Dialectic is simply the progression of argument from “Thesis” to “Counter-Thesis” to “Synthesis” to “Counter-Synthesis” to “Super Synthesis”. He recognized that there are similar progressions in other fields. In warfare there is measure and counter-measure. In strategy there is move and counter-move. In history there are trends and counter-trends. In markets there are cycles and counter-cycles. If you look for it, you can start seeing Dialectic everywhere.

And one of the implications of Dialectic is that for every argument there is a counter-argument. That seems innocent enough. But if you really think about it, you realize that no matter what you believe to be true, there is a counter-truth, a counter-argument. And if you give up your truth and embrace that new truth, you’re not safe there either. Because there is a new counter-argument.

This is very paralyzing at first. You realize that movement is pointless. It is a kind of Zeno’s Paradox for Truth itself instead of Motion. You feel like you’re half way closer to the truth, but you never arrive. What’s the point of realizing a new truth if it is false; if it has a perfectly valid and persuasive counter-argument?

But it is also very practical. It tends to make you skeptical, because you can always see the Dialectic. You can see the view past their point of view, and the view past that. So skeptics tend to be harder to fool. They tend to be more “objective”, “realistic” and “pragmatic” about the world, because ideologies and stories don’t work as well on them. “What? You think you’re some kind of Jedi or something, waving your hand around like that? Mind tricks don’t work on me, only money!” They’re good chess players and strategists because they’re always thinking a move ahead. They’re good at making investments because they can see trends. They make good artists for the same reason. They make good critics and good politicians because they’re great at argumentation.

But enough with pragmatism. Because the really interesting quality here is spiritual. If you embrace Dialectic, one of its implications is “that everything is true and not-true.” And this is another way of arriving at The Principle Of Explosion.

One of Kant’s big ideas was to divide reality into the “Noumenal” and the “Phenomenal”. The “Noumenal” realm being the realm of symbols, words, numbers, stories, meanings, interpretations. And the “Phenomenal” world being reality itself: infinite, multi-layered, in all of its complexity.

If you really understand this concept, you recognize that we are constantly labeling reality, but reality itself is infinite, connected, and unlabel-able. Reality defies full comprehension and understanding. We are just making up a story about it.

In my post on Non Contradiction I talked about the infinite complexity of a table. That is a Kantian idea. If you fully understood everything there is to know about any object — say, that grain of sand from Blake’s poem — you would know everything there is to know about everything. But we despair. Because in a classical age we may have dreamed that someday we would unravel the mysteries of the universe, but in our age, we realize that the mysteries of the universe tend to unravel us. They are infinite pursuits. You’ll never reach “The End” of Science, say, or even of any of the fields of the Arts and Humanities.

There’s a similar and very important concept called Bonini’s Paradox. Asimov talked about it in his science fiction series The Foundation Series. Thousands of years in the future, our galaxy is governed by a single massive empire, and Hari Seldon is a “psychohistorian”, who has proven that in theory it is possible to perform massive computations to predict the future. But in practice, he realizes it is impossible to construct an accurate simulation of reality smaller than reality itself. In other words, to run a simulation of the universe, you would need to create the universe. Every simulation that is smaller than the universe is going to be inaccurate to some degree. All maps are lies. All models are abstractions. All words are distortions. All truths are false.

Aha! We’ve arrived. You see it? 
A contradiction. We’ve arrived.

Reality is infinite, complex, and multi-layered. The Phenomenal cannot be reduced to The Numenal without being distorted. Reality itself contains infinite contradictions. Reality itself is a contradiction. Or maybe it isn’t. But you can’t prove it. Because to prove it, you’d need to use maps, models, words, simulations, words — some kind of distortion. You’d need to deny some truths to make other truths prominent.

In The Tao Te Ching it says,

When people see some things as beautiful,
other things become ugly.
When people see some things as good,
other things become bad.
Being and non-being create each other.
Difficult and easy support each other.

How similar!

And that’s what The Law Of Non-Contradiction is all about. It denies some truths, in order to emphasize others. It filters light. It filters reality. It blocks out possibilities. All of which is quite practical, but distortive.

Aha again! This takes us back to Gödel. Systems must be either consistent and incomplete or complete and inconsistent. They cannot be both consistent and complete.

What does this imply about The Law of Non Contradiction? 
It implies that The Law of Non Contradiction is governed by Bonini’s Paradox. We can build these awesome truth-systems that are very practical and that are very large, but in order to stay consistent, they have to be incomplete. In other words, they trade completeness for consistency.

But what if you want to go the other way? What if you want to trade consistency for completeness? And you can see how this might be practical. It is like prefering Creativity, which is messy, to Organization, which is tidy; because if you choose the path of Creativity, you get more done.

Completeness is very alluring. Just what our Civilization is lacking. We are so consistent, but our drive for consistency is breaking us individuals and as a society; distorting our perspective; over-filtering our life. That is the spiritual sense of it.

Ironically, the path to completeness is Deconstruction. If the thrust of Western philosophy is Constructive, the thrust of Eastern philosophy is Deconstructive. If we follow The Way Of Non-Contradiction we build things up, like legos. We use tools to build tools. We use truths to discover more truths to build truth systems. But at the end of all our construction, we arrive at these stuck places, these paradoxes, these disasters.

Breugel’s The Tower of Babel

This is Breugel’s The Tower of Babel. This is a Western story, but in the Judeo-Christian tradition more than the Classical tradition, as it is a scene from Genesis. And in Genesis, humans had this grand and daring venture, to build a tower all the way to the heavens. A kind of prehistoric architectural spaceship. There’s no more fitting image for the extent of man’s ambition, capacity for organization, energetic flair, pride.

And what happens? God sees this tower. He laughs at the pride of man. And instead of just blowing it up, or sending a flood, he makes an elegant, indirect move. God introduces languages. So humans speak different languages.

What does that do? It increases coordination costs, which are a type of Coasian transaction cost. And there you have it. Prophetic. Because coordination costs are maybe the crucial impasse in productivity in the 21st century economy. Coordinating and transacting is still way too hard. And it still prevents us from building the kinds of epic projects that we really want to build. You can’t grow organizations past a certain size without being crippled by these costs. In engineering, they call this “The Mythical Man Month.” In cooking, they call it “Too many cooks in the kitchen”. But it is the same problem.

So Construction hits a limit, and Deconstruction begins. Deconstructive philosophy is not just Eastern. As we’ve seen with Hegel and Kant. It is also Western. Jacques Derrida is formally called a Deconstructivist and although I’m not familiar with his work, the essence of it is that every ideology, every project, every person contains within it the seeds of its own destruction. A kind of Achilles Heel. The Tower of Babel is a perfect image of that.

Permit me another visual aid. There’s an artist named Michael Bierek that has this wonderful sketch of one of Zeno’s paradoxes: of Achilles chasing The Tortoise. I have it set as my profile picture right now. Here’s a link to the artist’s post on Instagram for photo credit.

Zeno’s Paradox: Achilles chasing The Tortoise, by Michael Bierek

This is another example of Deconstruction in the Western tradition. Thousands of years before Gödel, here is an ancient Greek mathematician already struggling with these very disturbing paradoxes. Zeno came to realize the “unreality of motion”. In other words, motion is an illusion.

If you’re not familiar with it, it goes like this. Achilles is trying to pass the Tortoise and the Tortoise has a head’s start. Achilles catches up quickly and is now half way to the Tortoise. But in this time the Tortoise has inched forward just a bit. Then Achilles closes the distance by half yet again, and the Tortoise inches forward again. If you keep doing this operation over and over again, you get closer and closer to the Tortoise, but never pass it. In other words, if you divide a distance in halves, you can subdivide it infinitely without every crossing the horizon. How, then, is it possible for Achilles to actually pass the Tortoise in reality? And aren’t we just mind-boggled by the infinities that exist between these two points?

This is such a rich paradox. It is the kind of brilliant insight that everybody misses. It takes a very special person to recognize that something absolutely bizarre is happening in front of us every day. Plausible explanations for Zeno’s paradox include the concept of Plank’s Length in physics and modern Calculus. Even then, they are not definitive resolutions. Zeno discovered a puzzle thousands of years ago that is still puzzling today.

This so offends our intuition that we dismiss it as absurd and look for any other plausible explanation. We don’t take the paradox seriously. We view it as a joke. A cute device. A trick. Or maybe a puzzle that has already been plausible solved. The same way we treat contradictions.

And yet the truth lies in paradox, as Kierkegaard would say. Kierkegaard, by the way, being another example of a Western philosopher who understood the power of Contradiction and Paradox as a valid starting point, and maybe as the only starting point for Faith. As a concept, Faith produces multiple paradoxes, and so it is a good example of a Deconstructivist tradition in the West. To be born again, we must be broken, humble, contrite. We must give up self. We must say “Thy Kingdom come, Thy Will be done.” We must admit that we do not know the answer. And that we need help and guidance and purpose. We have to get very very small. “Lord I believe, please help my unbelief.” And yet, somehow, through this miracle of powerlessness, the faithful experiences Identity with a Power beyond all imagining. Because the knowledge is a knowledge beyond reason, its reality is experienced, it can neither be proven nor disproven. So if you want to see for yourself you can’t just reason your way to it. You need to make the authentic leap.

Vanity, vanity all is vanity. All is but a chasing after the wind. In Biblical wisdom literature — in Psalms, Proverbs, Ecclesiastes, and Job , but especially Ecclesiastes and Job — there is this realization as well. No matter how many buildings you build, no matter how many wives you have, no matter how great your treasury, no matter how much you accomplish or experience, no matter how many admirers you have — what is the point? You arrive at this deeply nihilistic place. Your Towers of Babel come crashing down. Ars longa, vita brevis. You just don’t have enough time or energy to finish your great work in your lifetime. You’re just a mortal. Just a human. You’re already dying. The curse is on you. Wisdom is accepting and letting go. Detach. Deconstruct.

I need to read more Nietzsche. But what I have read makes me want to include him at this juncture. Because he reached this point of nihilism. But the thrust of his energy is assertive of individualism. The individual stares into the abyss, into the purposelessness of life, into God’s face, and shouts: I am an individual! I have a purpose! I have a story! I have mind! I have actions! I have plans! I make meaning! I create! My will be done, my kingdom come.

Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.

There’s this question of whether Explosive or Deconstructive philosophy is practical… because if everything is true and not true, don’t you just get paralyzed? How can you be motivated to do anything when you realize you are God, that you and the flower and the spider and the dirt and the waves and the lightning are one, and nothing, and that you have everything you need and want, and that you aren’t even really a “you” at all, that the Past and Future are illusion and all that exists is The Present?

These are valid questions. Historically, one could argue that The East did fall behind, and maybe because of this. Anecdotally, I know people who “got lost” in deconstruction, and don’t seem very motivated to come back into society and do anything with their enlightenment.

But in Buddhism there is this messianic archetype called the Bodhisattva. The Bodhisattva is the one who experiences total enlightenment, and instead of leaving or dying or chilling out, comes back into society and fully participates, in service to humanity.

There are these powerfully practical traditions rooted in Eastern, “Explosion”, or Deconstructive philosophy. There is the tradition of the Zen Samurai, or even just the Zen layman, who does his craft as a meditation on excellence. There is this assertion that one can create from a beginner’s mind, not just an expert’s mind. That one can conquer from a place of peace, not just a place of war. One can create from love, not just from stress or fear. One can achieve understanding from non-belief, not just belief. That indeed, our beliefs often hold us back as much as they help us. So the deconstruction and unraveling of belief systems that hold us back is very powerful.

“Everything is true and not-true, including that statement.”
Think about that. 
You’ll realize that the implications are… massive. 
Everything exists. Nothing exists. 
Good is good. And good is bad. And neither good nor evil exist. 
Light is dark and dark is light. 
God is God and God is the Devil and neither exist and both exist. 
All possible worlds and all possible universes exists. 
All products of the imagination exist. 
All possible fantasies and all possible horrors.

Imagination unleashed. 
We fear the nightmares more than we love the dreams.

You see, contradictions are explosions!
They are singularities. 
They are like black holes. 
They swallow everything.

But where did our universe come from? 
What was The Big Bang? 
What’s on the other side of a black hole? 
How do we know that blach holes don’t contain universes? 
How do we know that we’re not in a black hole? 
How do we know that God is a contradiction? 
That a contradiction created The Big Bang? 
Or that every contradiction IS a Big Bang?

You really can’t know anything. 
Nothing is certain. 
You already know everything. 
You? Who is you? What is knowing? 
Everything implies anything implies something implies nothing. 
What if everything is one massive implication?

The Edge of Words.
The Edge of the Noumenal. 
Where the Phenomenal begins.

In the beginning was The Word. 
The Word was with God. 
The Word was God.
And the word spoke. 
Let there be light. 
And there was light.

THE BIG BANG! 
BOOOOOOOOOOM!
Contradictions! Creativity! Explosions! Energy!
Then slowly… 
congealing into consistency, order, organization, form, matter.

“The tao that can be told
is not the eternal Tao.
The name that can be named
is not the eternal Name.
The unnamable is the eternally real.
Naming is the origin
of all particular things.
Free from desire, you realize the mystery.
Caught in desire, you see only the manifestations.
Yet mystery and manifestations
arise from the same source.
This source is called darkness.
Darkness within darkness.
The gateway to all understanding.”