Mental models

I quote an old fable: Someone asks a philosopher what the world is like.
—The world is one big ball resting on the back of a big turtle.
—And what does that big turtle lean on?
—On an even bigger turtle.
—Well, but… where is the second turtle leaning?
—In a bigger one, sir. There’s always an other turtle underneath.

It’s an idea of the world based on an endless pile of turtles. You can’t say it’s
a consistent mental model because it’s based on infinity. In this case, an
infinite number of ever-larger turtles.

When the infinite appears, we’re in trouble.
In the real world nothing exists in infinite quantity. It is a characteristic of
materiality that there is a specific, defined quantity. However, some people
believe that space could be infinite because it is empty, that it could be
considered as nothing, and nothing has no quantity.

Fake. We know that empty space, without matter, still has a certain energy
that is called the energy of the void. Space is “something,” even though we
still cannot explain what that something means, what its true nature is.

That is why mental models that resort to infinity to sustain themselves have
an imaginary foundation. They construct buildings on a mirage.

For example, the flat earth model. It has no limits, extends endlessly in all
directions and uses the problematic infinity as its argument.
Some assume that’s what the ancients believed: that the earth was flat. But it
really is an urban myth. The thinkers of other times were not as naive as
some people imagine today. Some of them were really cool.

Eratosthenes, a director of the old library in Alexandria, set out to calculate
the size of the planet. He had two vertical rods placed in two distant cities,
Siena and Alexandria, and measured their shadows at noon.

The shadows turned out different. By calculating the curvature needed to
create those shadows, he got the full circumference with that curvature.
He obtained a certain number of stadiums, an old measure, equivalent to
about 40,000 km. —nearly 25,000 miles— Today we know that the equatorial
circumference measures 40,075 km.
Eratosthenes made that calculation about 200 years before Christ.

Today, in a world of cell phones and the Internet, we couldn’t be fooled with
unsustainable ideas; at least we think so. Perhaps it is true in everyday life
since current problems and tasks require common sense.

But ideas that are beyond the everyday level are outside of what we call
common sense. One such idea is that matter is made up of molecules, atoms
and various elementary particles such as the electron or proton.

Then a mental model emerges that is obvious to us. All matter in the
universe is made up of particles, except for radio waves, wifi waves, and the
like such as light. But what is palpable, concrete, is made of really small,
ultra-microscopic canon-balls of matter.

That’s obvious. What’s the problem?
The problem is in the idea of small canon-ball matter.

We were taught that they are the building blocks, the smallest possible
scale. The bricks that build the ultimate, final, definitive reality.

Well, I regret to inform that such idea is inconsistent. It doesn’t work.

I’m hurrying to explain before it’s too late, with a thought experiment.
Suppose that something supernatural, God or the devil, gave us an infallible
machine to cut matter, no matter how hard or how small it is. If there’s
something solid, it will cut it in half.

We place a sheet of A4 paper, for example, and see that the machine cuts it
into two perfect pieces, as it should. We put one of the pieces in its place,
which is again cut in half.
And now the million dollar question: How long will that machine be cutting
up the paper?

Everything learned about molecules, atoms, electrons, etc., is out of the
question. Only ideas that use our own logic are valid, as the ancient Greek
philosophers did. —How long will that machine be cutting up paper?

—Until there’s nothing left —it’s a frequent response.

Good. Using the scientific method, we tentatively accept that answer.

Admitting that there is a precise moment when there is nothing left, it
follows that at the previous moment there was still some microscopic piece of paper. Since there was something, the machine cut it and got… two pieces of nothing.

Clearly, we won’t achieve anything by dividing something. So the
alternative answer would be to continue splitting the paper forever.

That’s easy to say. But the universe could come to an end and the machine
would still keep on cutting for all eternity; cutting for an infinite time. We’re
invoking the famous infinity to justify the answer.

The idea of a final ball of matter is problematic. It creates paradoxes.

The ancient Greek philosophers realized the paradoxes, so they postulated
that there should be an atomon, a final indivisible partition. This is precisely
what Democritus of Abdera postulated, without explaining the cause that
prevents the division of the atomon.
Because Democritus didn’t talk about physical details. He was just making a
logical argument. There were no particle accelerators in those days.

Today’s science has another answer based on something called fields, such
as the magnetic field or gravitational field, but defined at the quantum level.
An electron field is defined, for example, that gives rise to electrons. You
could imagine it as an ocean of invisible energy, where there are waves that
would be the electrons. -Although the waves wouldn’t be a very good
example.
Let’s say rather that an electron is like a whirlpool of energy in a stable
quantum field. It’s concentrated energy, not a ball of matter.

That stops our machine. It can’t cut energy.

The standard model of physics today is field theory, not particle theory. But
it’s hard to take in, and that’s why we keep talking about particles.
They call it a model agreement because it was an international agreement of
the scientific community. It was the most successful model in the history of
science. It created the technology that changed everyday reality for good.
However, this consensus model can not explain everything.

The current expansion of the universe requires a mysterious force they call
dark energy. Galaxies spin as if they have a mass far greater than that
detected by telescopes. Perhaps they have dark matter inside them that
produces a huge gravitational field. We don’t know yet.

To achieve a Theory of Everything, that is to say, a mathematical structure
that could support all physical phenomena, was the dream pursued by
scientists in the last century. Today, it seems like a very distant goal.

Hawking said: “If we ever come to a theory of everything, it will be nothing
but equations. What is it that breathes fire into those equations so that a
physical universe emerges from them?”

It means that we don’t really know what’s behind the laws of physics for
them to exist and to work. We don’t really know what life is, or what
consciousness is, or what causes this gigantic and mysterious universe.

These are the big questions. Some are outside the realm of science because
there are no physical resources to address them. They become questions
beyond the physical: they are metaphysical. As the reason for a universe
with living beings, if there are reasons or purposes for their existence.

The answers are philosophical ideas, religious beliefs, myths and legends.

Implicit in the scientific community is an existential nihilism. These are
difficult words to say that there is no proof that life has any purpose or any
objective meaning, nor is there any proof of the purpose of the universe.
Which is very true: there is no proof. Although that doesn’t prove anything
either.
Furthermore, if the world is created by blind forces without meaning or
purpose, it becomes difficult to maintain values based on subjective,
changing, unpredictable human agreements.

The great religions sought to avoid this situation by means of precepts given
by God himself, according to dogma, to govern human conduct.
This worked pretty well for millennia. If the stars revolved around us day
and night, we were the center of creation. Therefore, God was certainly
aware of us, contemplating and judging our actions.

But that picture has changed. The technology of large telescopes and space
probes confirmed, definitively, that we are not the center of any creation nor
the center of the universe.

What’s more, it revealed the size of that universe with billions of galaxies,
where each one is like an ocean of suns with countless numbers of planets.

We currently know that our world is a speck of dust at infinity.
At this time we are coming, I think, to the end of the childhood of reason.

That is why I show a paradigm that can be placed between nihilism and
dogmas. A millenary idea of the world maintained for generations through
chains of knowledge of instructors and practitioners.

They talked about galaxies long before large telescopes and also about the
relative perception of time, as relativistic physics did later.

They described a type of matter that does not evolve in time and does not
exist in our world, much like what we now call black holes.

Finally, they said that the universe is a living, conscious entity in very
different degrees. A gigantic web of existence on every level.

That age-old paradigm is a mental model that has a strange consistency.
It would be worth considering, in addition to the current ones.

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