Welcome to today's deep dive. Now, to start off,
grab a pen and just, you know, try to turn the
number three into an eight. It takes almost zero
effort, really. Right. You just close the two
loops on the left side and suddenly you have
a completely different digit. And for centuries,
that single simple pen stroke cost banks, merchants
and accountants an absolute fortune and fraud.
People would literally just alter the ledgers.
Exactly. Yeah. But eventually. Someone invented
a secret mutated version of the number 3 to stop
it. And I guarantee that mutated version is hiding
in your house right now. Oh, it is absolutely
hiding in plain sight. I mean, we spend our lives
surrounded by these invisible mechanics. We really
do. We treat the number 3 as just a simple placeholder
for counting, you know, merely the stepping stone
between 2 and 4. But when you look at the historical,
mathematical, and anthropological data we are
covering today, you start to see that 3 isn't
just a quantity. It's something much bigger.
Yes, it represents a fundamental structural stability.
It's almost like a kind of inviolable law built
into the physical universe and hardwired right
into our psychology. And our mission today for
you, the listener, is to explore that profound
ubiquity. Our sources pull from a massive range
of disciplines. We're tracking this single concept
from the evolution of the physical digit itself
deep into early human cognition. There are some
genuinely mind -bending mathematical anomalies,
too. Yeah, and finally into the life or death
roots of global superstitions. OK, let's unpack
this, starting with the literal shape of the
number. How did we land on this curvy little
character? Well, the physical shape we use for
three is the result of a massive geographic and
cultural evolution. If you look at many early
writing systems, and even some still in use,
like Roman and Chinese numerals three is just
denoted by three distinct lines. So just like
tally marks. Exactly. And that was the original
representation in the Brahmic numerical notation
in ancient India too. But originally, those three
individual lines were stacked vertically. Just
three vertical tally marks standing next to each
other. That makes intuitive sense for counting.
It does. But language always trends toward efficiency.
During the Gupta empire in India, Writers started
modifying those vertical signs by adding a little
curve to the top of each line. Okay, I can kind
of picture that. Yeah. And later, as the Nagari
script developed in the region, scribes actually
rotated those lines clockwise. So now they were
lying horizontal, and they ended each line with
a short downward stroke on the right side. Oh,
wow. It's like the distinct tallies are slowly
melting and flowing together into a single block
of ink. Right. And that flow is entirely driven
by the physical act of writing. As cursive scripts
gained popularity, scribes naturally wanted to
write faster. Because lifting the pen off the
parchment three separate times slows you down.
Exactly. So those three horizontal strokes were
eventually connected into a single continuous
flowing motion. It ended up looking very much
like our modern numeral three, but with an additional
third loop or stroke hanging down at the bottom.
So it was essentially a three -tiered shape.
Precisely. And the journey gets really interesting
when you track its movement out of India. By
the ninth century, these digits spread to the
Islamic caliphate. And this is where a major
geographic and typographical split happens. A
split, like they couldn't agree on how to draw
it. Sort of. Around the 10th century, the western
territories of the Caliphate places like the
Maghreb in North Africa and Al -Andalus in Islamic
Spain modified the symbol. The scribes there
just dropped that bottom stroke entirely to write
even faster. Wait, so just slicing off the bottom
loop created our modern three. Yeah, that specific
regional shorthand created the modern Western
three we know today. Did the Eastern territories
just reject that shorthand or what? They took
a completely different approach. The Eastern
Arabs actually retained and even enlarged that
bottom stroke, and then they rotated the entire
digit one more time. Oh, fascinating. Yeah, that
yielded the modern Eastern Arabic digit for three,
the symbol that visually looks like a backward
capital E pointing upward. So we have geography
literally dictating typography. That actually
brings me back to the fraud prevention tactic
I mentioned earlier. The sources highlight a
specific graphic variant used in modern commerce
called the Banker's 3. Yes, the Banker's 3 is
a fantastic example of form following necessity.
It is a variant of the digit that features a
completely flat horizontal line at the top, followed
by a jagged zigzag before curving into the bottom
loop. It looks somewhat like the phonetic letter
S, right? It does, yes. Wait, so you're telling
me the typeface on my standard 52 - card playing
deck or like the UPCA barcode on my cereal box
wasn't chosen by a designer for aesthetic reasons.
It's basically an anti -counterfeiting measure.
In many commercial and standardized formats,
absolutely. Because of that sharp, flat top,
a forger cannot easily take a pen and round out
the edges to turn the three into an eight. The
angles fight against the natural loops of an
eight. That is so clever. It is. What's fascinating
here is tracing the broader implications of these
symbols. When you look at a banker's three on
a barcode or the curvy three on a handwritten
note, you are looking at centuries of human behavior.
Yeah, you're literally tracing ancient trade
routes across the Maghreb. Exactly. And you are
seeing the physical defenses we built to protect
our commerce. Every curve is a historical fingerprint.
But, you know, while the symbol for three went
through countless revisions to accommodate human
behavior, the human concept of three represents
this absolute immovable cognitive wall in our
early history. Let's talk about the biological
limits of counting. Right. This requires looking
at early human anthropology, specifically how
isolated civilizations perceived quantities.
Anthropologists and linguists have studied numerous
indigenous groups in completely disparate, unconnected
regions. Like where? Well, like isolated tribes
deep in the Amazon rainforest, or specific aboriginal
groups in Australia and the jungles of Borneo.
And many of them independently developed the
exact same counting system. Which was what? They
count one, two, three, and thereafter, any higher
quantity. is simply labeled many. Here's where
it gets really interesting for me. How do we
know that is an actual cognitive ceiling and
not just a quirk of their language? Maybe they
just didn't bother inventing words for four and
five because they didn't need them. That is the
exact question researchers had to answer. They
conducted tests that didn't rely on spoken language
at all. They would use matching games. Okay,
how did that work? A researcher might place five
stones in a row and ask a tribesman to place
the exact same number of stones in a parallel
row. For quantities of one, two, or three, the
participants could match them perfectly and instantly.
But what happened with four or five? The exactness
vanished. The participants would just grab a
handful of stones and place down an approximate
pile. They couldn't reliably match the exact
quantity without counting them out sequentially,
which their language didn't support. Man, it's
like trying to hold objects in your hands. If
I toss you an apple, you got one. I toss you
a second, you have two. I toss you a third, you
can still distinctively hold and recognize those
three separate apples. Right, you can manage
three. But if I toss you a fourth or a fifth...
You just have an armful. You stop perceiving
the individual units and just perceive the mass.
That is a perfect analogy. In cognitive psychology,
this ability to instantly and accurately recognize
the quantity of a small group of objects without
actually counting them is called subitizing.
Subitizing. Yes. And the biological limit of
human subitizing is almost universally capped
at three or four. The sheer anthropological significance
of that is staggering. because it's a universal
human trait. Exactly. The fact that entirely
disconnected populations across the globe hit
the exact same mathematical threshold heavily
suggests that 3 is deeply hardwired into basic
human cognition. It acts as the biological boundary
of exactness. Up to 3 we count, beyond 3 we estimate.
We basically cross over from precision into just
volume. Exactly. It's our built -in cognitive
ceiling for intuitive quantity. But, okay, if
our brains naturally tap out at three for intuitive
counting, mathematicians eventually realize that
three is actually the gateway to infinite numerical
complexity. We have to dive into the arithmetic
because three is mathematically stubborn in ways
that border on magic. It certainly holds a lot
of unique titles in number theory. It is the
first odd prime number. It forms a twin prime
pair with the number five. and a cousin prime
pair with the number 7. It's everywhere. It really
is. It is deeply woven into how we calculate
the fundamental geometry of the universe, serving
as a rough integer approximation for both pi
and Euler's number. But the most interactive
property, the one we teach early on, is its divisibility
rule. Oh, this is the rule where you add up the
digits, right? Yes. If you want to know if a
massive natural number is cleanly divisible by
3, you don't need to do any long division. You
just sum its individual digits. So if that sum
is divisible by 3, then the entire massive number
is as well. Let's give a quick example as you
listen. Take the number 1 plus 2 plus 3, you
get 6. 6 is divisible by 3, which means 123 is
cleanly divisible by 3. Yep, it's that simple.
And the wildest part of this rule is that any
permutation of that number, like 321 or 213,
is also inherently divisible by 3. And this isn't
just a random trick of mathematics. It works
specifically because of the base 10 system we
use. 10 is exactly 1 more than a multiple of
3, which is 9. Ah, OK. Because of that structural
relationship, the positional value of the digits
essentially collapses when you're looking for
factors of 3. And to add a layer of depth, that
rule works in any positional numeral system whose
base leaves a remainder of 1 when divided by
3. So you'd see the same elegant pattern in base
4 or base 7. OK, I track the divisibility rule.
But I have to push back on one highly specific
fact from the math section of the sources because
it requires some unpacking. Sure. The text notes
that three is the only prime number in existence
that is one less than a perfect square. Can you
break down why that makes three so incredibly
lonely in the infinite landscape of numbers?
Like, why is it the only one? It does seem counterintuitive
that in the infinity of mathematics, only three
holds that title. To understand why, we just
need to look at the algebra behind it. Any number
that is one less than a perfect square can be
written as the formula n squared minus one. Okay,
assuming n is our base number. Right. Now, in
algebra, there is a fundamental rule for the
difference of squares. The formula n squared
minus one can always be factored or broken down
into two smaller multiplied pieces. Which are?
The quantity of n minus one multiplied by the
quantity of n plus one. The formula basically
breaks into two distinct chunks. Precisely. Now...
Recall that a prime number, by its very nature,
refuses to be broken into smaller whole parts.
It has no factors other than 1 in itself. Right.
So if your algebra formula mandates that the
number breaks into two separate factors, n minus
1 and n plus 1, the resulting number can't possibly
be prime. Oh, wait. Unless the smaller of those
two factors happens to be exactly the number
1. Ah, you see the trap. Let's test it. If we
make our base number n equal to 2, then our factors
are 2 minus 1, which gives us 1, and 2 plus 1,
which gives us 3. And 1 times 3 is 3, so it remains
prime. Exactly. But what happens if we go higher?
Let's try n equals 3. OK. Our factors become
3 minus 1, which is 2, and 3 plus 1, which is
4. 2 times 4 is 8. 8 is clearly not prime. Yeah,
it totally falls apart. If n is 4, the factors
are 3 and 5, making 15 not prime. Because the
smaller factor in that formula will always be
2 or greater from that point on, the product
can never be a prime number again. That is wild.
That specific algebraic mechanic isolates 3 as
mathematically solitary. It is entirely inviolable.
It just refuses to break down. But does that
abstract solitary math actually matter to me
when I drive over a suspension bridge? Does mathematical
stubbornness translate into the physical world?
it translates directly into the physical world
through geometry. That... mathematical inviolability
becomes physical inviolability in the shape of
the triangle. The classic three -sided shape.
Yes. A triangle is a polygon made of three sides.
It is the smallest non -self -intersecting polygon
possible, and uniquely, it is the only polygon
that does not have proper diagonals. Which means
it has nowhere to fold. If you push on a square,
it can skew into a rhombus. Exactly. Because
it has no diagonals to shear, the triangle is
the most stable physical shape in existence.
When you apply force to any one point or joint
of a triangle, those two other sides immediately
brace against it. So the physical load is perfectly
distributed across the structure. That is why
every steel bridge, every construction crane,
and every architectural truss holding up a roof
is just a vast interlocking lattice of triangles.
So three is mathematically isolated in arithmetic,
physically unbreakable in structural engineering,
and biologically hardwired as our ceiling for
exact cognition. It really is foundational. Like,
did they notice that three was holding the universe
together? They absolutely did. And the jump from
recognizing that mathematical perfection to developing
spiritual reverence is a very natural human progression.
Pythagoras and his followers in ancient Greece
were profoundly obsessed with three. What are
they calling? They called it the triad. They
viewed it as the ultimate symbol of harmony because
it is the only number to equal the sum of all
the terms below it, one plus two equals three.
They believed it contained the beginning, the
middle, and the end of all things. And when you
look at the sources, it seems like nearly every
major world religion took that concept of the
triad and built their theology around it. Oh,
without a doubt. You have an incredible array
of triple deities across entirely unconnected
cultures. There's the Hindu Trimurti and Tridevi,
the Triglav literally translating to the three
-headed one who was the chief deity in Slavic
mythology. Right, and it goes on. You have the
three jewels of Buddhism, the three pure ones
of Taoism. In Christianity, you have the Holy
Trinity, visually represented by the shield of
the Trinity diagram. You also have the triple
goddess of Wicca. Humanity seems completely desperate
to categorize the divine in sets of three. And
that desperation to categorize doesn't stop at
high theology. It bleeds directly into our everyday
language and superstitions. Sometimes it's purely
linguistic. For example, in Chinese culture,
the number three is considered highly auspicious.
Is that tied to the geometry or is it a language
quirk? It's linguistic. In Mandarin, the pronunciation
of the number three san sounds very similar to
the word for alive or life -shing. Oh, that makes
sense. Yeah. And this positive association is
reinforced by its stark contrast to the number
four c, which sounds almost identical to the
word for death, san. So what does this all mean?
We have ancient gods, Chinese lucky numbers,
and of course the classic Western idiom, third
time's the charm. But then paradoxically, you
also have superstitions that insist bad luck
comes in threes. It is a bit of a paradox, isn't
it? It almost feels like the ultimate narrative
structure. Think about how we inherently tell
stories. We demand a setup, a conflict, and a
resolution. A beginning, a middle, and an end.
Three represents a complete cycle. We just inherently
feel that after three beats, the tension has
to break. If we connect this to the bigger picture,
it comes down to the human craving for patterns.
The world is inherently chaotic, dangerous, and
unpredictable. Finding a pattern gives us an
illusion of control. It makes us feel safe. Exactly.
We subconsciously took the structural stability
of the physical triangle that perfect distribution
of force, and we applied it to our spiritual
and psychological worlds. We use the triad to
make sense of life, death, failure, and luck
because we desperately want our life experiences
to be as stable and predictable as a triangle.
We want that structural need for a setup, a conflict,
and a resolution in our lives. And there is no
starker example of that narrative pattern than
the visceral superstition that emerged from the
World War I trenches, the myth of three on a
match. I saw that in the sources. The superstition
dictates that it is incredibly unlucky for three
people to light their cigarettes from the exact
same match. Yes. And the logic born in those
trenches was brutally practical. If you are standing
in a dark trench and you strike a match, an enemy
sniper across no man's land sees that first flare
of light and becomes alert. Set up. Wow. As the
match is passed to the second soldier, the sniper
uses that sustained illumination to take aim.
Conflict. And as the match moves to the third
soldier, the sniper fires. Resolution. The tragic
application of the pattern. A literal life or
death sequence. Whether that myth was statistically
true in combat or just a psychological coping
mechanism to maintain discipline in the constant
peril of trench warfare, the number three became
the physical boundary between safety and death.
A hard limit. Just as early humans in the Amazon
saw three as the boundary of exact counting,
those soldiers saw three as the boundary of survival.
That is incredibly heavy, but it perfectly encapsulates
how deeply this single concept rules our lives.
Okay, let's take a breath and recap this journey
for you, the listener. We started with the cursive
strokes of ancient empires, watching trade routes
and fraud prevention mutate the very ink we used
to write. It's been quite the journey. We explored
the biological limits of human cognition, realizing
our brains naturally tap out at three. We broke
down the isolated algebraic mathematics of the
primes and the unbreakable geometry of the physical
triangle. And we ended with humanity's desperate
need to find patterns in the chaos, from triple
deities all the way to the mud of the First World
War. It is a profound testament to the interconnectedness
of human knowledge. I would challenge you listening
to this right now to take a moment and just look
around your room. Look at the architectural structures,
the physical design of your furniture, the way
items are aesthetically grouped on a shelf, or
even the narrative beats of the podcast or song
you might listen to next. It's everywhere. It
is. Pay attention to how many things in your
immediate environment are secretly reliant on
the geometry, the mathematics, or the psychological
categorization of three. It is everywhere once
you open your eyes to the pattern. It truly is
a structural law of reality. But before we go,
I want to leave you with one final thought from
the source material to ponder long after this
deep dive ends. During the 19th and early 20th
centuries, there were two authors, Augustus Le
Plongeon and James Churchward. Ah, yes. They
proposed the existence of a mystical lost continent
called Mu. Think of it like a Pacific Atlantis.
They wrote exhaustive volumes about this vanished,
highly advanced civilization. And what do they
claim was the ultimate symbolic representation
of this entire lost world? The number three.
The simple, perfectly balanced number three.
We are so reliant on the stability of this number
that we used it to summarize the glory of an
entire mythical world. Just imagine all of human
imagination and pattern -seeking, summed up by
the exact same digit that stops a forger from
altering a barcode, supports the weight of a
steel bridge, and dictates when you blow out
a matchstick in the dark. A single digit carrying
the weight of both the physical world and our
collective imagination. Keep an eye out for those
triangles, everyone. Catch you on the next Deep
Dive.