Imagine, if you will, an ancient empire that
was so completely terrified of an empty table
that they like actively and aggressively banned
the entire mathematical concept of nothing. Right.
I mean, an empty table. It just feels so completely
natural to us today. Yeah, exactly. Usually when
we talk about counting, we just expect it to
be obvious. You know, like, it's the most intuitive
thing in the world. You have three apples on
a table. You take one away, you have two. You
take another away, you have one. You take the
last one away, and you have, well, nothing. Right.
But then you look back through human history
and suddenly that empty table is just it's the
source of absolute chaos. It really is like we're
looking at a historical and mathematical landscape
where nothing was honestly a genuinely terrifying
concept. Oh, absolutely. It was the absolute
definition of a conceptual blind spot for humanity.
Well, welcome to the deep dive. Today we are
looking at a singular massive source that we've
compiled for you, which is a comprehensive Wikipedia
article on the number zero, the big zero. Yeah,
the big zero. And our mission today is to unpack
how the concept of nothing went from being this.
philosophical impossibility, something that ancient
scholars literally violently rejected, to becoming
the fundamental building block of your modern
digital world. It's quite the journey. It really
is. And I just have to say up front, I am in
sheer amazement that something you and I take
for granted every single day, something a toddler
inherently understands, actually had to be, like,
invented. I know. It is wild when you step back
and really look at it. Yeah. Because what's fascinating
here is that zero isn't just a number. Right.
It is a profound conceptual leap. I mean, it
completely rewired human logic. If we start at
the beginning of recorded history, early civilizations
didn't just forget to invent zero. Right. They
didn't just overlook it. Exactly. Yeah. They
actively, almost stubbornly, avoided treating
nothing as a real mathematical entity. OK, so
let's unpack this. Because when we say they avoided
it, we don't mean they didn't know what the word
empty meant. I mean, if a basket had no grain
in it, they knew it was empty. Yeah, exactly.
They understood the physical reality. Let's...
Let's look at ancient Egypt, for example. They
had a very robust base 10 numeral system. OK.
But they did not have a positional zero like
we do. So when an Egyptian scribe, say around
1770 BC, was recording daily incomes and expenditures
for the Pharaoh's court. They obviously needed
a way to show that the accounts balanced. Right.
They needed to show that what came in equaled
what went out. But they didn't use a number zero.
Instead, they actually used this hieroglyph called
NFR. Which is such a weird pivot because looking
at the source, NFR is a symbol of a heart with
a trachea attached to it. Yeah, it's highly specific.
And it didn't even mean zero. It translated to
like beautiful or pleasant or good. Right. So
if we connect this to the bigger picture, they
were basically using a qualitative concept like
beauty or goodness to represent a zero balance.
That is so strange. It is. And they also use
this exact same symbol in construction. Like
if you look at ancient drawings of cooms and
pyramids, NFR was used to indicate the base level.
Oh, like the ground line? Exactly. The ground
line. So distances were measured as above or
below this NFR line. Ah, OK. So it was a state
of being. It was a baseline. It wasn't actually
a number you could add or subtract. Precisely.
It was a reference point, not a quantity. And
you see a very similar reluctance when you move
over to Babylon. Right, the Babylonians. Yeah,
but the second millennium BC, the Babylonians
had incredibly sophisticated mathematics. I mean,
they were using a base 60 system. Which, by the
way, is exactly why we still have 60 seconds
in a minute and 60 minutes in an hour today,
right? Yeah, that's the one. It stuck around.
But here is the catch. To indicate a zero value
in a specific position, like distinguishing between
the number 11 and the number 101. What did they
do? They just... left a space. Wait, they literally
just left a blank space on the clay tablet. A
literal blank space. That seems like a terrible
system for keeping records. It was. Which is
why, later on, around 700 BC, scribes started
using three little hooks as a placeholder to
make it a bit clearer. And by 300 BC, they evolved
that into two slanted wedges. But... And this
is a really crucial distinction. These punctuation
marks were strictly placeholders. They were never
used alone. Right. You couldn't just write the
wedges by themselves to mean the concept of zero.
It sounds like early civilizations treated zero
the way we treat a blank space in a crossword
puzzle. Oh yeah, that's a good way to look at
it. Like, the black squares separate the real
words and they give the puzzle structure, but
the black square itself isn't a word. That is
a perfect analogy. It's structural. not substantive.
And that distinction becomes the central conflict
when we reach ancient Greece. Oh, the Greeks,
they had some strong opinions. They really did.
The Greeks had a deep, visceral, philosophical
opposition to zero. I mean, they were obsessed
with geometry, with shapes, with tangible realities
you could actually draw in the sand. Right. So
they looked at the idea of zero and asked this
paralyzing question. How can not being be? Which
honestly just sounds like a late night dorm room
riddle. Yeah, totally. But for them, it was a
hard roadblock. The sources say, and I'm quoting
here, the whole of the Greek universe rested
on this pillar. There is no void. Because if
you admit that nothing is something, you essentially
break their entire understanding of nature. Wow.
This is actually what led to Zeno's famous paradoxes.
Zeno essentially argued that motion is an illusion.
Wait, really? How did he justify that? Well,
he said to walk across a room, you first have
to walk halfway. then half of that remaining
distance, then half of that new distance. Right.
You're constantly dividing space into infinitely
smaller fractions. Exactly. And the Greeks feared
that if an absolute void -like, a true zero existed
between these fractions, the math would just
break down. You'd fall into the void. You'd never
actually reach your destination. So to them,
admitting zero existed meant admitting that reality
itself was fundamentally broken. Exactly. Now,
there was one notable exception in the classical
world, which was the astronomer Ptolemy around
AD 150. He was heavily influenced by Babylonian
data. Ptolemy was doing complex mathematical
astronomy, trying to measure solar and lunar
eclipses down to the minute of immersion. That's
incredibly precise. It is. And to do that math,
he needed a reliable placeholder. So he used
the Greek letter Omicron with a line over it.
Which is funny, because Omicron looks exactly
like our modern zero. It's just a circle. It
is. But even for Ptolemy, when calculating the
exact magnitude of the moon passing over the
sun, it was still just your crossword puzzle
black square. Ah, gotcha. It meant an empty column
in his data, but not nothingness as a standalone
mathematical quantity. Essentially, the old world
was stuck. Their philosophy just completely trapped
their mathematics. So how does humanity actually
break out of that trap? Because looking at the
source, we don't just jump forward in time. We
actually have to completely shift gears in terms
of human needs. We do. We have to look at societies
that weren't bogged down by all this Greek philosophy,
but instead had a desperate practical need to
measure deep time. We are heading across the
ocean to the pre -Columbian Americas. It really
is one of the most striking parallel inventions
in human history. In Mesoamerica, they developed
the long -count calendar. Okay, tell me about
that. This was a vigesimal system, which basically
means base 20. And if you are trying to make
a base 20 calendar work across vast mythological
expanses of time, spanning thousands of years,
you absolutely require a reliable placeholder.
just to keep your massive numbers aligned? Exactly.
And because they didn't have old Greek guys yelling
at them about the void, they just, you know,
went ahead and invented it. So when did this
happen? Incredibly early. The earliest date found
on a stone stela in Chiapas, Mexico goes all
the way back to 36 BC. Wow, 36 BC. Yeah. The
Mayans and possibly the Olmecs before them were
actively using zero. And what I love is how they
represented it. They commonly used a glyph shaped
like an empty tortoise -like shell. See, that
feels like a massive conceptual upgrade from
a Babylonian punctuation mark. A shell is a physical
container. It's meant to hold something. Right.
So showing it empty implies that the absence
of something is actually a state worth measuring.
It's a brilliant visual metaphor. And further
south, the Incan Empire developed an entirely
different, incredibly tactile system to solve
the exact same problem. Yeah, this part of the
source blew my mind. They didn't use writing
as we know it. They used the kipu, which is a
complex device made of knotted chords, to record
accounting and data. This is just wild to me.
It's a base 10 positional system, but it's literally
made of string. Right. It's a spreadsheet made
of string. Yeah. And how do you think they represented
zero on a piece of string? I mean, following
the logic, no string. Close. It was represented
by the simple, deliberate absence of a knot in
the appropriate position on the chord. Oh, I
see. So if the hundredth position had a knot,
And the ones position had a knot, but the tens
position was just smooth cord. That smooth space
was zero. Exactly. OK, this raises a really speculative
question for me. If the Mayans and the Incas
invented zero completely independently from the
rest of the world just to make their calendars
and their accounting work, does that mean the
concept of zero is like a hardwired mathematical
truth just waiting to be discovered? That's the
million dollar question. Right. Or is it just
a cultural invention? Well, that is the eternal
debate about the nature of mathematics, isn't
it? Is math invented or is it discovered? The
fact that isolated cultures developed a placeholder
for nothing strongly suggests that zero is a
necessary structural truth of the universe. It
definitely points that way. But here is the catch.
To make the leap from a placeholder, like an
empty shell or a missing knot, to an actual standalone
mathematical entity that you can add, subtract,
multiply, and divide for that, we have to travel
back across the world to ancient India. Right,
because this is where zero gets its true superpowers,
where it goes from being just a missing piece
to being a real player on the board. How does
that transition actually happen? Slowly, and
then all at once. We see early glimpses in the
third or second century BC. There was a Sanskrit
scholar named Pingala, who was analyzing the
rhythms of poetry. To do this, he used binary
sequences of short and long syllables, sort of
like an early Morse code. And to mark his sequences,
he explicitly used the Sanskrit word shinya,
which translates directly to void or empty. Later
on, we see the Bakhshali manuscript, which is
an early arithmetic manual, and it used a solid
black dot for zero. And there's physical evidence
of this evolution too. Our source highlights
this stone tablet found in the ruins of a temple
in Cambodia dating to AD 683. Yes, the Sambor
inscription. Right. It contains the number 605
and right there in the middle is the oldest firmly
dated use of zero as a decimal figure. Just a
little circle. It's amazing to actually see it.
But the real breakthrough, the moment zero became
a true, manipulating number, happened in the
7th century with the Indian mathematician Brahmagupta.
Brahmagupta, what did he do differently? He didn't
just write a symbol for zero. He established
the actual mathematical rules for it. Oh, wow.
He stated clearly that the sum of zero with itself
is zero. He defined how it interacted with positive
and negative numbers. He did have one little
hiccup though, according to the article. Brahmagupta
actually got division by zero wrong. He claimed
that zero divided by zero was zero. He did, yeah.
Division by zero is a notoriously tricky mechanism.
It actually took until the 12th century for another
Indian mathematician, Bhaskara II, to correct
this. And what did he say? Bosco II stated that
a quantity divided by zero actually becomes an
infinite quantity. Okay, stop right there. I
have to push back on this because this always
hurts my brain. How can dividing a normal number
by nothing magically equal infinity? Explain
that to me like I'm five. Okay, think about it
as a shrinking fraction. If you divide 1 by 0
.1, you get 10. Right. You divide 1 by 0 .01,
you get 100. If you divide 1 by 0 .0001, you
get 10 ,000. OK, I'm a following. As the number
you are dividing by gets closer and closer to
absolute zero, the result just explodes. It gets
closer and closer to infinity. Wow. OK, so the
smaller the piece I'm trying to carve out, the
more pieces I end up with, until I'm literally
carving out nothing and I end up with everything.
Exactly. And what's really amazing is how Bhaskara
II explained this to his contemporaries. He didn't
just use fractions, he used a really poetic theological
analogy. Oh really? Yeah, he compared dividing
by zero to the infinite and immutable God who
remains unchanged no matter how many worlds are
created or absorbed. That is fascinating. Wait,
so the definitive mathematical rule for dividing
by zero was explained using theology. Yep. It's
like they needed the concept of an infinite god
just to make sense of the math of nothing. It
perfectly illustrates why the concept thrived
in India while it struggled so hard in Greece.
Indian philosophy already had a very comfortable,
profound relationship with the concepts of the
void. nothingness, and the infinite. Right. They
weren't terrified of the void like the Greeks
were. They embraced it. And because they embraced
it culturally, they could finally define it mathematically.
So we have this fully functioning number zero
in India tied to the divine and the infinite.
How does it get from there into, you know, my
bank account today? Well, it followed the trade
routes. Practicality usually wins out over philosophy
in the end. In the 9th century, during the Islamic
Golden Age, a Persian mathematician named Al
-Khwarizmi was tasked with synthesizing Greek
and Hindu knowledge. Al -Khwarizmi, wait, I know
this. His translated name in Latin was algorithm,
which is literally where the modern word algorithm
comes from. That's the one. He wrote a groundbreaking
book explaining the use of Hindu numerals, including
zero. Okay. He instructed that if no number appears
in the place of tens, a little circle should
be used to keep the rows. And he called this
little circle ifr, which was the direct Arabic
translation of the Sanskrit word shunya, meaning
empty. And then the baton gets passed to Europe,
but not by a philosopher. by a guy named Fibonacci.
Ah, yes. It's the year 1202. Fibonacci is an
Italian mathematician, but he actually grew up
in North Africa because his dad was a state official
working in the customs house for merchants. Right,
he had that exposure. So Fibonacci learns this
Hindu -Arabic numeral system from Arab merchants,
and he brings it back to Europe in his famous
book, Lieber Abaci. Because he realized, quite
rightly, that calculating with nine digits and
this new sign for zero, was vastly superior to
the clumsy Roman numerals everyone in Europe
was still using for their accounting. I mean,
put yourself in their shoes for a second. Imagine
trying to do your taxes using Roman numerals,
trying to multiply 7 by 14. It's an absolute
nightmare. Your accountant would quit. Exactly.
The merchants didn't care about the philosophical
dread of the void. They just cared about balancing
their ledgers quickly. Which is such an amazing
irony. You have Greek philosophers agonizing
over whether nothing can exist for centuries.
But ultimately it was just traveling merchants
and a customs official's kid who forced Europe
to accept zero simply because it made bookkeeping
easier. And we can actually trace the linguistic
journey of this practical tool right into the
English language. It's a really fascinating evolution.
You start with the Sanskrit shunya. Right, meaning
void. That gets translated to the Arabic eifer.
Then when Fibonacci writes his book, He translates
afer into Latin as zephyrum. Influenced by Zephyrus,
the west wind, right? Correct. Then in the Venetian
dialect, zephyrum contracts into zevro. And finally,
they get shortened to the word we use today,
zero. What a massive game of historical telephone.
Shinya, Ifir, Zefram, Zevaro, Zero. So what does
this all mean for us today? Because zero has
completely transitioned from an accounting trick
into something much bigger. It is essentially
the DNA of our modern reality. Oh, without zero,
higher mathematics simply collapses. It is the
origin of the complex plane. It is the only real
function that is both even and odd. Right. And
one of the most beautiful quirks of math, the
factorial of zero, which is written as a zero
followed by an exclamation point, actually equals
one. Wait, wait, wait. Full stop. I'm going to
need another ELI -5 here. You're telling me the
factorial of nothing equals something. How does
that work? It sounds like a paradox, but it's
about combinatorics. Yeah. Basically how we arrange
things. A factorial tells you how many different
ways you can arrange a set of items. Okay, track
it. So the factorial of three is three times
two times one, which equals six. There are six
ways to arrange three items. Okay, following
so and so. The factorial of two is two times
one, which equals two. Two ways to arrange two
items. Right. The factorial of one is one. There's
only one way to arrange a single item. So what
is the factorial of zero? How many ways can you
arrange zero items on a desk? I mean, I guess
there's only one way. You just leave the desk
empty. Exactly. There is exactly one way to arrange
nothing. Therefore, zero factorial equals one.
It maintains the internal logic of the math perfectly.
That is strangely poetic. And zero is so thoroughly
embedded in our culture and language now. Like,
we don't just use the word zero. Oh, definitely
not. If you're reading a phone number or postcode,
you'll probably just say, oh, we say zilch, zip,
nada. In sports, it has its own slang. In cricket,
a score of zero is a duck, which is short for
a duck's egg. Yeah. And in tennis, if you have
zero points, it's called love. Which actually
likely comes from the French word l 'oeuf, meaning
the egg. Again, they're referencing the physical
round shape of the number zero. But where zero
really flexes its modern superpowers, where it
literally runs the world you and I live in, is
in computer science. Modern computers store information
in binary. The entire digital alphabet is just
two symbols, one and zero. And that's not arbitrary
at all. It represents the physical reality of
the hardware. It's the presence or absence of
electrical current in a microscopic wire. Exactly.
One means the switch is on. Zero means the switch
is off. Every website, every digital photo, every
single piece of software is built on millions
of micro decisions between something and nothing.
And because humans and computers think differently,
the quirks of zero show up everywhere in programming.
Our source talks about this famous debate over
zero based index. Yes, this is a classic. It's
about how you count items in a list. Normal humans
start counting at one. First item, second item,
third item. Early programming languages like
Fortran mirrored this and started counting at
one. But languages like C, which heavily influenced
modern computing, start counting at zero. So
if you have a list of groceries in a computer
program, the milk isn't item number one, it's
item zero. Exactly. It represents an offset.
How far away is this item from the start of the
list? Well, the first item is zero steps away
from the start. There's also the concept of the
Unix epoch in computing. This one just blew my
mind. Ah, yes. When a computer needs to know
what time it is, it can't just look at the clock
on the wall. it counts the seconds forward from
a specific zero time stamp. Right. For Unix systems,
which run most of the world's servers, time literally
began at the midnight before January 1st, 1970.
That is their big bang. January 1st, 1970 is
zero. Which actually reminds me of another mind
-bending fact from the dating system section
of our source. When we look at our own human
calendar, transitioning from BC to AD... There
is no year zero. There is no year zero. It goes
from 1 BC directly to 81. We just skipped it
entirely. It feels absolutely absurd when you
think about it. It really is. But it highlights
how unnatural the concept of zero still was when
the calendar was originally formalized. The monks
creating the calendar just didn't have a concept
for a zero year. So they just didn't include
one. Nope. It wasn't until modern astronomers
needed to calculate intervals backward in time
that they had to force an astronomical year zero
into existence just to make their math work.
So, to summarize all of this, if numbers were
a building, 1 through 9 are the bricks. They
are the tangible things you can hold, stack,
and count. But zero is the mortar. I love that.
It's the invisible stuff, the nothingness, that
holds the entire structure of mathematics and
the digital age together. You just can't build
a skyscraper without mortar. I think that's a
brilliant way to frame it. I really want you,
the listener, to think about this the next time
you check a digital clock or type in a postcode
or even just pause this audio file. Yeah, exactly.
This very audio you are listening to right now
is currently being processed by your device as
a rapid -fire sequence of binary zeros and ones.
You were relying on a concept that ancient empires
actively fought against, that terrified Greek
philosophers, and that Indian mystics had to
tie to the concept of an infinite god just to
make it comprehensible. It is a massive heavy
legacy for just an empty circle. And I want to
leave you with one final provocative thought
from the source material. We've spent this whole
deep dive talking about zero as a human invention,
a cultural milestone that took us thousands of
years to figure out. But cognitive science and
biology have recently revealed something stunning.
Certain animals, like crows and honeybees, actually
display an awareness of the concept of zero.
It's incredible. They have a numerical abstraction
for nothing. Which completely upends the narrative.
It really does. Exactly. So I leave you with
this. If a tiny honeybee inherently understands
nothingness, then was zero ever really a human
invention? Or is it a fundamental law of the
universe that we simply finally opened our eyes
to? Think about that the next time you're looking
at an empty table.