for transmitting information --

perhaps dating back to the first controlled use of fire.

It allows one person to influence another's belief state --

across a distance.

Because with the ability to notice

either the presence or absence of something,

we are able to switch between one of two belief states.

One difference. Two states.

And ff we look back in history,

we find that this was of great importance to military powers,

which all rely on effective communications.

And a great place to begin

is with the Greek myth of Cadmus --

a Phoenician prince who introduced

the 'phonetic' letters to Greece.

The Greek alphabet --

borrowed from the Phoenician letters --

along with light, and cheap, papyrus --

effected the transfer of power

from the priestly to the military class.

And Greek military history provides clear evidence

of the first advancements in communication,

stemming from the use of signal torches.

Polybius was a Greek historian born in 200 BC.

He wrote 'The Histories,' which is a treasure trove of detail

related to the communication technologies of the time.

He writes: "The power of acting at the right time

contributes very much to the success of enterprises.

And fire signals are the most efficient of all devices

which aid us to do this."

However, the limitation of a signal fire was clear to him.

He writes:

"It was possible for those who had agreed on this

to convey information that, say, a fleet had arrived.

But when it came to some citizens

having been guilty of treachery,

or a massacre having taken place in town --

things that often happen, but cannot all be foreseen --

all such matters defied communication by fire signal."

A fire signal is great when

the space of possible messages is small --

such as 'enemy has arrived' or '[enemy has] not arrived.'

However, [as] the message space --

which is the total number of possible messages -- [grew],

[so grew the] need to communicate [more] differences.

And in The Histories, Polybius describes a technology

developed by Aeneas Tacticus --

one of the earliest Greek writers on the art of war --

from the 4th century BC.

And his technology was described as follows:

"Those who are about to communicate

urgent news to each other by fire signal

should procure two vessels

of exactly the same width and depth.

And through the middle should pass a rod,

graduated into equal sections --

each clearly marked off from the next,

[and] denoted with a Greek letter."

Each letter would correspond

to a single message in a look-up table

which [contains] the most common events that occur in war.

To communicate, they would proceed as follows:

First, the sender would raise his torch

to signal he had a message.

The receiver would then raise his torch,

signaling he was ready to receive it.

Then, the sender would lower his torch,

and they would both begin to drain their vessels

from a bored hole of equal size at the bottom.

Now, when the event is reached,

the sender raises his torch

to signal that they should both stop the flow of water.

This results in equal water levels,

denoting a single shared message.

This ingenious method

used differences in time to signal messages.

However, its expressive capabilitiy was limited,

mainly due to its [slow] speed.

Polybius then writes of a newer method --

originally devised by Democritus --

which he claims was "perfected by myself,

and quite definite and capable of dispatching --

with accuracy --

every kind of urgent message."

His method -- now known as the 'Polybius Square' --

works as follows:

Two people, seperated by a distance,

each have 10 torches -- separated into two groups of five.

To begin, the sender raises a torch

and waits for the receiver to respond.

Then, the sender lights a certain number

from each group of torches -- and raises them.

The receiver then counts

the number of torches lit in the first group.

This number defines the row position

in an alphabetic grid they share.

And the second group of torches

signifies the column position in this grid.

The intersection of the row and column number

defines the letter sent.

Realize, this method can be thought of

as the exchange of two symbols.

Each group of five torches is a symbol,

which was limited to five differences --

from one to five torches.

Together, these two symbols multiply

to give 5 x 5 = 25 differences --

not 5 + 5.

This multiplication demonstrates

an important combinatorial understanding in our story.

It was explained clearly in a 6th-century-BC

Indian medical text, attributed to Sushruta --

an ancient Indian sage -- as follows:

"Given 6 different spices,

how many possible different tastes can you make?"

Well, the process of making a mixture

can be broken down into in six questions:

Do you add A? Yes or no?

Do you add B?

C?

D?

E?

[or] F?

Realize, this multiplies into

a tree of possible answer sequences --

2 x 2 x 2 x 2 x 2 x 2 = 64 ...

64 different sequences of answers

are therefore possible.

Realise that given n yes-or-no questions,

there are 2^n possible answer sequences.

Now in 1605, Francis Bacon clearly explained

how this idea could allow one to send

all letters of the alphabet,

using only a single difference.

[Regarding] his 'bilateral cipher,' Bacon wrote, famously:

"The transposition of two letters by five placings

will be sufficient for 32 differences.

For by this art, a way is opened whereby a man

may express and signify the intentions of his mind --

at any distance of place -- with objects which are capable

of a two-fold difference only."

This simple idea of using a single difference

to communicate [all of the letters of] the alphabet

really took flight in the 17th century,

due to the invention of the telescope

by Lippershey, in 1608, and Galileo, in 1609.

Because quickly, the maginification power of the human eye

jumped from 3, to 8, to 33 times -- and beyond.

So the observation of a single difference

could be made at a much greater distance.

Robert Hooke, an English polymath interested in

improving the capability of human vision, using lenses,

ignited progress when he told the Royal Society, in 1684,

that suddenly, "with a little practice,

the same character may be seen at Paris,

within a minute after it hath been exposed at London."

This was followed by a flood of inventions

to pass differences more effectively

across greater distances.

One technology, from 1795, perfectly demonstrates

the use of a single difference to communicate all things.

Lord George Murray's 'shutter telegraph'

was Britain's reaction to the Bonapartist threat to England.

It was composed of six rotating shutters,

which could be oriented as either 'open' or 'closed.'

Here, each shutter can be thought of as a single difference.

With six shutters, we have six questions: open or closed --

providing us with 2^6, or 64, differences --

enough for all letters, digits, and more.

Now realize that each observation of the shutter telegraph

can also be thought of as the observation

of one of 64 different paths through a decision tree.

And with a telescope, it was now possible to send letters

at an incredible distance between beacons.

However, an observation in 1820

led to a revolutionary technology,

which forever changed how far these differences

could travel between signaling beacons.

This ushered in new ideas

which launched us into the 'Information Age.'