Leonid Grinin http://www.socionauki.ru/authors/grinin_l/

PERIODIZATION OF HISTORY:

A THEORETIC-MATHEMATICAL ANALYSIS

Presentation at XXI World Congress of Philosophy. Rethinking Philosophy Today. July 30 –

August 5, 2008. Seoul National

University, Seoul, Korea.

There is

no

doubt

that

periodization is

a rather effective

method

of

data

ordering

and

analysis, but

it

deals

with

exceptionally

complex

types

of

processual and

temporal

phenomena

and

thus

it

simplifies

historical

reality. But

as

Karl

Jaspers

noted, "…

the purpose

of

such

simplifications

is

to

indicate

the

essentials".

I’d

like

to

suggest

a model

of

periodization of

history

based

on

my

theory

of

historical

process. I shall

also

demonstrate

the possibilities

of

mathematical

modeling

of

temporal

processes

in

historical

development.

According

to

the

theory

that

I propose, the historical

process

can

be

subdivided

more

effectively

into

four

major

stages. The

transition

from

any

of

these stages

into

another

is

the

change

of

all

the

basic

characteristics

of

the

respective

stage. However, in addition

to

this

principle

basis

of

periodization, we

need

an

additional

basis, by

means

of

which

the

chronology may be worked out in deta

il.

As

such

an

additional

basis

I propose

the production

principle

that

describes

the

major

qualitative

stages

of

the

development

of

the

world

productive forces.

I single

out

four

principles

of

production:

1. Hunter-Gatherer2. Craft-Agrarian3. Industrial4. Information-Scientific

The

change

in

production

principles

is connected

with

the

three

PRODUCTION

REVOLUTIONS. The

three

production revolutions

are

the

following:

•

the Agrarian (or

Neolithic

)

Revolution;

•

the Industrial Revolution;

•

the Information-Scientific Revolution.So

the

starting

point

of

such

revolutions

can

be

regarded

as

a convenient

and

natural

point

from

which

the chronology

of

stage

change

can

be

established.

There has

been

written

a lot

about

each

of

the

three production

revolutions. However

there

is

a small

number

of

studies

concerning

these

revolutions

as

recurrent

phenomena, each

of

them

representing

an

extremely

important

landmark

in

the

history

of

humankind. So

I try

to

develop

a theory

of production

revolution

that

I now

present

to

your

attention.

According

to

this

theory

each

production

revolution

has

its

own cycle. We

can

speak

about

two

qualitative

phases

and

a sort

of

interruption

between

them. Each

phase of

a production revolution

represents

a major

breakthrough

in

production.

A general scheme of two phases of production revolution within my theory looks as follows:

Agrarian Revolution:

•

the first phase is the transition to primitive hoe agriculture and animal husbandry;

•

the second phase is the transition to irrigation or non-irrigation plough agriculture.

Industrial Revolution:

•

the

first phase is

the

vigorous

development of seafaring and trade, mechanization on the basis of water engine and

other

processes

in

the

15th

and

16th

centuries;

•

the

second phase is

the

industrial breakthrough of the

18th

century

and

the

first

third

of

the

19th

century

which

is

connected

with

the

introduction

of

various machines

and

steam

energy.

Information-Scientific Revolution:

•

the

first phase began

in

the

1940s and

1950s with breakthroughs in automation, production of synthetic materials,

but

especially

in

the

development

of

electronic means of control, communication and information.

•

However, it

appears

possible

to

speak

about

its

forthcoming second phase which

may

start

within

a few

decades. Judging

by

the

recent

scientific, biotechnological

and

medical

inventions, the

second

phase of

this

revolution

may

start

with

changing

human

biological

nature.

The

overall

cycle

of

the

production

principle

can

be represent

in

a cycle

concluding

6 phases.

•

The

first

phase –

"transitional". •

The

second

phase –

"adolescence".

•

The

third

phase –

"florescence". •

The

fourth

phase –

"maturity".

•

The

fifth

phase –

"high

maturity". •

The

sixth

phase –

"preparatory".

After

this

in

some

societies

a transition

to

a new production

principle

can

take

place, and

a new

cycle

begins.

I believe

that

the

production

revolution

is connected

with

the

first

three

phases

of

the

production

principle. So

the

production

revolution can

be

regarded

as

an

integral

part

(the

first

"half") of

the

production

principle. In

this

Figure

you

can

see the

correlation

between

the

phases

of

production

principles

and

phases

of

production

revolutions.

Figure

1. Correlation between Phases of Production Principles

and Phases of Production Revolutions

I suppose

that

it

would

be

better

speak

about

the historical

process

not

since

the

modern

datings

of

the

emergence

of

Homo sapiens sapiens (100,000 –

200,000 years

ago) but

only

from

the

period

about

40,000 −

50,000

years

ago. That

is

because

I believe

that

only

after

the landmark

of

40,000 years

ago

we

can

speak

about

the

first

indisputable

indications

of

truly

human

culture

and

society.

Unfortunately

I can’t

give

details

of

every

phase of

my chronology

because

it

will

take

too

much

time. I would

like

to

dwell

only

on

some

datings. But

you

can

see

the

datings

of each

phase of

all

principles

of

production

in

this

Table

Table 1. Chronology of Production Principle PhasesProduc-tion principle

1st phase 2nd phase 3rd phase 4th phase 5th phase 6th phase Overall for pro-duction princi-ple

1. Hunter-

Gatherer

40 000–30 000

(38 000–28 000BCE)

10

30000–22 000

(28 000–20 000BCE)

8

22 000 –17 000

(20

000–15 000BCE)

5

17000 –14 000

(15

000–12

000BCE)

3

14 000–11 500

(12 000–9500BCE)

2.5

11 500–10 000(9500–8000BCE)

1.5

40 000–10 000

(38 000–8000 BCE)

30

2. Craft-

Agrarian

10 000–7300

(8000–5300BCE)

2.7

7300–5000

(5300–3000BCE)

2.3

5000–3500

(3000–1500BCE)

1.5

3500–2200

(1500–200

BCE)1.3

2200–1200(200

BCE –800 CE)

1.0

800–1430 CE

0.6

10 000–570(8000

BCE–1430 CE)9.4

3. In-dustrial 1430–16000.17

1600–17300.13

1730–18300.1

1830–18900.06

1890–19290.04

1929–19550.025

1430–19550.525

4. Infor-mation-

Scientific

1955–2000

(1955–1995)

0.04–0.045

2000–2040

(1995–2030)

0.035–0.04

2040–2070

(2030–2055)0.025–

0.03

2070–2090

(2055–2070)0.015–

0.02

2090–2105

(2070–

2080)0.01– 0.015

2105–2115

(2080–2090)0.01

1955–2115(2090)

[forecast]0.135– 0.160

•

In

this

table

you

can

see

close-up

the

dating

of

each

phase of Hunter-Gatherer

principle

of

production.

Production principle

1st phase 2nd phase 3rd phase 4th phase 5th phase 6th phase Overall for pro-duction

principle Hunter-Gatherer

40 000– 30 000

(38 000– 28 000 BCE)

10

30000– 22 000

(28 000– 20 000 BCE)

8

22 000 –17 000

(20 000–15 000 BCE)

5

17000 – 14 000

(15 000–12 000 BCE)

3

14 000– 11 500

(12 000– 9500 BCE)

2.5

11 500– 10 000 (9500– 8000 BCE)

1.5

40 000– 10 000

(38 000– 8000 BCE)

30

Table 1 (1). Chronology of Hunter-GathererProduction Principle Phases

•

During in

the first phase of Hunter-Gatherer production principle (c.40-30,000 BP) some new types

of

tools

appeared. For that period more

than

100 types

of

tools

are known.

•

The

third phase lasted

till

18,000 –

16,000 BP. This

is

the period

of

the

maximum

spread

of

glaciers

(referred

to

as

the

glacial

maximum).

•

The

sixth phase (c. 12,000–10,000 BP) was

also

connected with

continuing

climatic

warming, environmental

changes

culminating

in

the

transition

to

the

Holocene

and considerable

progress

in

stone

industries

during

the

Neolithic

period.

Table 1(2). Chronology of Production Principle Phases

Production principle

1st phase

2nd phase

3rd phase

4th phase

5th phase

6th phase

Overall for production

principle

Craft-Agrarian

10 000–7300

(8000– 5300 BCE)

2.7

7300– 5000

(5300– 3000 BCE) 2.3

5000– 3500

(3000–1500 BCE)

1.5

3500– 2200

(1500– 200

BCE) 1.3

2200– 1200 (200

BCE – 800 CE) 1.0

800– 1430 CE

0.6

10 000–570 (8000 BCE–1430

CE) 9.4

In

this

table

you

can

see

the

datings

of

each

phase of Craft-Agrarian

principle

of

production.

•

The

first phase of Craft-Agrarian productioin

principle was connected

with

the

beginning

of

agriculture

which

is

dated

within

the

interval

12,000 to

9,000 BP.

•

During

the

third phase, 5000–3500 BP the

second

stage

of Agrarian

revolution

starts; animal

husbandry, crafts

and

trade

are

differentiated

into

separate

branches

of

the

economy.

•

The

sixth phase lasted

from

the

9th

century

till

the

first

third

of

the

15th

century

CE. At

its

end

one

can

observe

the

beginning

of

urban

and

economic

growth

in

Europe.

Table 1 (3). Chronology of Production Principle Phases

You

can

see

the

datings

of

each

phase of Industrial principle of

production

in

this

table.

Production principle

1st phase 2nd phase 3rd phase 4th phase 5th phase 6th phase Overall for pro-duction

principle

Industrial 1430– 1600 0.17

1600– 1730 0.13

1730– 1830 0.1

1830– 1890 0.06

1890– 1929 0.04

1929– 1955 0.025

1430–1955 0.525

•

The first phase of Industrial production principle was connected with the beginning of the industrial revolution of the 15th

century to the late 16th

century.

•

The

third phase of the industrial production principle began in the second third of the 18th

century in England. It

was connected with

the

second

phase of

the

industrial revolution

that

led

to

the

development

of

the

machine-

based

industries

and

the

transition

to

steam

energy.

•

The sixth phase continued till the mid 20th

century.

A vigorous

intensification

of

production

and

the introduction

of

scientific

methods

of

its

organization

took

place

during

this

period.

•

The

first phase of

the

information-scientific

production principle

took

place

between

the

1950s and

mid

1990s,

when

because

of

information-scientific

revolution

a vigorous

development

of

information

technologies

and

the

start

of

real

economic

globalization

were

observed.

•

The

second phase started

in

the

mid

1990s in

conjunction with

the

development

and

wide

diffusion

of

user-friendly

computers, communication

technologies

and

so

on. It continues

up

to

the

present.

•

The

information-scientific

production

principle

is

only

at

its beginning; its

first

phase has

just

been

finished

and

the

second

one

has

just

started. However, its

main

results

are

still

forthcoming.

• The

third phase may

begin

approximately

in

the

2030s –

2040s•For

the

expected

lengths

of

the

fourth, fifth, and

sixth phases

of

the

information-scientific

production

principle

see

the

Tables

. Of course, all

the

calculations

of

the

following

phases' lengths

are

highly

hypothetical.

Table 1 (4). Chronology of Production Principle Phases

Production principle

1st phase 2nd phase 3rd phase 4th phase 5th phase

6th phase Overall for production principle

Information-Scientific

1955– 2000

(1955– 1995)

0.04–0.045

2000– 2040

(1995– 2030)

0.035–0.04

2040– 2070

(2030– 2055)

0.025– 0.03

2070– 2090

(2055– 2070)

0.015– 0.02

2090– 2105

(2070–2080)

0.01–0.015

2105– 2115

(2080– 2090)

0.01

1955–2115 (2090)

[forecast]

0.135–0.160

Table 2. Production Principles and Their Phase Lengths (in thousands of years)

Production principle

1st

phase2nd

phase3rd

phase4th

phase5th

phase6th

phaseOverall for production principle

Information- Scientific 0.04–

0.045

0.035 –

0.04

0.025 –

0.03

0.015 –

0.02

0.01–0.015 0.01 0.135–

0.160

In

general, Information-Scientific production principle may

finish

by

the

end

of

this

century, or

by

the

beginning

of

the

next

one. This

implies

an

immense acceleration

of

development

that

can

be

hardly

compatible

with

the

biopsychic

human

nature

because

in

view

of

the growing

life

expectations

all

the

immense

changes

(from

2040s to

2090s) will

happen

within

the

span

of

one generation

that

will

appear

in

the

2010s. But

if

they

occur

within

a lifespan

of

one

generation, it

is

not

clear

whether human

physical

and

psychic

abilities

will

be

sufficient

to

stand

this; what

price

will

be

paid

for

such

a fast adaptation?

Now

let’s

pass

to

the

mathematical

part. The proposed

periodization is

based

on

the

idea

of

change

of

the

production

principles

as

recurrent

developmental cycles

(each

of

them

includes

six

phases). You

can

see

the

four

macrocycles

in

the

Diagrams. You’ll

see

curves

of each

of

them

have

similar

exponential

shape.

Diagram 1. Hunter-Gatherer Production Principle

40000 (38000 BCE.)

10000(8000 BCE)

11500

14000

17000

22000 (20000 BCE)

30000

600080001000012000140001600018000200002200024000260002800030000320003400036000380004000042000

Phase I

Phase II

Phase III

Phase IV

Phase V

Phase VI

(8000) (4000)years BP(BCE.) (38000) (28000) (20000) (14000) (12000)

Diagram 2. Craft-Agrarian Production Principle

1430 CE

800 CE

200 BCE

1500 BCE (3500 BP)

5300 BCE

8000 BCE (10000 BP)

3000 BCE

Phase VI

Phase V

Phase IV

Phase III

Phase II

Phase I

CEBCE9000 8000 7000 6000 5000 4000 3000 2000 1000 0 1000 2000

Diagram 3. Industrial Production Principle

1955

1929

1890

1830

1730

1600

1430 CE

1400 1430 1460 1490 1520 1550 1580 1610 1640 1670 1700 1730 1760 1790 1820 1850 1880 1910 1940 1970 2000

Phase VI

Phase V

Phase IV

Phase III

Phase II

Phase I

н. э.

Diagram 4. Information-Scientific Production Principle

19551955

2040

2070

2090

2105

2115

2000

2030

2055

2070

2080

2090

1995

1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 2130

Phase I

Phase II

Phase III

Phase IV

Phase V

Phase VI

Note: the broken line indictates the forecast version for the expected development of tproduction principle corresponding to dates in brackets in the 5th line of Table 1.

However, each

subsequent

cycle

is

shorter

in

time than

the

previous

one

due

to

the

acceleration

of

historical

development. This

is

obviously

seen

especially

in

the

Table that

presents

the

absolute

lengths

of

the

phases

in

thousands

of

years.

Table 2. Production Principles and Their Phase Lengths

(in thousands of years)

Production principle

1st

phase2nd

phase3rd

phase4th

phase5th

phase6th

phaseOverall for production principle

1. Hunter-Gatherer 10 8 5 3 2.5 1.5 30

2. Craft-Agrarian 2.7 2.3 1.5 1.3 1.0 0.6 9.4

3. Industrial 0.17 0.13 0.1 0.06 0.04 0.025 0.525

4. Information-

Sci-entific 0.04–

0.0450.035–0.04

0.025–0.03

0.015

–0.02

0.01–0.015 0.01 0.135–

0.160

No

doubt

these

are

recurrent

cycles, because within

each

cycle

in

some

respect

the

development

follows

the

same

pattern: every

phase within

every cycle

plays

a functionally

similar

role. Moreover, the

proportions

of

the

lengths

of

the

phases

and

their combinations

remain

approximately

the

same. You

can

see

this

in

the

following

Tables

which

also present

the

average

rates

for

all

the

production

principles.

Table 3. Ratio of Each Phase [and Phase Combination] Length to the Total Length of Respective Production

Principle [%%] (presents

results

of

my

calculations

of

the

ratio

of

each

phase's

length

to

the

length

of

the

respective

production

principle

using

a rather

simple

methodology).

Production principle 1 2 3 4 5 6 1–2 3–4 5–6 1–3 4–6

1. Hunter-

Gatherer 33.3 26.7 16. 7 10 8.3 5 60 26.7 13.3 76.7 23.3

2. Craft-

Agrarian 28.7 24. 5 16.0 13.8 10.6 6.4 53.2 29.8 17 69.1 30.9

3. Industrial 32.4 24.8 19 11.4 7.6 4.8 57.1 30.5 12.4 76.2 23.8

4. Information-

Scientific 28.1 (29.6)

25 (25.9)

18.8(18.5)

12.5(11.1)

9.4 (7.4)

6.3(7.4)

53.1(55.6)

31.3(29.6)

15.6(14.8)

71.9(74.1)

28.1(25.9)

Mean 30.6 25.3 17.6 11.9 9 5.6 55.9 29.6 14.6 73.5 26.5

Table 4. Comparison of Phase Length Ratios for Each Production Principle [%%]

employs

a similar

methodology

to

compare

lengths

of

phases (and

combinations

of

phases) within

one

production

principle.

Production principle

1:2 2:3 3:4 4:5 5:6 (1+2):(3+4)

(3+4):(5+6)

(1+2+3) :

(4+5+6)

1. Hunter-

Gatherer 125 160 166.7 120 166.7 225 200 328.6

2. Craft-

Agrarian 117.4 153.3 115.4 130 166.7 178.6 175 224.1

3. Industrial 130.8 130 166.7 150 160 187.5 246.2 320

4. Information-

Scientific 112.5(114.3)

133.3(140)

150(166.7)

133.3(150)

150(100)

170(187.5)

200 (200)

255.5(285.7)

Mean 121.4 144.2 149.7 133.3 160.9 190.3 205.3 282.1

In

general, my

mathematical

analysis

represented

in diagrams

and

tables

indicates

the

following

points:

•

evolution

of

each

production

principle

in

time

has

recurrent features, as

it

is

seen

in

the

Diagrams

•

there

are

stable

mathematical

proportions

between

lengths of

phases

and

phase combinations

within

each

production

principle

as

it

was

seen

in

the

Tables

•

the

cycle

analysis

clearly

indicates

that

the

development speed

increases

sharply

just

as

a result

of

production

revolutions

as

it

is

seen

in

following

Diagram

Diagram 5. Evolution of Historical Process in Time

3000

21152105209020702040200520001955192918901830

16001730

1430800

2001500

5300

8000

120001050015000

2000028000 38000 BCE

(40000 BP)

Formation I(hunter-gatherer production principle)

Formation II(craft-agrarian production principle)

Formation IV(information-scientific production principle)

Formation III(industrial production principle)

BCE 0 CE

If

we

calibrate

the

Y-axis

of

the

last

diagram, the

curve of

historical

process

acquires

a hyperbolic

rather

than

exponential

shape, which

indicates

that

we

are

dealing

here with

a blow-up

regime. You

can

see

it

in

the

final

diagram.

Diagram 6. Hyperbolic Model of Historical Process Dynamics

-400

-200

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-50000 -40000 -30000 -20000 -10000 0

CEBCE

38 000 BCE

8 000 BCE

1430 CE

1955 CE

2000 CE

Thank you for attention!Thank you for attention!