1 Tutorial 3 Nature’s Monte Carlo Bakery: The Story of Life as a Complex System

1

Tutorial 3

Nature’s Monte Carlo Bakery:The Story of Life as a Complex System

2

GEK1530

Topics covered

1. Turing Machines2. Reproduction versus Replication3. Replication versus Metabolism4. Summary on The Origin of Life5. Genetic Drift

3

GEK1530

Turing Machine

A Turing machine is a very simple machine, but, logically speaking, has all the power of any digital computer. It may be described as follows:

What is Turing Machine?

1. There is an infinite tape with squares on it.2. Each square may contain a symbol from a finite alphabet but

there can be only finitely many non-blank square on the tape.

3. There is a read-write head which is positioned somewhere on the tape.

4. The machine is in one of a finite number of states.5. There is a set of rules that tell the machine what to do given

a certain state and a certain symbol read from the tape.

4

GEK1530

Turing Machine

What is Turing Machine?

The rule is of the following form:(current state, current symbol, new state, new symbol, left/right)

This rule means that if the Turing machine is now in current state, and the symbol under the read/write head is current symbol, change its internal state to new state, replace the symbol on the tape at its current position by new symbol, and move the read/write head one square in the given direction (left or right).

If a Turing machine is in a condition for which it has no rule, it halts.

5

GEK1530

Turing Machine

0Head

State

Tape

Rules are defined in this format: (current state, current symbol, new state, new symbol, left/right)

X

Start with the symbol X on the tape and in state zero.Then apply the rules until the machine stops.

> = Right, - = write or do nothing

Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >

6

GEK1530

Turing Machine

0Head

State

Tape


X


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >

Let us go through this algorithm step by step

In the beginning (this is also called the initial condition) we have:

Step 0 - Read Apply rule 1.

7

GEK1530

Turing Machine

0Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 0 - Write State=0/Write=‘K’

8

GEK1530

Turing Machine

0Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 0 - Move Do not move

9

GEK1530

Turing Machine

0Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 1 - Read Apply rule 2

10

GEK1530

Turing Machine

1Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 1 - Write State=1/Write nothing

11

GEK1530

Turing Machine

1Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 1 - Move Right

12

GEK1530

Turing Machine

1Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



13

GEK1530

Turing Machine

1Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 2 - Write State=1/Write=‘E’

E

14

GEK1530

Turing Machine

1Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E

15

GEK1530

Turing Machine

1Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E

16

GEK1530

Turing Machine

2Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E

17

GEK1530

Turing Machine

2Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 3 - Move Right

E

18

GEK1530

Turing Machine

2Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E

19

GEK1530

Turing Machine

2Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 4 - Write State=2/Write =‘N’

E N

20

GEK1530

Turing Machine

2Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N

21

GEK1530

Turing Machine

2Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N

22

GEK1530

Turing Machine

3Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N

23

GEK1530

Turing Machine

3Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 5 - Move Right

E N

24

GEK1530

Turing Machine

3Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N

25

GEK1530

Turing Machine

3Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 6 - Write State=3/Write=‘N’

E N N

26

GEK1530

Turing Machine

3Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N N

27

GEK1530

Turing Machine

3Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N N

28

GEK1530

Turing Machine

4Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N N

29

GEK1530

Turing Machine

4Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 7 - Move Right

E N N

30

GEK1530

Turing Machine

4Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N N

31

GEK1530

Turing Machine

4Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 8 - Write State=4/Write=‘E’

E N EN

32

GEK1530

Turing Machine

4Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N EN

33

GEK1530

Turing Machine

4Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N EN

34

GEK1530

Turing Machine

5Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N EN

35

GEK1530

Turing Machine

5Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 9 - Move Right

E N EN

36

GEK1530

Turing Machine

5Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N EN

37

GEK1530

Turing Machine

5Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 10 - Write State=5/Write=‘T’

E N E TN

38

GEK1530

Turing Machine

5Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N E TN

39

GEK1530

Turing Machine

5Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N E TN

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GEK1530

Turing Machine

6Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N E TN

41

GEK1530

Turing Machine

6Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 11 - Move Right

E N E TN

42

GEK1530

Turing Machine

6Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N E TN

43

GEK1530

Turing Machine

6Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 12 - Write State=6/Write=‘H’

E N E T HN

44

GEK1530

Turing Machine

6Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N E T HN

45

GEK1530

Turing Machine

6Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N E T HN

46

GEK1530

Turing Machine

7Head

State

Tape


K


Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >



E N E T HN

47

GEK1530

Turing Machine



Rules:

1) 0,’X’, 0, ‘K’, -

2) 0, ‘K’, 1, -, >

3) 1, -, 1, ‘E’, -

4) 1, ‘E’, 2, -, >

5) 2, -, 2, ‘N’, -

6) 2, ‘N’, 3, -, >

7) 3, -, 3, ‘N’, -

8) 3, ‘N’, 4, -, >

9) 4, -, 4, ‘E’, -

10) 4, ‘E’, 5, -, >

11) 5, -, 5, ‘T’, -

12) 5, ‘T’, 6, -, >

13) 6, -, 6, ‘H’, -

14) 6, ‘H’, 7, -, >


Step 13 - Move Right

Fantastic! The function of this Turing machine is to print out my name!

7Head

State

TapeK E N E T HN

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GEK1530

Replication

Reproduction versus Replication

In biology, replication is the act or ability to make a copy. Mostly commonly meaning molecular replication.

For a molecule, to replicate means to construct a precise copy of itself by a specific chemical process

Reproduction

For a cell, to reproduce means to divide into two cells with the daughter cells inheriting approximately equal shares of the cellular constituents, just like photocopying.

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GEK1530



Cells can reproduce but only molecules can replicate!

In modern times, reproduction of cells is always accompanied by replication of molecules, but this need not be the case in the past!

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Metabolism

Replication versus Metabolism

Metabolism is the uptake and digestion of food, and the disposal of waste products in living organisms.

Roughly, metabolism is the sum of a cell’s chemical reactions.

In general, metabolism can be split into 2 groups of reactions: •Catabolism, which breaks down molecules, releasing energy.

•Anabolism, which uses energy from ATP to synthesize large molecules, including macromolecules.

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John von Neumann


He observed that replication and metabolism are logically separable.

He made the distinction between what is now called:

Hardware Software

process information embody information

Protein is hardware and is the essential component for metabolism.

Nucleic acid is software and is the essential component for replication.

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John von Neumann


Introduced analogy between automata and living organisms.

Hardware Software

rules symbols, statesAutomata

metabolism replicationOrganisms

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Implication


The separability between replication and metabolism implies:

• Possible to postulate organisms that are composed of pure hardware and capable of metabolism but incapable of replication.

• Possible to postulate organisms that are composed of pure software and capable of replication but incapable of metabolism.

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Implication


The basis functions of life: Replication and Metabolism.

Two logical possibilities for life’s origin:

• Life began only once with the functions of replication and metabolism already present and linked together from the beginning.

• Life began twice, with separate kinds of creatures, one kind capable of metabolism without replication, the other kind capable of replication without metabolism.

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Experiment: Synthesizing of Biological Building Blocks

Summary on The Origin of Life

Stanley L. Miller

Juan Oró• Showed that nitrogenous base in the nucleotide acid can

be synthesized from naturally occurring molecules in a reducing environment.

• Demonstrated that amino acids are easy to synthesize from naturally occurring molecules in a reducing environment.

Problem: The environment of the early Earth was not reduced!!

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Experiment: RNA polymerization


Manfred Eigen

Leslie Orgel• Showed that nucleotide monomers can polymerize into

RNA given a suitable template without any enzyme.

• Demonstrated that nucleotide monomers can polymerize into RNA using an enzyme but without any template.

Problem: RNA is made using both templates and enzymes in living cells!!

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Theories: Alexander I. Oparin


The order of events in the origin of life: cells enzymes genes.

He observed that oil liquid in water form a stable mixture called a coacervate.

He proposed that life began by successive accumulation of more and more complicated molecular populations within the droplets of a coacervate. This became the physical framework of the cell.

Enzymes came in later to organize the random population of molecules within the droplet into metabolic cycles. Lastly, the genes came in.

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GEK1530

Theories: Manfred Eigen


The order of the events in the origin of life:

genes enzymes cells

He believed that life began with self-replicating RNA. Enzymes appearing soon afterwards to build with the RNA a primitive form of the modern genetic transcription apparatus, and cells appearing later to give the apparatus physical cohesion.

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GEK1530

Theories: Cairns-Smith


The order of the events in the origin of life:

clay enzymes cells genes

He believed that the beginning of life was a natural clay crystal directing the synthesis of enzyme molecules absorbed to its surface.

The clay and enzymes learned to make cell membranes and became encapsulated in cells.

The cells contained clay crystals performing in a crude fashion the functions in a modern cell by nucleic acids.

Later on, a cell discovered that RNA is a better genetic material than clay and hence the RNA-based life survived.

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Theories: Freeman Dyson’s Conclusion


The Cairns-Smith theory is a double-origin theory.

It has the first origin of life mainly concerned with the building of a protein metabolic apparatus.

The second origin of life is the replacement of the clay component by an efficient replicative apparatus made of nucleic acids.

Cairns-Smith supposed that the two origins of life to be separated by a long period of biochemical evolution so that cells could have highly organized with protein enzymes and lipid membranes.

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Theories: Freeman Dyson’s Conclusion


Both Oparin theory and Eigen theory were single-origin theories. Each of them supposes the origin of life to have been a single process.

Oparin places primary emphasis on metabolism and barely discusses replication. Eigen places primary emphasis on replication and imagines metabolism falling into place rapidly as soon as replication is established.

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Freeman Dyson’s Double-Origin Hypothesis


The life began twice, with two separate kinds of creatures, one kind capable of metabolism without exact replication and the other kind capable of replication without metabolism.

The spontaneous emergence of protein structure and of nuclei acid structure out of molecular chaos are BOTH unlikely.

It would be easier to imagine two unlikely events occurring separately over a period of time than occurring simultaneously!

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Freeman Dyson’s Double-Origin Hypothesis


The first beginning must have been with proteins and the second beginning with nuclei acids.

The first protein creatures might have existed independently for a long time, eating and growing and gradually evolving a more and more efficient metabolic apparatus.

The nucleic acid creatures must have been parasites from the start, preying upon the protein creatures and using the products of protein metabolism to achieve their replication.

Dyson believes that hardware should come before software!

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Genetic Drift

Genetic Drift

Genetic drift refers to random changes in the gene frequencies of a population from generation to generation as a result of sampling error.

In each generation, some individuals may, just by chance, leave behind a few more descendents (and genes of course) than other individuals. The genes of the next generation will be the genes of the “lucky” individuals, not necessarily the healthier or “better” individuals.

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Genetic Drift – Sampling Error

Genetic Drift

Imagine a game in which you have a bag holding 100 marbles, 50 of which are brown and 50 green. You are allowed to draw 10 marbles out of the bag. Now imagine that the bag is restocked with 100 marbles, with the same proportion of brown and green marbles as you have just drawn out. The game might play out like this:

It’s clear that the ratio of brown to green marbles “drifts” around (5:5, 6:4, 7:3, 4:6 . . .).

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Genetic Drift

Genetic Drift

This process causes gene frequencies in a population to drift around over time. Some genes may even “drift out” of a population (i.e., just by chance, some gene may reach a frequency of zero).

In general, genetic drift has the effect of decreasing genetic variation within a population.

Due to many random factors, the genes in one generation do not wind up in identical ratios in the next generation, and this is evolution. While this is evolution, it is evolution due to chance, not selection.

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Genetic Drift

Genetic Drift

Imagine that our random draws from the marble bag produced the following pattern: 5:5, 6:4, 7:3, 4:6, 8:2, 10:0, 10:0, 10:0, 10:0, 10:0... Why did we keep drawing 10:0? Because if the green marbles fail to be represented in just one draw, we can’t get them back—we are “stuck” with only brown marbles.

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Genetic Drift

Genetic Drift

The 10:0 situation illustrates one of the most important effects of genetic drift: it reduces the amount of genetic variation in a population. And with less genetic variation, there is less for natural selection to work with.

Selection cannot increase the frequency of the green gene, because it’s not there for selection to act on. Selection can only act on what variation is already in a population; it cannot create variation.

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Genetic Drift

Genetic Drift

Genetic drift acts faster and has more drastic results in smaller populations. This effect is particularly important in rare and endangered species.

In general, genetic drift would not result in changes that are more adaptive.

Genetic drift is an evolution due to chance!!

Documents

1 Tutorial 3 Nature’s Monte Carlo Bakery: The Story of Life as a Complex System