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MAS.961 How To Make Something That Makes (Almost) Anything. Complexity, Self Replication and all that…. [email protected] What governs the cost of placing atoms where we want them? What are the limits?. Si Wafer with Area sufficient for 2 Billion Transistors Cost: ~$0.50.

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MAS.961

How To Make Something That Makes (Almost) Anything

Complexity, Self Replication and all that…

[email protected]


What governs the cost of placing atoms where we want them? What are the limits?

Si Wafer with Area sufficient for

2 Billion Transistors

Cost: ~$0.50

Flash Memory

Transistor Count: 2B

Cost: ~$3

Itanium Quad Tukwila

Transistor Count: 2B

Cost: ~$100

NetBook

Cost: ~$200

Sand (Chips and Screen)

Cost: ~$0

Plastic Resin / Metal Ore

Cost: ~$4


Fabricational Complexity What are the limits?

Where is the yield per fabricational step

A

G

T

C

G

C

A

A

T

N

Fabricational Complexity for N-mer or M Types =

Fabricational Cost for N-mer =

Fabricational Complexity Per Unit Cost

Complexity Per Unit Cost

Complexity Per Unit Time*Energy


Fabricational Complexity What are the limits?

Application: Why Are There 20 Amino Acids in Biology?

(What is the right balance between Codon code redundancy and diversity?)

N Blocks of Q Types

Question:Given N monomeric building blocks of Q different types, what is the optimal number of different types of building blocks Q which maximizes the complexity of the ensemble of all possible constructs?

The complexion for the total number of different ways to arrange N blocks of Q different types (where each type has the same number) is given by:

.

And the complexity is:

For a given polymer length N we can ask which Q* achieves the half max for complexity such that:


Fabricational Complexity What are the limits?

Application: Identifying New Manufacturing Approach for Semiconductors

…Can we use this map as a guide towards future directions in fabrication?


Printed Electronics What are the limits?

Lithography

Printed Electronics

+

Liquid Inorganic

Semiconductors[1]

High Speed Printing

~ 3Weeks of

7x24 Processing

~Minutes

[1] Ridley et al., Science, 286, 746 (1999)

Science 297,416 (2000)


Fabricational Complexity What are the limits?

…Can we use this map as a guide towards future directions in fabrication?


DNA Synthesis What are the limits?

template dependant 5'-3'

primer extension

3'-5' proofreading

exonuclease

5'-3' error-correcting

exonuclease

Example: [A] Synthesize 1500 Nucleotide Base Gene. Error Rate = 0.99

(0.99)1500 ~ 10-7. [B] 3000 Nucleotide Base Gene. (0.99)3000 ~ 10-13.


Fabricational Complexity Per Unit Cost What are the limits?

2 Ply Error Correction

Non Error Correcting:

A

G

T

C

2Ply Error Correcting:

A

G

T

C

A

G

T

C

p=0.99


Fabricational Complexity Per Unit Cost What are the limits?

3 Ply Error Correction

(c)

(a)

(b)

Non Error Correcting:

A

G

T

C

3Ply Error Correcting:

A

G

T

C

A

G

T

C

,

For values of

A

G

T

C

and R increases exponentially with N.


Resources for Exponential Scaling What are the limits?

Resources which increase the complexity of a system exponentially with a linear addition of resources

1] Error Correcting Fabrication

2] Fault Tolerant Hardware Architectures

3] Fault Tolerant Software or Codes

4] Quantum Phase Space


Advanced_Automation_for_Space_Missions_figure_5-29.gif What are the limits?

Self-Replicating Systems


Information Poor Replication What are the limits?

Autocatalytic Chemistry

Replicated Parts Lack Complexity


Information Rich Replication What are the limits?

(Non-Protein Biochemical Systems)

J. Szostak, Nature,409, Jan. 2001


Replication Cycle What are the limits?

Parts

+

+

+

Template

+

+

+

Machine

Step 1

Step 2

Step 3

Threshold for Life

What is the Threshold for Self Replicating Systems?

Measurement Theory

DNA

Error Correcting

Exonuclease

(Ruler)

Watson Crick

.18 nm

/sandwalk.blogspot.com/2007/12/dna-denaturation-and-renaturation-and.html

http://en.wikipedia.org/wiki/File:Stem-loop.svg

How Well Can N Molecules Measure Distance?

Probability of Self Replication

Number of Nucleotides


Threshold for Life What are the limits?

Generalized Theory

Measurement Theory

Machine of N Blocks at Temperature T

Measures the Correctness of the new added block.

Energy: Energy consumption per replication (dominated by measurement just like in Szilard Maxwell’s Demon):

Must Determine size (position) to within 1 atom: Heisenberg limit: lambda / number of photons

0.1 nm = 5000 * 500nm photons ~ 5 Kev per addition

Number of Building Blocks: N Block machine must serve as a stable reference point to make measurement on

the new added block.


Autonomous self replicating machines from What are the limits?

random building blocks


Mechrep What are the limits?

Emthingy

Rep5mer

In Presentations/Saul


Lipson et. al. What are the limits?


Exponential Fabrication What are the limits?


  • Mean-Green von Neumann Machine What are the limits?

  • X Prize Rules

  • Prize Awarded to First Team to construct multiple copies of a machine that:

  • Consumes readly available raw materials (garbage,rocks, soil, air, water)

  • 2. Produces renewable energy at reasonable area/power (concentrated solar,photovoltaic cells, wind)

  • 3. Manufactures every part required to replicate itself


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