Boolean Logic and Steady State Machines


Boolean Logic: a system of logic in base 2 where each bit has a value of true (1) or false (0)
Before one can truly understand how steady state machines, one must have at least a general idea of what Boolean logic is and how it works. First, to get an understanding of Boolean numbers, one must first look at our current system of numbers, which is base 10.  Remembering back on the days when one first learned scientific notation, a common decimal number such as 1234 can be expressed as 1 x 10³ + 2 x 10² + 3 x 10¹ + 4 x 10º.  Now, the only difference with binary numbers and a common decimal number is the base that is used; while decimal uses base 10, decimal just uses base 2.  So breaking down the binary number 101 results in the equivalent value of 1 x 2² + 0 x 2¹ + 1 x 2º, which is 5 in decimal form (base 10).  Because the system uses base 2, the only possible values then are 0 (false) and 1 (true), just as in decimal there is not a single digit greater than 9.  Boolean logic, then is just doing different logic operations with numbers in base 2.  The most commonly seen logical operators (also called gates) are AND and OR.  The AND operator is just as you would think. If input 1 AND input 2 are both true (1), then the result is true. However, if either input is false (0), then the final result is also false.  The other logical operator often seen is the OR operator.  This operator returns true (1) if either input is true or if both inputs is true and false (0) if both inputs are false.  For a list of more Boolean gates and how they work, check out the following site: http://en.wikipedia.org/wiki/Logic_gate
And Gate                                Or Gate
Steady State Machine: a diagram showing the different states that can exist and the transitions that occur between then when certain Boolean conditions are met.
A steady state machine is just a collection of different states.   A state can just be defined as a specific logic combination. For example, if we had a simple state machine that had two different inputs, then the possible states are 00 (0), 01 (1), 10 (2), or 11 (3).   The other important part of steady state machines are that the inputs and directly connected with the outputs.  In other words, the inputs determine the output, and that output then acts as an input in another equation. A simple way to think of a steady state machine is a door that has sensors to determine whether the door is open or closed. The condition of the door (open or closed) then represents the state.  A slightly more complex, but better picture of a steady state machine is a washing machine.  A washing machine has several different states: fill with warm water, agitate, drain, rinse, and spin dry.  The transitions between the states are then determined by different input sensors, such as whether the timer is done or whether the washer is empty or full of water.  Eventually, no matter where one starts in the washing machine cycle, the final state will be an idle state.  In other steady state machines, the end will not be a single state but a recurrent loop of states called a state cycle.  In either case, changing any of the inputs has no long-term impact on behavior of the system. To see how the states change over time and patterns can form, check out the following application: http://www.bitstorm.org/gameoflife/
State Machine
Relation to issue of origins
The issue of steady state machines and its relation to origins is presented in an excerpt from Stuart Kauffman’s book, At Home In The Universe. In chapter four, Kauffman uses the example of steady state machines and specific Boolean rules to show how disorder and chaos can turn into order and design.   In his example, the primary objects are light bulbs. If a specific condition is false (represented by a 0), then the light bulb will be off.  However, if that condition is true (represented by a 1), then the light bulb will be in the on position. What Kauffman is trying to show by using the example of steady state machines is that if a given set of rules is applied to the initial conditions, then patterns can emerge and what originally looks like disorder can turn into order.  Applying this to the origins of life, Kauffman is saying that if we apply the emergent rules of the universe to the initial conditions of apparent disorder that existed before life formed, then over time order can and will emerge, and that order is represented by living things.  In other words, just as different binary combinations all eventually end up in the same state, life on earth was inevitable given the emergent laws of the universe.


Riggleman 2009