Tag: logic

The Ethics of Knowing

Mark Davis2 Comments

In the modern American political climate, I’m constantly finding myself at sea in trying to unravel the motivations and thought processes of the Republican Party. The best summation I can arrive at involves the obvious manipulation of the electorate—but that is not terrifically new—combined with a persistent avoidance of evidence and facts.

In my day job, I research a range of topics trying to get enough of a grasp on what we do and do not know such that I can form a plan that innovates from the known facts towards the unknown. Here are a few recent investigations:

  • What is the state of thinking about the origins of logic? Logical rules form into broad classes that range from the uncontroversial (modus tollens, propositional logic, predicate calculus) to the speculative (multivalued and fuzzy logic, or quantum logic, for instance). In most cases we make an assumption based on linguistic convention that they are true and then demonstrate their extension, despite the observation that they are tautological. Synthetic knowledge has no similar limitations but is assumed to be girded by the logical basics.
  • What were the early Christian heresies, how did they arise, and what was their influence? Marcion of Sinope is perhaps the most interesting one of these, in parallel with the Gnostics, asserting that the cruel tribal god of the Old Testament was distinct from the New Testament Father, and proclaiming perhaps (see various discussions) a docetic Jesus figure. The leading “mythicists” like Robert Price are invaluable in this analysis (ignore first 15 minutes of nonsense). The thin braid of early Christian history and the constant humanity that arises in morphing the faith before settling down after Nicaea (well, and then after Martin Luther) reminds us that abstractions and faith have a remarkable persistence in the face of cultural change.
… Read the rest

The Deep Computing Lessons of Apollo

Mark DavisLeave a comment

Apollo 11With the arrival of the Apollo 11 mission’s 45th anniversary, and occasional planning and dreaming about a manned mission to Mars, the role of information technology comes again into focus. The next great mission will include a phalanx of computing resources, sensors, radars, hyper spectral cameras, laser rangefinders, and information fusion visualization and analysis tools to knit together everything needed for the astronauts to succeed. Some of these capabilities will be autonomous, predictive, and knowledgable.

But it all began with the Apollo Guidance Computer or AGC, the rather sophisticated for-its-time computer that ran the trigonometric and vector calculations for the original moonshot. The AGC was startlingly simple in many ways, made up exclusively of NOR gates to implement Arithmetic Logic Unit-like functionality, shifts, and register opcodes combined with core memory (tiny ferromagnetic loops) in both RAM and ROM forms (the latter hand-woven by graduate students).

Using NOR gates to create the entire logic of the central processing unit is guided by a few simple principles. A NOR gate combines both NOT and OR functionality together and has the following logical functionality:

[table id=1 /]

The NOT-OR logic can be read as “if INPUT1 or INPUT2 is set to 1, then the OUTPUT should be 1, but then take the logical inversion (NOT) of that”. And, amazingly, circuits built from NORs can create any Boolean logic. NOT A is just NOR(A,A), which you can see from the following table:

[table id=2 /]

AND and OR can similarly be constructed by layering NORs together. For Apollo, the use of just a single type of integrated circuit that packaged NORs into chips improved reliability.

This level of simplicity has another important theoretical result that bears on the transition from simple guidance systems to potentially intelligent technologies for future Mars missions: a single layer of Boolean functions can only compute simple things.… Read the rest