From 4d81434f2c00dc73b1364a92edd05a62cd4be2a7 Mon Sep 17 00:00:00 2001
From: bnewbold <bnewbold@eta.mit.edu>
Date: Fri, 27 Feb 2009 13:39:56 -0500
Subject: draft notes

---
 draft/motivation.txt           | 26 +++++++++++++++++++++++
 draft/physical-motivations.txt | 35 +++++++++++++++++++++++++++++++
 draft/types-operators.txt      | 47 ++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 108 insertions(+)
 create mode 100644 draft/motivation.txt
 create mode 100644 draft/physical-motivations.txt
 create mode 100644 draft/types-operators.txt

diff --git a/draft/motivation.txt b/draft/motivation.txt
new file mode 100644
index 0000000..0336bd4
--- /dev/null
+++ b/draft/motivation.txt
@@ -0,0 +1,26 @@
+======================================
+Motivation
+======================================
+
+* reuse of tools, models, system, code both "up" and "down": can be built upon
+  and extended, or built "under" and applied as an extension to other existing
+  systems
+
+* seperation/abstraction of model, methods, and types from implementation,
+  allows for metaprogramming, compilation, symbolic analysis, potential for
+  proofs
+
+* conceptual simplicity/purity of a reference implementation allows it to serve
+  as a blueprint or recipe for similar systems or reimplementation
+
+* open source allows the entire heirarchy, tool chain, and implementation to be
+  explored, shared, extended, abused
+
+* unambiguous notation and syntax checking
+
+* educational exploration
+
+* same tools for theoretical development (symbolic, checking, searches) and
+  efficient numerical computation (compilation, parallelizing combinators,
+  evaluation flow control, optimization)
+
diff --git a/draft/physical-motivations.txt b/draft/physical-motivations.txt
new file mode 100644
index 0000000..5d665f4
--- /dev/null
+++ b/draft/physical-motivations.txt
@@ -0,0 +1,35 @@
+=========================================
+Physical Observations, Applications
+=========================================
+
+
+Michealson-Morley and Gravitational Redshift <=> Locally Lorentz
+--------------------------------------------------------------------
+(motivational)
+
+
+Precession Perhelion of Mercury <=> Schwartzchild?
+------------------------------------------------------
+(explicit calculation)
+
+
+Deflection of Light <=> Geodesics
+-----------------------------------
+From Carroll p292,
+G M_sun /(c^2) = 1.48e5 cm, R_sun = 6.96e10 cm, deflection angle of 1.75 arcsec
+
+
+Gravitational Waves <=> Weak Field Approximation, Perturbation Theory
+---------------------------------------------------------------------------
+See Carroll p293
+
+
+GPS Corrections <=> Geodesics with E&M
+------------------------------------------
+(order of magnitude?)
+
+
+Gravity Probe B <=> Frame Dragging, geodetic
+----------------------------------------------------------------------------
+(probably not...)
+
diff --git a/draft/types-operators.txt b/draft/types-operators.txt
new file mode 100644
index 0000000..68bd058
--- /dev/null
+++ b/draft/types-operators.txt
@@ -0,0 +1,47 @@
+===============================
+Types and Operators
+===============================
+
+The careful definition of abstract types and the manipulation and handling of 
+instances by operators is the heart of any computational algebra system
+(or indeed any data-driven symbolic system). 
+
+The [R5R2] defines a simple "tower" of number subtypes (p.19):
+
+    number
+    complex
+    real
+    rational
+    integer
+
+Each subtype is a subset of the subtype above it, so that each rational is
+a complex but not every real is an integer. Additionally, every Scheme
+number is either exact or inexact. The selection of the appropriate 
+implementation of operations like addition, exponentiation, or rounding for
+arbitrary combinations of numbers and their return types is usually called
+*operator dispatch*. For an operator of N arguments of M possible types, one
+can imagine an M**N cell table defining the appropriate procedure (or 
+built-in hardware instruction) and return type for each combination of types.
+
+Such a table would be come unmanagably large for systems with even a modest
+number of operators and types: for example each of the basic binary operators
+(*, /, -, +, exp) would require it's own 2**(2*5)=1024 element table for the
+basic types described above. Procedural operator dispatch and coersion allow
+for more natural handling of type heirarchies.
+
+More rigorously defined algebras do not necessarily follow the simple strict
+ordering of types like the Scheme number tower, or even a proper tree
+structure:
+
+[figure: geometrical spaces from Merseve Geometry]
+[figure: number types from Merseve Algebra]
+[figure: math object hierarchy from Tegmark?]
+
+Types and Operators for Differential Geometry and Field Theories
+------------------------------------------------------------------------
+
+[topics: disjointness, 
+
+Implementation
+------------------------------------------------------------------------
+
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