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act65 · Dec 1, 2024 · a8a0c8c · a8a0c8c
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diff --git a/_bibliography/auto-int.bib b/_bibliography/auto-int.bib
@@ -22,4 +22,29 @@ @article{JMLR:v21:19-346
   number  = {132},
   pages   = {1--62},
   url     = {http://jmlr.org/papers/v21/19-346.html}
-}
+}
+
+@misc{iravanian2022symbolicnumericintegrationunivariateexpressions,
+      title={Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression}, 
+      author={Shahriar Iravanian and Carl Julius Martensen and Alessandro Cheli and Shashi Gowda and Anand Jain and Yingbo Ma and Chris Rackauckas},
+      year={2022},
+      eprint={2201.12468},
+      archivePrefix={arXiv},
+      primaryClass={cs.SC},
+      url={https://arxiv.org/abs/2201.12468}, 
+}
+
+@article{Jia_2017,
+   title={Integration by differentiation: new proofs, methods and examples},
+   volume={50},
+   ISSN={1751-8121},
+   url={http://dx.doi.org/10.1088/1751-8121/aa6f32},
+   DOI={10.1088/1751-8121/aa6f32},
+   number={23},
+   journal={Journal of Physics A: Mathematical and Theoretical},
+   publisher={IOP Publishing},
+   author={Jia, Ding and Tang, Eugene and Kempf, Achim},
+   year={2017},
+   month=may, pages={235201} }
+
+
diff --git a/...nical-posts/autoint/2022-10-13-autoint.md → _drafts/autoint/2022-10-13-autoint.md b/...nical-posts/autoint/2022-10-13-autoint.md → _drafts/autoint/2022-10-13-autoint.md
@@ -17,12 +17,12 @@ Why not? Where is it? What would it look like?
 
 I'll use this page collect my thoughts on the subject.
 
-- (WIP) I try to [motivate]({site.baseurl}/autoint/motivation) the need for automatic integration. What kind of problems could it solve? How could it be used?
-- (WIP) I cover [automatic differentiation]({site.baseurl}/autoint/autograd) and how it works.
-- (WIP) A tutorial on [symbolic integation]({site.baseurl}/autoint/symbolic-int) and why its so hard (it's not a closed operation).
-- (WIP) An exploration of the [history of integration]({site.baseurl}/autoint/history) and how it has been automated in the past.
-- (WIP) A [tutorial on calculus]({site.baseurl}/autoint/calculus). Back to basics!
-- (WIP) A [literature review]({site.baseurl}/autoint/lit-review) of recent integration ideas.
+- (WIP) I try to [motivate]({{site.baseurl}}/autoint/motivation) the need for automatic integration. What kind of problems could it solve? How could it be used?
+- (WIP) I cover [automatic differentiation]({{site.baseurl}}/autoint/autograd) and how it works.
+- (WIP) A tutorial on [symbolic integation]({{site.baseurl}}/autoint/symbolic-int) and why its so hard (it's not a closed operation).
+- (WIP) An exploration of the [history of integration]({{site.baseurl}}/autoint/history) and how it has been automated in the past.
+- (WIP) A [tutorial on calculus]({{site.baseurl}}/autoint/calculus). Back to basics!
+- (WIP) A [literature review]({{site.baseurl}}/autoint/lit-review) of recent integration ideas.
 
 <!-- - [State of integration tools]({site.baseurl}/autoint/state-of-int) -->
 <!-- - [This]({site.baseurl}/autoint/numerical-int) post explores numerical integration and why its so useful, but also limited. -->

diff --git a/...ical-posts/autoint/2024-10-10-autograd.md → _drafts/autoint/2024-10-10-autograd.md b/...ical-posts/autoint/2024-10-10-autograd.md → _drafts/autoint/2024-10-10-autograd.md
@@ -11,7 +11,7 @@ scholar:
 
 ## Automatic differentiation
 
-Automatic differentiationis a method for computing the derivative of a function. It is a generalisation of the chain rule and the product rule. It is also known as algorithmic differentiation, computational differentiation, and sometimes just autodiff or AD.
+Automatic differentiation is a method for computing the derivative of a function. It is a generalisation of the chain rule and the product rule. It is also known as algorithmic differentiation, computational differentiation, and sometimes just autodiff or AD.
 
 ### Why is it useful?
 
@@ -23,6 +23,8 @@ AD has many applications in machine learning, where we often need to compute the
 
 AD works by building a computational graph of the function that we want to differentiate. The computational graph is a directed acyclic graph (DAG) that represents the function as a sequence of primitive operations. Each node in the graph represents a primitive operation, and the edges represent the flow of data between the operations. The graph is then evaluated using the chain rule to compute the derivative of the function.
 
+
+
 ### Calculus background
 
 The derivative of a function $f(x)$ is defined as;
@@ -51,6 +53,12 @@ $$
 ### How is it implemented?
 
 (ie how does jax work?)
+https://jax.readthedocs.io/en/latest/autodidax.html
+
+- Taylor-Mode Automatic Differentiation for Higher-Order Derivatives in JAX
+- On the numerical stability of algorithmic differentiation
+- Achieving Logarithmic Growth of Temporal and Spatial Complexity in Reverse Automatic Differentiation
+- Doubly Recursive Multivariate Automatic Differentiation
 
 ### How is it different from symbolic differentiation?
 

diff --git a/...ical-posts/autoint/2024-10-10-calculus.md → _drafts/autoint/2024-10-10-calculus.md b/...ical-posts/autoint/2024-10-10-calculus.md → _drafts/autoint/2024-10-10-calculus.md
@@ -25,11 +25,6 @@ Then F is uniformly continuous on [a, b] and differentiable on the open interval
 {% bibliography --cited %}
 
 
-
----
-title: "Calculus"
----
-
 Six pillars of calculus;
 
 - limits

diff --git a/...al-posts/autoint/2024-10-10-lit-review.md → _drafts/autoint/2024-10-10-lit-review.md b/...al-posts/autoint/2024-10-10-lit-review.md → _drafts/autoint/2024-10-10-lit-review.md
@@ -10,8 +10,10 @@ permalink: /autoint/lit-review
 ---
 
 In depth look at papers;
-- [Integration by differentiation]({site.baseurl}/autoint/int-by-diff)
-- ???
+- [Integration by differentiation]({site.baseurl}/autoint/int-by-diff) {% cite Jia_2017 %}
+- {% cite iravanian2022symbolicnumericintegrationunivariateexpressions %} [Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression](https://arxiv.org/abs/2201.12468)
+
+<!-- would be great to benchmark some of these -->
 
 ## current state of integration tools
 

diff --git a/...al-posts/autoint/2024-10-10-motivation.md → _drafts/autoint/2024-10-10-motivation.md b/...al-posts/autoint/2024-10-10-motivation.md → _drafts/autoint/2024-10-10-motivation.md
@@ -9,6 +9,47 @@ scholar:
     bibliography: "auto-int.bib"
 ---
 
+
+
+Problems that people cared about
+
+- surges in electrical wires
+- predicting tides
+- missile guidance
+
+https://americanhistory.si.edu/collections/object-groups/mechanical-integrators/harmonic-analyzers-and-synthesizers
+
+<!-- and how did they solve them? mechanical integration? -->
+
+## Applications
+
+### Tides
+
+Laplace's tidal equations
+https://www.whoi.edu/cms/files/lecture03_21374.pdf
+https://www.google.com.au/books/edition/Tides/78bE5U7TVuIC?hl=en&bshm=rime/1
+
+### Planetary motion
+
+Antikythera
+http://dlib.nyu.edu/awdl/isaw/isaw-papers/4/
+
+### Bomb / missile guidance
+
+https://www.amazon.com/Bomber-Mafia-Temptation-Longest-Second/dp/0316296619
+
+
+Green's theorem
+
+Ball-and-disk integrator
+
+- the water integrator
+- the mechanical integrator https://www.youtube.com/watch?v=s-y_lnzWQjk
+- ford's integrator
+- planimeter
+- harmonic analyser
+- longimeter https://en.wikipedia.org/wiki/Steinhaus_longimeter
+
 # Motivation
 
 <!-- uses / motivation -->
@@ -55,4 +96,7 @@ And in general, any PDE.
 
 <!-- uses / vision -->
 
-Slot into existing autograd frameworks.
+Slot into existing autograd frameworks.
+
+
+<!-- entropy -->
diff --git a/...posts/autoint/2024-10-10-numerical-int.md → _drafts/autoint/2024-10-10-numerical-int.md b/...posts/autoint/2024-10-10-numerical-int.md → _drafts/autoint/2024-10-10-numerical-int.md
diff --git a/...-posts/autoint/2024-10-10-symbolic-int.md → _drafts/autoint/2024-10-10-symbolic-int.md b/...-posts/autoint/2024-10-10-symbolic-int.md → _drafts/autoint/2024-10-10-symbolic-int.md
diff --git a/_drafts/autoint/2024-10-10-theory.md b/_drafts/autoint/2024-10-10-theory.md
@@ -0,0 +1,13 @@
+---
+title: "The theory of symbolic integration"
+subtitle: "???"
+layout: post
+categories:
+    - "research"
+scholar:
+    bibliography: "auto-int.bib"
+---
+
+What needs to be answered in order to understand and trust symbolic integration?
+
+- 
diff --git a/_drafts/inbetween-posts/2024-07-20-capitalism.md b/_drafts/inbetween-posts/2024-07-20-capitalism.md
diff --git a/_drafts/inbetween-posts/2024-10-10-capitalism-london.md b/_drafts/inbetween-posts/2024-10-10-capitalism-london.md
@@ -10,10 +10,14 @@ categories:
 <!-- 
 a historical fiction story about living in 1800-1900s london.
 where capitalism is the most recent 'big idea'.
+a revolution has occured. down with the kings and queens.
+now we have freedom.
+
 and the city is a place of chaos and opportunity.
 
 the main point of this story is to show how scary true capitalism can be.
-pure freedom and competition.
+pure competition. economic darwinism.
+where the strong survive
 -->
 
 
@@ -22,6 +26,7 @@ ill need quotes from famous economists?
 along the lines of; 
 - the goal of capitalism is financial democracy.
 - capitalism is the best system for allocating resources.
+- people are __rewarded for their contributions to society__, with a token, we call this money. they are __free__ to spend that token as they see fit.
 - 
  -->
 
@@ -35,9 +40,8 @@ commoners did not have the freedom to trade.
 (apply for a license to trade? or get allocated to work as a ???)
 now, a man can be his own master.
 
-
-
 ***
+
 how can i build this story around a character?
 options;
 

diff --git a/...hnical-posts/pits/2024-08-10-pits-demo.md → _drafts/pits/2024-08-10-pits-demo.md b/...hnical-posts/pits/2024-08-10-pits-demo.md → _drafts/pits/2024-08-10-pits-demo.md
diff --git a/...hnical-posts/pits/2024-08-10-pits-flow.md → _drafts/pits/2024-08-10-pits-flow.md b/...hnical-posts/pits/2024-08-10-pits-flow.md → _drafts/pits/2024-08-10-pits-flow.md
diff --git a/...sts/point-waves/2024-10-09-pilot-waves.md → ...fts/point-waves/2024-10-09-pilot-waves.md b/...sts/point-waves/2024-10-09-pilot-waves.md → ...fts/point-waves/2024-10-09-pilot-waves.md
diff --git a/_drafts/technical-posts/autoint/2024-10-10-history.md b/_drafts/technical-posts/autoint/2024-10-10-history.md
diff --git a/...ts/inbetween-posts/tvs/2024-11-01-docs.md → _drafts/tvs/2024-11-01-docs.md b/...ts/inbetween-posts/tvs/2024-11-01-docs.md → _drafts/tvs/2024-11-01-docs.md
-Original file line number
+Diff line change
@@ Expand Up @@
     {% bibliography --cited %}
-    ---
-    title: "Calculus"
-    ---
     Six pillars of calculus;
     - limits
@@ Expand Down @@