Test
Published: 28 May 2024
Some text here.
We can try a simpletest of a parenthetical.
Now testing a math-typeparenthetical.
And next…
An inclusion of a code-typeparenthetical.
I recently discovered one that surprised me. It came from talking to one of the folks in charge of the reproduction of the Globe near where it originally stood. They invite experienced Shakespearians to perform a play with little rehearsal. Over time, the production matures as the cast anneals with each other and the place. A thing to look for is how the physical nature of the place informs the plays. The plays are video taped at the beginning of the run and at the end.
At some point, a clever student will pull out these videos and note the spatial effects on the dynamics of the mature performances. They interest me greatly and in framethrower, we proposed analyzing and annotating these videos in the context of a three dimensional model of the theater. The reconstruction is not quite accurate I believe and my visit was to query whether they would more seriously consider the scholarship of Frances Yates into the nature of the space.
Yates was able to place the Shakespeare company in a certain set of traditions that now would be called esoteric, and not likely to be touched by conservative institutions like those that run the reconstruction. I describe all this in my GeoKabbailtter history project elsewhere in this site.
Apart from those really interesting dynamics are some that do not have the esoteric baggage. You should know that the theater had two areas for viewers. One was cheap; the poor people would pay very little and stand on the dirt floor in the center of the theater. We did not appreciate until the reconstruction that their heads were about level with the stage.
The more expensive seats were actual seats in booths that formed much of a circle around the stage. (This design was novel at the time and why the theater was named the Globe.) As it happens, there are many times in the plays where an actor breaks the fourth wall and addresses the audience. Standing on the stage, one can see that it is easy to make a clear distinction between the classes of viewers. Looking through the plays, one can find many cases where it is clear that the playwright is playing one group off another, indicated by both the sophistication of the language and the complexity of the concept.
This nutshell episode in Hamlet is one such. (Another is in King Lear.) Hamlet says: “I could be bounded in a nutshell, and count myself a king of infinite space, were it not that I have bad dreams.” When the original site was excavated, the standing room area was found to be covered with deep layers of nutshells from nuts that were sold through the performance. The continuous crunching of feet on these would have been well known to the audience. The Globe itself was nutshell shaped.
(defn dfs
"Depth first search. Short form of the method passes through all the nodes of the graph even if it's disconnected .
(nodes-fn graph) expected to return list of all the nodes in the graph.
(child-fn graph node) expected to return list of all the nodes linked to the given node.
Returns hash-map where nodes are associated with a pair :idx, :leader.
:idx stores finishing index of the node traversal (post-order counter)
:leader first finishing index of the current DFS."
([graph nodes-fn child-fn]
(second
(reduce ;; Start DFS from each node of the graph
(fn [[idx result passed :as args] next-node]
(if (not (passed next-node)) ;; Don't do DFS if node is marked
(dfs idx idx result passed graph next-node child-fn)
args))
[0 {} #{}] ;;Initial index, result, set of passed nodes
(nodes-fn graph))))
([idx leader result passed graph node child-fn]
(let [[idx result passed]
(reduce (fn [[idx result passed :as args] child-node]
(if (not (passed child-node))
(dfs idx leader result passed
graph child-node child-fn)
args))
[idx result (conj passed node)]
(child-fn graph node))]
[(inc idx)
(assoc result node {:idx idx :leader leader})
passed])))
(defn pass-two
"Calls DFS making sure that traversal is done in the reverse :idx order."
[graph result child-fn]
(let [nodes-fn
(constantly (->> result
;;Sort by :idx in reverse order
(sort-by (comp :idx second)) reverse
;;Return only nodes
(map first)))]
(dfs graph nodes-fn child-fn)))
(defn scc
"Finds strongly connected components of the given directed graph.
Returns lists of nodes grouped into SCC.
(nodes-fn graph) expected to return list of all the nodes in the graph.
(incoming-fn graph node) expected to return all the nodes with transitions towards the given node.
(outgoing-fn graph node) expected to return all the nodes with transitions from the given node."
[graph nodes-fn incoming-fn outgoing-fn]
(let [result (dfs graph nodes-fn incoming-fn)The Lorenz Equations
\[\begin{matrix} \dot{x} & = & \sigma(y-x) \dot{y} & = & \rho x - y - xz \dot{z} & = & -\beta z + xy \end{matrix} \]
The Cauchy-Schwarz Inequality
\[ \left( \sum_{k=1}^ n a_k b_k \right)^2 \leq \left( \sum_{k=1}^ n a_k^2 \right) \left( \sum_{k=1}^ n b_k^2 \right) \]
A Cross Product Formula
\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \]
The probability of getting \(k\) heads when flipping \(n\) coins is:
\[P(E) = {n \choose k} p^ k (1-p)^{ n-k} \]
An Identity of Ramanujan
\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]