Background

In the 60s, economists that the pricing of options were independent of pricing of underlying assets. Nowadays, we can see that, if the underlying assets were obeying of a Brownian Motion, there is no additional degree of freedom that options can bring: that knowing the stocks will tell you exactly through a DiffEQ how the option will evolve.

The idea, then, is that you can replicate options: by dynamically buying and selling pairs of securities in the same way as the option, your new portfolio can track the option exactly.

function that returns the input that maximizes the expression.

finding argmax

direct optimization

Typical maximization system. Take derivative, set it to 0, solve, plug in, solve. THis is pretty bad during times are not differentiable.

gradient ascent

We take steps following the direction

\begin{equation} \theta_{1j} = \theta_{0j} + \eta \pdv{LL(\theta_{0})}{\theta_{0j}} \end{equation}

additional information

argmax of log

see argmax of log

• When you make an array, you are making space for each element
• When you create a pointer, you are making space for 64 bit address
• arrays “decay to pointers”: when you identify an array by name, you are sharing the location of the leading element
• &arr gets an address to the FIRST element — don’t do this, &ptr gets the pointers’ address

Array is a special type that represent a segment of contiguously allocated memory. You can’t reassign an array to be equal to a new array.

Require: analyze movie + quote [story + bellows]

ineffability of language vs. Sapire-Wolf

Foreignizing Time in Heptopod B

Louise’s ability to re-express her temporally-independent thoughts in English after learning Heptopod B represents a successful act foreignization of Heptopod thought for an English L1 audience despite this audience’s supposed limitations in understanding temporally-independent concepts according to the Sapir-Wholf Hypothesis.

Heptopod B does not have temporality

• RUSSIAN SCIENTIST: “Their final words translate to, “There is no time, many become one.” I fear we have all been given weapons because we answered the timeline wrong, please, if you - -”
• “Explain it by saying that light minimized the time needed to travel to its destination, and one saw the world as the heptapods saw it.”

So it seems like quintessential Sapir-Wholf: time hard to express with Heptopod, and so their way of thinking work around it.