don't let LLMs erode first principles thinking

2025-01-12

background

consider a trader who is backtesting a series of alphas that target the 30 DTE contracts on the S&P 500 Index options chain. to increase sample size, the trader uses a window of +/- one day from the target.

the trader considers the following:

• $\mathit{\text{if presented with multiple equivalent contracts on a given trading day,}}$ $\mathit{\text{how should the backtest and live trading code handle DTE selection?}}$

in order to avoid adding complexity where unncessary, the trader starts question the premise:

• $\mathit{\text{under what circumstances does such a choice even exist?}}$

use an llm!

through the selectively biased lens of my day-to-day experiences, it seems increasingly more common to default to $\mathit{\text{machine-first}}$ thinking instead of $\mathit{\text{human-first}}$ thinking. stated another way, there seems to be an upward trend of $\mathit{\text{outsourcing logic and reasoning}}$.

for clarity, $\mathit{\text{machine-first}}$ thinking is not the same as $\mathit{\text{machine-aided}}$ thinking. in my mental model, $\mathit{\text{machine-aided}}$ thinking is a subset of $\mathit{\text{human-first}}$ thinking:

• (h)uman-first | ${\text{conjecture}}^{\text{h}}\to {\text{reasoning}}^{\text{h}}\to {\text{outcome}}^{\text{h}}$
• (m)achine-first | ${\text{conjecture}}^{\text{h}}\to {\text{reasoning}}^{\mathbf{\text{m}}}\to {\text{outcome}}^{\text{m}}$

of course, $\mathit{\text{machine-first}}$ thinking is represented in a reductive manner above; to capture the notion that a human supervises the $\mathbf{\text{reasoning}}$, let us expand the notation a bit:

• (m)achine-first | ${\text{conjecture}}^{\text{h}}\to {\text{reasoning}}^{C(1-\epsilon )\mathbf{\text{m}}+\epsilon \text{h}}\to {\text{outcome}}^{\text{*}}$

the expression of $C(1-\epsilon )\text{m}+\epsilon \text{h}$ simply captures:

• if a human spends $\epsilon$ effort supervising, the machine spends $1-\epsilon$ effort reasoning with whatever catch-all constant $C$ satisfies the inequality between human-to-machine reasoning.

for example, one might say that someone who blindly accepts machine reasoning has $\epsilon =0$:

• ${\text{conjecture}}^{\text{h}}\to {\text{reasoning}}^{C\mathbf{\text{m}}}\to {\text{outcome}}^{\text{m}}$

furthermore, by definition, $\mathit{\text{human-first}}$ thinking blindly rejects machine reasoning i.e. $\epsilon =1$:

• ${\text{conjecture}}^{\text{h}}\to {\text{reasoning}}^{\mathbf{\text{h}}}\to {\text{outcome}}^{\text{h}}$

while i am admittedly a staunch contrarian when it comes to the topic of LLMs, i do concede they have realized utility in some applications. my intention is not to debate the utility curve of LLMs; rather, i aim to invite deeper thinking about effects of human-LLM interactions.

$\mathit{\text{outsourcing logic and reasoning}}$ may be perfectly valid in some contexts, but not all contexts. what i worry about most is that continuous exposure to $\mathit{\text{outsourcing logic and reasoning}}$ in valid contexts erodes the human detection mechanism responsible for drawing that line in the first place.

as of writing, machines cannot reason from first-principles; therefore, humans must become more resilient in explicitly protecting the spaces in which $\mathit{\text{outsourcing logic and reasoning}}$ may lead to less than ideal outcomes. a serendipitous, cherry-picked personal example follows for those interested in virtually useless proofs.

virtually useless proof

if one were to take trading days $T$ and weekends $W$ as such:

$$T=\{0,1,2,3,4\}$$

$$W=\{5,6\}$$

if today $t\in T$ and target DTE $D$, one might observe that deriving day of the week $d\in \{T\cup W\}$ for $D$ is simply:

$$(t+D)mod7=d$$

for 30$\pm 1$ DTE strategies, one is never presented two equivalent choices for days-to-expiry in non-holiday conditions.

using the above, one observes when the possibility of a choice may arise:

$$d\in W⟺t\in \{3,4\}$$

that is to say, a choice may only happen on Thursday or Friday. given, two choices: $D_{-1}\text{'}$ and $D_{+1}\text{'}$ representing 29 DTE and 31 DTE, respectively:

$$(3+D_{-1}\text{'})mod7=4$$

$$(3+D_{+1}\text{'})mod7=6$$

$$(4+D_{-1}\text{'})mod7=5$$

$$(4+D_{+1}\text{'})mod7=0$$

thus, $t=3$ is always presented $D_{-1}\text{'}$ while $t=4$ is always presented $D_{+1}\text{'}$.

visual proof

using $0$ to indicate the current trading day, there exists a nice visual proof; make note of when $t=3$ (thursday) is the current day $\left(0\right)$ and $t=4$ (friday) is the current day $\left(0\right)$.

closing thoughts

questioning assumptions and re-stating base truths often can combat misguided efforts, such as adding complexity where none is required. this is the essense of $\mathit{\text{human-first}}$ thinking that must continue to be protected in the age of $\mathit{\text{outsourcing logic and reasoning}}$.

as always, it is helpful to take a step back every now and then and ask,

$\mathit{\text{why?}}$

appendix: llm responses

note: in no way are the results below meant to be cherrypicked, i do not pay for any LLM services. as such, the results below are derived using the "smartest" free model i could select.

additionally, there's usually more than one way to do the same thing; i am sure there exists a "$\mathit{\text{machine-first}}$ power user" who could likely construct the proof above (or some similarly acceptable proxy of the proof) in a similar amount of time that i spent constructing it $\mathit{\text{human-first}}$... perhaps even shorter?

Prompt

SPXW options have 5 daily expirations (Monday-Friday) I want to trade an options strategy that buys 30 DTE contracts, but I want to include +/-1 day in my range (29-31 DTE) to ensure I get enough samples when 30 DTE isn't available.

Give me a list by weekday (Monday-Friday) of which expiries (29, 30, 31 DTE) are available.

ChatGPT Response

Monday

• 29 DTE: Tuesday 4 weeks ahead
• 30 DTE: Monday 4 weeks ahead
• 31 DTE: Friday 5 weeks ahead

Tuesday

• 29 DTE: Wednesday 4 weeks ahead
• 30 DTE: Tuesday 4 weeks ahead
• 31 DTE: Monday 4 weeks ahead

Wednesday

• 29 DTE: Thursday 4 weeks ahead
• 30 DTE: Wednesday 4 weeks ahead
• 31 DTE: Tuesday 4 weeks ahead

Thursday

• 29 DTE: Friday 4 weeks ahead
• 30 DTE: Thursday 4 weeks ahead
• 31 DTE: Wednesday 4 weeks ahead

Friday

• 29 DTE: Monday 4 weeks ahead
• 30 DTE: Friday 4 weeks ahead
• 31 DTE: Thursday 4 weeks ahead

Notes:

• SPXW options expire daily, so you will always have an expiration available for 29, 30, or 31 DTE.
• Adjusting your strategy to include this 3-day range ensures sufficient samples regardless of your starting point in the week.

Gemini Response (2.0 Flash)

Here's a breakdown of the available SPXW expirations (29, 30, and 31 days to expiry) by weekday:

• Monday: 31 DTE, 30 DTE, 29 DTE
• Tuesday: 30 DTE, 29 DTE
• Wednesday: 29 DTE, 30 DTE
• Thursday: 30 DTE, 31 DTE
• Friday: 31 DTE, 30 DTE, 29 DTE