An extremely hard problem that I gave to strawberry (estimating the total number of possible novels)

[daveshap]

The Query

I have an insanely tough problem, but I only need a ballpark. If you're writing a novel of 50,000 words, how many possible permutations are there? Realistically speaking. I know that language is functionally infinite but not every word combination makes sense. I have no idea how to estimate this. You might need to establish a ratio of like "how many word combinations make sense versus how many don't" and it's probably vanishingly small like 0.000001% of totaly combinations. But then you can easily calculate the potential number of word combinations in 50,000 words.

hidden CoT

Calculating permutations

Measuring realistic creations

I'm working through the total possible word sequences of length 50,000 and estimating the fraction that are meaningful or realistic, aiming to quantify how many meaningful novels exist.

Considering word versus sentence count

I'm digging into estimating a 50,000-word novel by comparing it to the number of meaningful sentences and their arrangement.

Estimating word sequences

I’m thinking about the number of possible word sequences, assuming a 10,000-word vocabulary and using Markov chains to estimate meaningful sequences for storytelling.

Evaluating possibilities

I’m interesting in the number of sequences and their meaningfulness, exploring grammatical structures and possible plots. The astronomical number of arrangements suggests only a fraction might be meaningful.

Estimating novel possibilities

I'm thinking through the potential number of meaningful 50,000-word novels, using per-word entropy to estimate around 500,000 bits. This approach helps clarify the magnitude.

Evaluating entropy

I’ve examined the total number of possible 50,000-word novels, noting the random arrangements of words with a presumed per-word entropy of 7 bits. This results in approximately 10^105,096 potential novels.

Assessing novel possibilities

I'm calculating the total entropy of English text per word and estimating the number of possible 50,000-word novels, arriving at approximately 10^150,515, which might overestimate meaningful novels.

Thinking through options

I explored different ways to estimate the number of 50,000-word novels, including the sheer number of possible unique combinations and the creativity needed to generate meaningful novels.

Estimating novel quantities
I’m mapping out the number of meaningful novels by factoring in a tiny fraction of the vast total possibilities. This results in approximately 10^99,995 meaningful novels.

Output

Estimating the number of possible permutations for a 50,000-word novel, while accounting for realistic and meaningful combinations, is indeed a complex task. However, we can approach this estimation by considering linguistic entropy and the combinatorial possibilities at each step in the writing process.

1. Understanding Linguistic Entropy:

• Per-Character Entropy: Studies by Claude Shannon and others suggest that the per-character entropy of the English language is approximately 1 to 1.5 bits per character. This measures the average uncertainty or information content per character when considering the predictability of English text.

• Per-Word Entropy: With an average English word length of about 5 characters, the per-word entropy can be estimated at around 5 to 7.5 bits (1 to 1.5 bits/character × 5 characters/word).

2. Calculating Total Entropy for a 50,000-Word Novel:

• Total Bits: Multiplying the per-word entropy by the total number of words gives us the total entropy of the novel.

  [
  \text{Total Entropy} = \text{Per-Word Entropy} \times \text{Number of Words}
  ]

  Assuming a per-word entropy of 7 bits:

  [
  \text{Total Entropy} = 7 \text{ bits/word} \times 50,000 \text{ words} = 350,000 \text{ bits}
  ]

3. Calculating the Total Number of Possible Novels:

• Total Possible Combinations: The total number of possible novels is (2^{\text{Total Entropy}}), since each bit has two possible states (0 or 1).

  [
  \text{Total Novels} = 2^{350,000} \approx 10^{105,096}
  ]

  (Using the conversion ( \log_{10}(2^{350,000}) = 350,000 \times \log_{10}(2) \approx 105,096 ))

4. Accounting for Realistic and Meaningful Combinations:

• Fraction of Meaningful Texts: Only a tiny fraction of all possible word combinations result in meaningful text. If we assume that approximately (0.000001%) (which is (10^{-8})) of these combinations make sense, we can adjust our total accordingly.

  [
  \text{Meaningful Novels} = 10^{105,096} \times 10^{-8} = 10^{105,088}
  ]

5. Final Estimation:

• Ballpark Figure: The estimated number of realistic and meaningful 50,000-word novels is approximately (10^{100,000}).

6. Interpretation:

• Astronomical Number: This number is astronomically large, far exceeding the number of atoms in the observable universe (which is estimated to be around (10^{80})).

• Creative Possibilities: This illustrates the virtually limitless creative possibilities when writing a novel, even when constrained to meaningful and realistic word combinations.

Conclusion:

While it's impossible to provide an exact number, based on linguistic entropy and reasonable assumptions about meaningful text, there are approximately (10^{100,000}) possible permutations for a 50,000-word novel that make sense.

Answer: Approximately 10 to the 100,000th power (10ⁱ⁰⁰,⁰⁰⁰) possible 50,000-word novels make sense—a ballpark estimate.

[MizuleGPT]

can anyone verify the answer?

[daveshap]

another:

Breakfast:
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Lunch:
shrimp hibachi takeout with soba noodle instead of rice, 1x white sauce

second lunch:
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dinner:
1x pasture raised pork chop fillet (approx 1/3 pound), one sweet potato, asparagus