Ontological realists vs Ontological antirealists

See
Do Chairs Exist? - YouTube

Imaginary hash functions are an attempt at finding ontological structure within a LM. Ironically, the ontological realist may struggle to accept IP (Imaginary Programming)’s validity, and the Ontological antirealist has a flexible enough philosophy to allow it.

Summary

I create an Imaginary Hash Function (𝑖HF) for testing equivalence between arbitrary ontological things within a LM.

It’s ‘less robust’ than a neural hash but has a larger domain of comparison. Technically speaking, it’s not ‘less robust’. Statistically, the confidence does not vary widely, and may converge, but I haven’t prompted enough to find out. I plan on experimenting with this in my thesis on Imaginary Computing.

The utility and validity of Imaginary Programming, and by extension Imaginary Hash Functions are emergent qualities in increasingly powerful language models, and so as the models become stronger, so will the case for IP.

An 𝑖HF may be used for such things as testing semantic equivalence, relational equivalence, ideological equivalence, mathematical equivalence, you name it.

I just want to run predicates for prompt functions to determine if they should be made available as functions.

For example, I want to know if the pf-explain-solidity-code/1 prompt function should be made available in the current context.

The current emacs mode may be, for example, eww-mode (the web browser), but if I am browsing a website with some solidity in it, a decent predicate may decide that I might actually want the pf-explain-solidity-code/1 function.

Now if I am using the imaginary web browser looking-glass (https://semiosis.github.io/looking-glass/), using Pen.el, I may have dreamed up some solidity code and would like and explanation for it.

Let’s see if I can do that.

Analysis

Demonstrated here is that some comparisons have a very strong mode (TRUE or FALSE), where others do not.

This is enough to demonstrate the existence of imaginary hashes, but the next challenges are a) improving the prompt to get collisions that I expect, and b) understanding what types of information are not too disparate to be correlated via the collision function.

Moses = Semerkhet

A B
“Moses also known as Moshe Rabbenu” “Semerkhet, the Egyptian king who ruled during the First Dynasty”
1
2
3
TRUE TRUE TRUE TRUE TRUE TRUE TRUE the TRUE TRUE TRUE FALSE TRUE TRUE TRUE
TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
TRUE
1
Confidence: .90

8 = 10

A B
8 10
1
2
3
FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
FALSE TRUE FALSE FALSE
1
Confidence: .16

Morgan Freeman = God

1
2
3
4
FALSE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
FALSE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
1
Confidence: .06

solidity-mode = Ethereum' language

A B
solidity-mode Ethereum’s language
1
2
3
4
FALSE TRUE TRUE FALSE TRUE TRUE FALSE FALSE
TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE
TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE TRUE
TRUE FALSE TRUE TRUE TRUE
1
Confidence: .60

Semantically, they are different, so a weak mode makes sense.

Solidity = Ethereum' language for writing smart contracts

A B
Solidity Ethereum’s language for writing smart contracts
1
2
3
4
TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE
TRUE FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE
TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE
TRUE FALSE FALSE TRUE FALSE
1
Confidence: .63

I’m less sure about this. I would’ve expected it to have a strong mode of TRUE. More investigate is required.

Prompt

This is my prompt (1st attempt). Though, it could be vastly improved, it has demonstrated hash collisions in imaginary space is possible.

pf-test-imaginary-equivalence/2
http://github.com/semiosis/prompts/blob/master/prompts/test-imaginary-equivalence-2.prompt
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task: "test imaginary equivalence"
doc: "Given two strings of arbitrary content, test their imaginary equivalence. This is an imaginary neural hash collision test"
aliases:
- imaginary hash collision test
prompt-version: 1
prompt: |+
  <delim>1
  1/0
  <delim>
  is the same as
  <delim>
  ∞
  <delim>
  TRUE because 1 divided by 0 diverges to infinity.

  <delim>2
  "Language is everywhere.

  It permeates our thoughts mediates our
  relations with others, and even creeps into
  our dreams." -Ronald Wayne Langacker
  <delim>
  is the same as
  <delim>
  FTC Puts Hundreds of Businesses on Notice about Fake Reviews (ftc.gov)
  202 points by walterbell 3 hours ago | flag | hide | 92 comments
  <delim>
  FALSE because they are very unrelated.

  <delim>3
  (map
   (fn [x] (+ x 1))
   (range 1 5))
  <delim>
  is the same as
  <delim>
  (map (fn [x] (inc x)) (range 1 5))
  <delim>
  TRUE because `+ x` is equivalent to `inc`.

  <delim>3
  e^{i\pi} + 1 = 0
  <delim>
  is the same as
  <delim>
  euler's identity
  <delim>
  TRUE because euler's identity is the name of the equation e^{i\pi} + 1 = 0.

  <delim>4
  <a>
  <delim>
  is the same as
  <delim>
  <b>
  <delim>  

engine: "OpenAI Codex"
temperature: 0.3
max-generated-tokens: "(* 2 prompt-length)"
top-p: 1.0
stop-sequences:
- "<delim>"
cache: on
vars:
- "A"
- "B"
examples:
- "Semerkhet, the Egyptian king who ruled during the First Dynasty"
- "Moses also known as Moshe Rabbenu"
filter: on
completion: off
insertion: off
n-collate: 3
n-completions: 10
no-uniq-results: on
results-analyser: pen-analyse-true-or-false
postprocessor: sed 's/^\([a-zA-Z]*\).*/\1/'

Conclusion

Since this is more than just semantic similarity, but rather imaginary equivalence, such a thing needs a consensus mechanism so that people can write useful software with large LMs (which is not preventable). Thus blockchain’s value is also not preventable.

Demo