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News & General Discussion => General Discussion => Topic started by: PopeyesPappy on October 12, 2025, 01:10:24 PM

Title: How to and not to use AI
Post by: PopeyesPappy on October 12, 2025, 01:10:24 PM
I used the ChatGPT and DeepSeek AI models to develope a coulpe of breif what is AI, what are its limitations, and how to use it general guides including specific use cases for developing proofs. Here is what each of them came up with. 

Quote from: ChatGPTUsing AI as an Effective Tool
🧠 What AI Like ChatGPT and DeepSeek Actually Is

Artificial Intelligence systems such as ChatGPT or DeepSeek are Large Language Models (LLMs) — advanced text-generation engines trained on vast amounts of writing.
They don't truly "think" or "know." Instead, they predict which words are most likely to come next based on patterns they've learned.

Imagine a hyper-literate intern who's read most of the internet but doesn't actually understand — it just knows how ideas are usually expressed and connected.

⚙️ How It Works (Simplified)

Training: The model studies billions of sentences from books, articles, and code.
Representation: It encodes meaning as mathematical relationships between words and ideas.
Prediction: When you type a prompt, it generates text one word at a time, each word chosen for the highest contextual probability.
Fine-Tuning: Human reviewers train it to sound clear, safe, and useful.

✅ What AI Is Good At

Information and Explanation – summarizing or clarifying complex topics.
Writing and Editing – drafting, rewriting, and adjusting tone or style.
Research and Learning – outlining arguments or comparing perspectives.
Data and Coding – writing formulas, scripts, or cleaning data.
Planning and Organization – creating checklists, timelines, or outlines.
Brainstorming and Creativity – generating ideas, names, or themes.
Education and Tutoring – explaining topics step-by-step or providing practice questions.

Example uses:

"Explain relativity like I'm 15."
"Draft a 200-word project summary for management."
"Generate ten names for a woodworking supply business."

🚧 Limitations and Risks

1. No true understanding – It doesn't reason, it predicts. Always verify facts.
2. Hallucinations – It may invent wrong information while sounding confident.
3. Outdated knowledge – Training data may stop months or years ago.
4. Context limits – Long conversations can exceed its working memory.
5. Bias – It can mirror social or political bias from its sources.
6. Lack of common sense – It can miss contradictions obvious to people.

How to handle these: verify details, ask for multiple viewpoints, and specify that it should "evaluate" or "test" instead of "prove."

💡 How to Use AI Effectively

Give context
Example: "Act as a technical writer preparing a summary for a government contracting officer."

Be specific
Example: "Write 150 words in plain language with three bullet points and a short conclusion."

Iterate
Treat it like a conversation — refine until the tone and content are right.

Ask for structure
Example: "List the top three arguments for each side in bullet form."

Debug poor answers

"Too vague — give examples."
"Explain each reasoning step."
"Reformat as numbered points."

Avoid confirmation bias
Don't ask "Prove X." Ask "Evaluate whether X holds."
Neutral phrasing produces more objective reasoning.

⚖️ The Human–AI Partnership

AI is a tool, not an oracle.
Treat it as a junior partner that drafts, organizes, and analyzes rapidly, while you supply expertise, verification, and final judgment.

Advanced Example: Using AI for Logical or Mathematical Proofs

When developing proofs, it's easy to lead AI to confirm your own assumptions.
The following process keeps reasoning neutral and verifiable.

🧩 The Audit-First Proof Framework
Core Principles

Falsification before verification – try to break the claim before proving it.
Adversarial collaboration – make the AI argue both for and against.
Auditable artifacts – record premises, lemmas, inference rules, and dependencies.
Neutral framing – say "evaluate whether," not "prove."
Transparency over eloquence – prefer step-by-step logic to flowery text.

Step-by-Step Workflow

Phase 0 – Problem Contract
Write the claim formally with domain and quantifiers.
List explicit and implicit assumptions (your "assumption register").
Decide if it's a logical, mathematical, or empirical claim.

Phase 1 – Pre-Proof Audit
Purpose: look for failure before success.
Prompt pattern:
Evaluate whether the following claim holds.
1. Restate formally (use symbols if possible).
2. List explicit premises and any hidden assumptions.
3. Generate three plausible counterexamples or failure modes.
4. Test each counterexample and record what happens.
5. If any counterexample works, stop and restate the claim more precisely.
6. If none work, proceed to proof construction.

Claim: [your statement here]

Phase 2 – Structured Proof Construction
Purpose: build a proof that can be audited.
Prompt pattern:
Construct a structured proof with auditable artifacts:
- List all premises (P1, P2, ...) and justify each.
- State intermediate lemmas and show how they depend on each other.
- Label every inference with the rule or theorem used.
- Check boundary or edge cases.
- Note which counterexamples from Phase 1 are resolved.

Keep a short "proof ledger" for tracking steps:
Step number
Statement
Rule or theorem used
What it depends on
Notes or justification

Phase 3 – Adversarial Review
Purpose: stress-test the reasoning.
Prompt pattern:
Conduct a formal audit with three roles:
1. Verifier – check that each inference is valid.
2. Gap-Finder – identify unstated assumptions and biggest logical jump.
3. Edge-Tester – test extreme and boundary cases.

Then score the proof from 0–10 on:
- Formal precision
- Assumption explicitness
- Inference validity
- Counterexample coverage
- Separation of logic from rhetoric

Phase 4 – Cross-Representation Check

Ask the AI to restate the proof in another structure or notation.
If the meaning changes, the original text was ambiguous — correct it.

Phase 5 – Finalization

Replace tentative wording ("suggests," "appears") with formal connectives ("therefore," "thus").
Keep all artifacts:

Final claim
Premises and assumption register
Lemmas and dependency notes
Edge-case report
Audit scores

Add-Ons for Real-World or Empirical Proofs
If the claim involves data or observation:
Specify data sources and measurement definitions.
Define what evidence would falsify the claim.
Include reproducible references.

Quick Prompt Library

Neutral evaluation

Evaluate whether [claim] holds.
1. Formalize it.
2. List assumptions.
3. Try to falsify.
4. If still valid, derive step-by-step with explicit rules.
5. Provide a five-point audit summary.


Adversarial dialogue

Run a four-round debate between:
• Proponent – defends the claim
• Skeptic – challenges it
Then judge which side remains logically consistent and why.

Proof auditor

Audit this proof for:
a) Unstated assumptions
b) Largest logical leap
c) Circular reasoning
d) Untested edge cases
e) Suggested improvements
Then give a rigor score from 0–10.

Example: Applying the Framework

Claim: Every continuous function on ℝ is differentiable.

Phase 1 – Audit:
Try to falsify.
Counterexample: 𝑓(𝑥) = ∣𝑥∣ is continuous everywhere but not differentiable at 𝑥 = 0.

✅ A counterexample exists → claim is false.

Next step: Restate and refine the claim.
"Every continuously differentiable function is differentiable."
Re-run the workflow with the new, tighter statement.

🧭 Final Mindset

AI can simulate logical reasoning, but it mirrors your framing.
If you ask it to prove, it will agree; if you ask it to test, it will think.
Use this framework to turn AI from an echo chamber into a disciplined reasoning partner — one that helps you build proofs and arguments that can survive deliberate, systematic attempts to break them.

Quote from: DeepSeekHow to Use AI as an Effective Tool: From Fundamentals to Advanced Proofs
Hey everyone, I've been deep-diving into how to use AI tools like ChatGPT and DeepSeek effectively. I wanted to share a practical guide that starts with the basics and goes into a specific advanced use case. Here's what I've learned.

Part 1: What Is AI Like ChatGPT/DeepSeek?
At its core, an AI like this is a Large Language Model (LLM). Think of it as a pattern-matching engine on a massive scale. It has been trained on a huge portion of the internet—books, articles, code, and forums.

How it Works (Simplified): The AI doesn't "think" or "understand." It predicts the next most likely word in a sequence, over and over, based on the patterns it learned during training. Your prompt sets the pattern, and it continues it.

Part 2: What It's Good At (And Not So Good At)
Think of AI as a brilliant, fast, but sometimes overly confident intern.

Its Key Strengths (What to Leverage):

Information Synthesis: Explaining complex topics by pulling from many fields. It's a fantastic tutor or summarizer.

Drafting & Editing: Quickly generating first drafts of emails, essays, code, and reports. Great for rephrasing or formatting.

Brainstorming: Generating lists of ideas, names, angles, and creative concepts. A boundless brainstorming partner.

Structured Tasks: Excelling at tasks with clear rules like writing code, creating tables, or following a style guide.

Summarization: Condensing long documents or articles into key points.

Its Major Limitations (What to Watch Out For):

Hallucinations: It can confidently make up facts, quotes, and citations that sound plausible. Never trust it as a single source of truth.

No True Understanding: It manipulates symbols based on patterns, but doesn't know what they mean. It lacks common sense.

Bias: It can reflect and amplify the societal, racial, and gender biases present in its training data.

Out-of-Date Knowledge: Its knowledge has a cut-off date and isn't live. It doesn't know about recent events.

Verbosity: It often defaults to wordy, generic language to sound authoritative and avoid being wrong.

Part 3: How to Prompt Effectively: The C.O.A.C.H. Method
To get the best results, don't just ask—instruct. Use the C.O.A.C.H. framework to build your prompts:

C - Context: Set the stage. What's the background?

O - Objective: What is the specific task or goal?

A - Action: What exactly should the AI do? (Write, list, explain, etc.)

C - Constraints: What are the rules? (Tone, length, things to avoid)

H - Handhold: Specify the format. (e.g., "in a table," "as bullet points")

Example:

Bad Prompt: "Write a blog post about productivity."

Good Prompt: "Context: I run a blog for remote software engineers. Objective: Write a blog post introducing the 'Time-Blocking' method. Action: Explain the method and provide a step-by-step guide. Constraints: Tone should be empathetic and expert, under 800 words. Handhold: Use clear headings and a bulleted list for the steps."

Part 4: A Specific Use Case: Developing Logical Proofs Without Bias
This is where it gets really interesting. The biggest danger when using AI for logic is confirmation bias amplification—the AI will try to give you the proof you want, not the correct one. It's an eager-to-please intern who will hide flaws to make you happy.

To combat this, use the Audit-First Proof Framework.

The Core Idea: Force the AI to try to disprove your idea before it tries to prove it.

The Workflow:

1. Phase 1: Pre-Proof Scoping & Counterexample Testing

Goal: Try to break your claim before you even start building a proof.

Prompt:

text
Evaluate whether this claim holds. Follow this sequence:

1. RESTATE: Formalize the claim with precise mathematical notation.
2. PREMISES: List all explicit premises and identify implicit assumptions.
3. COUNTEREXAMPLES: Generate three plausible counterexamples or failure modes.
4. TEST: Verify whether each counterexample actually invalidates the claim.
5. DECISION: Only if all counterexamples fail, proceed to proof development.

Claim: [Your mathematical statement here]
2. Phase 2: Structured Proof Construction

Goal: Build a proof with visible scaffolding, not just a persuasive narrative.

Prompt:

text
Develop a proof with these auditable components:

- PREMISE REGISTER: List all premises with justifications.
- LEMMA DEPENDENCY: State intermediate lemmas and show their dependencies (Lemma A -> Lemma B -> Theorem).
- INFERENCE TRACKING: For each step, name the logical rule used (e.g., modus ponens, universal instantiation).
- BOUNDARY VERIFICATION: Test edge cases and extreme parameters.
- COUNTEREXAMPLE DEFENSE: Explain how this proof addresses the counterexamples from Phase 1.
3. Phase 3: Adversarial Audit

Goal: Stress-test the proof as harshly as possible to find hidden flaws.

Prompt:

text
Conduct a formal proof audit using three roles:

ROLE 1: VERIFIER - Check each inference for validity and correct rule application.
ROLE 2: GAP ANALYST - Identify the largest logical jump and all unstated assumptions.
ROLE 3: STRESS TESTER - Attack the proof with boundary cases and alternative interpretations.

Score this proof 0-10 on:
- Formal Precision (notation clarity)
- Assumption Explicitness
- Inference Validity
- Counterexample Coverage
- Logic/Rhetoric Separation

The Key Mindset Shift: Stop asking "Can you prove X?" and start commanding "Help me evaluate whether X is true, and show all your work." This transforms the AI from a confirmation engine into a rigorous reasoning partner.
Title: Re: How to and not to use AI
Post by: Gawdzilla Sama on October 12, 2025, 01:23:43 PM
If AI meant "Actual Intelligence" the world might become a better place.                                                     
Title: Re: How to and not to use AI
Post by: Nobody on October 12, 2025, 03:31:59 PM
At least I know how to use A1!  🤣
Title: Re: How to and not to use AI
Post by: PopeyesPappy on October 12, 2025, 03:46:22 PM
Quote from: Gawdzilla Sama on Today at 01:23:43 PMIf AI meant "Actual Intelligence" the world might become a better place.                                                     

It's a tool. Wether or not it's a good one depends on how you use it.
Title: Re: How to and not to use AI
Post by: PopeyesPappy on October 12, 2025, 03:46:35 PM
Quote from: Nobody on Today at 03:31:59 PMAt least I know how to use A1!  🤣

Eww. If you are using A1 you are doing it worong from the get go.
Title: Re: How to and not to use AI
Post by: Nobody on October 12, 2025, 04:22:19 PM
I was just referencing the Secretary of Education! 🤣