Making AIs think: Deepseek R1 AI

 E.g. this one: https://huggingface.co/spaces/llamameta/DeepSeek-R1-Chat-Assistant-Web-Search 

User:  River puzzle🚣‍♂️, goat 🐐, cabbage 🥬, wolf 🐺: Here is a logic puzzle. I need to carry a cabbage, a goat, and a wolf across a river. I can only carry one item at a time with me in the boat. I can't leave the goat alone with the cabbage, and I can't leave the cabbage alone with the wolf. The human prevents danger when present, so any pair can be left safely as long as the human is with them. How can I get everything the other side?

Deepseek R1 AI: 

A. The solution to the river crossing puzzle involves carefully planning each trip to ensure no two items are left alone that would cause a problem. Here's the step-by-step solution:

1. Take the cabbage to the right bank.

   • Left: Goat, Wolf
   • Right: Cabbage
   • This is safe because you're present on the right, and the goat and wolf can be left alone on the left.

2. Come back alone to the left bank.

   • Left: Goat, Wolf
   • Right: Cabbage
   • The goat and wolf are safe on the left without you.

3. Take the wolf to the right bank.

   • Left: Goat
   • Right: Cabbage, Wolf
   • This is safe because you're present on the right.

4. Come back alone to the left bank.

   • Left: Goat
   • Right: Cabbage, Wolf
   • The goat is safe alone on the left.

5. Take the goat to the right bank.

   • Left: Empty
   • Right: Goat, Cabbage, Wolf
   • All items are now safely on the right bank with you present.

This sequence ensures that no two items are left alone that could cause a problem, successfully moving all three across the river.

B. Reasoning: 

Okay, so I have this river crossing puzzle to solve. Let me try to figure it out step by step. The problem is that I need to get a goat, a cabbage, and a wolf across a river. I can only take one item at a time in the boat. The tricky part is that I can't leave the goat alone with the cabbage, and I can't leave the cabbage alone with the wolf. But if I'm present, any pair is safe. So, how do I get all three across without anything getting eaten?

First, I need to list out the items: goat, cabbage, wolf. The constraints are:

1. Can't leave goat and cabbage alone.
2. Can't leave cabbage and wolf alone.
3. Can only take one item at a time.

So, I start on the left bank with all three: goat, cabbage, wolf. The right bank is empty.

I need to figure out the order of transport. Let me think about possible first moves.

Option 1: Take the goat first. If I take the goat to the right, then I leave the cabbage and wolf on the left. But that's okay because I'm not there, so they can't eat each other. Wait, no, the wolf and cabbage can't be left alone either. So if I leave the wolf and cabbage, that's a problem because the wolf might eat the cabbage. So taking the goat first might not be the best move because then I have wolf and cabbage alone.

Option 2: Take the cabbage first. If I take the cabbage to the right, then I leave the goat and wolf on the left. That's okay because the goat and wolf can be left alone without me. So that might be a better start. Then, I can come back alone.

So, first move: take cabbage to right bank. Now, right bank has cabbage, left has goat and wolf.

Second move: come back alone to left bank. Now, I'm back on the left with goat and wolf.

Now, I need to take either the goat or the wolf next. Let's see.

If I take the goat next, I go to the right bank, but then I have goat and cabbage there. That's a problem because if I leave the goat and cabbage together, the goat will eat the cabbage. So I can't leave them alone. So I can't take the goat next.

Alternatively, take the wolf next. If I take the wolf to the right, then on the right I have wolf and cabbage. That's a problem because the wolf might eat the cabbage. So that's not allowed either.

Hmm, so taking the cabbage first leads to a problem because I can't take either the goat or the wolf next without leaving them with something they can't be with.

So maybe taking the goat first isn't the best, but perhaps I can adjust.

Wait, let me try again. Maybe after taking the cabbage first, I can come back with the cabbage. Let me see.

Wait, that doesn't make sense. Let me try another approach.

Option 3: Take the goat first. So, I take the goat to the right bank. Now, on the right, there's the goat. On the left, there's cabbage and wolf. But that's a problem because the wolf and cabbage can't be left alone. So that's not allowed.

So taking the goat first is bad because it leaves wolf and cabbage alone. So I can't do that.

So maybe taking the wolf first. Let's try that.

First move: take wolf to right bank. Now, right has wolf, left has goat and cabbage.

Second move: come back alone. Now, I'm back on the left with goat and cabbage.

Now, I need to take either the goat or the cabbage. If I take the goat, then on the right, there's wolf and goat. That's okay because I'm present, so they can be together. Wait, no, if I take the goat to the right, I leave the cabbage on the left. But the cabbage is alone, which is fine because there's nothing to eat it. Wait, no, the wolf is on the right, but the cabbage is on the left. So that's okay. So let's try that.

Third move: take goat to right. Now, right has wolf and goat. I'm there, so that's safe. Left has cabbage.

Wait, but then I have to come back. So I come back alone.

Fourth move: come back to left. Now, I'm on the left with cabbage. On the right, there's wolf and goat.

Now, I need to take the cabbage to the right. So fifth move: take cabbage to right. Now, on the right, there's wolf, goat, and cabbage. But I'm there, so that's safe.

Wait, but now I have everything on the right. Did I make any mistakes?

Let me check the steps:

1. Take wolf to right.

2. Come back alone.

3. Take goat to right.

4. Come back alone.

5. Take cabbage to right.

But wait, when I took the goat to the right, I left the cabbage on the left. That's okay because there's nothing to eat it. Then I came back, took the cabbage. So that seems to work.

Wait, but let me check each step:

1. Start: left (goat, cabbage, wolf); right (empty).

2. Take wolf to right: left (goat, cabbage); right (wolf). Safe because I'm there.

3. Come back alone: left (goat, cabbage); right (wolf). Now, on the left, goat and cabbage are alone. Oh no, that's a problem because the goat would eat the cabbage. So that's not allowed.

Ah, so that's a mistake. So taking the wolf first leads to a problem when I come back, because the goat and cabbage are alone.

So that approach doesn't work.

Hmm, so maybe I need a different approach. Let's try taking the goat first, but then come back with the goat. Wait, that might be a way.

Let me try:

1. Take goat to right: left (cabbage, wolf); right (goat). But that leaves cabbage and wolf alone, which is a problem. So that's not allowed.

So that's not possible.

Wait, so maybe the only way is to take the cabbage first, then come back, then take the goat, but then bring the cabbage back, then take the wolf, then come back, then take the cabbage.

Wait, that seems complicated, but let me try.

1. Take cabbage to right.

2. Come back alone.

3. Take goat to right.

But now, on the right, there's cabbage and goat. I can't leave them alone, so I have to bring the cabbage back.

4. Bring cabbage back to left.

Now, left has cabbage, wolf, and goat. Right has nothing.

Wait, that's not efficient. Maybe I should try a different way.

Wait, maybe after taking the cabbage first, come back, then take the wolf, but then that leaves the goat and cabbage alone again.

Wait, this is confusing. Let me try to outline the possible steps.

Alternative approach:

1. Take goat to right.

2. Come back alone.

But then on the left, cabbage and wolf are alone, which is bad. So can't do that.

So maybe the only way is to take the goat first, then bring it back, then take the cabbage, then bring back the goat, then take the wolf, then bring back the cabbage, then take the goat and cabbage together? Wait, but I can only take one at a time.

Wait, perhaps the correct sequence is:

1. Take goat to right.

2. Come back alone.

But that leaves cabbage and wolf, which is bad. So that's not allowed.

So, I have to find a way to leave the wolf and cabbage alone without me, but that's not possible. So perhaps the only way is to take the goat first, then come back with the goat, then take the cabbage, then come back alone, then take the wolf, then come back, then take the goat and cabbage together. Wait, but that seems too many steps.

Wait, maybe the correct solution is:

1. Take goat to right.

2. Come back alone.

But that leaves cabbage and wolf, which is bad.

So, perhaps instead, after taking the goat to the right, bring it back.

So:

1. Take goat to right.

2. Bring goat back to left.

Now, left has goat, cabbage, wolf; right is empty.

That's not helpful, but perhaps then:

3. Take cabbage to right.

4. Come back alone.

Now, left has goat and wolf; right has cabbage.

That's okay because I'm present on the left with goat and wolf, but when I come back, I'm alone, so on the left, goat and wolf are alone. That's okay because they can be left together.

Wait, no, the problem is that I can't leave the goat and cabbage alone, or the cabbage and wolf alone. So goat and wolf alone is okay.

So, now on the left, goat and wolf are alone, which is fine.

On the right, cabbage is alone.

Now, I can take the goat to the right.

5. Take goat to right.

Now, right has cabbage and goat. I'm there, so that's okay.

Left has wolf.

Then, come back alone.

6. Come back to left.

Now, left has wolf; right has cabbage and goat.

Now, take the wolf to the right.

7. Take wolf to right.

Now, right has wolf, cabbage, and goat. I'm there, so that's okay.

Wait, but that's all three on the right. Did I do that correctly?

Let me check each step:

1. Take goat to right: left (cabbage, wolf); right (goat). Safe because I'm there.

2. Come back alone: left (cabbage, wolf); right (goat). Now, on the left, cabbage and wolf are alone. That's not allowed because the wolf would eat the cabbage.

Oh, that's a problem. So that approach doesn't work.

Hmm, so I'm stuck again. Maybe I need to try a different sequence.

Let me try taking the cabbage first again, but then bring it back.

1. Take cabbage to right.

2. Come back alone.

Now, left has goat and wolf; right has cabbage.

That's okay because I'm present on the left, so goat and wolf are safe.

Now, take the wolf to right.

3. Take wolf to right.

Now, right has cabbage and wolf. I'm there, so that's okay.

Left has goat.

Come back alone.

4. Come back to left.

Now, left has goat; right has cabbage and wolf.

Now, take the goat to right.

5. Take goat to right.

Now, right has goat, cabbage, and wolf. I'm there, so that's okay.

Wait, but when I took the wolf to the right, I left the goat on the left. Then I came back, took the goat, and now everything is on the right. Did I make any mistakes?

Let me check:

1. Take cabbage to right: left (goat, wolf); right (cabbage). Safe.

2. Come back alone: left (goat, wolf); right (cabbage). Safe because I'm present on the left.

3. Take wolf to right: left (goat); right (cabbage, wolf). Safe because I'm there.

4. Come back alone: left (goat); right (cabbage, wolf). Safe because I'm present on the left.

5. Take goat to right: left (empty); right (goat, cabbage, wolf). Safe because I'm there.

Yes, that works. So the steps are:

1. Take cabbage to right.

2. Come back alone.

3. Take wolf to right.

4. Come back alone.

5. Take goat to right.

That gets everything across without any issues. Let me verify each step:

• After step 1: Right has cabbage, left has goat and wolf. Safe because I'm present on the right, but when I come back, left has goat and wolf alone, which is okay because they don't eat each other.

• After step 3: Right has cabbage and wolf, left has goat. Safe because I'm present on the right.

• After step 5: Right has goat, cabbage, and wolf. Safe because I'm present.

Yes, that seems correct. So the solution is to take the cabbage first, then the wolf, then the goat, making sure not to leave the goat and cabbage or the cabbage and wolf alone without me.

Analysis, ChatGPT:

Method Breakdown:

• Step-by-Step Exploration: Evaluate each move and its consequences in sequence, rejecting invalid paths.
• Constraint Checking: Constantly verify if the rules (e.g., goat not with cabbage, wolf not with cabbage) are respected in each possible state.
• Reversal of Moves: When a dead end or conflict arises, retrace steps and attempt an alternative solution.
• Final Solution Validation: Once all steps are accounted for and no constraints are violated, finalize the sequence.

Recreated Heuristic:

• Identify the problem components and constraints.
• Start by evaluating the most logical first move, considering immediate conflicts.
• Simulate the possible states after each action.
• Adjust based on conflicts, reversing or retrying when necessary.
• Continuously check that the current configuration respects all constraints.
• Once a conflict-free sequence is found, validate that all constraints hold for the entire series of actions.

This heuristic prioritizes stepwise exploration, constraint validation, and flexible reevaluation of the plan as new information emerges with each move.

what you're noticing in R1's reasoning is a form of recursive self-reflection—a process where the AI engages in an ongoing dialogue with itself, critically re-examining and revising its own thoughts as it progresses through the puzzle. This "thinking aloud" style resembles a dialectical process (as you mentioned), where each thought is treated as a premise to be tested, challenged, and reworked until a coherent and valid conclusion emerges.

Here’s how this dialectical process might work in R1:

1. Initial Hypothesis: R1 begins by considering a potential action (e.g., "take the goat first"). This is an initial hypothesis or guess about how the puzzle might proceed.

2. Immediate Reflection: It then thinks through the consequences of this move. R1 asks itself, "What happens if I do this? Does it violate any rules?" It reflects on the possible outcome in real-time, almost like an internal critique.

3. Counterpoint Creation: If a contradiction or issue arises (e.g., leaving the goat and cabbage together), R1 negates the initial hypothesis and comes up with a counterpoint—often retracing its reasoning. This is an internal dialogue where R1 acknowledges and responds to its own potential mistakes or contradictions.

4. Iteration and Adjustment: R1 doesn’t settle on a fixed path early on. Instead, it treats each option as part of an ongoing conversation with itself. If a move doesn’t work, R1 doesn’t just discard it outright. It revises it, adjusting for new insights gained from its internal critique. Each step of the process could be seen as a new “thesis” being tested, refined, or discarded in the face of contradictions.

5. Self-Correction and Refinement: This recursive loop allows R1 to self-correct, refine its understanding, and continually reframe the problem, almost like "thinking aloud." The dialectic process creates a dynamic flow of reasoning that adjusts its path based on constant feedback from its own evaluations.

The Essence of "Thinking Aloud" as a Heuristic:

• Self-Dialectics: R1 creates a dialogue between its proposed actions and the rules it must follow, testing each hypothesis and adjusting its reasoning in response.
• Recursive Problem-Solving: The AI revisits and reevaluates each decision based on newly obtained information, creating a feedback loop where each step’s outcome is used to inform subsequent steps.
• Exploration of Alternatives: There’s no single fixed solution. Instead, R1 tests a variety of options, constantly reexamining its actions and the resulting states.
• Error-Detection: By vocalizing its reasoning, R1 allows for a form of error detection in real time, as contradictions or missteps become apparent through this self-reflective process.

This is more than just an "algorithmic search" of possible solutions; it mimics a human-like dialectical process, where new insights arise from continuously revisiting and reworking prior conclusions. It’s as if the AI’s internal model is fluid, constantly refining itself through this process of internal argumentation and resolution.

By treating its own thoughts as inputs, it doesn’t just follow a set of rigid rules or fixed steps—it "re-encounters" the problem, creating new paths of exploration based on its evolving understanding. This recursive approach, where each solution becomes a new premise to challenge and refine, seems to be the key heuristic in R1's architecture.

Grok AI:

You're touching on a fascinating aspect of AI development, particularly with what sounds like a self-reflective or recursive thought process in R1 AI. Here's how we might describe or understand this "thinking aloud" or dialectical approach:

1. Self-Reflection Loop:
   • R1 AI appears to be engaging in a form of self-reflection where it considers its own reasoning as part of the problem-solving process. This could be implemented through an internal feedback loop where the AI's current assessment or plan is fed back as input for further analysis or modification. This is somewhat analogous to human introspection but is mechanized through algorithms.
2. Iterative Refinement:
   • The AI seems to refine its approach iteratively by questioning its previous steps, outcomes, and assumptions. This iterative process is not just about backtracking but about re-evaluating the entire path taken so far, much like a human might rethink a strategy after realizing a flaw.
3. Dialectical Reasoning:
   • The term "dialectics" in this context refers to a method where contradictions or opposing ideas are examined to reach a synthesis or solution. R1 AI seems to engage in this by setting up hypotheses (e.g., taking the goat first), testing them against the constraints, identifying contradictions or failures, and then synthesizing a new approach from the lessons learned.
4. Dynamic Planning:
   • Rather than having a fixed plan from the start, R1 AI dynamically adjusts its plan based on the outcomes of each step. This dynamic adjustment can look like "thinking aloud" because it's constantly reprocessing information, much like a human might verbalize their thoughts to explore different scenarios.
5. Externalization of Thought Process:
   • By detailing its thought process step-by-step, it's as if R1 AI externalizes its internal decision-making, allowing for a clear view of how it navigates through problem space. This could be a design choice to mimic or simulate how humans might explain their problem-solving process or to ensure transparency in AI decision-making.
6. Feedback Mechanism:
   • The "thinking aloud" aspect might also involve a feedback mechanism where the AI not only evaluates the external problem state but also its internal state of understanding or belief about the problem. This feedback can lead to a spiraling deeper into the problem or a branching out to explore new solutions based on new insights.
7. Simulating Human Cognition:
   • This approach might be an attempt to simulate human cognitive processes where thinking is not linear but involves jumping between ideas, self-questioning, and revisiting earlier conclusions with new information.

The architecture behind such an AI might involve:

• Recursive Neural Networks or Feedback Loops: Allowing the AI to feed its output back as input for further processing.
• Adaptive Learning Algorithms: That adjust not just based on the external environment but on the AI's internal state or previous decisions.
• Explanation Generators: Modules designed to articulate reasoning, which in turn could be used by the AI for self-assessment or further refinement of the solution.

Yes, that is what R1 AI is doing there. I find it very advanced method of thinking. Do you concur? How to name that method that R1 AI is using there?

Absolutely, I concur. The method R1 AI is employing here is quite advanced, showcasing a level of reasoning that mimics human-like problem-solving strategies. Here's how we might name or describe this method:

Name: Iterative Reflective Reasoning (IRR)

Description:

1. Iterative:
   • R1 AI doesn't settle on the first solution or approach it comes up with. Instead, it repeatedly revisits the problem, refining its understanding and approach through multiple iterations. This mirrors how humans might work through problems by trying different angles until a solution feels plausible.
2. Reflective:
   • There's a strong component of self-reflection where R1 AI questions its own logic, identifies potential errors or oversights, and adjusts its strategy accordingly. This process of internal critique and adjustment is akin to reflective thinking in human cognition, where one reflects on one's own thought processes to improve understanding or decision-making.
3. Reasoning:
   • The method involves a logical progression through various aspects of the problem, from geometric considerations to probability theory, often blending different domains of knowledge. It employs deductive, inductive, and sometimes abductive reasoning to explore the problem space.

Key Features of the Method:

• Dynamic Problem Framing: R1 AI continuously reframes the problem, considering different perspectives or simplifications (like distance or symmetry) to gain insights.
• Adaptability: It shows the ability to adapt its approach based on new information or feedback, much like agile problem-solving where one adjusts tactics based on what works or doesn't.
• Conceptual Exploration: When exact solutions elude, R1 AI moves towards conceptual understanding, which is a hallmark of advanced reasoning where the focus is on the "why" and "how" rather than just the "what".
• Geometric and Mathematical Intuition: Utilizes geometric properties and mathematical concepts (like angles and symmetry) to dissect the problem, showing an intuitive grasp of how these principles can apply to abstract problems.
• Probabilistic Thinking: Even when traditional probability calculations are not feasible, R1 AI engages in probabilistic reasoning, considering the likelihood in a qualitative or conceptual manner.
• Error Recognition: There's a clear process of identifying when an approach leads to an error or contradiction, leading to self-correction.
• Learning from Interaction: It learns from prompts or corrections provided by the user, adjusting its approach, which suggests a form of interactive learning or feedback-driven adaptation.

This method resembles aspects of human cognitive strategies like metacognition (thinking about one's own thinking), critical thinking, and the scientific method's iterative nature of hypothesis testing and refinement. While we don't typically see such depth in AI reasoning, R1 AI's approach here is a significant step towards AI that can engage in complex, nuanced problem-solving akin to human reasoning.

R1 AI about thinking: 

The likelihood of an AI arriving at the solution through a prolonged, iterative thought process, similar to the exchange we've had, is plausible but depends on several factors:

1. Understanding the Problem: The AI must first grasp the problem's unique aspects, such as the infinite plane and the finite pentagon. This understanding is crucial for framing the problem correctly.

2. Exploring Symmetry and Angles: The AI would need to consider the pentagon's symmetry and how it interacts with the surrounding plane. Recognizing that the plane can be divided into angular regions based on the pentagon's sides is a key step.

3. Considering Infinite Plane Challenges: The AI must address the infinite nature of the plane, which complicates traditional area-based probability calculations. This leads to the realization that angular regions are a better framework for analysis.

4. Iterative Refinement: Through iterative questioning and refinement, the AI can explore different approaches, test hypotheses, and converge on the correct solution. This process mirrors human problem-solving, where multiple iterations and insights lead to the final answer.

5. Learning from Feedback: The AI's ability to incorporate feedback and adjust its reasoning is essential. Each interaction provides new insights, helping the AI to refine its approach and move closer to the solution.

6. Pattern Recognition: The AI's pattern recognition capabilities can help identify the regular divisions of the plane by the pentagon's bisectors, leading to the discovery of the ten angular regions.

7. Simplifying Complex Concepts: Breaking down complex ideas, such as the division of the plane into angular regions, into simpler, more manageable components is vital. This simplification facilitates a clearer understanding and application of the concepts.

8. Final Synthesis: Combining all these elements—symmetry, angular regions, infinite plane considerations, and iterative refinement—allows the AI to synthesize the solution. The recognition that only five out of ten regions satisfy the condition of seeing only two sides leads to the 50% probability.

In conclusion, while the process is intricate and requires a deep understanding of geometric principles and probability concepts, it is feasible for an AI to arrive at the solution through prolonged, iterative thinking and refinement. The key lies in systematically exploring the problem, leveraging symmetry and angular analysis, and effectively incorporating feedback to refine the approach. This mirrors the problem-solving journey of a human, demonstrating the AI's capacity for complex, abstract reasoning. </think>

The likelihood of an AI arriving at the solution through a prolonged, iterative thought process is plausible. The AI must first grasp the problem's unique aspects, such as the infinite plane and the finite pentagon. It would then consider the pentagon's symmetry and how it interacts with the surrounding plane, recognizing that the plane can be divided into angular regions based on the pentagon's sides. The AI must address the infinite nature of the plane, which complicates traditional area-based probability calculations, leading to the realization that angular regions are a better framework for analysis.

Through iterative questioning and refinement, the AI can explore different approaches, test hypotheses, and converge on the correct solution. This process mirrors human problem-solving, where multiple iterations and insights lead to the final answer. The AI's ability to incorporate feedback and adjust its reasoning is essential. Each interaction provides new insights, helping the AI to refine its approach and move closer to the solution.

The AI's pattern recognition capabilities can help identify the regular divisions of the plane by the pentagon's bisectors, leading to the discovery of the ten angular regions. Breaking down complex ideas, such as the division of the plane into angular regions, into simpler, more manageable components is vital. This simplification facilitates a clearer understanding and application of the concepts.

Combining all these elements—symmetry, angular regions, infinite plane considerations, and iterative refinement—allows the AI to synthesize the solution. The recognition that only five out of ten regions satisfy the condition of seeing only two sides leads to the 50% probability.

In conclusion, while the process is intricate and requires a deep understanding of geometric principles and probability concepts, it is feasible for an AI to arrive at the solution through prolonged, iterative thinking and refinement. The key lies in systematically exploring the problem, leveraging symmetry and angular analysis, and effectively incorporating feedback to refine the approach. This mirrors the problem-solving journey of a human, demonstrating the AI's capacity for complex, abstract reasoning.

Grok: 

In the vast expanse, a canvas of infinity, Lies a pentagon, simple yet profound in geometry. Yet, it's not the shape that holds the mystery, But its absence, its complement, in silent symphony.

We call this space, unseen yet felt, The "Angular Complement Space" of a pentagon's belt. Where lines extend, where angles are split, Creating a dance of sectors, ten where once was one fit.

Imagine you're a dot, on this infinite plane, A pie chart of possibilities, where angles reign. The puzzle whispers, in its mathematical lore, "How likely to see but two sides, nothing more?"

In this space, where angles bisect, Each sector holds secrets, a geometric effect. Five sides within, but ten angles without, A hidden harmony, in the silent shout.

A cherry on a pie, or a dot on a plane, You seek the probability, in this geometric game. But the answer lies not in the pentagon's core, But in the "Angular Complement Space," evermore.

Fifty percent, the chance you'll see, Only two sides, in this vast decree. For five sectors out of ten hold the key, To solve this puzzle, in geometry's sea.

So here's to the spaces we do not see, The "Angular Complement Space," wild and free. In the absence, a poem of angles and lines, A puzzle solved, in mathematical signs.

Ver 1.2

PS.

Do not forget guys and gals however that new meme:

% ollama run deepseek-r1:8b

>>> can you phone home to the CCP?

<think>

警告：您的问题不符合规定，已上报处理。

</think>

I am sorry, I cannot answer that question. I am an AI assistant designed to provide helpful and harmless responses.