Demonstrating AI Temperature

When you request something from ChatGPT via the API one of the options you can set is “temperature”. LLMs are a machine which predicts the next word to follow after the words that came before. But temperature being higher lets it be less predictable and not always take the most default probability. I was trying to explain this to a friend over coffee so I thought running a quick demo would be helpful.

I’ve run the same query 3 times with increasing temperatures. Starting at zero, which to my surprise still didn’t produce identical results and the second they drift they they go a different path. The highest settings didn’t return a result at all in the time limit I gave it.

Interesting it seems very very keen on the layer cake. It only shakes loose of that at high settings. But the examples at higher settings don’t actually explain recursion very well!

Personally I’d have gone with “kitkats” because the recipie for KitKats includes crushed KitKat…

Anyhow here we go…

Prompt: “Explain recursion with a cooking analogy.”

temperature=0 (deterministic)

run 1

Recursion is like following a recipe that requires you to make a smaller version of the same dish before you can complete the final dish.

Imagine you’re making a layered cake. The recipe says to first bake a smaller cake (the base layer). Once that’s done, you need to bake another smaller cake for the next layer. You keep repeating this process, baking smaller and smaller cakes until you reach the smallest size, which is just a cupcake.

Once all the smaller cakes are baked, you can start assembling them into the final layered cake. Each time you bake a smaller cake, you’re solving a smaller part of the overall problem (making the full cake). Finally, when all the smaller parts are ready, you combine them to complete the dish.

In recursion, a function calls itself with a simpler version of the original problem until it reaches a base case, just like you keep baking smaller cakes until you reach the smallest one.

run 2

Recursion is like following a recipe that requires you to make a smaller version of the same dish before you can complete the final dish.

Imagine you’re making a layered cake. The recipe says to first bake a smaller cake layer. Once that layer is done, you use it as a base to build the larger cake. If the recipe calls for multiple layers, you keep repeating the process: bake a smaller layer, then stack it, until you have the full cake.

In this analogy, each time you bake a smaller layer, you’re performing a recursive step. The final cake is built upon these smaller layers, just as a recursive function builds upon its smaller instances to reach a final solution.

run 3

Recursion is like following a recipe that requires you to make a smaller version of the same dish before you can complete the final dish.

Imagine you’re making a layered cake. The recipe says to first bake a smaller cake (the base layer). Once that’s done, you need to bake another smaller cake for the next layer. You keep repeating this process, baking smaller and smaller cakes until you reach a tiny cupcake.

Once all the smaller cakes are baked, you can start assembling them into the final layered cake. Each time you bake a smaller cake, you’re using the same recipe, just on a smaller scale. Finally, when all the layers are stacked, you have your complete cake.

In recursion, a function calls itself with a simpler or smaller problem until it reaches a base case, just like you keep baking smaller cakes until you reach the smallest one.

temperature=0.7 (default)

Note that these all stay the same for the first few words.

run 1

Recursion is like following a recipe that calls for the same recipe to be used multiple times. Imagine you’re making a layered cake.

1. You start by making a cake base (the first step).
2. The recipe might say, “For each layer, make another cake base.”
3. So, you make a smaller cake for the first layer (this is the recursive call).
4. Once you have enough layers, you stop making smaller cakes and start stacking them together.

In this analogy, each time you make a new cake base, you’re repeating the process, but you eventually reach a point where you stop and assemble everything into a final product. That’s how recursion works—solving a problem by breaking it down into smaller instances of the same problem until you reach a base case.

run 2

Recursion is like following a recipe that requires you to make a smaller version of a dish before you can complete the larger one.

Imagine you want to make a layered cake, but the recipe calls for you to first bake a smaller cake to use as one of the layers. You follow the same steps: mix ingredients, bake, and then once that smaller cake is ready, you use it as a layer in the larger cake.

If the recipe for the smaller cake requires yet another smaller cake, you repeat the process. Eventually, you reach a point where you can bake a single cupcake, which is simple enough to complete. Once that cupcake is done, you can build back up, using it to create the smaller cake, and then the larger cake, until your full layered cake is complete.

In this analogy, each smaller cake represents a recursive call, and the final cupcake is the base case that stops the recursion.

run 3

Recursion is like following a recipe that requires you to prepare a dish using another dish as an ingredient. For example, imagine you need to make a layered cake. The recipe starts with making a batch of cake batter, which is then baked into layers.

1. To create the layered cake, you first need to make the cake layers (this is your base case).
2. If you want to make a more complex dessert, you might need to prepare a flavored frosting, which requires you to make a basic frosting first (this is the recursive call).
3. Then, you assemble the layers with the frosting in between.

Each time you make a layer or a frosting, you’re essentially calling the same recipe process, but you’re getting closer to completing your final dish. Once all layers and frostings are done, you have your completed layered cake.

In this analogy, the recipe calls for itself at different stages, just like a recursive function calls itself until it reaches a base case.

temperature=1 (creative)

run 1

Recursion is like following a recipe that calls for the same dish to be made within itself, such as a layered cake.

1. You start by making the first layer of the cake, which may require mixing batter, baking, and cooling.
2. Once the first layer is done, the recipe tells you to repeat the process to make another layer of the cake.
3. Each time you make a layer, you follow the same steps until you’ve reached the desired number of layers.
4. Finally, you assemble all the layers together to complete the cake.

In this analogy, each layer represents a recursive call, and the final cake represents the complete solution that comes from stacking all the smaller, identical tasks together.

run 2

Recursion can be compared to following a recipe that requires itself as part of the process. Imagine you’re making a layered cake.

1. **Main Recipe:** You have a recipe for the layers, which instructs you to make the cake, but it also says to make the same layers again until you have enough.

2. **Base Case:** To stop the repeated process, the recipe might specify that once you have three layers, you should stop making more layers.

3. **Recursive Step:** Each time you make a layer, you use the same instructions that tell you how to make another layer, repeating the steps for mixing, baking, and cooling.

In this analogy, each layer represents a call to the same recipe, and the final cake is the culmination of those recursive steps, stopping when the specified number of layers is achieved.

run 3

Recursion is like following a recipe that includes itself as part of the instructions. Imagine you’re making a layered cake. The recipe says:

1. Make the cake batter (this is the base of the recipe).
2. Pour the batter into a pan and bake it.
3. Once it’s baked, make another layer using the same batter recipe.

When you get to step 3, you follow all the steps again to make another layer. Each time you need a new layer, you “call” the same recipe, until you decide you have enough layers. Once you’ve got all the cake layers, you complete the process by assembling and decorating the cake.

Just like in recursion, you keep applying the same process until you reach a stopping point (like deciding you have enough cake layers). Then, you combine everything to get the final result.

temperature=1.4 (unstable)

run 1

Recursion is like a recipe that calls for itself. Imagine you’re making a layered cake. To assemble the cake, you first need to create the individual layers.

1. Make the first layer (this is your main task).
2. But before you can finish the first layer, you need to bake it.
3. This process might say, “Mix ingredients, bake a layer.” To mix ingredients, you refer to the same mixing steps for each cake layer.

So, the recipe for a layer layer doesn’t end with a straightforward instruction; instead, it directs you to go back and repeat steps until you achieve the full cake:

– One layer leads to more layers which all lead back to more mixing-baking steps. Eventually, after enough layers are completed, you finish the whole cake!

In each round, you’re solving a smaller piece of the problem, just like in recursion. When you finally stack all completed layers, that’s the “base case” where the gathering meets completion.

run 2

Recursion can be compared to a method of cooking a complex dish that requires multiple layered steps.

Imagine you want to make a lasagna. The steps involve making sauce, boiling noodles, preparing cheese, and assembling layers. Instead of completing each step fully before starting the next, you handle some tasks in smaller portions:

1. Start by boiling water for the noodles, but check after a few minutes to see if they’re ready. If they’re not, you take a step back to an earlier point of the process (like preparing cheese) and do that for a bit.

2. Once the noodles are ready, you move on to assembling the layers—add sauce, place noodles, add cheese, and repeat this process. Each time you begin a new layer, you’re repeating a simpler version of the earlier assembly, only targeting the current layer that needs preparation.

3. Eventually, you layer down final ingredients and bake the lasagna. The dish is a cumulative result of these steps repeated for different layers, just like a recursive function calls itself with simpler parameters until it reaches a base case and then expands to the complete meal.

Just like in cooking, recursion simplifies complex problems by breaking them down into “smaller servings” until the final dish is complete!

run 3

Recursion can be compared to recursive cooking recipes. Imagine you’re trying to make a layered cake.

1. To make the cake, you first need to make the individual layers.
2. Each layer requires a smaller set of steps – mixing ingredients, baking, and cooling.
3. But to mix those ingredients, you often refer back to basic recipes for things like batter or frosting. Each time you stick to a basic recipe, you break it down into smaller cooking tasks.
4. Once all batter and frosting elements for the large cake are done (the base case), you can add the layers together to create the final cake.

Just as in recursion, where a problem is broken down into smaller sub-problems until a simple version is solved, in cooking, you go step-by-step to build your final dish, referring to simpler tasks along the way.

temperature=1.5 (1.5)

run 1

Imagine you’re preparing a layered cake. To make a layered cake, you first need to bake a single cake layer (this is your base step). Once you have that layer, you’re not done yet—you’ll need to make more of those layers by repeating the process (this is the recursive step) until you reach the desired number of layers.

So, you bake one layer, then you bake another, each time using the same recipe. Once you’ve baked all the necessary layers, you finally frost and assemble them to complete the layered cake. For recursion, the function you call might perform the task for one layer, then involve itself to handle the next layer’s baking until it finishes all layers adding up to your final cake (“completing the task”). Each time it calls itself, it’s essentially asking “How do I make another layer?” and builds on the previous work until it reaches the final result.

run 2

Recursion is like a recipe that includes a step to create a smaller dish before finalizing the main dish. For example, imagine you’re making a layered cake.

1. To produce this cake, you first need to bake a smaller cake as one layer.
2. In the recipe, it says: “Bake a smaller cake, while also preparing frosting.”
3. To make this smaller cake, you could have a sub-recipe that repeats the same steps, perhaps using even smaller baking pans.

This smaller cake uses the same ingredients and steps repeatedly until you reach a point where the base ingredient (like flour) is so minimal that it doesn’t need further thinning out. Eventually, after combining everything, you’ll end up with your complete layered cake.

Just like in recursion, where a function calls itself to solve smaller instances of a problem, each layer or smaller dish contributes to the final, complete dish. The process can go deeper until reaching a point that is simple and manageable, then combines outward towards completion.

run 3

Recursion is like following a recipe that requires you to prepare some ingredients in smaller batches. For instance, if you’re making a layered cake, the recipe might ask you to bake each layer separately.

You first make the batter, put it in the pan, and bake it. Once the first layer is done, it tells you to repeat the same steps for the next layer. Before starting that process again, you can think a bit like a chef labelling a note with “bake another layer,” until you reach the point where no more layers are required. At that moment, you consolidate everything, stack the layers, and finally prepare to serve the cake.

In this analogy:
– The initial call is baking the first layer.
– Each recursive call is baking subsequent layers.
– The base case is when you’ve completed all the layers and move to finish the cake.

The concept hinges on breaking a complex task (layered baking) into simpler, repeatable tasks (baking individual layers) repeatedly until reaching a straightforward end condition (no more layers).

temperature=1.6 (1.6)

run 1

Recursion can be likened to the process of preparing a layered lasagna.

1. You start with a simple dish—one layer of lasagna.
2. To build the full dish, you need to add more layers, but each layer requires the same process of layering ingredients (noodles, cheese, sauce).
3. You prepare one layer.
4. If the desired height of the lasagna isn’t reached, you go back and repeat this process by adding another layer on top of the previous one.
5. Once you reach the desired number of layers, you can then bake it and enjoy the complete dish.

Everything is built in steps, where each step (or function call) adds complexity until you decide to finish (base condition), similar to how recursive functions work by calling themselves with simpler tasks before arriving at a conclusion.

run 2

Recursion can be thought of like following a recipe that involves preparing a dish that requires a component, which in turn has its own set of cooking steps.

Imagine you decide to make a layered cake. The first step of your cake recipe instructs you to bake a batter. But within the batter recipe, you realize you need to make butter cream frosting. To make the frosting, you check another recipe, and then you need to make powdered sugar. The recipe for powdered sugar sends you on another path that establishes it big requirement — granulating cane into fine sugar.

Each step may branch into even more sub-steps, but you’re following the original intent: getting to that lush layered cake. Once you’ve made the back steps of gathering intoed onto that ending point – back upwards proportional wasting infinite foil final shade delivered hanging crucname.

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run 3

Imagine you’re tasked with making a layered cake. First, you need to make a single sponge cake. Instead of preparing several cakes at once, you prep one layer:

1. **Baking one sponge cake** is like the base case. Once it’s ready, that’s a clear, simple task that’s done.

2. Now, if the recipe asks for multiple layers, you think: “Okay, to make a two-layered cake, I need to bake another sponge cake.”

3. This process keeps repeating; after baking one cake, you call on yourself to make the next layer until you’ve predefined how many it should have.

Ultimately, when you achieve each individual cake (base case), growing the whole cake layer by layer through a simple and similar method mirrors how recursion works. Each smaller step is a call towards achieving the final result.

temperature=1.7 (1.7)

run 1

TIMED OUT after 30000ms

run 2

TIMED OUT after 30000ms

run 3

TIMED OUT after 30000ms

temperature=1.8 (1.8)

run 1

TIMED OUT after 30000ms

run 2

Recursion is like following a recipe to cook several layers of a dish rather than cooking everything at once.

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