Lambda Pouch

The lambda pouch was originally an apprentice wizard's failed attempt to create a bag of holding. It’s easily obtainable nowadays, due to its propensity for creating more of itself.

The only item you can store inside a lambda pouch is another lambda pouch. However, the pouch you stored can itself contain another pouch, which can contain yet another pouch, etc. But you cannot put two pouches into one pouch side by side, nor will it accept any other object.

It has the same weight-nullifying abilities of a bag of holding, so it will always weigh 5 lbs no matter how many pouches are nested inside. There's no known limit to how many you can nest together (Through experimentation I've determined that it's well over a thousand).

Seems completely useless, doesn't it? And indeed it would be a pointless curiosity, were it not for another interesting property it has. A lambda pouch can be enchanted, so that when a pouch is placed inside, it will be magically transformed into a new lambda pouch according to the rules of the enchantment and then ejected. The enchantment is written with a system of runes, which you inscribe onto the bag itself.

When I purchased my lambda pouch, it came with a simple enchantment. However, all it did was spit out the same bag you placed inside unchanged. In effect, hardly enchanted at all, and even more useless as a container. The unscrupulous merchant who I purchased it from muttered 'fool' under his breath as I walked away, so for simplicity, let’s refer to this enchanted pouch as the 'fool's pouch'.

Luckily, I was able to borrow a second pouch from a colleague. Suppose I replaced the useless enchantment with this enchantment: "Whatever you put in, it will come out with a copy of itself inside". We’ll call this the "conjurer's pouch". If you drop in a pouch, it will come out containing a new pouch. Voila! With two starting pouches, you can create as many new pouches as you want.

The conjurer's pouch does not create a paradoxical container that contains itself. The pouch on the inside is merely an exact copy of the input pouch at the moment it was put in.

Care must be taken whenever you produce an enchanted pouch with something inside it, as once enchanted, the pouch ceases to be a storage object. For example, if you drop a fool's pouch inside the conjurer's pouch, the result is a fool's pouch which contains a fool's pouch. In this case, no harm done as the fool's pouch just ejects the fool's pouch, but if you are not careful with your enchantments, you may start a chain reaction that spits out pouches beyond your control.

Consider what would happen if you put a conjurer's pouch inside another conjurer's pouch. It will produce a conjurer's pouch containing a conjurer's pouch, and that pouch will spit out yet another conjurer's pouch containing a conjurer's pouch. Each pouch it creates will immediately create another one. Thus, a conjurer's pouch within another conjurer's pouch is called an "Omega pouch". At least it does not replicate itself exponentially, I shudder to think about what would happen if it did.

A filled enchanted pouch will not activate as long as it's inside another pouch, including the brief moment it spends inside another enchanted pouch before it's ejected. Therefore, you can contain an endlessly replicating pouch by stuffing it inside an unenchanted one. With this trick, you can hold nested enchanted pouches "in stasis”, as long as you do not remove or enchant the outermost layer.

Fortunately, this deactivation property also prevents one from accidentally creating an infinite number of lambda pouches nested together. If you could, my guess is the effect would be similar to putting a bag of holding inside another one.

Enchantments are capable of a kind of "memory", where it consumes the input pouch and encodes its properties into the enchantment of the output pouch. A simple example: "take the input pouch (for clarity, let's call it alpha), create a new empty enchanted pouch, which always transforms its inputs into alpha."

Now let's take any pouch, say a duplication pouch, and put it inside. The duplication enchantment seems to be lost, and you receive a pouch with a mysterious new enchantment. But put anything into this pouch, and you will get a duplication pouch out.

We can call a pouch that always produces the same output a "printer". In this case, we made a printer for duplication pouches. The pouch which creates printers from its input can be called the "copier" (which is not to be confused with a printer for printers)

If you find yourself inundated with problematic pouches, a printer for something harmless is a good way to destroy them.

By starting with pouches that represent fragments of enchantments, and throwing one into another, You can compose them into a single larger enchantment. Iterate this a few times, and you can create some very complicated enchantments without having to write the rune by hand.

One of my colleagues experimented with the idea of using lambda pouches to perform complex arcane calculations, and created the “addition pouch”. If you give it a pouch with a specific enchantment that represents the number three, it will produce an “add three” pouch. Next, placing a “four” pouch inside the “add three” pouch will produce a “seven” pouch. This will work for any two natural numbers, though it will produce a few excess pouches in the process.

Another enchantment she rather ingeniously devised is the "factorial pouch". But even for small inputs, it will spit out a massive number of intermediary pouches. She gave up on her experimentation after her study was buried in a mountain of lambda pouches.