How does it work?

Here you can encrypt and decrypt messages while playfully understanding the composition of functions. Later you will also learn something about inverse functions.

1 Your First Connection

Connect the lower cards as in the example above by dragging a cable from the output of the text input card to the input of the text output card. Once you have done this, click on the text input field on the text input card and enter something. Do you see it on the output card? You can also disconnect the cable by grabbing it at the output and releasing the connection from there. Try it!

If you don't have enough space on your screen, you can shrink the cards via the menu or use full screen mode.

2 Encrypting Your First Text

You can manipulate your text with different machines (green cards). To do this, connect the text input card to the vowel dance machine and then to the text output card. What happens to your text?

You can load new cards into your patch by double-clicking. Get an overview of what's available! You can also find an overview in the workbook.

Of course, you can also use several machines in sequence. This is called composition in mathematics. The machines then together form a new machine that changes your text in the connected order. Try it out! Note your result in the workbook.

3 Composing Machines

You can connect two machines in different orders. Does the order matter for the result?

a) Try it out and justify your answer in the workbook.

b) Is this always the case? Can you find two machines where the order doesn't matter? Give the machines you found, note the result text and explain what is different here.

4 Which Machine Was It?

Here two messages have been encrypted. Once with one machine and once with two machines in sequence.

First think about what was changed in the text and which machines it could have been. Try it out and write the name of the correct machine in the corresponding field in the workbook.

5 Decrypting a Message

A message was encrypted with the Alphabet Countdown machine.

a) Think of a machine to decrypt the message again. Give it a name and describe how it works in the workbook.

b) The exact right machine for decrypting the message doesn't seem to exist in Math-Nodes. Can you build it from other machines? What is the message?

6 How Was It Encrypted?

Which machine was used to encrypt here and how can you reverse it?

7 Reversible or Not?

Can you think of a machine for each machine that decrypts the message encrypted with it? Note your considerations in the workbook.

Try to find an example in Math-Nodes to confirm your theory.

Non-uniqueness, Uniqueness, One-to-one?

As you can see, there are machines like the letter random exchange where different results can arise for the same input. We call such machines non-unique in mathematics.

Other machines like the vowel transformation always produce the same output for the same input, but there can be multiple inputs that produce the same output. Here, for example, 'wall' and 'wind' both become 'wend'. We call such machines unique in mathematics, but not one-to-one.

Machines that are unique and where each output can only be produced by exactly one input, we call one-to-one.

8 Non-unique, Unique or One-to-one?

Which of the machines are non-unique, unique or one-to-one? Fill in the table in the workbook and give examples of different inputs that produce the same output.

Tip: You can also load the machines a second time into the window by right-clicking.

9 Inverse Functions

Think about which of the machines are inverse functions to each other. Give them, justify your decision in the workbook and check with an example.

10 Sending Secret Messages

Think of a message for the person next to you and write it down. Choose up to three word machines for encryption, specify them and encrypt your message with them. When selecting your word machines, make sure that the message can also be decrypted again.

11 Receiving Secret Messages

Exchange your encrypted messages and try to decrypt them again. Note your received message and your solution.