## Wonderland without Numbers?

$\Leftarrow$ Previously in ‘Numbers in Wonderland’

Alice followed the Friendly Minotaur as he walked deeper into the forest. Any other little girl would have been at least a bit frightened by the shape of the large beast and the shadows cast on him by the looming trees, but Alice was too excited to find out what the Minotaur was going to tell her. Alice really didn’t like numbers, so if the Minotaur would tell her that we don’t really need numbers, that would be great! ‘I will go back to the Hatter and the other tea-party-goers and tell them that I never want anything to do with numbers!’ Alice smiled as she thought of this. ‘no more of those boring math classes for me.’

Suddenly the Minotaur stopped walking. Alice almost bumped in to him, immersed as she was in her thoughts, and she saw that they had reached an open spot in the forest. There were no trees, but only very tall grass. When she looked more closely, she saw that the grass in some places hid a brick wall. Then it struck her. This was the Minotaur’s labyrinth! Ever since Alice had read about the labyrinth in her sister’s books this was how she had imagined the Minotaur’s home to be: as a large, circular and stoney structure. Hidden somewhere far away in the middle of nowhere. The Minotaur turned around and started to speak: “you ask me whether we really need numbers… well I can tell you one thing; I don’t need them. The Architect, who designed my home for me, gave me several lists each of which tells me where to find a particular room. For example, if I want to find the way to my bedroom,” the Minotaur said while pointing one of his hoofs in the direction of the labyrinth, “I take the list with the title ‘bedroom’ and simply follow the directions that are listed. That is how I know where to go. Numbers are difficult things. It’s better to stay away from them.”

The Minotaur’s words puzzled Alice. On the one hand she was delighted to hear someone say that mathematics is not as all-important as her big sister always said, but on the other hand she felt that there was something not quite right about what the Minotaur said. “But,” Alice said, “what kind of directions are there on the Architect’s lists?”

“Well,” the Minotaur answered, “the list tells me to walk a bit and then turn, and then walk a bit more and make another turn… and then hopefully, after a few such bits and turns I am where I want to be.”

Alice didn’t have to think very long about her reply. Being the clever girl that she was, she had come up with the idea that the Minotaur, although he had told Alice to stay away from numbers, made use of numbers himself! Only the numbers that the Minotaur used were cleverly hidden away by the Architect in the lists with directions. Alice mumbled, half to herself, half to the Minotaur “If all that the directions on these lists say is something like ‘walk a bit, and then turn’, then how do you know how much is a bit?” With a stern voice (which Alice had often heard her mother use when Alice and her sister had misbehaved) Alice asked the Minotaur “isn’t there something more on the lists? …distances perhaps? …and aren’t those distances… numbers?”

The Minotaur sighed and lowered his head. After having stared at his feet for a while, he looked again at Alice. The pride Alice had felt upon having discovered the numbers that she believed the Architect had hidden in the Minotaur’s lists disappeared instantly when she saw that the Minotaur had tears in his eyes. “Why are you crying?” She asked, now with a soft voice.

“I never learned how to count,” the Minotaur said while trying to wipe away his tears (which was quite difficult due to the sharp edges of his freshly-trimmed hoofs), “so specially for me the Architect made lists with directions without numbers. Every direction just says: ‘turn right and walk until you can’t go any further’ or ‘turn left and walk until you can’t go any further'”.

“Oh,” said Alice, feeling very sorry for the Minotaur. “But…” she suddenly remembered what the Hatter had told her. The Hatter had said that the Minotaur must know very much about mathematics because the Minotaur’s name, just as the word ‘mathematics’, starts with an ‘M’. “Then why does your name start with an ‘M’?” Alice asked.

“I hope Mr. Hatter has told you” said the Minotaur, who had difficulty with wrapping a handkerchief around one of his hoofs (actually, the Minotaur had never wrapped a handkerchief around a hoof before, because minotaurs almost never cry), “that I am usually called ‘the Friendly Minotaur’. My mother gave me that name because she wanted me always to remember that we can be Free of Mathematics. And that’s also why she never taught me how to count.”

Alice couldn’t understand how it was possible that someone can’t count. ‘If I couldn’t count’. she thought, ‘I wouldn’t even be able to trim my nails properly.’ Alice always counted her fingers while she was trimming her nails because she was afraid that she might miss one if she didn’t (Alice didn’t realise that since the hoofs of Minotaurs are split only in two they don’t need numbers to trim them without missing any hoof-parts).

‘So we still don’t know whether we need numbers,’ Alice thought while frowning sadly. Again she addressed the Minotaur: “so you don’t need numbers, but that doesn’t mean that nobody needs them. How do you think the Architect made the lists with directions in the first place?”

“Well… I don’t know” the Minotaur said hesitatingly, “maybe we should ask the architect himself? I am told he lives on a steep hill beyond the forest’s rim.”

“let’s go on an adventure then; let’s go to the Architect!” – said Alice.

In the next episode of ‘Numbers in Wonderland’ Alice and the Friendly Minotaur will meet the White Rabbit and they’ll find out that the Rabbit’s watch is a strange thing indeed!

Next episode of ‘Numbers in Wonderland’ $\Rightarrow$ The White Rabbit’s Watch

Philosopher of physics at Amsterdam University College and Utrecht University, managing editor for Foundations of Physics and international paraclimbing athlete
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