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Achilles and the Tortoise -
and the Hedgehog
Achilles
was the fastest runner in Old Greece. He had won plenty of
olive-branches at
the Olympic Games. One day, however, the hedgehog challenged him: ”You
are quite fast, but I am faster than you.“ ”You
miserable dwarf! You believe you can get the better of
me?“ Achilles laughed. ”Just wait,“
answered the hedgehog.
The
hedgehog did what hedgehogs always do if they want to win against
people who
are faster than them. He invited one of his fellows for a plot. He let
Achilles
run, but at the finishing line, the second hedgehog emerged from his
hiding-place. Unfortunately, Achilles was not as fast in thinking as he
was in
running and fell for the simple trick. Thus, the hedgehog won the
prize,
foolish Achilles reaped mockery and derision.
In
low spirits, he adressed wise Aenon for help. ”Poor
little fool,“ said Aenon and explained: ”When
you
start, the second hedgehog is watching you and emerges from his
hiding-place. To
win against him, you’d have to be faster than light. It needs a little
while to
get from the start to the second hedgehog. It’s not until then that he
knows
it’s his turn. Otherwise, he’d be early or late.“
Achilles
didn’t quite understand so far, but as he had been humiliated as a
sports
champion, he reacted immediately.
”Well,“ he
said, ”next time I’ll be faster than
light.“
Now
Aenon was perplexed, and an instant later even more dumbfounded as
Achilles
continued: ”You know quite
a lot, don’t you. Can you tell me a proper training method?“
Aenon
wanted to kick him out of his house, but then an idea came into his
mind.
”That’s Greek to me,“
Achilles interjected. ”Explain.“
”Take a tortoise
as your partner.“
Again,
it was Achilles turn to be dumbfounded.
”But give it a
little advantage.“
Achilles
face turned red. He took a stone and brandished it over the
philosopher.
”Give it a big
one, if you like.“
This
was no great appeasement for Achilles. ”I’m
faster
than a tortoise, may it have a lead, as long as the way from Marathon
to
Athens.“
”Yes, indeed.
The point is: When approaching the tortoise, you will get faster and
faster. In
the very end, you will be faster than light.“
”You are either
an utter fool or a genius,“ Achilles shouted and cast the stone away.
”A stone can’t
be faster than light,“ Aenon said, ”but
you can –
you only have to catch up with the tortoise. Look: To cover the
distance from
your starting line to the starting point of the tortoise – this is part
one –
you need, for example, about two hours.“
”By far less,“
Achilles boasted.
”Meanwhile, the
tortoise has moved a little forward. This is part number two. For this
one, you
only need a few minutes.“
”By far less,“
Achilles boasted again.
”You really are
Speedy Achilles. For part number three, you need even less time; and so
on for
number four, five, six, seven. Less and less time per distance, this
means
effectively: higher and higher speed, doesn’t it?“
”Less and less
time per distance,“ Achilles repeated thoughtfully. ”Less
time per distance, this is faster, that’s what my old
fitness coach said, too. Less and less time per distance, this is
higher and
higher speed, of course!“
”Logically. One
should systematize such conclusions one day,“ Aenon pondered. ”And,
as the tortoise nevertheless continues to creep a
little further all the time, you never stop to get faster; finally, you
will be
faster than light – and, subsequently, faster than the second
hedgehog.“
”Unbelievable!
You are a genius! And this is true for sure?“
”As true as I
am a Cretan.“
Presently,
Achilles started his training competiton against the tortoise. However,
due to
his feverish ambition, he forgot to eat enough before the race. Being a
great
athlete, he nevertheless catched up with the tortoise near Athens.
Unfortunately,
he felt giddy a few steps before reaching the tortoise; then he blacked
out. ”Well, that’s how it is when you surpass
light, if you
surpass other runners, you don’t see them any more either.“
As
he stopped a short time later and his senses became clear again, he
turned
around. He had left the tortoise far behind him. Happily he returned
and
challenged the hedgehog for a return competition.
The
hedgehog agreed, engaged his partner again and won his second
olive-branch.
Foaming
with rage, Achilles knocked at Aenon’s door. ”You’ve
promised that it is impossible for me to lose!“
”You’re all
liars down there!“
”Don’t shout
around so loudly. It’s really not necessary. Remember, we’re well known
for our
self-criticism…“
”I will never
ask your advice again. Next time, I’ll counsel Zenon. He’s much wiser
than you
are.“Achilles
walked away.
”Well then, go
to your friend Zenon,“ Aenon said with a smile that Achilles couldn’t
see any
more, ”you will see how far you’ll get
there…“
Janosch
Jandar
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