Absolutes are relative

I came upon a realisation in my first year of university. There are very few absolutes in the universe.

I was sitting in the lecture theatre, taking notes of the professor’s lesson. I was in my first year, and in my first semester, and I haven’t any friends I knew there. “Friends” were people I saw frequently (if you could call the first 2 weeks “frequently”). After two and a half years of being conscripted in the army, my brain was raring to go (about the most mentally strenuous activity I remember was figuring out how dBase IV and FoxPro work [those are database systems by the way]. Oh and how to make the records print nicely. That’s interesting, considering that I had to send letters to over 500 military personnel, and one choke of the printer sent hours and tons of paper to waste. Lining up address information on the paper could be quite challenging. Another story for another time…).

It was a maths lecture (not surprisingly…) about fundamental logic (I think). I learnt of the term “for all” (or “for every” or something similar), which is represented by an inverted capital A. For example, for all even numbers, one of the factors is 2.

This “for all” term is not used lightly. When you say, “for all”, it means for all conditions, circumstances, situations, universes, even alternate realities, that the next statement is true.

And as the professor said, all you need is one example of the statement being false, and the whole statement collapses.

A related concept is the negative. For example, “There is no such thing as a zombicorn.” First, there’s no such thing as a zombie. Second, there’s no such thing as a unicorn. Uh, I’m not going to contest you on that. Go Google it or something…

What you mean by “There is no such thing as XYZ”, is that for all conditions, circumstances, situations, universes, even alternate realities, that the statement is true. And all you need is the existence of XYZ for that statement to be false.

Because of this, the professor also said that it’s impossible to prove a negative. We just barely found Earth-sized, possibly habitable planets at the outer reaches of our exploration of space. How can anyone possibly search the entire known (and unknown) to find that one existence of proof? Have you searched all the planets out there? Do you know for sure, that there is absolutely no way that XYZ can possibly exist?

This is why I find maths interesting. Some of its concepts can be proven. For example, the statement “There is no such thing as an even number with a factor that’s 2.” All I need to disprove that statement is find the existence of an even number with 2 as a factor. For example, 6 (with 2 and 3 as factors).

Once I realised that about the only absolute statements are in maths (and possibly physics, but I suck at physics, so, yeah…), and even then those absolute statements are held in the strictest of scrutiny, I also realised that (almost?) everything is relative. Yes, I know I’m way behind some fellow named Einstein who mentioned some theory of relativity somewhat…

The notion that nothing is absolute scares the hashbrown out of some people. Those people need to know that this is right and that is wrong. That this is black and that is white. That there are clear cut lines with which they can stand behind of. That there are “right” arguments and opinions they can back themselves with.

For example, the statement “You’re always late.” really means the person is saying you’re always late in the person’s mind. Never mind the few times that you are early, because that person will conveniently forget about those instances (because of cognitive dissonance. The person had to convince herself that she’s right about you being always late, and thus fabricates proof that substantiates her opinion). Also, it presupposes that you will continue to always be late. And all you need is to be early once, and that statement is false (but cognitive dissonance will thwart your attempts at defending yourself).

This taught me to be tolerant of other people’s views. When nothing is absolute, then nothing is certain. Like I said, this scares the cranberry out of some people.

And this coming from a maths lecture. More interesting still, it came from a discipline that’s known for its strictness.

Carcerian Stones – Where is this Arofell fella?

We’re continuing the D&D adventure story. Previously, we found our adventurers at the gates of Havenswerd, and the bard declared he’s a criminal in the city. We have Ryan the human DM, Dan playing Toth the goliath warden, James playing Heoriss the eladrin invoker, Ian playing Iofae the eladrin sorcerer, and Klenn playing Phileas the half-elf bard. And now…

Wait, there’s also a puzzle hidden in the story. And now…

*****

Ryan: Havenswerd is a big city. You’ll need some know-how to navigate the streets.
Dan: You’re throwing a skill challenge at us?
Ryan: 3 separate ones, in fact. One for shopping, one for the tavern investigation, and one for our bard reaching his friend.
Dan: But it’s just shopping!
Ryan: *shrugs* It’s a street maze. You’ll have to find the shops first.

Ian: How good are we at Streetwise? I have a 4.
James: I’m at ground zero.
Dan: I’m below ground zero… Negative 1! Never thought Streetwise to be useful…

Ian: Alright, we’ll have to swap then. My brother will still go to the tavern. Dan, you go with him. He might need help. And I’ll go shopping. Do I need a list of what they’re buying first? *looking at Ryan*
Ryan: No. You just need to find a shop first. I’ll let you buy for them then, even if these guys aren’t around.

Dan: Wait a minute. So we’re split into 3 groups with individual skill challenges?
Ryan: That’s right.
Dan: That’s not the way to do it.
Ryan: Well, you’re the one who split the party. Besides, it’s different.
Klenn: I think it’s fun, and saves time. So how do we do this?

Phileas gave the party some directions on how to reach the tavern. Through his friend, he’ll contact the party once he’s safe.

Ryan: Hold on a second. Uh, Klenn, you mind telling me who this trusted friend of yours is?
Klenn: Oh, he’s a thief lord, of some sorts. His name is Logan.
James: *shocked* You’re consorting with scoundrels?
Klenn: Let’s just say my character has… flexible morals.
Dan: *pounding on table* AHAHAHA! That’s a good one!

It was late afternoon, and though there’s still light, Phileas didn’t want to wait outside Havenswerd for night to fall (what with the wolves and all). He moved briskly along the side of the walls and disappeared into the shadows of the residential houses. The rest of the party will be split in 2. Iofae will attempt to navigate the streets to find the shops for purchasing much needed equipment. Toth and Heoriss will go to the tavern, retrieve Phileas’ belongings if they’re still there, and gather clues about the murder.

Ryan: So, which group wants to start first?
Klenn: Me. What am I to do?
Ryan: You’re trying to sneak around to reach your friend, so roll for Stealth first, then for Streetwise.
Klenn: *rolls d20*

Phileas reached his thief lord friend.

Klenn: Yes!
Ian: My turn. Streetwise huh? *rolls d20*

Iofae got lost in the maze of identically-looking streets.

Ian: Sorry guys… Now what?
Ryan: Hmm… Roll for Perception.

But he did notice a man slinking suspiciously into an alley. Iofae, lacking any other direction, decided to follow him. At the end of the alley, there was a door. But the man had disappeared.

Ian: I open the door.
Ryan: It’s locked.
Ian: I’m so glad I took this. I have Thievery. I try to pick the lock.
Ryan: Go ahead.

The locked door opened with a soft click. It was dark inside. Iofae moved in further and was stopped by the feeling of a sharp point propped against his neck. “Move any closer, and I’ll slit you.”

Torches lit up, and Iofae saw the man he was following holding a dagger to his neck. There was a group of men further in. He also saw Phileas among them.

Klenn: I am?
Ryan: Ian unwittingly stumbled into your friend’s hideout.
Ian: Oh cool!
Ryan: And you can get help with the shopping from these new friends. And now we turn to our CSI team here…

Medieval alley
[image by jewhyte]

Toth and Heoriss reached the tavern. They decided to go around to the back, where Phileas jumped off, instead of asking the good lady tavern keeper.

Dan: 2nd floor, right? Ok, I’ll heft you up.
James: I’ve got a better idea.

Heoriss blurred, and reappeared at the 2nd floor.

Dan: Bloody eladrins and their teleportations. *smile* Ok, I’ll climb up.
Ryan: Roll for Athletics.
Dan: *rolls d20* Yes!
Ryan: Now roll for Stealth.
Dan: What? Why?
Ryan: Because you’re trying to be quiet.

Toth managed to climb quietly up to the 2nd floor of the tavern, and entered what used to be Phileas’ room through the open window. The dead body was already removed, and there were signs of cleaning up, though there’s still a reddish stain on the floor.

Ian: Blood is notoriously hard to remove…
James: Ok, we search the room for Phileas’ belongings and any clues to the murder.
Ryan: Perception check.
James: *rolls d20* Alright, 20! That’s 29 total.

Heoriss finds a pouch with some money, a flute, and a long sword with some runes on it, hidden away in a corner behind a small cupboard. He also noticed a golden dagger jutting from the ceiling, stuck in a wooden beam.

James: Ok, you’re up.
Dan: Alright. Can I reach the ceiling, or do I have to jump?
Ryan: The ceiling’s low enough for you to reach with a small jump. To simplify things, I’ll just let you pass with the jump.

Toth looked at the golden dagger in his hands. A strange symbol is engraved at the hilt, but both of them didn’t recognise it. They heard someone coming up the stairs, and the voice of a woman saying, “I’ll be right back!”. They decided they’ve gotten what they could find, and left the room in the same manner they came in.

When they were on ground level again, they heard a psst. A shabbily dressed man, a beggar most probably, was looking at them. “Hey. You Toth and Hayoris? Pheeleeus sent me.” They followed the beggar, and reached the thief lord, Logan’s hideout. And the party was reunited.

It’s night time, but somehow, Logan managed to get their stuff bought.

James: We suck. We seriously need some cash. And quick.
Dan: Hear hear.
Ian: There’s not a lot we can buy. Hey, what about this Arofell wizard? We need quests. He seems like the kind of person who gives quests.
Klenn: Yeah. He’s at the Wizards Guild, right? Can we go to this Wizards Guild?
Ryan: So it’s decided? You’re going to Wizards Guild to look for Arofell?
Dan: Yup.
Ryan: You wanna do it at night?
Dan: Oh…

The Wizards Guild

The next morning, the party left to look for the Wizards Guild. Logan got Phileas a disguise, so the half-elf could move around the city.

Dan: Do we need a Streetwise check?
Ryan: *smile* Nope.

Logan also sent one of his underlings to guide the party to the Wizards Guild. It was mid morning by the time they reached the guild. The small guild “office” had a clerk, and the party asked him where could they find Arofell.

“Oh it’s my first day here. Perhaps you could ask the wizards back there. There’s a building behind this one that acts as their labs.”

They went around to the back and saw a 3-storey high building. They counted 1, 2, … 7 doors on each storey. A wizard or two hung around in the courtyard, and apprentices scurried back and forth.

“That nincompoop! I would sooner burn myself to death than to share the same floor as that useless excuse of a wizard!”
“Oh don’t mind him. He doesn’t like Arofell very much, so he moved to the top floor.”

“Who? Arofell? My master sent me to deliver a message to him once. I think his door was odd-numbered.”
“So what’s his floor?” Toth asked. But the apprentice had scurried away.

“Pardon me? You’ll have to speak louder, young man. I can’t hear you.” A wizened face was straining his eyes to look at the party.
“DO YOU KNOW WHERE TO FIND AROFELL?” Heoriss shouted.
“I’ve been on the ground floor for many years, and I’ve never known this Arofell wizard.”

“I only know all the wizards take larger numbers as their door numbers. Well, except for the one at the top floor, who took number 1. He always insult me whenever I pass a message to him, that arrogant, self-important piece of … Uh, you wouldn’t tell anyone about what I just said, would you?”

“Well, I do know the corner rooms of the 2nd floor aren’t taken.”
“How do you know that?” Iofae asked.
“Because, I uhm…” The young man was blushing furiously.
“Ahh, a tryst?” Phileas offered.
The young man blushed even more.
“If I work hard for a few years, I’ll be able to marry her, and get ourselves a house.”

James: Any more clues?
Ryan: That’s it.
Dan: Alright, math genius, this is your kind of thing.
Ian: Hmm… it’s elementary, my dear Watson.

The party deduced the correct room of Arofell, and entered the room. In it, they found piles and piles of paper and books. The candle on the desk had long ceased burning. A large book lay open on the desk, and a man, perhaps in his mid-forties, was snoring on top of it.

“Mr Arofell?” Phileas asked.

to be continued…

*****
P.S. Skill challenges are non-combat encounters. There’s a difficulty class (DC) for the appropriate skill and situation. For example, to pass a DC 16 for Athletics, you need to roll a d20. If the result plus your Athletics score (plus any other modifiers) is equal to or greater than 16, then you pass.

Update: I changed the sword of Phileas in the tavern from a magical short sword to a magical long sword. Yes, I know it sounds like innuendo. I just need him to deal a bit more damage, even if it’s all in my mind. … Alright, stop leering. You’re creeping me out…

The barber paradox

Suppose there’s a barber who shaves only those who do not shave themselves. The question is, does the barber shave himself?

That was the question I posed in a previous article. The hint to the answer was actually given in the article: “What if your original assumptions were wrong?”

So let’s begin, with two fictitious men, John and Ricky. John has this unfortunate streak of accidental cuts, so he doesn’t shave himself if he could help it. Ricky has this inexplicable fear of people wielding sharp objects around his face (ever watched Sweeney Todd?), so he shaves his own beard.

It’s actually a mathematical question on logic. So forming the statements, we have:

If John does not shave himself, the barber shaves John.
If Ricky shaves himself, the barber does not shave Ricky.

Here’s the interesting part. Let’s substitute “John” and “Ricky” with “the barber”.

If the barber does not shave himself, the barber shaves the barber.
If the barber shaves himself, the barber does not shave the barber.

Either way, the statements don’t make logical sense, each contradicting itself and creating a paradox. So what went wrong?

The statements were correctly formed. It’s our original assumption that’s wrong. What’s our original assumption? That

there’s a barber who shaves only those who do not shave themselves

So the correct answer is, there’s no such barber.