Who are the relevant experts?

The Pig that Wants to be Eaten

#34: Don't Blame Me

In which an expert is not an expert, except when they are.

Who is ultimately responsible for a person's actions? Your instinctive answer is probably that a person themselves is generally responsible for their own actions. This is correct. End of blog post.

...not quite.

Because people don't operate in a vacuum. Our decisions are influenced by events and people around us, and sometimes these factors are out of our control.

In particular, sometimes we obtain advice from others regarding the best course of action. If we then follow that advice, to what degree can we abdicate our responsibility for any negative consequences? For of course, people are happy to attribute positive consequences to their own behaviour.

Unfortunately, it's not as clear-cut as it first appears. For instance, if my company computer stops working and I ask a computer technician friend what to do, it seems reasonable that his advice should be followed. However if this advice only damages the computer further and the company is unhappy, is it fair to pin the blame on the friend rather than myself?

In some sense it is - my friend is a 'relevant' expert, which means that I ought to trust their opinion on this matter over my own. But relevance is relative. My friend might be an expert on computers, but not on giving advice about computers. Or he might not even really be an expert at all, and I'm just mistaken. So how are we to know how to apportion blame?

The key thing is that me choosing to ask my friend for advice and then choosing to follow it are my actions - I can't blame these on my friend. I can only blame him for the advise itself. If there's good reason to believe he is a relevant expert, then the burden of blame shifts more towards him, but it doesn't absolve me of blame completely.

So there's a spectrum of degree of responsibility, based on the suitability of the received advice. But determining the relevance of an expert is not necessarily straight-forward. For example, consider the following examples:

• "I'm dumping you, because my financial advisor told me to! You're bad for my bank balance!"
• "I'm dumping you, because my psychologist told me to! You're bad for my mental health!"
• "I'm dumping you, because my palm reader told me to! You're bad for my life line!"

Different people can have different opinions as to the degree of relative responsibility that can be placed on the dumper in each scenario.

So what can we conclude? Some degree of responsibility must lie with the person who performs an action. But maybe if they were advised by another to act in a certain way, we can't lay all the blame on them.

Up next: A Turing test

To heap, or not to heap?

The Pig that Wants to be Eaten

#94: The Sorites Tax

In which a heap is not a heap, except when it is.

Does increasing the tax level by 0.01% leave anyone worse off financially? Of course it does - you will have less money in your next paycheck. But will you be substantially worse off? Unless you believe all taxation is theft, the answer is probably no - someone earning the NZ minimum hourly wage of $15.75/hour would pay an extra 5 cents/week in tax[note 1], which is unlikely to break the bank.

But if the government kept up the tax increases daily for 300 days, suddenly that person's paying an extra $19/week in tax. For some people, that really would have a substantial impact on their finances. So how can we reconcile this apparent incongruity?

That's easy, of course - many small changes can combine to make a large one. We see this in protest movements, in bird migration, in the pollution of the ocean with plastics - every individual member of a group performs a small action, but the sum total of these actions is something major.

The situation here is slightly different, however. And it's a tricky, but interesting difference.

This problem as stated above is a modern version of one called the Sorites paradox. In the original problem, the question concerns a pile of sand grains and the definition of the word 'heap', and rests of the following principles:

      1a) A single grain of sand is not a 'heap'.
      2a) Removing a single grain of a heap from a 'heap' will keep it being a heap [or alternatively,  adding a grain of sand to a 'non-heap' will keep it a 'non-heap'].

Both of these principles seem valid on the face of it - but their co-existence is contradictory! They partition the world of sand piles into two groups: 'heap' and 'non-heap', with no amount of adding or removing grains able to transfer a pile from one group into another. But this is clearly absurd.

There are ways around this, of course. The easiest way is to reject principle 1a) - to say that all piles of sand with 1 or more grain are to be considered 'heaps'. This avoids the contradiction.

However, this is rather disingenuous - it flies in the face of the regular definition of the word 'heap'. Furthermore, it is equivalent to asserting that a tax increase of 0.01% does have a substantial effect on finances. But unlike the heap problem, the tax one can be diluted. Is it fair to argue that a tax increase of 0.001% has a substantial effect? 0.0001%? One-one millionth of a percent? One-one billionth? To claim these all have a substantial effect is logically consistent - but linguistically unacceptable.

There is another way around this, and it rests in principle 2a) - specifically, what I've written between the square brackets. It follows logically, of course - unless you consider the adding or removal of grains to a pile to itself be part of the pile and thus its 'heap-ness'.

For example, it we disregard the section between the square brackets, we could imagine a pile A, which is not considered a heap. We add a grain of sand, making a new pile B, which we do consider a heap. Now we remove a grain of sand from pile B, making a new pile C. By principle 2a) we must consider this to be a heap too. So what is the difference (if any) between piles A and C?

Well, there is no intrinsic difference. They contain the same number of sand grains; although the exact grains used and the arrangement of them may differ, they are essentially identical. However, there is one key distinguishing property - the manner of their creation. Pile C was created from a heap - perhaps this is sufficient to distinguish it from pile A?

A casual observer viewing piles A and C on a table would not be able to distinguish between them. So should only one of them be a heap? Again, this seems linguistically unacceptable. The corresponding argument in the case of taxation, that a particular total tax rate increase would only be substantial if it were slightly less than another substantial one, but not if it were simply raised to that level, is clearly absurd. We would have to conclude that (for example) a 2% tax rise is not substantial if done on its own, but a rise to 2.1% and then a drop to 2% relative to the original would be substantial.

But perhaps a heap of sand is a very specific measurement! Perhaps 10,000 grains make a heap[note 2], and not a single grain less. This defies principle 2a) as well, but it does it in a more linguistically appealing way. Perhaps we've found a solution after all?

In the case of the heap, this solution is fine, as long as we modify principle 2a) as follows:

2b)  Removing a single grain from a 'heap' will keep it a heap, unless it is a heap of 10,000 grains, in which case removing a grain will turn it into a 'not-heap'.

This lets us determine that piles with 10,000+ grains of sand are heaps, while others are not.

The biggest problem with this is that the determination of the precise number of grains in a pile is unlikely to have widespread agreement. This makes the word 'heap' rather useless if its job is to communicate meaning between people. But if you don't mind that either, then you've solved the heap problem!

Okay, I lied. That's the smallest problem. The biggest problem is a lot more subtle, and a lot more intractable.

Let's stop talking about heaps and start talking about dominoes for a second. Suppose you set up a row of dominoes, such that the following rules apply:

      1c) The first domino will be knocked over.
      2c) A domino that is knocked over will also knock over the next domino in the row.

It's easy to see that under these conditions all the dominoes will be knocked over[note 3]. Of course, that rests entirely on the guarantee provided by rule 2 that a domino will always knock over the next domino in the row. If this fails even once, then we can't conclude that all dominoes will fall.

The problem with applying this to the tax scenario is that in the heap scenario, all grains of sand are equal. However, this is not the case with tax; different people pay different amounts of tax based on their income levels.

And the argument is as follows. Suppose you earn $Y and pay $X on tax. This leaves you with $(Y-X) to actually spend. Now if taxes are increased by 0.01%, then X will increase slightly, so you will have slightly less take-home income. But now you'll have just as much take-home income as someone who earns slightly less than you did before the tax was increased. Since for them the 0.01% tax increase was basically negligible, it will be for you as well, since you're now in that position. So another 0.01% tax increase won't affect you.

And now we see that the argument proceeds like the dominoes above - each increase in tax must be negligible, and (the key part) it was already negligible for someone else earlier. So there's no way to say that "10,000 grains is a heap" - a tax increase of 1% for you is just as negligible as a tax increase of 0.99% for someone earning a bit less than you [where negligibility is measured by the volume of reduction in take-home income]. But we agreed originally that a 0.01% tax increase is negligible for everyone - we've run into logical trouble!

Because we can run the same argument in reverse - if we keep increasing your tax by 0.01% a day, then eventually you'll be paying a substantial amount more in tax. But on whatever day that occurs, someone who earns slightly more than you will have hit that limit the previous day. And you can continue that chain of reasoning back to conclude that even on the first day the tax increase was substantial for someone, even though that's absurd.

So we have the paradox. The usual way we understand the concepts of 'heap', and 'substantial', are shown to lead to impossible conclusions in this scenario. But relaxing our definitions and allowing more vagueness doesn't allow us to handwave all our problems away - because the vaguer our terms get, the less useful they are as words at all! So we are left scratching our heads.

Next up: The blame game...

Note 1: My maths might not check out, but the point stands that the increase is negligible.

Note 2: Archimedes called the number 10,000 a 'myriad', which is a much cooler word than 'heap'.

Note 3: If there's at least one domino that isn't knocked over, then we'll consider the earliest domino that isn't knocked over (i.e. the domino closest to the first domino that isn't knocked over). In particular, this can't be the first domino (impossible under rule 1), so it must have had a domino before it in the row - and this domino must have been knocked over (since our domino of interest was the earliest in the row to not be) and so by rule 2 our domino would have been knocked over too. This means such a domino must not exist.

Doctor Who - Season Six, Episode Eight

Let's Kill Hitler

Except actually, let's not.

He was barely in the episode at all.

I have apprehensive feelings about this episode. Even though I've already seen it. I can't quite put my finger on why I didn't like it. All the plot twists were surprising and the acting was great (ILU RIVER XOXO)

I'm guessing this clip will be from Episode 13

But I suppose the reason that I didn't like it is that it was kinda a gimmick. Like The Next Doctor before it, once you've seen it and know the ending (or in this case, that Hitler has nothing to do with the storyline and it could have been set anywhere) it loses some of its magic. Mels/River was absolutely amazing though. As were Robot Amy, Hitler-punching Rory, the Doctor (as always (although not a fan of that whole poisoning plot)) and Rose! Who will always be my favourite of course. Next week's episode looks quite scary. Although it's written by Mark Gatiss, so you never know.

Sorry.

So I haven't posted for two months, been kinda busy. But I couldn't wait to finish How I Met Your Mother so I've raced ahead and finished all six seasons. It's okay though because I have some plans!

• Review new episodes of HIMYM as they come out. This gives me a whole week for each episode.
• Do the same for Doctor Who, starting with Let's Kill Hitler in a few weeks time.
• Start watching Battlestar Galactica which is apparently really good.
• Finish Oliver Twist and Anne of Green Gables, and hopefully start another (more interesting!) book.

We'll see how that goes.

How I Met Your Mother - Season One, Episode Six

The Slutty Pumpkin

The slutty... pumpkin???

Halloween party costume gone wrong?

Costume?!?

Maybe Robin, who doesn't usually like Halloween, will dress up as a slutty pumpkin? Marshall's is made of wool so he can't be a pumpkin. Barney likes Halloween because girls unleash their 'inner hoebag'. Where is Ted?

Robin has been dating a man for several weeks!! who is this man Robin and Ted are destined to be star-cross'd lovers

This show does actually title drop every single episode. It's actually quite nice. But what is this slutty pumpkin?

So it's a girl Ted likes.

He saw her 4 Halloweens ago? Ted, you live in New York. She's probably dead. Get over it.

Ted has told this story so many times that Barney, Lily and Marshall know all the words. I guess this was a defining life moment for Ted

Sonny and Cher...

I wonder what Marshall and Lily are going to wear this year? I'll guess that wool line wasn't throwaway

Why (why, wby) would you write your number on a CANDY BAR WRAPPER ON HALLOWEEN??!? Does Ted not have a single other piece of paper or anything?

Ted Mosby: Socially inappropriate since at least 2001

Marshall is a good Captain Jack

The Curse of The Black Pearl surprisingly came out in 2003 (I was 10, WTF) so my fears that the movie copied the show are unfounded. Is Lily meant to be a parrot?

"You're going as my wingman. Flight suit up!"

How punny.
Am I supposed to know what Ted's costume is? Because I don't.

Barney has (somehow) gotten his a Ted passes to the Victoria's Secret Halloween party! Also ,I have a feeling I might have seen this scene before. It's kinda familiar.
Oh man, I bet Robin's 'joke' will be serioused in the form of Mike.

Yep, it is

Barney is not having fun at the roof party (why can't he go to Victoria's secret by himself? Or invite other friends? Does he have other friends?) while Marshall, Lily, Mike and Robin go on their double date.

Robin is not putting very much effort into her relationship. I don't think it is going to end well.

Barney is repping a second costume

Satan

in case he strikes out with the hottest woman at the party. Is he gonna try and get with lei lady again?

So what's the bet Barney has a third costume? I don't think saying "I'm a horny devil" is the way to get with someone

Has Robin ever had a boyfriend before??? she is emotionally stunted

Naww Robin just got dumped :-(

Oh man I was fooled again! The penguin is the slutty pumpkin!

I wonder how Ted will scare this girl off.

can she drink through that beak?

LOLOLOL IT'S BARNEY
Oh man I wish I had a friend like Barney

Marshall and Lily won YAY

Ted and Robin hang out and talk about how much of failures they are
I wanna live in a New York apartment building! they are cool

So that plot... was weirdly unresolved? I guess that was the point but I don't like it

How I Met Your Mother - Season One, Episode Five

Okay Awesome

So thanks to the predictive power of flash-forwards (our future is their past) Ted will go deaf in this episode. Although the title makes no sense to me. It's not even a proper sentence.

Well, I stand corrected.

"Okay? Awesome!"

Damn title dropping all over the place. So I guess Okay is the hottest nightclub in town? Maybe the music is really loud and Ted goes deaf??

"A friend of yours named you?"

So even Barney has not been to this exclusive place. It must be full of women.

Racial diversity

I'd have to take a drink if I were playing the How I Met Your Mother drinking game right now. Because Lily's school children have been shown.

Lily and Marshall have been doing 'mature things' because Lily feels embarrassed that she spends all her weekends drinking beer at Mclaren's. So they're not invited then?

"She's fun, she's smart, she lives in the moment-"

"Translation: she's ugly, she's ugly, she ugs in the ugly."

 Lily thinks Ted's blazer is gorgeous but it's  kinda... purple?

I'm getting a Willly Wonka vibe

Barney has a strategy for picking up women.

It involves grinding

Marshall is not having fun at his adult party. Also he doesn't want kids. I wonder if Marshall and Lily will have kids sometime? I think I've seen one more episode of How I Met Your Mother where Marshall and Lily were hiding in the bathroom and Lily really had to pee. Although that might have been a different show. I guess I'll find out!

Ted said "this place is loud" so I'm liking my 'Ted goes deaf from loud music' theory! I bet he doesn't end up with Kelly because of misunderstandings caused by the loud music

Really, really, loud.

Kelly and Ted have some conversational misunderstandings while Robin is rejected by the VIP room and Marshall makes a fool of himself at the party.

So Marshall just jumped out the bathroom window (which looks way too small for him to fit through it) and is on his way out! But how will he get into Okay? Maybe he can be one of Robin's bitches too. Also that bathroom (which I'm sure we haven't seen before this) strongly resembles the one in my imagination in which Lily needs to pee. I'm excited for that episode to happen now that I know the backstory of the characters and stuff!

Ted has to pay $34 for two bears while Lily is bored by talk of Nora Jones. Wait, has Lily realised Marshall is gone yet? She must think that he's been in the bathroom for ages.

OH GOD TED WHY WHY WHY WHY WHY WHY

Ted is, the biggest fool EVER.

Just because the music is loud does not mean you should shout ridiculousness because obviously it will stop just as you shout "I'm wetting my pants!" I am actually apprehensive to watch the rest of this scene because I am cringing for Ted right now. 

Oh no Robin has now been left outside because the bouncers have changed! At least hopefully Ted will come out in a minute and they can hang

Coat-wench... Emma from Glee?!?

Now Marshall has bumped into Ted so he probably won't leave. Poor Robin.

Marshall has dental problems.

Lily has also jumped out the window and is also on her way to Okay, tho confront Marshall. What are the people left in their living room going to do?

Marshall is high on pills?

Now Lily and Robin have got into the club by flashing the bouncer. Not at all a sexist entry

"Those were the four greatest and only breasts I have ever seen."

Ted is chatting to coat wench, while Lily and Robin split up to look for Marshall.

But he's right in the middle of things...

Literally

Barney's grindee knows him and runs off horrified? Is it his sister i predict so

Also, Ted is wearing lots of coats for some reason

It was Barney's cousin Leslie and Barney makes Ted promise not to tell anyone. But Ted's just told his children in the future!

Why isn't Robin catching the taxi with them? I guess she lives in a different part of town.

And that's the end.

How I Met Your Mother - Season One, Episode Four

Return of the Shirt

Hmm, what shirt? I don't remember there being a shirt in any of the previous three episodes. Not one that was especially important anyway. Maybe I'll find out through flashback.

Ted says that only one relationship can end in happily ever after, and the rest just result in people getting hurt. This involves someone getting hurt. So it's obviously not about the mother, then, is it?! Why are his children not ragin'

The shirt.

Ted wears the shirt to Mclaren's, where Lily and Robin think it looks good.

Barney wants Robin to say 'nipple' on TV. She's not keen.

"Step into my web."

I have a feeling that this isn't just a throwaway line though. Probably it will happen right at the end of the episode.

Ted's 'genius' plan to re-date one of his old exes is FILLED WITH DANGER, TED. Don't do it!

Danger, Ted Mosby!

Even though Ted's wearing a new shirt and everything, I think this is just another way for him to stay inside his comfort zone. He knows his exes, and they liked him once, so it's much easier to try an old girlfriend than it is to try and chat someone new up. But I can tell that this won't be the mother anyway, because of Ted's comments to his children.

"Hold on. There are only two reasons to ever date a girl you've already dated. Breast. Implants."

Oh, Barney, you are so great.

We are then treated to a quick run-through of Ted's old flames: Steph, who made 175 porn films in one month; Jackie, a hit-and-run driver; and Natalie, who is obviously 'the one'.

Robin has been called to her boss's office to receive a story at City Hall!

Robin is emotionally overwhelmed.

It would be pretty lol if it turned out that the story was about a boy stuck in a toy machine at City Hall

It's about a 50-year old hot dog stand AND ROBIN SAID NIPPLE!!!

How exciting!

How does Barney have so much money to give away all the time?!

And now Barney has whispered something in Robin's ear! I bet that will come up at the end of the episode.

Has Natalie seriously not changed her number in three years? Ted should just fb her

Oh man I'm not certain but I'm pretty sure Natalie is Amber from House!!!! I just Wiki'd it and I was right! It also said she was in two episodes so maybe she's in this one and the next one? Or maybe she comes back in like season 6 or something. Anyway I'm guessing Ted was a dick to her since she hung up on him.

LOL he dumped her on her birthday. Wait didn't the same lady play a character in Friends who was dumped on her birthday??

Yes, she did!!!!

Friends parallels are infnite

Turns out, Ted just left her a message. Whatta dick.

Wait, did Barney just say he's 35? That's quite a lot older than the others. But he has a younger sister?? Bet she turns up sometime to complicate things for Ted

"An occasion that was supposed to be joyous suddenly turned tragic when Ethel and Sadie Margolis, New York's oldest twins, suddenly passed away on this, the eve of their 100th birthday. [Pause] I'm a dirty, dirty girl."

I can't put the noise he is making into words

Robin's boss needs some dogly advice. And he's not mad at her for saying these things! So I reckon she will get even more extreme with them (although my predictions up until now have been a bit rubbish).

Ted goes over to Natalie's (with a giant stuffed animal??) to say sorry. She's not very keen. And now Ted has tricked his way in oh lol

Natalie was not expecting this!

Oh man. This show. Its crazy camera angles are always tricking me. Ted left his message while the room was full of all of Natalie's friends at her surprise party! I suppose Natalie has nursed this hurt for 3 years and, to be fair, Ted was kinda an idiot. Couldn't he have waited just one day?

Everyone looks happy...

Now Ted and Natalie are back together again. But I sense trouble. Surely Natalie can't be the mother?

Oh no Ted 'has to break up with her'. No you don't, Ted! BAD TED! BAD! TED!

I don't think you always fall in love with people straight away, Ted. Give it a chance, man!

"Wanna talk mature? I just wrapped up a live newscast by honking my own boobs."

You go, Robyn!

Barney wants Robyn to do some chant/dance about a sports player... something something. Idk, I imagine Robin will get caught/fired after this

It's Natalie's birthday again!!!!!!

Ted is the most hopeless love person, EVER.

"You've already given me the best present of all: I can trust again."

Staying single is looking pretty good right about now

Robin and Henry.

Robin's not going to do the dance, is she? Poor Barney.
Robyn just fell over lololol

Oh man, Ted just broke up with Natalie. But how will she react? It could go either way I reckon but she'll probably be mad

I am occasionally psychic

Yeah, she's really mad.

Oh god she knows karate

Tu meke pictures? Sorry but they're tu good

So one thing I do like about this show is they do drop little hints throughout the episode to things that are gonna happen in about 10 minutes. Maybe I should start paying more attention to everything, because I did not expect this.

Oh man Natalie must come back in like Season 5 or something probably with her new husband. Or something.

Phew, I'm 2.94% through! Only 132 eps to catch up to America! If I watch one episode a day, I should be caught up around the 27th of October. Which means I won't be caught up since Season 7 will have already started screening. But oh well.