Spherical geometry – a brainteaser or math funfact

This is a three part post. First there is a tiny bit of background, which you can skip if you don’t care why I wrote this post. Then there is an interesting mathematical challenge, that requires no calculations what so ever. It is however not a challenge at all if you already know how to prove the basics of spherical geometry. You can skip this as well, if you don’t want to think right now. And finally, after some spoiler-spacing, there’s the “Funfact”/solution to the challenge.

Tiny bit of background

So this morning I start thinking about spherical geometry in bed. Thinking about math at random times is not unusual for me, but not super frequent either, but on Thursday I had a four hour math test as a step towards getting a Massachusetts teacher’s license and it got me in math thinking mode.

It was a pretty good test, I think. The questions are varied and challenging, especially if you haven’t that particular kind of math for almost 20 years, or ever. For several of the more difficult questions I had to reconstruct bits of method that I couldn’t recall from first principles that I could. For instance I haven’t done much integration for the last 20 years and couldn’t remember the substitution rule, but I could figure it out from what I do remember about integration. Mind you, it was multiple choice, so I got some hints.

Something that I had never really done though, to my recollection, and which was on the practice test (I signed an NDA for the main test), was spherical geometry. And this morning I started thinking about that in bed.

Challenge

I’m going to start this challenge with some background as well, so scroll down past the picture if you just want “Math problem now!”

We live on a sphere, or close enough to one to make us appreciate problems like the ones I’m going to put to you. In most aspects of our lives (if we don’t work planning international air traffic corridors) we don’t appreciate the spherical nature of our world. In fact, our immediate surroundings are dominated by local bumps in the terrain and optical aberrations in the atmosphere to the extent that otherwise intelligent people can be flat Earthers. But spherical geometry becomes necessary if you’re flying across the Atlantic, or if you’re surveying all of North America and attempt to fit thousands of perfect squares onto it.

Sask-Manitoba-border

The jagged eastern border of Saskatchewan, Canada

The problem we face is first and foremost related to our indoctrination in flat geometry and our reliance on flat representations of the spherical Earth, the things we call maps. If you want the shortest route between two points on most flat maps, it is actually not what you get if you connect the two with a ruler (except on the equator, or straight North-South). It’s what is called a “great circle”. And the challenge to you is simply this:

  • Think of two points on a sphere and how to find the shortest path between them. Use this to explain what a great circle is and how you justify that it’s the shortest path.
  • If we define great circles as the straight lines of spherical geometry (which mathematicians do, I just looked it up), what can we say about parallel lines on a sphere?

That’s it. That’s what I was thinking about in bed this morning, and which I will explain after some spoiler space.

Spoilers ahead!

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history.

Solution

Imagine two points on a flat surface, like a black(or white)board. Now draw spherical arch segments between the two, with different radii. Which arch is the shortest route? Second shortest? Third shortest?

We see that the bigger the radius, the shorter the arch segment between the two points, and we’re ready to move onto a sphere. Imagine the two points are somewhere along the 45th parallel (i.e at latitude 45° N). For instance two points on opposite coasts of the US, and (very roughly) 5000 km straight north from the equator. (Also imagine the Earth is a perfect sphere, and not slightly squeezed from the poles.) Now on most maps the straight line between these two will be along the parallel, but that is not the largest circle we can draw in 3D-space through those points. The largest circle is the one that has it’s center in the center of the Earth (and not just on the axis, like the 45th parallel) and therefore the other side dips down to 45° S on the points exactly opposite our two locations. And between the two points it goes slightly north. It’s a longer line on the flat map, but since it has the largest possible radius, it is the shortest path on the sphere.

Another property the great circle has, when we think of the sphere as perfect, is that it divides the Earth in two equal halves, like the equator, or a line of longitude. And that can be used to tells us something about parallel straight lines on a sphere. Namely that they don’t exist, and that “the 45th parallel” is either not parallel, or not straight. Surprise! It’s the latter.

If you take any straight line on a sphere it will be a great circle and it will divide the world into equal hemispheres. Let’s call them A and B. Now take any point on the sphere not on this first line and draw a straight line through that. Is it possible to have this second straight line be parallel to the first one, i.e. for them never to cross? No. Because this second line also divides the sphere into equal hemispheres.

Let’s do a proper proof by contradiction based on this.

Assume that you can have a parallel straight line. This creates equal hemispheres C and D, and since they are half the size of the sphere, they are equal in size to A and B. Since the lines don’t cross, either C or D has to be completely contained in one of the original hemispheres, which means it’s smaller, but we just said they were the same size, so we can’t have a parallel straight line on a sphere.

And that’s what I was thinking in bed this morning.

 

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DNA-tests: Cousin matches

Okay, unless I get some questions that need to be answered, we have now come to the third and last installment in this series of posts on DNA-testing for genealogy.

The first was a general summary.
The second some details about ethnicity tests.
This one will be about cousin matches.

But before I get into that, I’ll due a little bit about how DNA is inherited. Skip ahead if that bores you.

Before you forge ahead though let me just say this. Although these posts talk down DNA-testing, there’s no reason not to take one if you think it’ll just be a fun thing to have done. And all contributors, even the ones who don’t put a lot of work into it, add information for the ones who do put the work in.

DNA Inheritance

Most of your DNA can be divided into 23 distinct bits called chromosomes. Most of the time you can’t tell which bits belong to what chromosome, as it’s all a ball of loose yarn, but when it’s time for a cell to divide the yarn is balled up into 46 elongated blobs. There’s one blob 1 from mom and one blob 1 from dad. There’s one blob 2 from mom and one blob 2 from dad. And so it goes up to and including blob 22.

But wait. 22 times 2 is only 44. Ah, yes. Blob 23 is special. It’s where we humans keep the mammalian XY-sex-chromosomes. Other mammals have different numbers of chromosomes, and non-mammals have completely different systems to decide biological sex. That is of course completely irrelevant to this post, but if it can be shoe horned into a topic one should always include the fun fact that crocodile eggs incubated warm turn into males and crocodile eggs incubated cool turn into females.

That isn’t exclusive to crocodilians either, but in humans the system is that if your 23rd blobs are both X, you grow up female, and if one of them is Y, you grow up male. (With various exceptions that are beyond the scope of this post.)

When egg cells and sperm cells are formed, they include just one blob of each pair, so they can come together and create a regular old 23 pair cell. And if the blobs never changed each of them would be the same as one of the blobs your parents got from their parents.

If that was the whole story you would get 11 or 12 chromosomes from each grandparent, on average, although you could theoretically get none. Your dad, for instance, could pass on to you only the chromosomes he got from his dad. But even with whole chromosome inheritance that would be unlikely.

On average the chromosomes you would share with your ancestors would be:

  • parents 23
  • grandparents 11 or 12
  • great-grandparents an average of 5.75
  • 2nd great-grandparents ~2.875
  • 3rd great-grandparents ~1.9375
  • 4th great-grandparents ~0.91875

Yeah since you have 64 fourth great-grandparents, there would be some you shared no DNA with, since you only have 46 chromosomes to play with.

Fortunately for DNA testing that’s not quite how it is though. When egg cells and sperm cells are formed each chromosome from that persons dad and each chromosome from that persons mom, the grandparents of the future offspring, get intimate and mix it up a little.

You can see the result if you compare a grandparent and grandchild. Like below where I’ve compared my test to my grandmas. (It only shows 18 chromosomes because that was all that fit on one screen and I couldn’t be bothered to glue image files together.)

temp1

All in all my DNA is about 19% bits passed down to me from grandma. Which means grandpa got to contribute almost 31%, which is quite atypical. For any statistics nerds out there, it’s barely inside the 99th percentile.

This shows two things. By shaking things up like this you are almost guaranteed to share DNA with your 4th great-grandparents. But you’re going to share wildly different amounts with each of them. And your cousins who share those many times great-grandparents will share different bits, and maybe none of the bits you share. For instance, whatever ancestry my grandma had on chromosome 4 or 17, I’ve received none of it.

Cousin matches

The above to some extent explains why the match lists for these tests show the results as, for instance, fourth to sixth cousins. There’s just no way to know, without comparing multiple tests and an actual family tree.

And at the 4th cousins distance there is a 30 percent chance two random cousins don’t share any DNA at all, even though it’s 95% sure they both inherited some DNA from each of the shared 5th great-grandparents.

Only for the closest relationships can the amount of DNA shared be used to disprove a relationship. If you don’t share between 30-50% with a sibling, there’s a 99% chance someone will have to search for their “real” dad.

But if on the other hand you share 1% with someone, which is the average for a third cousin, you could also be fourth cousins, or fifth or sixth … and you can only find out which it is if you both have family trees going back that far and if none of your ancestors have a different parentage than what is recorded. And figuring out which one of you has an “error” in your tree, and where, is really, really hard.

Sadly 1% is a big match. Some people have only a handful (or none) at that level, and most of the hundreds of matches you have are likely much smaller. So to get anything out of them you have to trawl through them all, looking for the ones that have family trees that hopefully match up with yours.

When you do though, your reward is threefold:

1. You can “paint” another bit of your DNA like in the image above, but for ancestors further back. Some people are absolutely obsessed with this and give all the distant cousins they known DNA tests for Christmas and birthdays.

2. You have another piece of evidence that your paper trail is correct. Or, if you’re really hard core, another piece of evidence to link an ancestor without a good paper trail to your tree.

3. You have another bit of evidence you can apply to figuring out all the other matches you have.

And as I said up top, even if you don’t do all the hard work, you’re adding data for all the people who do. Just don’t be the person who uses a pseudonym, doesn’t have a family tree and doesn’t reply to replies even from second cousins. 😉

DNA-tests: Ethnicity estimates

A lot of people take the genealogical DNA-tests just for the ethnicity estimate. How do I know that? Well there’s the indirect evidence of them not uploading family trees and not replying to messages. There’s the indirect evidence of people writing in discussion groups that they got their cousins to take a test for them by talking up the ethnicity estimates. And most importantly there’s the people who do reply to messages, but who answer “I don’t really known any names beyond my grandparents. I only did the test for the ethnicity estimates.”

And there is nothing, well, very little, wrong with that. But if you do it for the ethnicity estimates you should know how wide the brush is with which the companies paint your genome. And it’s a lot wider than they advertise on the front page.

I’ll use myself as an example. Now all the companies agree that I’m European AF. 23andMe, MyHeritage, Ancestry, FamilyTreeDNA (FTDNA) all agree that I’m 100 % European. They further think I’m 90-98% North- and Western-European. But after that they start disagreeing, and before stating how they disagree, let’s briefly examine what they are actually testing.

Genealogical DNA-testing

All of these tests, and most publicly available DNA-testing in the affordable range today, look at so called SNPs, pronounced Snips, which are spots in the DNA code where some humans have one letter, and some other humans have another letter. These are just a tiny part of the overall genetic code, after all we share 98 % of our DNA with Chimpanzees, and 85 % with zebra fish, but there are so many letters in our genetic code that the 0.3% that vary from human to human still make up 10 million SNPs.

The genetic testing companies look at between 600 thousand and 900 thousand of these, and not all the same ones. And then they compare them between individuals and between populations. To make up ethnicity estimates they have picked between a few tens and a few hundred individuals in various regions and determined in which way they are similar to each other, and different from people in the other regions.

They’ve tried to pick people with deep roots in the particular region. It doesn’t help much to pick someone in a isolated mountain valley in Norway whose grandparents were all mining experts from various Central-European countries. But Europeans have been mixing for centuries and the companies can’t be too picky.

Finding the true homebodies also creates the opposite problem, at least in countries like Norway where every valley was its own little world for centuries and people were more likely to marry a fourth (or hopefully fifth or sixth) cousin than someone from the next valley. The problem is that you end up labeling as “Norwegian” a combination that is actually only common in a tiny bit of Norway.

But you can’t test absolutely everyone, and the major market for these estimates are Americans who read them for entertainment and to create another thing to fight about with family at Thanksgiving. “No wonder you’re so cheap, you’re 3% more scottish than I am!” This means that all of the companies oversell their estimates just a tinsy, winsy bit.

Back to me

So what does this mean in practice? Well it means that three out of the four companies think I’m 6-8 % British, with Ancestry tacking on another 7 % Irish, Scotish or Welsh, while the fourth, MyHeritage, puts 0 % in both those slots.

FTDNA thinks I have 0 % Finnish in my genes, 23andMe and Ancestry will stretch to “less than 1 % but not zero”, while MyHeritage think I have 7.5 %.

Who to believe? Well I know I have some Finnish ancestors on paper, and I have a bunch of Finnish matches on MyHeritage and FTDNA with apparently pure Finnish pedigree. So …

And that’s the problem with these ethnicity estimates. For the purely broad strokes they are fine, but people will compare them to known family histories and jump to conclusions, compare results on different tests and pick and choose, and look for plausible explanations even if those explanations aren’t particularly reliable.

Instead of concluding “These aren’t particularly reliable or useful” they will go “Well I’ve seen people say Danish ancestry can show up as British, and I have known Danish ancestry so …” And by ‘they’ I mean me. I was at that stage last week.

And remember, when you get to your 3rd or 4th-great grandparents 150-200 years ago, you’ve inherited 3 % (3rd gg) or 1.5 % (4th gg) on average, so if what you’re trying to prove is that a single one of them had some exiting and exotic heritage, you will either get no proof or rubbish proof. (Especially if by exotic you include already diluted heritage like “She was quarter Apache”.)

I mean, even I get a non-zero hit on Native American in my Ancestry results! And there’s no way that’s because of an actual Native American. Although … it could be that Native Americans and Samii have some small commonality, and any Samii would be through my grandmother who Ancestry labels as a full 1 % Native American … aaaand there I go over-interpreting the results again.

Don’t trust them, except when tens of percents tell you which continent (and general west, south, eastern Europe) your ancestors came from. But if that alone is worth $60-$100 to you, go ahead and order a test. Or wait for the next installment in this blog series where I explain about the exciting world of cousin matches.

Should I get a DNA test?

Short answer: No. Although it would be useful to me personally, so also yes. But mostly no.

Also short answer: Maybe. If you think it’s worth the cost and you have a realistic idea of what you’ll get. I’ll try to inject some realism through the long answer.

If you find this interesting, I’m doing another couple of posts about what I get out of it, but here a slightly shorter summary.

Long answer: So what is it you will get?

Ethnicity estimate

Ancestry composition, ethnicity estimate, admixture or Origins, depending on who’s presenting the results, is an estimate of where your genetic ancestry comes from. This quite fascinating, but it is also not very precise. Having done three tests and had the results analysed by another company and a free genealogical site, I can tell that the results vary a lot, and that I don’t trust any of them more than … say 50%.

Furthermore the randomness of genetic inheritance means that if you’re looking for, say a Native American component from the early 1800s, there’s a chance you didn’t inherit any significant markers of that ethnicity even if the family lore is correct. So unless you’re not sure what continents your immediate ancestors, say up to great-great-grandparents, came from it’ll not be useful, but you might find it amusing.

Some tests also give you results comparing your DNA to samples thousands of years old, connecting your genetic heritage to population movement in prehistoric Europe (which is useless if you don’t have European heritage). Also fun, but not particularly useful.

I’ll go into more depth on this in a separate blog post about Ethnicity estimates.

Medical information

Don’t. Just don’t. Unless there’s a specific and compelling reason you should not test for medical reasons. A specific and compelling reason could for instance be that you have a family history of a disease with a well documented genetic link and there are choices you can actually make based on knowing or not knowing if you have that gene.

You’re much more likely to get a long list of markers that have been linked to slightly elevated or lowered risks of this and that, which you can do nothing about, and be left with nothing except a slight unease. This unease might then spread to your relatives as you blurt out that you have the IGB13-t gene at Thanksgiving and terrify them into taking a test themselves.

Genealogy and cousin-matches

Like regular genealogy, DNA-genealogy is either hard work, or rubbish. You get a long list of DNA-matches, many of whom took the test two or more years ago just for the heritage composition, or for some other reasons aren’t interested in figuring out who your common ancestor is, and you get a few matches that are really close and easy to figure out.

And like regular genealogy there is plenty of room for making errors.
Maybe it’s a false match. The testing companies try to balance between ignoring useless matches and keeping good ones, but the technology used means there’s always some ambiguity.

Maybe you can’t find the common ancestor because your paper trail is wrong.
Maybe you find a common ancestor, and then you stop, but in reality you also share other common ancestors.

And of course there’s the small but real risk you might find out something about your immediate ancestors you rather you hadn’t. Like you match none of the descendants of your great-grandfather’s siblings.

It’s possible, but not very likely for that to happen by random chance. It’s possible there was an adoption event and your great-grandfather knew. And it’s possible you can work out that a cluster of genetic 2nd half-cousins you knew nothing about all descend from the postman in your great-grandparent’s village.

Will you find this knowledge interesting, or horrifying? You better decide before you test.

And also all the really fun things you can do, like: – breaking through brick walls and finding your way past gaps in the paper trail,  – painting your DNA and learning which bit of your chromosomes came from which ancestral branches, – proving beyond a shred of doubt that the family tree you’ve researched reflects biology as well as society, all require a lot of hard work and are made a lot easier if you start pestering all your relatives to test as well. And you don’t want to be that guy, do you?

The case for never throwing anything away.

I have too much stuff and it’s not well organised, so while searching through papers this morning I considered making a start at organizing and downsizing at least some of the clutter. Like for instance piles of travel scraps.

I have two nice photo albums from my trip to Australia and my third trip to USA that include some receipts and tickets and such in between the photos, and for at least a half dozen trips after that I’ve been saving small piles of such stuff with the intent of replicating the previous successes.

But motivation has been lacking, because it’s a lot of work, I barely ever look at them, they’re of little interest to anyone I know, and zero interest to anyone I don’t know. So I just have small piles of travel scraps that maybe it’s time to throw away.

But then I start looking through them and I pick up a receipt for two muffins and milk at Calgary Zoo. And the way the human brain works this drags up from the depth of my memory that day at the zoo. Me wondering what to have for lunch, finding a place to sit, stray memories of parts of the park and of driving there. All just because I looked at an old receipt that takes up hardly any room. So why not keep it?

Then again how important is it that I got to take this particular trip down memory lane? My day would have been pretty good without it. And I also found a receipt from an Edmonton gas station that triggered no specific memories what so ever.

In the end I think I’ll keep the cafeteria receipt and throw away the one from the gas station. I’ll keep the one from a super market in the south of France that reminds me of having breakfast in a small park / median, and throw away a pile of student association leaflets that trigger no specific memories. And I’ll put what I keep in a box clearly labeled “mementos” so I don’t have to search through it when I’m looking for something important, but will have no problem finding it when I feel like a trip down random memory lanes.

Am I pulling my weight?

As with any headline ending in a question mark, the answer is very likely to be “no”. For instance the Slavery Footprint calculator says my consumption is supported by at least 20 slaves. Now I have a bunch of quibbles with how that estimate is calculated and presented, but there is no doubt the prices of the goods I consume would rise by some degree if there weren’t absolutely insane inequalities in the supply chain. Even ethical choices aren’t completely disconnected from the global economy. If I pick up a bar of fair trade chocolate it’s not going to be the case that everyone is working 37.5 hour work weeks and will receive an old age pension when they’re 67. So the question should perhaps instead be “What’s the magnitude of my over-consumption?”

Of course that is really difficult to evaluate, even on a small scale. Let’s go back to the question in the title and the situation where the phrase has its origin; sailors pulling ropes on sailing ships. A heavier and stronger man than the average might pull with the same force as the others, which would be less than what he was capable of, or he might pull with the same percentage of his capacity and be as exhausted as the others. In which case is he doing his fair share? Does your opinion change if he doesn’t get more food than the others to compensate for his larger baseline metabolism? How about if …

I could go on, but hopefully my point is already made, there is no way to perfectly evaluate if someone is doing and/or receiving their fair share. In a narrow context like the joint effort of a group of sailors, a consensus might arise, and the guy who never breaks a sweat might be ostracised, but our reality is one of being part of a global economy and I am well insulated from the effort and level of reward at the far end of the supply chains that end with me. And you the reader is likely to inhabit the same world of relative luxury.

But say we could easily evaluate who’s doing their fair share and who’s over-consuming. Let’s say we simplify and look at work hours. We’re then ignoring structural differences like how some countries have developed extensive infrastructure and automation, allowing production of more goods for the same work hours, but also how this development probably was supported by exploiting nations where this development hasn’t happened, so let’s put that aside for now. We look at how many hours people work and how many hours work their consumption represents and find …

At one extreme I could find that there’s minimal difference. So my over consumption doesn’t represent all that much of the world’s inequality. Say I work 2000ish hours and I consume goods representing 2100ish hours of work. Well then I don’t have much of an excuse for not changing my consumption, do I? I ought to consume a little less and pay a little more for what I do consume, preferably to those who’re “under-consuming”, allowing them to catch up. Easy peasy.

At the other extreme I could find that there are enormous differences. Maybe I consume 4000 hours worth of goods. Changing my consumption would then be a lot harder, but the immorality of not doing so would be much greater.

Over-simplified, sure, but if you live in the developed world, it is vanishingly unlikely that your personal truth doesn’t lie somewhere in between those two points, leaving the obvious conclusion: You’re not pulling your weight, at least not globally, and you’re consuming more than your fair share.

What the best choices are to remedy this may not be obvious, but perfect is the enemy of good, and it’s immoral not to bear this in mind when you make everyday choices. The available “ethical choices” might not be perfect, they might not even be better than the regular goods, but picking one over just plain “global economy output” shows you care and works to push the marketplace towards taking ethics into consideration and providing us consumers with the resulting information.

 

Avisfolk! Jobb saktere, rett fortere!

Medieverdenen er i rask endring for tida. Integrasjon med sosiale medier, kommentarfelt, publiseringshastighet og synkende inntekter er alle utfordringer der det ikke finnes noen perfekte løsninger tilgjengelig og der løsningene akkurat nå åpenbart ikke er gode nok. Det kan skrives mye om kildekritikk og hvordan slett journalistikk kan spres fra dårlige kilder til alle verdens medier før noen reagerer, men nå tenkte jeg jeg skulle ta tak i noe som burde være langt enklere, nemlig å skrive riktig og forståelig norsk, eller i hvert fall å rette til riktig og forståelig norsk når noen påpeker feil og mangler.

NRKs twitter-konto for eksempel burde går noe saktere fram. Kan ikke skjønne annet enn at det må være flaut når bildet har en overskrift med banale skrivefeil, eller som her, når Donald Trumps [sic] til evig tid vil “itere grunnlova”:

Men en skrivefeil i en tweet er jo ikke så ille, og det kan av ulike grunner være en helt grei strategi å la slike stå snarere enn å slette og republisere og dermed bryte delingskjeden. Da er det verre med feil i artikler, som denne i Dagbladet:

Forskerne skal også ha plantet flere seismiske skjermer rundt på den ubebodde øya, skriver International Business Times.

Med litt kreativ bakoveroversettelse, eller en sjekk av kilden ser man at det er snakk om “seismic monitors”, altså seismisk overvåkingsutstyr, men denne pinlige oversettelsesfeilen lar altså Dagbladet stå. Kanskje fordi jeg var den eneste som forsøkte å bruke Dagbladets eget “Rapporter feil i artikkelen”-verktøy, eller fordi det verktøyet ikke fungerer? Jeg synes i hvert fall det er litt underlig.

Ennå underligere synes jeg det er at Aftenposten ikke er i stand til å fange opp en melding til dem om at de har følgende ingress i en NTB-sak om bosettinger på Vestbredden:

David Trump har ikke kommentere Israels forsøk på å legalisere ulovlige bosetninger i de palestinske, okkuperte områdene.

David Trump altså, i tillegg til grammatikkfeilen. Og Aftenposten har ikke latt seg affisere av hverken twitter-meldinger, facebook-melding eller epost til nyhetstips-addressen, og noen bedre alternativer finner i hvert fall ikke jeg på aftenposten.no.

Det er fortsatt et stykke igjen før jeg sier opp abonnementet på Aftenposten. Det finnes foreløpig ingen fullgode erstatninger for de gode, gamle avisene, selv om man kun leser dem på nett. Men min framtidige leverandør av nyheter bør være i stand til å unngå disse pinlighetene, eller i det minste være i stand til å rette dem opp i løpet av mindre enn ei uke.

PS! Jeg regner med at Gauderes lov slår til i denne posten, men send meg en melding så retter jeg de uunngåelige feilene på null-komma-svisj.

Amatørselskapet Norwegian og flypassasjeravgiften

Når alt går bra er Norwegian en flott opplevelse med lave priser. Til Boston, som jeg kommer til å fly fram og tilbake til en del i nærmeste framtid, er de eneste direktforbindelse med Oslo. Lav pris, flotte fly, og en behagelig opplevelse for akkurat meg denne ene gangen. Men når noe går litt på tverke aner tydeligvis ikke Norwegian hva de skal gjøre. Det kan man se i flommen av hårreisende historier på Norwegian’s facebook-side. En kar som har ventet 15 dager på tilbakemelding på klage får til svar at “ting tar tid”, eller for å være presis:

Please be advised that all claims are handled in the order they were received, waiting time varies with the nature of the claim and the case load. You will receive a response as soon as possible. 

Men kanskje det er et skjevt inntrykk? Jeg får jo ikke analysert alle kundeopplevelsene eller sett alle som er fornøyd med kundeservice. Kanskje disse er sjeldne unntak blant svært mange tusen som har fått god hjelp av Norwegian ved problemer? Kanskje det er medias skyld at det kommer så mange flere oppslag om Norwegians kundebehandling og strandede passasjerer og konflikter med ansatte og innleie av fly  og …

Det er helt sant, men jeg kan skrive om min egen opplevelse av Norwegians håndtering av flypassasjeravgiften. Og med mindre de lagde en rekke “Kjære kunde”-eposter bare til meg, skjuler det seg garantert ikke en hærskare av passasjerer der ute som er fornøyde med den håndteringen.

Trinn 1: I mars annonserer Norwegian at har justert prisene for reiser foretatt etter 1. april.

– Billettprisene har blitt justert noe for å ta høyde for at den foreslåtte flypassasjeravgiften innføres, svarer kommunikasjonssjef Lasse Sandaker-Nielsen.

Trinn 2: I slutten av april kjøper jeg billett til Boston. Avreise 25. juni så allerede inkludert avgiften kunne man jo naivt regnet med hvis man ikke følger nøye med på budsjettforhandlinger og har fått med seg at Norwegian sier de avventer endelig vedtak og

– Vi legger selvfølgelig ikke på passasjeravgift etter 1. april hvis avgiften ikke blir innført, sier kommunikasjonssjef Lasse Sandaker-Nielsen hos Norwegian til Nettavisen.

Trinn 3: Avgiften blir endelig vedtatt etter en runde med EFTAs overvåkingsorgang, men gjeldende fra 25. juni, nesten to måneder etter den opprinnelig vedtatte startdatoen og Norwegian sender ut sutremail til kundene:

Norwegian beklager på det sterkeste denne avgiften som vi er nødt til å kreve inn fra våre passasjerer på vegne av den norske staten. Pengene går rett i den norske statskassen og ikke til Norwegian.

Stakkars, stakkars Norwegian, hvordan kan staten finne på å få gjennomslag for en avgift Norwegian har gamblet på at skulle bli stoppet? Norwegian sier de vil gjøre ting enklest mulig for kundene og belaste samme kredittkort reisen ble betalt med og får kunder og media på nakken både for dobbeltkommunikasjon om prising og avgiften og for å planlegge et antagelig ulovlig ekstratrekk på kundenes kredittkort.

Trinn 4: Jeg har reist på tur for lengst og kunne teoretisk ha slettet epostkontoen min, jeg har i hvert fall ikke noen avtale med Norwegian som tillater dem å sende meg viktig epost til kontoen i all framtid. Men det gjør de likevel. Et pålegg om å gå inn på sidene deres og betale avgiften med kort innen 1. august og mer sutring “Norske myndigheter har med virkning fra 1. juni innført en avgift på 80 kroner for alle som reiser fra en norsk flyplass.

Legg merke til at Norwegian stadig beskriver det som en avgift pålagt den reisende som de krever inn på vegne av staten, mens realiteten er at det er en avgift avkrevd selskapet, som de kan velge å dekke slik de måte ønske.

Hva er forskjellen? Når KIWI reklamerte med momsfritt på frukt og grønt var det et reklamegrep helt uten reell mening. Den reelle prisen inkluderte samme prosentvise andel moms uansett og KIWI la en høy og fiktiv “reell” pris til grunn og endte med omtrent samme priser som andre butikker. Norwegian derimot kunne valgt å øke prisene på framtidige flygninger, men krever inn avgiftene på denne måten som en rent politisk handling.

Trinn 5 og 6: Jeg glemmer selvfølgelig denne eposten, siden jeg antok at Norwegian ville ta til vettet og ikke dumme seg ut på denne måten, men neida. 8. august kommer påminnelse med ny frist, 15. august. Denne gangen hadde jeg faktisk tenkt til å betale, men jeg glemte det igjen og overså også eposten de sendte ut i går.

I dag har de så stengt muligheten for å betale avgiften på nett …

Og i hver epost tar de med “Les vedtaket her” med lenke til skatteetatens rundskriv, som om det er skatteetaten som bestemte at Norwegian ikke skulle ta høyde for at et politisk vedtak faktisk ville bli gjennomført, eller påla dem å bruke ressurser og goodwill på å kreve inn avgiften for allerede betalte billetter.

Jeg hadde lite til overs for Norwegians selskapskultur i utgangspunktet, og dette er dråpen. Jeg bruker heller noen tusen kroner og et par tre timer ekstra per reise enn å fly Norwegian igjen.

Life ideas

Saying things simply is sometimes good, so to try that out I have written this page about my thinking about life ideas using the Simple Writer made by that guy who writes the funny and thought creating stories with stick figures. The Simple Writer only allows you to use the ten hundred most often used words in this language I’m using, so one would think it might always become simple, but that isn’t always true. You will have to decide yourself.

All of us have some life ideas controlling what we think, decide, say and do, or how we tell if what we think, decide, say and do is good or bad. These life ideas have formed in our brains over time because of how the brain was when we were born, and because of all the things that have happened in our lives and brains so far. Some of these life ideas feel more important to us than others, and some we are more sure are right, and these two feelings often go together. If an idea feels more important, we’ll be more sure it is right and more willing to look for reasons our idea is right and other ideas like it but different are wrong. Sometimes this stops us from thinking clearly about ideas and it is important to understand this about our ideas and about how others feel about their own ideas.

This short page is not about my most important life ideas and how they are right, and how you should understand they are right if they are not already your life ideas. It is about how life ideas are not very often all right and all wrong, and how this makes it good to understand the very strong feelings people have about their life ideas, even ones you think are clearly wrong. So maybe this is about my most important life ideas, but I want those to be ideas about life ideas, rather than life ideas themselves.

1. You could be wrong

My first idea about ideas is that you should be admit to yourself that your ideas might be wrong. If you can’t do that, there is no point in thinking about your ideas at all.† And when thinking about your ideas to consider if maybe they are or could be wrong, it is important you remember your feelings might confuse your thinking. I think feelings are also very important parts of life ideas and ideas without them can be bad, even if they seem right, but that is for another page some other time. So when someone has an idea that is different from the one you have, don’t forget that it could be she is the one who is right.

2. Wrong people feel they are right, how can you change their mind?

Some life ideas are so wrong it is important someone point out they are wrong, but the most important thing isn’t that it’s pointed out they are wrong, it’s that the people who hold those ideas change their minds or at least don’t act on their wrong ideas or spread them to others. That’s why my second idea about life ideas is to always remember that people with very wrong ideas feel they are right ideas. Telling them they are stupid, their ideas are wrong and they should feel bad doesn’t work very often to make this important thing happen, even if it might feel good for you for a while. More often it creates a situation where the wrong person thinks “People who don’t agree with me try to make me feel bad, that must mean they are wrong, which isn’t a surprise because I already knew that, but every bit helps.”

Now deciding from this that one should never tell someone with very wrong ideas that they are stupid and should feel bad is a life idea, but the idea about ideas I wanted to explain is that you should remember about the feelings and think about them, even if you then decide shouting “You are a stupid person!” is a good thing to do. Maybe there is a better way though to turn this person from someone with a bad idea into someone who thinks about their ideas and understands they could be wrong.

3. Should all your ideas work together?

If you could write down all of the life ideas in your brain it is certain some of them would not work together well. Pointing this out when you can see it in what other people have said or done often feels good, but just as you should remember you could be wrong, or that other people also feel they are right, you should remember your ideas don’t all work together either.
Now ideas not all working together is both good and bad. It is bad when it happens often and the person having the ideas just picks one or the other without a reason. In that case you should, if the person is you, think about why this is happening, and if one of the ideas is wrong or if maybe they are both right but not at the same time, and if so, what times one is right, and what times the other one is right.
It is good when it stops your ideas from being so few and your thoughts so simple you are ignoring lots of ideas that could be right sometimes, and lots of times your ideas are wrong. The world, you see, is not simple.

4. How to find out if an idea is right?

This is where things get really hard. How to find out if an idea is right is a life idea in and of itself. Some would say it is a given, something that just is, or comes from the world around us or some being outside the world. Some would say it’s in what we want to happen when we follow the idea. Some what say it’s in what actually happens when we follow the idea. I say that the most important thing is telling the truth about why one thinks the idea is true, and that I myself think the best way to do this is to use more than one of those ways.

And that’s all I have to say today about my simple ideas about life ideas.


†unless you happen to be a very not usual person who only has ideas that are right, but even then you would not have the one important idea about ideas maybe being wrong

Saudi-Arabias ambassadør er ikke så god på “faktabasert”

Saudi-Arabia får mye pepper om dagen av ymse årsaker. En viktig grunn er elendig forhold til menneskerettigheter på mer enn én måte og da blir selvfølgelig litt plagiat mellom venner en ubetydelig sak, men det er jo litt festlig personlig, når det skjer en hobbyskribent som meg. Så la meg utdype:

Saudi-Arabias ambassadør Esam Abid Althagafi har i dag et innlegg på NRK Ytring med tittel Vi er ikke ekstremister der han … det blir kanskje slemt å si “etter beste evne forsøker å imøtegå kritikken”? Men innlegget er ganske så svakt. En lang ramse med usammenhengende punkter om hvordan kritikerne ikke forstår det saudiske rettsystemet, som dessuten er et indre anliggende vi ikke har noe med, og dessuten … Nei, jeg tøyser ikke, se bare dette avsnittet her:

Mitt brobyggerinnlegg er ikke kontroversielt eller tabloid, men skal man putte tanker i hodene til folk, bør de være faktabasert. Saudi-Arabia har ratifisert en rekke konvensjoner og er medlem av FNs menneskerettighetsråd. Vi er deltagende i de internasjonale arenaene. Det betyr ikke at det ikke eksisterer politiske, religiøse og juridiske forskjeller mellom oss. Saudi-Arabia holder seg unna interne anliggender.

Rotete greier, sant? Men jeg la merke til denne vendingen: «skal man putte tanker i hodene til folk, bør de være faktabasert». Jeg skrev nemlig nesten nøyaktig det i et innlegg publisert i Aftenposten Meninger i september: «og skal man putte tanker i hodene til folk bør de være faktabaserte». Kritisk innlegg med alt for lang tittel!

Greit nok, det er jo ikke en vending ingen andre kan ha kommet på, men jeg gjorde likevel et nettsøk og i akkurat den formen er det våre to innlegg som dukker opp. Mitt og den saudiske ambassadørens, om han da skriver innlegg selv. Så jeg leste innlegget et en gang til og fant et “lån” til: «Kritikerne bommer totalt på kjernen i kritikken, og forsøkene deres bør ikke få stå som siste ord i saken.»

Igjen kan man søke på «… bommer totalt på kjernen i kritikken, og forsøkene deres bør ikke få stå som siste ord i saken.» og stusse over at det bare gir to rene treff. Mitt innlegg fra september og dette fra Althagafi i dag. Forskjellen er bare at i mitt innlegg passer setningen perfekt til konteksten, mens i dette innlegget virker den som ennå et rotete element i en tekst som jeg nok tror ville fått tilbakemeldinger som “usammenhengende” og “svevende” av norsklærer-kollegaene mine.

Det er nok viktigere ting å diskutere rundt dette ubehjelpelige ikke-svaret på berettiget kritikk, enn litt klønete lån av vendinger, men det gjorde i hvertfall meg litt munter inntil jeg igjen kom på hvilket hårreisende regime Althagafi representerer.