Thursday, April 30, 2009
Let us again look a bit at the lottery in the Norwegian Lotto. You have to choose seven numbers, out of 34. Some choose special numbers like birthdays, anniversaries, ages, their house number and so on. Other choose random numbers. Or at least seemingly random, as our brains are notoriously bad at doing random.
Here is the numbers from the last 52 drawings of Lotto, 364 in all. We can see that there is quite the variance in the numbers frequencies. For instance 3 has been picked over twice as often as poor little 16! If you are going to play the lottery you surely should pick that one, as it's on a hot streak! Or... shouldn't we rather pick the ones that haven't been picked in a while, they must be due soon?
The correct answer is of course neither. Former results have no effect on what will be picked next. (Lotto takes special care that even things like wear and tear on the balls shall not affect the results)
Here's all the Lotto results from 1986 to today, 1196 drawings total.
Here we can see a slightly smoother distribution, but there are still peaks and nadirs. You will never see a totally flat distribution, not even with millions of iterations. Though the more we do the flatter it will get.
Ah, now we're talking. Nothing quite beats the coin flips for experiments with randomness.
Let us flip ten coins after one another, noting down the results as we go along. Of the following two results, which one is one that you are more likely to see?
Most of us (at least those of us without statistics education :) will answer A, because it looks "more random." In addition, it has an equal number of heads and tails, and given 50% chance for heads or tails we would expect approximately that.
But it would be dull if everything was as we thought it were! In fact, either result is exactly as probable to be seen in a random toss of ten coins. (Don't let yourself fool that ten tails in a row only has a 1/1024 chance, the exact sequence in A has also the same chance)
It is highly unintuitive for us to think about it this way. It will get even harder for us if we take the following exercise instead:
I will flip nine coins after one another, and record the flips. You try to guess what the tenth will be. Here is the nine flips in three different scenarios:
And of course again in all three of these the right answer is 'It is 50% chance for either heads or tails in all three scenarios.' But for most of us it is hard to imagine that right at the top of our heads. We try to see a pattern. For C you would like to say that the next one is Heads, as they have alternated heads and tails so far. Set B, after you have examined that the coin is not weighted of course, you'd like to think that it's due for a Heads soon. A also had a pattern, but it is a less apparent one, so it is more likely that you will just pick randomly rather than try and 'guess' which it will be.
Exercise, and do this without too much deliberation:
Think of a random number between one and ten (inclusive). Do this now before reading on.
I will state with about 75% accuracy that you chose either 3 or 7. The reason you chose either one of those is because your brain wanted it to look like you chose something random, something which is really hard for your brain to do. In wanting to choose a number that "looks random", you mentally eliminated all the other numbers for "not looking random." (How does a single number look more or less random than another, anyway?)
1 and 10 are in the extremes of the range, so they do not "look random." 5 is in the middle and thus is not random either. And for some reason, the even numbers 2, 4, 6 and 8 seem less random than the odd ones. That leaves 3 and 7 as the only two "random" numbers between 1 and 10.1
Had our brain been able to think randomly then the numbers 3 and 7 would not have been greatly overrepresented whenever someone takes this "test." The number 1 is exactly as random as any other.
Check this one out. Click it a couple of times and see if you think that the numbers generated look "random." They probably don't. Your brain will try to see a pattern in it. A pattern that does not exist, because those numbers there definetly are truly random.
We're wired from nature to try and see patterns. It's one of the things that has helped us survive as a species so far. Unfortunately it is very prone to false positives, to see a pattern where there is none. We see patterns in random numbers. We think that lottery numbers can be predicted. We also are not able to do random things ourselves.
Watch out. When coming from humans, random things are usually not.
1Did you notice I left out nine? There is a reason for that but I won't spoil that yet.
Wednesday, April 29, 2009
Our teacher, a sweet older lady named Mrs. Love, replied: Of course! If not, none of you would be here!
And now that I´m studying biology, I´m becoming increasingly aware of all the weird ways sexual reproduction happens. Some seem quite absurd to me, and not very fun at all. I´ve wondered about organisms with external fertilization. Is it as much fun for them without all the "interaction" that internal fertilizers get?
This is the first of a series of posts on the weirdness of sex.
The reason sexes exist in the first place is sometimes considered a bit of a quandary for biologists, seeing as how it reduces the number of possible mates by a factor of two. Also, with completely asexual reproduction, each individual bearing two children gives exponential growth, whereas when each individual combined with an individual of the other sex gives rise to two children, this results in a static population. Also, sex creates novel genotypes, more rapidly, in addition to a few other good things, such as it being fun. (It also helps in removing deleterious mutations by homologous recombination).
Earlier this year, paleontologists made a big discovery regarding sex. In english, sex (as in the act) and sex (as in gender) are often referred by the same word. It currently seems that sex (as in gender) is extremely old. Early eukaryotes seem to have been reproducing with distinct variants, and most multicellular creatures reproduce sexually. However, sex as in copulation is much more rare.
Paleontologists discovered a Placoderm (really old fish with massive armor, one of the earliest jawed fish) fossil with a tiny skeleton lodged inside. They thought it was the placoderms last meal. Upon furher investigation, they realized it was an embryo of the same species. And you know what that means. Babies on the inside, means the sperm needed to get inside. Internal fertilization!
The fossils are about 365 million years old, and demonstrate that internal fertilization was probably a lot more common earlier than previously thought.
Pharyngula as usual covers the story thoroughly and with comments on what this means for the evolution of our own ways of sex.
Monday, April 27, 2009
I´ll start with this large little item.
Sometimes really weird, fun, unexpected things turn up out of nowhere.
These amoeba may change the way we view evolutionary history!
In 2008, some researchers looking for deepwater fish found some large lumps of mud-covered stuff on the ocean floor. Behind each of them it looked like there was a track, left by some sort of motion, like they´d been rolling around, and some seemed to have rolled upwards. Some were about 50 centimeters long, and the organisms were the size of grapes. Back in the lab, it turned out that these grape-sized thingies were actually giant one-celled protozoa(early animals that eat other organisms)!
(These balls of weirdness were first discovered in 2000, but at that site there were no tracks, which turned out to be very important.)
Previously it has never been known that single-celled creatures can make tracks from motion.
The tracks are marked in the middle with a narrow ridge, and they look very similar to some fossilized tracks dated to be about 1.8 million years old. These tracks have been taken as a sign of possible multicellularity, or even that there were animals that were bilaterally symmetrical at this early stage. However,most other lines of evidence point to a development of multicellularity at about 600 mya. These tracks were then just about the only indication of multicellularity at such an early time.
This is interesting because there are differing ideas about how long of a warm-up there has been for multicellular diversification before the Cambrian explosion at about 542 mya. With the discovery that the tracks were likely made by single-celled protozoa, this removes our earliest signs of multicellularity, leaving us with pretty good consensus on multicellularity developing at around 700-600 mya.
This article contains a somewhat unfortunate quote from one of the discoverers of the tracks. He´s talking about how this discovery removes the long, slow start leading to the Cambrian explosion where we relatively suddenly see lots of new animals, major groups and diversification in the fossil record.
"It wasn't a gradual development of complexity," Matz said. "Instead these things suddenly seemed to burst out of a magic box".
Bah! I just hate it when scientists bring up magic in a sentence like this. You just know the creationists will be jumping all over it, claiming that biologists agree that there is too much weirdness in nature all to be explained by science.
I couldn´t disagree more. I wish he would have turned the phrase in a different direction.
I think it´s amazing and wonderful and that this discovery really demonstrates the power of natural processes and that nature can make huge changes come about in a relatively short period!
Drawing supernatural force into this is unjustified, unnecessary and a bit short-sighted.
Saturday, April 25, 2009
Our brain sure is impressive. It is capable of maths, logic, problemsolving, spatial awareness in addition to all those small things it does for us automatically (like, y'know, controlling our body...)
The way we use our brain though, is far too often not impressive. We will fall naturally into fallacious thinking and wrong judgments. This of course comes from our evolutionary background - we need fast judgments to survive. To better avoid predators and other dangers, we have a strong tendency to see patterns, but this often leads to us seeing patterns and shapes where there in reality are none.
In this series, I would like to shed some light on some common errors that most of us do fairly often. I would not claim myself to be immune to these - but if we are more aware of them then perhaps we can avoid them more often, which would be better.
Of all the things that our brain does correctly, estimating probabilities is not one of them. In fact, we downright suck at it. We like being cautious and prepared, but at the same time we grossly misrepresent chances at everything involving ourselves. Let me use the norwegian lottery "Lotto" as an example.
Norsk Tipping has this to say about the chances of winning: (translated)
It isn't easy to become a millionaire through Lotto but it is also not easy to say exactly how hard it is. At least not in practice. In theory one can say that it is almost impossibe to get seven correct numbers, but on the other hand on average four people manage this every saturday.
Already here we can see how hard it is to think about probabilities - and that is before we have even seen a single number! It is "almost impossible" but at the same time "four people manage this every saturday." Our brain does not have any problems reconciling these two statements. There is also present in the paragraph a clear theory-practice difference - in theory it is impossible but in practice it might happen. So far still good for our brains even if with a bit of proper logical thinking you might see that these statements are in fact contradictory.
Let's instead move onto looking at the exact numbers and chances to win. Lotto has 34 numbers, of which you have to correctly pick seven. According to Norsk Tipping the chance of hitting that is 1:5.379.616. One out of every five million four hundred thousand, rounded. The main thing here is that no matter how you try to illustrate or visualise it, it is such a large number (or to be more correct, such a small number) that our brain cannot visualise or imagine it. And then our brain falls back to overestimating just to be on the safe side.
Norway has a little less than five million inhabitants. Thus the chance of actually winning would be about the same as to take a random phone book, open it to a random page, random column, and point to a random row and point at your own name. (Strictly speaking you have a greater chance of pulling off this feat, as we are not 5.4 million only 4.8 million still... but the point stands)
The odds are still astronomical. With enough tries, even the most astronomical odds can be overcome. It's very easy to fall for the fallacy "It has happened to someone therefore it can (will) happen to me." It can happen but probably not. And that is where most of us trip and fall.
Other examples of where our way of dealing with probabilities messes up our brain:
- The Birthday Paradox, or, if you have gathered 23 random people then the chance of two of them sharing a birthday is 50%. The reason is that we think "Oh, there are 365 days in a year so the chance of two people sharing a birthday is 1/365" and then multiply that by 23 giving 23/365. This however is the wrong way of working out the probability. In reality the probability is 23*(22/2) since you have quite a number of pairs that can match. In a group of 23 people there are 253 distinct combinations of people that can be compared!
- We give higher probabilities to things we recently have thought about. Airplanes and airtravel is astoundingly safe and reliable, thanks to all the work the airlines put into making them safe and reliable. However just after an airplane accident (they do happen, just quite rarely) air flights take a noticeable dip, even if the chance of another crash happening is not corellated with the first one. On the contrary, the argument could be made that due to the extra awareness of the flight crews following another accident, you are less prone to experiencing an incident, but that does not stop us from not flying after a crash.
- Likewise, the chance of you being involved in an automotive accident dwarfs the chance of you crashing in a plane. But still, we worry excessively about one and not the other, when it should be reverse.
- Hollywood does not help the cause either. In all movies and TV-show the most improbable things will happen with incredible frequency. Of course, it is understandable, a movie would be quite boring if only things that were statistically likely happened. Imagine a movie about an airplane that does not get hijacked, a bank that does not get robbed, or a statesman who does not get assassinated. Quite dull in that case, but it is the norm for every day for the rest of us. Still, it poisons the mind in such a way that we can get used to expecting the incredulous to happen.
1At age 12, after my horoscope recommended it, I played Lotto. I wagered 10 Kroner (bought five sets of seven numbers) and won 53 kroner from it. I have never gambled since.
Wednesday, April 22, 2009
Read the whole article (in Norwegian) here.
I will summarise it for our international readers.
Three reporters filled in the test on the Scientology website. They used their real names but did not specify that they were reporters. All three consider themselves normal, healthy, fulfilled persons. Two of them filled in all the answers truthfully, while the third took a role and filled in everything as depressing as he could.
After submitting the test, they were informed that they had to show up in person to receive the results. They did so, with concealed cameras.
The result was that they were all, individually, told that they were mentally unstable, unreliable, introverted and depressive people. (The reporter who fibbed his answers to appear depressive, even more so. "On the same level as an inanimate object" was his diagnosis.)
The way to fix this was of course courses and counseling which the Church of Scientology would be more than happy to oblige with, for a small fee of course.
You can see pictures of their scoresheets in the linked article.
One of the reasons that this is relevant in Oslo is that about a year ago, Kaja Ballo, the 18-year old daughter of politician Olav Ballo, committed suicide after having had her personality analysed by the Church of Scientology and came out negative.
Olav Ballos book about his daughter came out this week, I have not read it yet but now I intend to.
Olav Ballo says to VG that these tests are "destructive, depression-causing and pure scams" when shown today's article.
The "Church of Scientology" creates a false depression in people, and then tells them that they are the only cure available. If you have even the slightest doubt about yourself they will grab that and spiral it downwards until you truly are depressed. The way Scientology acts is not helpful to being human. They are, until Dianetics can be proved correct using proper peer-reviewed processes, replicated experiments and good Science, frauds, hucksters, quacks and downright dangerous to people who would need psychiatric help.
I am quite happy to see media focus on Scientology again. Every time we hear some of their claims it just reinforces to me how ridiculous they are. The ball's in the media's court right now. I hope they run with it some more. VG asked some good questsions to the CoS, but the response was vague, generic and unsatisfactory.
Every couple of weeks I see a stand just outside my office with a big sign saying "Free stress-test." (I cannot remember seeing them recently, but that may be coincidences depending on when I leave work from day to day) Sometimes I even spot an E-meter on their table. If I go closer I can see that they have a big stack of Dianetics books there. There is usually a person sitting there talking with them. Probably listening to what they have to say.
I have never bothered to actually go and talk to (or troll) them, as usually I have had a greater interest in getting home for dinner. One of these days though I am going to take Marit with me and, armed with a copy of Operation Clambake, talk to these people.
Monday, April 20, 2009
If I take to my senses, this should be one of my last entries in Norwegian.
Pass opp, skamløs selvpromotering og namedropping følger.
Jeg er i New York på ferie. Jeg besøker en venninne her. Jeg tenkte at jeg burde sjekke ut vitenskapelige og skeptiske events mens jeg var her, siden skeptiker-miljøet er bedre her, og det er mer sirkulasjon på gode vitenskapsfolk her.
Fant til slutt ut at Phil Plait skulle snakke på Hayden Planetarium samme kveld som jeg reiser hjem. SKUFFA! Men, jeg sendte en epost til NYC skeptics og spurte om de ikke skulle eller kunne arrangere en liten event ekstra med ham, for det er jo ikke så ofte han er i området. Og sannelig! Noen dager senere fikk jeg beskjed om at de skulle ha vin og småmat-kveld med ham, og jeg meldte meg på. Og wohoo, den kvelden var i dag!
Jeg har akkurat kommet hjem, og la meg bare si at Phil er akkurat så kul og festlig som man tenker seg. Han sa selv at han knapt kan skrive navnet sitt med mindre enn 450 ord, og jeg skjønner det, for han kan snakke! Og han er kjempefestlig. Jeg rakk å bli litt venn med ham, og vi gikk til og med på bar etterpå. (Han og jeg og to til.)
Jeg møtte også denne mannen. George Hrab! Jeg har hørt navnet mange ganger før, men aldri hørt på podcasten. Nå skal jeg begynne! Også en kjempefyr.
En stor mann i en liten kropp var også der; John Rennie fra Scientific American. Han bare dukket opp! Alle andre enn Phil bare dukket opp egentlig. Wow!
Og sist, men ikke minst, Rebecca Watson. Som skepchick-in-training må jeg nok si at å treffe henne var nesten like kult som å treffe main attraction Phil. Hun er vittig og kvikk og vet masse kule ting! Jeg har sagt hun kan bo hos meg etter TAM London, og det kan hende det skjer. Jeg håper det.
Phil sa at etter at bloggen hans hadde blitt plukket opp til Discover veddet han med redaktøren. De ble enige om at hvis Phils blogg hadde 2 mill av 5 mill totale hits en måned skulle begge ta tatovering. Det skjedde i mars. Nå må de bare finne ut hva de skal ta. Noen foreslo "Neptune on Uranus". Phil klagde over at det ikke hadde skjedd i desember og at de skulle satse igjen i mars, for da var det trettien dager i måneden. Rebecca Watson: yeah, unlike december!
Lengre post med bilder kommer når jeg kommer hjem på tirsdag (eller noe sånt).
Saturday, April 18, 2009
Neida, det er ikke Janteloven som er tema her. Det som derimot er tilfelle er at vi alle overvurderer sterkt sjansen for at noe godt skal skje oss, og nedvurderer sjansene for at noe negativt skal skje.
Vi er alle klar over bilulykkesstatistikkene, hvor stor sjanse det er for at en tilfeldig valgt person blir utsatt for en ulykke i trafikken. For "andre folk" er statistikken helt grei for oss å forstå. Men hvis vi prøver å bruke den på hvor trygge vi selv føler oss i trafikken, så ender vi opp med å ta feil.
Samme med hvis man spiller Lotto eller andre rene sjansespill. Vi overvurderer betraktelig mulighetene for å vinne hvis man tenker selv på sjansene sine. En til fem millioner sjanse virker mye mer trolig når man spiller selv.
Andre vanlige feil når det gjelder tanker om seg selv er å sette forskjellige regler og kriterier for seg selv. Det er greit hvis jeg låner med meg kontorutstyr hjem, men ikke andre. Jeg har jo en god grunn! Vi er fullt kapable til å dømme andre for ting som vi ikke ville dømt oss selv for. Vi gjør unntak for oss selv i regler. Ofte så tenker vi "Det gjør ikke noe hvis bare jeg gjør det" men det er en tankefeil i seg selv (som kanskje blir del 6 av denne serien :)
Ikke bare seg selv men også grupper man tilhører vil man gjøre unntak for. Vålerenga-klanen-rabatt. Møter man en annen nordmann på ferie i Italia vil man gjerne slå av en prat og bli kjent med personen, men dette er noe vi ikke ville gjort hvis vi hadde møtt ham på T-banen i Oslo eller hvis han var italiener. Disse her er det riktignok evolusjonære grunner til, men fra et rasjonelt synspunkt er det ingen grunn til det.
Sunday, April 12, 2009
Wednesday, April 08, 2009
Alt vil drive mot sin normale stand. Dette er veldig vanskelig å se i seg selv, men passer veldig godt sammen med de tidligere temaene jeg har diskutert hittil. (Især "post hoc ergo propter hoc" men tar med sannsynlighetsberegningstemaet også)
I USA er det en mye om at sportsatleter som havner på forsiden av "Sports Illustrated", på esken av frokostblandingen "Wheaties", eller foran på "Madden"-spillene, går det alltid dårlig med etterpå. Vi går ut ifra at det ikke bare er at vi legger merke til det derfor husker vi det bedre-tankefeilen, men at det faktisk er tilfelle. Forklaringene er veldig enkle, og har ikke noe med jinxing å gjøre: (En eller flere av disse vil gjelde)
Når man havner på forsiden av Sports Illustrated så er det på toppen av karriæren sin. Derfor må det gå nedover etterpå.
Store fluktueringer er veldig vanlige i sportskarriærer. Når man blir eldre blir man oftest svakere også.
Eller: Man ignorerer de elementer som ikke passer inn i hypotesen. Dette er veldig lett for oss mennesker å gjøre. Som kontrapunkt til Sports Illustrated-jinx-hypotesen så kan man legge frem at Michael Jordan var på forsiden 49 ganger uten å miste karriæren sin av det.
Hvis en by opplever en krimbølge, byinnbyggerne svarer med å velge en ny ordfører, og så synker kriminaliteten igjen, så vil man jo gjerne tro at det hadde noe med det å gjøre. Men fra et historisk-statistisk synspunkt så tar alle bølger av etter at de har vært på toppen, og alle daler går opp igjen etter at de har vært i nadir. Det er tingenes naturlige tilstand. Og i vår leting etter umiddelbare cause-effect forhold så blir det vanskelig å se at noen ganger så går ting bare "av seg selv."
For mer lesing på dette temaet anbefaler jeg boken "Freakonomics" av Stephen Dubner og Steven Levitt.
Friday, April 03, 2009
(Del 2 - Tilfeldigheter)
Del 3 - post hoc ergo propter hoc eller på godt norsk etterpå derfor på grunn av.
Post hoc ergo propter hoc er den tredje, sannsynligvis vanligste, vanskeligste å bekjempe, tankefeilen vi kan gjøre. Den har med å ikke forstå cause-effect forhold slik at man kan tro at hendelse A var grunn til at B skjedde, men i virkeligheten så var det C som sto for det.
Kvakksalvere skor seg godt på denne feiltanken. Hvis du tar en pille og så forsvinner hodepinen din så vil du gjerne tro at det var pillen som fjernet den, når den like greit kunne forsvunnet på egen hånd. Dette er også kilden til det meste overtro og folketro.
Som et eksempel på hvor lett det er for oss å gjøre feil her, la meg bruke et eksempel fra en av mine personlige favorittpsykologer, B.F. Skinner.
Skinner satte en due i et bur sammen med en maskin som var programmert til å gi ut mat på komplett tilfeldige intervaller. Hvis duen akkurat hadde gjort noe merkbart før mat kom, så ville duen fortsette å prøve å gjøre det samme. For eksempel hvis duen akkurat hadde sett seg over skulderen før mat ble gitt ut, så ville den tro at det at den så seg over skulderen var det som ga den mat, og fortsette med det. Høres simpelt ut hittil, og dette er jo bare en due med hjerne på størrelse med en fingernegl så...
Vel, ikke like mye. Eksperimentet har blitt gjengitt på mennesker gang på gang, og slår sjelden feil. Reglene kan være så kompliserte eller så enkle man hvil. Sålenge offeret har blitt fortalt eller forstått selv at belønningen ikke er tilfeldig men deterministisk, så vil dette gå som forventet. Eksempel: Sett et menneske i et tomt rom med en poengtavle. Personen blir fortalt at han skal prøve å få så mange poeng som mulig, og at det er et komplisert regelsett som forteller hvilke handlinger som gir poeng. I virkeligheten så gis poeng bare ut helt tilfeldig, i tilfeldige intervaller og mengder.
Denne personen vil stadig prøve de samme tingene som han tilfeldigvis prøvde før et poeng ble gitt ut. Det at det ikke virker igjen senere vil heller ikke stoppe ham.
Verden er et komplisert sted med hundrevis av faktorer til enhver tid som påvirker hva som skjer. Vi har alle våre lykkerutiner, disse kommer av en positiv opplevelse en gang som så blir låst i tankene våre. Det er mer enn bare en ting som påvirker en annen, men vi ser bare det som er ferskest i tankene våre.
Det finnes ikke noen mirakelkur for å gjøre seg immun mot denne. Uansett hvor skeptisk man er så vil man alltid ha tanken "Men hva om det var hendelse A som gjorde at Z skjedde". Sålenge vi lever i et deterministisk univers, men våre sanser og oppfattelsesevner ikke klarer å få med seg alle faktorer, eller at vi eliminerer ting som faktorer fordi vi tror at F ikke påvirker Q så kommer vi til å tenke feil her.
Thursday, April 02, 2009
Flaks er statistikk tatt personlig.
Hvis fotballaget har flaks, så har er de ikke like flinke som resultatet i går vil tilsi. Hvis man har ferdigheter så behøver man ikke flaks.
Personlig foretrekker jeg ferdigheter over flaks, den er pålitelig. Hvis man jevnlig har flaks (mer enn hva statistikken vil tilsi at man skal ha) så har man ikke flaks lenger, da har man ferdigheter.
Selvsagt, hvis man vil være nøyaktig, så er det ikke noe slikt som flaks, bare en uventet hendelse med positivt utfall.
Relatert så anbefaler jeg Richard Wisemans bok Quirkology, som tar for seg temaet flaks i et av sine kapitler. Wiseman har også skrevet "The Luck Factor" som kapittelet i Quirkology var basert på, men jeg har ikke lest den selv.
Wednesday, April 01, 2009
Den er visstnok nå det nest lyseste objektet på nattehimmelen, etter månen.
Det er nylig blitt publisert noen fantastiske bilder av romstasjonen. Anbefaler en titt på dem! Hver gang jeg ser på sånne bilder mister jeg meg selv littegrann og forsvinner ut i rommet.
Forresten skal jeg til New York neste uke, og da gleder jeg meg som et barn til å gå på verdensberømte Hayden Planetarium, som bestyres av Neil DeGrasse Tyson (som jeg la ut en video med for en ukes tid siden).
I tillegg skal jeg få møte Phil Plait, og så kjent som The Bad Astronomer. Han har skrevet to herlige bøker: Bad Astronomy og Death from Above! og er forfatter av den festlige bloggen Bad Astronomy.
Han er også leder for James Randi Educational Foundation som er en ressurs innenfor kritisk tenkning. Jeg gleder meg som et barn til det og!
Jeg skal si fra hvis det skjer noe festlig.