Category: Super fact

The Surprising Monty Hall Problem

Superfact 22: Suppose you’re on a game show, and you’re given the choice between three doors: Behind one door is a car; behind the other two doors there are goats. You want to pick the car. You pick a door, and the host, who knows what’s behind the three doors, opens another door revealing a goat. Now the question is, is it to your advantage to switch door choice? The answer is yes. And that is the surprising Monty Hall Problem.

There is a blue door on the left, a red door in the middle, and a green door on the right | The Surprising Monty Hall Problem
The Monty Hall gameshow Three Doors Problem. There is a car behind one door, and goats behind the other two. You pick a door. Monty Hall, the gameshow host, opens one of the other doors and it has a goat. Should you change your choice of door? Yes, you should. But why? – Monty Hall Problem Stock Illustration ID: 1881849649 by SATYA94.

It is quite common to argue that it does not matter. You don’t know what is behind the two remaining doors so it should be 50/50 right? In a test involving 228 people only 13% chose to switch. However, you should switch.

Monty Hall, the gameshow host of the Let’s Make a Deal television game show, knows where the car is, so he never chooses the door with the car. And by curating the remaining two doors for you, he raises the odds that switching is always a good bet. By switching your choice, you have a 2/3 chance of winning the car but if you stay with your original choice, you only have a 1/3 chance of winning the car.

So why is this a super-fact? First, we know it is true. It is mathematically proven and experimentally verified that switching door is the best choice. Secondly, this was widely contested and is still surprising to people. Finally, probabilistic thinking is the key to being rational and making good decisions. This fact is true, important and disputed and thus a super fact.

One way of viewing the situation is by noting that there is a 1/3 chance that the car is behind any door that the contestant picks and a 2/3 chance that the car is behind one of the other two doors.

The picture shows three doors, one marked 1/3 and two more grouped together under 2/3 | The Surprising Monty Hall Problem
The car has a 1/3 chance of being behind the contestant’s pick and a 2/3 chance of being behind the other two doors. Picture from Wikimedia commons public domain.

If Monty opens one of the two doors that the contestant did not pick there is still a 1/3 probability that the car is behind the door the contestant picked and a 2/3 chance that the car is behind one of the other two doors. However, one of the doors that the contestant did not pick is now known to feature a goat. Therefore, the probability that the car is behind the other door is 2/3.

The picture shows three doors, one marked 1/3 and two more grouped together under 2/3. The last door has a goat, and it is marked by 0. The door in the middle is marked by 2/3.
The host opens a door. The odds for the two sets don’t change but the odds become 0 for the open door and 2/3 for the closed door. Picture from Wikimedia commons public domain.

The table below is probably (no pun intended) a better way of illustrating the situation. In the table door 1 is the door designated to be the contestant’s first choice. Monty opens one of the remaining doors that has a goat behind it.

Behind door 1Behind door 2Behind door 3Result if staying at door 1Result if switching to door offered.
GoatGoatCarWins goatWins Car
GoatCarGoatWins goatWins Car
CarGoatGoatWins CarWins goat

There are various other ways of explaining the situation including Steven Pinker’s approach. It is easy to test this is real life and repeated experiments and simulations shown that if you switch you have a 2/3 chance of winning.

As an example of the controversy this probability puzzle caused was Marily Savant’s column in Parade Magazine. As a side note, Marilyn Vos Savant is the person who has the highest recorded intelligence quotient (IQ) as stated in the Guinness Book of Records. In response to a question regarding the Monty Hall game show problem she wrote that you should switch. She received letters from 10,000 readers disputing this, including 1,000 with PhDs. In the long run she prevailed.

To see the other Super Facts click here

Neutering or spaying a dog at 6 months old can be dangerous to their health

Superfact 21: Neutering or spaying a dog at 6 months old can be dangerous to their health depending on breed. It is often recommended that you should neuter or spay your dog by the age of 6 months even as early as 8 weeks. This may be OK for some smaller breeds but is dangerous to the health and longevity of many larger breeds.

Many dog welfare organizations, SPCA, ASCA, etc., recommend that dogs are neutered or spayed by the age of 6 months, or even as early as 8 weeks. It is also a common advice in dog books.

In addition, some veterinarians still hold onto this belief. It is easy to understand why. Dogs running loose and causing unwanted pregnancies resulting in puppies having to be euthanized is a sad problem we don’t want. 

Unfortunately, research has shown that neutering or spaying a dog at 6 months old can be dangerous to their health depending on the breed. You may need to wait 18 months or two years, and some breeds should not be neutered at all. In addition to the scientists in the relevant fields, professional and certified breeders, AKC and dog breed clubs and veterinarians who kept themselves informed on this issue are all aware of this.

In other words, we know this to be true, it is an important fact since so many of us own a dog, roughly half of all US households do, and yet this information is highly surprising to many. This is why I consider it a super fact.

Our yellow lab Baylor is on the left. Our brown-black German Shepherd Baby is on the right | Neutering or spaying a dog at 6 months old can be dangerous to their health depending on breed
This is our Labrador Baylor and German Shepherd Baby. Too early neutering and spaying can severely harm their health.

This less than a year-old article from the AKC states that “an age of six to nine months of age may be appropriate for neutering or spaying a toy breed puppy or small breed puppy but a larger or giant breed may need to wait until they are near or over 12-18 months of age.” The article also provides the following interesting information.

Research conducted by the University of California – Davis reveals that for some dog breeds, neutering and spaying may be associated with the increased risks of certain health conditions such as joint disorders including hip or elbow dysplasia, cranial cruciate rupture or tear, and some cancers, such as lymphoma, mast cell tumor, hemangiosarcoma, and osteosarcoma.

The research conclusions are not surprising. Sex hormones are important in the development of any animal.  We know they affect psychological development as well as the musculoskeletal, cardiovascular, and the immune system.

I believe this is the University of California – Davis article in question. It is from 2020. Notice that the suggested guidelines for age of neutering is beyond 23 months for several of the giant breeds in the table featuring 35 breeds.

Bronco, our Leonberger puppy is looking straight into the camera. He is wearing a red bandana | Neutering or spaying a dog at 6 months old can be dangerous to their health depending on breed
Our three months old Leonberger Bronco. The Leonberger is a giant breed you can neuter when they are older than two years old.

Recommended Ages for Neutering and Spaying

Below is a list of recommended ages for neutering and spaying for selected dog breeds.

  • Australian Shepherd, for neutering and spaying it is your choice.
  • Bernese Mountain Dog, you should neuter beyond the age of 23 months, but for spaying you have a free choice.
  • Boxer, neuter and spay beyond the age of 23 months.
  • Boston Terrier, neuter beyond 11 months, but for spaying you have a free choice.
  • Doberman Pincher, never neuter, and you need to spay beyond the age of 23 months.
  • German Shepherd, neuter and spay beyond the age of 23 months.
  • Labrador Retriever, neuter beyond 6 months and spay beyond 11 months.
  • Corgi, neuter beyond 6 months, but for spaying you have a free choice.
  • Great Dane, despite being a very large dog you have a free choice for both neutering and spaying.
  • Rottweiler, neuter beyond 11 months, but for spaying beyond 6 months.
A mini-Australian Shepherd puppy is peeking out behind a sofa chair.
Our mini-Australian Shepherd puppy Rollo. You can neuter this breed at an earlier age.

We used to own a male Leonberger dog, which is a giant breed. Our breeder told us to wait beyond two years before neutering him, for health reasons. This article from Hillhaven Leonbergers states the following “We recommend not neutering until at least 2 years of age…Some Vets would recommend from 6 months but this is NOT a good idea.” To read more about the neutering and spaying of Leonberger dogs click here.

Our Leonberger dog Bronco is standing on a red leather sofa. He is stretching to give me a hug.
Our Leonberger dog Bronco is giving me a hug. He was about one year old in the picture. That is still too early to neuter him.

This article from the Saint Bernard Club of America states that “above all, no giant breed puppy should be altered before the growth plates in the bones have matured and closed, usually between 15 and 24 months of age.” This Newfoundland dog magazine states : Currently, the recommended age that a Newfoundland dog should be neutered is 18 to 24 months due to the possible health problems that can arise from altering before that age.

A Saint Bernard dog carrying the typical cognac container. There are mountains in the background | Neutering or spaying a dog at 6 months old can be dangerous to their health depending on breed
According to the article above you should wait to neuter Saint Bernard Dogs until they are close to two years old. Saint Bernard Stock Photo ID: 1713912484 by fred12.
A dark brown Newfoundland dog standing on a stump in the forest.
According to the article above you should wait to neuter Newfoundland Dogs until they are between 18 to 24 months old. Newfoundland dog Stock Photo ID: 1925281937 by Marsan.

Even though the expert advice regarding the best age for neutering and spaying varies, it is clear that doing it at six months old is too early for many breeds and can harm their health.

To see the other Super Facts click here

There are flying Turkeys

Superfact 20: Domesticated Turkeys and Wild Turkeys are the same species, but Wild Turkeys can fly. So yes, there are flying turkeys.

I think this is a super-fact, because the Turkey is a very important bird to Americans and at the same time a lot of people, including Americans, do not know that Turkeys are not flightless birds.

Domesticated turkeys are flightless but wild turkeys are not flightless. Wild turkeys can fly distances of more than a mile, sometimes at speeds of 55 miles per hour. I’ve seen it with my own eyes on turkey hunts. I’ve seen turkeys fly and glide across the sky at the height of 30-50 feet. I’ve seen them flap their wings and then take off.

A standing male turkey with a white head, red neck, and fluffed up feathers | There are flying Turkeys
The turkey my oldest son shot when he was 11 years old.
My son is standing next to truck holding a dead turkey by the legs.
My son holding the turkey he shot.

The photo above is a Tom, a male turkey, that my oldest son shot when he was 11 years old. Male turkeys are called Toms and females hens. We took it to a taxidermist for preservation and mounting. I should add that we typically ate the meat of everything we shot. Taking a wild turkey to the taxidermist makes eating the animal more complicated but you can typically ask for the breast meat of the turkey.

Personally, I think that legal hunting is a lot more humane than eating meat from animals from factory farms.

A male turkey in the middle of flight | There are flying Turkeys
Eastern Wild Turkey Meleagris gallopavo flying over the snow in Ottawa, Canada Stock Photo ID: 1358163995 by Jim Cumming.

I should add that legal hunting is often encouraged for conservation and population management. For example, moose are hunted in Sweden (my native country) to manage their large population (400,000 moose), which can cause damage to forests and agriculture, as well as starvation among moose, if not managed. Illegal hunting, on the other hand, is something nefarious. Below is a video showing wild turkeys flying (video is about one minute long).

I wish everyone a very happy Thanksgiving

To see the other Super Facts click here

Accents are very difficult to lose

Superfact 18: Accents are very difficult to lose. People may speak and understand a second language perfectly and still have a strong accent in that language assuming they did not learn the second language in childhood. This is a fact that is well known to the 20.6% of people in the US who are bilingual and to the 43% of people in the world who are bilingual. Yet many monolingual people are unaware of and surprised by this basic and important language fact.

I can’t lose my accent

On one occasion when I took my oldest son to the playground a guy doing the same started talking to me. Hearing my accent, he asked me where I was from (Sweden) and how long I had been here (10 years). Then the guy said, “I am surprised that after all these years you still have an accent”.

This is a sentiment I’ve come across many times here in the US, but not as often in Europe. Monolingual people are surprised to hear bilingual people’s accent. When I tell people about the reality of accents and that it is difficult to lose one without major speech therapy, they act very surprised. It is a basic and important language fact that is surprising to those who don’t know it. That’s why I think this counts as a super fact.

Black dog with a Swedish flag | Accents are very difficult to lose
Photo by Efrem Efre on Pexels.com

I have difficulty hearing my own accent, which is to be expected according to this article . However, my accent becomes obvious to me when I hear myself speaking on a recording such as when I was interviewed by NBC about the tornado that ravaged our neighborhood five years ago. At first, I was thinking “oh shoot my accent is so obvious and now the whole world knows”, then I was thinking it is no big deal. If you want to hear my accent, click on this link. It is NBC news and my interview is located at : 1 minute and 11 seconds.

Accents are very difficult to lose

What monolingual people typically do not know but practically all bilingual people do know, is that it’s difficult to lose an accent as an adult learning a new language. Children can do it but not adults, not without major speech therapy. This article states that the cut off age is around 12 years old.

According to a test I took, my vocabulary and understanding of English grammar at the time of the incident above was above the average for native English speakers, and it was just as easy for me to understand, speak, read and write English, as Swedish. Yet my accent was obvious.

It should not really come as a surprise to monolingual people, but it does. After all, if you think about it, famous foreign actors such as Arnold Schwarzenegger, Werner Herzog, Marion Cotillard, Stellan Skarsgård. etc., speak with an accent even after living in the US and/or working for Hollywood, several decades, and they are not faking it. I have several friends and relatives who speak with a strong foreign accent after living in the United States for 30, 40, 50, and 60 years. If they came as adults, they still have their accent.

Arnold Schwarzenegger is holding a gian machine gun pointed into the camera. There is fire and smoke in the background.
Arnold Schwarzenegger a bilingual man Stock Photo ID: 2501506607 by Ralf Liebhold

As this article states, “accents are extremely difficult to lose because our infant brains codify a lifetime’s worth of sounds before we’ve spoken our first word”. As this article explains as we age our brains become more specialized in our native language sounds, making it harder to accurately perceive and produce new sounds from another language, a phenomenon often referred to as the “critical period hypothesis” in language acquisition; essentially, the window for easily acquiring perfect pronunciation closes during childhood.

On the left, a business guy speaking a whole bunch of languages indicated by flags coming out of his mouth. On the right another businessman surrounded by question marks | Accents are very difficult to lose
Past childhood it is much harder to accurately perceive and produce new sounds from another language Stock Photo ID: 1818291203 by pathdoc

A few second language facts

The most popular second language in the world with respect to the number of non-native speakers (data taken from this site).

  • (1) English – 1,140 million non-native speakers
  • (2) Hindi – 264 million non-native speakers
  • (3) Chinese (Mandarin) – 199 million non-native speakers
  • (4) Urdu – 162 million non-native speakers
  • (5) French – 132 million non-native speakers
  • (6) Arabic – 109 million non-native speakers
  • (7) Russian – 107 million non-native speakers
  • (8) Spanish – 74 million non-native speakers
  • (9) Bengali – 43 million non-native speakers
  • (10) Portuguese – 28 million non-native speakers

The most popular second language in the world with respect to number of countries.

  • (1) English – 55 countries
  • (2) French – 14 countries
  • (3) Russian – 13 countries
  • (4) Spanish – 8 countries
  • (5) Creole – 8 countries
  • 6) Arabic – 6 countries
  • (7) Kurdish – 4 countries
  • (8) Portuguese – 4 countries
  • (9) Italian – 3 countries
  • (10) Quechua – 3 countries

To see the other Super Facts click here