# The Faulty Thermodynamics of Children’s Stories

SteelyKid is not yet at the stage where I can usefully read to her– she likes sitting on my lap while I read just fine, but she’s more interested in trying to eat the pages than listening to the story. I was reminded this morning, though, that when she gets to bedtime-story age, I’m going to face some real dilemmas. Some of the classic stories teach dangerously wrong lessons about physics.

Take, for example, the story of Goldilocks and the Three Bears (referred to at the end of the previous post). In the usual telling, Goldilocks comes upon the Bears’ house and finds three bowls of porridge. The bowl for the Papa Bear is too hot, the bowl for the Mama Bear is too cold, but the Baby Bear’s bowl of porridge is just right, and she eats it all.

The story may convey a useful moral message, but it’s way off base on the physics.

After all, the Papa Bear, being the biggest, presumably has the largest bowl of porridge. Here, the story fits what we know about thermodynamics, as the largest bowl should take the longest time to cool, and thus should be the hottest at any time before the porridge bowls reach thermal equilibrium with their environment.

The description provided of the other two bowls, though, is not consistent with known physics. The Mama Bear, as the other adult, ought to have the second-largest bowl of porridge, which, in turn, ought to be the second-warmest bowl of porridge (assuming that equilibrium has not been reached). But the story says that this bowl is too cold! Meanwhile, the Baby Bear, who ought to have the smallest portion of porridge, has a bowl that is “just right,” neither too not nor too cold. As the smallest bowl, though, the Baby Bear’s porridge ought to be the coldest of the three (until equilibrium is reached, of course). There is no way for the bowls as described to have the temperatures described, while being consistent with the known laws of thermodynamics.

The only way that the story can make sense is if, for some reason, the Mama Bear has the smallest portion of porridge. In which case, this is a story with a very different moral than the original– it’s a story about the oppression of the Mama Bear, either because the patriarchy is forcing her to eat only the scraps left behind after her husband and child have had their fill, or because the unhealthy woodland media culture has saddled her with a negative body image, leading to an eating disorder.

Or, possibly, it’s a story about the importance of knowing your physics. Upon entering the house and finding that the smallest bowl of porridge was hotter than the medium-sized bowl of porridge, Goldilocks should have known that something was amiss. She should have noticed that the normal laws of physics did not apply, and thus she was in the sort of story in which talking bears are likely to show up and eat you for trespassing in their home.

Rather than trying out the chairs and beds, she should have left the scene at once, and reported her findings to the nearest reputable physics lab, where they could bring in the equipment and expertise necessary to understand such peculiarly anti-entropic behavior. She would then have been rewarded with co-authorship on the resulting paper, rather than a nasty mauling at the paws of annoyed bears.

So, kids, pay close attention to your physics lessons. Thye may save your life, and put you on the fast track toward a tenured faculty position!

## Comments

1. #1 Stefan Krzywicki
May 4, 2009

Of course, there is one other way for the temperatures to be correct. If the Mamma Bear’s porridge were served out long before the other’s, hers could be coolest.

2. #2 Ahcuah
May 4, 2009

Heh.

Or maybe Mama Bear poured her bowl first, got called to change a dirty diaper (you surely don’t think Papa Bear would do such a thing), and then finished pouring the other two bowls once she finished diaper duty.

By that time, her bowl was cold.

3. #3 Tim Eisele
May 4, 2009

Actually, when reading to my daughter, I make a point of mentioning things in the stories that are obviously wrong or not properly thought-out. She loves it. My wife rolls her eyes a bit when I go on these digressions about how things would *really* go, but what the hey.

4. #4 bumblebrain
May 4, 2009

Have you read any Jasper Fforde? He’s written a novel called “The Fourth Bear” where he points this out and it ends up as evidence in a porridge smuggling/murder mystery. I can’t remember how he resolved this problem though.

5. #5 Janne
May 4, 2009

Papa bear likes his porridge piping hot. Mama bear prefers cold porridge and takes it chilled. Baby bear gets warm, but not hot, porridge as infants are sensitive to temperature extremes.

No need to make everything so complicated :)

6. #6 Breton bienvenue
May 4, 2009

Alternately, we can explain it via bowl shape. My wife likes her food to stay warm so she uses a deep bowl (really a big latte mug). I like my food cooler so I use a wide, shallow bowl. The difference in surface area makes a big difference in how fast food cools off, at least in my sample of n=2.

7. #7 Winter Toad
May 4, 2009

The bears, having suffered financially during the recent market problems, are not well off. Their tableware consists of one adult-sized bowl, one child-sized bowl, and a large, shallow dish. The mother, self-sacrificing sort that she is, eats out of the dish. Because her serving of porridge is poured onto a large, flat surface, it has a much higher surface to mass ratio than either of the servings in the bowls, and so equilibrates more quickly.

8. #8 highschoolphysics
May 4, 2009

I think we can let this slide in a universe that is populated by talking bears that eat porridge.

9. #9 Moderately Unbalanced Squid
May 4, 2009

It’s not commonly known, but Momma Bear likes her porridge a little watery. Papa Bear thinks she just pours in some water, but in fact it’s slightly chilled whisky.

10. #10 Eric Lund
May 4, 2009

The other posters have presented plausible solutions to this thermodynamics problem, to which I don’t have anything to add. However, it seems to me that you might have a harder time explaining why Papa Bear and Mama Bear sleep in different beds, when [I hope] she will know (N=1, but she won’t know yet that that doesn’t mean anything) that Mommy and Daddy sleep in the same bed. How can one bed be both too hard and too soft?

11. #11 Eofhan
May 4, 2009

Many others have explained how Momma’s dish was colder than expected, so I’ll take that as given. I suggest that Baby’s was indirectly dished, being taken from Momma’s and Poppa’s servings. A combination of the two sources, it would be intermediate in temperature.

P.S. If things like this bother you, Jasper Fforde may induce seizures. I am fond of his books, but my “suspension of disbelief” generators tend to whine and smoke while reading them.

12. #12 Moderately Unbalanced Squid
May 4, 2009

However, it seems to me that you might have a harder time explaining why Papa Bear and Mama Bear sleep in different beds, when [I hope] she will know (N=1, but she won’t know yet that that doesn’t mean anything) that Mommy and Daddy sleep in the same bed.

They don’t sleep in the same bed. Why do you think Mama Bear needs whisky in her porridge every morning? They’re just holding it together for Baby Bear really, and he’s going to need lots of therapy in the future because they’re not holding it together *well*.

13. #13 Clark
May 4, 2009

You can buy beds with individually adjustable firmness settings. Perhaps the bears have one of these, and because of the contrast in hardness between the two sides of the bed, Goldilocks found it more fitting to describe them as two different beds. While physically one bed, the factor that was most important in distinguishing a bed it it’s firmness, ergo, her description leading to decades of misunderstanding.

14. #14 Matt Springer
May 4, 2009

Maybe all the bowls were initially filled with porridge from the refrigerator, which the bears then microwaved individually in accordance with their personal preference.

15. #15 Kate W
May 4, 2009

If you think bedtime stories are bad, grades k through 12 are going to kill you. You are going to be hit with the urge to redesign curriculum like crazy.

16. #16 csrster
May 4, 2009

Daddy Bear obviously has orthopedic problems, requiring a firmer bed. Alternatively, they both use a nice soft bed for sleeping and a firmer mattress for other nocturnal ursine activities.

17. #17 Steinn Sigurdsson
May 4, 2009

In the version of Golidlocks I originally heard, the problem with the bowls was the salting of the porridge – too salty, not salty enough, just right.

I think the whole temperature thing is modern revisionism, along with the mangling of Humpty Dumpty.

18. #18 Thony C.
May 4, 2009

Papa Bear is a big strong manual worker who needs a big portion. Baby Bear is a hyper active growing kid who also needs a big portion but not as big as Papa’s. Mama Bear is a figure conscious female whose on a diet and only eats a small portion. So where’s your problem Chad?

19. #19 mdiehl
May 4, 2009

Not at all physics related, but a reading hint . . . one board book for SteelyKid to chew on the edges, no consumption of said thereof allowed while Dad reads another.

20. #20 Radha
May 4, 2009

So the thermodynamics bothers you, but not the depiction of bears eating porridge or sleeping on beds and talking? Or of Papa Bear being involved in the Baby Bear’s upbringing and not killing her?

The story’s really about variation of personal preference. Explain it in that light (Papa Bear likes his hot, Mama likes hers cool, and baby likes it warm.) Done.

Or that Mama’s porridge was under a draft from the A/C.

21. #21 Brian X
May 4, 2009

Or maybe “Baby” Bear was actually a teenage bear and had the biggest portion, and Goldilocks got Baby and Papa’s bowls confused?

22. #22 Lara
May 4, 2009

Another explanation would be found in the conductive properties of the bowls. If Mama Bear’s bowl had higher heat conductive properties, and Papa’s was more insulating, then Mama’s would cool more quickly.

23. #23 Alex Whiteside
May 4, 2009

You’re overthinking this. I’ve always understood it as meaning that they were each served their porrage at different temperatures. It helps to emphasise that they’re going to be back any minute and that Goldilocks is making the cardinal mistake of a horror film, namely hanging around the house when there are godless eating machines on their way.

I wonder what got the bears to walk off from dinner anyway. I figure Goldilocks was a vagrant who lured them away to steal their food.

24. #24 Anon
May 4, 2009

I ran a daycare for a bit. I remember reading a book at story time, in which a woodpecker was helping out by hammering in the nails to repair a hole in the roof. The 2- and 3- year olds might not have understood my comment, but one parent got a chuckle when I told them “and this, my friends, is what we call ‘revisionist history’.”

25. #25 becca
May 4, 2009

I used to think it was all about the oppression of Mama Bear, since I do not care overmuch for cold porridge. However, I believe two other factors may provide more palatable, as well as thermodynamically-valid, explanations.

First, bowl shape and material could result in very different conduction properties.
Perhaps Papa Bear eats his porridge directly out of the pan, because he is a large bear and cares not for social niceties as much as getting sufficient porridge.
Mama Bear might eat her porridge out of a beautiful blue china bowl, which is a bit shallow and cools rapidly.
Baby Bear eats porridge out of a non-breakable bowl that would also not produce nasty burns for safety reasons. (I suspect Baby Bear’s bowl would be plastic, or perhaps wood, if plastic is insufficiently rustic for the Bear’s cabin).

Alternatively, Mama Bear also adds the most delicious cream to her porridge, which is properly chilled for food-safety, and therefore cools her porridge the most.

26. #26 Bob
May 4, 2009

Yes, the bowl temperature and sizes bothered me when I was young. But that’s when TV parents slept in separate beds also, so no issue there.

But then 1 day I realized, that bears sleep in a cave, eat rare meat or garbage and that the story was a fairy tale, so if the author can have them live in a cottage, sleep in beds, and break other laws of reality, why not break the laws of thermodynamics as well…

27. #27 capella
May 4, 2009

I always figured Mama Bear, being a mother, intentionally made her porridge colder (i.e. by serving it first) so she could point out her martyrdom.

28. #28 Mu
May 4, 2009

Actually, Momma Bear had been snacking on dried salmon all morning while watching Oprah, and had only taken a token helping, pretending she was on a diet.

29. #29 Julianne
May 4, 2009

Mu — I think you may have meant to say that Momma Bear’s porridge was too cold because she got up before everyone else, served herself a bowl before getting distracted by uploading her latest paper to Nature.

30. #30 Art
May 4, 2009

A little known fact about highly domesticated bears, those that eat at tables and sleep in beds, is that the male bears and the young, prone to breaking finer things, eat from durable and inexpensive wooden bowls. The lady bear of the house, being properly dainty, eats from a bowl made of fine china.

The fine china is by far a better conductor of heat and so the momma bears porridge always cools off more quickly than the porridge in the wooden bowls.

This is something of an advantage for the busy mother bear who serves porridge to herself last, eats quickly so she can get a head start of cleaning up after the meal. The children and daddy bear tend to eat at a more leisurely pace variously playing with their food and lounging between bites.

31. #31 cicely
May 4, 2009

Physics aside, a team of biologists would no doubt be interested in studying these talking bears, perhaps with an eye to comparisons in diet, lifestyle, etc., with the more usual, non-taling bear.

Besides, who are we kidding? She’d sell the story to some scandal rag for cash money.

32. #32 Chris Noble
May 4, 2009

Everthing can be explained with THERMITE!

33. #33 passerby
May 4, 2009

Have you read “Alice in the wonderland”? You have no idea what the children books are about, they are NOT physic lectures!

34. #34 Marc Fleury
May 4, 2009

Actually, Baby Bear’s and Mama Bear’s porridge were the same temperature. It is only because Goldilocks tried Mama Bear’s porridge immediately after trying the too-hot porridge that it seemed too cold. The difference in temperature was much greater, and this confused her senses and made her think it was too cold.

35. I think that the people who are accusing Chad of over-thinking this are over-thinking this.

36. #36 Winawer
May 4, 2009

Somebody should probably reverse the polarity of the neutron flow on that porridge.

37. #37 cm
May 4, 2009

In the original German, Mama Bear’s porridge was liquid-nitrogen cooled to around -346°F, and Goldilocks found it not just “too cold” but “far colder than any reasonable person could possibly imagine.” Traditionally, parents explained that Mama Bear was insane.

In subsequent retellings through history, the Mama Bear’s bowl now simply given as “too cold”.

38. #38 Thony C.
May 5, 2009

Have you read “Alice in the wonderland”? You have no idea what the children books are about, they are NOT physic lectures!

Posted by: passerby | May 4, 2009 5:40 PM

You are of course right; “Alice in Wonderland” is not a physics lecture its a wonderful discourse on philosophy and formal logic!

39. #39 jim
May 5, 2009

Could we be talking about spice, rather than temperature?

40. #40 Samskara
May 5, 2009

This assumes that the bowls are all the same type, as if the family uses matched China. In fact, in a family with a very young child, this seems unlikely. You don’t even have to stretch the imagination too far to realize that Papa Bear’s portion was the largest, and retained the most heat, but Mama Bear had a smaller portion which cooled more rapidly — but Baby bear had a typical children’s bowl, insulated, with room for warm water that would hold the temperature at the “just right” level. While this design seems to have fallen out of favor in recent years — Amazon offers a dish that can be chilled in the freezer, but not heated in the microwave, implying that Baby prefers his food cold — the dishes that can be used for warming are still available, or might be a family heirloom (also, this is an old story.) One of these dishes is available on-line for \$24.99 plus S&H.

41. #41 weatherman
May 5, 2009

My favorite book to insert snarky comments to my children was the classic ‘Good Dog Carl’, where a baby is left unattended for several hours, it appears, and is cared for by the large black family dog, Carl. Fed from the fridge, and bathed in a deep tub, how this baby survives is a mystery. The parents, out shopping, would be up on charges of abandonment!

42. #42 Hugh Mannity
May 5, 2009

I remember an illustrated version of this story which not only described the porridge as “too salty”, “not salty enough” and “just right” but also showed Mama Bear’s bowl as being a delicate china (Willow pattern, IIRC) while Papa and Baby had more robust wooden bowls.

But of course, no one in America puts salt in porridge. Like almost everything else it’s sweetened to within an inch of its life.

43. #43 ~~Silk
May 5, 2009

Mama Bear is Jewish. Explains everything.

44. #44 Another theorist
May 6, 2009

Mama bear has type 2 diabetes, and had a very small portion of porridge to go with her scrambled eggs.

45. #45 Trent
May 6, 2009

Just wait until you hit Winnie-the-Pooh (our current bedtime staple), where in the very first chapter, you have Christopher Robin blowing up a balloon (apparently with air his lungs just drew from the surrounding atmosphere) so that Pooh can then go floating up to the precise level of the bee hive up in the tree. Now that’s some creative physics!

46. #46 Edith
May 7, 2009

Okay, first off, Mama Bear does not have the middle-sized portion. Mama Bear, bowing to the unequal demands of a society that expects her to function like a super-wife, a super-mom and a super-model all at once, is on a diet. Now the person that wrote this article does not pay attention to the fact that the size of the bowl is irrelevant. What matters are the size of the portion and the surface area exposed to the air. Mama Bear, being on a diet, has the smallest portion. Tending to Papa Bears demands and working overtime to make sure everything is “just right” for Baby Bear, she has had no time to heat up her paltry serving of porridge in the first place. But she’s used to it. Now, of course, also bowing to Papa Bear’s complaints that his porridge is too hot, she goes on a walk with him while his cools down and hers gets positively stone cold. Been there, done that.

47. #47 Kids stories
May 11, 2009

Ha ha…. I think people are think way too much into this, after all it is a story that is aimed at children.

Goldilocks and the Three Bear is a golden oldie when it comes to chldren’s stories though.

48. #48 Wally
May 24, 2009

Well, that perfectly explains why humans have been able to evolve so much faster than bears. That’s because they don’t have all those “bear problems.” Or something…

49. #49 jim
April 20, 2010

Temperature is often subjective.
The porridge could all have been roughly the same measure temp, but to the subjective tastes of the individual it could easily have been too hot, too cold, or just right.
and i actually experienced this during lunch today – also, the too hot and too cold individuals were quite finicky.

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