Eggs are evolutionarily designed to survive falling out of nests and perches. You assume that the egg is dropping onto a hard surface, but there is no mention of that in the puzzle.
That's even assuming it's a chicken egg, but other eggs may be more resilient. It may not even be a biological egg, but an artifically designed egg, that is resilient to drops onto harder surfaces.
(Following Haldane's observation that "You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes.")
I wonder about this. Realistically, what fate awaits the egg that dropped from the nest in the tree branch, even if it survives the fall?
“Hypotheses proposed for the adaptive function of egg shape typically invoke a decrease in egg loss for cliff-nesting birds laying conical eggs that roll in a tight circle; an increase in incubation efficiency when egg shape is associated with the number of eggs in a clutch; or other advantages related to strength, diet, and development. For example, spherical eggs might be advantageous because the sphere is uniformly strong and would be robust to incidental damage in the nest.
Spherical eggs, with their minimal surface-area-to-volume ratio, also require the least amount of shell material for a given volume and possibly optimize gas exchange by providing a large surface area for pores. In contrast, conical eggs may be beneficial because they can accommodate an increased concentration of pores at the blunt end, creating a specialized respiratory site for accelerated neural development in precocial birds. Moreover, conical eggs may protect the blunt end (from which chicks usually hatch) from debris contamination or, in colonial breeders, increase resistance to impacts because a larger proportion of the eggshell is in contact with the substrate. Finally, it has also been proposed that adaptations for flight influence egg shape indirectly through the morphology of the pelvis, abdomen, or oviduct.”
and concludes
“Our macroevolutionary analyses suggest that birds adapted for high-powered flight may maximize egg size by increasing egg asymmetry and/or ellipticity, while maintaining a streamlined body plan”
It doesn’t even mention “better protection against drops”.
Arguably surviving may happen less often for the shock-proof egg than for the egg that is better in some alternative aspect (including quantity).
(Maybe the hard egg has other advantages though. Could also be used to produce a better skeleton.)
Is a harder shell which has higher costs than benefits selected out? Maybe we’re all repeating the same thing.
So this is a pretty common mistake people make when discussing evolution. It’s not about what is advantageous, it’s about what survives the selection process. A combination of odds that play out.
Our eyes are not advantageous or chosen by evolution, our eyes were just acceptable enough for us to survive while other variations were not. There was no decision or work/progress towards an end goal. A creature developed along a certain line by chance, the situation in nature was such that they survived and passed on that trait, while others did not. Natural selection in action.
Please keep in mind the original comment I was responding to:
> Eggs are evolutionarily designed to survive falling out of nests and perches.
My response is "no, they are not". First, like you said, they are not "designed" in any way. But that's the pedantic response. Second, there's no selective pressure for eggs resistant to dropping from a nest, since they are lost anyway and won't pass any genes. It's likely that something else is being selected for -- or at least, that the more resistant shell is not harmful to reproduction of the species -- but there's no selection for nest-drop-resistant eggs because that confers no advantage. Maybe it's just harmless, which can make the trait survive. See the difference?
> There was no decision or work/progress towards an end goal.
It helps to assume everyone understands this, otherwise we cannot get to the meat of the discussion without nitpicking every single sentence.
Off topic, but indirectly supports your point.
"Instead of giving students realistic situations that they could analyze, textbook authors began to fill books with make-believe contexts – contexts that students were meant to believe but for which they should not use any of their real-world knowledge."[0]
I think for a math puzzle that people choose to do for fun, pseudocontext is fine. We can suspend our disbelief and engage with the math as it's intended to be engaged with.
In a classroom setting, on the other hand, I think it's best to stay away from pseudocontext. Either make the context realistic, make it clearly fantastical, or just use math as the context without trying to dress it up in real-life details.
Pseudocontext in a teaching environment is problematic because it requires learners to ignore the common-sense reasoning that they'd apply to a real-life problem and it reinforces the impression that math has nothing to do with the real world.
In this case, we could call it a dragon egg and that would be enough I think to transform it into a fantasy context, since nobody has preexisting assumptions about how durable a dragon's egg might be.
[0] https://blog.mrmeyer.com/2010/pseudocontext-saturdays-introd...
For one, I think the egg experiment is already sufficiently fantastical and its rules follow logically.
Ignoring common sense reasoning is an important skill. We need rigorous answers where they are available, and the common sense answer is almost always very wrong.
I still agree that school textbooks take this much too far in many cases, but this riddle is fine.
- This is a typical bird's egg. Most insect eggs for instance can survive any fall.
- This is a hard floor, not water, snow,...
- There is nothing to protect the egg.
- Floors are typical ~3m floors, not floors from a doll house.
- The experiment is done on earth
The point of maths is that it doesn't need to be grounded into the world. It is a "if A then B" machine. If A applies to a world then B will apply to that world too, and it will always be the case, it doesn't depend on experimental results.
It is great because scientists, engineers, etc... only have to show (with their experiments and measurements) that A applies to our world, and maths automatically tell them that B applies too, no need for extra experiments and measurements, except for verification.
So in this problem, if you use your "real world" experience with eggs, you only solve the problem for a limited set of preconditions. If you solve it properly, using maths, then it will work in any situation that matches the data of the problem, even for people of Pluto.
Also, if you want to talk "real life", I am not sure a 100 story building exists (there is 101, but exactly 100?). And if that building exists, does it have windows you can drop an egg from at every floor?
IIRC, the Hancock tower, briefly the 2nd tallest building in the world and then Chicago is 100 floors.
The problem isn't with mathematicians.
By going against the intentions of the thought experiment and blurting out "0 floors, eggs can't survive very far falls", the individual is deliberately trying to stamp out creativity & problem solving skills, as well as any attempts at getting others thinking about their approaches to the aforementioned problem. To them, the strict adherence to practical reality must be imposed 100% of the time, and there should be no time for playful thinking.
Maybe someone doesn’t enjoy these types of problems, but objecting based on the obviously-contrived premise not being realistic just makes them look dumb.