Egg-Cracking Problem

   (Contributed by Ernie Davis ( davise@cs.nyu.edu), New York University, U.S.A. (18th September 1997))

  • A cook is cracking a raw egg against a glass bowl.
  • Properly performed, the impact of the egg against the edge of the bowl will crack the eggshell in half.
  • Holding the egg over the bowl, the cook will then separate the two halves of the shell with his fingers,
  • enlarging the crack, and the contents of the egg will fall gently into the bowl.
  • The end result is that
    • the entire contents of the egg will be in the bowl
    • with the yolk unbroken, and that
    • the two halves of the shell are held in the cook’s fingers.

   But what happens if

  • The cook brings the egg to impact very quickly?
  • Very slowly?
  • The cook lays the egg?
  • The cook lays the egg in the bowl and exerts steady pressure with his hand?
  • The cook, having cracked the egg, attempts to peel it off its contents like a hard-boiled egg?
  • The cook tries this procedure with a hardboiled egg?
  • With a coconut? With an M & M?
  • The bowl is made of loose leaf paper? of soft clay?
  • The bowl is smaller than the egg? 
  • The bowl is upside down?

Representations, but not solutions despite claims, to the Egg-Cracking Problem


LOGICMOO's full solution to the Egg-Cracking Problem

Before we could begin, we had to invent a logic that allows
  1. the proof of solution to be viewed or defined at any level of detail
  2. a problem to be definable at any level of detail
  3. The problem to be viewable (we can ask questions) at any level of detail
  4. The solution to be viewable in at least one level of detail
  5. To calculate when a solution is possible or not
  6. To explain why a solution is possible or not
  7. Even when 1000s of details and background are unknown, it may still be used invent a complete representation
  8. Through a process, that object (egg, bowl, cook, etc.) can safely be replaced
  9. Can report when certain details are removed or added creates what will be the incompleteness or completeness of representation and solution
  10. At each stage, the ability to create complete and incomplete representations by separation of details
  11. The use common-sense defaults
  12. The ability to detect unrelated details
  13. .

Yes, but the real world is much more complicated

Most organisms live in ever-changing environments, and are at times exposed to adverse conditions that are not preceded by any signal. Examples for such conditions include exposure to chemicals or UV light, sudden weather changes or infections by pathogens. Organisms can adapt to withstand the harmful effects of these stresses. Previous experimental work with microorganisms has reported variability in stress responses between genetically identical individuals. The results of the present study suggest that this variation emerges because individual organisms take random decisions, and such variation is beneficial because it helps organisms to reduce the metabolic costs of protection without compromising the overall benefits.

"The theoretical results of this study can help to understand why genetically identical organisms often express different traits, an observation that is not explained by the conventional notion of nature and nurture. Future experiments will reveal whether the predictions made by the mathematical model are met in natural systems."

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