If You Give a Toddler a Time Machine…

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Now you know.
Now you know.

Like most parents, I am frequently struck by similarities between raising a child and quantum paradox. In this post, I have attempted to sketch a few thought experiments illustrating the myriad mathematical and logical labyrinths of parenthood.

Hat tip to mathmetologist Kevin F. Clark for his collegial editing and freundschaftsbezeigungen.

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Now you know.
Now you know.

The Verschränkung of the Napping Toddler:
A toddler is instructed to nap, and is enclosed in a sealed room within which they cannot be directly observed. After a period of time, the effect of opening a door to observe the toddler’s napping state will either a) wake the toddler if they are asleep, ruining everybody’s afternoon, or b) catch the toddler tattooing their face with contraband permanent marker, ruining everybody’s afternoon. The child thus exists in a superposition of all possible states, and from the standpoint of quantum mechanics, must be understood as simultaneously napping peacefully and ruining everybody’s afternoon.

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The Reductio Ad Absurdum of Co-Sleeping:
A toddler joins a sleeping parent in the center of a bed, and shoves their limbs under the adult’s body for warmth and comfort. With each passing hour, the toddler’s wedging shovels the parent away from their initial resting position, reducing the distance between the parent and the edge of the bed by half. Due to the infinitely divisible nature of space, co-sleeping thus ensures that by morning the quantity of bed surface area for the parent asymptotically approaches zero as they are bulldozed infinitely close to the limiting edge of the bed, while the sleeping area for the toddler approaches infinity.

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The Grandparents’ Dilemma
Two grandparents are suspected of giving a toddler an illegal serving of mocha chip ice cream, and are subjected to questioning in separate rooms. Each grandparent is unable to communicate with the other, and are informed that while the parents of the (now quite high) toddler don’t have enough evidence to know for sure that both grandparents are guilty of the main offense, they are offered a Faustian bargain:

  1. If each grandparent blames the other, neither grandparent will be permitted to watch Frozen with the toddler, which would be too bad because said toddler is super cute when he sings and sashays.
  2. If one grandparent blames the other and the other remains silent, ie the grandmother blames the grandfather and the grandfather says nothing, the grandmother will be permitted to take the toddler to the zoo while the grandfather is forced to go buy wipes at Costco and is not permitted to buy themselves a pizza snack.
  3. If neither grandparent blames the other, they will be regarded suspiciously for an arbitrary amount of time, and will likely not be trusted around ice cream, but ultimately the incident will pass without fanfare.

While it seems intuitive that each grandparent would blame the other out of rational self-interest, thereby minimizing sentencing for themselves, in practice one observes a cooperative behavior out of keeping with classical rationalism. However, in long-form iterations of The Grandparents’ Dilemma (for example, following the “mocha chip” variation with the “Who taught the toddler the Yiddish racist epithet for Lutherans?” variation and the “Who let the toddler watch the original Dumbo cartoon where the black crows scat and call each other ‘brotha’?” variation) grandparents are more likely to use ensuing games to retaliate for the outcomes of previous ones, statistically ensuring that the longer the family is together for Thanksgiving, the more likely it is that only the toddler enjoys themselves.

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The Bathtime Paradox, or The Fractal Foreskin
According to Euclidean geometry, a filthy child can be bathed by repeatedly passing soap in a straight line the discrete distance from its head to its toes, while rotating the child on any axis. Such a mathematical model, while advantageous in terms of time expended per bath, is of limited use in terms of the elimination of dirt, as Euclidian distance does not take into account the curvature of the child, and thus does not get said child terribly clean. By employing calculus to determine more efficient geodesic paths, one can devise a bath-time strategy to accommodate irregular, inverse contours of, for example, armpits. Yet the more fastidiously one cleans, paradoxically, the more and ever smaller patches of dirt may be observed. The deployment of fractal geometry is necessary to comprehend the true measure of a child’s cleanable surface area, because the closer one cleans (adjusting the measure of scale to ever smaller finite levels), the closer that child’s surface area approaches infinity. In this way, fractal mathematics confirm what parents have long intuited: bathing a toddler is the surest route to gaze upon the abyss of infinitude.

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The Impossibility of Disproving a Double Negative
Suppose, at any past or future moment, a toddler were given a time machine. Given that alterations to the time stream made by said toddler would result in new future memories of an adjusted past, we uncover a curious exception to the post hoc ergo propter hoc fallacy: because new future memories would result from and camouflage disruptions to the arrow of time, it is therefore impossible to disprove that toddlers don’t not have time machines.

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