Paradoxical Undressing

Twenty to fifty percent of hypothermia deaths are associated with paradoxical undressing. This typically occurs during moderate to severe hypothermia, as the person becomes disoriented, confused, and combative. They may begin discarding their clothing, which, in turn, increases the rate of heat loss.

A Polar Bear or Ursus Maritimus

Rescuers who are trained in mountain survival techniques are taught to expect this; however, some may assume incorrectly that urban victims of hypothermia have been subjected to a sexual assault.

One explanation for the effect is a cold-induced malfunction of the hypothalamus, the part of the brain that regulates body temperature. Another explanation is that the muscles contracting peripheral blood vessels become exhausted – known as a loss of vasomotor tone – and relax, leading to a sudden surge of blood and heat to the extremities, fooling the person into feeling overheated.

The victim’s warm blood rushing from their core, coupled with the removal of warm clothing, causes their body temperature to fall even faster. This serves to hasten death from hypothermia and results in another case of paradoxical undressing.

Mountaineers with hypothermia have been known to push aside warm clothing and resist rescuers’ efforts to warm them. It is interesting to note that there are no known hypothermia victims who have reached the stage of paradoxical undressing and survived without outside intervention.

Unfortunately, the most likely place where hypothermia will occur is in a freezing situation, and the last place you would like to take all your clothes off is at such a cold place.

On top of that, it might be ironic to note that in the event you encounter a polar bear and you find yourself in a position where you are not able to defend yourself or flee by means of a car or sledge, you can take your clothes off one-by-one and leave them behind. This will buy you some time because the intrigued polar bear will stop chasing you in order to smell your clothes. Again, you will most probably encounter a wild polar bear in a place where your clothes are vital equipment to ensure your survival.

It is still unknown whether slowly undressing while fleeing from a polar bear instead of running away when remaining dressed increases your chances of survival. According to American (turned British) comedian Rich Hall: the best way to stay out of the reach of a polar bear is not to outrun it, but simply to outrun your friend.

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Gödel’s First Incompleteness Theorem in Relation to the Liar Paradox

Gödel’s first incompleteness theorem states that: “Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”

Kurt Gödel

How does Gödel’s first incompleteness theorem relate to the liar paradox?

The liar paradox is the sentence: “This sentence is false.” An analysis of the liar sentence shows that it cannot be true – for then, as it asserts, it is false – nor can it be false – for then, it is true.

A Gödel sentence G for a theory T makes a similar assertion to the liar sentence, but with truth replaced by provability: G says “G is not provable in the theory T.” The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.

It is not possible to replace “not provable” with “false” in a Gödel sentence because the predicate “Q is the Gödel number of a false formula” cannot be represented as a formula of arithmetic. This result, known as Tarski’s undefinability theorem, was discovered independently by Gödel when he was working on the proof of the incompleteness theorem.

Falling Tree Paradox

A Juglans Regia Tree in Ticino, Switzerland

A tree fell down in the middle of the forest. If no-one was there to witness this – did it make a sound or not?

The answer is both or neither. A tree falling in the forest may or may not make a sound, depending on if you ask a semanticist or a neurologist.

For a sound may be something that is perceived by the vibration of the ear drum or the vibration of the source of the sound. But if there was no ear close enough to the tree – there could not have been a sound. After all, no-one heard the falling tree. The sound on the other hand, was most probably there for anyone to hear, but we cannot be sure of that, simply because no man can claim there is a sound if there is or was not a sound to be heard.

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Buttered Cat Paradox

The buttered cat paradox is a paradox based on the tongue-in-cheek combination of two adages:

Buttered cat

  1. Cats always land on their feet.
  2. Buttered toast always lands buttered side down.

The paradox arises when one considers what would happen if one attached a piece of buttered toast – with the butter side up – to the back of a cat, then dropped the cat from a large height.

Some people jokingly maintain that the experiment will produce an anti-gravity effect.

They propose that as the cat falls towards the ground, it will slow down and start to rotate, eventually reaching a steady state of hovering a short distance from the ground.

Meanwhile, the cat remains in the air rotating at a high speed as both the buttered side of the toast and the cat’s feet attempt to land on the ground.

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The Epimenides Paradox

The Epimenides paradox is a problem in logic. It is named after the Cretan philosopher Epimenides of Knossos who lived around 600 BC. Epimenides was also a religious prophet who, against the general sentiment of Crete, proposed that Zeus was immortal, as in his Cretica poem:

“They fashioned a tomb for thee, O holy and high one
The Cretans, always liars, evil beasts, idle bellies!
But thou art not dead: thou livest and abidest forever,
For in thee we live and move and have our being.”

Also, the Epistle to Titus makes reference to Epimenides. The author states:

‘One of themselves, even a prophet of their own, said, The Cretians are alway liars, evil beasts, slow bellies. ‘ (Titus 1:12)

A paradox of self-reference is commonly supposed to arise when one considers whether Epimenides spoke the truth. However, if Epimenides knew of at least one Cretan who was not a liar, then his statement is a non-paradoxical lie in that it does not lead to a logical contradiction.

The negation of the statement, “All Cretans are liars” is the statement, “Some Cretans are not liars,” which might be true at the same time as the statement, “Some Cretans are liars.”

Schrödinger’s Cat

Diagram of Schrodinger’s Cat Theory

A cat, along with a flask containing a poison and a radioactive source, is placed in a sealed box shielded against environmentally induced quantum decoherence.

If an internal Geiger counter detects radiation, the flask is shattered, releasing the poison that kills the cat.

The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when we look in the box, we see the cat either alive or dead, not both alive and dead.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a blurred model for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

Boy or Girl Paradox

“Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?”

In this problem, a random family is selected. In this sample space, there are four equally probable events: ‘Older child Younger child’.

Only two of these possible events meets the criteria specified in the question (e.g., GB, GG). Since both of the two possibilities in the new sample space (GB, GG) are equally likely, and only one of the two, GG, includes two girls, the probability that the younger child is also a girl is 1/2.

A Young Girl Kisses a Baby on the Cheek

“Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?”

This question is identical to question one, except that instead of specifying that the older child is a boy, it is specified that at least one of them is a boy. If it is assumed that this information was obtained by considering both children, then there are four equally probable events for a two-child family as seen in the sample space above. Three of these families meet the necessary and sufficient condition of having at least one boy. The set of possibilities (possible combinations of children that meet the given criteria) is: ‘Older child Younger child’

Thus, if it is assumed that both children were considered, the answer to question two is 1/3. However, if it is assumed that the information was obtained by considering only one child, then the problem is an isomorphism of question one, and the answer is 1/2.