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Mathematics' Quirks: the Barber Paradox

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Mathematics' Quirks: the Barber Paradox The Clovis Tutorial Center’s I N S I D E THIS ISSUE: WRITEVOLUME 16, ISSUE 4 NOWDECEMBER 2016 Leadership 2 Stories and 2 Legends Mathematics’ Quirks: The Barber Paradox Joining the By Taylor Lopez 3 Conversation I love paradoxes; they make ry this problem can not be that couldn’t create a loop Essential Math 3 people question the way resolved. This paradox was like Russell’s paradox. After Pick-Up Lines that humans use some theo- discovered in 1901 by the publishing the three vol- Tutors of the ries to interpret the world. aforementioned Bertrand umes of Principia Mathemat- 4 Month Can things we take for com- Russell. At the time, this ica in 1910, 1912, 1913, and mon knowledge be incor- was a huge problem for the a second edition in 1927, his Working at rect? Does 1+1 really equal foundations of mathematics. work was highly regarded as 4 the Zoo 2? One of my favorite phi- One hundred years previ- the greatest logical theory losophers, Bertrand Russell, ous, Gottlob Frege tried to since Aristotle’s Organon. Sudoku 5 attempted to solve a para- develop a foundation for all Unfortunately Kurt Gödel’s dox of set theory in his mathematics using symbolic incompleteness theorem Word of the magnum opus Principia Math- logic. Frege established con- that finally showed that the 5 Month ematica. Russell’s paradox can nections like x=5, stating Principia Mathematica could be described with a riddle, “If the the value of x is 5. This not be both consistent and Math It! 5 a barber shaves all and only makes intuitive sense but complete. those men in the village who leads to Russell’s paradox. If So the answer to the rid- A Party in do not shave themselves, does we write x = 5 in set nota- dle: it depends on what type 5 Your Drink he shave himself?” Given this tion, we get that x = {n : n is of set theory you use. You statement to be true, who an integer and 4 < n < 6 }. can remove the barber from Word Search 6 shaves the barber’s beard? Seemingly, any description the set of people who do We can break this down into of x could fit in after the not shave themselves, you mathematical terms to try and colon, e.g. x = {n : n is not can say the barber is female F E A T U R E D draw a conclusion. in n }, which was discovered and doesn’t have the char- AUTHORS A set is simply a grouping by Russell and led to his acteristics of someone who Taylor Lopez of numbers that we can de- paradox. When Russell dis- needs a shave, etc. There is Jason Lee scribe, typically with a varia- covered this paradox, Frege no definitive answer and this Blake Wilson ble e.g. A = { 1, 2, 3 }. In immediately saw that it had reality doesn’t allow mathe- Ramleen Boparai English this reads, the set of a devastating effect on his matics to be based in pure Isaiah Trujillo A has the values one, two, system. Even so, he was logical axioms, we have to Mary Papikian and three, and A’s size is unable to resolve it, and make intuitive assumptions Robbie Hill three and that A doesn’t there have been many at- about math. Our current Spencer Shadley contain itself. So given a set tempts in the last century to understanding could be in- Ben Bohan R that contains all sets avoid it. Russell’s solution is correct, does 1+1 really Samuel Montgomery whose members do not to enable a hierarchy of equal 2? Does the barber contain itself, does R con- types that inherit from each get to keep his fantastic tain itself? Can the barber other. He undertook this moustache? I urge you to FACULTY shave himself without violat- mission to essentially prove take a dive into math, look ADVISOR ing this predicate condition the fundamentals of mathe- at its quirks, and explore its Adelaide Mitchell that he only shaves people matics from purely logical mysteries. who do not shave them- axioms. Allowing for con- selves? With naive set theo- sistent logical statements P A G E 2 Leadership By Jason Lee Leadership: the elusive skill you'll remember is the collec- where you mentor and dele- set that seems to require tive hours of learning points gate, etc. This is perfectly endless hours of training and and lectures. Thus the best acceptable, but the bottom overcomplicated procedures. approach, as with any task, is line is that you are really in I am no expert on the subject to keep it simple and follow that position for one specific myself, but I have had a fair the aforementioned golden purpose: make sure that the bit of experience with the rule. That takes care of sum- nonsense stops at your desk good and the bad during my ming up the thrust of all and does not make it to own attempts to be a leader. leadership classes and advice your team. Simply put, keep The golden rule to any leader- so that you will not be going “it” from rolling downhill ship position is “Don’t be off and forgetting your prime any further. For more tips Jason is a tutor here arrogant.” With any position directive. The largest miscon- and tricks on keeping it sim- at Clovis Community comes a myriad of responsi- ception about leading is that ple, just find the nearest College. He rides a bilities, and the last thing you have a special role Marine. motorcycle . Stories and Legends “He would spend By Blake Wilson between his targets, the took a shot, his target would entire days going distance growing continually, move across the sky and he Archibold Flechingham of back and forth until one day he realized he would miss: piercing the Nockshire was an archer. was going around in a circle. thick black veil of the night between his targets, He stood as tall as a sequoia At this revelation he be- leaving only a small pinhole and was as strong as thun- gan to tell others about how of light. And no matter how the distance growing der. He cloaked himself the earth was round and not far he lead his shot, he still with entire fields of cotton continually, until flat; however, the people did could not hit it. After a and bathed in the largest of not believe him. He tried to while, he began to travel the one day he realized summer storms. Even as a get them to follow him world in search for the tall- child he towered over the around the world but no est mountain top so that he he was going around mountains and roamed the one would go. So to prove would be closer to his tar- forests freely, hunting for in a circle.” his discovery he showed the get. food for himself and his people the only way he Each day he would hike to town. He wielded a bow could think of. He climbed the peak of the tallest with a three-ton draw, the tallest mountain in the mountains he could find would use entire trees for area and placed a single ap- with his bow and a quiver of the shafts of his ple on his head. He readied arrows, and as soon as night arrows, and was a his stance and took his shot. fell he would begin to fire at deadly shot. After some time had passed his target. He tried tireless- Blake is a His shot was so his arrow came whizzing by, ly, night after night, to hit his precise that it was taking the apple off his head mark until he had complete- tutor here on said he could shoot and not a hair more. ly filled the entire sky with campus. He a wing off of a fly. Despite his accuracy, there these small holes of light enjoys ener- He constantly chal- was one target that was known to us as the stars. gy drinks and lenged himself by always able to elude the To this day he still wanders black t-shirts. shooting smaller and strike of his arrow. The the earth hunting that great smaller targets, far- Moon. From birth, he as- white beast, and if you ther and farther pired to hit that great target watch closely you can see away. He would as it hung in the pitch black his arrows shoot across the spend entire days sky. Every night he would night sky with a quick streak going back and forth try to shoot the moon. of light. However, every time he W R I T E N O W VOLUME 16, ISSUE 4 P A G E 3 Joining the Conversation Should Murderers’ Names be Made Public? YES, NO, In 2015, there were 375 mass From mass shootings to a singular shootings in the US. The reasons murder, a certain degree of delicacy behind these shootings? We may is needed when presenting the infor- never know. Each killer is different. mation of the incident to the public. Most of them are not in the right No doubt, the public is entitled to state of mind during these shoot- know about the various events occur- ings. But regardless of whatever the ring in their community; however, Ramleen Boparai Isaiah Trujillo reason may be, the families that there are some pieces of information have to bear the tragic loss of their that can be omitted without compromising the integrity of loved ones, deserve to have a sense of peace.
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