Piazza ken mutters the word aloud

This time it's at the request of no fewer than two contributors, so I can pretend I'm not just writing this because of my huge ego as usual (though I do admit their requests have further inflated my ego accordingly).

Today, I will recount the tale of the most on-point birthday present I have ever received.

To be continued, in a future issue…

itorED
Editor, mathNEWS

ARTICLE OF THE ISSUE

This week's article of the issue goes to water for Stairway Constants, part [4.5,7], though really it's for the series as a whole. On the one hand it's the most actual math we've had in mathNEWS in a while, on the other hand the Stairways Constants series have been by far the hardest articles to format since Zethar's cuneiform magnum opus, so you best be damn grateful we've deigned to give you the prize 😛

mathASKS 142.5
FEATURING PROF. KEVIN HARE, INTERIM DEAN OF MATHEMATICS

On a related note, I have been told that the Math House can't have a paternoster, so I'm really hoping to get my way with the washroom plans.

water: what is your favourite stairway constant? (referring to the number line in the north-
northeast stairwell of mc)

I feel that students (and the wider university community) have the right to hold their university to account if they feel that it is not meeting its responsibility. This is equally true be it on environmental issues such as its involvement in the fossil fuel industry, social issues such as equity, diversity and inclusivity, or upon the quality of education. The previous list is in no way exhaustive. I feel it is the responsibility of the University to take such concerns seriously, and change if necessary. This does not mean that everybody will always agree, but everybody should always be willing to listen and try to understand, and to act as their conscience dictates. When the University says that today's students are the leaders of tomorrow, it is more than just empty words. We strongly believe, and I personally strongly believe, that this is true. If you would like advice on the best avenues to advocate, please reach out to my office (deanmath@uwaterloo.ca). Alternately I am sure that both WUSA and MathSoc would also be able to give excellent
advice on this matter.

itsh: what is your fursona?

Good

alumniutus: are you excited to come to grad ball? what advice would you give to the current graduating class?

I hope to be able to annex at least three Engineering buildings before June 30th, and have plans well in hand for the incoming dean to annex the rest before the end of the year.

My hopes for math students in general is to have sufficient repurposed Engineering buildings to meet their paint ball / laser tag / indoor humans vs zombies needs.

I normally pour skim milk on my cereal in the morning. So I guess in answer to the second question — my spoon.

untitledmathpublication: how often do you
collaborate with kathryn hare? alternatively, how often do others confuse the two of you?

I don't often cut my sandwiches. I think the distribution is about 1% vertical, 1% diagonal, 98% can't be bother to cut them.

terrified: which engineering building would you annex first?

Across the room, marking the epicentre of the innumerable emanating threads, is a singular word, varying in visibility under the straggling candle. It contains an unremarkable six characters, but to Ken it is treacherous, bizarre, and arcane, its definition forever eluding him. He wasn't sure how, but his supreme mathematical intuition told him that something, somehow, connected it to djao. "Piazza,” Ken mutters the word aloud, shaking his head as he does so.

Ken nears the bottom of the stack. The candle has waned and the only perceptible features remaining in the room are Ken's hunched over figure, the discarded papers within a metre radius of him, and his audible lamentations as the end of the pile looms nearer. With a pitifully sized stack remaining, his hope had all but been devoured by the fraught, acceler-ating dread. But then, second from the bottom of the pile, he unearths it. A wild, uninhibited grin breaks through and he leaps to his feet, as if the paper had dispelled all the treachery that had so imperilled him. He looks back down at the book, as if confirming it wasn't a hallucination. His grin returns.

SupermagicTesseract

Taste: There's a wide spectrum of taste here, from the mildly gross pairing of a cold lager with Cheerios all the way down to the pits of hell that is a warm IPA with Fruit Loops.

Blasphemy level: Even my cereal-munching, beer-loving friends don't support this.

Taste: Cheesy, chocolatey goodness. Even better mixed with the vomit in my mouth.

Blasphemy level: Ohmygodiwanttothrowupjustwritingthis

Blasphemy level: Uhhh

garlic mashed cornflakes

beereal

Crunchy bread × liquid bread. Just bread, bread, bread. Dip your actual bread in it for good measure, too. Need I say more?

humveemus

Hummus brought on combat tour to Afghanistan, returned due to being past the expiry date, now on liquidation before it gets drafted into World War III.

Kombucha, treated with Ultra High Temperature pasteurization.

Slogan:None of the taste with none of the health benefits!

☘️☘️FLAG REVIEW 7: PROVINCES OF IRELAND EDITION☘️☘️
FLAG REVIEW 👏👏

Whenever there's talk of Irish flags, politics is guaranteed to Nth Edition, we will cover the following terms. Ireland in this will have clear modifiers for its meaning.

connacht

Design Score: ★★★★☆

Subjective Score: ★★★★☆

his control. The Pale is entirely located within Leinster. So. it's seen how the use of the harp as a symbol for Ireland by Henry VIII lead to a more specific usage since for Leinster.

This next flag has some doppelgangers. Don't confuse these three crowns on a field of blue as the other three crowns on a field of blue commonly associated with Sweden, as seen on their coat of arms and in official government contexts. As this design has been around since basically antiquity at this point, it's very unlikely that there exists anything to conclusively prove how the design was independently created in Munster as did in Sweden.

ulster

Design Score: ★★★★★

Subjective Score: ★★★★☆

For the next mathNEWS issue, I have some peculiar flags in mind. It will be quite the challenge to review them, so it's yet to be seen how that will turn out. As always, you can send in flags for me to review too. Bonus flags never hurt anyone.

boldblazer

from the blood of the hacked-off hand.

WIND

Whereas the Region of Waterloo has declared a climate emergency2; and

Whereas the fossil fuel industry contributes negatively to the climate crisis; and

Be it further resolved that MathSoc believes that funds students voluntarily pay into should not invest in the fossil fuel industry; and

Actuarial Science - I don't know what it is but it has “science” in it so it should be in science.

Applied Math - Taking this is the equivalent of raising your hand in math class and asking “When are we going to use this in the real world?”

Data Science - Is that like statistics?

FARM - I see Financial Analyst and think of Estee Lauder from A Series of Unfortunate Events.

Pure Math - ??? Are you guys okay???

Software Engineering - Please repeat this slowly and tell me why these peeps aren't in Engineering?

Residents of Ontario were shocked last week when one of Doug Ford's policy decisions actually had a positive impact. By refusing to even bargain in good faith with the teachers he is effectively stopping large gatherings of people that could spread the disease.

Critics were quick to point out that if Doug Ford just kept class sizes at their previous numbers, like the teachers want, that would also limit the virus spread by having smaller
gatherings of students . The premier replied that this is why his mandatory e-learning policy is truly preparing students for this modern society where everyone is quarantined at home. Members of the press were a little skeptical at this explanation given the fact that these policy decisions were made before the start of the current crisis and that technically it was the teachers striking for the students' well-being that was causing the effect.

STAIRWAY CONSTANTS, PART [4.5,7]

foreword and correction

We left off here last time. Between here and the top is about 1/3 of MC's height, but only around 1/5 of the stairwell constants live here. Big numbers just aren't as special, for the most part.

Just a few tick marks right of the big pink 4.5 is the first of the last stairway constants.

If you handed that expression to someone and told them that it's the answer to a pretty fundamental question in number theory, I bet they would be very surprised. As with many of the constants in this stairwell, Freiman's constant has to do with rational approximations. Suppose I gave you a real
number x. We can measure how well a fraction p q (in lowest terms) approximates x with an efficiency function:1

(For more digits, see OEIS A006890.) Mitchell Jay Feigenbaum passed away recently in 2019. He was an American mathemat-ical physicist whose work on turbulence led him to study chaos. Specifically, Feigenbaum used a simple pocket calculator (highly advanced by 1975 standards) to play with a
chaotic recurrence relation called the logistic map:

xn+1 = rxn(1 − xn)

Let's run with it for now. Even if x0 is 1 person out of 7.77 billion, this is going to escalate as long as r > 1. Grant
Sanderson from the math YouTube channel 3blue1brown gives 1.15 as the current best guess for r.

Let's use the number from Worldometer: 45,039 active
coronavirus cases at the time of writing.3 Then the exponential model predicts less than 87 days until we're all infected by early June 2020. Obviously, you can see the model falling apart. It falls apart completely by mid-July, when it starts to predict trillions of infections. The key problem with an exponential model is that in a city where everyone's coughing on everyone else, there should be no new infections because there's nobody left to infect. In general, more sick people means fewer healthy people you can encounter and infect.

As r increAses Along the horizontAl Axis, the points of stAbility double fAster And fAster until All hell breAks loose. Image by Jarosław Bielak.

Five. V. Olympic rings, toes, platonic solids, senses (in the classical sense), and categories of hurricanes. Google “star” and you'll see a bunch of five-pointed, probably-yellow figures used in many rating systems (which are also often out of 5).

The centuries-old Goldbach's weak conjecture states that 5 is the last odd number that can't be written as the sum of three (not necessarily distinct) prime numbers. It is generally accepted that the Peruvian mathematician Harald Helfgott achieved the first proof of this in 2013.

The correct value should be 5.16771278004997… How many other errors are there in this stairwell? I'm not going to check.

There are a bunch of ways to derive the volume of the unit sphere in R6 yourself. In homage to the next constant up ahead, the volume of the unit sphere in R5, I'll show you a way to compute it from that number.

(For more digits, see OEIS A164103.) (The last digit on the plaque is off by 1…) Aha! That's what ω5 is. ω5(1)5= ω5 is the

volume of a 5D sphere of radius 1. Now we can plug it in and finish computing the volume of the 6D unit sphere.

As you reach another big pink number, you realize that this time it only took 10 steps, breaking the pattern of 11 steps per flight that's been in force since floor 1. It stays that way for the rest of the stairwell.

floor 6

τ
Tau
6.2831853071…

You can find a whole lot more at https://tauday.com/. Unfortunately for the rebels, their campaign barely makes ripples in the face of the establishment, because…

1. τ looks uglier.

Finch's Mathematical Constants. Apparently, in 1963 the
Romanian mathematician Alexandru Froda exhibited a proof that this number is irrational, but I can't find the paper. All sources that mention this proof also add a mysterious remark that nobody (not even Froda, if he were still alive) knows whether the proof is valid.

In general, it is very hard to prove if a number like the Froda constant is rational. The problem is the weird composition of crazy numbers. Other numbers whose rationality is unknown include various spellings of “pie” like π + e, πe, π e, and πe. That said, we do know that e2 and eπ are definitely irrational, since they are transcendental.

The stairway constants are done, and I hope you've learned something along the way. Slightly to the right of the big pink 7, the number line ends just as it started — it runs straight into the wall and stops. I guess Peano was wrong after all, and Randall Munroe was right — there really aren't any numbers above 7.6 Maybe if they made MC taller…

Despite the huge pipes that run straight through the number line, it's not too loud up here. If you listen closely, you can hear the invisible dragons that nest on the roof of MC.
“Thanks for not taking the elevator,” they whisper.

2e
Froda constant
6.5808859910…

(For more digits, see OEIS A262993.) This constant manages to escape the mostly-exhaustive coverage of Steven R.

5. “Sexy prime” is serious mathematical terminology.

6. See the extremely strong Goldbach conjecture (xkcd 1310).

But I'm not here to talk about how great it is. No, I'm here to talk about the very worst part of the game.

Beneath all the good, there are still a few things in Black Mesa with which I take issue. Some of these are holdover issues from Half-Life, and some are new issue. One of the biggest issues I have is, perhaps unsurprisingly to many, the chapter INTERLOPER. It's pretty much unanimously regarded as the worst chapter of Half-Life, and despite the best efforts of the Black Mesa developers, it still just sucks so bad. God it's the worst.

Then later, INTERLOPER starts, and it's cool! Look at all of the enslaved aliens and the factory equipment. It's a little morbid, but intriguing. Some nice environmental storytelling going on.

But then the environmental storytelling starts running dry, and the chapter starts to overstay its welcome. Then it drags on. And drags on. And it just feels like it'll never end. Beyond some environmental eye candy here and there, nothing extra interesting really happens beyond the first level. The sense of progress fades, and you're left frustrated, seemingly forever damned to a loop of platforming and occasional annoying combat encounters. You can't even see the Nihilanth's lair in the distance like you could in XEN, which was a nice visual indicator (and a gorgeous one at that) of your progress to the finish line, reminding you of what it's all for.

Another very real potential issue (this one comes from that last thing about early access) is that people suck at giving feedback. By and large, players praised everything in the Xen beta. Not necessarily because everything was perfect, but because, for the most part, Xen was actually really good! It had a really strong, beautiful opening two quarters, a pretty but boring quarter, and then a really strong, beautiful ending sprint with NIHILANTH. But that means that, by the time you've beat the game, you've probably almost forgotten that INTERLOPER wasn't that much fun. You probably won't even remember it as well as XEN and NIHILANTH (the first and final Xen chapters, respectively) afterwards — likely some primacy/recency effect at play.

Lastly, saving the bulk of Xen's beta release until a few months before the final release may have hurt it in the long-run.

MCS IN MC: AN
INTRODUCTORY POST

Friends, strangers, people, acquaintances.

Instead of pining away on your sub 100 Karma Reddit account and crywanking like every other UW student (way to live up to the stereotype!), why not send a tweet to @UWmathNEWS, or email a lovelorn email to mathnews@gmail.com?

Long gone are the days of longwinded, sweet words of poetry that the bards of old sang and crooned and recited to their object of affection — without crywanking. Perhaps it's time to revisit the atavistic mating rituals of our ancestors and compose a nice poem or two for your MC in MC.

MCS IN MC

I rushed to campus at 6:15pm on a Tuesday, desperate to print and hand in my assignment for the 3-hour long elective course I had chosen to torture myself by taking. I had managed to catch you the last time this happened, but I was not so lucky this time. The door I usually found you waiting behind was locked, and when I knocked you did not answer. I miss you. It's not the same using the W print printers in the hallways of MC. I hope to encounter you again on a different Tuesday evening, and send my document to your heart so that it may be printed for my records.

The personality quiz you never knew you needed! Thanks, water.

the rules

B) Yes, but I'm not shy. I just don't say a lot, especially during small talk or conversations about topics I'm not interested in.

C) I'm much more talkative around my friends than around others.

A)10–11PM.

B) I do a lot of studying at night, so around 1–2AM.

B) I feel good about it — I studied a lot over the term for this course, so I feel prepared.

C) I'm mentally steeling myself for the worst. I start to doubt myself and the preparation I've done, frantically going over my notes before the exam doors open.

D) Sloth.

C) I treat breakfast as a full meal like lunch — I'll spend more than 20 minutes in the morning making it.

D) Something light, like a slice of toast or a fruit.

q7: WhAt Are your thoughts on tAking personAlity tests like the myers-briggs or enneAgrAm?

A) I don't like them. Taking them feels vain and self-absorbed.

E) They're very fun to take. Not nearly as fun as the super esoteric BuzzFeed quizzes though.

q8: hoW tAll Are you?

E) I'm tall.

tiebreaker: pick A pie flAvour.

A) Cherry. Finchey

B) Pecan.

If you answered with (A) the most, you are ϵ (epsilon: an arbitrarily small positive number). You're quiet, mysterious, and when most people bring you up in conversation, they hardly have much to say about you. Not that you fault them: you are a pretty private person. You're also extremely self-effacing and self-sacrificing, nearly to a fault. Taking a stand for yourself and carving out your own rightful place on the number line one of these days may not be such a bad idea.

If you answered with (B) the most, you are σ1(the smallest known Salem number: 1.1762808183…). Being σ1 is no easy task, as I'm sure you know. It's a busy life being a Salem
number — and you're the smallest one to boot. You have a pioneering spirit abundant in perseverance, and you seek to be a leader in your field and among your friends. But
remember where your roots lie: you're also a root of Lehmer's polynomial, a sibling to nine others who weren't nearly as lucky as to be inducted into Salem's ranks. Check up on them once in a while, ya know?

As of lately, my music taste has been quite messy in (what I'd like to consider) the best way possible. From A$AP Rocky to Caroline Polachek, I really love having a variety of artists from various genres to keep my playlists interesting and fun. I'm not really sure why but I really can't pick one aesthetic to dream about and live by to save my life. Usually I'm striving to be a rich corgi owning self-made millionaire lady living in a fancy penthouse in an upscale Toronto neighbourhood, but lately I've been listening to music that has influenced my current aesthetic goals to make me want to feel as if I'm starring in a coming-of-age film. So with that, I present to you: “n bops to listen to when you want to feel like you're the lead in a coming-of-age film”.

are you bored yet? by wallows (feat. clairo)

yam yam by no vacation

Yam Yam is the perfect bedroom pop song for a day at the beach. From the calming vocals to their cute rhythms, this song is just so great to bump to when you imagine yourself as a character in a coming-of-age film staring at your ceiling for hours in your bedroom or even like driving with your windows rolled down as you speed down the expressway.

seventeen by peach pit

Peach Pit is also an amazing indie pop band based in Canada.

https://music.apple.com/ca/playlist/songs-to-

make-you-feel-like-youre-lead-coming-age-movie/

HOW LONG DOES IT TAKE TO GET FROM MC TO RCH?

juste à temps

[LEAK] MATH
ORIENTATION 2020 TEAM NAMES

PMATH/AMATH/C&O
MATHSOC COUNCILLOR OFFICE HOURS

Are you a Pure Math, Applied Math, or Combinatorics
and Optimization Mathematics Teaching major who has academic concerns? Think a certain course is missing from the curriculum? Concerned that certain courses aren’t being offered often enough? Have literally any complaint about anything related to your undergraduate experience? Then come to your PM/AM/CO Mathematics Teaching MathSoc Councillor’s office hours from 4:00–5:00pm 10:30–11:30am every Tuesday Wednesday in the PMAMCO TSA Club room (MC 3033 3031) and complain to me. I will bring your
complaints to MathSoc Council, and hopefully get something done about it. If 4:00–5:00pm 10:30–11:30am every Tuesday Wednesday doesn’t work for you, then try coming by the PMAMCO TSA Club room at any time. I’m usually there, especially in the afternoon and evening.

For other constituencies, refer to teamup.com/ks2e3xr8n5au-myc48s to see when your Councillor’s office hours are.

I've given a collection of arts minors a rating out of 5 based purely on the structure of the course requirements, NOT the content of the courses. Minors get points for not being too restrictive while still providing a roadmap to make sure you actually know what you're doing. This list is incomplete; more to come!

fine arts studio

8 courses with a cumulative average of ≥70, including one of (AFM 102, AFM 123), HRM 200, 2 of (PSYCH 238, PSYCH 339, PSYCH 340), three of (HRM 301, HRM 303, HRM 305, HRM 307), and one additional course from the above or from (HRM 400, PSYCH 439, PHYCH 467, MSCI 311, PACS 202)

One of the most restrictive minors; by virtue of this, the structure is mostly guaranteed. Despite this, there are structural failures in the list — for example, of the PSYCH classes on the list, leaving out PSYCH 238 will leave you unable to take PSYCH 439 later.

While a wide range of courses are permitted, the list of courses is long and difficult to parse, and the required courses aren’t particularly useful for fulfilling prereq requirements for other courses you’ll want to take.

★★★☆☆

history

8 courses from HIST with a cumulative average of ≥65,
including 2 courses numbered above 250, and no more than 2 at the 100 level.

human studies

8 courses with a cumulative average of ≥65, including HUMSC 101, HUMSC 102, one of (HUMSC 201, HUMSC 301), one of (HUMSC 401, PHIL326J), two of (PHIL 100J, PHIL 118J, PHIL 120J, PHIL 204J, PHIL 210J, PHIL 218J), one of (SOC 355J, SOC 369J), and one of ITALST 291, ITALST 311, ITALST 312, ITALST 360, ITALST 370)

This looks quite restrictive, but actually takes a similar form to the ECON minor, with the difference being there are much more than 8 ECON courses at the 200 level or above. This does make the program more restrictive, of course, but you can't fault the person who designed this program for that — unfortunately the final result is the same.

★★☆☆☆