Random uncategorized nonsense

1. Ultrapizza theories

Let F be the set of foodstuffs. If we had a solid definition for what it meant for a food to be a pizza we could write pizza(x) to denote that we judge x in F to be a pizza. Then, pizzas would be the set of x in F where pizza(x). Lacking a solid definition, we resort to defining a pizza theory to be a subset P of F, where an x in P is called a P-pizza. Some basic properties of pizza theories are (1) any subset of a pizza theory is once again a pizza theory, bottoming out with the trivial pizza theory in which nothing is (knowably) a pizza and (2) the union of two pizza theories between like-minded people is once again a pizza theory. This second property is surely controversial, but we assume anyone who has ever had a pizza knows a pizza.

Consider the set of pizza theories {Pi} indexed by pizza-eaters i, where Pi is the set of food pizza-eater i knew was a pizza. Any particular Pi may be empty if pizza-eater i has poor taste or judgment.

There is an ultrapizza theory generated by these {Pi}, which is a maximal collection of pizza theories with properties (1) and (2), subject to a third property that for any potential pizza theory Q, either Q or the complement FQ is in the ultrapizza theory. An ultrapizza theory exists by Zorn’s lemma.

Given a particular food x, either {x} or F − {x} is a pizza theory in the ultrapizza theory generated by the pizza eaters. If F − {x} were a pizza theory, then every pizza theory would be a subset of F − {x}, and so "pizza" would mean anything which isn’t x, for instance a banana. This could happen if no pizza eater believed a banana was a pizza, and in this case the ultrapizza theory is called principal.

On the other hand, suppose no F − {x} were a pizza theory in the ultrapizza theory for any x, that is if it were a nonprincipal ultrapizza theory. One consequence in this case is that every food, at some time or another, would have been considered by someone to be a pizza – if F were finite this would be a contradiction, but people have infinite ambition for eating. With this we can construct a nonstandard pizza theory on the set of subsets of F: a set of foods is called a pizza if the set is in the ultrapizza theory, and otherwise the set is not a pizza. In fact, due to maximality, the complement of any set of foods which is not a pizza according to the ultrapizza theory is itself a pizza.

While it would be theoretically interesting for a nonprincipal ultrapizza theory to exist, the resulting nonstandard pizza theory is uncountable, contradicting the countability of pizzas. This implies that there is some non-pizza against which all pizzas are defined in relief, though the identity of which is beyond the current theory.

2. A song once stuck in my head

Somehow this song got stuck in my head, a bizarre variant which made me laugh:

Hush little baby don’t say a word
‘cause momma’s gonna buy you a diamond ring.

And if that diamond ring don’t shine,
Momma’s gonna buy you a diamond ring.

And if that diamond ring is cracked,
Momma’s gonna buy you a diamond ring.

And if that diamond ring is broke,
Momma’s gonna buy you a diamond ring.

And if that diamond ring’s no good,
Momma’s gonna buy you a diamond ring

And if that diamond ring’s a joke,
Momma’s gonna buy you a diamond ring.

And if that diamond ring’s... (ad nauseum)

3. Things one may try

4. Toponymics

Something from Naples is a Neapolitan (derived from the Latin name of Naples, namely Neapolis). Should someone from Minneapolis be called a Minneapolitan? I’ve never heard this term before, but it sounds fairly nice.

The reason for thinking about this is that something from Mars is Martian, and there do not seem to be any other places which end in ‘s’ which turn into -tian.

5. Phrases

6. Idioms I don’t like

7. Ten days before

From circa January 2009.

Ten days before the last friday before the last Tuesday of the month prior to the twenty-second advent of the third lunar eclipse of the fifth season of the tenth decade of the last millennium next to the syzygy of the fifth and seventh planet in our solar system, nothing notable happened. Why do I even reference this then? Truly, there is no good reason. I just wanted to point out that such days and times exist in life. However, the day after the day I just mentioned, which is nine days before the last friday before the last Tuesday of the month prior to the twenty-second advent of the third lunar eclipse of the last season of the tenth decade of the last millennium next to the syzygy of the fifth and seventh planet in our solar system, something semi-notable did, in fact, happen. In fact, this day, the day nine days before the last friday before the last Tuesday of the month prior to the twenty-second advent of the third lunar eclipse of the fifth season of the tenth decade of the last millennium next to the syzygy of the fifth and seventh planet in our solar system, which I really must reiterate, was full of hidden surprises that no historian had ever uncovered before, until now, that is. On this very fine day, a day before the last friday before the last Tuesday of the month prior to the twenty-second advent of the third lunar eclipse of the seventh planet in our solar system by nine days, we have reason to believe that bystanders knew full well that this was, in fact, the day nine days before the last friday before the last Tuesday of the month prior to the twenty-second advent of the third lunar eclipse of the fifth season of the tenth decade of the last millennium next to the syzygy of the fifth and seventh planet in our solar system. And this I find simply amazing.

8. Nihilism

About absolute nihilism: You need something in which you can gauge the lack of meaning. How would you know exactly how much of a lack you have without an absolute benchmark?

This is not to be confused with Absolut Nihilism: a brand of vodka that instills a sense of emptiness and lack of meaning in one’s heart. It gives new meaning to the phrase “to drink one’s troubles away.”

9. Flatness

From when I was a freshman, Fall 2008.

The motivation for this is that the function

f(x) = e−1/x2

(with f(0) = 0) is really flat near the origin.

Let us define a few things:

Definition 1. For a given function f(x), we say the flatness at a given point a in the domain of f is the maximum n such that

 = 0

for 1 ≤ i ≤ n.

Definition 2. We say the flatness of a function f is the maximum flatness of f at a for any a in the domain of f. This maximum flatness is called the flatness order of f.

Examples. The function f(x) = x2 has flatness 1 at x = 0. It also turns out that this is the maximal flatness in all of f so we can say f has flatness of order 1.

On the other hand, g(x) = x4 has flatness 3 at x = 0. And, again, this is the maximal flatness, so g has a flatness order of 3. We can also say then that g is flatter than f. ∎

Now, let h(x) = x5x3. At x = 0, there are two derivatives which equal 0, so the flatness there is 2. When x =  ± 1, only the first derivative is zero, so the flatness is 1. However, the flatness of h is 2 since this is the maximum flatness.

Theorem 1. If a function f has a non-zero flatness for all points in an open interval in its domain, then f is necessarily the constant function over that interval.

Theorem 2. (or The [current] Fundamental Theorem of Flatness) Given functions f and g, let

c = lim h → 0
f(a + h)
g(b + h)

where a is in the domain of f and b is in the domain of g. Then:

  1. If c = 0 then f at a is flatter than g at b.
  2. If c is indeterminant then g at b is flatter than f at a.
  3. Otherwise, f at a and g at b have the same flatness.

10. Checks and Balances

Czechs and Dalliances: A Governmental Story of Scandalous Democracy

Coming to a theater near you this summer.

In AP English, for want of treating boredom, Alec and I continued making horrible things along the same lines:

Cheques and Valences: The funding of the development of the Bohr model

Checks and Gallances: The chivalrous world of chess

Decks and Saliences: The deep-fried world of the Boardwalk

Czechs and Alliances: The Road to WWI, or: The failure of the French buffer zone

Pecks and Talliances: Measuring pideons’ behavioral responses

Decks and Talents’: The strategy of poker

Necks and Parlances: A discorse of social intercourse

Necks and Ball-Lances: Safety precautions in modern jousting

Flecks and Ol’ Ranches: A history of the gold rush

Treks and Phalanxes: The challenge of long-range infantry transportation

Sex and our Prances: An analysis of gender identification on the desire to frolic

Rex and Blancmanges: The desire for a noble dessert

Treks and Silences: Adventures of mute explorers (N.B., this one was written by the teacher when he saw what we were doing.)

Wrecks and Ball Dances: Sophisticated parties on sinking ships

The Crux of where Hal Lance is: The police report of a previously missing person

Pecs and Dopances: The ethics at the competitive edge

Eycks and Romances: An analysis of the painter’s symbolic representation of love

X and Romances: The civil rights leader’s interpretation of love as an administration

X and Violences: The strategies of a civil rights leader

X, a Pedant Is: Society’s intolerance of the learned among us

Flex, what Pliance Is: A material engineer’s pocket reference

Specs and Entrances: The intricacies of ocular fashion

Text and Sentences: A styleguide

11. This is a sentence...

This is a sentence that will never end, but you may not believe me in this respect, this being the only respect mentioned thus far, but I do have my ways to create such a sentence using such devices as commas, semicolons, a lack of run-ons, and coordinating conjunctions—and, of course, dashes (em dashes, in fact) to set off other ideas—without much typographical license at all, typographical license meaning I am, in effect, cheating and not accomplishing the purported goal of the infinite sentence (plus, I’m not sure about what sort of typographical tricks would allow me to continue with this sentence unabated [or, as some may say, “unterminated” where a period is considered a terminal symbol (which shouldn’t be confused for a terminal in computing, a console for operating with the system, it being the end point of output, or in formal grammars, both of which can in their own ways be interesting to those who find such things interesting) as it is the termination of a sentence, which isn’t apparent in this one, and although a definition of a sentence may be a logical sequence of words with an accompanying delimiting mark (a period), a better definition may have to do with grammatical structure, which may perhaps be painful to indulge at the moment], unless you count the atrocity I have just committed), but it is quite possible to reach this lofty goal, and to prove this I must first reiterate that this is a sentence that will never end, but you may not believe me in this respect, [. . .]

12. A very common day

These were sentences which incorporated a particular phrase as required for the assignment, for instance “the garden everyone loved which was planted by his neighbor.”

It was a common day for the residents of Brighton, California, a very common day indeed for everyone who didn’t notice the chromatic, pulsating glow of the incoming solar wind with its magnificent tail of downed communication satellites and airplanes, but the number of those who remained oblivious was rapidly approaching zero as more and more consumer electronics were erupting like little firecrackers, and the citizens of the town were quite certain it was not the Fourth of July, but the Sixth.

Suddenly, as a young boy was grabbing another buttered biscuit from the wicker picnic basket, it being an especially bright day with a thick, comforting fog of ozone, the nearby harbor sunk to the depths of the especially turbulent bay, and, the town being especially low in elevation, a rogue wave engulfed the especially sunny park.

A news report quickly reached a corporate executive in a nearby villa, and he was enraged over the loss of his industrial park which was a very significant investment for him, but the boy continued munching his biscuit happily until his lungs were oxidized, and he passed out with a contented smile on his face as the foaming waves took him away with the last vestiges of thought flowing through his young mind, remembering the garden everyone loved which was planted by his neighbor, but due to his lack of consciousness, perhaps, we can only guess he did not realize this garden, too, was being washed away, interestingly enough.

13. Candy dispenser

Wow was I angsty back in Fall 2007...

I seriously considered submitting this for the Introduction to Engineering and Design class for a project where we had to design a “candy dispenser” and make candy shapes to go with it. I wanted to scream.

It is important to model an idea before making a final prototype because otherwise there is a greater chance of blowing it, and blowing it badly. The idea may be unworkable, or worse, just plain dumb.

The challenge of working as a large team is that other people generally don’t care because there was nothing in this project to excite them. Making “fun, unique candy shapes”? I could do it all day.

A design brief is a document that briefly describes a design. It is a part of engineering that we call “communication.” This definition isn’t a circular definition (which is a definition that’s circular) since I used different forms of the words.

Besides three-fold brochures (which actually only need two folds to make), the design could be communicated with a giant poster board with equally giant letters emblazoned across the top: “CANDY DISPENSER DESIGN POSTER.” Then, no one will be at a loss to explain what has been made.

Something different that I would do in this process is the fiddly bits along the edges of the device. They’re too modern. I’d rather have them rounder.

I’m hard-pressed trying to find any moment in which I found any meaning over the course of this project. I still have images of wanting to stab my arm with my mechanical pencil rather than fillet another god-forsaken edge. I usually don’t believe life has much meaning, if any at all, but I realized there is at least more meaning doing something else than to make this candy dispenser.

14. Favorite romantic couple in fiction

This was by my brother Mark, and I found it kind of funny. It’s really reminiscent what’s immediately above for some reason.

Writing Prompt:

7) Who’s your favorite romantic couple in fiction? Why?

My favorite romantic couple in fiction would probably Beauty and the Beast. The main reason for this is that I can’t think of any other romantic Disney couples at the moment, and the reason for that is that I don’t want to. But they are my favorite choice out of the one choice I can think of because they loved each other even though one of them was terribly hideous. Bell didn’t give up on the Beast because she knew he was good on the inside, she knew he could show it no matter how hated he was (at least I think the beast was a boy).

15. Muffins

Widely regarded as gastronomical delights, muffins are a mushroom-shaped species from the genus Tricticeae Muffinus. Feral muffins are natively found in northern Europe, where their doughy hide protects them from the elements. Sadly, with the industrialization of the global economy over the course of the last one-hundred years, the final tracts of land which the muffins have traditionally roamed have been nearly wiped out by heavy-handed treatment of the environment by industry. Many wildlife conservation groups are currently concerned about the safety of our baked friends and are now taking active strides in their protection.

15.1. Evolution of muffins

The family tree for muffins goes back farther than that of Homo sapiens. Due to their simplistic shape and substance, it was relatively easy for the primordial muffins to evolve. Scientists presume that the first muffin walked the earth roughly three-hundred billion years ago at a time when rocks were still the second most sentient beings. Very little else is known due to a limited fossil record.

15.2. Muffin trauma

Perhaps the most well-known trauma ever to be recorded in muffin history was the Great Muffin Famine of 1891 where millions of Swedish farmers starved when the much-expected muffin crop failed. The generally-accepted theory for the cause of this disaster was that the manufacturer for the little paper cups that wrap muffin were of low quality and that the muffin herds froze to death during that exceptionally frigid winter.

15.3. Muffin society

Dr. Linda B. Peterson, a world-renowned muffin researcher, has been studying our savory friends by sitting in on muffin herds for the last 20 years and documenting their activities. She has found a surprisingly intricate social structure. According to her research, the muffins are aggregate themselves into groups of tribes of 6 or 12 in a gridded hierarchy. They almost always stay with their own flavor, and blueberry has never been observed to intermingle with raisin. The tribes lack a central authority figure and appear to make all decisions in a grid-like structure without any perceptible movement. Dr. Peterson also reports that the muffins always seem to be in the state of decision and hypothesizes the muffins value unanimity in democracy.

15.4. Cultural references

Ever since muffins have had widespread fame, they have had an inextricable link to our culture and most basic values. The references to muffins in arts an entertainment are much too numerous to record. However, many professors of deconstructionist muffinology seem to agree it would be advisable to look deeper than the lowest level usually encountered in analysis and grapple with the obvious muffin roots we all cherish.

15.5. Further reading

The Great Door. A short story about muffin ethics and culture.

16. There’s a circle of Hell for that...

After reading The Inferno for 11th grade English, we had to write about a sin for which a circle of Hell would be reserved. I chose the hoarding of chairs in the lunchroom.

One EPHS crime that should be punished is the hoarding of chairs. The commons have a general shortage of chairs due do some people obtaining and guarding a surplus of them at their tables. A casual lunch eater will find that these chairs are “saved” and irretrievable for actual use, presumably because there is a chance that friends of the chairs’ “owner” will at some point make use of them for some jolly lunchtime conversation. These people who save chairs at the expense of others’ lunches deserve to go to the fourth circle of hell to join the hoarders and wasters since in life they thought only of having enough chairs, destroying the light of God. Instead of moving large weights in this circle, those who are guilty of this crime must forever collect and carry stacks of chairs on their shoulders without rest, thereby burdening the guilty with their own hoarding. Also, all of the chairs have no seats so they will have no hope of sitting for any jolly lunchtime conversation.

16.1. Marble-based computing

July 2007. Marble computing is the way of the future for all of our computational needs. It will solve all of our greenhouse emission problems for energy use since there is no cleaner energy than falling marbles. Basically, we need to get a giant vat of glass beads suspended in the air, and release the beads one at a time into complex chutes to yield the answers to our problems. I estimate we could run computers up to a few cycles per second. We can carry over some of the main ideas of electronics to the newfound field of marbletronics.

Voltage, which is the potential, can be modeled by

V = gΔh

where g is the gravitational constant and Δh is the change in height that the marble can experience. The marbletronic equivalent for the coulomb can be thought of as one marble (or 1M). Thus, current is measured in marbles per second. To then find the total power used by a marbletronic device, where x is the number of marbles per second falling through a height of h meters,

P = IV = xgh
M ⋅ m2

The concept of resistance can be developed. Since

V = IR and R = 

and so

R = 
M ⋅ s

From these ideas, the rest of marbletronics can be constructed to provide the theory for efficient marble computer creation.