Math - Divisibility of Numbers

Recently, I saw this video by Michael "DONG" Vsauce about divisibility rules for certain numbers and why they work. The bulk of his video talked about the digits 1-9. I'd seen videos like this before, on YouTube and I think in a lecture on Great Courses. He ended the main portion of his video by noting that, no, it's not faster to do this kind of thing; figuring out these divisibility rules is still slower than any calculator; however, it is fun, and helps us get to know numbers, and math in general, better.

So then I started thinking about divisibility myself. Specifically, I wanted to look at prime numbers larger than 10. It's easy enough for something like is n divisible 15, since "does n have a 0 or 5 at the end?" accounts for 5, and an easy divisibility check accounts for 3 (adding up the digits and seeing if that number is divisible by three). If both of those of those check out, then it is divisible by 15.

But what about 13? 17? These prime numbers can't be broken into easier checks. I wouldn't be able to tell at a glance in most cases if some random string of 2 or 3 digits is divisible by 17.

So in trying to come up with a divisibility rule, I broke down the justification for the others. Let's look at the equation here:

abc = 100a + 10b + c

abc being a three digit number, like 351. How could I determine if it's divisible by 3? There's two ways. First, there's the easy way of adding up the digits: 3 + 5 + 1 = 9, and so it is divisible. In fact, 351 = 3 * 117. The second way is basically the same, but goes through a few extra steps. First, we restate the previous equation like this:

abc = 99a + a + 9b + b + c

abc = (99a + 9b) + (a + b + c)

We know intuitively that 3 goes into both 99 and 9, so we then know that it divides 99a and 9a. Does it divide a + b + c? We can take those digits and apply the method we used above.

But we can also apply this technique to large prime numbers as well. Let's try 17. First, we split it into the two sections. What's the largest multiple of 17 less than 100? We'll restate 100a as 85a + 15a, like so:

abc = (85a) + (15a + 10b + c)

In this case, we don't get a simple version like with 3. 17 only goes into 100, and not 10 or 1. However, it is a tiny bit simpler. We know that 17 divides 85, so we also know that it divides 85a. Does it divide the latter part? Let's use 351 as an example.

15(3) + 10(5) + 1

15 + 50 + 1 = 66

A quick check of 85 - 17 = 68 shows that 17 does not divide 66. Therefore, it should not divide 351. And, a quick check on a calculator shows that 351/17 = 20.647058823529412, and is thus not evenly divisible.

This is a naive approach, since easier methods for 1-10 are well-known, and I'm sure most prime numbers between 10-100 already have easier methods. But it was fun to use the logic for numbers 1-10, and apply it to others myself, even if I didn't come up with a crazy new method of figuring out divisibility.

Film - Spider-Man 2: The Importance of Being on Time

So, Spider-Man!

Just a couple weeks ago, I finally got around to playing the copy of Marvel's Spider-Man that I had laying around. Zowie, it's so good. Also around the same time, my aesthetics and history of cinematic arts class got the assignment requirements for the final paper of the class. We'd have to look at scene(s) from a movie that'd impacted us, and use the knowledge we gained in class to examine it.

I was initially headstrong to write about The Land Before Time. In fact, I still want to write about it in some capacity. Goodness knows I haven't posted anything on Academia since I got the account in the first place. However, I was dissuaded against doing so. Not by my Mother, who seemed to have some kind of vendetta against it in favor of Jurassic Park.

No, I remembered a striking image from a scene of Spider-Man 2. Specifically, I remembered a crucifix/t-pose like stance that Spider-Man had to take while stopping a runaway train car in that famous scene. And also because I'd just finished the main story of the PS4 Spider-Man game.

I won't go into the stuff that my paper cover about the different shots in the scene, or the elements of cinema they use, etc... because I realized something else while going through the scene selection to rewatch my chosen scene. (I wanted to refresh my memory a bit, and maybe find a few new things to discuss.)

I remembered one of the lines that I'd repeat from the movie was from the scene in which Mary-Jane is caught off-guard by the presence of a Mr. Peter Parker. "I am glad" or something to that effect. The play in question is The Importance of Being Earnest. When I first saw the movie, I'd never seen or read the play before. I just knew that MJ was in some kind of play that Peter missed the first time.

It was only when I was reminded of its presence in the movie now that I could start connecting some points. I have, since then, read it as a class assignment for two classes at two different colleges, and watched a filmed version of it for the later class. It was interesting to watch because it featured Paul McGann as one of the title Earnests. In fact, it was rather amusing to watch, rather than read, because the subtext became clearer.

But that's all getting off track.

One key concept that I will take away from Aesthetics and History of the Cinematic Arts is the idea that nothing on the screen happens by accident. Similar to a "Chekhov's Gun," if something's on-screen, then it's there for a reason. Or, in this case, if Wilde's long form pun is in a movie, then it's there for a reason.

(Since this is a plot/story point, I probably wouldn'tve been able to discuss it in my final paper. But I can here!)

Why is The Importance of Being Earnest featured as MJ's starring play? To answer this, let's take a look at the play itself for a bit. Earnest is a comedy of manners written by Oscar Wilde sometime in 1895. In it, spoiled people stand around and talk about themselves, and there's a "long-lost brother" plot-line somewhere in there.

OK, maybe that's a bit of a reduction.

Two central ideas are that of identity and deception. Who IS Ernest? He leads a double life - Ernest in town to his friends and relations, but Jack to his ward and acquaintances in the country. Similarly, his friend Algernon also leads a double life, and is prompted to further deceive Jack/Earnest's ward by making an unwelcome appearance as "brother Ernest," Jack's supposed relation. By the end of the play, the reversal is again reversed, as Ernest is found to have actually been Ernest the whole time.

The Importance of Being Earnest makes two significant appearances in the movie. First, when Peter is still struggling with his double life as Peter Parker and Spider-Man, and he is the "empty seat" to which MJ sadly looks. At this point in the play, Cecily (here played by MJ) discusses with Gwendolen whether or not Jack-Ernest and Algernon-Ernest should be forgiven for deceiving them as they had. Our last glimpse of the play ends with Cecily's reply to the question "Then you think we should forgive them?" - "Yes. I mean no." A bit of indecision reflecting MJ's own struggle with her relationship with Peter.

I am glad

We see Earnest for a second time after Peter has hung up his mantel, becoming "Spider-Man no more." In fact, MJ is caught off-guard by his presence and misses her cue. This scene is earlier in the play than the previous excerpt. Here, Cecily is meeting Algernon aka "Ernest" for the first time. Because of what she's heard about him, she chided him and wishing "I hope you have not been leading a double life, pretending to be wicked and being really good all the time. That would be hypocrisy."

Whose "double life," though? (Besides the characters in the play itself, I mean) True, the obvious answer would be to point to Peter Parker and his role as the masked vigilante Spider-Man. However, it would be just as easy to point to MJ herself. She's engaged to be married to J. Jonah Jameson's Son, The Astronaut, but she still harbors a deep connection to both Peter Parker and Spider-Man. In effect, she is the collectively imagined Ernest - simultaneously set to be involved with two people.

Wowie!

Back in 2004-2014, I would have never thought or known about the play, let alone the relevance it had as a plot point in the movie. I feel like I could connect the two better with a more concerted study of the film and play. For now, I think I'll leave it there.

~~~~    ~~~~    ~~~~    ~~~~
Screencaps from Marvel's Spider-Man camera mode and movie-screencaps.com/spider-man-2-2004

Life - Southeast Game Exchange MMXIX-2

Despite my best efforts, I still arrived at the second day of SeGE 2019 almost into the afternoon. My resolve to sleep in defeated my resolve to have more time for looking around. However, I was in enough time to eat lunch there.

Which brings me to my one major gripe about the new location. The concession food and beverages are way expensive. I can almost justify a fully loaded hot dog being around $5-6, but I am completely flabbergasted at the notion of $4 for a 20-liter bottle of soda. One could argue that I'd pay that much eating out anywhere, but at least restaurants offer combos with fries and refills on the drink. And I suppose the other gripe is that it feels short, but that's not a very strong complaint.

Whining done.

I did get more time to look around, although it was essentially reduced because in the last 0:30 of the day, most vendors were getting ready to pack or were already packing stuff away. Still, despite the larger size of the Greenville Convention Center's large room, I was still able to see everything - even if I wasn't able to play much of the free play stuff. The spread was the usual combination of video game stores, individual game sellers, art people and a few non-gaming booths, like a display with a drawing for Hilton. Some of the art was really cool and tempting, but owing to the size of the perler-on-canvas and burnt wood stuff, I would have no place to display them.

Mainly I looked around, but I did attend one panel: a publisher called Limited Run Games was holding a panel on their history and origins. I'd already purchased a game from them the day before, so I was interested to hear about them. They're a publisher that takes mainly digital-only games and gives them a limited physical run (hence their name). It was a most interesting panel, delving into why he and his compatriot decided to start it in the first place, how they managed to make it big publishing for the PS Vita, and other dealings they'd had. We even got heads up on a few future releases.

Also, there was a games giveaway - the people who asked questions played rock-paper-scissors to narrow the field - and I managed to snag Star Wars: Bounty Hunter (for the PS2 for the PS4) from it. By the time the panel was over, I went back to trying to find some good deals.

At the end, I was scrambling to find the Legend of Zelda: Triforce Heroes and Star Wars: Episode I Racer I'd seen; I managed to negotiate the former from $15 to $10, and found the later for $5. I already have Racer on Dreamcast and PC, but I wanted to see how it compared to the other versions. Triforce Heroes I was just curious about. Oh, and I got another over-sized Lantern ring, this year being the orange "Greed" one.

The only thing I regret missing was a loose Gameboy Advance SP that I could have either cleaned up and used, or opened up, looked at, and possibly fixed if it was broken. My overall budget was fairly limited, but I wasn't looking to add too many games to my collection, and I wouldn't have been able to get much of any hardware.

It was still a fun time. As always, I am resolved to do better in the cosplay contest next year. I'd also be interested in other cons happening at the GCC in the future - despite the risk of giving in and buying more comics than I need, for an example. I'll definitely keep this space posted if I do go to another convention in the future.

Life - Southeast Game Exchange MMXIX-1

The annual Southeast Game Exchange finally rolled around again, and I was semi-prepared this time. Sure, I didn't have as much spending money as I would have liked, but that was for a pretty good reason - the cosplay contest!

I can't remember when, but I started preparing for the contest in advance. I'm not super creative about this kind of stuff, so it was more of a "scavenge the right clothes" type costume. Some, like the jacket and pants, I already had. I managed to just barely get the right shirt in time. However, the key pieces of the ensemble - the tie and rubber hand - had to be sourced. (Oh, I also got my hair bleached. I would like to say it was entirely for the costume, but I also had to get a "natural" non-blue hair color for my day job.)

He likes the Mona Lisa

Having just finished catching up with the anime JoJo's Bizarre Adventure, I was insisted to go as the Part 4 villain, Yoshikage Kira. The synergy of needing a "natural" hair color, being a costume with relatively mundane parts, and having a simple prop all came together.

My original plan was to paint a wooden model hand and carry it around. However, a trip to Sally's revealed small, already ready rubber hands. All I had to do was add some fake nails and paint some blood/bone on the end for extra effect. It's a good thing that it was JUST a prop for effect, since my skills in applying nails would have failed any kind of technical inspection.

I actually spent most of the day at the cosplay stuff. After arriving too late for the speedrun panel, I had enough time to sign up for the contest, go to a panel, change into my costume, and look around a little bit before going back to hang out before the line-up.

I can't remember exactly, but the categories were: child and/or teenagers, adult novice, adult advanced, and group. I am (still?) very glad that there is a novice category, since some of the costumes were extremely elaborate - stuff like sculpted swords, hand-made clothing, etc... I didn't win, but I did have a few people that recognized and/or liked my costume. Also, some people even asked to take pictures with me!

I feel like I should have started off in costume, for two reasons: (1) my small suitcase was still big enough to be annoying to wheel around, and (2) I could have been looking at video games while carrying the hand around, talking to it, and being a little bit in-character. Maybe next year?

Afterwards, it was 3:something, so I managed to find some time to actually look around. There were a ton of tables this time. I think the location (new location again) is even bigger - at least, the ceiling was way higher! (As were the concession prices...). My "haul" was GTA: San Andreas and Dragon Fantasy. The latter was from the Limited Run table, and I was motivated to get it because I wanted a nice little indie JRPG-like game. I might go back and get another, possibly.

I think tomorrow I will try to peruse more and play some of the free play stuff. There was VR, arcades, pinball, and a whole row I missed.

Math - The Joy of 8

Greetings! Long time no write? Oof. Thanks to my class and work, I'd gotten distracted ... a bit. I should remedy that with musings on some lovely properties of a certain number!

For this past Christmas, I got myself and some of my family members a subscription to The Great Courses Plus. I'd used a trial before and found a ton of stuff that I liked - music, math, literature, etc... I went through almost 3 courses on Calculus. Then, I forgot about it for a while. That is, until recently.

One of the courses is called "The Joy of Mathematics," with a various assortment of "Joy of X," with X being some topic in math. One lecture was titled "The Joy of 9." The basic gist of the lecture was exploring the fact that numbers divisible by 9 (i.e. 81, 171, 1611) were all made up of digits that added up to 9. Crazy, right?

Curious about this, I spent some time making a table of numbers to see what the results for the others were. Actually, I did a dumb my first attempt. I thought "Why not include one at the top?" at the same time that I had the numbers going 1-9 on the side. In the end, my chart was just an overly-complicated way of arriving at a basic times table. Derp.

My big OOF reconstructed

However, I eventually figured out a layout to see the lists of each number, with the corresponding "digital roots" next to each one. I found several interesting patterns, actually.

Tables of Numbers with Patterns - weeee

I found that half of the numbers (2, 4, 5, 7, 1) went through all 9 digits once before repeating that cycle. 3 and 6 were a little more interesting - they repeated "3, 6, 9" and "6, 3, 9" respectively. 1 didn't stray from what you'd expect - even after 9, since 10 gave 1 and the cycle began again. And, of course, 9 gave all 9s.

However, one of them stood out to me - 8. Unlike the other cycles, the digits were in order, but unlike 1, they were descending rather than ascending. It was then I realized another interesting property of counting up numbers - the last digit cycled consistently. On its own, that is a "well, duh" type fact. Of course they're going to repeat eventually, I'm adding the same number every time. But I didn't stop at that.

At the beginning, both the last digit and digital root were the same. Writing out the last digits for the rest, I wondered - when do the last digit and digital root coincide?

After the first time, I found that they coincided at 12*8, 23*8, and 34*8. Also, the order they came in was the same as the pattern for 8's digital roots - 8, 6, 4, 2! (Not factorial, I'm just expressing surprise.) It didn't include the zero of the last digit sequence for obvious reasons. Once I got to 45*8, the pattern started breaking down. The last digit was in fact 0, but the number itself was 360 - nonzero - and thus could not provide the matching digital root.

And that's cool, at least to me. No, it's not a neat, easy fact like "9 is divisible by numbers whose digits equal 9" that can be turned into a neat trick for parties, but it's a cool pattern nonetheless. With a little more time, I could find more points of coincidence between 8's digital roots and its last digits, maybe even try to find another hidden pattern, However, that's all from me for now.

8.

Life - The Rest of SeGE 2018

The second day of the 2018 Southeast Game Exchange concluded a few short hours ago. This time, I managed to make it at opening. There weren't as many people waiting outside to get in, but there was still a decent group of people. I saw a few random people that I remembered seeing the day before. Who knows, I might have run into them at my local video game store too.

The first panel was pretty nice - a guy came in and did two speedruns of Super Mario Bros. 3 for us: any% (no wrong warp), and plain ol' any%. The NWW run was basically what a lot of people had been doing for years - grabbing the two warp whistles and heading straight to World 8. The any% run proper was the cooler one. It features the same opening - grabbing the two whistles - but he then goes to World 7. Then there's some shenanigans with literally writing code in game, and he goes right to the credits. He even had some Pannenkoek-style diagrams to show what was going on under the hood.

Next, there was video game music trivia with some YouTubers, so naturally I had to go. The guy's channel is called NES Addict, so all the selections were from the console. There weren't very many "deep cuts," so I was able to recognize most of them, even if other people got their hands up first. The prizes were just silly McDonald's toys and their logo sticker - there was extra after, so I managed to snag a rare and desirable trophy.

The next next panel was "Reproduction vs Bootleg with BP Retro Power." I'd heard a lot of the stuff he talked about before - the difference was that he had examples of repro boards, among other things, to pass around. We even learned a few ways to tell fake stickers and/or boards from the real thing. It was cool.

After that, I stuck to the main floor for the rest of the day. One of the nice features was some free play consoles, so I tried out a little Cuphead co-op with a kid that was hanging around. We actually managed to get through a vegetable boss, but didn't get far with the next one. There was also Crazy Taxi and Spyro, among others.

My overall "haul" wasn't very big, but decent: an oversized Star Sapphire ring (because it was pink, you see), LEGO Batman 2: DC Super Heroes (PS Vita), Mega Man Legacy Collection (3DS), and Luigi's Mansion: Dark Moon (3DS). I even managed to haggle the first and latter games down from $6 to $5, and $15 to $10, respectively. The nice thing about non-store vendors is that ability to try plying them towards the end of the day.

I'm upset at myself, though, because there was a Waluigi amiibo for a decent price, and by the time I got back to it, it was gone. I'm no collector, but that would have been a nice one for my collection (consisting of a retro Mario one.)

Overall, I had a great time at the Southeast Game Exchange, and the $15 two-day pass was definitely worth it. I look forward to next year, and maybe actually having a decent cosplay for once.

Maybe.

Life - Southeast Game Exchange! Yay!

It's finally here! The Southeast Game Exchange started today (ending tomorrow). Thanks to some creative saving, trading in, and art commissioning, I'd managed to get a two-day pass in advance, as well as have some spending money. Part of me wishes it was just a LITTLE bit later so that I could have gotten my first paycheck, but it still worked out.

I must say, I think I liked the venue better than previously. It seemed like there was more room - although it was hard to tell when the corridors were full of people at the beginning. Also, I appreciate the reasonably priced concessions that were available. There were a lot of tables and video games to look at, as well as a few art tables. Part of me regrets not having a table this year, but it was nice to be free to walk around and attend the panels at my leisure.

Speaking of which, I went to two today: one by a voice actor and another by some cosplay ladies. Both were fairly entertaining and/or informative. I actually entered the cosplay contest in my green jacket, dress shirt, tie and glasses; it was probably too weak even for the 'novice' category. I'm definitely looking forward to the speedrunning panel tomorrow.

On the other hand, I did win an item; the door prize I won is an N64 game called Shadow Man. I've never heard of it, but it was nice to win something.

I regret being too intimidated to try playing the Mario Kart 8 Deluxe to try and beat the time best - it was one of the tournaments going on, and the only game there that I actually have any experience or skill in. Oh well! The time was pretty low anyway.

I never know what I want looking around a large collection of games like that; one thing'll remind me that I want a wired Xbox 360 controller, or an NES Mega Man will remind me that it'd be cool to find the Genesis collection one day. I think the key is to have a larger budget than I have right now, as well as a wish list and a pad of paper to write down if I want to compare prices. In fact, I can still do the latter.

Despite being terrible at them and not having my NES with me, I am enamored with the idea of getting an NES Mega Man game. Most of the ones I saw were around $30, which is almost all the money I have available. Maybe tomorrow I'll see something that I missed, or something that catches my eye more. We'll see.

I even got to see a college acquaintance!

It was a nice time.

---- ---- ---- ----
Image source: southeastgameexchange.com