#so if I do get around to it any other further discourse (i.e. rants) will be addressed in another post

[yaz-the-spaz]

I just came on here to share something of note related to my job that I felt was somewhat relavent to fandom. I don't tend to like to reveal too much about my personal life on here especially as it relates to my job since I don't necessarily want anything irl connecting back to me on here so I'll keep this very, very general but I currently work for a nonprofit that centers around a very specific subfield within an acronym of the STEM umbrella. Most of what we do involves public outreach and education on that specific field through online articles, videos, magazines/journals, and events, etc. (as well as helping fund research, grants, and mentorships/job opportunities for people in the field, particularly of underrepresented groups).

Anyways I'm saying all this to say that today I saw we'd made arrangements to pay for media training for a few of our more higher up volunteers to help prep them for media interviews and to be good brand ambassadors for our org. The training includes things like reviewing talking points and going over sample interviews and interview tips and is expected to encompass at least a couple of hours per person. We dropped well over 10k on this expense. And this is all just for a few VOLUNTEERS for a relatively small nonprofit org in a very specific subfield/subject. Like I said we're a non-profit so we're obviously not just in this for the money or the good PR it may bring, even if we do still realize that those things are integral to our success as an org. And yet we still dedicated a sizable chunk of money and time to this endeavor for people who are not even technically employed by us. I just want y'all to let that sink in for a second and think about how much the scale of that extrapolates to ppl like celebrities doing what they do on the world stage.

Imagine how much more intense and in-depth something like media training gets when you/your image is literally the brand you're acting as ambassador for, and a shit ton of ppl behind the scenes all have their own stake in your success as a brand in the particular image/version of you (accurate or not) they want portrayed. now imagine you're a young impressionable child being made to sit through potential hours of mock interviews, being drilled with questions and "appropriate" talking points and the like until the ppl in charge of you are satisfied (tbh it's not hard to see how/why rebecca ferguson described it as akin to being brainwashed), and being foisted with all that responsibility/pressure in every single thing you do or say in front of a camera. Is it any wonder that you might eventually get to a point where you just paste on a smile and say/do whatever you're told to like a wind-up robot playing along with the role you've been given even to your own detriment (liam)? Or that you might get to a point where you just stop wanting to do almost any interviews at all cause you're sick of being party to all the fakery and bullshit (z@yn)? It's two sides of the same coin but both could very much be read as a trauma response

Anyway I just needed to rant a bit cause the stuff with work brought all this to the forefront of my mind and it forever infuriates me to no end that people still don't see (or don't want to see) how much of what we're shown and/or told is fabricated in the name of staying on brand for whatever version of their image a celebrity may be trying to sell in that moment

[gaslightgatekeepgodot]

A (sizeable) rant/essay concerning my experiences in the Tumblr JJBA fandom.

None of you asked to hear this, but I’m getting pretty pissed off at some people in particular (I will not name names, though I may heavily implicate some people) and it’s finally started to kinda spill over. So I’m letting it spill; take it or leave it.

I’m... Fairly irate at the moment, and writing out my feelings does tend to help me calm down in situations like this, so if I was going to put this anywhere the best place for it is probably on the public internet. Again, take it or leave it: this is the internet, you don’t have to interact with me if this concerns you or your ideals. Just click that handy little block button on my profile and you never have to see little Nat mouthing off again.

If you want me to summarise (I know not everyone wants/is able to read a fluffed-up pillar of text) or explain my reasoning behind anything I’ve said below the cut, feel free to direct message me here or on Discord @nati bati yi#1462. Once I get this off my chest I’ll be more than willing to chat to people about it. <3

(Before I say anything else, this is not intended to be a callout in any way, shape or form. I don’t mention the specific names of anybody, and the actions I do mention here will only point to specific people if you know them too. Anyone on the outside should have zero idea of who anyone I bring up is; I do not want anyone to get harassed over this, and I very much do not want to start drama - that’s what inspired me to go off and write this hunk of garbage in the first place. I’m just... Sick to death of the fandom as a whole.)

Anyway. Here we go.

From what I’ve been able to tell, being in this fandom for just under a year now, there are two main halves to it: the gay-hating, stale-meme-parroting dudebro side, who seem to mostly congregate around YouTube and Reddit, and... Whatever the side based on Tumblr (and probably now Twitter) is. I don’t spend a lot of time on Reddit, so naturally I’ve been more exposed to the Tumblr side of the fandom, and after experiencing the ideals some people here want to force on other people I’ve come to the conclusion I’d almost rather be immersed in the bigoted dudebro side. And I say this as an ace-spec/gay trans man.

I’ll start with the blocklist.

I think most of us on Tumblr came to the conclusion that the blocklist was utter bullshit, but I did see a few people in a Discord server I have since left (I will expand on this later) defending the reasoning behind some ships being on there, citing the fact they had been abused in a relationship with a similar age gap. I can definitely see why that would bother a person, and I do not want to erase the fact that people have been and will be abused in similar relationships, but you can’t project your singular experience onto every fictional, non-canon character relationship and every person who ships it. For one, not every relationship is going to turn out the same just because it meets this one criteria of “the age gap is too big”, and, also, you don’t have to write fiction to totally reflect reality. You are in full creative control. Maybe if the characters were real people they wouldn’t click, but if you’re drawing a picture or writing a fanfic you don’t have to go along with that. You can write them so that they’re good to each other, while still keeping it in character. Araki has said that Jotaro and Kakyoin’s personalities don’t work together very well, and that they wouldn’t have become friends or even spoken to each other if Jotaro wasn’t a Stand user... But Jotaro/Kakyoin just happens to be the most-written about JJBA ship on AO3. Me? I love Jotakak. It’s about the only thing I do ship. And I’ve read some quite frankly amazing fanfiction where the two boys are paired and they work together, and it’s still very much in character. Of course, I’m very much against loli/shota content or content depicting characters who don’t look very old- if someone drew Koichi in a sexual situation I would be pissed as all hell, but I don’t have to engage with that content any further. I can just filter out the tag/block the OP and move on. You don’t need to make a fuss and tell/imply to people that they are paedophilic for enjoying well-written content where a 17-year-old is in a healthy relationship with a 22-year-old, platonic or otherwise.

My second point brings in some of the things I’ve learned while studying media this past year. My main point here: not everyone in an audience is the same. There is a reason differential decoding and the uses and gratifications theory exist. The uses and gratifications theory states, at its most basic, that the audience of a media text is active, not passive; i.e. they are not just absorbing every piece of data thrown at them by the text they are consuming, and they are consuming different media to satisfy a need- for JJBA, that need could be entertainment, escapism, identifying with a character similar to yourself or to give you something to talk about with your friends. Differential decoding arises when someone consuming a piece of the media does not entirely go along with the creator’s preferred reading of it- an example might be how a sizeable amount of people enjoy villainous or “disgusting” characters such as Dio, Cioccolata, Stroheim or Melone, when they were clearly written in canon to be abhorrent, unlikable people for varying reasons. I can also say that, because the audience is active, and consume media based on their personal needs, that somebody writing fanfic of a ship you don’t like isn’t going to make incest or paedophilia more socially acceptable. I don’t consume that content, because I don’t feel the need to. Sure, real paedos might, but they’re a minority. Just because a couple hundred people or so read a fanfic on the free web where a grown adult does the dirty with a little kid, doesn’t mean to say everyone in the world will suddenly start thinking it’s ok. Mention it to any sane person in real life and they will not like that idea any more than you do.

And my third point is more a personal thing than anything else, but there is a community I used to be part of (and was part of almost from the beginning) where I didn’t feel welcome because of people causing drama over things like what I mentioned above. I started multiple discourses entirely by accident by saying I didn’t understand why everyone though X ship was horribly problematic and worth getting mad at people over. I still don’t feel like anyone deserves to be harassed over characters and ships they enjoy, but that doesn’t mean to say I support all of it. Along with generally feeling ignored by a lot of the moderators of that server, as well as their friends, I was just sick to death of how they seemed to single out some certain people to say, “hey, don’t do this” when other people seemed exempt. I was verbally warned for posting innuendos in a general chat (but it’s not like I could anywhere else on the server, because I’m not 18 yet), but at least once every day I would see two people flirting in-character in whatever channel they happened to meet in, and it never seemed to be in a roleplay channel- I couldn’t see into NSFW to check if they did it there too, but the fact it would leak out into gen concerned me. They would throw innuendo after innuendo at each other, and they never seemed to stop, or be told to stop. Yes, I could have messaged the moderators to say it made me uncomfy, but one of them was a moderator themselves, so I felt a little out my element doing so. 

Another thing that bothered me is when I tried to join an offshoot of that server for kin, and the admin - I assume - of said offshoot server messaged me (with some other conversation concerning it in between) that, despite the fact I only wanted in to help me figure out what it meant to me, I wasn’t allowed in because somebody was uncomfy with doubles. I completely understand that, but I had spoken to the only person it could have been (I wasn’t given a name, but it wasn’t difficult to figure out who it was) multiple times about that character and how similar we were- hell, we had even roleplayed together as doubles of that character and no problems were ever expressed to me. If anything it seemed like we left off in a spot we could have carried on from later. It might not have been intended that way, but being told I wasn’t allowed in there made me feel excluded from the community nonetheless, especially because I’d had a few people tell me the night before that they wanted more people in there and that I’d be totally welcome. I was also told, before any of this happened, that the same person blocked a friend of mine in another server for going on a small rant about how they didn’t like the way Josuke acted in the episode where he plays dice with Rohan and ends up burning his house down, because they kin Josuke..? At least, that’s what was relayed to me.

But, hey ho, it’s all behind me now. I won’t lie; I don’t really plan on ever going back. I don’t want to engage anymore, because it makes me uncomfortable and anxious thinking about it, so I most likely will unfollow most (if not all) of the blogs pertaining to that community tonight. I do have a few people still there who I miss speaking to, but I’ve DM’d all of them on Discord at least once since I’ve left and talked to them about either how I miss them or something entirely unrelated to the server. I’d like to talk more with them, but DMs are always awkward for me to begin with... I have a feeling they might not want to talk after reading this, and I think I’m ready to accept that? Might be difficult not being able to scream about fanfic as much, but I won’t impose on anyone if my presence makes them uncomfy. I don’t want to be that guy.

I’ll say it again: now that I’ve got this off my chest and subsequently calmed down a lot, I’m more than willing to talk about any of it. Just shoot me a message on Discord and I’ll reply when I’m able and feeling up to talking about it again. For now I’m probably just going to go back to pissing about on Flight Rising or play Smash or something

[cartoonessays]

“This Wasn’t Made For You”

WARNING: The following piece contains spoilers for Bao and other films.

I ranted about Pixar shorts a few years ago, mystified by what I saw was a decline in quality.  I was feeling like ever since Paperman, Disney and Pixar got stuck in telling the same tired and generic “boy meets girl” love stories with their shorts, Lava being their nadir.  They were creating new and amazing art aesthetics with shorts like Paperman, Blue Umbrella, and Feast, but my nagging thought watching these was that imagine if they used these boundary pushing aesthetics to tell a story that’s actually worth a damn.

There’s good news, though.  I think there’s been an improvement since then.

I haven’t seen or remember every Pixar/Disney short since 2015, so I’ll bring up the ones I remember off the top of my head.  Sanjay’s Super Team was like a breath of fresh air, especially after the embarrassing Lava.  I don’t really remember the hermit crab short that came before Finding Dory.  The short right before Moana about the dude’s internal organs was mediocre.  I didn’t see the short before Cars 3 and the half-hour Christmas special before Coco starring Mater the Snowman was pretty excruciating.  As of this writing, the most recent short is Bao, which is about a Chinese woman doting on a little dumpling she made as her child.

I liked this one very much.  I absolutely loved the cartoony way the human characters were designed and the cartoony way they were animated.  And while the story of the growing rift between the doting mother and the dumpling child wanting to go his own way in life as he grew up didn’t move me to tears, it was nonetheless very touching.

The short was directed by Domee Shi, a Chinese-Canadian woman and just like with Sanjay’s Super Team and its director Sanjay Patel, Bao draws on Shi’s Chinese background.  There seems to be a weirdly polarizing reception to Bao, attracting a lot of praise (particularly from other Asians) and confusion (particularly from white people).

Bao’s story is particularly resonant to Asians raised by immigrants in a Western country.  I’m not Asian, but I didn’t think the story was so uniquely Asian or Chinese that it’s completely unrelatable to anyone outside of that culture.  Bao is basically a condensed version of A Goofy Movie.  It shares parallels with Brave and the aforementioned Sanjay’s Super Team too.  So I’m completely mystified that there has been such a big chunk of people so detached to this that they can only come away from it baffled.

I’m also the child of immigrant parents who’s culture has not been represented in any of the cartoons I grew up watching or have watched since growing up.  Relating to all the white, Japanese, and anthropomorphic characters that inhabit all my favorite animated shows and films was never a problem for me.  As a matter of fact, I always found it even cooler when those shows introduced me to parts of their culture I wasn’t familiar with.  I’m not Jewish, so I was introduced to Passover and Hanukkah through episodes of Rugrats.  I learned what a bar mitzvah was through Hey Arnold!.  I’m not Persian, and one of my all-time favorite films is Persepolis.  The concept of Bao and the emotional gut-punch scene where the mother, fed up with her dumpling child’s defiance, devours him is no less confusing than CatDog’s mom and dad being a big blue Sasquatch thing and a big nosed frog.  They’re all metaphors for the points they’re getting at.

Asian fans of Bao were also mystified by some of the glib and dismissive responses the short has gotten from some white audience members.  Some of these fans argue and defend its cultural specificity to Asian immigrant culture by suggesting they should suck it up because this isn’t for them and there’s a billion other media that centers their experiences anyway.

(I don’t know how to embed tweets on Tumblr posts....)

I don’t agree with this take either.  Like I mentioned before, I don’t think Bao is so specific to Chinese culture that it can’t be relatable to anyone outside of it.  Domee Shi’s perspective is still one that comes from growing up in the West and she directed this film for a Western studio that primarily targets Western audiences i.e. audiences that aren’t Asian.  A studio like Pixar would never release a film that would only be relatable to a small cultural niche.  When Disney or Pixar portrays any cultures outside the dominant, they always package it in a way that allows for those outside of it to engage, for better or for worse.

However…

In This Corner of the World is a movie adaptation of a manga about a young artist who lived in Hiroshima during World War II.  I watched this movie last fall and I didn’t like it.  I found it too mundane and it was a struggle to keep from dozing off or to keep my attention on it.  This is a film that has garnered critical acclaim so I was confused by what I was missing, especially because I really liked other films/manga like Grave of the Fireflies and Barefoot Gen.  But then I realized something.

Most of In This Corner of the World takes place before Hiroshima is bombed by the United States.  The story mostly revolves around the young artist named Suzu getting married, moving in with her new husband’s family, and adjusting to her new duties as a wife.  These aren’t things that readily come to my mind when I think of Hiroshima.  When I think of Hiroshima, I think of the ravages and the immediate drama portrayed in Barefoot Gen or Grave of the Fireflies (although that didn’t take place in Hiroshima).  I don’t think of marriage or domestic home life when I think of Hiroshima.

And this is what is so pivotal about In This Corner of the World.  It portrayed Hiroshima and its residents before the bombing, laying them bare as no different than any other town in Japan (or anywhere, really).  The people there get up in the morning, go to work, get married, raise children, play, laugh, and cry just like anyone else.  Even as the war rages on in the background, the people of Hiroshima do their best go on with their lives.  The tragedy of the film is that the reality of living in a war-torn country steadily disrupts their lives more and more until it is unavoidable.  It started with taking shelter during the occasional air raid.  Then it continues with Suzu occasionally seeing bombs exploding in the sky.  Then it continues with food and water rations.  It continues further when the air raids increase in frequency and devastation.  And then it hits close to home when Suzu’s older brother is killed in action.  It hits even closer to home when Suzu’s sweet little niece is blown up by a time-delayed bomb.  This all culminates at the end of the film when the nuclear bomb is dropped on Hiroshima.

Hiroshima will forever be haunted by the specter of the nuclear bomb, even as the surviving residents continued to live on as best as they can for the next 70+ years.  There are several generations of Japanese people who only know a Hiroshima after the bombing.  So it is a big deal that In This Corner of the World provides their audience with a vision of what Hiroshima was before the bomb and what it could have been if not for the bomb.  I can only imagine how powerful this is for Japanese audiences, especially those from Hiroshima, those who have relatives from Hiroshima, or those who have loved ones who died in Hiroshima.  I specifically say “I can only imagine” because this was not my response to the film.  I have no cultural or personal connection to Hiroshima at all, and I think this why my response to this film was so lukewarm.

In other words, In This Corner of the World wasn’t made for me.

This isn’t to say it could only resonate with Japanese people or people from Hiroshima.  Based off of its critical acclaim, it clearly has wider appeal.  I’m just acknowledging this as the likely reason it didn’t personally resonate with me.

So for those that didn’t like Bao, they don’t have to like it.  I just think it would do them some good to think about why it might resonate more with others and to demonstrate more thoughtfulness in their discourse.

Hell, I don’t doubt there are people who did culturally relate to Bao and still didn’t like it.  Actually, I related pretty strongly to Riley’s gradual descent into depression in Inside Out and it’s nonetheless one of only two Pixar films I didn’t like.

[drunk-math]

Let'sh shay there ain't no 'nfinny!

Imagine there's no heaven, it's easy if you try... take a look at Carathéodory's notion of entropy and it'll tell you something about the nature of consciousness.  Anyway.

Onto the greatest bugaboo of mathematics, infinity.  Essentially, in the universe, there's no such thing as infinity, and yet so much mathematics today is about the various subtleties of it.  Consider in particular the infamous axiom of choice - if all sets are finite, then the axiom of choice is trivial.  Of course it's ridiculous to believe that all sets are finite, as ridiculous as it is to believe that the set of all sets does or does not contain itself.

So consider two paradoxes, Russell's and Galileo's.  Galileo who's worshipped by proddies for poking the holy bear (...well, I guess the holy bear per se'd be further East) until he bit came up with the mindblowing paradox that there are infinite even numbers and infinite odd numbers, and came to the conclusion that the notions of greater than and less than make no sense for infinite sets.  Should've been left there, but someone had to cant his diagonal Canticle over Canticles and make manifest the notion of multiple infinities and therefore of infinite sets.

"But wait!" you say, "weren't there always infinite sets?  What about Euclid's proof that the primes were infinite?  Hell, what about the very notion of natural number?"  Well, yes, but are those sets?  That's where Russell's paradox comes in.  The notion of a set as "a bunch of shit" doesn't work, because then you could have all the shit that doesn't have its own shit, which both does and doesn't have its own shit.  (Incidentally, while the doctor was a woman - both large and small D going into 2018 - the barber was definitely a man.  Making the barber a woman misses the point.)  Although... actually, maybe the barber sort of is a woman?  Maybe.

Basically, what I'm saying is woman = class.  And the first thing you need to know about classes, i.e., women, is that they don't exist.  I mean, nothing in math quite exists, but these especially don't exist, and their nonexistence is critical to understanding them.  These objects, such as the universe of discourse, are not in the universe of discourse, and therefore can't be discussed.  What's the universe of discourse?  It'd be the set of all sets, but that doesn't exist, so it's the class of all sets, which also doesn't exist, and since it doesn't exist, it's a class.

Why doesn't it exist?  Because the only way you can make sense of sets is by saying that, for any set and coherently expressed property, if you have a set, you have a subset consisting of those elements that have that property (even if there aren't any, in which case it's the empty set, and that's fine).  If the property is not containing itself, then the set of all sets would have that property iff it didn't have that property.  That's Russell's paradox, and that means that a distinction has to be made between sets, which do exist, and classes, which don't.  In particular, you cannot be allowed to make the statement, even in the negative, "this class is a member of..."

So why should infinite sets be allowed?  Be rid of the axiom of choice and the axiom of infinity; replace the latter with an axiom of finiteness and an axiom of empty set.  This will give you Peano arithmetic, and it will make the notion of countability nonsense.  What Cantor diagonals would reveal has already been revealed by Galileo.  But then what about sets on the real line?  Because even restricted to rationals, let alone proper superclasses, that would fail the axiom of finiteness.

So how to define finiteness?  The normal definition involves a bijection with a cardinal set, the normal definition of which (a sort of canonical set of a given natural size) essentially is the axiom of infinity, so that's right out.  Easiest to axiomatize would be Tarski finiteness, which means that, given a set and a set of subsets of that set such that for every pair of elements one contains the other, then one of those elements is contained in no other.  (I'm really tempted to try to write that in symbolic language, but I will have behaved myself so well so far.)  Normally, this doesn't imply finiteness in the first sense without the axiom of choice (which is obviously right out), but ZF alone - without infinity or regularity - is enough to show it implies Dedekind finiteness (no proper subset has a surjection onto the whole set, or equivalently, no subset has a bijection to the natural numbers), and that Dedekind finiteness of the set of subsets of the set of subsets is enough to imply natural-number finiteness; therefore, if every set is Tarski finite, then the power set of the power set stupid double subset thing I just mentioned of a given set must be Tarski finite, and therefore Dedekind finite, so every set is natural-number finite.  (The definition of the natural numbers - which don't comprise a set - will be a bit ad hoc.)

(This is where that entire Banach-Tarski rant from the last post went.)

Of course the theme of this post gets rid of that paradox, so forget the entire last paragraph.  In fact, it collapses any number of paradoxes into what amount to one mega-paradox with fewer metamathematical consequences.  I don't know what those are, but what they are they really aren't, are they?  After all, the probability of the destruction of mathematics is impossible to assess (any truly rigorous definition of the set of definable numbers would do it - although there are many contingent ones, even contingent ones that can be without contradiction established by fiat to be, per Skolem's paradox - but that lies behind a wall of universal Skolemization) - and perhaps all probabilities are impossible to assess, with such a recasting of set theory.  I'm not the first person to suggest this - Kronecker being the most celebrated - although perhaps the first so incoherently (I expect this post, indeed, the entirety of this blog, is just the right combination of informed and erroneous to be infuriating to every level of mathematical acumen), and there are untold hurdles, one of which I've just mentioned.  So let's go back to that thing I harp on all the time - PNT.  Let's build from the ground up, sort of, in an unholy fusion of Euclidean geometry and set theory applied to modern analysis and number theory.  That might be getting me where I'm going.  The Lebesgue integral certainly relies on infinite sets as a part of measure theory, so best to stick with the Riemann.

Of course, that brings up the notion of how to define limit.  In ZF, it's impossible to prove without countable choice that the epsilon-delta definition of limit is equivalent to the existence of a sequence that comes to the limit in question.  In this universe, the latter definition is incoherent, since no infinite sequence exists at all.  The former can be restricted harmlessly to the rational numbers, which raises the question of what exactly the limit is; the limit is the rule, which is finite.  Similarly, the twofold - two is less than infinity ("less than" expressed as an ordering of the set of cardinalities with at least one infinite cardinality as an element) - composition of limits (one of those limits being a series) in the definition of the integral is a composition of rules.  (This computational approach makes me essentially the set-theoretic equivalent of the "nullity" guy, by the way.  Well, that's not fair; he got better grades.)

Now, recall the "evidence."  Now, it might seem shocking to try to work with the Euler product, in either form, without infinite sets (the reals themselves - Dedekind cuts - are infinite sets), but an infinite sequence, speaking informally, need not imply an infinite set, as long as the rule is finite.  What's generated, then, provided the series is convergent, is a Dedekind cut, which would be a proper class under the axiom of Tarski finiteness.  However, that's not really important, but rather, what's important is the rule, and manipulations of this rule under the arithmetic operations by a sort of composition; a rigorous definition not found in this post would most likely come from the theory of computation.

I remember how much easier I found vector calc than I did linear algebra.  This was because in vector calc, I had already guessed most of the basic operations from simply generalizing the rules from one-dimensional high school calculus.  At that age, I couldn't wrap my head around the fact that this clearly wasn't enough.  To some extent, modern set theory's treatment of analysis is a formalization of this misapprehension, so that it ceases to be a misapprehension.  Let's take the alternative perspective, Turing standing on Peano's shoulders rather than Zermelo's for the hypercomputability hierarchy to replace Gödel's.  Let's enhance our confusion to create a grand certainty.

Back to the point.  To recap, the "evidence" is that if you take the logarithmic derivative of the zeta function you get the logarithm of each prime in turn divided by one minus that prime to the negation of the parameter, which can alternatively be expressed, per Euclid, as the logarithm of that prime multiplied by the sum from zero to infinity of one over the powers of the prime in question to the parameter (remember, though, that this is a finite rule as opposed to an infinite set).  Considering that, all terms being positive, this converges absolutely, the terms can be rearranged; note that the terms that are generated by the rule are exactly fractions with prime powers raised to the parameter in the denominator with the log of the base in the numerator, so let's put them in the order of the prime powers.

Before we go on l let's go back to that sentence, "considering that this converges absolutely, the terms can be rearranged."  Remember when we all learned that in high school?  But the concept of a permutation on an infinite set is taken as read there, so it's imperative to prove the equivalent principle again in this new framework.  By the definition of limit, we can always run the partial long enough that it'll be within some given distance of the sum.  In that, provided we have some idea where the terms are going, there must be a maximum destination, which must be equal or greater.  Therefore, it must include all the terms, and more.  If they're all positive, then this can only be larger.  Therefore, it's true of the absolute value.  Term-by-term summation following from that of the partials and the arbitrarily low upper bound on the tail, you get from there and the convergence of a subseries to the case of absolute convergence.

Anyway, back to the "evidence."  From here it's pretty clear.  You can make this sum by layering up integrals that start at each prime power, which will each be the parameter times the log (when there is one) divided by the index to the power of the parameter plus one.  So moving the sum inside the integral (since it's absolutely convergent - same argument as before, only this time with Riemann sums slid in) you'll get the second Chebyshev function divided by the parameter of the integral to the power of one plus the parameter of the zeta function, all multiplied by the parameter of the zeta function.  If you plug in one, the derivative of the log of the zeta function blows up, and so this integral blows up as well - which is what you'd expect if the second Chebyshev function asymptotically approached identity, because then you'd be dividing identity by the square to get the reciprocal so that would blow up.  You'd also expect, then, that subtracting the reciprocal would cause it not to blow up, and in fact this would imply the asymptotic approach.  The suggestion of this comes from the fact that if you multiply the zeta function in the log by one less than the parameter, the derivative manifestly converges.

So that's the "evidence," but it's not the proof because we can't obviously move the limit inside, not even with the normal machinery of set theory/analysis.  So why can we move the limit inside?  The short and incoherent answer is because there are no zeroes on the edge of the critical strip.  The proof of this I won't restate - it's just algebra and trig - but the connection still isn't inherently obvious.  From there, what's left is the Wiener-Ikehara theorem, which it's even more imperative to view now in terms of Fourier analysis, that is to say, constructing a function from an uncountable accumulation of sinusoids.  Might be some kinks to work out there in the absence of infinite sets.

So basically, as I said before, the actual proof is based on the notion of an "approximation of unity," a family of functions of integral one that approach zero bar an infinite isolated point.  (Again, none of these concepts exist, but speaking in shorthand, that's what it is.)  Multiplying this by offsets of another function allow you to show that that function approaches a constant, and in this case to show that the second Chebyshev function approaches the identity.  The fact that this approaches a limit comes from the equation discussed before.

Now, so far, I'm just drunkenly ruminating on cud already so thoroughly chewed.  What's interesting, though, is that not only are all these limits determined by finite rules, but that they themselves are their solutions, and these rules for arithmetic operations axiom schemata, rather than inferences.  The question, then, isn't whether they follow, but whether they're eliminable in whatever context is important to our purposes.  And that's what brings us back to Euclid.

Remember, the challenge there is to build from the sparse postulates of his geometry and "number theory," to which not even he can hold himself entirely, to get to such a radical conclusion regarding the prime numbers.  In his terms, as before, it can be expressed only in terms of the harmonic series - at least without great difficulty.  New chapters might be introduced bringing it to modern terms (i.e., at the very least, terms in which RH in prime-number form would be meaningful) without a modern notion of infinity, but these would be lengthy chapters.  For now, let's go with the prime counting function and the harmonic series.  I said then that we would need definite error bounds, but let's replace that with "as close as we like."

Let's work backwards.  We first need to start with the fact that an increasing (non-strictly) function that's convergent when you add it up (at integers because no infinity - note that this is an integral of a function of countable range in the ordinary paradigm) subtracting identity and dividing by the square must approach in ratio identity.  This follows from the divergence of the harmonic series in effect - if it didn't approach identity in ratio, then the ratio would either approach a number greater or less than one, or it would diverge, being unable to oscillate due to the function's monotonicity.  If it did those things, the function wouldn't converge.

From there, two things remain to get us to "as close as we like."  If only I could remember what they were.  (I suppose I should mention on this point that my hippocampus is a pickled seahorse on a toothpick.)  I suspect they're to show that the increasiness is finite for positive parameters and that it reflects the limit.  The former is easy enough to show from series (to wit, by saying that it holds for any power, however small, the concept being expressed easily enough geometrically), the latter coming from Fourier analysis.  In any case, really, there's no real logic to this other than what I mentioned before, only the relevance of it to this notion of mathematics without infinite sets.

So let's not fuck around.  Fourier analysis, the analysis of periodic functions on the real line expressed as the integral of an uncountable set of sine waves, without infinite sets.  How?  Well, not at all, really, but basically by geometry, obviously.  Sine waves, after all, come from sines, the string of a bow the chord, the musical sense of "chord" after all coming from the chord a string made against a lyre (as far as you know), and Euclid knew the law of cosines in a geometric, very Alexandrian form (propositions twelve and thirteen of book II).

So let's go back to the very beginning of this blog.  The normal distribution.  Now, the slovenly proof I gave then doesn't really show anything and isn't the normal (so to speak) approach anyway.  A better notion of probability comes through set theory and measure theory, the latter of which certainly doesn't work as normally understood in a finitist paradigm.

So you'll remember I explained (ish) why a series of fair coinflips should approach the standard normal, but I didn't explain probability beyond that at all.  So what is probability?  Well, you take a set, a subset of that set's power set closed under complementation (relative to the base set) and countable union, and a function from the latter to [0, 1] such that the empty set maps to zero, the union of countable disjoint sets maps to the sum of those sets' image (implying the union of countable non-disjoint sets is less than or equal to the sum of those sets' image), and the whole shebang maps to one.  That's a probability space.  Now, if the set has to be finite, you're golden to model, e.g., cards or dice, but you're SOL if you want to model a dartboard, unless you feel like working it out at the quantum level, but even there there may or may not be infinities where probability is concerned.  Therefore, under this paradigm, the base set and space would have to be understood in terms of the rules that generate them - but aren't they anyway?

So with that in mind, the notion of approaching a probability space via a series of fair coinflips is analogous to the notion of approaching a real, computable or uncomputable, by a Turing-equivalent machine.  Now, I didn't bring up Turing machines (exactly) above because even in this paradigm uncomputable numbers can be defined, such as the sum of two to the power of the negations of successive busy beaver numbers.

I've been writing this for months now, and I'm sure it's wicked self-contradictory and flows like tar, but fuck it, it's going up.