Why Do We Use The Symbol For Partial Derivatives As The Symbol For Boundaries Of Manifolds?

Why do we use the symbol for partial derivatives as the symbol for boundaries of manifolds?

More Posts from Middlering and Others

4 months ago

the craziest part is how it ends with the prototype local hero theme


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4 months ago

AU where the odyssey takes place entirely in ikea


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4 months ago
jaydaigle.net
This week we continue our exploration of what numbers are, and where mathematicians keep finding weird ones. Last time we defined the real

I have a new post up on my blog, continuing the Fictional History of Numbers series. In part 1 we started with the natural numbers and built up the algebraics, which let us solve equations. In part 2 we started asking geometric questions, and constructed the real numbers.

But the real numbers are weird and hard to define. In part 3 we see one way they're extremely strange, and then talk about why we want them anyway. In the end, we shouldn't worry about the definition of the reals; we should worry about what they allow us to do. And it turns out they're exactly what we need to make calculus function as it should.


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2 weeks ago
So I Recently Stumbled On The Wikipedia Article For The Grothendieck-Riemann-Roch Theorem, Which Is An

So I recently stumbled on the Wikipedia article for the Grothendieck-Riemann-Roch theorem, which is an algebraic geometry thing that I'll hopefully learn some day once I actually have the prerequisite knowledge =w= But at the top of the article was this letter, which I thought was a wild thing to have at the top of a Wikipedia article about a niche abstract math thing - here's a translation:

Witches' Kitchen 1971 Riemann-Rochian Theorem: the latest craze*: the diagram

So I Recently Stumbled On The Wikipedia Article For The Grothendieck-Riemann-Roch Theorem, Which Is An

is commutatif**! To give this statement about f: X->Y some approximative meaning, I had to abuse the listeners' patience for nearly two hours. In black and white (in Springer's Lecture Notes) it seems like it will take up to about 400, 500 pages. A gripping example of how our thirst for knowledge and discovery indulges itself more and more in a(n il?)logical delirium far removed from life, while life itself is going to hell in thousandfold ways - and is threatened with absolute annihilation. High time to change our course! (6.12.1971) Alexander Grothendiek

* "der letzte Schrei" is a reasonably common German idiom meaning "the latest craze", but here it could alternatively be translated non-idiomatically as something like "the last cry". I think its more fun to imagine he means the idiom. ** I'm assuming this is a weird old-timey spelling probably taken from french but googling it I can find no examples of anybody using this spelling in German besides this letter

Note that this is 20 years before all of this happens:

So I Recently Stumbled On The Wikipedia Article For The Grothendieck-Riemann-Roch Theorem, Which Is An

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4 months ago

I got the Thrilling Adventures of Lovelace and Babbage for free from Thriftbooks (after much fussing about getting the book rewards points spent for the best value) and it's like YES, SOMEONE WHO LIKES FOOTNOTING THEIR COMICS AS MUCH AS ME.

Also it's an amazing set of 4 panels

I Got The Thrilling Adventures Of Lovelace And Babbage For Free From Thriftbooks (after Much Fussing

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4 months ago
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.
He's Like A Stress Ball To Me.

he's like a stress ball to me.


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4 months ago

Morten Morland (@mortenmorland) gives Nick Clegg and Chris Huhne the cartoon-test

“It’s simple, really. If a person is easy to draw, he’ll do well [in politics]. Because the likelihood is he’ll have other interesting characteristics too, which will make him appealing to journalists, thus raising the party’s profile in the media. And people watching are more likely to remember him, which is a bonus!

A quick cartoon-test shows that Nick Clegg, probably the favourite in the party at the moment, will lead the party into eternal oblivion, if elected. He is Mr. Some Bloke embodified – despite the fact that he can speak several languages.

I did a couple of quick sketches, and worringly for him, the best caricature came after I in frustration drew a lifeless mask.

People will see Nick Clegg on TV and wonder whether he’s that guy from marketing whose name they can’t recall – or someone they’ve met at All Bar One.

Chris Huhne on the other hand, is better. Not great, but better. He’s got a prominent crazy eye – a feature that he famously shares with both Maggie and Tony. His mouth is similar to that of a hamster…or a mouse, and remember, those ears will keep growing.

Between Clegg and Huhne, there really is no contest.”

In full here: http://poldraw.wordpress.com/2007/10/15/lib-dems-insist-on-having-an-election/


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2 months ago

Wisdom of the creative arts and its significance in life

People sometimes look at me thinking that I’m simply ‘obsessed’ over the creative arts such as stories, characters, art, music, poetry, movies, games (yes I consider them an art form but that’s a story for another time) etc.. I understand why it’s easy to believe that I have characters on my wallpaper ‘just because’ I like them. There is nothing wrong with admiring characters simply because they’re cool or enjoy stories because they bring you joy. However, what frustrates me is how often people overlook WHY people like me care about the creative arts, and how easy it is that others undermine the deeper value and insights we gain from these stories, these characters, and the more abstract arts.

Creative art forms are often a microcosm of the world filled with the creator(s)’s own soul(s), coloured with the reflections of humanity - a beautiful, yet sometimes horrifying mosaic of our dreams, our nightmares, and our nature. It expresses what cannot be easily conveyed or rationalised. It is a form of wisdom meant to be felt viscerally and experienced, a unique form of communication that transcends time, diversity and logic. Just like other forms of knowledge and wisdom, this too, requires practice and learning to fully appreciate and grasp. However, unlike other disciplines, the creative arts is perhaps the most versatile due to its nature, with some of the greatest pieces bearing the capability of creating waves amongst people by touching their hearts and by caressing what makes us human.

For those of us who lack guidance and support in life, the creative art forms such as books, art, music and even games can help enlighten and educate us when others can’t. Yes, fiction is fiction, and non-fiction may be filled with biases or flawed views, but it can still be a lighthouse for those who seek light, and an anchor to those who are lost wandering about. There is much to gain, be it empathy, open mindedness, soft knowledge, resilience, discipline etc. from these creative art forms. It can encourage others to learn how to develop critical thinking skills, and to develop their own opinions and perspectives after digesting various truths and angles of the world. Of course, it is important to separate fiction from reality, and understand what can be applied in the real world, and what cannot. But the protection and guidance it brings cannot be undermined. As someone who sought solace in literature, music, art, dance, poetry etc. they have each formed a big part of who I am, and in shaping the values, principles, priorities, choices and ideals I hold in life. I have also gained numerous advice, mindsets and encouragement from them as I tackle the challenges of life. I found comfort in the creator’s message - in their embrace, in their message to me, in their experiences. I also found companionship in their arms, in knowing that I wasn’t alone in thinking certain ways, in feeling certain emotions, in hoping for certain ideals, in fearing various demons. It also inspired me to see how much effort creators put in their works to accurately convey their insightful thoughts, feelings and messages. How could I go through books, listen to music, look at art, without allowing myself the privilege and honour to thoroughly go through these works that are soaked in the blood, sweat and tears of the creators? Call people like us obsessed for spending time to dismantle these works, but it is through effort in understanding these arts, in creating these arts, that we can slowly gain wisdom from them.

There is nothing wrong in enjoying the creative arts as they are, without breaking them down into pieces to digest its value and wisdom, and applying it to your life. I often find myself using the creative arts as an outlet to escape reality and to express myself, but the wisdom of the arts is too often overlooked for the other disciplines. It saddens and frustrates me to see people think of art as a simple thing, that there is nothing to be gained out of art. But tell me, if there really is nothing to be gained in the creative arts - why has it lasted this long? Why can people still shed tears, or laugh in joy, when faced with these beautiful art forms? Why should there be this rigid hierarchy in disciplines where certain knowledge rank higher than others? Isn’t life too complex to be held onto such a strict standard where certain ‘skills’ and ‘knowledge’ are said to be ‘closer to truth’, and ‘closer to wisdom’ than others?

Is it not a form of wisdom itself to express one’s complex emotions with such clarity? To convey a message so powerful that these pieces would get banned? To spark a flame that would move a society? To become a mirror that reflects humanity better than any logic or science can convey? How can we easily overlook the effort, the time, and the skills it took, to create such complex and beautiful pieces that can move us in ways others can’t?

Of course, perhaps like the others, I sound ‘obsessed’, but I believe that as long as these creative art forms don’t interfere with the quality of one’s life, as long as your own unique balance is formed in enjoying the arts and in gaining the right wisdom for your real life, I think that’s the best gift the creative arts can offer someone.

Perhaps there are others that rely too much on the creative arts, those who become addicted, who make it their whole life - but in those cases, what are the chances that it is the creative arts that are their last thread to life? Their last anchor, their last hope, their last salvation amongst the chaos of this world? (Cough *Kim Dokja*) Is it so wrong to hold on to something that will help you take another breath, to be brave enough to live through another day, to give you hope when you see none? (Okay, that’s another tangent and gray area of discussion for another time) Of course, art is not salvation, but perhaps it may be enough to prolong someone’s sanity or life, before they can seek the help they need. Then, there are those few geniuses, those ‘lunatics’ as called by others - perhaps to them, they are willing to pay the price of becoming one with their art, compared to sacrificing their overwhelming love for the arts for a life in reality. But I can’t say much about that, as I’m not them. Then there’s also this notion of ‘balance’ that everyone preaches, to balance time in your dreams, in your clouds, in your stories vs. Reality. But that’s a tough discussion to navigate, as everyone has a different balance that suits their life, temperament, values, priorities and circumstances. 

I’d like to end with this quote from Honkai Star Rail

‘When it comes to gaming, things like race, lineage, allegiance, destiny, beliefs… they’re all insignificant. It’s good to remember that.’

Of course, the reality is more nuanced than that. Our race, lineage, allegiance, beliefs and environment influences us and hence, shapes the things we create. However, the result of these works, be it games, literature, music etc. can affect anyone, regardless of these things that separate us. It is often used to unite us, and enable us to communicate with one another in spite of these differences. It can even transcend time! Why do you think certain books have either been promoted or banned in the past? Why have certain artworks been criticised so heavily or enjoyed? Why have certain music been roughly casted away in shadows or promoted?

Anyways, I’m running out of steam. But coming back to the beginning, when I say that I have characters on my wallpapers, or carry stickers or keychains of them, I carry them with me because they remind me of values and principles I wish to uphold in life, they remind me of my ideals and encourage me by giving me strength. They remind me of our hopes, our despair, and most importantly - our resilience and strength. Yes I like them, but in much deeper ways than most people assume. I carry reminders of how I’d like to live my life, and of wisdom I’ve gained through these stories and arts. I take what I can apply to real life, and I take reality to see what influenced creators to create what they’ve created. 

Perhaps one day I’ll make a post about why I have certain characters on my wallpaper (my phone is on photo shuffle - it makes me happy to see different characters on my wallpaper). I also have certain music I hold dear to me, lyrics I have analysed, plays I love, poetry I enjoy, all for various reasons, and all of which I’ve put in energy to understand and apply in my life.

Anyways, thanks for reading my ramblings. I did not expect to write this much. I was explaining to someone recently about why I have wallpapers on my phone and it led me to yap to them about this topic, and I thought, why not write about it? This, alongside the issues with AI art influenced me to talk about this. I might post another one like this later that’s better written and thoroughly read through, since this was written in one sitting within the span of ~1 hour right before I go to sleep. I’m currently sleep deprived and exhausted from running certain errands and work today. Not sure if this will make sense to everyone, but I hope my sentiments come across, and I truly do wish others feel the same way I do. I cradle the arts with such intensity and warmth every day, and it is an important fuel that sparks the flame within me and gives me light in the form of wisdom and hope.

Edit: Just wanted to add, some people might say characters and art is all about perception and subjective. While that is a good point as there are definitely people who don’t see the value in other art forms or have the same perspective on them as I do + the fact that there are many valid and rational reasons why it is overlooked, but it still is true that the creative art forms we take in and learn influence the way we express ourselves and ideas. It is also all around us in photographs, news articles, blogs, YouTube, posts, TikTok, social media, or opinion articles (language can be loaded and biased), or in the music we listen to the daily, religious music, cultural music, Ads, memes, shows etc. There is perception, and how we ‘view’ the creative arts, and there is also a certain amount of truth that art can impact reality and people no matter how much we ‘value’ or ‘perceive’ it. I just feel like there’s a big gap between how we view art vs. how much it actually impacts us and our reality.

Of course, art is often more of a luxury, and with the state of the world and various circumstances, it is understandable it is overlooked. I’m just a little frustrated at this ‘gap’ in how we perceive art as a society vs. How much it ACTUALLY impacts us and influences us without us knowing. Our own perspective of how important something is and how much we ‘think’ it impacts us doesn’t always correlate to the truth of how significant something is, and how much the creative arts are actually involved in our lives. They influence a lot of things that we don’t perceive. They’re just not in a typical ‘creative’ or ‘abstract’ ‘art form’ that we think they exist in.

Wisdom and truth remains, even if we don’t ‘perceive’ it or ‘value’ it, no matter what form it comes in.


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3 weeks ago

Blatantly Partisan Party Review XV (federal 2025): Katter’s Australian Party

Running where: QLD. The party is contesting three House divisions: Bob Katter himself for Kennedy, plus candidates in Herbert and Leichhardt, while in the Senate, a candidate is second on a joint ticket with Rennick First for Group G

Prior reviews: federal 2013, federal 2016, federal 2019, federal 2022

What I said before: “For those of us on the left, KAP has a few things to like and a lot to detest.” (federal 2022)

What I think this year: I’ve already covered a bunch of “dontcha know who I am?” cult-of-personality parties, and here is perhaps the most larger-than-life personality of the Australian political scene: the North Queenslander in the big hat, the man who would let a thousand blossoms bloom, part of the parliamentary furniture itself, the one and only Bob Katter.

Now, Bob is a character but he's consistent one, so instead of reprising the greatest hits that I've featured before, I thought I would present you with some history to contextualise him and his electorate. Katter’s seat of Kennedy is a vast one. It stretches from the Coral Sea coast between Cairns and Townsville, across the Great Dividing Range, and through Outback towns such as Charters Towers, Hughenden, and Cloncurry out to Mount Isa, across to the NT border, and up to the shores of the Gulf of Carpentaria. Bob Katter has seemingly stomped the length and breadth of it to become an enduringly popular local member. Although Kennedy is one of the original 65 electorates from Federation in 1901, Katter is remarkably just the seventh person to hold it.

Kennedy was in Labor hands from 1929 to 1966 while Darby Riordan and then his nephew Bill held the seat, but for the last 59 years it has been a family business for the other side of politics:, a Katter has represented Kennedy for all but 3 years. Bob’s father, Bob Katter Sr, won it for the Country Party (later renamed the Nationals) and held it from 1966 until his death in 1990, while the young fella learned the family business as a state MP from 1974. Bob Jr served as a cabinet minister from 1983 under another larger-than-life Queensland pollie, Joh Bjelke-Petersen, and in August 1989, Sir Joh unsuccessfully endorsed Katter as his successor as premier. Instead, Bob Jr had an annus horribilis: he went into opposition at the December 1989 Queensland state election, his dad died days before the March 1990 federal election, and Kennedy fell to Labor. The new MP, Rob Hulls, however, only got one term representing this sprawling constituency (and yes, Victorian readers with long memories, that is the Rob Hulls, deputy premier to John Brumby in 2007–10; quite the change of scenery!).

Katter shifted to federal parliament at the 1993 election, winning back the seat of dear old dad, and he has held Kennedy ever since. In 2001 he left the Nationals to sit as an independent: he disagreed with the rise of neoliberal economics (good!) and with some of the Coalition’s more socially liberal policies (bad! especially as the Coalition is uhh not very socially liberal!). In 2011, he founded Katter’s Australian Party, which met with very little success outside Queensland at the 2013 and 2016 federal elections and has since focused on winning seats in North Queensland. It really ought to be called Katter's North Queensland Party.

Bob’s son Robbie has been the party leader since 2020, and at state level KAP holds three seats that overlap with the Division of Kennedy. But Bob is the only KAP representative at federal level; ex-One Nation lunatic Fraser Anning briefly joined KAP as a Senator in 2018 but proved to be too barmy even for the Katters. I see little reason to anticipate any change to the party’s representation this year. If you live in Kennedy, you probably know Katter is a strong favourite to retain his seat; if you don’t, I hope the history above helped make this explicable.

What is Bob emphasising in his campaign this year? Well, per the homepage, “KAP = Castle Law”. Yes, their core focus is a fear campaign that “crime in Queensland is out of control” and people have a “right to defend their home against intruders without facing legal consequences”. Look, I spent my teenage years in a conservative Queensland setting where A Current Affair was as serious a source of news as the 7:30 Report, but shooting dead a trespasser in your garden is disproportionate. KAP states that “Under the current law, people must demonstrate they have only used ‘necessary’ force under the ‘reasonable belief’ that the intruder was entering their home to commit a serious crime”. Seems fine to me! But they think that people “cannot always make split-second, measured decisions in moments of crisis”. The existing law as per their own description already accommodates this: a person fiddling with your gate is obviously a different degree of threat to somebody confronting you in your bedroom with a knife, and going out all guns blazing at the former is not "reasonable". KAP's policy is a solution in search of a problem.

Other policies? Still on crime, KAP has a four-step “send ‘em out bush” policy for young offenders that in practice would just make them more resentful. You won’t be surprised to learn that KAP wants harsher sentences in general for youth offending and backs the LNP’s “adult crime = adult time” approach. Turning to energy, KAP want more coal, more gas, and new nuclear. Other infrastructure policies focus mainly on roads and on dams to support agriculture. Unsurprisingly for a party whose largest donors are from the gun lobby, KAP’s approach to firearms is permissive. And maybe one of their odder policies is that “KAP wants flying foxes gone from populated areas” and supports culling them. Did a flying fox steal your dog Bob? Come on man. Three of seven species of flying fox in Australia are listed as vulnerable or endangered.

And, of course, for a party led by a man whose most famous remark is about crocodiles tearing people to pieces in North Queensland, there is a policy that “values human life above crocodiles”. Enjoy. Should this move you, perhaps you might also want to buy an official “let there be a thousand blossoms bloom” shirt. If so, Bob’s got a shop for that. I am not kidding.

Recommendation: Give Katter’s Australian Party a very low preference in the House and a weak or no preference in the Senate.

Website: https://kattersaustralianparty.org.au/

(For the pol nerds: Bob is currently Father of the House, i.e. the longest-serving current MP, but at just over 32 years in office he is not yet in the top ten ever. If the new parliament goes to term and Bob does not retire before the election, he will be either 10th or 11th  on the all-time list depending on the exact day of election. He needs to serve five years from today to get into the top five, 10.5 years to get into the top two, and just shy of twenty years to pass Billy Hughes’ record of 51 years and 213 days. Keep in mind that Bob turns 80 next month. Now, yes, he served 18 years in Queensland’s state parliament, so as of this year he has been in a parliament for half a century, but Billy Hughes served in the NSW parliament for 7 years; to exceed Hughes’ cumulative time, Katter needs to be in office for another 8.7 years)


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middlering - 下一站:中環。 Next station: Central.
下一站:中環。 Next station: Central.

Interchange station for a variety of parallel lines

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