Today on the blog I start a new project: where do numbers come from?
By which I mean, mathematicians deal with lots of weird kinds of numbers. Real numbers, complex numbers, p-adic numbers, quaternions, surreal numbers, and more. And if you try to describe the more abstract types of "numbers" you sound completely incomprehensible.
But these numbers all come from somewhere. So I'm going to take you through a fictional history of numbers. Not the real history of the actual people who developed these concepts, but the way they could have developed them, cleaned up and organized. So in the end you can see how you, too, could have developed all these seemingly strange and abstract concepts.
This week in part 1, we cover the most sensible numbers. We start with the basic ability to count, and invent negative numbers, fractions, square roots, and more.
But that will still leave some important questions open—like, what is π? So we'll have to come back for that in part 2.
Note: This is almost impossible to get exactly accurate and should be viewed as hypothetical. Wodehouse himself seemed to pay little attention to chronology and consistency of cultural references, so the best I can do is guess. The novels in particular are difficult to arrange, since they are supposed to take place in such a short time period, yet seem to require more time if they are to occur as described.
According to this hypothetical timeline, Bertie Wooster was born around 1901. If so, he would have been seventeen when World War I ended and so could not have participated. If we suppose Jeeves to be ten to twenty years older, he would have been born around 1881-1891, making him between twenty-three and thirty-three when WWI began and ensuring that he would definitely have “dabbled in it to a certain extent,” as he tells Lord Rowcester in Ring for Jeeves.
“Jeeves Takes Charge” – Summer 1925 (Bertie is twenty-four, and the narration is taking place six years in the future, presumably 1931.)
“Extricating Young Gussie” – September 1925 (This story isn’t usually included in the series, but its events are referred to in later stories and so it’s clearly part of the timeline.)
“The Artistic Career of Corky”- Autumn 1925-sometime in 1926 (Necessarily takes place over a long period of time, possibly the entire New York trip.)
“Jeeves and the Hard-boiled Egg” – Autumn 1925 (A few months into the NY stay.)
“Jeeves and the Chump Cyril” – 1925 or 1926
“Jeeves and the Unbidden Guest” – Autumn 1926 (Set during Coolidge’s presidency (1923-1929), about a year into the stay in NY, “about the time of the year when New York is at its best.”)
“The Aunt and the Sluggard” – Spring 1927
“Jeeves in the Springtime” – April/May 1927
“Scoring off Jeeves” – Summer 1927
“Sir Roderick Comes to Lunch” – Summer 1927
“Aunt Agatha Takes the Count” – Summer 1927
“Comrade Bingo” – Late July or early August 1927 (Around the time of the Goodwood Cup.)
“The Great Sermon Handicap” – August 1927
“The Purity of the Turf” – August or September 1927 (Three weeks into the stay at Twing.)
“Bertie Changes His Mind” –
“The Metropolitan Touch” – November-December 1927 (A Friday, December 23 is mentioned, making the only possible years in the right range 1921, 1927, or 1932. In light of information in later stories, 1927 seemed the most plausible option.)
“The Delayed Exit of Claude and Eustace” – Probably early in 1928 (Set during the time of an unspecified Oxford term. Bertie’s age is given as around twenty-five or –six.)
“Bingo and the Little Woman” – Between October 1927 and February 1928 (Invitation received to go shooting in Norfolk indicates that it’s sometime during the hunting season.)
“Without the Option” – March or April 1928 (Boat Race Night is usually the last weekend in March or the first weekend in April.)
“Clustering Round Young Bingo” – Sometime in 1928
“Jeeves and the Impending Doom” – Spring[?] 1928
“The Inferiority Complex of Old Sippy” – Spring[?] 1928 (Takes place sometime before June 1.)
[“The Rummy Affair of Old Biffy” – The mention of the British Empire Exhibition at Wembley would set it around April-October 1924 or 1925. However, this does not fit the timeline as I’ve guessed at it, because it’s clearly set after Bertie’s brief engagement to Honoria Glossop. Adjusting the timeline to fit around this date would cause other problems, so I’ll call this an anomaly.]
“Fixing It for Freddie” – Summer[?] 1928
“Jeeves and the Yule-tide Spirit” – December 1928
“Jeeves and the Song of Songs” – Sometime in 1929
“Episode of the Dog McIntosh” – Spring[?] 1929
“The Spot of Art” – Summer[?] 1929
“Jeeves and the Kid Clementina” – Summer[?] 1929
“The Love that Purifies” – August 1929
“Jeeves and the Old School Chum” – Autumn 1929
“Indian Summer of an Uncle” – Sometime in 1929
“The Ordeal of Young Tuppy” – November 1929
“Jeeves Makes an Omelette” – Winter 1929 or 1930
Thank You, Jeeves – July 1930
Right Ho, Jeeves – July 29-31, 1931 (Cannot take place the same year as Thank You, Jeeves, because TYJ begins around July 15 after a three-month trip to America, while RHJ opens around July 25 after a trip to Cannes that started at the beginning of June.)
The Code of the Woosters – Autumn 1931
“Jeeves and the Greasy Bird” – December 1931 (It’s said to be more than a year after Sir Roderick’s engagement in Thank You, Jeeves, and Bertie’s awareness of the Junior Ganymede Club suggests that it’s after The Code of the Woosters.)
The Mating Season – April 1932 (The events of Right Ho, Jeeves occurred the previous summer, while the mention of Boat Race Night and Bertie’s cousin Thomas returning to school—presumably for the summer term—suggest an early April date.)
Joy in the Morning – Summer 1932
Jeeves and the Feudal Spirit – July 1932 (Aunt Dahlia is said to have been running Milady’s Boudoir, first mentioned in “Clustering Round Young Bingo,” for three years.)
How Right You Are, Jeeves – Summer 1933 (Jeeves goes on holiday, not the same one mentioned in Jeeves and the Feudal Spirit. Bertie’s moustache from the previous book is mentioned as having occurred a year ago. Aunt Dahlia is said to have run her journal for four years. The one thing I can’t account for is the claim that the events of Right Ho, Jeeves occurred the previous summer, so for purposes of expediency I will consider it an error.)
Stiff Upper Lip, Jeeves – Fall[?] 1933
Jeeves and the Tie That Binds – Fall[?] 1933 (Tuppy and Angela have been engaged for two years.)
Aunts Aren’t Gentlemen – Spring or summer 1934
Ring for Jeeves – June, sometime between 1946-1953 (Set explicitly post-World War II, with an emphasis on societal changes in the UK. Television is mentioned.)
I'm boggled. This isn't the same thing as in the letter, is it?
Thank you so much for the ask!! Good job on spotting the difference!
Posting the letter again for reference:
So you're right, on the rock it reads 張仲仁 (Cheung Chong Yan in standard cantonese romanisation), while on the envelope the name is 張仲文 (Cheung Chong Man). Hergé’s real life Chinese friend is 張充仁 (Cheung Chong Yan), so the romanisation would be the same as the name in your ask.
HOWEVER, those are just romanisations (which are less accurate but easier for foreigners to pronounce). Their actual pronunciations in cantonese (spoken in Hong Kong) / mandarin (spoken in mainland China including Shanghai) are different:
張充仁 = Tcheung Chong Yun* / Zhang Chongren
張仲文 = Tcheung Tchong Mun / Zhang Zhongwen
張仲仁 = Tcheung Tchong Yun / Zhang Zhongren
* 'Tch-' is similar to J sound; '-ong' is OW-ng; '-un' as in under
As you can see, there’s a bit of a mix and match. But I think it makes sense to change the first word in his given name into 仲 given that the story says Chang is from HK, because we seldom use 充 in our names (perhaps more common in mainland China, not 100% sure).
Another fun fact for you on the meanings of those given names~
充 = full of
仲 = still be (only in cantonese)
仁 = love for all beings/ benevolence
文 = cultured/ gentle
Both 仁 and 文 are commonly used here across different generations and genders. So I think both translations are pretty nice!!
Also, I just spotted that the stamps in the top right corner are of Queen Elizabeth II and King George VI:
Not so good at maintaining consistency but good attention to detail, I must say :)
“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/
What issues would a Jewish Werewolf face? I mean with a lunar calendar and so many of the holidays near the full moon, they would have to get pretty inventive, just think about sleeping in the succah, or since Yom Kippor is about 4 days from the full moon, it should make things interesting as in most stories weres start to lose control near the full moon.
HMMM! (and thank you for sending me these anons!)
I suspect it depends on what tradition we’re drawing from. Werewolves as a whole are mostly a European thing, although people changing into or communing with animals is pretty much a worldwide myth.
Some things to think about: If you’re not fully conscious (or not conscious in the same way) when you’re a wolf, are you accountable for any destruction you cause? Does transformation count as work? (Also, if you can’t stop yourself from doing work, you probably aren’t breaking Shabbat..) Can you attend synagogue as a wolf?
And we do have recorded cases of nice werewolves! In Latvia in 1692, an eighty-year-old man named Thiess confessed to being a werewolf who, with other werewolves, regularly went to Hell three times a year to fight Satan to ensure a good harvest. This would be a great tradition for Sukkot, Shavuot, and Tu B’Shevat, and I propose we all adopt the custom immediately!
Liz Kendall has returned to a quiet life as a backbencher and constituency politician, but due to border change legislation passed by a gloating Tory Government, her constituency is now Hades.
Yvette Cooper is serving a ten year sentence for the murder of her husband Ed Balls after his 167th utterance of “At least I lost to the Millibands…”
Jeremy Corbyn, in what is considered one of his more unusual leadership moves, proposes legislation to ban the word “Crown” from any and all pub names. The Labour conference that year is held in the “People and Anchor” pub in Islington.
Andy Burnham turned back into a wooden doll at the stroke of midnight after the leadership election, where he came third place, as a result of the particular brand of contractual wish magic that gave him life.
I learned today that the International Baccalaureate organization (the ones who run the IB tests) consider the topics lists for their courses to be copyrighted and confidential. They won't share them without a signed release.
I'm genuinely offended by this. I don't know how the fuck you're supposed to evaluate or understand the program without knowing what topics it covers! (They'll share the topics list with me, specifically, in the course of evaluating the test for my university; but I have to sign a release, and have to promise not to share them with colleagues, because they want my colleagues to sign the same release.)
And there's, like, no point to this. It's not a major secret what the topics a calculus course should cover are. (And sure, they do some stats and matrices or something too, and that's all the added info.) I think you can't even legally "copyright" the contents of these lists, because it's factual information and that's not copyrightable.
I'm really seriously tempted to issue an official recommendation to my university to stop giving any credit for IB tests until this policy gets reversed. If they won't freely share information on the program and the test, we'll have to assume that it's valueless and shouldn't earn credit.
(My only hesitation to that is it's probably a quixotic quest that would just hassle some innocent IB students. But if I can get a bunch of other departments to sign on I'll absolutely do it; IB can't sustain that policy if universities stop rolling over for it.)
Take the definition that two words rhyme if and only if they end with the same sound.
Reflexive: Every word rhymes with itself.
Well, if two words are the same, all their sounds have to match, including the final one, so this point holds.
Symmetric: If A rhymes with B, B rhymes with A.
This one’s really hard to prove, because it’s so obvious. If A rhymes with B, then the final sounds of A and B are the same. They will still be the same if we swap the words around. Please don’t make me explain it more, I’ll cry.
Transitive: If A rhymes with B and B rhymes with C, then A rhymes with C.
Call the sound at the end of word A ‘&’. If A rhymes with B, then B also has to end with ‘&’. If B rhymes with C, and B ends with ‘&’, then C also has to end with ‘&’. This means that both A and C end with ‘&’, and so A rhymes with C.
There we go. The argument no one cares about but me has been made. Rhyme is an equivalence relation. You can all go home.
Just stumbled upon a great philosophical debate while listening to a playlist on shuffle.
The esteemed philosopher Bill Joel puts forward that "It's still rock and roll to me" confidently declaring that rock and roll remains to some extent constant in how much it rocks.
However, his point is immediately challenged by philosopher Bob Seger who posits that "Todays music ain't got the same soul" and that he "Likes that old time rock and roll". Confidently declaring that rock and roll has declined in its rockness.
This is truly one of the most important debates facing philosophy today.
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.
new rules for chess:
1. Friendly Fire ON
2. Landmines
3. If a player loses both of their bishops, the king can now legally divorce the queen without the papal go ahead. This puts the queen into FRENZY mode.
4. Once per game, a player may change one letter in a piece's name to change its role. The rook is now a book. The pawn is now a PAWG. The queen is now...well...I shan't say
5. Knights are now Horses
6. Horses are immune to landmines
7. Pawns can move back a space if they forgot something
8. A bishop can be combined with an adjacent rook to create the Wizard Tower piece
9. Each player now has 2 rows of pawns
Interchange station for a variety of parallel lines
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