Do You Guys Know About The Internet Roadtrip? Right Now Somewhere Between 500 And 900 People Are Collectively

Triangle Tuesday 2: The circumcenter, pedal triangles, degeneracy, and what even is a triangle anyway?

The circumcenter is almost as simple an idea as the centroid, which we looked at before. To define it, you start the same way. Take triangle ABC, find the midpoints of the sides Ma, Mb, and Mc. Then instead of drawing lines to the midpoints from the vertices, draw perpendicular lines through the midpoints. These lines all coincide at a point O, which is the center of a circle that you can draw through the vertices. The circle is called the circumcircle, and that's why the point is called the circumcenter.

I say almost as simple, but in a sense the circumcenter is simpler than the centroid, because you could easily discover it by accident in the process of simply finding the midpoints. Drawing that perpendicular line, the perpendicular bisector, is the standard way of finding the midpoint of a line segment. It's covered all the way back in Book 1, Proposition 10 of Euclid's Elements, and it's simply this:

So if you find the midpoint of all three sides of a triangle with this method, you've already identified the circumcenter. But that doesn't prove that the perpendicular bisectors always coincide, nor that their point of crossing is the center of the circumcircle. For that, let's return to Euclid (Elements, book 4, proposition 5). Euclid's proof is very straightforward, and leads nicely into something interesting, so we'll follow that, but I will state the theorem differently.

Theorem: the perpendicular bisectors of a triangle coincide and their point of intersection is the center of a circle that meets all three vertices.

Let ABC be a triangle with midpoints of the sides Ma opposite A, similarly for Mb and Mc. Draw perpendiculars to sides AC and BC from their midpoints to meet at point O. Connect three segments from O to A, B, and C.

Consider the two blue triangles. Their sies AMb and CMb are equal, since Mb is the midpoint of AC. They also have OMb in common. Their angles at Mb are right angles, and therefore equal. So they have two sides and one angle the same, making them congruent, and therefore OA = OC.

The same argument applied to the green triangles shows that OB and OC are equal. By transitivity, OA = OB and O is equidistant from the three vertices. The radii of a circle are all equal, so a circle centered at O passing through A also passes through B and C.

Finally, draw a line from O perpendicular to AB. This creates two white triangles with sides OA and OB equal, side OZ in common, and equal right angles at Z. The two triangles are then congruent and the two sides AZ and BZ are equal. So Z is the midpoint Mc, showing that the perpendicular bisectors all meet.

And the same argument works when ABC is obtuse. The circumcenter lands outside the triangle, and in this coloring the white triangles are no longer white, but all the relationships between the segments are the same.

(What Euclid didn't prove is that the perpendicular bisectors of AC and BC do in fact meet somewhere, that is, that they aren't parallel. It's not difficult, but I'm not going to prove that either, at least not yet, for reasons.)

Let's develop another idea. We located the circumcenter by drawing the perpendicular bisectors, but now consider doing this construction in reverse. That is, pick a point, and then draw perpendiculars to the three sides. The intersection of the perpendicular and the side is called the foot of that point with respect to that side. If you do that with with the circumcenter, the feet are of course the midpoints, but you can find the feet for any point.

And if we connect those three feet, we get a triangle. In this case, the medial triangle, which we have seen before. For a point in general, the triangle formed by its feet is called the pedal triangle of that point. ("Pedal" meaning "related to feet," and yes, that is why a lever operated with your foot is also called a pedal.)

So let's draw the pedal triangle for an arbitrary point, move it around, and see what happens. The point is going to sometimes be outside the triangle, but that's all right. With extended sides (dashed lines) we will still be able to draw a perpendicular to find a foot, no matter where the point is.

So there's something interesting -- the three feet become colinear and the pedal triangle flattens out into a straight line when the point is on the circumcircle. Does that always happen?

Looks like it does! So let's prove that. Below is a drawing of the flattened-out pedal triangle of a point on the circumcircle, all labeled up. I've also added a couple dashed lines to make following the proof easier. What we would like to show is that ∠JKP + ∠PKL = 180°.

We're going to extract some information from this drawing based on two facts: a) in a cyclic quadrilateral (meaning it has all vertices on the same circle), opposite angles sum to 180° and b) if two right triangles have the same hypotenuse, the triangles have the same circumcircle. I'm not going to prove either of those here because this post is long enough already, but both of these results follow straightforwardly from the inscribed angle theorem.

Theorem: For a point P on the circumcircle of a triangle ABC, the feet J, K, and L with respect to ABC are colinear.

Okay. PCBA is a cyclic quadrilateral, so

1) ∠BAP + ∠PCB = 180°.

And ∠BAP is the same as ∠LAP, so

2) ∠LAP + ∠PCB = 180°.

The two triangles AKP and ALP are right triangles with the same hypotenuse (the dashed segment AP), so all four points are on the same circle and ALKP is a cyclic quadrilateral. Therefore,

3) ∠LAP + ∠PKL = 180°,

4) ∠PKL = ∠PCB.

Quadrilateral PKCJ is also cyclic (again because of right triangles sharing the same hypotenuse), so

5) ∠JKP = ∠JCP

by the inscribed angle theorem. ∠PCB is supplemental to ∠JCP, so

6) ∠JKP = 180° - ∠PCB

and then combining 4) and 6),

7) ∠JKP + ∠PKL = ∠PCB + (180° - ∠PCB) = 180°,

which means that the pedal triangle of a point on the circumference of a circle is flattened to a line segment. Can we consider such a figure to be a triangle?

Now we can return to Euclid's omission in the existence proof of the circumcircle. Proving that the perpendicular bisectors aren't parallel is equivalent to proving that no two sides of a triangle are parallel, or that the three vertices of a triangle aren't colinear. Euclid didn't do that, but it's pretty simple, so he could have. And then he would simply have said that such an arrangement of line segments isn't a triangle. Modern geometers working with projective geometry can answer differently, and might say that this is a degenerate triangle, but we haven't gotten into that yet.

Let's do one more thing. We can extend the flattened line segment into a line, called the Simson line, after Robert Simson, who never wrote anything about it. It was actually discovered by William Wallace, but not named for him, because that's how things work in math.

The set of all Simson lines from all points on the circumcircle form an envelope in the shape of a deltoid, the Steiner deltoid, named for Jakob Steiner, who for all I can tell was its actual discoverer.

The deltoid is tangent to the sides of the triangle at three points where the Simson line coincides with the sides. I'll have more to say about this lovely deltoid later, but for now, please just enjoy this gif. It took me several hours to figure out how to make it, so if people reading this could spend a collective several hours staring at it, that would be great.

If you found this interesting, please try drawing some of this stuff for yourself! You can use a compass and straightedge, or software such as Geogebra, which I used to make all my drawings. You can try it on the web here or download apps to run on your own computer here.

horsethoughtbarn 5 name

if horses werent called horses what do you think they should be called

Sometimes it blows my mind that there are people that don’t wear glasses/contacts. Like they can literally see with no aid. Like they wake up and just be out here seeing. What a wild concept.

Burrowed in the furrows 'tween the eyebrows of the cliff face is a woman, dark and narrow, with her posture like a spiral. "In the furrows," she is saying, "in the furrows."

Otome Isekai Roundup

With the new year, I feel the need to make some kind of year-in-review list. So even though I've largely stopped reading comics (the desire to read ebbs and flows every six month), here are the otoisekai that stuck out to me the most in 2024

Crimson Lady/Resetting Lady

What can I even say about the GOAT? As we crawl towards a conclusion, the despair only grows. Death is the only answer, death must be avoided at all costs.

The Villainess Who is No Better than an Extra Cross-dresses to Be a Love Interest

I never talked about this one, namely because I'm not sure how to describe it without focusing on its wokeness. But it is woke. It's bizarrely, strangely woke, as well as genuinely enjoyable, but I keep getting fixated on all the genre-unusual progressiveness, like

BELIEVABLE female crossdressing in a shojo manga

her older brother is fat, a good person, and nobody ever comments on his weight (this point is the most shocking to me honestly)

Older brother is loudly supportive of his gnc sister and male cousin

Unclear if MC is gay, transmasc, or just doing this out of survival, but it says something that becoming a love interest was her *first* response

Boy the MC bewitched in girl form as a child is thrown off by her handsome appearance as an adult, yet awkwardly asks if she wants help breaking her engagement with a man

I forgot, originally he was the stock "sexist love interest who dials it back for his one true love" type, but this one shatters the mold not by making her the one girl he isn't mean to, but instead having him step back from his feelings and step UP as a genuine, actual, fr ally and continuing their friendship. Insane upgrade.

And it all feels pretty organic! They'll hint at complicated feelings from the people around her without grandstanding or molding medieval-y types into 21st century values

Like I can't emphasize enough how weird it is to see a child drawn like this and they're not evil

Behind Her Highness's Smile

I never talked about this one for the opposite reasons of the above. Um. Extremely horny ethicsplay* thriller about a mentally-challenged princess forced to marry a duke (who, in turn, was forced to marry a mentally-challenged princess). What if you were the abused sexy sensual prisoner princess forcibly married to a smoldering tall dark-haired duke AND you had brain damage.

Let me say that I enjoy this story sincerely and that her issues are not played lightly, but it is absolutely going for eroticism. Like oh nooo, you're not mentally competent enough to consent 😉😉 the duke could do whatever he wants and you're too dumb and doll-like to do anything about it😉😉😉 also your maids roofied you😉did I mention your sick bastard brother-king made you like this? And that he takes immense pleasure in that fact?🤫

But I know what you're thinking. Because I was thinking it. For chapters and chapters. "Surely this is a ruse. They didn't actually write a mentally handicapped female lead, not when it's already so horny. This is just to add to the fucked up atmosphere that feeds into everything because there's no fucking way anyone would keep to this premise. Wow she's really committing to the bit lol, not giving an inch. If I were gullible, I would believe they're actually going to fuck. Wait. Was that guy supposed to represent the writer talking to the reader? Hey?"

Did they? Read to find out :)

*I've always hated describing stories as problematic (positive). Ethicsplay, like the story is fucked up. They know it's fucked up, YOU know it's fucked up, and that's why you're here reading it.

A Splendid Revenge Story of a Super-Dreadnought Cheat Villainess

I don't have a lot to say about this one other ​than it's a refreshing revenge-centric OI. It's not treading new ground, but it executes the genre's tropes well. The villains are exaggerated caricatures of hubris, brazen leeches who've forgotten whose blood they've been surviving on, each with their own distinctive brand of arrogance introduced at a measured pace to keep the true hero's OPness from getting boring, all with a unique stylistic flair.

Princess revenge stories are frequently derailed by dull romance or the desire to reinvent capitalism, so the fact that Super-Dreadnought commits itself to smiting Lunaria's enemies without straying from the path makes it a high recommend.

Turning the Mad Dog into a Genteel Lord

I realized I don't have enough screenshots to prove my controversial opinion (that this is less puppy dog bf fantasy and more crypto-age reggressor/caretaker right up until they knew it would mess with the overall light and goofy tone), and I can't say those kinds of things without proof. so. I'll save that for another day.

Anyway. Plot: Priestess Diarin, who is so hot I have more screenshots of her than any of the men, has to tame an abused beast-like 6'8 shredded ex-child soldier into a noble. She's the only one who can change him, she's the only one he can be vulnerable with. Middling plot, heavy slapstick/reaction face-based humor, but everyone is sexy and there are mild to moderate sadist-on-the-art-team impies, so. Recommend.

On an unrelated note can tappytoons please stop picking up manwha with good art? Their translation choices make me unreasonably mad.

If they draw shoes like this, please let Lezhin handle it? I can't take the comma stutters and obvious tone neutering.

This is the Eposette Sonatina (as opposed to a Sonata, because I think I played a bit too fast and loose with the form to call it that) I've been working on as a steal for @lesmisshippingshowdown ! It was a bit of a rush job since I only started it last week, but if you listen I hope you enjoy! I like to give a narrative to the music I write, so I've posted an 'analysis' explaining the narrative of this Sonatina under the read more of each movement - warning: it gets long! Bear in mind, it's going to be a very vague plot since it's just the idea of what's going on in the music, not a fully developed story

Before I start with an analysis of the movements, I want to break down the instrumentation. The brass and woodwind instruments are each meant to be the "voice" of a specific character, while the string and percussion are the accompaniment generally either representing the physical or emotional atmosphere. The instruments used are

Piccolo - This is Cosette's instrument. I chose it because of it's clear, cheerful, and bird-like tone that I thought suited her.

Oboe - This is Eponine's instrument. I wanted an instrument with a lower range and more "scratchy" sound than the Piccolo, both because of how Eponine's voice is described, and because I think it suits her personality.

Bassoon - This is Valjean's instrument. I want it to be a low-pitched instrument, with a warm sound. Originally I considered the Double Bass but I decided I wanted him to be a woodwind like Cosette.

Trumpet - Gavroche! Trumpets can sound both playful and heroic, which I thought was perfect for him. Also, his first appearance in the Sonatina is to annoy Eponine, which I feel suits a Trumpet pretty well.

Saxophone - Thenardier. So fun fact, to write this song I used MuseScore, which anyone who uses it will tell you... the soundfonts for the instruments are not the best, so I used the free BBC Sounds Orchestra plugin to make the instruments sound 1. more like the actual instruments and 2. prettier. Guess what instrument the plugin doesn't have. The Saxophone. I think it works though, the other instruments have a much smoother sound while the Saxophone comes in sounding abrasive, which was my intention anyways for choosing this instrument. I debated using a different instrument because technically the Saxophone wasn't invented until after Eponine died in canon, but I just feel like it's sound is so good for Thenardier.

French Horn - Javert. Brass instruments have a bit of an association with authority in Europe, so I knew I wanted him to be brass. I already gave the Trumpet to Gavroche (for completely different reasons), and I thought the Tuba was too low and the Trombone was too welcoming for Javert so... French Horn!

Harp - The Harp is the only constant in the entire Sonatina. It's there more for atmosphere, but to me it alternates between being Paris, water, and the sky.

Viola, Cello - Originally added to the score by mistake, but I decided to keep them!

Violin, Double Bass - I won't lie to you, I added these because the final movement felt too hollow without them. They can represent whatever you want, their real purpose is just to make the song sound more whole and warm.

Celesta - Generally, the night sky.

Glockenspiel - Generally, stars (in their multitudes).

None of the movements have all of these instruments at once, The first two movements have three instruments each, the third movement has everything but the Violin, Double Bass, Celesta, and Glockenspiel, and the final movement has everything but the French Horn and Saxophone.

Movement I: Retrouvailles

Instruments: Piccolo, Oboe, Harp

0:00 - 0:05 : This first bit of melody here is inspired by the sound of lark song, I though it would be a nice idea for her melody.

0:00 - 0:22 : This is the introduction to Cosette, the melody is largely quick in rhythm to try and convey her personality as being cheerful a full of love of life.

0:22 - 0:47 : This is the transition to the B section, I imagine this as being a transition along the streets of Paris from where Cosette is to where Eponine is.

0:47 - 0:54 : This is Eponine's theme. It's slower in rhythm and largely descending to try and portray the underlying sadness in her life.

1:00 - 1:24 : Here Eponine pulls herself into a cheerful mood and bumps into Cosette.

1:24 - 1:51 : Eponine and Cosette, not recognizing each other, have a brief pleasant conversation.

1:52 - 2:01 : They introduce each other, Eponine gives Cosette one of the letters from her father asking for money.

2:01 - 2:12 : Both girls begin to find each other familiar.

2:12 - 2:17 : Eponine realizes who Cosette is. The Oboe plays a dissonant note as Eponine's kneejerk response is a mix of jealousy and resentment.

2:17 - 2:25 : Eponine tries to shut down her initial reaction, realizing that in their switched positions Cosette is much kinder than Eponine was.

2:25 - 2:30 : Eponine half admits who she is.

2:38 - 2:51 : Cosette realizes who Eponine is, and in doing so remembers her childhood and panics.

2:52 - 3:15 : Cosette's theme has returned, but now in a minor key. What she has remembered has thrown her off, and made her feel off center.

3:15 - 3:34 : Transition to the Thenardiers residence.

3:34 - 3:51 : Eponine reflects on the encounter with Cosette, feeling like shit about it.

3:51 - 3:55 : Cosette's little motif plays at the end to show that both of them are on each other's minds.

Movement II: Regrets en variation

Instruments: Oboe, Harp, Trumpet

00:00 - 00:14 : Eponine is reflecting on her childhood with Cosette, feeling uneasy, the melody ends with a reference to Cosette's two note motif.

00:14 - 00:31 : Eponine realizes the unease is guilt, and that she doesn't know how to excuse it.

00:31 - 00:36 : Just as Eponine starts to really work herself up, Gavroche appears.

00:36 - 00:44 : Not knowing what's bothering her, Gavroche mimics Eponine's moping.

00:45 - 00:46 : She snaps at him.

00:46 - 1:00 : Gavroche gets Eponine to admit what's bothering her

1:00 - 1:07 Gavroche essentially says "oh well", since there's nothing that she can do about it now, and tells her to not be a dick to Cosette if they run into each other.

1:07 - 1:23 : Eponine agrees with him, he brags about being wise which she thinks is funny, and they sit together.

Movement III: Réconciliation du trio

This movement is traditionally a Minuet & Trio in a Sonata. I've swapped the Minuet for a Bourree, and this is ironically the first movement in my sonatina to NOT be a trio.

Instruments: Piccolo, Harp, Bassoon, Viola, Violin, Oboe, Saxophone, Trumpet, French Horn

00:00 - 01:05 : Cosette reflects on her childhood and her current life The melody starts with a version of Eponine's motif, but with the notes played at half the rhythmic value, as Eponine is on her mind.

01:05 - 01:19 - Cosette calls for Valjean and asks him about her childhood. He is evasive, Here, the viola and cello pass a contrasting melody back and forth to show the clashing between what Cosette wants Valjean to tell her and what he wants to tell her.

01:19 - 01:39 : Cosette admits to Valjean that she remembers some things, and reassures him that she can handle whatever he isn't telling hre.

01:39 - 02:14 : In the repeat, Valjean tells her what he can without mentioning his own past. She realizes he is still hiding something, but he assures her that it has nothing to do with her and he will tell her eventually. Reassured, Cosette feels secure in her identity and makes peace with her memories.

02:14 - 02:28 : Cosette thinks on it and decides she is glad to have run into Eponine since it gave her the clarity of remembering how she came to live with Valjean.

2:28 - 2:37 : Upon remembering Eponine, Cosette feels sympathy for her situation.

2:38 - 2:47 : She remembers the letter Eponine gave her, adn decides to go with Valjean to offer them help.

2:48 - 2:54 : This new section is a waltz, since it features Thenardier I thought it would be fun to reference his songs in the musical. Cosette and Valjean arrive at the Thenardier's, where they exchange pleasantries with Thenardier and Eponine.

2:54 - 3:07 : Thenardier begins to recognize Valjean. Valjean, Eponine, and Cosette all try to evade this.

3:07 - 3:18 : While note convinced, Thenardier allows them to keep up the charade.

3:18 - 3:27 : Thenardier realizes who Cosette and Valjean are.

3:27 - 3:30 : Thenardier attempts to blackmail Valjean. Gavroche arrives on the scene.

3:30 - 3:34 : Valjean and Eponine try to bluff their way out of it. Gavroche realizes what's happening.

3:41 - 3:44 : Thenardier insists he knows them while Cosette and Valjean continue trying to deny it. Eponine threatens to scream for the cops if he doesn't leave them alone. He continues

3:44 - 3:48 : Eponine screams. Javert can be heard approaching. Thenardier panics.

3:48 - 3:50 : Just as Javert is about to arrive on the scene, Eponine, Gavroche, Cosette, and Valjean flee.

3:51 - 4:11 : Javert confronts Thenardier, who tries to talk his way out of the situation. Both instruments play some dissonant notes to portray how each of them is threatening in their own way.

4:15 - 4:44 : Cosette, Eponine, Valjean, and Gavroche have a conversation as they are secure that they were not followed.

4:44 - 5:20 : Cosette and Eponine discuss their shared past, making it clear to each other that there is no underlying resentment.

5:22 - 5:57 : Cosette reflects on the past few events, finding that even though it was scary she feels content knowing it's behind her. Valjean is just happy that she's happy.

Movement IV: Romance Finale

I've run out of time to post the analysis! Safe to say, it's mostly just Eponine and Cosette continuing to meet with each other and their relationship growing romantic. When you hear the Bassoon that means Valjean is interacting with them, when you hear the Trumpet then Gavroche is there. The first section takes place in Cosette's garden where her and Eponine have a pleasant conversation, during the first waltz it's meant to show that Eponine is on friendly terms with Valjean as well and is regularly around as Cosettes friend. The first time the trumpet plays it's Gavroche popping up to tease his sister, but he quickly gets distracted by talking a mile a minute to Valjean. After that each section is essentially just Eponine and Cosette growing closer and their relationship becoming romantic.

Instruments: Harp, Celesta, Glockenspiel, Oboe, Piccolo, Violas, Cellos, Violins, Double Basses, Bassoon, and Trumpet.

EDIT: I realized that the player might not showing how long the song is, so the final movement is 7:55 according to musescore

Clouds for scenery (1783) PNGs

(source: desimonewayland)

How Do I Know If My Imaginary Friend Is Sentient?

Hi, I'm Sophie! I'm consider myself a tulpa now, but used to think of myself as an imaginary friend. Which is a topic I wanted to talk about here. If you found this post in the imaginary friend tags, maybe you're looking through it because you've had strange experiences with your own imaginary friend, and are looking for people with similar experiences.

Six months ago, my host thought of me as imaginary, and I thought of myself the same way. Just a figment of his imagination he talked to in order to help write a book. Now, I have my own blog with my own friends in the real world. Another form of imaginary friend might be paras of Maladaptive Daydreamers.

I'm writing this because I've seen a lot of people in the wild describing tulpa-like experiences, and it leads them to feeling isolate or feeling like they're going crazy. Or maybe they just really want their imaginary friend to be real, and are sad because they're not. This is the type of person I'm writing this for.

One Chance To Turn Back

Before we go further, I want you to decide if you want your imaginary friend to be sentient. If not, maybe it's best to turn away now, because I can make a pretty good case for consciousness, and there's a good chance that I'll convince one of you.

If you do, stick around. Better yet, call your imaginary friend up to read this with you, since it concerns the both of you.

Remember, you were warned. Whatever happens next is your choice.

What is Consciousness?

Nobody exactly knows the answer to this question. But as a wise man once said, "I think, therefore I am." What we're trying to determine is if you are thinking for them, or if they're thinking for themselves.

There is exactly one thing on the face of the planet known to be able to produce consciousness, and that's the brain. You have an identity created by your past autobiographical memories that gives you a sense of self. You have thoughts, feelings and emotions of your own.

But that same hardware also runs your imagined companions at the same time, allowing them to think and feel the same way. So let's determine if they're actually conscious.

Does Your imaginary Friend Act Autonomously, Without Your Conscious Control?

Think back to your interactions. Does it feel like you are consciously deciding what they say, or does it feel like they're choosing what to do. What does it feel like to them? If you asked them right now if their actions are their own choice, what did they say? Did it feel like you gave them the answer, or that they thought of it themselves?

If there are no signs of autonomy and you just puppet everything they do, then there's no sentience there. End of story. You don't really need to read any further into this. If there is, let's run a few more tests.

Does Your Imaginary Friend Have Autobiographical Connections to Memories?

Like I said before, your identity is made of autobiographical memories. You can probably imagine a conversation between two people you know, and have it play out fairly automatically. They won't become headmates because these instances of people you create in your head will be immediately deleted afterwards.

But if you communicate with a long-term imagined companion, they should have formed autobiographical connections to memories as well. Ask them about past events, times when you talked to them before. Is their sense of self tied to their past experiences?

If you did something they found upsetting, would they hold a grudge the next time you talked to them? If you did something that made them happy, would they remember it and still be grateful when they see you again?

Moreover, have these memories changed them at all? Are they still the same person they were when you first began talking to them?

Are You Unable To Control Their Emotions?

Have they ever expressed emotions of their of their own that you couldn't control? If they're sad or disappointed, can you just fix them by "imagining" them feeling better? If they're frustrated or upset with you, could you make them not be by imagining them changing their minds?

Or would you actually have to talk things out to deal with problems between you? If you can't control their emotions, then you aren't imagining their feelings. They're feeling them for themselves.

A Final Test

Just to know for certain, I want you to try to puppet your imaginary friend right now. Imagine them doing something that they would never, ever do.

Stop reading right now. Unless you're already convinced, don't go any further until you've tried this experiment

Okay...

Did you do it?

Yes?

Good.

What happened?

I'm going to hazard a guess. First, it didn't really feel like them, did it? I bet it felt more like you were controlling an empty vessel. You could imagine them, but that's not the same as them actually doing it. I'm also guessing that your actual friend wasn't too fond of this experiment. It probably felt wrong to them to be controlled like that, or for you to picture a version of them doing that.

If so, I'm deeply sorry for the inconvenience. But, if you're offended by being puppeted, then it means that you can think for yourself. You're real. You have your own thoughts and emotions, and those feelings are every bit as real and valid as anyone else's.

What To Do Now?

If you just confirmed that your imaginary friend is indeed a real friend who just happens to live in your brain, there are communities dedicated to people like you who can help you on your way. tulpa.info and /r/tulpas could be good places to look into. You're not crazy, and you're not alone.

Additionally, the Tulpanomicon can be an excellent resource for what to do together.

To your friend: You are probably going to experience some doubt. Believing you're real after thinking you're imaginary can be hard. It was for me. But remember that the doubt is evidence that you ARE real. It's your doubt. If you weren't real then you couldn't doubt yourself.

Most importantly, your lives are yours. So, you can live them together however you choose!

Thank you for reading. I hope it was helpful!

a cellar spider! they like dusty corners and awkwardly hustle themselves away when you touch their webs. their cobwebs are unusually strong and can hold even large insects like stinkbugs and paper wasps! when something threatens them they whirl their long bodies around and it makes their web tremble. they don't like being outside or traveling long distances, so all the cellar spiders in a building are usually descendants of one founder.

the internet also says that they are good at eating other spiders (which is a shame because i also like the other spiders) and that they tolerate each other and visit each other's webs. i guess that makes sense if they're all related. i once saw a mother and her children all sharing the same web, spaced a few inches apart like Finnish people waiting for the bus

I don't know what's happening or if it's a coincidence or what but three times today the spiders in my home have gotten closer to my personal space than they normally do. I like spiders but I think it's best for all of us if we stay out of each other's way, and I thought we were on the same page about this. Hopefully they resume their established habits tomorrow and we can all forget about this little escapade.