Just Stimming…

A land we can share (a place I can map)

A Fifth Is Two Sine Curves

with 60 comments

(This post could be seen as a self-narrating zoo-exhibit with bonus spot-the-theory-of-mind. I hope you’ll take it as a follow-up to The Obsessive Joy Of Autism, as equally about the experiences of visual processing impairments and synesthesia as about ~autism, and as a case study in the inadequacy of traditional verbal language. If I’d been taught earlier that experiences which exist independent of words are still meaningful and sufficient, I never would have had to write this.)

(This whole essay represents a dozen years of heartache, a fractured self-image knit back together, and the entire reason why I will never, ever talk about the instinctive simplicity of video editing.)

(Note: as is typical of my writings, pieces are rarely finished in the same day they are started. The voice lesson I refer to as “today” is in reality long past; in fact, due to circumstances regrettably beyond my control, it turned out to be my last. I have been unable to further explore the discovery my voice teacher and I made, and it aches.)

(This entire piece is written in a voice I don’t very much care for. My apologies.)

(I can either keep apologizing in parentheses for a lifetime, or just tell it to you.)

A fifth is two sine curves, and this is the most beautiful thing.

I’ve had a dozen years of classical musical training, and I’ve been playing with calculus for about the same amount of time. I don’t talk about either of these things with much frequency. I don’t like to sing in front of people, and I have a passionate love affair with math but hated and barely passed my classes in high school. I drink up geometry videos on youtube, and once a week I go to my voice teacher’s house and sing for the best hour of the week, and these things are secrets. Very few people know how important music and math are to me, and that’s been a deliberate choice on my part.

I don’t talk about the most sacred things, because it’s the fastest way to destroy them.

I have an intense and embodied relationship with music. Music is a lot like people, and songs are linguistic and therefore social exercises. Music teases and tells and remembers and reflects and transforms and encodes and transmits. I experience music kinesthetically, emotionally, and intimately. It is shattering.

I know a lot about music. I hate talking about it, because the things I know aren’t the same as the things you know.

My left hand doesn’t have enough coordination to permit me to play any instruments. I can, and do, sing, and I’ve spent 12 years learning to do so with surgical precision. I can’t sight-sing–I can peel apart the layers of a piece for theory, no problem, but identifying pitch and tempo and dynamic and a note’s place in the overall piece, and integrating those elements, factoring in timbre and placement, and singing them, in realtime, is simply not possible with my visual processing impairments. I rely on an ear I’ve spent years training–if there’s one other singer, or a pianist accompanying, I can do a passable imitation of first-time sight-singing even pieces I’ve never heard before.

Ever since I first joined an (auditioned, highly-selective, then-prestigious) youth choir at age eight, I’ve known that I do music wrong. At first, that took the form of being shamed for moving when I sang–music shouldn’t be a physical, embodied, tactile experience. In later years, my inability to process visually rapidly enough to sight-sing, and my difficulty holding a harmony, made rehearsal a living hell. Yet I was never kicked out, because I could still sing circles around 2/3 of the other singers, and it wasn’t that I couldn’t harmonize, just that I might sing any one of a range of acceptable harmonies and not necessarily the one I was arbitrarily assigned (or the one the composer had written,) and as long as I didn’t talk about it, no one knew I couldn’t sight-sing. (I did, of course, talk about it; lying didn’t occur to me until later years.) I trained my ear, led the 1st sopranos because the melodic options are necessarily restricted and usually sensical, kept my joy at things I had the wrong words for to myself, and kept singing.

(My life goes on
in endless song
how can I keep from singing?)

It destroyed me. I loved this, I was so good at it, it felt good and right and perfect, and yet any attempts to communicate about this were miserable failures. Singing is the only time I ever feel at home in my body, and yet I felt like a fraud; sure I could learn a new song faster than anyone using only my ear, but I couldn’t sight-sing. Clearly this was some elaborate hoax I’d engineered, clearly I didn’t have any real aptitude, and clearly, my decision not to pursue college or career in music or performance was the only ethical option.

Despite this, despite the guilt and shame and confusion, I’ve kept going to weekly lessons. It’s an hour, just me and my teacher and a piano, and as we pull songs apart and test what my throat can do, the songs resonate between my ribs. It is, essentially, an hour of breathing exercises, so it’s the most effective therapy I’ve ever had. And I’ve kept going, and today, finally, after 12 years, we figured it out.

There were signs. The music teacher at my high school had almost worked it out; he’d play two notes, and I’d hear a third, and not every student could. He talked about harmonics and melodic structure; I listened, and adored him, but had trouble talking to him. With my voice teacher, I complained that the standard system of music notation was nonsensical, bearing no correspondence to the way music actually worked, and relied on a flagrant disregard for basic arithmetic. I struggled with the idea that a fourth is supposed to sound “smaller” than a fifth, and though I could sing any note back perfectly, I couldn’t tell you which notes were higher or lower. None of the language used to communicate about music made any kind of sense to me. The spatial metaphors simply would not map. I had my own rich, dynamic, embodied and visiospatial experience of music, I could feel and see the music move, and sheet music couldn’t come close.

I’ll tell you what my teacher and I learned today, but first I need to give away my other secret: math.

My history with mathematics is, if possible, even more tortured and rapturous and bewildering than my relationship with music. As a small child, I was in love with arithmetic; my mental calculation abilities are noted on my earliest evaluations (and dismissed, of course, as splinter skills.) One of my earliest memories is of not being able to explain to a concerned teacher why 2+3=5. “Because it is,” I said. “And it’s beautiful. It just fits.” Manipulatives were meaningless for me–my eyes couldn’t process them easily, and they didn’t bear any relation to the ladders and scales of numbers in my head. I simply had to close my eyes, and think of an equation, and I would feel myself swing from number to number, landing effortlessly and securely on the answer. Easier than walking.

(There’s a hint to the eventual reveal, there.)

While I had some small troubles learning the language for arithmetic (especially for fractions, which are fun and clever enough as pointless rituals but beautiful when you realize that they actually signify multiplication and division, that you are performing meta math,) mathematics was an easy joy. Note, please, that I am talking about the art of mathematics, not the drivel and formulas we’re drilled on in school. Mathematics really is an art, and it’s inherently playful. It’s a game of “what if” and “how can I.” And when I was eight years old (and still now,) what I wanted most to figure out was how I could model, and therefore predict, events in the world around me. In particular, I was fascinated by the rate at which raindrops crossed and accumulated on my car window as my mom drove me to therapy.

So I invented the fundamental theorem of calculus.

I didn’t know I was doing this at the time, of course. I didn’t know what algebra was yet; if I’d heard of calculus, I thought it was about calculators, which I found woefully inefficient. I’d never heard of Liebnitz, and Newton had only been hit on the head by a terrifying apple, as far as I knew. I didn’t use the greek alphabet or sigma notation; I didn’t use any notation at all. I just ran some dimensional transformations in my head, checked my model for accuracy, and had a nice visual to keep myself comforted when my hands needed to be still.

Eight years later, my AP Calculus/Physics class was asked to prove the relationship between derivatives and integrals, and I got up and drew the model, and not a single one of my classmates understood. After a moment of studying what I did, Mr. Morris said, “spoiler alert, Julia just skipped to the end of the lesson and proved the fundamental theorem of calculus.”

I can’t draw it for you now; I lost the image, along with some of my more unusual human-calculator prowess, when my psychiatrist put me on the anti-psych medication regimen that ended in me dropping out of college. But I could then, and before that day, I hadn’t realized that my classmates couldn’t see that basic, innate relationship, the reason why calculus is beautiful enough to ache. I didn’t have the language for it, had never even heard of the fundamental theorem until my teacher told me that was what I’d done. I’d just been amusing myself with models and transformations, when I should have been paying attention in class.

See, that’s the thing. I struggled in math class from Algebra 1 on. I never actually took the AP calculus exam–Mr. Morris thought I’d do fine, but since I was technically auditing his class, I didn’t want to try and sit for it. And this is where the agony comes in.

Much like music, the way I experience and represent mathematics cognitively is fundamentally different from the conventional language we are taught for it. With arithmetic, this difference only really caused difficulty when new terms were being introduced. But 2+3 is always 5, and I had enough innate understanding and motivation to preserver through even the most ridiculous name choices.

This all fell apart when I got to algebra. It’s not that I lacked understanding–I’d been solving for the missing number since I was nine, and the only hardship I’d had there was, again, in comprehending the linguistic absurdity of mixing letters and numbers and shifting the missing piece to the left side of the equation. As soon as I got over that, I immediately started attempting to teach the game to anyone around me, including my four-year-old sister. Algebra wasn’t the issue. The way we represented it, modeled it, and talked about it? That was a nightmare.

Graphs on a cartesian plane have a lot of meaning for me–for another purpose (clue.) They also bear absolutely no relation to the kinesthetic and visual models I see when I craft algebraic equations. Zero. None. And I couldn’t articulate this in high school, anymore than I could make myself care about pitch or slope whether the equation came in point-slope or some other form. I didn’t understand why we were talking about graphs at all. It wasn’t until algebra 2 that someone explained to me that all of our equations were supposed to be models for those lines.

I was enraged.

I still am, thinking about it. What a stupid waste of my time. Who the fuck cared about lines? I wanted to know how to model the age distribution of my peers around me and how it shifted in relation to me as we moved through the grades, how to fit equilateral triangles with a side length of 2in inside a hexagon with 6in sides as efficiently as possible, how to predict prime numbers. Why on earth would I make an equation for a line I couldn’t even make my hands draw reliably half the time?I wouldn’t! This possibility had never occurred to me! I had better things to do!

So I didn’t care about graphs. Later, in college, my math major friend would teach me the theory behind linear algebra in half an hour, and I would concede that graphs were pretty fucking intense, but in high school, all I knew was that I was being asked to humor, to indulge teachers who were never sure if I was a genius or in the wrong class in their fetish with graphs that my eyes, more often than not, couldn’t even process as a whole.

It did not go well.

There were parts of algebra, of course, that I loved. I enjoyed modeling numeric patterns (“series,” I was told, and “summations,” I just called it numbers) like 2n + 7, and there were moments when the graphs for these, or for my favorite exponents, lined up with the stacks of numbers I saw in my head, and the graph became, fleetingly, meaningful. (It was argued that graphs themselves were by definition simply visual models of numeric patterns, and therefore should have been my favorite thing. I defy anyone to look at something like THIS

graph of 2n + 7

and honestly tell me that they instinctively see either 2n + 7 or 9, 11, 13, 15, etc. in that.) Systems of equations were a game that made me laugh and resembled the way I’d play with numbers in my notebook margins when we were supposed to be caring about matrices. Matrices were for our calculators; I was a human calculator, insulted by their existence.

My first three algebra teachers understood none of this. I did well in algebra one, as long as I wasn’t asked to graph anything; as far as I was concerned, I was doing slightly fancier arithmetic and then humoring Mr. Morris by labeling things as he wished. Algebra 2 was all about graphing though, and it made me want to die–and now, in an exciting plot twist, the equations had gotten long enough, and the graphs complex enough, that my visual process started undermining me, scrambling letters and transposing numbers and fragmenting graphs, and with it, my grade. But I passed, by the skin of my teeth, and had a brief reprieve in geometry, and then got a better teacher for precalculus who, in the last two weeks of class, realized I had a language processing problem. We stayed after school one day and hacked enough accommodations that I could FINALLY start to use the conventional vocabulary and start training my eyes to read equations like stories again, the way 2+3=5 is, and then graph the story out accordingly. Just in time for the bonus unit on calculus.

I looked at a derivative for the first time, and my models and raindrops and joy came rushing back, and I was in heaven.

Derivatives and integrals made sense because the transformations they undergo are multi-dimensional, just as the ones I assign my models are. But I didn’t ace calculus. I took an introductory course at Stanford the summer before my senior year of high school and passed on sheer intuition despite missing 1/3 of the classes, but the first few tests I took in my AP class came back with failing grades.

My teacher and I worked it out. It was, as always, a visual processing issue: permitted to solve an equation on a white board, standing up, with more space than I could possibly use, colored markers, writing as large as I needed, and only one problem presented at a time, I could earn 100%. Give me the same test, after I’d already taken it on the whiteboard, but this time package it as a two-page test on an 8×11 inches sheet of paper, and I’d get a 40%.

It seemed easy enough to accommodate: let me take my tests on a whiteboard, with my teacher dictating each problem to me one at a time, and I could be the best in the class. The beauty of reasonable accommodation! But it wasn’t that easy; the teachers were working to contract in protest of their current salary, so my teacher couldn’t stay after school or come in early to test me. If I’d had an IEP I would have been protected, but my parents were told that students with IEPs weren’t permitted to take AP classes. The solution, the administration declared, was that I would audit the class. I could sit in on every class, do every lab and homework, receive no credit, have my motivation and self-esteem destroyed by a year of failing every test but doing any in-class problem on the board perfectly, teach my class the fundamental theorem of calculus but be humiliated every day by my inability to correctly read and copy equations off a sheet of paper, and everybody won.

I don’t remember much of the class. I was an anxious, humiliated, depressive mess, unable to concentrate, still haunted by graphs. It was a combined calculus/physics class: I loved the modeling, but my language processing made the word problems we were given for physics exhausting. There are bright memories, of course–drawing out the fundamental theorem, hacking labs, solving problems at the board, practicing integrals with Tommy for fun, tutoring a classmate over Facebook chat for a test that I failed with a record- breaking amount of transcription errors but she got an A+ on. But I hesitate to call myself mathematically inclined now, and that needlessly hellish year is why.

Math and music are some of the most sacred and meaningful things in the world to me. I don’t talk about them, because that requires a 12-year trauma history and interfacing with a language that treats these two things exactly opposite of how the should be.

(Do you know the secret, yet?)

This is what I learned, at the last music lesson I ever took: I see musical compositions as the graphs I spent years being tortured with perversions of, and I move through numbers like a song.

The spatial metaphors we traditionally use for music (notes are higher or lower; a second is a whole step, a third is two whole steps, etc.) fall apart for me not only because of their flagrant disregard for basic mathematics, but also because my primary concept of music lies in harmonics: in the spaces between tonic and supertonic, in the beats of the frequency of a given pitch, and all the different ways we can stretch and collapse and layer and color them. This is what I see, this is what I hear (and the two are, in this instance, the same,) every time music plays. Sheet music is as pale an imitation of this as a graph of y=3x is of the multiplication table. And yet, the transformations I drag my models through, the process of solving an equation (and I’ve never been much of one for solving, really; just give me a model and I’m happy, and maybe that was the problem with algebra all along,) is actually perfectly encapsulated by the language and metaphors musicians use to interpret sheet music.

And I just wish that once, at some point, just once during those long twelve years, someone said to me “this language isn’t working for you. Let’s find a new one.” Because then I could have told you, at eight years old, before I could even conjugate reliably or deviate from my scripts, that:

this is what C sounds like:

sine curve

this is what G sounds like:

sine curve

this is what a fifth sounds like:

two overlapping sine curves

and this, Mrs. Lowenthall, is why 2+3=5:

sheet music

Written by Julia

October 31, 2012 at 10:02 pm

60 Responses

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  1. yes. just yes. and thats all the words I have. just yes. thank you.

    E (The Third Glance)

    October 31, 2012 at 10:39 pm

  2. Wonderful. Thank you. If there is a way to help you back to voice lessons, please know that I, at least—a complete internet stranger—would gladly help.

  3. I am breathless. Speechless. (thank you.)

    Carolyn Ogburn

    October 31, 2012 at 10:54 pm


    Paula C. Durbin-Westby

    October 31, 2012 at 11:29 pm

  5. See if you had tried to tell me the formula for the lines I’d have no idea what you are talking about, but those lines make sense as soon as I translate it to movement.

    Also, lots of crying from me.

  6. Listening to the beats between two pitches. Very fun, very joyful. I used to tune organs. Loved listening to the sound waves. I can’t do all the math like you can, I could just hear the beats and could (and probably still can) hear 13 or so overtones given a starting pitch low enough and without a lot of what sounds like white noise in it. By saying “can’t do the math like you can” I mean I have a math learning disability, or I think I do. But I will have to think about that, since it could be that I am experiencing something mathematical in music. Your pictures of what C and G and a 5th sound like make sense to me but I am not sure why.

    Paula C. Durbin-Westby

    October 31, 2012 at 11:55 pm

  7. I taught myself to sing (somewhat) by recording my voice over and over and over until the recording sounded like what I wanted it to sound like. This was after a music teacher told me I was “too old” to train my voice. One of the many bad music experiences that I tried to turn around. I am very protective about what I share re: music, due to bullying at various times.

    Paula C. Durbin-Westby

    November 1, 2012 at 12:02 am

  8. Two things:

    1) Is not being able to sight sing a visual processing thing?!?!!?! My CP causes some interesting processing issues and I was NEVER EVER EVER able to sight sing, which is why doing NYSSMA terrified me, even though I loved singing in front of a judge and having them hear what I could do.

    2) “My parents were told students with IEPs couldn’t take AP classes” I’m sure you know this already but that is some FUCKED UP BULLSHIT. I had an IEP all throughout school and I took a shit-ton of AP classes, including 4 my senior year.

    Cara Liebowitz

    November 1, 2012 at 12:28 am

    • My son had an IEP and they wouldn’t let him take a language or even the tests for a regents diploma – they said people with IEPs can’t get regents diplomas. They surely didn’t let him take AP courses. Then agian they wouldn’t give him an ipad either because they said he would be different from teh other students and get bullied… now here we are ten years later and my youngest is in the same high school and ALL kids are issued an ipad – nothing is done from textbooks or on paper anymore. The public schools were a nightmare for us and I’m so glad that I took my son out at 16 and had him get his GED since he couldn’t get a regents anyway – figured, same diploma but less time for them to mess up my kid.


      December 30, 2017 at 10:22 am

  9. I understood very little of what you just wrote.
    Neither math or music I understand well.
    But thank you for describing how language put you in a place where you couldn’t access what you knew, not for the purposes of grades anyway.
    I am so sadend by what I’ve read here, but I am also moved by the poetry you experience in something I cannot see at all.


    November 1, 2012 at 12:44 am

  10. […] What does it mean to be a neurodiversity activist? We think that, among other things, it means to create spaces – virtual spaces, cultural spaces, and places in the world – where people of all neurological differences are accepted and valued. Sometimes it doesn’t mean anything more than to say “thank you” for someone’s honesty in sharing their story. Thank you, Julia. […]

  11. altho, considered neuro-typical,..(is there such a thing as normal? typical?) i could absolutely follow this…math to music, a bit of a synesthetic, numbers are music i hear, patterns in algebra are strains of symphony, and my favorite intervals are fifths!
    while i can sight read, it is like looking at a page of polynomial equations for me..
    i drove my math teachers nuts all through school with the way i got the right answers in my own shortcut ways. now my autistic daughter benefits, because i find rote memorisation of addition facts or the multiplication tables unnecessary to the relationships going on within a numerical phrase. (she is good at math and bad at memorising.
    thanks for sharing this.
    now i feel a bit less strange


    November 1, 2012 at 8:01 am

  12. wow. i’m blown away by how little i understand, while simultaneously being blown away by the beauty of this and how much it resonates. it makes so much sense. i’m going to reread this every once in a while and if/when i go into education i’ll continue to take it to heart and hopefully be able to give it to someone else.
    thank you.


    November 1, 2012 at 4:58 pm

  13. love the colors of synesthesia!


    November 1, 2012 at 10:56 pm

  14. Thank you for sharing this. Your efforts to communicate this, will help others. You are brave. Congratulations on your epiphany!


    November 2, 2012 at 1:37 am

    • Julia, there is an electronic analytic instrument called an oscilloscope that portrays pure tones exactly as you have illustrated. You can get it as an app for nearly any computing device.


      November 2, 2012 at 8:14 pm

  15. Julia, there is an electronic analytic instrument called an oscilloscope that portrays pure tones exactly as you have illustrated. You can get it as an app for nearly any computing device.


    November 2, 2012 at 8:16 pm

    • The oscilloscope view would be different to Julia’s diagrams. She shows the C and G as the same frequency but shifted along; in the oscilloscope, G does 3 cycles to every 2 of C’s (and a “fifth” is the frequency relationship 3:2, and a “fourth” the frequency relationship 4:3). G is halfway between C and the next C (on a log scale).

      I never understood music as a kid, but was good with maths; but when my friend explained this to me then it was like a light going off and everything else about music fell into place. I internalize a “fourth” and a “fifth” as the same interval but one is upside down.

      I don’t understand Julia’s diagrams but wish I did 🙂


      April 7, 2013 at 8:31 pm

  16. I have a problem because both those notes on the graph seem to be the same frequency but phase shifted. I would have expected a difference in frequency and summing the sinewaves would highlight overtones. But I’m not musical.


    November 6, 2012 at 6:42 am

  17. This’ll be really quick (HA HA HA!) because I have to go vote and buy a computer that actually WORKS, but you are not alone here. I have many of the same interesting quirks as you do, music-wise, including the ones that really stump professional musicians, like not being able to sight-read despite knowing how, grammatically, the sheet music works, and being completely unable to tell you which tone is higher or lower, but only whether they match or not. I tried to teach myself guitar once and found I couldn’t for the life of me tune the guitar to the output of an electronic tuner, because the waveforms didn’t match — but I have a sort of half-assed phonographic memory, and I would have been just fine if someone had let me know that it’s supposed to play the first few notes of “Also Sprach Zarathustra”. (I also snapped at quite a few people who tried to find out how I tuned the thing by ear, because just asking me to think about whether it’s too high or too low, or which way I was turning the peg, completely destroyed my ability to do goddamn ANYTHING with the instrument.)

    And I also have random math brilliance but fail math classes HARD. I did great when I was young and the school’s policy was to reward me for learning things by teaching me other things as fast as I could go, and didn’t much care how I worked problems mechanically as long as I got the right answer. After I was basically told I could take math classes that followed the standard pedagogy or not at all, I flunked things left and right, because they were boring as hell and didn’t at all match how I modeled things in my head. On the other hand, it’s made me a great tutor for people who are learning disabled in some way — because I think about a lot of things in a non-standard way, I come up with analogies in a lot of different sensory modes, and if I keep trying long enough I’ll eventually hit on one that makes sense to someone else.

    Out of curiosity, have you ever read any of the books by Richard Feynman? He was unquestionably brilliant, but had a knack for thinking about things in what his conventional colleagues considered puzzlingly weird ways. He tended to run models in his head that were visual or involved spatial motion — his story about the “fuzzy oranges” is pretty charming. He modeled people the same way, which may be of some use to you if you’re interested in finding out how other people’s theory-of-mind works, in an intellectual sort of way.

    Arabella Flynn

    November 6, 2012 at 1:02 pm

  18. Calculus IS achingly beautiful! That’s all I can say for now.



    November 15, 2012 at 9:17 pm

  19. Details not the same, and I don’t think I’m as good at it as you are, but this describes really well something I’ve been trying to explain to my friends forever about me and math. Somehow they got it more about music. Also I didn’t have as many problems in math class and I’m starting to realize I’m lucky. I had a really good handwriting tutor before I got to anything very visual in math that helped but work out a few general characteristics to convert everything to tactile. My biggest problems are still always notation, but I can at least get the data in to try to find the pattern, like solving a weird sort of code.

    Anyway, seriously thank you for writing this.


    November 17, 2012 at 2:15 am

  20. … [Trackback]…

    […] Informations on that Topic: juststimming.wordpress.com/2012/10/31/a-fifth-is-two-sine-curves/ […]…


    November 20, 2012 at 2:08 pm

  21. What a fascinating lesson! I never would have paired music or arithmetics together – because I am not skilled in either – but you’ve told the story of their relationship so beautifully!

    zoetic * epics

    November 21, 2012 at 9:52 am

  22. These are two things I would have never connected. What an interesting piece. Thank you for sharing.

    Jeremy Truitt

    November 21, 2012 at 10:04 am

  23. Absolutely stunning! I knew music and math were inextricably linked together but this is just pure magic.


    November 21, 2012 at 10:24 am

  24. Interesting post. I was not very good at music or math during high school. I never took any type of musical classes until my 10th grade year. I started with learning scales and quickly figured out where B flat and FFF were on the scale and on the instrument. But I absolutely could not understand how to read music. But i did know how to read a tape measure. Then one day it hit me like a ton of bricks….1 inch became whole notes. One quarter inch became quarter notes. One eighth inch became eighth notes. I’m still not good at reading complicated music but I can read the basic stuff.


    November 21, 2012 at 12:55 pm

  25. I to have a profound hatred for calculators. I was no fan of graphing either (I prefer my numbers in equations, not as a line with no value). And don’t get me started on graphing calculators. The only math class I ever failed was the result of 85% of the class being done with a graphing calculator. The thing cost more than my first car and sat like a large electronic paperweight in the bottom desk drawer for four years. I’m a math major in college, and I still cannot properly run a graphing calculator. It’s nice to meet others who love their numbers as much as I do!

    Notes From The Backseat

    November 21, 2012 at 2:43 pm

  26. This is incredible. I think you may have just helped me to decide what topic to base my Physics Pre-U investigation on. I too am fascinated by the link between maths and music and this has definitely persuaded me to look further into the science of harmonics!


    November 21, 2012 at 3:41 pm

  27. Yes! At last!


    November 21, 2012 at 5:24 pm

  28. Wow.
    I loved maths as a little kid, but nobody every told me it was maths.
    When I was three, we had an octagonal table at Kindergarten. I saw it and said “if it had more corners, it would be a circle”. It made sense to me without counting the corners or sides, because it was closer to a circle than a square table was. It just looked like a wonky circle to me.
    We used to play games with quadratic equations as well, but we didn’t acll them that. It was “I’m thinking of two numbers. If you add them together you get 11. If you multiply them, you get 24.” It was fun, and nothing whatsoever to do with school.
    Now, I sit at the back of the class with my friends, and chat. We have a good time, and draw funny pictures. Occasionally one of us takes notes. But of the three of us, we don’t need to listen, because we can just work things out in the exam. In year 8, there was a choice to take the year 9 paper, just to see what level you got. The last question was about simultaneous equations, and it was just so intuitive. You need to have one equation, and this is how you’re going to get it.
    I know this isn’t exactly what you were talking about, but this is what your post reminds me of.
    Thank you.


    November 21, 2012 at 5:25 pm

  29. I always tell my students that math and music are related, but I think you’ve explained it in terms I’ll never be able to dictate.

    Facetious Firecracker

    November 21, 2012 at 6:31 pm

  30. I never thought of cines in this manner before!


    November 21, 2012 at 9:41 pm

  31. What an amazing post. I am not musical, and I do well in mathematics but I know that I don’t understand it. This shows the side of things that I don’t have.


    November 21, 2012 at 9:59 pm

  32. Reblogged this on Oyia Brown.


    November 22, 2012 at 3:55 am

  33. i enjoyed this line – “I spent years being tortured with perversions of..”


    November 22, 2012 at 10:16 am

  34. This is an amazing read!!! Music is close to my heart. I also have many years in classical music.. Never had voice training though… And I can relate on so many more things you spoke about!! Keep it up!! Cheers 🙂

    Crystal Mitzi

    November 22, 2012 at 1:53 pm

  35. Reblogged this on Sunglasses & Raincoat.


    November 22, 2012 at 5:02 pm

  36. OMG! This is exactly how i see music – and, mathematics. Shapes and patterns. And writing, which is what I do the most of. I’d prefer music, I learned hands-on piano playing for many years, but I never really had the co-ordination. It may seem odd that writing is about shapes and patterns – and, for me, about the way they collide. The words, like Royal Schools notation, are merely an imperfect device for expressing what arrives as the inexpressible.

    Matthew Wright

    November 22, 2012 at 10:13 pm

  37. This is so inspirational! Things like this make me want to write music differently, to approach it in a different way, notate it differently and play it differently. Thank you!


    November 25, 2012 at 5:44 pm

  38. Hi; I found you via a Facebook link and simply *had* to come by and learn more. I’m autistic and proud, and am always happy to meet fellow autists and parents of autistic children (my son is profoundly autistic and I only just got my diagnosis recently – but I’ve always known).

    I’m really looking forward to reading more of your blog 🙂

    Missus Tribble

    January 13, 2013 at 10:35 pm

  39. hello julia.i get your very intertesting blog/ i am a adult with asperger syndrome. i can not work all so have m.e and lot health problems.i do take part in a lot lot research from universities.if you would like to ask me any thing please do.I AM WONDERING IF YOU MITE HELP ME… I WOULD VERY MUCH LIKE TOO GET A BLOG CALLED …ABNORMALDIVERSITY.. BY ETTINA.CANADA… I HAVE TRIED 3 TIMES ALL TIMES COME BACK..FAILED.. CAN YOU HELP ME PLEASE..my e.mail. markkent1962@hotmail.co.uk


    mark kent

    February 9, 2013 at 5:32 pm

  40. Integration is the inverse of differentiation. Right?


    March 27, 2013 at 11:01 am

  41. nordling- yes. That’s correct


    April 4, 2013 at 4:02 pm

  42. […] Another post I read is a beautifully crafted piece exploring synesthesia ( crossing of senses) in the author’s ability to visualize mathematical functions and music ,  giving rise to an inherently intuitive and enviable understanding of math , all the while unable to pursue an education in either because of her inability to process visual cues such as those found on sheet music or math exams at the level which most education establishments demand . She states that should there have been an alternative for her in taking exams – being dictated the problems on a bigger surface like a whiteboard, for example, to space out the stimulus, she would have been able to , but as it is, there are not enough provisions taken to support those with differing operating systems . […]

    The issues we’ve had with them are not the same (I’m just a tenor second,) but I hear these, and I feel them, and some of your notations for it even makes sense.
    And what they did. That is horrible.

    Alyssa (Yes, That Too)

    July 13, 2013 at 9:24 pm

  44. […] discovered via this post called "Quiet Hands". how can i not love her ?  – the way she talks about maths, seriously ! […]

  45. Aie, calculus and music, stop being so beautiful.

    If I could give you a lot of hugs, I would (especially as my friend and I both have the different-exam-provision thing). I think about both completely differently though – my head works in maths so I have to work twice as hard at everything that isn’t maths to understand it and like to think of things as mathematical puzzles. So I can explain it to you perfectly well in numbers or even with graphs, though I’m crap at visualisation (although the line thing is useful, I admit), but I find words more cumbersome to use. Plus I have the double whammy of synaesthesia and absolute pitch, so numbers and notes have taste and colour in my head (and it means my method of reading music doesn’t work for anyone else).

    I also physically felt those sine waves, which was odd…


    October 18, 2013 at 11:21 am

  46. I wish I knew you. We could have some amazing conversations about both music and math, which happen to be the two categories into which everything I love thinking and dreaming about fits.

    I have my own music theory, based on the mathematics of harmonics, which I use to invent my own keys — major, minor, harmonic minor, and double harmonic are just the beginning, and there are so many other flavors to be experienced — and which I also use to explain what chords fit where and why. (It’s a predictive theory, so I can also tell you with some degree of confidence what keys will sound good before I hear them, what notes can naturally act as tonics or root notes, which chords will sound harmonic, which chord transitions will sound natural, what keys will be implied by which chord progressions, etc., etc. Ask and I’ll tell you more.) Like you, I hear other notes in chords than just those that are being played. I also hear the chords that go with a melody, just from the melody alone. And when I hear a song, I keep hearing it mentally long long after it is over, even if I only heard a tiny piece of it. Sometimes just mentioning something associated with a song will make me hear it in my head.

    When I think about anything, it is in terms of math. Math came so naturally and automatically to me that my teachers would get on to me for not showing my work, but I couldn’t bear to because of the painful slowness of it; the answers were obvious to me, and how/why am I supposed to explain what should be obvious? I even understand English in terms of math. (It’s hard for me to understand how people don’t see the connection.)

    I love trying to understand how other people think, especially when it’s a unique perspective. I have a unique perspective on almost everything, but when I talk to most people, they all sound the same. They make the same assumptions and observations, and jump to the same conclusions. My mind goes in a different direction — not illogical or fragmented or anything like that, just striking out on its own to see truths and patterns that other people don’t grasp while ignoring many of the things they think are obvious. So when I read what you wrote here, I sat up with interest. Here is another mind that strikes out in its own direction, with its own insights. The value of a thought to me is proportional not only to its correctness, but to its uniqueness, and you sound like you are full of unique thoughts. You obviously have some real gems, surprising insights that come out of left field. Perhaps we could share…

    Aaron Hosford

    October 31, 2013 at 2:26 pm

  47. Hi Julia, I”m not very good at math. But your struggles with the language of music resonated with me. For me music is very intuitive. At least when it comes to my voice. Ever since I was little I could sign virtually anything I heard. The problem was when it came to physically playing it with my hands. I struggled for years as a kid simply to play a C major chord. When I finally figured it out, it felt as if the heaven had opened up. I can now play a simple accompaniment while I sing on the piano. But playing anything the requires hand independence is basically beyond me.

    As far as musical language is concerned, anything beyond a simple 7th chord and my mind goes blank. But here’s the thing, I can sit down at the piano and start improvising and the most amazing chords will come out, but I have no idea what they are theory wise. I can sort of figure them out if I stop and play each note of the chord one by one, but even then, it’s a struggle processing wise.


    November 20, 2013 at 11:48 pm

  48. Sheer brilliance!


    March 23, 2014 at 2:37 am

  49. I just found your blog tonight. I am moved by your honesty, yes… but it’s the clarity with which you describe your intensely personal viewpoint that has left me in tears. I am so thankful for first hand accounts like you have shared. As a mother, I am desperate to be of help and guidance in any way that I can. I am often left feeling incapable and fearful that I am not “enough” for my son (he is 5 years old and diagnosed on the spectrum last November). I look forward to hearing more about your experiences! You have blessed me more than you could know!

    Hayley McDaniel

    March 23, 2014 at 4:27 am

  50. I am not autistic, nor am I particularly brilliant at math or music. But I have been the weird kid in math class who annoyed the teacher by coming to the answer intuitively instead of doing it the “right” way.

    I’ve also been a teacher of students with learning differences–not really by training, I just happen to be someone who was good at school and happened to know brilliant “learning disabled” people who struggled with subjects I knew they were “smart enough” to grasp, and I became fascinated at a young age with how different people’s brains process things differently.

    Last year, I found myself making a living off of my interest in how people learn when I took on tutoring jobs after dropping out of graduate school. It was nothing special–I was doing SAT test prep for the most part, painfully dull. But the beautiful thing was that I was working one on one, and I got to spend time really trying to understand where the disconnects in understanding my students had came from. I had one student who was convinced she was “too dumb” for math, and who particularly struggled with geometry. For several sessions we circled the issue maddeningly, with me failing to grasp why she could articulate so many of the “rules” to me, but fail so miserably at using them to approach a novel problem.

    In one of our last sessions, the student mentioned off-hand that she has a vision problem that means she has never had normal depth perception. A few minutes of discussion, and everything fell into place: the conventional ways we draw 3-dimensional objects on paper were completely nonsensical to her, and over the years she had developed such an aversion to ANY math problem involving pictures. She’d also gotten into the habit of claiming to understand explanations from instructors despite being entirely lost any time certain types of language were used to describe physical relationships, because that language fundamentally failed to reflect how she saw/understood things.

    Basically, this student had major deficits in spatial reasoning related to a vision/visual processing issue, and not once in her entire educational career had someone taken the time to try and understand how SHE saw things. And instead, this brilliant, sweet, thoughtful student had been left to believe that she was dumb, and to close off huge areas of possibility for herself because she was clearly “too dumb to learn math”.

    In the brief amount of time I had left with her, I spent a lot of time reading about methods for teaching geometry to students with visual impairments, and together the student and I managed to come up with a few hacks to allow her to complete at least the simpler geometry problems on the SAT. But I desperately wish that I had been able to give her MORE, and that every student who experiences/learns differently could have teachers with the time, inclination, and training to reach them.


    April 4, 2014 at 5:24 pm

  51. Thank you for this.

    I sang “How Can I Keep From Singing” alone, at night, to stop being afraid.

    I took AP calculus and knew what mathematics really was about for the first time, and that I liked it.

    And other things; private play of reference and allusion, the way schedules and words are so much harder than they understand, learning slowly to be Autistic and proud.

    Thank you for this.


    February 8, 2015 at 12:57 pm

  52. Thank you for sharing this; that was amazing. As a fellow synesthete I understand where you’re coming from.

    Star Kwafie

    September 19, 2015 at 11:48 am

  53. This is so beautiful. Loved it.


    January 30, 2017 at 10:28 pm

  54. […] harder to not just fall through the cracks of the world. We’ve also experienced uniquely intense beauty and joy, as well as many of the common experiences and challenges of growing up that most […]

  55. Reblogged this on Autism Candles.

    Autism Candles

    April 2, 2021 at 2:29 pm

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