You just keep on trying, until you run out of cake.

Yesterday, I wrote:

Well, the power just went out, so it's time for me to pack up my Mac and head out to a cafe with WiFi where I can work on my novel in front of people and get this posted. The weird thing is, while it's likely going to take an hour at least from the time I finish writing this paragraph until it actually posts on the internet, there is no perceived delay from whoever reads this, because as far as you're concerned, the post didn't exist until it was published, though it already existed for me.

Um. Yeah. I'm sure someone who's actually studied physics is going to knock me around for that, but since my knowledge of the field is limited to what I've picked up on my own, it's a fun thought exercise.

Okay, little post, go sit in an eigenstate for the nice people.

Reader Gevmage says:

Your analogy is reasonable. The post existed on your laptop while you drove to the coffee shop, in a state such that it was stable but not portable. Once you got to the coffee shop, by connecting to the internet, you promoted it to an energy state where it could slide easily through the intertubes to our screens.

Since quantum mechanics describes ONLY the behavior of the very small, it has problems when extended directly to the macroscopic (which the idea of Shroedinger's cat is an illustration). You extended the notion as well as it could be.

The eigenvalue then is just a scalar logical value indicating if the post is visible to the world. Every eigenvalue has to have a corresponding operator; the operator is a complicated set of tests of whether or not if you point our browser at, you get a certain character string that's in the post.

Why yes, I am procrastinating, why do you ask? πŸ˜€

Even though I don't understand the math behind quantum physics, I have a good enough grasp of the theory behind quantum physics to allow me to follow along when the math is discussed. Put another way: I know enough French and Spanish to put together what someone is telling me, but not enough to actually sit down and compose a letter in that language.

I'm sure I've just oversimplified the whole thing, and insulted a lot of actual scientists and mathematicians, so let me apologize for that before I continue, because I think I'm about to make it even worse.

I was easily bored as a kid. I wasn't athletic, strong or coordinated, but I was smart and I loved to read. I still enjoyed playing tag, hide and seek, and riding bikes, but none of that stuff satisfied me the same way that exploring imagined worlds in my mind did. Those imagined worlds were usually delivered in the form of Science Fiction and Fantasy books, within D&D modules, and occasionally created (or spun off from existing imagined worlds) using action figures. (I guess it's no surprise, then, that I make my living and found my place in life using my imagination.)

I always loved exploring strange new worlds in books and magazines (Dear Asimov's, I never thought it would happen to me, but …) and there was even a time in my late teens when I actively sought out all the weird conspiracy, occult, UFO and supernatural stuff I could find (I truly despise that crap today) because even though I knew it was bullshit, it was yet another weird and fantastic imagined world to explore.

As I wrote in an old Things I Love post, it was the book Hyperspace that fundamentally changed my worldview:

[S]omeone (I think it was my brother) suggested that I read A Brief History of Time. I picked it up, read it in just a couple of days, and realized that my life could be divided into before I read it, and after I read it. On my next trip to the bookstore, I went straight to the science section, and looked for something – anything – to continue my education.

My eyes fell on a book with an interesting cover, and a provocative title: Hyperspace: A scientific odyssey through parallel universes, time warps, and the 10th dimension. It was written by a guy called Michio Kaku. I pulled it off the shelf, and after just a few pages, I was hooked.

There's a story in Hyperspace, right at the beginning, that I'm going to paraphrase. It's the story that grabbed my attention, captured my imagination, and fundamentally altered the way I thought about the nature of existence. I already had "before and after" with A Brief History of Time, and when I got to the end of this story, I had "before and after I read about the fish scientists." The story goes something like this:

In San Francisco, there's this botanical garden, and near the entrance there is a pond that's filled with koi fish. Dr. Kaku describes standing there, looking at the fish one day, and wondering what it would be like if the fish had a society as complex and advanced as our own, but the whole thing was confined to the pond, and they had no idea that there was a whole other world just beyond the surface of the water. In the fish world, there were fish scientists, and if a human were to pluck one of them from the pond, show it our world, and return it to the pond, it would go back to the other fish scientists and say, "Guys! You're never going to believe this. I was just doing my thing, and suddenly, this mysterious force pulled me from our world and showed me another, where the creatures don't need gills to breathe, and walk on two legs!"

The other scientists would look at it, and ask it how it got to this new world, but it wouldn't be able to explain it. They'd want the scientist to recreate it, but it wouldn't be able to. The fish scientist would know, however, that the other world was there, and that there was something just as complex as life in the pond on the other side of some mysterious barrier that they couldn't seem to penetrate.

I'm sure I've mangled the story, but that's essentially what I remember from it. I thought, "Well, shit, if there could be a world like that in the pond, maybe we are in something else's pond!" I didn't know if it was possible, I didn't know if it was just science fiction, but I didn't care. It was this incredible possibility, and my world opened up again. I felt like I'd been granted membership in a secret society. I devoured the book, and I began to think about the nature of existence in ways that I'd never even considered before. When I finally read Flatland a few years later, I was blown away that Abbot had written essentially the same story a hundred years earlier, in 1884, and I was thrilled that I could actually understand it.

My elementary school teachers were real good at putting the fear of God into us kids, but they were just horrible at teaching us math. I tried and tried, but I never understood it, and "you have to learn this because you have to learn it" wasn't the type of inspiration that worked for me. Even today, I'm not very good at math, never having found that teacher who could translate it into something I could actually use and appreciate. 

Growing up, I was a creative kid, an imaginative kid, and while I loved reading and learning about scientists and mathematicians, I never had a teacher or tutor who could help teenage me understand their work the way I understood their lives. (NB: My tutor while I was on Star Trek, Marion, who took me through most of high school, did everything she could to help me get excited about math, but to borrow from a parable: that ground in my brain had never been cultivated, and it just wasn't fertile enough to bear fruit.)

My lack of mathematical ability held me back in science, and it prevented me from ever studying physics or astronomy at anything exceeding the "for dummies" level. Here's a sad and embarrassing truth: I still can't sit down and develop equations for things, I struggle to calculate simple problems that my kids can do in their heads (they were taught math in a fundamentally different way than I was) and few things make me feel as stupid and frustrated as a simple algebra problem.

But when I sit down to read books like Hyperspace, articles about the LHC, anything my friend Phil Plait writes, or comments like the one I quoted above, I understand what they're talking about. I get excited, and take a look at a world that seems fantastic and imagined, but is actually real and right here.

I seem to have wandered away from the reason I sat down to write this post, so let me try to bring it all back together: I love exploring fantastic worlds that only exist in books and my imagination. But I also I love exploring the real world, which is so amazing, it just seems imagined.

(I once read a story about this for an audiobook. I forget the title, but it was about a kid who wanted to leave Earth with a dimension-hopping guy to explore the universe, and the dimension-hopping guy tells him that he shouldn't leave Earth for parts unknown until he really explores all the wonderful and incredible things that Earth has to offer, because due to the laws of dimension-hopping, it's a one-way trip. I wonder if that's still in print? I'd love to listen to it.)

I still wish I had a better understanding of the science and math that makes understanding and exploring the most fantastic parts of our real world possible, but until I do, I'm happy I have a pocket phrase book and a tourist map to help me get around a little bit.

88 thoughts on “You just keep on trying, until you run out of cake.”

  1. You absolutely *must* sit down and read Elizier Yudkowsky’s Quantum Physics sequence.
    It’s very low-math (only one of the posts has anything significant, and it’s not necessary to understand that one to get the rest), but EY is *very* eloquent and persuasive in describing just wtf quantum physics is, from a modern physicists perspective.
    He’s also staunchly in the Many-Worlds camp (like most theoretical physicists), so it’s a very interesting romp through something that you don’t get from your standard pop-science articles.
    There’s nothing mysterious or weird or hard to understand about quantum physics. It’s all very simple and easy to grasp the concepts, if you just keep from convincing yourself that it *must* be weird and confusing. The way scientists thought about quantum physics *was* weird and confusing at first, which is why it was wrong.

  2. Two excellent math books; Of Men and Numbers by Jean Muir. Opened my eyes. And then, A Tour of the Calculus by David Berlinski. These are written in a way that make you smack your forehead and shout, “I get it! Why didn’t they teach it this way in school?”

  3. Dude, I know.
    I learned to read at age 3, and devoured books my whole childhood and further on. I love science type stuff, all kinds of discovery channel goodness, all that stuff. I’m not stupid. I do high tech things all the time. Math leaves me stuttering. It’s like that part didn’t develop, or because I am good at copy editing, spelling and language, the equation side of my brain isn’t the dominant. I can pass algebra, but I can’t retain the information. It’s like it just isn’t there. I can’t do math in my head beyond simple calculations. It’s frustrating, but I guess that’s how my brain works.
    I wish I could absorb those kinds of calculations I see on discovery science, like I can absorb words without a blink. My memory is nearly photographic sometimes. I can even remember numbers without effort. I just can’t manipulate them.
    But it’s like looking for an onion in my fridge when I don’t have any. Looking harder won’t make an onion magically appear. It just isn’t there.
    I get it.

  4. Wow, for the first time, I don’t feel like an ass about my lack of math skill. I had crap math teachers for the most part, up to high school where my choices were “take the class with the drunk, or the bigot”.
    I LOVE the ideas and concepts in science and physics and all of it, but I struggle at the basics in math, which has never made trying to learn programming easy either.
    Seriously, thank you for posting this, it makes me feel alot less inadequate about it.

  5. Awesome post, as usual, Sir Wil. I too struggle with math past a certain point (mine’s a little farther along than yours, but still…). Just an FYI (and I tweeted this too), the story you read for the audiobook was “Why i Left Harry’s All-Night Hamburgers” by Lawrence Watt-Evans. I remember listening to that while vacuuming the floors at my first job, clerk at a used bookstore. Good times, good times.

  6. I hate to add to the pile. I’m fairly proficient at math and science (I’ve got an ME degree), but I’m much better at grasping concepts than applying them. This is why I loved Fabric of the Cosmos by Brian Green. It’s heady, but not too much.
    I had some great teachers in high school and college that helped foster my curiosity, but they also proved I had some sort of aptitude for math. I should probably go back and thank them at some point.
    As for marveling at the real world; I actually still marvel at “mundane” things such as bridges, airplanes, some buildings, and most heavy equipment. Sitting back to realize the amount of ingenuity and effort involved in creating them still boggles my mind.

  7. I suck at math, and always have. The one year I had a good enthusiastic math teacher I got a B. Once. The rest of that year was C.
    My company works with statistical models, and it’s my job to explain how they work to laymen. I am good at this because I *don’t* get math. If I could do it, then I’d explain it the way math people do that non-math people don’t get. I can understand how the calculations work, but couldn’t do the math behind them. Therefor, I can explain what a weighted moving average does and how the inverse log of such-and-such has this kind of an effect, but couldn’t tell you what that looks like on paper.
    Its all about turning the negative into a positive :)

  8. Part of the problem is the way math is taught- by rote. One plus one is two, two plus two is four, five minus two is three, three times four is BORED ALREADY! Very seldom do teachers use practical applications of mathematical principles to illustrate both the methodology and usefulness of the particular principles being demonstrated. This is one reason that so many children have trouble with fractions, for example, and how to add and subtract them (not to mention multiply and divide)– yet many of these same children would INSTINCTIVELY know they were getting screwed over if their sibling got 3/8th’s of a pizza and they only got 1/4th…

  9. Math IS hard you know.
    For the most part, we get taught math by folks who don’t really get math themselves. So all they do is use the teacher’s edition of the textbook and make us memorize rules, and we become formula-plugger-iners. Hard to break the cycle since our teachers were taught this way too. Folks good at math do not generally become school teachers. They did the math and figured out that teachers just don’t make that much money for the time invested.

  10. I have my copy of “Hyperspace” lying next to me, and I even started to take notes while reading. It’s so much more interesting than what I actually do at university (English/American Studies undergrad).
    It bugged me when I wrote (or thought of) a science-fiction story that uses some more higher advanced stuff than I’ve learned in high school/saw on television, and I couldn’t explain within the story the science,now it’s at least a “dumbed down” version πŸ˜‰ But I also like do further reading. (” Elizier Yudkowsky’s Quantum Physics sequence” sounds interesting.)

  11. And while Gevmage is correct that Shroedinger’s cat is an illustration of quantum physics using a broader analogy, it is not a macroscopic expansion, as the deciding or acting factor is usually described as the movement of a quantum particle (which, of course, is impossible to measure, therefore rendering it a thought exercise). Shroedinger’s cat is used to illustrate the concept of superposition, which is counter to the Multiverse or Many Worlds theory.

  12. I know you don’t want to hear about how good at math or science someone else is, and if someone gave you the choice of (a) being taught a new way now to approach an algebra equation or (b) being shot in the leg, you’d probably choose the latter, but I thought it was worth mentioning that my mathematical ability actually fostered my interest in the more fantastical/science-fictional/chimerical parts of the world. Granted, I was blessed with knowledgeable and enthusiastic teachers, and I hail from a completely different plane of the universe than a lot of people (I attended a math/science high school, went to college at 15, mastered calculus-based physics at 16). I’ll never forget my first algebra lesson: “The equal sign is the universe, and the universe demands what? Balance.”

  13. If only all students could be taught math by Project SEED methods, there wouldn’t be anyone left who could say “I suck at math.” If anyone has any of the right connections to help get this four-decade old, proven program noticed more, it would be a good thing.
    I teach algebra to college students, and I tell them right off that they’re not “allowed” to say that they’re bad at math. I don’t believe in that. As you said, Wil, it’s just a matter of not having had the right teachers. Project SEED shows that (most) anyone can do math.

  14. If you want an absolutely fantastic different way to learn about physics and this kind of stuff, I strongly recommend the Science of Discworld books by Terry Pratchett. I admit the comedy is undeniably British, but being British myself, that just makes it all the much better!

  15. The cool thing is that for all of this stuff to become the explanations for the real world, someone had to have the imagination to look for it. The true pioneers in the world are the ones who combine not only the imagination of the writers of the world, but the ability of the scientists of the world. Most of the truly wonderful things that have been created or discovered are a combination of two great minds. Being a dwarf standing on the shoulders of giants does not diminish the beauty of the newly-sighted discovery.

  16. Yep, my math and science skills suck beans too! I have always been one for using the imagination…remember the little boy in The Neverending Story from 1984??? Well, that’s me. Give me a book and it comes alive. That is why I loved Stand By Me so much. You guys went on a mission, which was something I always was doing when I was a Also, when reading a book, you can imagine it the way you want to, unlike a movie that has it set up for you.
    Your writing shows how creative you are, and gives frumpy people like me a glimpse of hope:) Hey, who knows, your books might make it to movie status one day..they are THAT good!!
    What was that you told Chris in Stand By Me…”you can do anything you want man” (if I am remembering the quote correctly)…well that is so true. Your passion is writing and here you are. mug arrived today and I LOVE it!! See, you can do or make anything you want, just have to try!! Best wishes Wil:)

  17. This post spoke to me in two ways. One, I can’t do math. I can understand mathematical principles and theories but when it comes to working with the actual numbers, I invariably mess it up. I think part of it is that as a kid I was never inspired by numbers. Words I loved. Words I understood and enjoyed.
    Numbers, not at all.
    My experience, when talking about this with other people, is that the world is made up of number people and word people and a very small minority who deeply understand and capably deal with both.
    Secondly, your discussion of other worlds and exploring what “might be”, even if it isn’t, totally struck a chord for me. I’ve always loved stories, doesn’t matter what shape they take, what they’re about or who is telling them. I love that if I take a moment to think about them they always reveal something to me about my life, the world I live in and/or how I understand both of these phenomena.
    My favourite stories, and the ones that have meant the most to me over the years, are almost all stories about the possibility of impossible things. These stories allow me to create the connections, to think about how the story relates to the world I know, and to interpret the material in a more personal and involved manner; they challenged me and encouraged my inclination to explore and play with ideas.
    A prime example of authors who do this well, and whom I thoroughly enjoy reading, is Neil Gaiman. I love the way his novels take “the real world” and twist it just slightly, offering us a glimpse at what it would be like if some of the things we take for granted were not actually what we understood them to be.
    To end of this ridiculously long response (perhaps there is such a thing as enjoying words too much), I’d like to toss out a Shaw quote that seems appropriate: β€œYou see things; and you say, ‘Why?’ But I dream things that never were; and I say, ‘Why not?’”
    Thanks Wil, for the inspiration to reflect and the opportunity to express!

  18. As a math teacher and someone who loves math, I don’t think learning by rote is necessarily a bad thing. Most students understand what addition and multiplication are. At that point memorizing the tables brings another level of understanding and helps with the next level.

  19. Wil, I have to say that your post brought back all sorts of memories for me. You spoke of experiences that sounded all too familiar. I thought, for years, that I just didn’t get maths and never would. Like you I loved science but was held back by my poor ability in maths that even my world class tutor couldn’t really help. Our stories take a different turn though. When I grew up a little (21) I went back to maths and suddenly my brain was able to get all the things I struggled with in school and I studied until I got into degree level maths and then a year in I hit a brick wall – My brain: Sorry dude, no further! Me: But I wanna! My Brain: Nope.
    In retrospect I’m grateful for the path I have taken. I’m sure everyone here will agree with me that we’re extraordinarily grateful that your life (and its limitations) has taken you to this time and place. You are a source of an inspiration that’s hard to fully measure. If you had gotten ‘it’ back then you’d no doubt be a great physicist/mathematician and we would have been robbed of an exceptional and inspirational writer!
    Where the hell did we get the idea that we had to be good at everything? More so, where did we get the idea that we should be able to do everything?! (Sorry for blabbing on but like I said, the post brought up a lot of stuff for me.)
    p.s. Math is often taught by those who excelled at it in school and college. It really needs to be taught by those that struggled with it. I taught maths for a couple of years and took tremendous pleasure from the joy my students who “couldn’t do maths” took from the discovery that they in fact could.

  20. Well, no matter the teaching method, some people do suck at math, due to a condition known as dyscalcula. In dyslexia, the order of letters in words gets scrambled in the head; in dyscalcula the same thing happens with numbers. Nothing to do with intelligence, just perception.
    That link for the mp3 of “Why I Left Harry’s All-Night Hamburgers” just gave me a 404, but I did find a bibliography, for those who still read actual words on paper… :) (Copy and paste – my html-fu is weak.)

  21. I wish I had time to contribute more, but as a new vocational teacher teaching technology, I am having a similar experience every day. Not that I can explain it, but one of the new teacher things we’re being taught is something called “multiple intelligences” which I know I will find a way to explain the way my head is wired.

  22. I absolutely adored Flatland. As brilliant a thought-stretcher as I’ve ever read.
    I have similar difficulties with maths, leading to a very fun situation in physics classes where I’d talk to my teacher about the shape of the universe and how antimatter and black holes work, while the rest of the class learned about batteries.
    I did terribly on my exam, by the way. Turns out you actually needed to know about batteries. C’est la vie!

  23. Hey Wil,
    Thanks for quoting me! Pretty cool; some friends from college found out before I did. One of them texted me about it; I’ve been working all afternoon (other than some brief bouts of procrastinating), and didn’t know until I got a message about.
    There are some pretty cool comments here.
    Oh, and it sucks about the whole math teacher thing. I had reasonable math teachers, and as I recall, and mostly very good science teachers (explains why I went into physics, I guess). I had some pretty horrid english teachers in Jr. High. I had a couple of really good english teachers in high school, but the damage was done. I married someone who’s now an english professor, so I’ve gotten over my problems with it, but it’ll never be a good subject for me.
    Take care,
    Craig Steffen

  24. First – the real world only exists out of imagination. All is a creation of thought. All is a harmonic vibration that can be counted by beats. The fact that you can imagine means that you can create, and that is what life is about. Your big capacity for imagination equates to power in the real world if you know how to direct and believe in it accordingly.
    Second- you are already very aware of math in your daily life and seem to be in sync with it. Math is just about time, timing. You listen to music and you make it yourself(which you aught to do more of!). Music is nothing more than vibration and math. It has to have the right timing or it does not sound good. You are also very much into comedy, others and your own. Comedy is all about timing, or the joke fails, so it boils down to math too. Even sex needs to be in the right timing for it to be really good. Living in the moment requires one to be on time, on their mark, so that opportunity can flow, which are all mathamatical equations of possibility. To live in the eternal now, you need pull yourself out of time and live in the eye of the storm, to count yourself in. No past, No future. Wait, there is a future, but it is one you create by counting your blessings!
    Third, you need not understand complex math equations to understand the spiritual implications that quantum physics shows us. You understand the principals then extrapolate with your imagination. This helps in understanding universal laws that can put you in control of your life. I am pretty sure you are very aware of many things, yet you may be looking for spiritual answers in math because you need that scientific proof. Math is a pure science, and if you follow science far enough you find the spiritual truths of the universe! I have found many answers by using my vivid imagination combined with personal experience to extrapolate evidence from the basics I know from science.
    Fourth – you are a humanist, not a scientist, so don’t fret at what you think you lack compared to others. You are an entertainer and an every day super hero. Your writing reaches out to the masses just as your performances. When you are done recaping your life and telling us about you(as you need to do to find yourself)…you will then be teaching us about bigger things you have learned about life, as a humanist. You most likey do not need to know that info if it does not come easily to you. Stop pressuring yourself to be perfect. You already are, in your own way, th4e way you were created to be. Everyone has a different job to do, and you can not be everything all the time. Focus on your strengths!
    Five- you already know math like I said, but you feel it and internalize everyday, instead of having to figure out the equations out side of yourself, you know math in a place with out words or numbers.
    To help quicken your ability to add: group together numbers to make 10’s or 100’s quickly in your mind. Then add those numbers together. Example: 7, 33, 55, 6, 24. The quick way to add would be 7+33=40 so you carry the four, then add 24+6=30. forget the zeros until the end. 4+3=7. 5+7=12 then add the zero or left over number, in this case 5. 120+5 so the answer is 125. It goes really quickly in your head when you group numbers into easy to work with piles, then sew them together. This is the base.
    I hope this helps.
    I too used my imagination to live in other worlds as a child using my stuffed animals to represent the people who were in my super hero team. As I got older, I became squashed by a “reality” that seemed far too hellish for me to accept so I peeled off layers of conditioning to reveal that the imagined world in my head was far better than the one I see before my eyes, so I started to believe in it again. Guess what? All my dreams started coming true and I realized I AM a super hero leader and rock star like I knew as a child. Ya see I knew then what my soul purpose is and was acting things out in my imagination that would one day come true. Everything comes full circle. I know that “My Reality” is better than the “reality” that is shoved down my throught by the society. I also know it is my duty to change “reality” in the perceptions of others so that we can make the world better than it is. Imagination is the key to manifesting anything you want or need. If you can see it in your mind’s eye, and you believe it is real, it will be. Only exception to the law is that you cannot impose your will onto another, but there will always be someone willing to play that character for you if needed.
    Math is simple. You know the rules. You win the game. Such is life.
    I can see Wil, that you have much more potential to be explored, and that you have always been on track with the storyline of your life.
    Now I have to ask you, what do you think the biggest problem in the world is? And what can you personally do about it, now?

  25. The fish story reminds me of the moment my friend and I came to the same conclusion, but we phrased it like this: What if said universe was inside an atom in another universes’ toilet bowl?
    The Toilet Bowl Theory was intended to be hyperbolic irreverence. I mean, for so many years there’s been those that have maintained our innate greatness (center of the universe and the music of the spheres type rot), when in fact the nature of the universe(s) may well be that our next door neighbour is a piece of feces.
    I’ve always liked the idea of pwning human arrogance.

  26. Wil, as a holder of a completely disused physics degree, I have to say that you didn’t do so badly as you think. You did better than those hosers that got caught with their pants down during the infamous Sokal affair.
    At any rate, there’s a limit to describing physics without the awful math. Richard Feynman once said (paraphrasing here) that math is the language of nature, and that scientists have little choice but to use math to “converse” as it were. (He also allegedly said that, “to understand physics, all one needs to do is understand the simple harmonic oscillator”, a refrain I repeatedly heard throughout my college education)
    But that’s if you want to work as a scientist (or engineer). For laypeople a conceptual understanding is great, and it’s something that most people don’t even possess. Quantum mechanics is voodoo crazy talk to most people and usually gets used to peddle pseudo-scientific scams. So are both of Einstein’s big theories, which get twisted into bad philosophies and bad science fiction. And t-shirts and coffee mugs with “E=mc2″.
    I think Wil gets a +5 to his Math skill when he’s playing D&D. I mean, ok, quantum mechanics is tough, sure, sure, but try calculating THAC0 or deciphering grappling rules.

  27. I think a love of reading is more valuable than any math you might have been taught (or not as the case may be) in school. It seems like too much education is focused more on rote learning and less on exploration. I tend to go where the wind takes me with books and what inspires me now might not inspire me 6 months from now and so on. A quick perusal of my bookshelf yields “The Radicalism of the American Revolution” by Gordon S Wood, “Three Roads to Quantum Gravity” by Lee Smolin (I’d recommend this one since you’re interested in physics) and “Bright’s Old English Grammar and Reader” (don’t ask lol). So it’s a bit…eclectic. I guess what I’m driving at though is that reading all of those eclectic books has taught me a lot more than I learned in 8 years of college education earning a degree I don’t even use.

  28. I know how you feel. My parents spent a lot of time and money on math tutors, to no avail. My brain just goes into pause mode or something. I can balance a checkbook but don’t ask me to double a recipe because I can’t do the fractions.
    In college, I wrote a thesis on “Einstein’s Special and General Theories of Relativity as Shown in Three Works of Science Fiction.” Meaning, I totally understood Relativity and could write a thesis on it’s use in a literary context, but I could never, ever in my wildest dreams do the math.
    I even kept the note card the physics professor made for me so I could remember the facts of time dilation. It had squiggles and Windtalker code and hieroglyphics and magical runes on it. I swear.

  29. According to the “many worlds interpretation” of quantum mechanics, there was also a version of your house that didn’t lose power and where you posted your blog entry from home. Had you not talked about the power going out in your house, we the readers would have never known about that. The state of our experience would have been unchanged and from our perspective you would exist in an eigenstate in which the power went out and the power did not go out (much as you are today for me).
    However, since you wrote about the power going out, you’ve collapsed that eigenstate into one in which the power did indeed go out for you from the perspective of all of your readers (although there is suppose there is still the eigenstate where the power didn’t go out and you lied about it, but I think that is a very small space).
    You are also in an eigenstate where you did and did not win the lottery today (and so am I). I’m trying to figure out a way to collapse that eigenstate into “I won the lottery” for you in the hopes that it will increase the chance of the eigenstate collapsing in the same way from my perspective. Preferrably I would like to do this without falling into madness.
    BTW, I won the lottery next week.

  30. Thanks JonS253 for mentioning Dyscalculia. I just nodded through most of what Wil posted because it sounded so familiar to me. In High School, my freshmen class took standardized tests that told us how we ranked individually compared to all the other High School freshmen in the state. in Reading/Comprehension I was in the top 10 percentile in the state, in Math, I was in the bottom 90. I require a lot of personalized attention when I’m learning anything math related, and unfortunately no matter how hard I try (and I tried very hard in school) even if I learned stuff to the point of being able to explain it to someone else, it would soon disappear like I had never learned it. Point is, some brains aren’t designed to grasp math easily, and some have no trouble at all.

  31. I don’t normally pimp websites that sell stuff, but if you want to get into math, check out the Joy of Mathemathics dvd available at The Teaching Company – . It’s a very entertaining introduction to some of the amazing things you can do with math. I’ve been watching it with my 8 and 13-year-old kids and while some of it’s over their heads, they get most of the concepts very quickly, and we’ve have none of the usual “math is boring” complaints.
    But don’t pay full price – the prices look outrageous, but they seem to put everything on sale once a month or so for much more reasonable cost.

  32. I had an utterly flattening experience in freshman college “Calculus for Scientists & Engineers” or whatever it was. I struggled with pure math, but excelled in physics courses using that same math (I get it when I can play with it, but not when I just have to think about it, I guess?).
    Anyway, I get to that first calc class and the professor is a dude who hadn’t taught below graduate-level math for a long time, but got stuck doing intro calc due to staff needs. He was an older dude who would come in exactly on time, never looking up at the huge classroom & sat his briefcase down, turning around to immediately start scrawling on the chalkboards and muttering fantastic incantations.
    I remember being completely blown away and confused as I wrote down everything he wrote and tried to keep up, until he would then turn around briefly and say “and therefore, obviously…” and turned back around to continue muttering & scrawling.
    “Obviously” what??!?? Most of the class muttered and looked around uneasily to see if they were the only ones totally baffled. Well, I was one of the totally baffled and unfortunately, I think it was possibly that singular experience that veered me away from engineering as my childhood-long ambition and toward what ended up still being very rewarding: music. Weird, I suppose.
    Now, I know tons of science things, programming & such, but I’m all self-taught. I really wish I had found a way to make it through those early calculus years to see where that life could have lead.
    (I’m also from back when “pre-calculus” was only barely showing up in high schools. I had geometry, trig. & algebra, but no calculus before college… ugh. That was brutal!)
    Anyway… why am I typing all this here?? Thanks for sharing again, Wil. Wonderful, as always. :)

  33. To this day (I’m 32), I refuse to play Yatzee because I hate adding up all the dice.
    That said, D&D has helped me improve my simple math skills somewhat. I just wish I had discovered it in elementary school instead of this past February.

  34. “Being a dwarf standing on the shoulders of giants does not diminish the beauty of the newly-sighted discovery.”
    I adore that line.
    I was fair to good at math and science in school, but nothing too advanced. Then again, for the most part, I had good teachers. Then I made the mistake of teaching my grade 4 math to my younger brother, and he skipped Kindergarten and was hailed as the ‘smart one’ πŸ˜›
    Anyhoo, I too get the basic theory behind things but have problems when you come down to the actual numbers. Recursion especially…I make good infinite loops that crash the computer I’m trying to program on.

  35. All students studying quantum mechanics fall into the instrumentalist interpretation camp while they are studying it. It does have a catchy slogan: “Shut up and calculate”

  36. I really do think that a lot of kids in our generation were totally handed the short end of the straw when it came to Math teachers when we were kids, which subsequently held us back in Science as well. I identified with a lot of what you had to say in your post because I remember just hating the shit out of Math because I just couldn’t understand what the hell I was being “taught” but I absolutely loved Science. I remember wanting so badly to be able to learn more about Astronomy in particular, which requires the kind of Mathematical knowledge that was way beyond my scope of comprehension and there’s a lot of physics/astrophysics involved with it as well.
    My parents spent A LOT of money on my education, even though we were basically just basically a lower middle class income family. We just scraping by, actually because let’s face it, I live in Philadelphia, and as much as I love my city, the school system here sucks. Plus there was the whole being raised in the Irish Catholic tradition, and my parents just took it on faith (much like they took their religion) that Catholic schools were superior to public school, which they are to some extent, but not in the ways that they thought. There are actually a few really great public schools in our school system, but they pick students by a lottery system that is a little bit more than unfair in my opinion. So I went to Catholic school, just as my parents did and their parents did before them. My Math teachers in grade school didn’t even understand what they were teaching us, and my parent’s couldn’t help me because they had no fucking idea what an equation was. And I suffered horribly in Math as a result.
    I was fortunate enough to have a really great Algebra teacher in my first year of High School, which opened up the door for me to place high enough to get into the more advanced Math and Science courses my Sophomore year, but the problem with that was the teacher I drew for Math that year was burned out, about to retire and could not give a fuck less if we learned anything in his class or not. Basically, if you showed up for class, he passed you. There was no motivation or any levels of enthusiasm involved. He did NOT hold his A’s. So naturally, by my Junior year, I was so in over my head that I barely even passed Math and didn’t place high enough on my test scores to get into the more advanced Science classes, which at the time, I took very personally against myself. I just thought that I was too stupid to keep up and completely gave up trying by that point. Which really sucks, because the High School that I attended has one of the best Trigonometry and Calculus teachers in the entire Country, Sister Alice Hess, who is a wonderful Math teacher who has won a lot of impressive awards, including the National Tandy Technology Scholar Award and The Presidential Award for Math Teaching. She’s been featured in several major Math publications, as well as national public exposure in USA Today. If I had drawn her as a teacher instead of Mr. Burnout Don’t Give a Fuck, I don’t even want to think about it. It’s too depressing.

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