4 ms·

On behalf of my fellow English majors, may I just say: What?? I love Hacker News because it exposes me to a great deal of things like this. I intend to do as d

On behalf of my fellow English majors, may I just say: What?? I love Hacker News because it exposes me to a great deal of things like this. I intend to do as deep a dive I can muster into the provided lecture notes. But boy howdy, are certain topics I encounter here humbling. If I were fully honest with myself I would avoid a certain subset of the content on hn. Sometimes I think it only fuels my impostor syndrome.

noman-land 3y ago
Don't worry, I had the same reaction. But you're not an impostor for spending your time learning whatever it is you're learning instead of this.
- jahsome 3y ago
  My issue is, I seem to only ever be interested in learning the things I struggle with...
  - noman-land 3y ago
    Why bother learning things that are easy?
    - CoastalCoder 3y ago
      Some learning is for necessity, rather than for its own enjoyment.
    - jahsome 3y ago
      When it's somewhat irrelevant to focus on the hard things, which are more appealing, I find it's frustrating not being motivated to solve the more pressing, easier issues because they're not "fun"
      - zBard 3y ago
        True, but in some cases , it’s just a case of pedagogical mismatch . May I recommend https://www.scottaaronson.com/democritus/lec9.html https://www.scottaaronson.com/democritus/lec9.html ? I have cribbed from this endlessly when explaining quantum computing , and it’s certainly my goto talk for explaining quantum computing.
  - dclowd9901 3y ago
    I read your first comment and it could’ve easily been mine. Currently a software developer but I started off in journalism. I love, love, love learning but I feel like I have some… granite wall of impenetrability when it comes to quantum computing. I simply cannot figure it out. I’m a very adept person and a quick learner, but everything about quantum theory just leaves me feeling like a complete idiot.
    - jahsome 3y ago
      Heh, my degree is in journalism. It's been a weird ride, but I wouldn't trade it for the shiniest CS education.
1letterunixname 3y ago
Every new concept requires a mapping to metaphors and/or analogies. And when the mapping is mismatched between learner and author's content, elucidation hangs in the balance. Thus, the expertise of lecturers lies in expertise of public speaking coupled with mapping concepts to the intended audience. QC and general relativity are daunting topics that don't lend themselves well to short-form, self-paced content. These are topics that need foundational perquisites and subject matter experts to catechize. It would be like hopping out of a helicopter mid K2 without any training or acclimatization and expecting to summit. Start smaller and work your way up one step or idea at a time. :)
- jahsome 3y ago
  Pattern recognition and analogy are my secret weapons, for sure. I'm really only a good engineer because I'm good at organizing and communicating my thoughts. It's the only reason I've made it so far in my career -- definitely not any innate propensity for "hard" cs concepts. I faked it til I made it, and now I'm pretty darn good at it. I think in my particular case the concepts around quantum ____ are so abstract I'm unable to find anything to liken it to. It certainly doesn't help I lack any substantial background in mathematics. Hopefully one day I'll get there. Or maybe I'm already there and not there at the same time! Who knows!?
abdullahkhalids 3y ago
I am sure there are areas which you know a lot about, which I know nothing about. And conversely for every pair of people in the world. I spend plenty of my time dealing with my own imposter syndrome, often because there are many people in my own field who know far far more about it than I do. Peter Shor, the OP, for instance. But its fine. You do what enjoy and best at, and find satisfaction in doing it. That is the way to live.
currymj 3y ago
trying to elaborate on the OP a little by avoiding math terminology: part 1 here is essentially the idea of logic circuits. you can write these down in terms of large vectors of 0s and 1s, and operations transforming them as large matrices -- which is useful because it takes familiar ideas (to a CS student) and casts it using mathematical formalisms that are later required for weird quantum stuff. this could be unfamiliar if you haven't learned about matrix/vector multiplication. but ultimately it's just a different way of talking about combinations of AND/OR/NOT on truth values. part 2 just says, go from vectors of 0s and 1s to probabilities between 0 and 1. the "L1 norm" (aka Manhattan or taxicab distance) in this situation just means that all the values together have to sum up to 1, the way probabilities do. this includes part 1 as a special case, and extends it naturally. part 3 is indeed where the weird quantum stuff comes in. no easy explanation, you do have to get an idea of how complex numbers work. but again, the familiar logic circuits of part 1 are still a special case. the "L2 norm" for real numbers is just the regular straight-line distance -- I can't provide a good intuition for complex numbers though.
havnagiggle 3y ago
Here's a brief example paired to some of the nomenclature in the parent post: Linear algebra are equations that do not have exponential independent variables. For example (a,b,c,d,e) are constants: aw + bx + cy + dz = e. You won't find an x^2, z^3, etc. Everything is of order 1. "classical n-bit states are 2^n length binary vectors": Binary is 1's and 0's. A binary vector is a list of them where each entry is a particular dimension. 2-bit state vector will have 2^2 entries. <1, 0, 1, 1> is 2-bit state binary vector. "gates are 2^n x 2^n binary matrices": A matrix is a table of values that map one vector to another vector, i.e. a transformation. |a b| |c d| Is a 2x2 matrix. If the matrix is binary then a,b,c,d can only be the values 0 or 1. A matrix is just a condensed notation of a set of linear equations. Let's make a vec x (aka input) and vec Y (aka output) where subscripts indicate the dimension (entry) of the vector (list): vec x = <x_0, x_1, x_2, ...>, and vec Y = <y_0, y_1, y_2, ...>. If matrix A is the 2x2 matrix above, then vec x * matrix A = vec y is a set of two linear equations: a * x_0 + b * x_1 = y_0 c * x_0 + d * x_1 = y_1 The math is pretty easy if it is 1's and 0's everywhere. A 2-state vector and matrix will then be: <x_0, x_1, x_2, x_3> * |a b c d| = <y_0, y_1, y_2, y_3> |e f g h| |i j k l| |m n o p| (apologies the matrix is probably not going to render nicely, it is a 4x4). This is just the equations: a * x_0 + b * x_1 + c * x_2 + d * x_3 = y_0 e * x_0 + f * x_1 + g * x_2 + h * x_3 = y_1 i * x_0 + j * x_1 + k * x_2 + l * x_3 = y_2 m * x_0 + n * x_1 + o * x_2 + p * x_3 = y_3 A "gate" is a chain of transformations that result in some computation. For classic computation that's just binary. Most silicon chips are made of NAND gates: NOT(X AND Y). Most other gates can be created from combinations of NAND gates. For quantum computation this will not be just binary 1 and 0 as the output, hence... "Introduce probabilistic classical computation: Now the states/vectors have real entries in [0,1] and obey the L1 norm (the critical feature). Similarly, the gate matrices.": Now the entries in vectors and matrices are not just 0 and 1, but any real value between and including 0 and 1. This is important for statistics because it can represent the likelihood of something happening. 0% to 50% to 100% and everything in between. The L1 norm turns a vector of numbers into just one number. L1 is particularly easy: just add up the absolute value of all numbers (all numbers are positive here anyways). ||vec x|| = x_0 + x_1 + x_2 + ... "Now, argue that quantum computing just requires the same linear algebriac structure but we (1) work over the complex number field, (2) norm is L2.": Now entries in the vectors are complex numbers. Complex numbers are a pair of real numbers that have a different multiplication transformation. Complex numbers have the form z = <z_0, z_1>. Adding complex vec e and vec g is straight forward, add the pairs of components: <e_0 + g_0, e_1 + g_1>. Multiplication of complex vec e * complex vec g is <e_0g_0 - e_1g_1, e_0g_1 + e_1g_0>. This is also just linear algebra. Complex numbers are these 2 dimensional vectors, but being just "numbers" themselves, they have a short-hand notation: z=x + iy. "i" is not a variable and not a constant. It represents a second dimension to the number. To quickly do the matrix math, any time you have "i * i" replace it with -1 and you will have done the matrix multiplication. For example: (1 + 2i) * (3 + 4i) = 3 + 4i + 6i + 8i^2 = 3 + 10i - 8 = -5 + 10i "i" may be some other symbol, like "j" depending on whatever math dialect is being used. Complex numbers are algebraically closed, which basically means if you make an equation out of them, the solutions will also be in the set of complex numbers. This is not the case for real numbers, e.g., the solutions to x^2 +1 = 0 are not real numbers, they are complex numbers. Complex numbers model rotations/spinning/something "periodic" as simple algebra, which is very important for trigonometry and sinusoids, making them a nice tool for a lot of disciplines. L2 is another measure of vectors. L1 can be thought of as a calculation of a vector's perimeter (add up all the dimensions). L2 is a calculation of distance. L2 is adding up the squares of all dimensions and taking the square root (i.e., Pythagorean's theorem but generalized). Linear algebra, L2 norm, etc. all work out nicely for complex numbers. "The reason I like this development is that it takes at least some of the mystery out of quantum mechanics. It is not a strange model of computation, completely divorced from classical. Just a variant of it, that happens to be the one the universe runs on." The above are all classic topics in advanced high school and undergraduate math, and important to ~every discipline of engineering. Linear algebra, real numbers, complex numbers, statistics, measurements (L1, L2), etc. all have really nice geometric properties that can improve understanding, which I can't do justice here. The other important part to remember is that all these ideas took hundreds of years to discover and be refined. Highly recommend diving into them though because they are a lot of fun. They should be pretty accessible from online texts and videos. Cheers edit: I can't believe how shitty the formatting options are on HN.

noman-land 3y ago

Don't worry, I had the same reaction. But you're not an impostor for spending your time learning whatever it is you're learning instead of this.

jahsome 3y ago
My issue is, I seem to only ever be interested in learning the things I struggle with...
- noman-land 3y ago
  Why bother learning things that are easy?
  - CoastalCoder 3y ago
    Some learning is for necessity, rather than for its own enjoyment.
  - jahsome 3y ago
    When it's somewhat irrelevant to focus on the hard things, which are more appealing, I find it's frustrating not being motivated to solve the more pressing, easier issues because they're not "fun"
    - zBard 3y ago
      True, but in some cases , it’s just a case of pedagogical mismatch . May I recommend https://www.scottaaronson.com/democritus/lec9.html https://www.scottaaronson.com/democritus/lec9.html ? I have cribbed from this endlessly when explaining quantum computing , and it’s certainly my goto talk for explaining quantum computing.
- dclowd9901 3y ago
  I read your first comment and it could’ve easily been mine. Currently a software developer but I started off in journalism. I love, love, love learning but I feel like I have some… granite wall of impenetrability when it comes to quantum computing. I simply cannot figure it out. I’m a very adept person and a quick learner, but everything about quantum theory just leaves me feeling like a complete idiot.
  - jahsome 3y ago
    Heh, my degree is in journalism. It's been a weird ride, but I wouldn't trade it for the shiniest CS education.

1letterunixname 3y ago

Every new concept requires a mapping to metaphors and/or analogies. And when the mapping is mismatched between learner and author's content, elucidation hangs in the balance. Thus, the expertise of lecturers lies in expertise of public speaking coupled with mapping concepts to the intended audience. QC and general relativity are daunting topics that don't lend themselves well to short-form, self-paced content. These are topics that need foundational perquisites and subject matter experts to catechize. It would be like hopping out of a helicopter mid K2 without any training or acclimatization and expecting to summit. Start smaller and work your way up one step or idea at a time. :)

jahsome 3y ago
Pattern recognition and analogy are my secret weapons, for sure. I'm really only a good engineer because I'm good at organizing and communicating my thoughts. It's the only reason I've made it so far in my career -- definitely not any innate propensity for "hard" cs concepts. I faked it til I made it, and now I'm pretty darn good at it. I think in my particular case the concepts around quantum ____ are so abstract I'm unable to find anything to liken it to. It certainly doesn't help I lack any substantial background in mathematics. Hopefully one day I'll get there. Or maybe I'm already there and not there at the same time! Who knows!?

abdullahkhalids 3y ago

I am sure there are areas which you know a lot about, which I know nothing about. And conversely for every pair of people in the world. I spend plenty of my time dealing with my own imposter syndrome, often because there are many people in my own field who know far far more about it than I do. Peter Shor, the OP, for instance. But its fine. You do what enjoy and best at, and find satisfaction in doing it. That is the way to live.

currymj 3y ago

trying to elaborate on the OP a little by avoiding math terminology: part 1 here is essentially the idea of logic circuits. you can write these down in terms of large vectors of 0s and 1s, and operations transforming them as large matrices -- which is useful because it takes familiar ideas (to a CS student) and casts it using mathematical formalisms that are later required for weird quantum stuff. this could be unfamiliar if you haven't learned about matrix/vector multiplication. but ultimately it's just a different way of talking about combinations of AND/OR/NOT on truth values. part 2 just says, go from vectors of 0s and 1s to probabilities between 0 and 1. the "L1 norm" (aka Manhattan or taxicab distance) in this situation just means that all the values together have to sum up to 1, the way probabilities do. this includes part 1 as a special case, and extends it naturally. part 3 is indeed where the weird quantum stuff comes in. no easy explanation, you do have to get an idea of how complex numbers work. but again, the familiar logic circuits of part 1 are still a special case. the "L2 norm" for real numbers is just the regular straight-line distance -- I can't provide a good intuition for complex numbers though.

havnagiggle 3y ago

Here's a brief example paired to some of the nomenclature in the parent post: Linear algebra are equations that do not have exponential independent variables. For example (a,b,c,d,e) are constants: aw + bx + cy + dz = e. You won't find an x^2, z^3, etc. Everything is of order 1. "classical n-bit states are 2^n length binary vectors": Binary is 1's and 0's. A binary vector is a list of them where each entry is a particular dimension. 2-bit state vector will have 2^2 entries. <1, 0, 1, 1> is 2-bit state binary vector. "gates are 2^n x 2^n binary matrices": A matrix is a table of values that map one vector to another vector, i.e. a transformation. |a b| |c d| Is a 2x2 matrix. If the matrix is binary then a,b,c,d can only be the values 0 or 1. A matrix is just a condensed notation of a set of linear equations. Let's make a vec x (aka input) and vec Y (aka output) where subscripts indicate the dimension (entry) of the vector (list): vec x = <x_0, x_1, x_2, ...>, and vec Y = <y_0, y_1, y_2, ...>. If matrix A is the 2x2 matrix above, then vec x * matrix A = vec y is a set of two linear equations: a * x_0 + b * x_1 = y_0 c * x_0 + d * x_1 = y_1 The math is pretty easy if it is 1's and 0's everywhere. A 2-state vector and matrix will then be: <x_0, x_1, x_2, x_3> * |a b c d| = <y_0, y_1, y_2, y_3> |e f g h| |i j k l| |m n o p| (apologies the matrix is probably not going to render nicely, it is a 4x4). This is just the equations: a * x_0 + b * x_1 + c * x_2 + d * x_3 = y_0 e * x_0 + f * x_1 + g * x_2 + h * x_3 = y_1 i * x_0 + j * x_1 + k * x_2 + l * x_3 = y_2 m * x_0 + n * x_1 + o * x_2 + p * x_3 = y_3 A "gate" is a chain of transformations that result in some computation. For classic computation that's just binary. Most silicon chips are made of NAND gates: NOT(X AND Y). Most other gates can be created from combinations of NAND gates. For quantum computation this will not be just binary 1 and 0 as the output, hence... "Introduce probabilistic classical computation: Now the states/vectors have real entries in [0,1] and obey the L1 norm (the critical feature). Similarly, the gate matrices.": Now the entries in vectors and matrices are not just 0 and 1, but any real value between and including 0 and 1. This is important for statistics because it can represent the likelihood of something happening. 0% to 50% to 100% and everything in between. The L1 norm turns a vector of numbers into just one number. L1 is particularly easy: just add up the absolute value of all numbers (all numbers are positive here anyways). ||vec x|| = x_0 + x_1 + x_2 + ... "Now, argue that quantum computing just requires the same linear algebriac structure but we (1) work over the complex number field, (2) norm is L2.": Now entries in the vectors are complex numbers. Complex numbers are a pair of real numbers that have a different multiplication transformation. Complex numbers have the form z = <z_0, z_1>. Adding complex vec e and vec g is straight forward, add the pairs of components: <e_0 + g_0, e_1 + g_1>. Multiplication of complex vec e * complex vec g is <e_0g_0 - e_1g_1, e_0g_1 + e_1g_0>. This is also just linear algebra. Complex numbers are these 2 dimensional vectors, but being just "numbers" themselves, they have a short-hand notation: z=x + iy. "i" is not a variable and not a constant. It represents a second dimension to the number. To quickly do the matrix math, any time you have "i * i" replace it with -1 and you will have done the matrix multiplication. For example: (1 + 2i) * (3 + 4i) = 3 + 4i + 6i + 8i^2 = 3 + 10i - 8 = -5 + 10i "i" may be some other symbol, like "j" depending on whatever math dialect is being used. Complex numbers are algebraically closed, which basically means if you make an equation out of them, the solutions will also be in the set of complex numbers. This is not the case for real numbers, e.g., the solutions to x^2 +1 = 0 are not real numbers, they are complex numbers. Complex numbers model rotations/spinning/something "periodic" as simple algebra, which is very important for trigonometry and sinusoids, making them a nice tool for a lot of disciplines. L2 is another measure of vectors. L1 can be thought of as a calculation of a vector's perimeter (add up all the dimensions). L2 is a calculation of distance. L2 is adding up the squares of all dimensions and taking the square root (i.e., Pythagorean's theorem but generalized). Linear algebra, L2 norm, etc. all work out nicely for complex numbers. "The reason I like this development is that it takes at least some of the mystery out of quantum mechanics. It is not a strange model of computation, completely divorced from classical. Just a variant of it, that happens to be the one the universe runs on." The above are all classic topics in advanced high school and undergraduate math, and important to ~every discipline of engineering. Linear algebra, real numbers, complex numbers, statistics, measurements (L1, L2), etc. all have really nice geometric properties that can improve understanding, which I can't do justice here. The other important part to remember is that all these ideas took hundreds of years to discover and be refined. Highly recommend diving into them though because they are a lot of fun. They should be pretty accessible from online texts and videos. Cheers edit: I can't believe how shitty the formatting options are on HN.