dhruvp

Hi - thanks for pointing this out. I've added a note clearing up that as you correctly write the quantum interpretation makes sense at the single photon level. Obviously it's hard to generate and manipulate single photons without the right equipment (especially with a phone like in my case) but I do believe this still provides a nice intuition for what's going on. Thanks for your suggestion!

Hey, you're right you could use a stick on a piece of paper etc. Totally fair. That being said this is in fact a real application where a qubit can model things a standard bit can't. Professor Aaronson describes it in this paper: https://www.scottaaronson.com/papers/qcoin13.pdf. Additionally, it's described in his lecture notes here: https://www.scottaaronson.com/qclec/5.pdf

Hey - this is perfectly reasonable and constructive feedback - thank you! I see your point that the polarization example can be explained using classical approaches. I wanted to explain it in terms of individual photons as I wanted to use this to help provide some visual intuition for qubits. Photon polarization is a nice, visual way of interpreting qubits and as such lent itself well to the task.

EDIT: I've gone ahead and added the footnote. Thanks for the suggestion!

Yes - I used the term computer because it really does allow you to mock this quantum algorithm: https://www.scottaaronson.com/papers/qcoin13.pdf. It's described in Professor Aaronson's lecture notes here: https://www.scottaaronson.com/qclec/5.pdf

Hey - you totally could to mock this exact setup like you're suggesting. However, in a real quantum computer setup you would take one qubit and apply either the positive or negative rotation gate to it again and again and rotate the state of that qubit. The "stick" in the quantum computer would be the qubit (or photon in this case). So the post is meant to show what would happen in a real setup. Hope that makes sense.

Thanks for the kind words! I've been told to improve my handwriting but here I finally have proof I don't need to haha

Hi! Author here - If you have any feedback on what can improve please let me know! Thanks for reading and feel free to shoot me a note at [email protected] if you'd like to see something edited.

This article does point out a lot of things that have failed this decade - all fair points. But in focusing on failures it fails to capture that casual education (not formal, school education) has fundamentally shifted this decade.

Today, I can learn almost anything I want for free on the internet.

- I can get a world class mathematical education from 3Blue1Brown (seriously this guy's videos are just out of this world good).

- I can get incredible guitar lessons on any song I want from youtube (I've taught myself guitar this year through it!).

- I can find scores of language education podcasts to help me learn Spanish (I use coffee break spanish).

- I can get world class SAT prep from Khan Academy (for free!).

- I can get awesome yoga classes online for free (did this also this year).

Seriously the wealth and quality of information available to us today is insane - it's the Library of Alexandria a search bar away.

As someone who enjoys learning, there's no way I would ever go back 10 years in time.

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Over the last 5 years, insurance companies are increasingly pushing high deductible plans on to employers. As a result, patients are way more price sensitive than they used to be. If you had no deductible, you probably wouldn’t care too much about drug price differences because the copays wouldn’t be that different. However, due to these new plans you care a lot more and hence services like GoodRx and Blink become a lot more important.

Hey! I wrote this article - “we” is referring to people who had a similar educational experience to me. I was introduced to matrices as a tool for solutions to systems of equations. I always wish I was taught the functional perspective from the beginning.

Hey!

Thanks for the feedback. I go into this in the next post on eigenvectors here: https://www.dhruvonmath.com/2019/02/25/eigenvectors/. I start by discussing basis vectors which I believe is what you’re looking for in your comment.

Hey OP here!

When I first was introduced to matrices (high school) it was in the context of systems of equations. Matrices were a shorthand for writing out the equations and happened to have interesting rules for addition etc. It took me a while to think about them as functions on their own right and not just tables. This post is my attempt to relearn them as functions which has helped me develop a much stronger intuition for linear algebra. That’s my motivation for this post and why I decided to work on it. Feedback is more than welcome.

Fixing! Thanks for the catch.

Hi! I’m the author of this post. Would love any feedback on how to make it better. Thanks!

OP here: Your approach is pretty on point because Planetary Motion was actually the first recorded motivation for eigenvectors. Cauchy published a paper on planetary motion in 1829 which made use of what we now call Eigenvectors. See here for more info: https://www.maa.org/press/periodicals/convergence/math-origi...

I know! I’ve just been a little lazy. I’ll get a domain later today.