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 dhruv.parthasarathy@gmail.com 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.

For those wondering, here’s how GoodRx works and makes money:

1. GoodRx obtains prices of drugs at all pharmacies through contracts it has with PBMs (middleman that determines insurance payouts to pharmacies).

2. Pharmacies have wildly different prices from one another - going to one pharmacy over another can save you and your insurance a lot of money.

3. When you use a GoodRx coupon, the insurance company pays GoodRx a small amount as they had to spend less on their patient thanks to the coupon (i.e they didn’t use a super expensive pharmacy).

4. The pharmacy pays GoodRx a referral fee (kind of like a restaurant pays yelp a referral fee when you use a yelp coupon).

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.

Hey!

Author here. Really appreciate the kind words. If you have any feedback on what I can do to improve the explanation further, I’d love to hear it.

Also, if you’re interested, I’ve written some other posts on explaining concepts in Math and ML following a similar approach:

1. Brief History of CNN based Image Segmentation: https://blog.athelas.com/a-brief-history-of-cnns-in-image-se...

2. Understanding Baidu’s Deep Voice for voice synthesis: https://blog.athelas.com/paper-1-baidus-deep-voice-675a32370...

3. An intuitive explanation of matrices as linear maps: https://dhruvp.netlify.com/2018/12/31/matrices/

This is a common problem in healthcare and I think it comes down to these issues:

1. Pharmaceuticals have natural monopolies on these drugs (due to regulation, market power, etc.).

2. The public and end consumers are largely unaware when these monopolies are exercising their power to increase costs. This is because there is no one price, you don't actually pay the actual price (if you're on insurance), and it's difficult to actually realize what the price of a drug is.

3. Many insurance companies don't have strong incentives to combat price increases. [1] As these prices increase, consumers become more and more reliant on insurance. [2] Insurance companies have targets for what percent of their expenses they are allowed to devote to administrative costs (buildings, salaries. etc). As the cost of drugs rises, they can increase salaries etc. while keeping the percent devoted to administrative costs constant. [3] Insurance companies are also largely monopolies. End consumers usually take whatever their employer gives them and in most states there are only a few providers. As such, they don't have much pressure to have more competitive plans.

4. Pharmaceuticals companies respond to demands to increase shareholder value by increasing drug prices. This is exactly what we'd expect them to do as per their incentives.

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The solution to me is the following:

1. Allow the safe import of drugs from overseas to create a more competitive market (the US has strong regulations against importing drugs mainly due to safety concerns). See this(https://www.pbs.org/newshour/health/u-s-make-easier-import-p...).

2. Regulate pharmaceuticals and insurance companies as the monopolies they are, or dramatically lower the barriers to entry in the space.

3. Reduce the power of pharmaceutical companies to lobby and reinforce the regulations that help them preserve their monopolies. They have every incentive to lobby for protection and it's no surprise that healthcare industry has by far the biggest lobbying spend in the US - nearly double that of Oil & Gas (https://www.opensecrets.org/lobby/top.php?indexType=i&showYe...).

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The book American Sickness(https://www.amazon.com/dp/B01IOHQ9LO/ref=dp-kindle-redirect?...) discusses just how far we are from any type of perfect competition in this industry and the resulting effects on consumers. I really enjoyed it and it's a great book if you're interested in the space.

If you want to read more on this topic, I highly recommend An American Sickness (https://www.goodreads.com/book/show/31253737-an-american-sic...). It's written by the current Editor in Chief of Kaiser Health News.

Wow this essay is fantastic. The idea that the amount of people who "need" financial aid has stayed constant while tuition prices have increased 170% (way outpacing wage growth) is unreal.

Conrad if you wrote a book about this I would buy it. Super fascinating stuff. Colleges are clearly massive financial instruments that need to be analyzed further.

I think the more interesting point here is how easily people are manipulated by coordinated marketing/information campaigns. And I think this may be not be a flaw of facebook but rather its ultimate business value.

At the end of the day facebook is an advertising platform - isn't influencing people the ultimate goal of advertisement/marketing? At what point do we call marketing manipulative vs. effective? Obviously you shouldn't allow foreign countries to engage in these markets for elections but those same strategies can be carried out within a nation by competing forces and they come with similar consequences.

I think this is a fundamental problem worth addressing because representative democracies rely on well-informed, independent electorates for good outcomes. Marketing on the other hand aims to influence individuals in a coordinated manner towards a given outcome. How do democracies ensure electorates continue to make independent decisions in a world where marketing and advertising tools are increasingly powerful? I think this is a bridge we have to cross - these tools to influence are here to stay and democracies and electorates will need to adapt accordingly in ways outside of just regulation.

Theoretically, the argument against tariffs stems from the idea that a market increases the net surplus for everyone involved in the trade. This is because each individual in the economy would be able to focus on their 'comparative advantage' and trade to obtain a larger basket of goods than if they tried to create everything themselves.

The way the US is expected to enjoy this trade surplus (in a world where it is a net importer) is through lower prices for goods. The benefit the US gains from this reduction in prices etc. is meant to on the whole offset the loss in jobs, exports etc that might come from globalism. Whether this happens or not is clearly a moot point.

I believe the issue might be that while the US has enjoyed the surpluses of globalism, it has not redistributed that surplus well. In a tariff world, the need for redistribution is less - factory workers get the money directly in the form of a paycheck etc through their protected jobs. In a non-tariff world, these jobs no longer exist but the government would ideally now offset that loss through investments in education, infrastructure, new job opportunities etc.

Hope this answers why globalism is supposed to work and where it may not be working.

If you're interested in learning more about this stuff the head of the Pixel team (Marc Levoy - Prof emeritus at Stanford) has an entire lecture series on this stuff from a class he ran at Google. They are here along with lecture notes:https://sites.google.com/site/marclevoylectures/home

What's really cool is you can see him talk about a lot of these ideas well before they made it into the Pixel phone

Pretty cool idea to go to private, well constrained areas so that it scopes down the problem and allows for quick iteration. Good luck! Excited to see autonomous vehicles in these environments.

If there's one thing to learn I think it's that men can do far far more (like the intervening guys in the article) to step in and be far less tolerant of such grotesque behavior. Most men here (of which I'm one) have all probably witnessed some creepy comments and acts from our guy friends or colleagues and let it go. I think that has to come to an end. I know personally I can do better and would hope that if anything, we all demand more from each other.

Thanks for the kind words! I feel as though research papers are not always the easiest way to communicate ideas with a non-research focused audience. I think there's room for more people (like distill.pub) to take the main ideas from the research papers are share the underlying intuition with a larger audience.

I'll try and add more notebooks next time - totally fair point and would make it more interactive.

Thanks for the feedback!

Dhruv

Hi!

We are indeed using CNNs in some parts of our pipeline. You can read more about the general idea of how we use them here: https://blog.athelas.com/classifying-white-blood-cells-with-...

I love how Stripe does so many things that provide value to the developer community from their awesome blog posts to their open source retreats and now finally to this magazine. They're a model to me of how to earn the good will of your users through providing authentic value.

If you're interested in this field check out this talk by Bharath Ramasundar from Prof. Pande's lab at Stanford: https://youtube.com/watch?v=sntikyFI8s8. He's also the author of http://deepchem.io - a deep learning library for drug discovery.

Hey OP! I've been using it extensively and it's definitely more than good enough for most tasks you'll be doing. If you're going this route, I'd highly recommend following the Keras' authors guide on how to set up the instance and connect to it with a jupyter notebook: https://blog.keras.io/running-jupyter-notebooks-on-gpu-on-aw.... This will boost your productivity a ton in the long run.

Best of luck!