That's quadratic, but definitely not exponential, and doesn't really look like the curve he drew.
I know the guy's argument doesn't really depend on the shape of the curve, but it's a pet peeve of mine that exponential growth is always presented in an inaccurate way.
I can understand that, and largely I feel the same. But over the past 20 years since completing my PhD I've learned on occasion to let go of the details and look to the underlying point. Sometimes, indeed, often, the example or the calculations are fundamentally wrong, but the point is sound.
I've found I've learned a lot after having learned to look beyond the specifics of a given example. It doesn't suit everyone, it doesn't work for everyone, and I wouldn't claim that everyone should do it.
I really disliked this article and found it a complete waste of time to read. On this web site, I would expect this article to lead to something scientific, something related to programming, or perhaps information that would be beneficial to someone starting a business. While off topic content is certainly acceptable at times, this is really pointless to me and contributes nothing. It was not worth reading, and the only reason why I am even responding is to hopefully contribute by having others consider their content before linking worthless content to the site. I cannot really see how it has been rated so highly, and it makes me wonder if I am missing something. It is neither accurate nor useful in any way. It does not even benefit me in a way to get me thinking in a positive manner or to help me generate ideas.
Hey, author here. I don't usually comment on my own articles on HN, but this comment was one of the more negative ones I've seen here.
A lot of us here on Hacker News (formerly Startup News) are working on startups. One of the biggest challenges facing startups is finding the determination to work hard during the long initial period where you might see very few fruits from your labors. Personally, I like to read pg's "How Not to Die" frequently (http://www.paulgraham.com/die.html). It was in this light that I wrote the article. I submitted it to HN and apparently it struck a chord with a lot of readers here, and they upvoted it.
Not every article on HN is going to appeal to every reader. Perhaps you're not working on a startup, so this article doesn't really apply to you. Maybe my next one will. Recognize that not all HN readers are in the same situation in life; enjoy the articles that apply directly to your situation, and read the others to give you perspective on the lives of your fellow HNers.
agreed ... your blog post tried to convey a very simple and punchy idea, and you didn't make any pretenses about it being 'mathematically accurate' or whatever, so i'm astounded that people have nitpicked on your curves not being accurate or whatever.
a piece of presentation advice i've heard for creating graphs and diagrams is that if you don't want people to nitpick on details, make a really crappy low-fidelity sketch so that people don't have an expectation of precision. i once got ripped on because i drew a line that looks like 1 / x^2 to talk about inverse correlation, but people nitpicked on whether it was a power law, 1/x, whether the integral converges, etc., which was totally irrelevant to my argument. if i had made a crappy hand-sketch on the board, then people might not have been as critical
And don't include mathematical equations. They are meant to be precise.
A closer analogy might have been with growth of a bacteria colony: It's more or less exponential and you have to keep the right conditions up --- even in the beginning where you do not see anything, yet.
I'm a developer - I've been working on a startup for two years now and have some momentum. But it's hard work and great things don't happen overnight.
"Overnight success ... takes years" is a great reminder, and the idea of my software as a little box with a magical engine in outer space is delightful :-)
Personally, I enjoyed this article and loved its simplicity. It's a nice change of scenery from the technical articles which seem to make up the majority of HN. Sometimes, it's good not to overthink.
That's quadratic, but definitely not exponential, and doesn't really look like the curve he drew.
I know the guy's argument doesn't really depend on the shape of the curve, but it's a pet peeve of mine that exponential growth is always presented in an inaccurate way.
EDIT: fixed embarrassing calculus error