We can formally add and subtract simplices. Homology is (very roughly) counting holes using the modulus (%) operator with respect to this addition and subtraction.
There's an old joke that goes something like this.
A math professor was giving a lecture and then remarked that something was trivial. Somebody raises an objection and asks why. The professor stops and thinks hard for the rest of the lecture, then finally remarks: "Yes, I'm right, it is obvious."
Starting an entire company based on collaborative writing is a junk idea. It's a niche service without much room for improvement, and it's currently being provided for free by one of the largest software companies in the world.
There is no way that this will ever achieve anything close to $500k/year. For this to happen, at $8/month it needs to attract 5000+ subscribing, paying users. This is not going to happen when anyone can just use Google docs for free. Especially when Google is more well-known, better maintained, and integrates into existing Google accounts. There is just no good reason to sign up for a new service.
Most people have never heard of draft or etherpad. I'm willing to be that they are not actually generating any substantial revenue either, which is the benchmark for whether it's a good idea to start a business or not.
That's nonsense. Their are whole industries that could use better collaborative tools (such as the book publishing industry). Have you tried writing a book? The tools are so limited.
Google docs for example is not a great tool for writing books, in fact there are very few tools that are particularly nice to use that are web based and strong on the collaborative front.
I think the problem perhaps with Editorially is too much pressure to get things going early. If there's 10+ people with salaries, sales better be good. I think a bootstrapping approach or an open source approach a la WordPress would be much more viable. Editorially seems to have only failed because of their specific criteria, not because there's isn't a need for a better tool.
No, I don't think there is much of a demand, at least not enough to sustain an entire business. You would need to be pulling in serious money from publishers, and on top of that, you're trying to change a system that largely already works. I've published myself, and e-mailing drafts was fine. The only times I've ever seen collaborative documents being used by average people were a) real-time coding interviews, and b) filling out forms. People would not be willing to pay money in either case, no matter how good it is.
A store is the wrong analogy for the point you're trying to make. A store has the dimension of locality, which means that a store that duplicates another one exactly but is in a different location can still propser. (Starbuck's, McDonald's, etc.)
If you're selling worse quality products at a higher price than Wal-mart, then yes, it is silly to start a store right next door. You will probably lose money, like most startups based on bad ideas.
> So what? Why is lowering wages a bad thing? If the wages are lower across the industry, it means consumers get lower prices. You're totally ignoring the consumer side of the equation.
This is incredibly naive. There are many good reasons for deregulation, but propagating arguments like this just gives libertarianism a bad name.
This is completely wrong. Nobody expects an academic career anymore, and all the PhD students I know are doing it because they really like their subject. It's like aspiring to be an artist.
No. Feynman never took issue with integration notation or how integration is defined or taught. The story you're referring to is how he learned of a technique for computing integrals that was not covered in schools. The technique is called "differentiation under the integral", and is arguably even more involved.
Many mathematical concepts cannot be translated into programming, since computation is by definition discrete. For example, even a simple concept like irrational numbers cannot be completely captured by code.
Mathematicians do not compute numbers.