An interesting article but I can't help but feel the author is a little confused. He seems to think his ideas are unorthodox however he's just going over a lot of old ground covered by Cantor etc.

If Steve wants to count the grains inside a circle drawn on the sand, and call that the area, then that's fine. But it's not very interesting. The rest of us will continue to define the circle as the set of points satisfying x² + y² = r² (or any manner of other equivalent definitions) and Steve can count sand to arrive at a finite pi, and call us wrong. That's fine by me, since we are talking about different things. I'm not going to call him a heretic for it.

Medium-quality trolling based on category error. He's leaning heavily on "abstract concepts do not exist", which basically makes formal logic impossible.

Article flagged for trolling. It'll probably attract several hundred comments eagerly disagreeing with the author, which is his goal.

Something that is proven by logic has only one answer. There are no differing opinions/measurements/data possible. Disagreeing with it is the same as agreeing with "true == false". Unless you can find (and proof) a mistake in the proof.

I don't think you're "not allowed" to disagree. You just take the consequences of claiming that "true == false".

May main point is calling this a dogma seems uncalled for. You can call particular mathematical conventions or notations a dogma if you like, after all those things are based on opinions (see e.g. pi day vs tau day).

The argument is that real world circles have real finite circumferences, which I don't think a rational person would argue against. It's just a lot of fuss pointing out that circles don't really exist, they're imaginary.

All I'll say is that just because something is more complex than you would like doesn't make it wrong.

So in other words, let's ignore everything other people have done, create our own definitions, derive dubious results, call them the same name, and then declare the other, longer standing results as wrong.

It appears that his "definition" of pi depends on each circle drawn. In other words, he has no single definition, and "the" value depends on the measurement taken in each case. So again, in other words, he doesn't actually have a single value.

So it's a diverting philosophical ramble, but for me it's been pretty close to a complete waste of time. I'd be interested to know if anyone here on HN thinks otherwise, and in particular, why anyone would think it's worth upvoting.

An amusing, if utterly wrong article. What I found funniest was how he constructs geometry out of points with a finite size, so that each circle's Pi can be directly measured as the ratio of the number of points on the circumference vs the number of points on the line from the center to the circumference. Sure that gives you a rational 'Pi', but, whatever value will this rational 'Pi' approach, as you increase the circle size vs point size ratio?

That the answer is simply the true Pi does not seem to bother him, or he hasn't considered it.

A relevant submission: https://news.ycombinator.com/item?id=14446708