Why you cannot divide by zero and why you can

Well this is going to be fun. Long ago, my thought experiments on dividing by zero detected a bug*, and therefore went in the direction of "you can divide by zero" and of course this left me on the outskirts of mathematics years ago. I set up a tent and made a home there, where I am quite happy. A brand new website now says the same thing, with better examples and clear reasoning. Of course, anyone worth their salt in mathematics will reject it (it's the way mathematics handles innovations around the number zero for many centuries now, so such rejection is not to be taken without... a grain of salt).

I've only had time to zoom through the site quickly, but it looks great, and I am looking forward to the time I get to sit down and go through it more carefully. Here now, for your viewing pleasure, are two sites. One, straying not one inch from the status quo, emphatically declares that you cannot divide by zero. This is what is commonly accepted.

The other declares that you can divide by zero, and shows what happens when you do, and does so coherently. My own argument in favor of the ability to divide by zero runs along these lines, but handles the problem of multiple infinities coinciding a little differently. I'm excited to see someone else writing up these ideas. This is an important step toward resolving a bug* in the way we handle zeros.

*As a software developer, I long ago learned to see anything that looks like our current way of handling zero as a bug, being covered up by programmers who are not smart enough to solve the underlying defect, but are smart enough to convince everyone it's a feature, not a bug. To me, it's a bug, and the solution is arriving.

Thank goodness, and well done, to Bill Shillito, who appears to have an audience of 16,000 subscribers. A quick review of comments indicate he's like another 3 blue 1 brown or njwildberger, whose similar videos I have enjoyed for years.

Posted in Developing Software, Mathy Stuff on Oct 01, 2018