Who invented octal number system?

Answer 1

Nobody knows for sure who first came up with the octal system, but the same can be said of all base systems. You might as well ask who invented counting. In order to count, there has to be some basis to the count which requires some formal understanding of base numbers, whether it be 2, 8, 10 or 60.

The decimal system we use today began development in India around 1AD and spread to Europe via the Western Arabs, hence it is known as the Hindu-Arabic numeral system. But prior to that, decimal systems were largely dismissed because of their lack of factoring; the number 10 has only two factors: 2 and 5. By contrast, 60 has five consecutive factors: 2, 3, 4, 5 and 6. Thus base-60 (sexagesimal) was favoured by the ancient Sumerian civilisation 5,000 years ago and is still used to this day: circles still have 360 degrees and the 24-hour clock still has two periods of 12 hours with 60 minutes per hour. Ultimately, any civilisation that can perform highly complex calculations in base-60 would have to have been more than familiar with all other bases, even if only to know why they were unsuitable in the first place.

Base-8 is clearly no better than base-10 in terms of factoring (2 and 4), but its close relationship to base-2 (binary) is hard to miss, even by ancient Sumerian standards. Indeed, the same can be said of all bases that are a power of 2 and if you can notate sexagesimal then you can certainly notate all bases below 60.

We do know that the Native American Yuki and Mexican Pamean cultures used an octal system because they counted using the spaces between the fingers rather than the fingers themselves. But this does not equate to an understanding of octal in the same way an ancient Sumerian understood sexagesimal. If anything, it merely demonstrates a complete ignorance of all other bases and almost certainly wasn't used to perform complex calculations.

But as to who actually invented octal first, nobody can possibly say for sure. I fancy the clever money would be on the Sumerian.