RPN the Road to 🍏
iOS Music Tech Standards
This series will discuss how iOS:
Mathematical Notation
Math Class
We're taught how to do math a certain way in school. Different generations have been exposed to different methods of interpreting the same mathematical symbols. We're inculcated with the idea of performing calculations in a specific order based upon the mathematical symbols and the rules of precedence associated with them.
I was taught to use this order of precedence in school, where what was in the parentheses was evaluated first and can be represented as ⭕️(). Other forum members learned to not give precedence to parentheses represented by 🚫(). The table below shows how those two groups would evaluate the same mathematical symbols and arrive at two different results. * Perhaps for some applications one system makes more sense. For example suppose a computer had a system where it does every operation as it comes in for maximum throughput?
| 🚫 () new | ⭕️ () old |
| 6/2(1+2) | 6/2(1+2) |
| 3(1+2) | 6/2(3) |
| 3+6 | 6/6 |
| 9 | 1 |
Convention as Truth
These differences are not significant provided the people or programs evaluating the expressions agree on the same set of criteria for evaluating them. It’s an issue of agreeing upon a shared convention not the measure of intelligence or who is right or wrong.
The mathematics is the same, people decide how they want to define the rules for describing it.
Persistent Childhood Memory
Why do people insist upon a particular convention and are unwilling to recognize another convention may be valid too?
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The neural pathways created during these periods of rapid nerve myelination will strongly influence our behavior over the course of our lifetime.
Calculator Wars
In the 1970s before personal computers were common place, people used handheld calculators.
TI Texas Instruments and
HP Hewlett Packard were the
Microsoft and
Apple of their day. HP calculators used
Reverse Polish Notation. Here's how the example expression would be evaluated with an HP.
| RPN |
| 6/2(1+2) |
| 3(1+2) |
| 3+2 |
| 5 |
The HP-35 Calculator
Someone who was used to using a TI calculator had no idea how to use an HP calculator though the reverse was not true as its method of punching in the expressions followed the dominant mathematical expression evaluation rules taught in school.
The HP calculator was prefered by many who later went on to form Apple computer.
Rather than conform to the way a person who grew up under the existing mathematical conventions, it used methods suited to a computer.
This led directly to being able to do more complex calculations than *`+, -, ,/`** on a device that fit into their shirt pocket, the iPhone of their day.
Originally humans were responsible for entering the expressions into the computer correctly so they'd get the results they were expecting. If they were expecting to get a 9 or a 1, and got a 5 instead, they’d get blamed for the plane falling out of the sky because they'd entered the wrong code into the computer.
The Rise of Apple
Apple led the way to reversing this trend so that the OS was designed to conform to human behavior rather than vice versa.
Shift to Mobile Computing for the people from Large computers in air conditioned rooms only available to large institutions where computer time was a commodity.
Shift from calculations to lifestyle.