Had Wittgenstein been in a position to avail himself of computer languages, as his student Alan Turing was starting to do, would he have found these sufficient to make his points regarding rule following in mathematics, or would he have taken the position that some formal logic, woven by not-computer-scientist philosophers, was essential fabric? I'm thinking he'd have found our world of programming languages sufficient for his purposes.
In Synergetics we see non-executing notations referred to as "empty set" versus another category of math notation as "operational". His math is of the latter type and seems destined to run on computers, both in serial and in parallel processes and threads. In the meantime, there's plenty of prose to munch on and run neurally, in search of tips and clues regarding generic heuristics. "Think in terms of planets" might be among the mantras we come away with. In other words: mnemonics that employ connected graphs in biospheres will help you play World Game more effectively. Peter Sloterdijk helped pave the way.
The challenge in elementary schools is to expand their horizons to needing to wrangle large numbers of numbers. That doesn't necessarily mean the numbers themselves have to be large. Imagine of herd of a billion numbers, all primes, plus negative one, and low order primes at that, no well established RSA number factors. Those would be too large. It's the billions and billions of numbers we need to work with. Store them. Process them. Save them. Return to them later.
Fortunately, none of these challenges are extremely new and without precedent. Businesses have always needed to track inventories, large and small, and to measure capabilities. The physics and chemistry world is keeping track of atoms and molecules, in terms of moles, in terms of various measures. Even individual molecules may be tagged and made to fluoresce. The mathematics of large quantities is ancient history. We just need more of it in the early grades. Supermarket Math to the rescue.
In Synergetics we see non-executing notations referred to as "empty set" versus another category of math notation as "operational". His math is of the latter type and seems destined to run on computers, both in serial and in parallel processes and threads. In the meantime, there's plenty of prose to munch on and run neurally, in search of tips and clues regarding generic heuristics. "Think in terms of planets" might be among the mantras we come away with. In other words: mnemonics that employ connected graphs in biospheres will help you play World Game more effectively. Peter Sloterdijk helped pave the way.
The challenge in elementary schools is to expand their horizons to needing to wrangle large numbers of numbers. That doesn't necessarily mean the numbers themselves have to be large. Imagine of herd of a billion numbers, all primes, plus negative one, and low order primes at that, no well established RSA number factors. Those would be too large. It's the billions and billions of numbers we need to work with. Store them. Process them. Save them. Return to them later.
Fortunately, none of these challenges are extremely new and without precedent. Businesses have always needed to track inventories, large and small, and to measure capabilities. The physics and chemistry world is keeping track of atoms and molecules, in terms of moles, in terms of various measures. Even individual molecules may be tagged and made to fluoresce. The mathematics of large quantities is ancient history. We just need more of it in the early grades. Supermarket Math to the rescue.
