Designing an Efficient Number System: What Factors Should Be Considered?

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Discussion Overview

The discussion revolves around the design of an efficient number system, exploring various factors that should be considered in its creation. Participants consider aspects such as base selection, ease of writing, learning curve, and the implications of different numeral systems.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that a number system should be based on a higher base than 10, such as base 20, to reduce the number of digits needed for representation.
  • Others emphasize the importance of ease of learning as a critical criterion for a new number system.
  • A participant argues that place value is essential for simplifying arithmetic and suggests that a placeholder for zero is necessary.
  • There is a suggestion that a base 20 system would require additional digits (0-19), raising questions about the trade-offs between digit count and numeral complexity.
  • One participant proposes a method for indicating exponentiation to simplify notation and arithmetic.
  • Another participant suggests that bases with many prime factors, such as base 12 or base 60, could offer advantages over base 10, particularly in terms of fractional representations.
  • A humorous suggestion for base 840 is made, highlighting the feasibility of using a large number of distinct numerals.
  • Some participants advocate for base 12 due to its many prime factors, while others defend base 10 for its connection to human anatomy (fingers).
  • There is a light-hearted exchange about the implications of number systems for fictional characters with different finger counts.

Areas of Agreement / Disagreement

Participants express a range of opinions on the optimal base for a number system, with no consensus reached. Some favor higher bases like 12 or 20, while others defend base 10. The discussion remains unresolved regarding the best approach to designing a new number system.

Contextual Notes

Participants mention various bases and their properties without resolving the implications of these choices. The discussion includes speculative ideas about numeral complexity and learning ease, which are not fully explored or agreed upon.

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Suppose you're to make a new number system. A good number system should have what? What do you think?

- Should be based on higher base than 10, for example 20 - less digits to write.

- its digits should be as easy as possible to write.

- what else?
 
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easy to learn should be one of the most important criterias ;)
 
In order to simplify arithmetic and to only have a small set of numerals...place value is absolutely essential.

We would also need a placeholder of types for nothingness, so a "zero" is needed.

The numerals shouldn't be that difficult to write...or maybe one or two really difficult ones that mean like 1 trillion or something just to screw with people.

But keeping it simple as in lines and curves/loops as in our system is key.

By the way, if we have a base 20 system, wouldn't we have to think of more digits? We'd need a digit from everything from 0-19.

Or do you mean big numbers could be expressed with less digits?

One last thing I could think of would be maybe a simple manner to indicate exponentiation, so you have easy access to factors of the base and could probably reduce notation a bit and thus arithmetic a bit.

Maybe like a dot, or a dash, or some cool thing on top of a number for it's first two base factors.

And now all of this crazy number system talk has made me hungry...so I'm done rambling. But, try to come up with one. I've thought about this many times before but never followed it through.
 
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If you're just talking about base systems, then having a base n system where n has a lot of prime factors would be better. Base 10 is slightly clumsy due to it's factors being 2 and 5. Base 8 or Base 12 would be much nicer. Base 60 would be even better but that's be somewhat over the top in symbols required.

Base 12 would mean that loads more fractions would have nice decimal representations. Like 0.3 would be 1/4 and 0.4 would be 1/3. I think those benefits would outweight having a base 20 system so you could write numbers in a shorter way. Base 20 offers no advantages over base 10 in terms of decimal expansions.
 
How about base 840? Every natural number less than 9 goes into 840 evenly. Just use the first 840 kanji in the Japanese writing system for each numeral :biggrin: There are 1,945 official kanji, so there's plenty of room for more numerals if you want :-p Oh, that's too many distinct numerals? Well, base 60 doesn't seem so bad now, does it?
 
my vote is for base 12, because of its many prime factors. And who said SI is better US, 12 is a great number!
 
Base 10 is very good because it is nicely related to the number of fingers we've got. :smile:
 
arildno said:
Base 10 is very good because it is nicely related to the number of fingers we've got. :smile:

But what about people who live in cartoons? They only have eight fingers. :rolleyes:
 
Rach3 said:
But what about people who live in cartoons? They only have eight fingers. :rolleyes:
That's why they never managed to develop a number system. :approve:
 

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