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Dozenal (base 12) Is better than base 10

BradK
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6/5/2014 7:10:05 PM
Posted: 2 years ago
I've tried having a few debates with people on this topic, but no one can really seem to beat me, in my opinion. I think that we chose the wrong number base. Honestly, and sincerely, I think we should all be using dozenal.

I don't see that as something that's up for debate though, for me the big question is can society actually become a dozenal society? It seems very unlikely that this could happen, but if there were some sort of hypothetical worldwide vote, I'd vote for dozenal.

Have you ever heard of dozenal? Do you know how much worse that base 10 is?
Subutai
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6/5/2014 8:27:54 PM
Posted: 2 years ago
At 6/5/2014 7:10:05 PM, BradK wrote:
I've tried having a few debates with people on this topic, but no one can really seem to beat me, in my opinion. I think that we chose the wrong number base. Honestly, and sincerely, I think we should all be using dozenal.

I don't see that as something that's up for debate though, for me the big question is can society actually become a dozenal society? It seems very unlikely that this could happen, but if there were some sort of hypothetical worldwide vote, I'd vote for dozenal.

Have you ever heard of dozenal? Do you know how much worse that base 10 is?

I've heard of it, and it's certainly an interesting thought. However, as you've said, it would take a lot of effort to implement, especially in business, considering the most businesspeople don't even know how to use binary, much less dozenal. This fact alone would understandably cost a significant amount of money. You'd have to make a very good case for it in order for the world to take the effort to implement it.
I'm becoming less defined as days go by, fading away, and well you might say, I'm losing focus, kinda drifting into the abstract in terms of how I see myself.
BradK
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6/5/2014 9:01:57 PM
Posted: 2 years ago
I've heard of it, and it's certainly an interesting thought. However, as you've said, it would take a lot of effort to implement, especially in business, considering the most businesspeople don't even know how to use binary, much less dozenal. This fact alone would understandably cost a significant amount of money. You'd have to make a very good case for it in order for the world to take the effort to implement it.

you'd have to start slow with it, gradually phasing it in, it's not like a change like that could be made instantaneously. I've thought maybe there could be towns that used only dozenal, for prices in stores or for representing numbers in other places. Maybe even make dozenal coins somehow... have a twelfth of a dollar, a sixth of a dollar, a third of a dollar, a quarter of a dollar, and a half of a dollar. I don't know how to implement it but it would be something worth doing. It's a shame to think we are stuck with base 10 forever.
Floid
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6/6/2014 11:54:29 AM
Posted: 2 years ago
At 6/5/2014 7:10:05 PM, BradK wrote:
Have you ever heard of dozenal? Do you know how much worse that base 10 is?

The choice of base is pretty much irrelevant in modern times. Back when difficult calculations were worked by hand by teams of human computers there may have been some advantages. Now days easy mental arithmetic is done based on memorization. Difficult arithmetic is mostly done by calculator/computer or guesstimation when precision does not matter. Base doesn't effect this.
dylancatlow
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6/6/2014 12:16:43 PM
Posted: 2 years ago
If all the dozenal system has going for it is convenience, then I'd say it's not worth the added complexity. The base 10 system is more convenient, because we have 10 fingers to count with (and for complex calculations, we just use a calculator anyway). I think it's wrong to conclude that it's superior just because, in principle, it is easier to do certain calculations.
dylancatlow
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6/6/2014 12:32:47 PM
Posted: 2 years ago
After reading your debate, I think it's clear that the dozenal system is unnecessarily complex. Its "superiority" is based on irrelevant and impractical criteria, and it is not obviously better by any means. It makes math that isn't just pushing numbers around harder to grasp, which is the math that really matters.
tahir.imanov
Posts: 272
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6/6/2014 4:19:33 PM
Posted: 2 years ago
The best choice would be sexagecimal, but world is full of dumb people, so dozenal would be optimal choice.
This is red.
BradK
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6/16/2014 3:20:46 PM
Posted: 2 years ago
At 6/6/2014 12:32:47 PM, dylancatlow wrote:
After reading your debate, I think it's clear that the dozenal system is unnecessarily complex. Its "superiority" is based on irrelevant and impractical criteria, and it is not obviously better by any means. It makes math that isn't just pushing numbers around harder to grasp, which is the math that really matters.

Dozenal isn't more complex, decimal is! If you read through my debate I would have hoped that would have been elaborated on.
dylancatlow
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6/16/2014 3:27:52 PM
Posted: 2 years ago
At 6/16/2014 3:20:46 PM, BradK wrote:
At 6/6/2014 12:32:47 PM, dylancatlow wrote:
After reading your debate, I think it's clear that the dozenal system is unnecessarily complex. Its "superiority" is based on irrelevant and impractical criteria, and it is not obviously better by any means. It makes math that isn't just pushing numbers around harder to grasp, which is the math that really matters.

Dozenal isn't more complex, decimal is! If you read through my debate I would have hoped that would have been elaborated on.

And why is that? (I have a feeling you're defining "complexity" in a very irrelevant way). In any case, the decimal system isn't a limiting factor by any means.
dylancatlow
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6/16/2014 3:33:39 PM
Posted: 2 years ago
I think you're underestimating just how much of a hassle it would be to make the transition, and overestimating how useful it would be compared to the decimal system.
dylancatlow
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6/16/2014 3:42:07 PM
Posted: 2 years ago
Just some problems that come to mind:
1. There would be a huge generational divide between those who grew up with the dozenal system and those who were out of school when it was introduced. People out of school cannot reasonably be expected to learn (or willingly adopt) the dozenal system. Problems with choosing to organize society around one or the other.
2. Every single thing with numbers would need to be replaced.
3. Most computer programs would need to be updated.
4. Street numbers would be wrong. Would need to be updated.
5. Phone numbers need to be updated.
6. General chaos and destruction.
dylancatlow
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6/16/2014 3:48:58 PM
Posted: 2 years ago
Inevitably, some countries would adopt it and some wouldn't. Scientific cooperation between them would be made much more difficult. And all this for convenience? Doesn't seem too convenient to me.
BradK
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6/16/2014 5:24:08 PM
Posted: 2 years ago
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.

We have switched before in the past though. Programmers had to use hex. Times are based on twelves. The biggest thing would be finding a way to introduce it. You would never be able to just start using it as sort of a "turnkey" kind of way of thinking. It would have to be segregated from the rest of society and gradually phased in somehow. It's impossible to imagine that happening when you think about the entire world switching at once. The trick is to think of it as gradually making a change and seeing that it is at least possible in theory.
dylancatlow
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6/17/2014 2:22:35 PM
Posted: 2 years ago
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.
BradK
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6/17/2014 2:45:24 PM
Posted: 2 years ago
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

A computer does math in a different base yet again. While it is true that any amount of precision is attainable with any radix, this is not the point.

If you were say... hypothetically... building the human society from scratch. You have to choose: would you choose to use dozenal or decimal?
dylancatlow
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6/17/2014 4:11:19 PM
Posted: 2 years ago
At 6/17/2014 2:45:24 PM, BradK wrote:
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

A computer does math in a different base yet again. While it is true that any amount of precision is attainable with any radix, this is not the point.

If you were say... hypothetically... building the human society from scratch. You have to choose: would you choose to use dozenal or decimal?

I'm not sure. Dozenal has advantages in some respects, but it's not obvious that having 12 digits isn't worse than 10 digits.
BradK
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6/17/2014 6:35:29 PM
Posted: 2 years ago
At 6/17/2014 4:11:19 PM, dylancatlow wrote:
At 6/17/2014 2:45:24 PM, BradK wrote:
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

A computer does math in a different base yet again. While it is true that any amount of precision is attainable with any radix, this is not the point.

If you were say... hypothetically... building the human society from scratch. You have to choose: would you choose to use dozenal or decimal?

I'm not sure. Dozenal has advantages in some respects, but it's not obvious that having 12 digits isn't worse than 10 digits.

At first it's not obvious, but over time it will become more apparent. Here's a link to a forum, and this is the sub-forum section on various dozenal societies that exist around the world:

http://z13.invisionfree.com...

You have to ask yourself the question "if we did use dozenal, would our society likewise have a number of "decimal" societies?". There's also a numberphile video on youtube about dozenal, you can search that up, it's a good reference. Just google "dozenal numberphile", and click the first video link that comes up.
Floid
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6/17/2014 7:39:46 PM
Posted: 2 years ago
At 6/17/2014 6:35:29 PM, BradK wrote:
You have to ask yourself the question "if we did use dozenal, would our society likewise have a number of "decimal" societies?".

Yes. There would be someone out there saying "We have 10 fingers so we should use decimal" just like you are saying "base 12 is divisible by more values so we should use dozenal".

The choice of base is irrelevant especially in modern times. If you have to pick a base because it helps you avoid fractions you aren't going to be very good at math anyway.
BradK
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6/17/2014 7:50:39 PM
Posted: 2 years ago
At 6/17/2014 7:39:46 PM, Floid wrote:
At 6/17/2014 6:35:29 PM, BradK wrote:
You have to ask yourself the question "if we did use dozenal, would our society likewise have a number of "decimal" societies?".

Yes. There would be someone out there saying "We have 10 fingers so we should use decimal" just like you are saying "base 12 is divisible by more values so we should use dozenal".

The choice of base is irrelevant especially in modern times. If you have to pick a base because it helps you avoid fractions you aren't going to be very good at math anyway.

Math isn't made easy by having the same number of digits as you do finger digits. It's made easier by extracting and noticing patterns. A factor dense number makes finding patterns easier, a trivial example would be in the dozenal multiplication table. It's much more transparent than the decimal one, because you can see that every 3 groups of 4 you get a multiple of 10. Every 4 groups of 3 you get a multiple of 10. Every 8 groups of 9 you get 60.

If the choice is irrelevant, why not choose base 17? Say that we were using base seventeen instead of base ten. Would we have the same computational efficiency throughout society, mentally and with computers?...
Floid
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6/17/2014 11:36:34 PM
Posted: 2 years ago
At 6/17/2014 7:50:39 PM, BradK wrote:
Math isn't made easy by having the same number of digits as you do finger digits.

It is if you are 4 years old.

It's made easier by extracting and noticing patterns. A factor dense number makes finding patterns easier, a trivial example would be in the dozenal multiplication table. It's much more transparent than the decimal one, because you can see that every 3 groups of 4 you get a multiple of 10. Every 4 groups of 3 you get a multiple of 10. Every 8 groups of 9 you get 60.

A factor dense base system makes describing basic arithmetic easier. But that takes us through about 2nd or 3rd grade arithmetic. Now what happens when you do non-basic operations? One of three things:
1.) You really understand what you are doing in which case base doesn't matter because you could work in any base
2.) You are able to learn an algorithm for solving operations without understanding what you are doing in which case base doesn't matter because the algorithm is essentially the same for any base.
3.) You are incapable of learning an algorithm for solving operations in which case base doesn't matter because you will not be able to perform non-memorized operations in any base.

What do all three cases have in common? Base doesn't matter in anything except it might slightly increase the range of values someone could memorize (what you do in elementary school when you learn the multiplication tables).

If the choice is irrelevant, why not choose base 17? Say that we were using base seventeen instead of base ten. Would we have the same computational efficiency throughout society, mentally and with computers?...

1.) There is nothing wrong with base 17. To use it you would have to memorize the multiplication tables up to 17x17 which is getting close to double the number of multiplication values most people memorize. But beyond that you could adapt the same algorithms you would use for base 10 or base 12 to base 17.

2.) Computers are a completely different subject.
AlbinoBunny
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6/22/2014 3:46:13 PM
Posted: 2 years ago
It could be tough to transition, but maybe not as tough as people make out. It depends on if children would learn two systems, which is the problem. Dozenal is better though.
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AlbinoBunny
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6/22/2014 3:47:23 PM
Posted: 2 years ago
At 6/16/2014 3:42:07 PM, dylancatlow wrote:
Just some problems that come to mind:
1. There would be a huge generational divide between those who grew up with the dozenal system and those who were out of school when it was introduced. People out of school cannot reasonably be expected to learn (or willingly adopt) the dozenal system. Problems with choosing to organize society around one or the other.
2. Every single thing with numbers would need to be replaced.
3. Most computer programs would need to be updated.
4. Street numbers would be wrong. Would need to be updated.
5. Phone numbers need to be updated.
6. General chaos and destruction.

You ought to not change to Metric either, too scary.
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AlbinoBunny
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6/22/2014 3:48:17 PM
Posted: 2 years ago
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

Because people have computers in their brains.
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AlbinoBunny
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6/22/2014 3:51:19 PM
Posted: 2 years ago
At 6/17/2014 7:39:46 PM, Floid wrote:
At 6/17/2014 6:35:29 PM, BradK wrote:
You have to ask yourself the question "if we did use dozenal, would our society likewise have a number of "decimal" societies?".

Yes. There would be someone out there saying "We have 10 fingers so we should use decimal" just like you are saying "base 12 is divisible by more values so we should use dozenal".

The choice of base is irrelevant especially in modern times. If you have to pick a base because it helps you avoid fractions you aren't going to be very good at math anyway.

Sure there'd probably be decimal societies, but maybe more for historical/traditional reasons, not for practicality reasons. That's like saying there are major base-fourteen societies.
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dylancatlow
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6/22/2014 4:12:43 PM
Posted: 2 years ago
At 6/22/2014 3:48:17 PM, AlbinoBunny wrote:
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

Because people have computers in their brains.

Important calculations are done with a computer. Calculations that we do in our head don't need to be very inefficient. Indeed, doing them in our head implies that much.
AlbinoBunny
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6/22/2014 5:12:18 PM
Posted: 2 years ago
At 6/22/2014 4:12:43 PM, dylancatlow wrote:
At 6/22/2014 3:48:17 PM, AlbinoBunny wrote:
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

Because people have computers in their brains.

Important calculations are done with a computer. Calculations that we do in our head don't need to be very inefficient. Indeed, doing them in our head implies that much.

You mean efficient? Who am I to decide whether people should calculate in their head or a follow computer? Whether they have a computer at hand when they need to do some important calculation?

Modern computing does reduce this need and probably will eventually eliminate it. That being the case then, why wouldn't we switch to teaching our children dozenal? We won't struggle because computers can quickly convert. In the case of a catastrophe we can have a more efficient mathematical base.

Also measurements are easier to divide and may not need to be rounded to the nearest point as often. Again being eliminated, but again may be useful in insurance policy situations.

Maybe we shouldn't implement it, but I feel that a lot of people underestimate the usefulness of better systems. In fact, better anything. Most people seem quite adverse to change, sometimes irrationaly so.
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dylancatlow
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6/22/2014 5:18:18 PM
Posted: 2 years ago
At 6/22/2014 5:12:18 PM, AlbinoBunny wrote:
At 6/22/2014 4:12:43 PM, dylancatlow wrote:
At 6/22/2014 3:48:17 PM, AlbinoBunny wrote:
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

Because people have computers in their brains.

Important calculations are done with a computer. Calculations that we do in our head don't need to be very inefficient. Indeed, doing them in our head implies that much.

You mean efficient?

No. Calculations that we do in our head don't need to be done efficiently, since if we want them done efficiently, we use a computer anyway.

Who am I to decide whether people should calculate in their head or a follow computer? Whether they have a computer at hand when they need to do some important calculation?

And who are you to decide that people should use dozenal?

Modern computing does reduce this need and probably will eventually eliminate it. That being the case then, why wouldn't we switch to teaching our children dozenal? We won't struggle because computers can quickly convert. In the case of a catastrophe we can have a more efficient mathematical base.

Also measurements are easier to divide and may not need to be rounded to the nearest point as often. Again being eliminated, but again may be useful in insurance policy situations.

Maybe we shouldn't implement it, but I feel that a lot of people underestimate the usefulness of better systems. In fact, better anything. Most people seem quite adverse to change, sometimes irrationaly so.

People are inherently resistant to change, but that doesn't constitute a rational argument in favor of switching to dozenal. Like I said earlier, the decimal system is not a limiting factor. Frankly, it's very easy to use.
AlbinoBunny
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6/22/2014 5:27:48 PM
Posted: 2 years ago
At 6/22/2014 5:18:18 PM, dylancatlow wrote:
At 6/22/2014 5:12:18 PM, AlbinoBunny wrote:
At 6/22/2014 4:12:43 PM, dylancatlow wrote:
At 6/22/2014 3:48:17 PM, AlbinoBunny wrote:
At 6/17/2014 2:22:35 PM, dylancatlow wrote:
At 6/16/2014 5:24:08 PM, BradK wrote:
The other side of it, is that it's a shame we are stuck with a worse system. If you had to build society from scratch, all mathematicians would agree, that dozenal would be the one to pick, not decimal. If we were using dozenal, it would be out of the question to think of switching to either base ten or base fourteen.


I wouldn't say it's necessarily "worse" in a non-trivial sense. Numbers don't have to be pretty in order to do math, especially considering that all calculations can be done with a computer.

Because people have computers in their brains.

Important calculations are done with a computer. Calculations that we do in our head don't need to be very inefficient. Indeed, doing them in our head implies that much.

You mean efficient?

No. Calculations that we do in our head don't need to be done efficiently, since if we want them done efficiently, we use a computer anyway.

You said they don't need to be "very inefficient" and then denied my correction with what I said?

Also I'm sure there are people who may need accurate and quick calculations without immediate access to a computer. Why should I be unfair to them?


Who am I to decide whether people should calculate in their head or a follow computer? Whether they have a computer at hand when they need to do some important calculation?


And who are you to decide that people should use dozenal?

I personally don't decide. It's about options.


Modern computing does reduce this need and probably will eventually eliminate it. That being the case then, why wouldn't we switch to teaching our children dozenal? We won't struggle because computers can quickly convert. In the case of a catastrophe we can have a more efficient mathematical base.

Also measurements are easier to divide and may not need to be rounded to the nearest point as often. Again being eliminated, but again may be useful in insurance policy situations.

Maybe we shouldn't implement it, but I feel that a lot of people underestimate the usefulness of better systems. In fact, better anything. Most people seem quite adverse to change, sometimes irrationaly so.

People are inherently resistant to change, but that doesn't constitute a rational argument in favor of switching to dozenal. Like I said earlier, the decimal system is not a limiting factor. Frankly, it's very easy to use.

Why not settle for the best though? I understand why we don't change, but the fact that dozenal is better gives reason to change. Not that I advocate change. Minimal changes in our everyday lives can add up to a big difference.
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