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Base 12 a better system than Base 10?

AlbinoBunny
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3/31/2013 12:13:59 PM
Posted: 3 years ago
Do you think that Base 12 is a better mathematical system than Base 10?

As in every point up of down is a power of 12 instead of 10?
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Skepsikyma
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3/31/2013 12:19:11 PM
Posted: 3 years ago
The thing about numerical systems is that they're all better for different calculations. Duodecimal would be better for 3s, 4s, and while decimal is better for 5s. What system you use would largely be determined by existing institutions and traditions (base twelve wouldn't play nice with the metric system, for example.)
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
Enji
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3/31/2013 12:22:49 PM
Posted: 3 years ago
Base 12 might be nice with miles and feet and yards (and time), however given the widespread use of the metric system I don't think it would be a useful replacement.
AlbinoBunny
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3/31/2013 12:26:28 PM
Posted: 3 years ago
At 3/31/2013 12:19:11 PM, Skepsikyma wrote:
The thing about numerical systems is that they're all better for different calculations. Duodecimal would be better for 3s, 4s, and while decimal is better for 5s. What system you use would largely be determined by existing institutions and traditions (base twelve wouldn't play nice with the metric system, for example.)

2's, 3's, 4's and 6's vs 2's and 5's. Plus I believe we're more likely to divide by 3 or 4 than we are by 5 (even under the influence of how easy it's made under the decimal system).

Obviously the metric system doesn't work with it, but we just need to make them powers of 12 instead of 10.

Unfortunately, it seems some SI measurements are locked into Base 10. I think it's foolish to lock our standard units into any Bases because one of it's goals was to get rid of extra constants, so it shouldn't be introducing any at all.
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AlbinoBunny
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3/31/2013 12:28:29 PM
Posted: 3 years ago
At 3/31/2013 12:22:49 PM, Enji wrote:
Base 12 might be nice with miles and feet and yards (and time), however given the widespread use of the metric system I don't think it would be a useful replacement.

In the past.

Given the widespread of the Imperial system, the Metric system wouldn't be useful. Even considering it would make our lives easier.
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Skepsikyma
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3/31/2013 12:29:21 PM
Posted: 3 years ago
At 3/31/2013 12:26:28 PM, AlbinoBunny wrote:
At 3/31/2013 12:19:11 PM, Skepsikyma wrote:
The thing about numerical systems is that they're all better for different calculations. Duodecimal would be better for 3s, 4s, and while decimal is better for 5s. What system you use would largely be determined by existing institutions and traditions (base twelve wouldn't play nice with the metric system, for example.)

2's, 3's, 4's and 6's vs 2's and 5's. Plus I believe we're more likely to divide by 3 or 4 than we are by 5 (even under the influence of how easy it's made under the decimal system).

Obviously the metric system doesn't work with it, but we just need to make them powers of 12 instead of 10.

Good luck with that xD

Have you seen the moronic system people in America still insist on using? It's hard enough to sell the metric system as is, trying to do it in base 12 would be impossible.

Unfortunately, it seems some SI measurements are locked into Base 10. I think it's foolish to lock our standard units into any Bases because one of it's goals was to get rid of extra constants, so it shouldn't be introducing any at all.
"The Collectivist experiment is thoroughly suited (in appearance at least) to the Capitalist society which it proposes to replace. It works with the existing machinery of Capitalism, talks and thinks in the existing terms of Capitalism, appeals to just those appetites which Capitalism has aroused, and ridicules as fantastic and unheard-of just those things in society the memory of which Capitalism has killed among men wherever the blight of it has spread."
- Hilaire Belloc -
philochristos
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3/31/2013 12:34:38 PM
Posted: 3 years ago
At 3/31/2013 12:13:59 PM, AlbinoBunny wrote:
Do you think that Base 12 is a better mathematical system than Base 10?

As in every point up of down is a power of 12 instead of 10?

I like to count on my fingers, and I only have 10 of them, so base 10 works best for me. Now, if I happened to be the six-fingered man, and if I had six fingers on BOTH hands, then base 12 might work better.
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muzebreak
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3/31/2013 12:36:05 PM
Posted: 3 years ago
At 3/31/2013 12:34:38 PM, philochristos wrote:
At 3/31/2013 12:13:59 PM, AlbinoBunny wrote:
Do you think that Base 12 is a better mathematical system than Base 10?

As in every point up of down is a power of 12 instead of 10?

I like to count on my fingers, and I only have 10 of them, so base 10 works best for me. Now, if I happened to be the six-fingered man, and if I had six fingers on BOTH hands, then base 12 might work better.

Count your finger joints on one hand.
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AlbinoBunny
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3/31/2013 12:40:37 PM
Posted: 3 years ago
At 3/31/2013 12:29:21 PM, Skepsikyma wrote:
At 3/31/2013 12:26:28 PM, AlbinoBunny wrote:
At 3/31/2013 12:19:11 PM, Skepsikyma wrote:
The thing about numerical systems is that they're all better for different calculations. Duodecimal would be better for 3s, 4s, and while decimal is better for 5s. What system you use would largely be determined by existing institutions and traditions (base twelve wouldn't play nice with the metric system, for example.)

2's, 3's, 4's and 6's vs 2's and 5's. Plus I believe we're more likely to divide by 3 or 4 than we are by 5 (even under the influence of how easy it's made under the decimal system).

Obviously the metric system doesn't work with it, but we just need to make them powers of 12 instead of 10.

Good luck with that xD

Have you seen the moronic system people in America still insist on using? It's hard enough to sell the metric system as is, trying to do it in base 12 would be impossible.

Unfortunately, it seems some SI measurements are locked into Base 10. I think it's foolish to lock our standard units into any Bases because one of it's goals was to get rid of extra constants, so it shouldn't be introducing any at all.

I think it starts with education and parallel integration. I know people don't like change, and sometimes that may be a good instinct, sometimes. But in the age we're in, I think it's important to make everything as efficient and convenient as we can. Being brought up on Metric, I like it, and think it's better than Imperial.

I know it will be a hard sell though, if it would ever happen at all.
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AlbinoBunny
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3/31/2013 12:44:52 PM
Posted: 3 years ago
At 3/31/2013 12:34:38 PM, philochristos wrote:
At 3/31/2013 12:13:59 PM, AlbinoBunny wrote:
Do you think that Base 12 is a better mathematical system than Base 10?

As in every point up of down is a power of 12 instead of 10?

I like to count on my fingers, and I only have 10 of them, so base 10 works best for me. Now, if I happened to be the six-fingered man, and if I had six fingers on BOTH hands, then base 12 might work better.

Look at your fingers palm-side on your hand. Each of your four fingers is divided into three. Count from the bottom of your index finger as one, to the top as three, you can point to it with your thumb. Then go to the middle finger and repeat, then the little finger. Once you've reached the top of the little finger you've reached twelve.

You can then place your thumb on the other hand at the bottom of that index finger to represent twelve, and release the thumb from the top of your little finger. You can count to decimal 144 using this method, and it seems quite easy to use for me.
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AlbinoBunny
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3/31/2013 12:45:37 PM
Posted: 3 years ago
At 3/31/2013 12:36:05 PM, muzebreak wrote:
At 3/31/2013 12:34:38 PM, philochristos wrote:
At 3/31/2013 12:13:59 PM, AlbinoBunny wrote:
Do you think that Base 12 is a better mathematical system than Base 10?

As in every point up of down is a power of 12 instead of 10?

I like to count on my fingers, and I only have 10 of them, so base 10 works best for me. Now, if I happened to be the six-fingered man, and if I had six fingers on BOTH hands, then base 12 might work better.

Count your finger joints on one hand.

Yes like that. I elaborated on his/her answer above.
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Enji
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3/31/2013 12:46:43 PM
Posted: 3 years ago
At 3/31/2013 12:28:29 PM, AlbinoBunny wrote:
At 3/31/2013 12:22:49 PM, Enji wrote:
Base 12 might be nice with miles and feet and yards (and time), however given the widespread use of the metric system I don't think it would be a useful replacement.

In the past.

Given the widespread of the Imperial system, the Metric system wouldn't be useful. Even considering it would make our lives easier.

In the past base 10 was still widely used. You could argue that instead of changing to the metric system the change to base 12 would have been better.
AlbinoBunny
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3/31/2013 12:50:15 PM
Posted: 3 years ago
At 3/31/2013 12:46:43 PM, Enji wrote:
At 3/31/2013 12:28:29 PM, AlbinoBunny wrote:
At 3/31/2013 12:22:49 PM, Enji wrote:
Base 12 might be nice with miles and feet and yards (and time), however given the widespread use of the metric system I don't think it would be a useful replacement.

In the past.

Given the widespread of the Imperial system, the Metric system wouldn't be useful. Even considering it would make our lives easier.

In the past base 10 was still widely used. You could argue that instead of changing to the metric system the change to base 12 would have been better.

I guess if I was to debate it I could.
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Ore_Ele
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4/7/2013 1:49:49 AM
Posted: 3 years ago
How about base 30?

That way you get 2, 3, 4, 5, and 6.

Really, any system would be good, if that is what everyone uses. It is like asking which language is better. For the most part, any language works to communicate ideas, so long as we are all on the same page.
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AlbinoBunny
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4/7/2013 2:22:43 PM
Posted: 3 years ago
At 4/7/2013 1:49:49 AM, Ore_Ele wrote:
How about base 30?

That way you get 2, 3, 4, 5, and 6.

Really, any system would be good, if that is what everyone uses. It is like asking which language is better. For the most part, any language works to communicate ideas, so long as we are all on the same page.

But there are advantages and disadvantages.

Base thirty does add more factors and may be a better base. It is a huge increase on the multiplication tables though. If the symbols can be made and remembered (I think they could be), then the benefits could be better multiplication, divisibility and shorter number length. Unfortunately I think the multiplication tables might be the death of it.

I agree that the advantages do hinge on general usage.

I also do think that we could create an artificial language which is better than our modern natural languages. I'm actually looking into it at the moment.
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Ore_Ele
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4/8/2013 1:08:37 AM
Posted: 3 years ago
At 4/7/2013 2:22:43 PM, AlbinoBunny wrote:
At 4/7/2013 1:49:49 AM, Ore_Ele wrote:
How about base 30?

That way you get 2, 3, 4, 5, and 6.

Really, any system would be good, if that is what everyone uses. It is like asking which language is better. For the most part, any language works to communicate ideas, so long as we are all on the same page.

But there are advantages and disadvantages.

Base thirty does add more factors and may be a better base. It is a huge increase on the multiplication tables though. If the symbols can be made and remembered (I think they could be), then the benefits could be better multiplication, divisibility and shorter number length. Unfortunately I think the multiplication tables might be the death of it.

I agree that the advantages do hinge on general usage.

I also do think that we could create an artificial language which is better than our modern natural languages. I'm actually looking into it at the moment.

But the advantages are fairly minute. The current SI system that the US uses is not based in anything. 12 inch to a foot, 3 feet to a yard, or 5280 feet to a mile. 16 oz to a pound, 2000 pounds to a ton. We just make stuff up and it sticks. Even with no base at all, it still works pretty well. So, yes, it could be argued that different bases are technically better, but are any of them so significantly better that we should change our entire structure for them?
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F-16_Fighting_Falcon
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4/8/2013 1:25:42 AM
Posted: 3 years ago
At 3/31/2013 12:40:37 PM, AlbinoBunny wrote:
At 3/31/2013 12:29:21 PM, Skepsikyma wrote:
At 3/31/2013 12:26:28 PM, AlbinoBunny wrote:
At 3/31/2013 12:19:11 PM, Skepsikyma wrote:
The thing about numerical systems is that they're all better for different calculations. Duodecimal would be better for 3s, 4s, and while decimal is better for 5s. What system you use would largely be determined by existing institutions and traditions (base twelve wouldn't play nice with the metric system, for example.)

2's, 3's, 4's and 6's vs 2's and 5's. Plus I believe we're more likely to divide by 3 or 4 than we are by 5 (even under the influence of how easy it's made under the decimal system).

Obviously the metric system doesn't work with it, but we just need to make them powers of 12 instead of 10.

Good luck with that xD

Have you seen the moronic system people in America still insist on using? It's hard enough to sell the metric system as is, trying to do it in base 12 would be impossible.

Unfortunately, it seems some SI measurements are locked into Base 10. I think it's foolish to lock our standard units into any Bases because one of it's goals was to get rid of extra constants, so it shouldn't be introducing any at all.

I think it starts with education and parallel integration. I know people don't like change, and sometimes that may be a good instinct, sometimes. But in the age we're in, I think it's important to make everything as efficient and convenient as we can. Being brought up on Metric, I like it, and think it's better than Imperial.

I know it will be a hard sell though, if it would ever happen at all.

SOME metric units are better than Imperial. I always find meters per second a convenient way to measure speed and integrate it with other units. Yet what is this kilometers per hour nonsense? Might as well use miles per hour if we are going to use complicated, pointless units since more Americans are familiar with it.
F-16_Fighting_Falcon
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4/8/2013 1:28:53 AM
Posted: 3 years ago
Also, binary seems like a cute base to use. We wouldn't have to worry about converting to binary as far as computers are concerned although it can be unwieldy for large numbers. Yet if we are used to it and we use binary scientific notation, why not?
Ore_Ele
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4/8/2013 1:32:53 AM
Posted: 3 years ago
At 4/8/2013 1:28:53 AM, F-16_Fighting_Falcon wrote:
Also, binary seems like a cute base to use. We wouldn't have to worry about converting to binary as far as computers are concerned although it can be unwieldy for large numbers. Yet if we are used to it and we use binary scientific notation, why not?

hexadecimal, or anything that is a power of 2 (so base 4, 8, 16, 32, etc) works.
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AlbinoBunny
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4/8/2013 10:06:40 AM
Posted: 3 years ago
At 4/8/2013 1:08:37 AM, Ore_Ele wrote:
At 4/7/2013 2:22:43 PM, AlbinoBunny wrote:
At 4/7/2013 1:49:49 AM, Ore_Ele wrote:
How about base 30?

That way you get 2, 3, 4, 5, and 6.

Really, any system would be good, if that is what everyone uses. It is like asking which language is better. For the most part, any language works to communicate ideas, so long as we are all on the same page.

But there are advantages and disadvantages.

Base thirty does add more factors and may be a better base. It is a huge increase on the multiplication tables though. If the symbols can be made and remembered (I think they could be), then the benefits could be better multiplication, divisibility and shorter number length. Unfortunately I think the multiplication tables might be the death of it.

I agree that the advantages do hinge on general usage.

I also do think that we could create an artificial language which is better than our modern natural languages. I'm actually looking into it at the moment.

But the advantages are fairly minute. The current SI system that the US uses is not based in anything. 12 inch to a foot, 3 feet to a yard, or 5280 feet to a mile. 16 oz to a pound, 2000 pounds to a ton. We just make stuff up and it sticks. Even with no base at all, it still works pretty well. So, yes, it could be argued that different bases are technically better, but are any of them so significantly better that we should change our entire structure for them?

For converting figures I think a uniform base like metric is better. Fairly minute? With the amount of people that use it and how often they will, the "minute advantage" will compound. When you teach children both systems, they'll gravitate towards the easiest system.
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AlbinoBunny
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4/8/2013 10:09:50 AM
Posted: 3 years ago
At 4/8/2013 1:25:42 AM, F-16_Fighting_Falcon wrote:
At 3/31/2013 12:40:37 PM, AlbinoBunny wrote:
At 3/31/2013 12:29:21 PM, Skepsikyma wrote:
At 3/31/2013 12:26:28 PM, AlbinoBunny wrote:
At 3/31/2013 12:19:11 PM, Skepsikyma wrote:
The thing about numerical systems is that they're all better for different calculations. Duodecimal would be better for 3s, 4s, and while decimal is better for 5s. What system you use would largely be determined by existing institutions and traditions (base twelve wouldn't play nice with the metric system, for example.)

2's, 3's, 4's and 6's vs 2's and 5's. Plus I believe we're more likely to divide by 3 or 4 than we are by 5 (even under the influence of how easy it's made under the decimal system).

Obviously the metric system doesn't work with it, but we just need to make them powers of 12 instead of 10.

Good luck with that xD

Have you seen the moronic system people in America still insist on using? It's hard enough to sell the metric system as is, trying to do it in base 12 would be impossible.

Unfortunately, it seems some SI measurements are locked into Base 10. I think it's foolish to lock our standard units into any Bases because one of it's goals was to get rid of extra constants, so it shouldn't be introducing any at all.

I think it starts with education and parallel integration. I know people don't like change, and sometimes that may be a good instinct, sometimes. But in the age we're in, I think it's important to make everything as efficient and convenient as we can. Being brought up on Metric, I like it, and think it's better than Imperial.

I know it will be a hard sell though, if it would ever happen at all.

SOME metric units are better than Imperial. I always find meters per second a convenient way to measure speed and integrate it with other units. Yet what is this kilometers per hour nonsense? Might as well use miles per hour if we are going to use complicated, pointless units since more Americans are familiar with it.

Which Imperial unite are better than metric? We use MPH but for science Km/h is easier to work with because like you said m/s is used. Also an hour might not be the best way to arrange time, as it isn't uniform to a day. I know that people like familiarity, and that's ok, but sometimes change is beneficial.
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AlbinoBunny
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4/8/2013 10:12:24 AM
Posted: 3 years ago
At 4/8/2013 1:28:53 AM, F-16_Fighting_Falcon wrote:
Also, binary seems like a cute base to use. We wouldn't have to worry about converting to binary as far as computers are concerned although it can be unwieldy for large numbers. Yet if we are used to it and we use binary scientific notation, why not?

It does have it's uses. I guess the multiplication tables may not be too bad. It is very uncompressed though; the numbers become really long quickly. That's mean that they're longer to read, to say ect. It's definitely something to consider though.
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AlbinoBunny
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4/8/2013 10:14:41 AM
Posted: 3 years ago
At 4/8/2013 1:32:53 AM, Ore_Ele wrote:
At 4/8/2013 1:28:53 AM, F-16_Fighting_Falcon wrote:
Also, binary seems like a cute base to use. We wouldn't have to worry about converting to binary as far as computers are concerned although it can be unwieldy for large numbers. Yet if we are used to it and we use binary scientific notation, why not?

hexadecimal, or anything that is a power of 2 (so base 4, 8, 16, 32, etc) works.

Yes hexadecimal would be the compressed form of binary. It doesn't have three as a factor though, which I think still leaves base 12 in a better position.

Also if we are arguing for familiarity, then base 12 is only two units of base 10. This by itself isn't a good reason to change though.
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Ore_Ele
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4/8/2013 8:09:36 PM
Posted: 3 years ago
At 4/8/2013 10:06:40 AM, AlbinoBunny wrote:
At 4/8/2013 1:08:37 AM, Ore_Ele wrote:
At 4/7/2013 2:22:43 PM, AlbinoBunny wrote:
At 4/7/2013 1:49:49 AM, Ore_Ele wrote:
How about base 30?

That way you get 2, 3, 4, 5, and 6.

Really, any system would be good, if that is what everyone uses. It is like asking which language is better. For the most part, any language works to communicate ideas, so long as we are all on the same page.

But there are advantages and disadvantages.

Base thirty does add more factors and may be a better base. It is a huge increase on the multiplication tables though. If the symbols can be made and remembered (I think they could be), then the benefits could be better multiplication, divisibility and shorter number length. Unfortunately I think the multiplication tables might be the death of it.

I agree that the advantages do hinge on general usage.

I also do think that we could create an artificial language which is better than our modern natural languages. I'm actually looking into it at the moment.

But the advantages are fairly minute. The current SI system that the US uses is not based in anything. 12 inch to a foot, 3 feet to a yard, or 5280 feet to a mile. 16 oz to a pound, 2000 pounds to a ton. We just make stuff up and it sticks. Even with no base at all, it still works pretty well. So, yes, it could be argued that different bases are technically better, but are any of them so significantly better that we should change our entire structure for them?

For converting figures I think a uniform base like metric is better. Fairly minute? With the amount of people that use it and how often they will, the "minute advantage" will compound. When you teach children both systems, they'll gravitate towards the easiest system.

Teaching both systems can be viewed as a waste of time and resources. Especially if it gets to teaching more than two. If all children had to learn SI, binary, hex, and be able to do any equations in any system, yes, they would gravity towards the easier system, but the time wasted in teaching them all of them would yield a net loss of efficiency.

I'd say that base 10 is simplier in all aspects to no base at all. Yet in the US, we are still able to function and thrive in science, technology and engineering. The "handicap" of not having a base is no minute, that it is excusable.
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Enji
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4/8/2013 8:31:47 PM
Posted: 3 years ago
At 4/8/2013 1:08:37 AM, Ore_Ele wrote:
At 4/7/2013 2:22:43 PM, AlbinoBunny wrote:
At 4/7/2013 1:49:49 AM, Ore_Ele wrote:
How about base 30?

That way you get 2, 3, 4, 5, and 6.

Really, any system would be good, if that is what everyone uses. It is like asking which language is better. For the most part, any language works to communicate ideas, so long as we are all on the same page.

But there are advantages and disadvantages.

Base thirty does add more factors and may be a better base. It is a huge increase on the multiplication tables though. If the symbols can be made and remembered (I think they could be), then the benefits could be better multiplication, divisibility and shorter number length. Unfortunately I think the multiplication tables might be the death of it.

I agree that the advantages do hinge on general usage.

I also do think that we could create an artificial language which is better than our modern natural languages. I'm actually looking into it at the moment.

But the advantages are fairly minute. The current SI system that the US uses is not based in anything. 12 inch to a foot, 3 feet to a yard, or 5280 feet to a mile. 16 oz to a pound, 2000 pounds to a ton. We just make stuff up and it sticks. Even with no base at all, it still works pretty well. So, yes, it could be argued that different bases are technically better, but are any of them so significantly better that we should change our entire structure for them?

Imperial measurements were actually based on base 12. 5280 is divisible by 12 (giving 4400 feet to a mile in base 12 for easy division in halves and quarters) and there are 12 inches to a foot and 12 ounces to the Troy pound.
AlbinoBunny
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4/8/2013 8:33:17 PM
Posted: 3 years ago
At 4/8/2013 8:09:36 PM, Ore_Ele wrote:
At 4/8/2013 10:06:40 AM, AlbinoBunny wrote:
At 4/8/2013 1:08:37 AM, Ore_Ele wrote:
At 4/7/2013 2:22:43 PM, AlbinoBunny wrote:
At 4/7/2013 1:49:49 AM, Ore_Ele wrote:
How about base 30?

That way you get 2, 3, 4, 5, and 6.

Really, any system would be good, if that is what everyone uses. It is like asking which language is better. For the most part, any language works to communicate ideas, so long as we are all on the same page.

But there are advantages and disadvantages.

Base thirty does add more factors and may be a better base. It is a huge increase on the multiplication tables though. If the symbols can be made and remembered (I think they could be), then the benefits could be better multiplication, divisibility and shorter number length. Unfortunately I think the multiplication tables might be the death of it.

I agree that the advantages do hinge on general usage.

I also do think that we could create an artificial language which is better than our modern natural languages. I'm actually looking into it at the moment.

But the advantages are fairly minute. The current SI system that the US uses is not based in anything. 12 inch to a foot, 3 feet to a yard, or 5280 feet to a mile. 16 oz to a pound, 2000 pounds to a ton. We just make stuff up and it sticks. Even with no base at all, it still works pretty well. So, yes, it could be argued that different bases are technically better, but are any of them so significantly better that we should change our entire structure for them?

For converting figures I think a uniform base like metric is better. Fairly minute? With the amount of people that use it and how often they will, the "minute advantage" will compound. When you teach children both systems, they'll gravitate towards the easiest system.

Teaching both systems can be viewed as a waste of time and resources. Especially if it gets to teaching more than two. If all children had to learn SI, binary, hex, and be able to do any equations in any system, yes, they would gravity towards the easier system, but the time wasted in teaching them all of them would yield a net loss of efficiency.

I'd say that base 10 is simplier in all aspects to no base at all. Yet in the US, we are still able to function and thrive in science, technology and engineering. The "handicap" of not having a base is no minute, that it is excusable.

I'm glad you can function without optimisation. What's the point in trying to make things easier for ourselves anyway?
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