The Instigator
RainbowDash52
Pro (for)
Winning
3 Points
The Contender
mostlogical
Con (against)
Losing
0 Points

What number system would be the best replacement for base 10.

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Post Voting Period
The voting period for this debate has ended.
after 1 vote the winner is...
RainbowDash52
Voting Style: Open Point System: 7 Point
Started: 1/25/2016 Category: Miscellaneous
Updated: 1 year ago Status: Post Voting Period
Viewed: 585 times Debate No: 85505
Debate Rounds (3)
Comments (3)
Votes (1)

 

RainbowDash52

Pro

I will be arguing for octal (base 8).

In round 1, my opponent will state what number system he thinks would be the best replacement for base 10, excluding base 8 or base 10. No arguments in round 1.

Pro will argue base 8 is the better replacement for base 10 to be used by people.
Con will argue whatever he/she posted in round 1 is the better replacement for base 10 to be used by people.
Burden of proof is shared.

Additional rules:
1. no kritiks
2. no semantics
3. sources cited must be freely accessible
4. no new arguments in the last round. Rebuttals are fine.

If you don't qualify to accept this debate, but would like to accept, post a comment and I might consider debating you.
mostlogical

Con

I accept and will be arguing that a base 12 (dozenal system) would be the better replacement
Debate Round No. 1
RainbowDash52

Pro

Doubling and Halving

There is this common math problem that goes as follows: If on day 1 I get paid one penny, and each day after that my number of pennies doubles, how much money will I have at the end of thirty days?
This is how many pennies you would have after each day in dozenal:
1: 1
2: 2
3: 4
4: 8
5: 14
6: 28
7: 54
8: A8
9: 194
10: 368
11: 714
12: 1,228
13: 2,454
14: 4,8A8
15: 9,594
16: 1,6B68
17: 31,B14
18: 63,A28
19: 107,854
20: 213,4A8
21: 426,994
22: 851,768
23: 1,4A3,314
24: 2,986,628
25: 5,751,054
26: B,2A2,0A8
27: 1A,584,194
28: 38,B48,368
29: 75,A94,714
30: 12B,969,228

This is how many pennies you would have after each day in octal:
1: 1
2: 2
3: 4
4: 10
5: 20
6: 40
7: 100
8: 200
9: 400
10: 1,000
11: 2,000
12: 4,000
13: 10,000
14: 20,000
15: 40,000
16: 100,000
17: 200,000
18: 400,000
19: 1,000,000
20: 2,000,000
21: 4,000,000
22: 10,000,000
23: 20,000,000
24: 40,000,000
25: 100,000,000
26: 200,000,000
27: 400,000,000
28: 1,000,000,000
29: 2,000,000,000
30: 4,000,000,000

The numbers in octal all have a 1, 2, or 4 followed by a series of zeros, while in dozenal, the answers are a seemingly random series of digits. For octal you just add a zero to the end every third day, while for dozenal, more math is needed and is impractical to do in your head or by hand. Octal makes repeatedly halving easy too. Example: 1, 0.4, 0.2, 0.1, 0.04, 0.02, 0.01, 0.004 . The simplicity of doubling and halving in octal has benefits in multiple areas including but not limited to calculating the amount of half-lives for carbon dating, and calculating the next tile number in the game 2048.

Binary Conversion:

Octal numbers can be converted into binary by simply converting each individual octal digit into its binary equivalence and combining them.
For example, 752:
7 in octal to binary would be 111;
5 in octal to binary would be 101;
2 in binary would be 010.
Put them together and you get 111101010, which is the binary equivalence of 752 octal. It"s that simple.

Dozenal on the other hand, take the number 25 dozenal:
You first find the biggest value that is 2^n where n is an integer, that is less than 25.
That number is 14 (2^4 dozenal)
Now we have 10000 (2^4 binary); you take 25 minus 14 and get 11,
Now we convert 11 (dozenal) into binary
8 (2^3) is the largest 2^n number under 11, so we add 1000 to the previous 10000 to get 11000.
We take 11 minus 8 to get 5 (dozenal).
5 in dozenal is 101 in binary, so we add 101 to 11000 and we get the final binary answer of 11101.

We have to do much harder work to convert to binary in dozenal than in octal, even when the dozenal number is much smaller than the octal number.

Computer Programming

Since computers use binary, it is beneficial to use a number system in which people can easily convert to and from binary. Let"s say you have a variable that can store a positive integer of 32 bits of length; What would the largest number it can hold be? It would be 2^32 -1, which in octal is a simple easy to remember 39,999,999,999 , while the answer in dozenal would be 9BA461593 , a number almost no one is going to be able to remember. It is beneficial for programmers to know the maximum number a variable can store instead of having to look it up on a calculator.

Converting base 12 "decimal", such as 0.B, to binary will always result in a number with infinite digits after the decimal point. enter 0.10000000000000 into the base n calculator cited at bottom for base 12 to base 2, and you will see the infinite 01"s at the end. Base 8 doesn"t have this problem, for example .1 octal equals .001 binary. Computers truncate infinite decimals, which creates rounding errors[1], which can lead to confusing results like .1 + .2 equaling .300000001 according to computers if dozenal were used.

Source: [1] https://docs.oracle.com... (Section: Rounding Error)

Base N Converter: http://korn19.ch...
Calculator: http://web2.0calc.com...
mostlogical

Con

Base 10 (what we use today) has 10 symbols = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

base 10


Base 12 has 12 symbols = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B (note: any symbol could be used to represent the two extra digits)

base 12


Counting and performing calculations would be easy. You may think children may find it hard to count in 12's because they don't have 12 fingers but each finger has 3 segments, meaning they can count twelve on each hand which is very useful if they are trying to do any maths involving time as there are 24 hours on a clock face.

The big advantage of using the dozinal system is when doing fractions because the number twelve has 6 factors which are 1, 2, 3, 4, 6, and 12, which is why clocks look the way they do.

A sixth in dozinal = 2/10 = 0.2
A qurater in dozinal = 3/10 = 0.3
A third in dozinal = 4/10 = 0.4
A half in dozinal = 6/10 = 0.6

Using dozinal means we don't get horrible repeating decimals like 0.333... in the base 10 system. And because we naturally count in twelves too e.g. 12 inches to a foot, it would an easy system to apply in everyday life.

The number 12 is a great number to divide by, before British currency was decimalised we had shillings which would be worth 12 pennies, "the penny was further sub-divided into two half pennies or four farthings (quarter pennies)" [1]

Memorizing the times table is easy in dozinal as there are so many patterns, the video below also shows how easy it is to count too
: https://www.youtube.com...

Most people are not computer programmers, so there is no need for everyone to count in octal. However it would be beneficial for everyone to learn to count in dozinal from a young age rather than our current counting system because the way time is divided, and the nature of our hands.


sources:

[1] http://resources.woodlands-junior.kent.sch.uk...





Debate Round No. 2
RainbowDash52

Pro

First I should mention I entered the wrong number in the previous round for 2^32 -1 in octal, it should be 37,777,777 instead of 39,999,999,999 since there are no 9"s in octal.

"Using dozenal means we don't get horrible repeating decimals like 0.333... in the base 10 system. And because we naturally count in twelves too e.g. 12 inches to a foot, it would an easy system to apply in everyday life."

You still get repeating decimals in dozenal. For example, for example 1/5 =
0.249724972497"

"Memorizing the times table is easy in dozinal as there are so many patterns"

The times table for base 8 is easier to memorize than for base 12 because base 8 has fewer digits. Base 8 and base 12 have 64 (8^2) and 144 (12^2) multiplications to memorize respectively. But if you exclude times 0 and times 1 since they are always equal to zero and itself respectively, you then get 36 ((8-2)^2) multiplications to memorize for base 8 and 100 ((12-2)^2) for base 12. So base 8 has only 36% as much multiplications to memorize for the multiplication table as for base 12. In addition, since there are fewer digits to multiply with each other in base 8, each individual single digit multiplication one does happens more frequently, since there are only 36 combinations excluding 1"s and 0"s. When a person is exposed to a question more frequently, it makes it easier for them to memorize it.

"Most people are not computer programmers, so there is no need for everyone to count in octal. However it would be beneficial for everyone to learn to count in dozenal from a young age rather than our current counting system because the way time is divided, and the nature of our hands."

Although it is true most people are not programmers, programmers use math much more than the average person, and that should be taken into consideration when weighing the advantages for programmers to advantages to everyone else. So it could be worth it for everyone to switch to base 8 even if hypothetically it is marginally worse for the average person but significantly better for the programmers who use math more frequently.
mostlogical

Con

Thank you for correcting your numerical error though this was not needed

There is a lower abundance of repeating decimals compared to using base 10 for simpler common fractions as I have shown e.g. thirds and sixths in dozenal appear much nicer and make a good replacement, 0.4 and 0.2 is better to work with than 0.333.... and 0.666... which we normally work with.

True, the only fractions that are simpler in decimal are 1/5 and 1/10 and their higher numerations. However there are an infinite number of primes so it is impossible to avoid repeating decimals for any system. I should have made my point clearer, I was trying to say that we don't get the same horrible decimals as we do in base 10.

Memorizing the times tables is easy in dozinal due to the patterns that can be seen, see video if you have not done so already.
True, there are less numbers in an 8x8 square than a 12x 12 square: http://mathforum.org...

However pupils learn up to their 12 times table in base 10 because that is a good amount of numbers to learn, and that was hard. If you learn the same amount of numbers in octal the table would have to be rectangular and I'm not sure if that would be easier or whether a square of 64 numbers would be sufficient.

If it is important for computer programmers or people learning programmiong languages to count in octal then I'm sure they can learn to do this, however if there is a practical system that is easier to learn at a young age for the majority of people then in my opinion that would make a better replacement. Everyone has to do maths when they make transactions, pay bills, manage their finances etc, so any replacement system should benefit everyone including computer programmers which it will when they are not working.
Debate Round No. 3
3 comments have been posted on this debate. Showing 1 through 3 records.
Posted by mostlogical 1 year ago
mostlogical
you won't lose any spelling or grammar points for making a numerical error, and you made your point clear anyway, plus there are further rounds too so I wouldn't worry about that. I have taken this debate up after doing a quick bit of research, and wanting to learn about this, I doubt I will be a strong opponent but I'll do my best to challenge you just reading up it now
Posted by RainbowDash52 1 year ago
RainbowDash52
Crap, just noticed the base 8 of 2^32-1 is 37,777,777,777 not 39,999,999,999. That's what I get for staying up late finishing before the deadline realizing the max number would be 2^32 -1 instead of 2^32, and assuming I was able to subtract 1 in my head. My argument still stands that the number number is simpler to remember, but I plan on conceding to spelling & grammar for entering the wrong number.
Posted by diarrhea_of_a_wimpy_kid 1 year ago
diarrhea_of_a_wimpy_kid
Good topic. I can think of pros for each side off the top of my head. Looking forward to it.
1 votes has been placed for this debate.
Vote Placed by Grandzam 1 year ago
Grandzam
RainbowDash52mostlogicalTied
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Total points awarded:30 
Reasons for voting decision: I agree with Con's side of the debate, but Pro's arguments were better than Con's because Pro was comparing and contrasting both sides of the debate, while Con was comparing his side of the debate to the current system, which makes all of Con's arguments irrelevant to the resolution. P.S. I am a programmer and I still think that I would prefer using dozenal over octal.