Where the author proves seximal is better:
Video on dozenal and seximal
7 posts
• Page 1 of 1

Double sharpDozens Demigod
 Joined: Sep 19 2015, 11:02 AM
I have previously mentioned this person's senaryadvocacy site here.

sunnyRegular
 Joined: Jun 30 2013, 08:58 AM
I was at some point, so convinced that Senary might be a lot better base than Dozenal because of it's more friendliness to 5ths and 7ths. But alas, you can't do clear cut 5ths and 7ths in senary without a "remainder", the good visual easy reptends of those after its fractional point doesn't help with the case and could be as bad as any more larger reptends in other base, 3rds in decimal or 5ths in dozenal doesn't matter as you can't do that in both however beauty or ugly it might be. In comparision, you get direct 'quarters' in dozenal where you have to leap forward a square in that heximal base number to get it. In exchange, you get a large base with minified digit length just when you put that another factor of 2.

KodegaduloObsessive poster
 Joined: Sep 10 2011, 11:27 PM
You know, he manages to put together a fun video, and he's got the chutzpah of youth, but he's cherrypicked divisibility tests and reptends as the beall endall criteria for what makes a good base. He completely glosses over the compactness issue with senary.
For example, in a decimal or dozenal world, tendigit phone numbers suffice. But in a senary world, they would need thirteen digits. An area code would need four digits instead of three. Likewise for an exchange number. And if you want enough individual lines in your exchange, you'd need five digits instead of four. Social security numbers in the US are also ten decimal digits, so likewise we'd need thirteen senary digits to accommodate the population. Zip codes in the US would need to be 6 digits rather than 5. That much more to remember, that much more to store, that much more space needed on displays, in paper advertisements, on government forms, yadda, yadda, yadda...
Sure, the multiplication table you have to learn in third grade is simpler, but in exchange for that you get costs, costs, costs, all the rest of your life.
[I originally posted this on the wrong thread, so I copied the text, deleted the post, came here and tried to post it. Nannystate tapatalk scolded me that I can't post the same text as I previously posted. Are you kidding me?? So the presence of this little rant at the end here is just to make this post different. Please ignore.]
For example, in a decimal or dozenal world, tendigit phone numbers suffice. But in a senary world, they would need thirteen digits. An area code would need four digits instead of three. Likewise for an exchange number. And if you want enough individual lines in your exchange, you'd need five digits instead of four. Social security numbers in the US are also ten decimal digits, so likewise we'd need thirteen senary digits to accommodate the population. Zip codes in the US would need to be 6 digits rather than 5. That much more to remember, that much more to store, that much more space needed on displays, in paper advertisements, on government forms, yadda, yadda, yadda...
Sure, the multiplication table you have to learn in third grade is simpler, but in exchange for that you get costs, costs, costs, all the rest of your life.
[I originally posted this on the wrong thread, so I copied the text, deleted the post, came here and tried to post it. Nannystate tapatalk scolded me that I can't post the same text as I previously posted. Are you kidding me?? So the presence of this little rant at the end here is just to make this post different. Please ignore.]
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Baseneutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Baseneutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

sunnyRegular
 Joined: Jun 30 2013, 08:58 AM
I merely think of fourths as an equally important factor alongside thirds, if not more. I think that the minimized digit length is merely a gift that dozenal provides us. If achieving more minimized digit length is better, then by including another factor of 2 in dozenal provides us 24 which could be more better in that regard, we just have to spend a much detailed time in learning multiplication tables. But once achieved, it would certainly cost less later in life. As using such a huge, pure base in practicality seems highly subjective, so 12 might be the sweet spot, considering 1/8ths as "not so needed" at the cost of that much sacrifice in learning so much numbers and their multiplication tables.
I still think ways to improve senary to make it more practical, but I just can't. The best way that I like is to use it say, as a compression using color codes:
"0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 10", which is respectively "0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 10", as the latter are in base 36 represented in today's world.
These are the numbers that represent 036 with "10" as the base number, the 36 itself, if we follow this pattern, the multiplication table seems good to grasp?, because you get only numbers from the subset 05, and the patterns could be achieved with them. It can be color that tells us how large the number is. It's not just the colors, we could replace them with different styles in terms of writing them like plain, strikethrough, vertical strikethrough, underline, overline and finally, say a dot on them. Anything works fine as long as the numbers in one subset is similar to others in different subset but easily distinguishable from others.
It seems complicated, but once achieved, it could minimize the word length to a great level and we could get patterns such as multiples of 2 end in 0, 2 and 4 and its family (0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4). Multiples of 3 would end in its family 0 and 3. Multiples of 4 would end in 0 and 4 from one subset (black, blue and yellow here) and end in 2 from others (violet, green and red here). Multiples of 5 would end in decreasing order 5, 4, 3, 2, 1, 0 and so on but next with alternating colors starting 5 from red again.. 5, 14, 13,.. and so on, Multiples of 0(six) would end in 0 always, that '0' could mean any color here. Multiples of 1(seven) would end in increasing order 1, 2 ,3, 4, 5, 10 but in alternating colors shifted from here on (skipping a color afterwards when this has reached 5, 10, skipped black '0' here by jumping from red 5 to violet 0).
I could go on like this, there could be an easy rule to find out if a number is divisible by another number which for that, we need to look up in the color of the number left to unit's place to determine. But if anyhow, if we could get the gist of the multiplication table easily and which color/style is larger in value than the other, the digit length of this number base is highly minimized but now with achievable practicality of its implementation.
Has something like this discussed elsewhere in this forum? I don't know if I had seen something like this here, or something alike as far I can remember (pardon me for not knowing it, because it's in my subconscious mind for many days so I may have borrowed the idea unknowingly)., or if there is any better way to do this written out here?
I still think ways to improve senary to make it more practical, but I just can't. The best way that I like is to use it say, as a compression using color codes:
"0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 10", which is respectively "0 1 2 3 4 5 6 7 8 9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 10", as the latter are in base 36 represented in today's world.
These are the numbers that represent 036 with "10" as the base number, the 36 itself, if we follow this pattern, the multiplication table seems good to grasp?, because you get only numbers from the subset 05, and the patterns could be achieved with them. It can be color that tells us how large the number is. It's not just the colors, we could replace them with different styles in terms of writing them like plain, strikethrough, vertical strikethrough, underline, overline and finally, say a dot on them. Anything works fine as long as the numbers in one subset is similar to others in different subset but easily distinguishable from others.
It seems complicated, but once achieved, it could minimize the word length to a great level and we could get patterns such as multiples of 2 end in 0, 2 and 4 and its family (0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4). Multiples of 3 would end in its family 0 and 3. Multiples of 4 would end in 0 and 4 from one subset (black, blue and yellow here) and end in 2 from others (violet, green and red here). Multiples of 5 would end in decreasing order 5, 4, 3, 2, 1, 0 and so on but next with alternating colors starting 5 from red again.. 5, 14, 13,.. and so on, Multiples of 0(six) would end in 0 always, that '0' could mean any color here. Multiples of 1(seven) would end in increasing order 1, 2 ,3, 4, 5, 10 but in alternating colors shifted from here on (skipping a color afterwards when this has reached 5, 10, skipped black '0' here by jumping from red 5 to violet 0).
I could go on like this, there could be an easy rule to find out if a number is divisible by another number which for that, we need to look up in the color of the number left to unit's place to determine. But if anyhow, if we could get the gist of the multiplication table easily and which color/style is larger in value than the other, the digit length of this number base is highly minimized but now with achievable practicality of its implementation.
Has something like this discussed elsewhere in this forum? I don't know if I had seen something like this here, or something alike as far I can remember (pardon me for not knowing it, because it's in my subconscious mind for many days so I may have borrowed the idea unknowingly)., or if there is any better way to do this written out here?

KodegaduloObsessive poster
 Joined: Sep 10 2011, 11:27 PM
Sunny the yellow color you used made those numbers completely invisible against the post background on my mobile phone (Samsung Galaxy 7 Android). Color is not advisable anyway because a significant fraction of people suffer from colorblindness (my brother, for example).
Using [09AZ] for hexatrigesimal compression is problematic partly because of the confusion of 0 vs O vs Q, or 1 vs I.
Using [09AZ] for hexatrigesimal compression is problematic partly because of the confusion of 0 vs O vs Q, or 1 vs I.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Baseneutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Baseneutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)

Double sharpDozens Demigod
 Joined: Sep 19 2015, 11:02 AM
The trouble with doing this kind of thing is that learning what order the colours or styles go in is just like learning them as if they were senary digits, which is what they are and how they act like: they may look nice early in the digit range, but try writing the hexatrigesimal tables for digits in the middle of the range and they start appearing in many different orders. So it is really not very different from learning the senary tables up to 100_{6} * 100_{6}, as you still have to think of senary to reconstruct many values in the middle of the table, instead of simply memorising them. The main difference is actually a negative difference, because you now have to add extra steps to convert colours and styles to senary digits and back. A further problem is that it may not be clear if the colour or styling is part of the digit or part of the context: if the text is coloured, what happens to the digits in the text?
I think this idea is probably at its best for a small mixed radix where the top subbase is very small, like 2 or 3. This allows the digits to be thought of as single entities and means that the difficulty of remembering the ordering of the styles and working with them is minimised, although it might perhaps be less confusing to simply be aware of the correspondences between digits at the same positions in their ranges rather than to make them look like each other with a stylistic difference. Indeed, Oschkar and I have considered this for what we have been calling the "higher naturalscale", but some anecdotal experimentation by the two of us suggests that the need for the digits to be thought of as single entities means that its limit at making big bases manageable may be very small, something like 18 or 20. You are then still stuck with a large multiplication table, but since addition has been effectively abbreviated to become only as difficult as the smaller subbase, you have more time to deal with it, and it isn't so large that you almost always have to break up the digits while multiplying them to get anywhere (like doing j * m in hexatrigesimal). The large multiplication table is also ameliorated by the way the digits can be broken up when you need them to be (e.g. for vigesimal patterns like 9i171g25 and so on) and not broken up when you need them not to be (e.g. for vigesimal patterns like 48cg10 and so on), so that you get to work with patterns from both the smaller subbase and the larger full base. But while I can get my head around this for octodecimal and vigesimal I already can't think of base 24 without always breaking it up as either 4on6 or 2on12, and while there may be some variation between individuals here I highly doubt you could get it all the way to base 36 as you would need to make it more attractive arithmetically (not mnemonically) to compress senary than to leave it alone.
I think this idea is probably at its best for a small mixed radix where the top subbase is very small, like 2 or 3. This allows the digits to be thought of as single entities and means that the difficulty of remembering the ordering of the styles and working with them is minimised, although it might perhaps be less confusing to simply be aware of the correspondences between digits at the same positions in their ranges rather than to make them look like each other with a stylistic difference. Indeed, Oschkar and I have considered this for what we have been calling the "higher naturalscale", but some anecdotal experimentation by the two of us suggests that the need for the digits to be thought of as single entities means that its limit at making big bases manageable may be very small, something like 18 or 20. You are then still stuck with a large multiplication table, but since addition has been effectively abbreviated to become only as difficult as the smaller subbase, you have more time to deal with it, and it isn't so large that you almost always have to break up the digits while multiplying them to get anywhere (like doing j * m in hexatrigesimal). The large multiplication table is also ameliorated by the way the digits can be broken up when you need them to be (e.g. for vigesimal patterns like 9i171g25 and so on) and not broken up when you need them not to be (e.g. for vigesimal patterns like 48cg10 and so on), so that you get to work with patterns from both the smaller subbase and the larger full base. But while I can get my head around this for octodecimal and vigesimal I already can't think of base 24 without always breaking it up as either 4on6 or 2on12, and while there may be some variation between individuals here I highly doubt you could get it all the way to base 36 as you would need to make it more attractive arithmetically (not mnemonically) to compress senary than to leave it alone.