Keyboard in base 60

Hi guys,
I am trying to build a keyboard to insert numbers in base 60 and I am very frustrated
because there is not any single example on internet about it.
The reason I'm doing this is that I believe the decimal system is wrong for many reasons
and the number 60 would be the best option for a new number system.
I created my own characters and I want to insert them on a LCD using an Arduino.
Possibly, I would like to make conversions from decimal and binary.
Up to now I have the following:
8/8 button matrix
and
64 button shield for Arduino
I don't know which Arduino would be better because I need 16 inputs from the 64 button shield.
Once everything connected, the biggest task will be programming.
Has anyone got any idea how to convert decimal and binary numbers to base 60?
Any suggestion would be very helpful.
Regards

Think you need a MEGA …

base 60 is just a representation of integers, just like binary and decimal and octal and septal and quintal …etc.

try this.

// converts long to string in some base
char* convertBase(long nr, int base)
{
  static char s[34];
  uint8_t digits[34];
  int idx = 0;
  boolean negative = false;

  // prevent overflow
  if (base<1) base = 2;
  // handle sign
  if (nr < 0)
  {
    negative = true;
    nr = -nr;
  }
  // strip digits
  while (nr >0)
  {
    digits[idx++] = nr % base;
    nr = nr/base;
  }
  int i=0;
  if (negative) s[i++]='-';
  while (idx > 0)
  {
    s[i++] = '0' + digits[--idx];  // mapping upon a readable part of ascii table
  }
  s[i] = '\0';
  return s;
}

void setup()
{
  Serial.begin(9600);
  for (int b=2; b<128; b++)
  {
    Serial.print(b);
    Serial.print("\t");
    Serial.println(convertBase(12345678, b));
  }
}

void loop(){}

reading base60 digits is left as an exercise for the reader :wink:

s[i++] = '0' + digits[--idx];  // mapping upon a readable part of ascii table

That part is going to be a bit tricky for base 60. If you're using your own character set, you can do something like:

s[i++] = glyph[digits[--idx]];

(I call "troll", BTW...)

insert numbers in base 60 and I am very frustrated because there is not any single example on internet about it.

No shit, I wonder why. Expecting aliens with 60 fingers to land soon?


Rob

The reason I'm doing this is that I believe the decimal system is wrong for many reasons
and the number 60 would be the best option for a new number system.

While there may be some things wrong with decimal, sexagesimal is hardly new. The Sumerians used it back in the bronze age.

The Sumerians used it back in the bronze age.

Very true, think the 24 hour clock with 60 minutes/seconds can be traced back to them.

But imagine the multiplication (clay)tables you had to learn in those ages, 1x1 to 60x60 :wink:

Not everything coming from bronze ages is old fashioned.
Just to clarify, money and the alphabet was invented during that time,
and maths was the first science to be adopted by humans. There are many other things
like Christianity, but this is not a philosophical discussion...
Regarding the aliens, we don't know how many fingers they have, but if they are advanced enough,
they definitely use the numbers in base 60 and 64. It's enough to know a bit of maths and electronics
to understand my point.
The only reason we use a decimal system is because French Revolution decided that, and know what?...
we are now too lazy to admit it is wrong.
Come on guys, it's not that hard to build a new computer keyboard in base 60.
Just think of the benefits. I'm not going to explain now all the reasons why the decimal system is wrong.
My idea might look crazy but all the great ideas seemed crazy until people begun
to understand them.
In a few years the decimal system will be useless. Numbers are getting already too big
and we don't have any idea how to deal with them.
What about this ridiculous binary system? By using numbers in base 64 we can
simplify km of computer code.
Thank you anyway.
You are free to make fun of anything you don't understand. In a few years perhaps will be my
turn to laugh.

Please clarify - how does base 2^6 simplify things?

Just think of the benefits.

Thinking…nope, it’s not coming to me.

I admit that if you could find a reliable way to represent say 64 levels in a single bit you’d be onto something, but that’s a slightly different story to building a keyboard.


Rob

I'm not going to explain now all the reasons why the decimal system is wrong.

You do not have to explain, just post a link (or more) is enough

in base 60 and 64

base 64 is a power of 2, and 2 is a fundamental base as it is the first integer base that allows for shorter representation of natural numbers. However 64 is 2^6 and 6 is not so fundamental. hexadecimal bas 16 is much more elementary as it is 2^2^2 = 2^4 = 16, 256 is the next in this line 256 = 2^2^2^2 and 65536 is 2^2^2^2^2 .

The only special thing of 60 is that it has many (12) dividers (1,2,3,4,5,6,10,12,15,20,30,60) That makes it easy to divide numbers and stay in the integer domain.
And yes that makes some things easy (like splitting an hour)

But:
Base 60 or base 10 or base 12 or ... whatever is just a (human) representation of the number. Numbers and their properties do not change by presenting it in another base. A number which is prime in base 10 will also be prime in base 2,3,4,5,6 until a zillion and more. numbers that are each other dividers are that in any base.

I am not familiar with any basic numeric property that changes (pos/neg) due to different base except for the letter=digit puzzles like:
give
more
------ +
money

OK what does wikipedia say :

  • Sexagesimal - Wikipedia -
    look at how in the Babylonian mathematics base 60 was represented: looks quite decimal to me ...

  • 60 (number) - Wikipedia
    the number pops up several times in some corners of the math universe but so does PI ...

so still not convinced that base 60 is better than base 10

There are 10 types of people in the world: Those who understand binary, and those who don't...

I guess we are moving from programming to philosophy.
Look, I am neither a mathematician nor a scientist but if I want
to write one billion in binary I need 30 digits. In base 64 I only need 5.
Isn't this clear enough?
I'm wondering who is able to memorize 30 digits.
A bigger base also offers more combinations creating less confusion when
handling the numbers. Believe it or not, information grows exponentially and we have
to store all of it in binary. I don't have any idea how many digits we need to translate
a book, for example. The answer must be something kilo-metric.
Of course, you are going to say that computers are increasingly powerful. I agree, but even
computers work in certain limits. Moore's Law cannot go for ever.

I'm wondering who is able to memorize 30 digits.

So how many symbols are we expected to memorize to use base 60 or 64?

Scientific/exponential notation is always good for the bigger numbers.
1E^3 = 1 thousand
1E^6 = 1 million
1E^9 = 1 billion
1E^12 = 1 trillion
1E^15 = 1 gazillion?
Still just need 0-9.

Agree with CrossRoads! (of course base64 can have its own exponential notation too :wink:

I agree, but even computers work in certain limits. Moore's Law cannot go for ever.

So? Those limits are way beyond human's limits in terms of amount of data processing...

How will base64 help with really big numbers like Ackermann(5,5)? - Ackermann function - Wikipedia -
(decimal notations fails here too)

So how many symbols are we expected to memorize to use base 60 or 64?

Not too many, compared to the number of apps people have on their smartphones.
There are more than 700000 apps, most of them useless.
People today are just so reluctant at learning anything useful!
We are so incredibly busy at doing nothing.
What we really need is some apps to teach people some basic maths.
So, perhaps we can expect to end this depression, or crisis or whatever it is.

Thank you guys for keeping this conversation interesting.

IIRC In the Scientific American / Scientist there was an article a few years ago about counting. The stories main line was that counting in its earliest form was "body part" based.
Even the most "primitive" civilizations understood the number 1 to 5 (fingers) Above that there was only infinity. For some others the next important frontier was 20 (fingers + toes) .
Can't find the article but a related link - http://www.es.flinders.edu.au/~mattom/science+society/lecture3.html -

This number 20 has still a separate name e.g. in French "vingt" , it is not the same grammatical construction like thirty (which derives from three-ten), in French you even have 80 called quatre-vingt 4x20.

Just to add to the confusion...

Q: how to represent negative numbers in base64? one or two complements? (is -0 an other number than +0)

The number of people who still do mental calculations is constantly decreasing. We don't have to worry
too much about the names of numbers in certain languages.
As seen in this article; http://www.es.flinders.edu.au/~mattom/science+society/lecture3.html -
the decimal system was nothing more than the product of an accident: biological or historical or both.
Now let's go back to the computers because most of the calculation are made with computers, and ask ourselves
an honest question: what is so special about the decimal system and why are we still using it?
For mobile phones it might be useful but in the case of computers it's a different matter.
The best option would be to use base 60 in parallel and to allow easier conversions between bases.
There is no need to be so obsessed with the decimal system just because we like to be nostalgic.

Think about Mona Lisa.
For about 500 years the entire planet ignored its existence. Then, because of an accident, it became the
most famous painting of the world. Now, we all agree about this but we still don't know why it is the most famous
painting of the world.

The story of the decimal system looks very similar to the story of Mona Lisa.

One could make the same argument between English units and Metric units, and time even, all based on some arbitrary standard.
Length of some kings foot, some (relatelively) poorly made distance between 2 points divided by a million, the number of vibrations of some atom.

I don't see much point in counting
0 1 2 3 4 5 6 7 8 9 a b c d e f
and then some arbitrary symbols that are equivalent to
10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
20 21 22 23 24 25 26 27 28 29 30 3a 3b 3c 3d 3e 3f
40 41 42 43 44 45 46 47 48 49 4a 4b

when in computing, which is definitely not going away, binary will always rule the day - 0 & 1 are the king of states.
Perhaps eventually "quantum computing" with "bits" that can have more than 0/1 states will see the light of general use, but that it aways away.

Only takes 26 letters to express ourselves clearly (versus thousands of pictures of words in other languages), and time/experience has shown that just 2 numbers, 0/1, and its shorthand for readability, 0-9 or 0-F, can get us everywhere we can go.

Now, we all agree about this

It's a nice pic but I've seen a lot better. In the art world you don't have to be good, you just have to kiss the right arse.

we still don't know why it is the most famous painting of the world.

For the same reason that some talent-less moron becomes famous these days, promotion and a brain-dead populace.


Rob