We Need Less Numbers

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you're being sloppy and lumping together one thing that could be evidence with a huge mass of things that are not evidence, or is even evidence against you.

The Mayans had the same level of astronomy Europeans had up to the time of Tycho Brahe (the last great astronomer before the age of telescopes).

The sky is right there above your head to be studied with out telescopes. Thats why Every culture had constellations, and myths to explain constellations. Stars are not like say...paramecia ...that you cant see without modern instruments (in that case a microscope). So its to be expected the humans around the world could keep track of stars, and might evolve a priesthood to specialize in the task, and that they could incorporate the knowlege into their archetecture (line up rocks with the solstice).

Its when you find some tribe that know about something that Tycho Brahe or the Mayans couldnt know ...without having the Hubble telescope that you might have something. And yes the Dogon tribe could be that kind of oddity. It is weird that they seem to know about an invisible to the naked eye campanion of a visible star. Could be evidence of something wierd. Could be a coincidence. But thats just one thing.

BTW- you're wrong that scholars at Copernicus's time "thought the world was flat".

Yes Copernicus was at odds with both his collegues and with the Church about how the solar system works, but not about the shape of the earth. His contemporary scholars KNEW the Earth was round. No one in the educated elite of Christendom ( nor of the Islamic World) thought the world was flat since pre Christian/pre Islamic Hellenistic times.

Copernicus was after Columbus and Magellan anyway (the later had sailed around the world).

Too much to cover crossing the millennia but let's stop at the Dogon

There is no dispute that the Dogon had knowledge of Sirius B but conventional scientific belief claims the tribe learned of the star from Europeans. The problem with this theory (espoused by among some notable luminaries such as Carl Sagan) is that Sirius B was not discovered by telescope until 1962 and the information was not published till 1970. The idea that some European randomly picked up this discovery and present it to the Dogon some time in the 1970s and they then mysteriously adopted this star in their creation myth is a little bit beyond farcical.

The Dogon called the star Po Tolo which is the same name they had for this star in the 1930s when explorers meticulously documented their belief system in the 1930s. . I would posit that astronomers trying to debunk the Dogon knowledge were a little sloppy.

base one:

= 0
1 = 1
11 = 2
111 = 3
1111 = 4
11111 = 5
111111 = 6
1111111 = 7
11111111 = 8
111111111 = 9
1111111111 = 10

(we don't need 0, just 1 - this is an extension and simplification of Roman Numerals)

This silly and bizarre number system is actually the basis of Morse Code and modern Infrared (IR) communications - used to represent bits 0 and 1 as separate digits using only one carrier frequency (Infrared). The length of time between clicks gives either dot (1 = 1) or dash (11 = 2). Infrared (IR) Remote controls and other devices use a similar trick.

See Also:

https://en.m.wikipedia.org/wiki/Unary_numeral_system

https://en.wikipedia.org/wiki/Turing_tarpit

https://en.wikipedia.org/wiki/Esoteric_ ... g_language

https://codegolf.stackexchange.com/ques ... ello-world

https://codegolf.stackexchange.com/ques ... great-good

See my atypical-neurology?
Ain't it weird?
Don't be Skeered
It's just an atypical-neurology
(with apologies to George Carlin )

One of the things that irritate me with morse code is how users of this form of communication can discern spaces between characters. Being able to process auditory signals and convert to text is ridiculously time consuming and complex and surely the longer the message the greater the chance for error. Morse code seems to be practical if you are sending short phrases provided they are repeated over a few cycles so the person listening understands where the message starts and stops before beginning decoding.

Morse would base two. Not base one. Wouldnt it?

Its not "dot dot dot dot". Its dots and dashes. Like ones and zeros.

Morse code is indeed one of those things that becomes automated by the brain, sending and receiving you don't actually "hear" or think about the di or the dah. Representing it with dots and dashes actually confuses the matter more.

When receiving morse as each character is heard it is building a string of text in your head that you write in all capitals, you don't actually think of the various short and long tones (di or dah or as some people think dots and dashes). There is even punctuation for those who wish to use it. The spaces between characters are there and are perceived by an experienced receiver. There are many abbreviations and expressions used which convey a meaning, including basic procedural matters to start and end a contact and convey meaning using the Q code system.

Sending and receiving morse really is like using another language that is translated in your head and to be good at it requires "speaking" it for many years. Indeed many telegraphers based their entire careers around it.

If you look at a book with Morse Code represented as dots and dashes with spaces between the words you really have at least three distinct symbols:

Dot = “.” = 1
Dash = “-“ = 2
WordSpace = “ “ = 0

As someone pointed out you could use another symbol to represent “end of message”

EndOfMessage = 3

So this could be base 3 or base 4.

But if you think about the old Morse Code clickers in the cowboy movies (current when Thomas Edison learned Morse as a boy) the apparatus used a spring and an electromagnet to create a clicker. When the “key” was down and the circuit was closed the leaver on the other side went down because of the electromagnet. Click. When the “key” went up the leaver on the other side went back up because of the spring. Click. The only difference between dot and dash is the length of time between clicks. This is where the similarity with base one is. The only difference between 1 and 11 is the length of the string of ones. Of course this is only part of the picture. There must be a way to tell if the base one number has ended. So there are at least two symbols in base one, but in base one three is 111 and in base two three is 011. In base one five is 11111 and in base two five is 101.
Even if you use a trailing 0 to represent “EndOfBaseOneInteger” they aren’t the same.

My first computer had a modem. The signal from the computer to the modem was binary. Voltage was either high (5 volts) or low (0 volts). The sending device (the Apple IIe desktop computer) and the receiving device (the modem) had to be set to the same Baud rate (bits per second) which also defined the length of time per bit (seconds per bit, or microseconds per bit). The amount of time to send 8 (base two) digits was fixed.

N microseconds of zero volts always meant 0 and N microseconds of 5 volts always meant 1.

For Morse the amount of time to send dot is less than the amount of time to send dash. The amount of time to send a WordSpace is less than the amount of time to send an EndOfMessage. So in my mind Morse is closer to base one than base two.

Let is call 1 key down and 11 key up. For a short period of time we use 1 and for a long period of time we use 11. This gives

Dot: 1 1 11
Dash: 1 11 11
WordSpace: 11 1 1
EndOfMessage: 11 11

Not quite right - we might want longer periods of time such as 111 and 1111 or even 11111111111

But that is the basics.

A binary transmission would be more like:

Dot: 01
Dash: 10
WordSpace: 00
EndOfMessage: 11

I recently read a page where someone was decoding an unknown IR transmission in order to duplicate it. It was much more like base one than base two.
But then the base one digits were being used to transmit binary at a higher level of abstraction. And the binary was being used to transmit 8 bit bytes (base 256).

More like Morse at the very lowest level. At the next level up morse uses dot and dash to transmit letters, decimal digits, abbreviations and punctuation. Something like base 36 (or more).

Some Esoteric Programming languages can ONLY represent numbers as base one. These are usually Turing Tarpits. But they are still Turing complete. Which means in theory (if you ignore code size in bytes and execution tome in seconds) they can so everything that a language like Java can do.

It gets weird down in the tunnels.

This is where either “hyper-focus” or “special interest” can take up hours of my time - and I am having fun. But most people don’t care.

By even 50 year old standards using telegraphy such as Morse is considered an obsolete and impractical way of communicating. Back in 1999 the last worldwide emergency services using morse for ships at sea were decommissioned and for all practical purposes had fallen into disuse about 10 years before then.

There are multiple efficient and faster ways of using on/off signalling including computerised digital modes in widespread use. When I did my amateur radio (Ham radio for the Americans) exams we were still examined on our ability to send and receive morse. It's something that the old timers keep using to keep the "language" alive but no doubt as these people pass it will disappear completely.

OK. you're right. When counting...when the message is an actual number then yes...it would be "base one".

Because the number is represented simply the number of dots (one equals one, seventeen dots equals the number seventeen, and so on). Crude as you can get, but it worked for a hundred plus years.

On the other hand the letters of the alphabet in Morse are represented by three transmissions. Each a different combination of dots and dashes (like ones and zeroes). So alphabetic data is transmitted in what amounts to a "binary code" - that presaged that of modern computers. Sorta.

Bet you dollars to donuts your infrared TV remote is still using base one at some level.

https://ofalcao.pt/blog/2017/decoding-o ... d-protocol

https://ofalcao.pt/blog/series/lego-ir-sniffing

https://ofalcao.pt/blog/2017/decoding-r ... d-protocol

http://courses.cs.tau.ac.il/embedded/pr ... erence.pdf

I used to love code books when I was a kit.

Here is another place you see base one: counting on your fingers.

One finger represents 1
Two fingers represents 2
Three fingers represents 3
. . .
Until you hit
. . .
Ten fingers represents 4 (where a thumb counts same as a finger).

But you could:
One finger on your right hand represents 1
Two fingers on your right hand represents 2
Three fingers on your right hand represents 3
Four fingers on your right hand represents 4
The right thumb represents 5 (all fingers closed again)
Thumb and one finger represents 6
Thumb and two fingers represents 7
Thumb and three fingers represents 8
Thumb and four fingers represents 9
One finger on your left hand represents 10 (all fingers - and thumb - closed on the right hand).
The left thumb represents 50.
You can count to 99 on your fingers this way - this is modeled on an abacus.
Some of my fellow students had learned this when they were younger - they could do really fast finger math.
(I had gone to a different school age 5 to 11 and never learned the trick).

Or you can count in binary on your fingers. It is kind of hard to do - the fingers don't like to bend that way.
You can count to 1023 this way.

It was easier to hard-wire an Iambic Keyer when I used the following parameters:

Dot = 1 0 (a two-step counter)
Dash = 1 1 1 0 (a four-step counter)
Letter Space = 0 0 (a two-step counter)
Word Space = 0 0 0 0 0 0 (a six-step counter)

Instead of the normally-taught parameters:

Dot = 1 ( "•" )
Dash = 1 1 1 ( "─" )
Dot/Dash Space = 0 ( " " )
Letter Space = 0 0 0 ( "   " )
Word Space = 0 0 0 0 0 0 0 ( "       " )

Good one Fnord. I was thinking my last "sketch" was a bit off, and probably more like the one you posted.

Another thought I had - If you accept that a number in unary doesn't really care what the symbol is then you have somethin like:

A = 1
B = 1
AA = 2
BB = 2
AAA = 3
BBB = 3
(and so on)

Now if you convince yourself the symbol doesn't matter, you stop needing a "end of integer" symbol. You can now represent:

01100011110000011111100000001111111100000001111111111 = 1 2 3 4 5 6 7 8 9 10.

If you use the rule that 1/300 of a second (300 baud) represents one 0 (0 volts) or one 1 (5 volts) and you actually record an old mechanical keyer signal you will get a pattern a lot like that.

You can't get rid of 9 because the the square root of 9 is 3 and the square of 9 is 81

And...you couldnt have either of the two Hollywood movies named "9" (though you could still have the Fellini original "81/2").


But seriously...it depends upon what the OP means. If they mean "switching from base ten to base nine" then you could still have the quantity we now call "9", but it would be written as '10'. And the quantity 81 would be written "100". Three would still be '3'.

But if we went from base 10 to base 9 we would all need to chop
off one of our fingers. And it would hurt.