Ma notation

Overview

Ma notation is a notation of units, sounds and alike for human beings on the planet Earth.

Why

Maths

base 2

2 = 2^1

2 is the smallest value for the base in the operations of the hyperoperation sequence that result for b>2 and n>2 in increasing values for increasing n.

base 4

4 = 2^2 = 2*2 = 2+2 (exponentiation, multiplication, addition)

base 8

8 = 2^2^2

base 16

16 = 2^^2 (tetration)

List

		n
a	b	0	1	2	3	4
1	0	1	1	0	1	1
1	1	2	2	1	1	1
1	2	3	3	2	1	1
1	3	4	4	3	1	1
2	0	1	2	0	1	2
2	1	2	3	2	2	2
2	2	3	4	4	4	16
2	3	4	5	6	8	134217728

Cycles that fit with the above bases

Cycle 4

Soccer World Cups, Regional Cups, Olympic Summer Games have a 4 year cycle.

Elections in some countries have a 4 year cycle.

Alphabet

Features

Sound groups:

• nasal = 2
• nasal + plosive = 8
• nasal + plosive + fricative = 16

In each of the groups nasal, plosive, fricative, the order labial, coronal, dorsal is followed.

Until

• 9,
  • among 63 alphabets (http://en.wikipedia.org/wiki/Latin-derived_alphabet) the letters appear in 56
• 11,
  • the Latin symbols have the value of the IPA, the symbols are pronounced similar in several languages
• 15,
  • even positions are voiceless
  • each voiceless is even
  • uneven are voiced

List

Approximant/Vowels

• A 0 a Open_front_unrounded_vowel
• Ä 1 ɛ Open-mid_front_unrounded_vowel
• E 2 e Close-mid_front_unrounded_vowel
• I 3 i Close_front_unrounded_vowel
• O 4 ɒ Open_back_rounded_vowel
• Ö 5 ɔ Open-mid_back_rounded_vowel
• U 6 o Close-mid_back_rounded_vowel
• Ü 7 u Close_back_rounded_vowel

• • ə Mid-central_vowel

Consonants

Base	N.	IPA	ULA	Manner s/o	Manner	Place	Voice	Link
base 2	0	m	M	sonorant	0 NASAL	0/0 LABIAL/bilabial	1	Bilabial_nasal
base 2	1	n	N	sonorant	0 NASAL	1/3 CORONAL/alveolar	1	Alveolar_nasal
extra for base 4	2	p	P	obstruent	1 PLOSIVE/stop	0/0 LABIAL/bilabial	0	Voiceless_bilabial_plosive
extra for base 4	3	b	B	obstruent	1 PLOSIVE/stop	0/0 LABIAL/bilabial	1	Voiced_bilabial_plosive
extra for base 8	4	t	T	obstruent	1 PLOSIVE/stop	1/3 CORONAL/alveolar	0	Voiceless_alveolar_plosive
extra for base 8	5	d	D	obstruent	1 PLOSIVE/stop	1/3 CORONAL/alveolar	1	Voiced_alveolar_plosive
extra for base 8	6	k	K	obstruent	1 PLOSIVE/stop	2/8 DORSAL/velar	0	Voiceless_velar_plosive
extra for base 8	7	g	G	obstruent	1 PLOSIVE/stop	2/8 DORSAL/velar	1	Voiced_velar_plosive
extra for base 12	8	f	F	obstruent	3 FRICATIVE/Non-sibilant fricative	0/1 LABIAL/labio-dental	0	Voiceless_labiodental_fricative
extra for base 12	9	v	V	obstruent	3 FRICATIVE/Non-sibilant fricative	0/1 LABIAL/labio-dental	1	Voiced_labiodental_fricative
extra for base 12	10	s	S	obstruent	2 FRICATIVE/Sibilant fricative	1/3 CORONAL/alveolar	0	Voiceless_alveolar_sibilant
extra for base 12	11	z	Z	obstruent	2 FRICATIVE/Sibilant fricative	1/3 CORONAL/alveolar	1	Voiced_alveolar_sibilant
extra for base 16	12	ʃ	C	obstruent	2 FRICATIVE/Sibilant fricative	1/4 CORONAL/postalveolar	0	Voiceless_palato-alveolar_sibilant
extra for base 16	13	ʒ	Y	obstruent	2 FRICATIVE/Sibilant fricative	1/4 CORONAL/postalveolar	1	Voiced_palato-alveolar_sibilant
extra for base 16	14	ç	Q	obstruent	3 FRICATIVE/Non-sibilant fricative	2/7 DORSAL/palatal	0	Voiceless_palatal_fricative
extra for base 16	15	j	J	sonorant	4 APPROX (ʝ FRICATIVE)	2/7 DORSAL/palatal	1	Voiced_palatal_approximant
extra	16	x	X	obstruent	3 FRICATIVE/Non-sibilant fricative	2/8 DORSAL/velar	0	Voiceless_velar_fricative
extra	17	h	H	?	3?4 (FRICATIVE)	4/12 LARYNGEAL/glottal	0	Voiceless_glottal_fricative
extra	18	r	R	?	6 TRILL	1/3 CORONAL/alveolar	1	Voiced_alveolar_trill
extra	19	l	L	sonorant	8 LATERAL-APPROX	1/3 CORONAL/alveolar	1	Voiced_alveolar_lateral_approximant
extra	20	w	W	sonorant	Approximant/(Co-articulated)	2/8 DORSAL/velar	1	Voiced_labio-velar_approximant

Numeral system

Grouping

Use grouping by 4 like in East Asia Myriad http://en.wikipedia.org/wiki/Chinese_numerals#Large_numbers

Also for the part after the hexadecimal separator http://en.wikipedia.org/wiki/MOS:NUM#Delimiting_.28grouping_of_digits.29 has grouping by 3 (physics) and by 5 (maths). Unify these.

Naming

For naming of larger numbers use something like

• 2^4 = 10^1 = tip
• 10^2 = pip
• 10^3 = bip
• 10^4 = tip

(10^4)^1	NM^T^N	1 0000		(ni)tinum (n=1)
(10^4)^2	NM^T^P	1 0000 0000	squared myriad	pitinum (p=2)
(10^4)^3	NM^T^B	1 0000 0000 0000	cubic myriad	bitinum (b=3)
(10^4)^4	NM^T^T	1 0000 0000 0000 0000	quartic myriad	titinum (t=4)

Unit prefixes

• kilo-gram ~ niti-gram
• mega-gram ~ piti-gram

• niti-joule, piti-joule
• piti-byte

Finger counting

• http://commons.wikimedia.org/wiki/File:Hexadecimal-counting.jpg

Place

Latitude

As degrees:

Ma	ISO 6709	Comment
0.4	90°	North Pole
0.3	67.5°
0.2	45°
0.1	22.5°
0	0	equator
-0.1	-22.5°
-0.2	-45°
-0.3	-22.5°
-0.4	-90°	South Pole

Longitude

Longitudes run from 0 to 1 in westward direction.

Distance:

• 0x0.1 = 360°/16 = 22.5°
• 0x0.08 = 11.25°
• 0x0.2 = 45°

http://anna.info/x/Peters_projection_-_Umnak_meridian_-_hextime.svg

Positions:

Ma	ISO 6709 in °	ISO 6709	Comment
.0	-168.75	-168°45'	Umnak
.1	168.75
.2	146.25		Wilsons Promontory N.P., Tasmania
.3	123.75
.4	101.25
.5	78.75		Issyk Kul (Kyrgyzstan), Meerut, East of New Delhi (India), West of Sri Lanka
.6	56.25
.7	33.75		Krym, Lake Victoria
.8	11.25	11°15'	Florence
.C	-78.75		East of Panama Canal (Panama), West of Quito (Ecuador), Juan Fernandéz Islands (Chile)

Compass direction

Hex	English	English acronym	Level
.0	North	N	1
.1	North-northeast	NNE	4
.2	Northeast	NE	3
.3	East-northeast	ENE	4
.4	East	E	2
.5	East-southeast	ESE	4
.6	Southeast	SE	3
.7	South-southeast	SSE	4
.8	South	S	1
.9	South-southwest	SSW	4
.A	Southwest	SW	3
.B	West-southwest	WSW	4
.C	West	W	2
.D	West-northwest	WNW	4
.E	Northwest	NW	3
.F	North-northwest	NNW	4

Time

Base unit: 1 earth day.

• 1 hexsec = 1 day / 2^16 = 24*60*60 sec / 2^16 = (86400/65536) sec = 1.318359375 sec

Clock

See also: Ma circle

Hex		hexsec (base 16 notation)		hexsec (base 10 notation)		Traditional
1	=	10000	=	65536	=	24 h
0.1 (hex hour)	=	1000	=	4096	=	1 h 30 min
0.01	=	100	=	256	=	5 min 37.5 sec
0.001 (hex minute)	=	10	=	16	≈	21.09 sec
0.0001 (hex second)	=	1	=	1	≈	1.32 sec
		0.c23	≈	0.759	≈	1 sec

Hex	ISO 8601	Comment
.0100	00:05:37.5
.0200	00:11:15
.0400	00:22:30
.0800	00:45:00
.1000	01:30:00	1.5÷24 = 1÷16 = 0.1
.8000	12:00:00	12÷24 = 8÷16 = 0.8
.F000	22:30:00	22.5÷24 = 15÷16 = 0.F
.F800	23:15:00

Epoch

Avoid negative year numbers for years since -53248 CE.

ISO (CE)	Ma (base 10)	Ma (base 16)	Note
-53248	0	0
-49152	4096	1000	Start of the 1xxx-years. First four digit year in hex notation.
-13926	39322	999A	starting with that year all 4-character hex notations until FFFF will include a letter and distinguish the notation from other systems of year notation.
-12288	40960	A000	Start of the Axxx-years. Starting with that year, all 4-character hex notations until FFFF will start with a letter and distinguish the notation even better from other systems of year notation.
-9558	45056	AAAA
-8192	45056	B000	Start of the Bxxx-years.
-4096	49152	C000	Start of the Cxxx-years.
0	49152	D000	Start of the Dxxx-years. Until 4095 CE all years start with the letter D.
1792	55040	D700
2000	55248	D7D0
2048	55296	D800
4096	57344	E000	Start of the Exxx-years.
10000	63248	F710	ISO calendar needs 5 digits.
12287	65535	FFFF	the last year that can be expressed with 4 digits in hex notation.

The year starts on the day of the Northward equinox. The length of Northward equinox solar year is relatively stable in the time from 6000 BCE to 10000 CE at 47:37 to 49:20 in excess of 365 days and 5 hours. The other equinox and the solstice years are less stable.

That means, the year starts on what is mostly March 20 or 21 in ISO 8601.

Frequency

Derived unit: 1/d

• 1Hz = 86400/d = 1.318359375 /md [m = milli 1/65536]
• 0x1/md = 0.75851851851 Hz
• 0x200/md = 388.361481481 Hz

Pitch

ETS = Equal-tempered scale with A4=435.921023988 Hz, which is 0.99072959997 of ISO 16 defined A4=440 Hz.

A4@440 Hz : 440*(60*60*24) cycles per day = 38016000 cpd. That is 2^(25.1801034055) cpd, in hex notation 2^(0x19.2E1B41BC854E556FEB6CC2).

Ma	2^(...)	Oscillation per day	Oscillation per hexsec (day/65536)	Hz	ETS	Midi approx
M0	0x0	2^0 = 0x1	2^(-16) = 0x0.0001	1/(60*60*24) = 0.00001157407	G-21
M1	0x1	2^1 = 0x2	2^(-15) = 0x0.0002	2^(-15)/(60*60*24) =	G-20
M16	0x10	2^16 = 0x 1 0000	2^0 = 1 = 0x1	(2^16)/(60*60*24) = 0.75851851851	G-5
D19	0x13.6AAAA	2^19*2^(5/12)	2^3*2^(5/12)=10.6787188334	(2^19)/(60*60*24)*2^(5/12) = 8.10000598916	C-1	0
M20	0x14	2^20 = 0x 10 0000	2^4 = 16 = 0x10	(2^20)/(60*60*24) = 12.1362962963	G-1	7
D20	0x14.6AAAA	2^20*2^(5/12)	2^4*2^(5/12)=21.3574376667	(2^20)/(60*60*24)*2^(5/12) = 16.2000119783	C0	12
M21	0x15	2^21 = 0x 20 0000	2^5 = 32 = 0x20	(2^21)/(60*60*24) = 24.2725925926	G0	19
M22	0x16	2^22 = 0x 40 0000	2^6 = 64 = 0x40	(2^22)/(60*60*24) = 48.5451851852	G1	31
M23	0x17	2^23 = 0x 80 0000	2^7 = 128 = 0x80	(2^23)/(60*60*24) = 97.0903703704	G2	43
M24	0x18	2^24 = 0x 100 0000	2^8 = 256 = 0x100	(2^24)/(60*60*24) = 194.180740741	G3	55
M25	0x19	2^25 = 0x 200 0000	2^9 = 512 = 0x200	(2^25)/(60*60*24) = 388.361481481	G4	67
N25	0x19.15555	2^25*2^(1/12)	2^9*2^(1/12)=542.445104312	(2^25)/(60*60*24)*2^(1/12) = 411.4546569	Gis4/As4	68
P25	0x19.2AAAA	2^25*2^(2/12)	2^9*2^(2/12)=574.700568734	(2^25)/(60*60*24)*2^(2/12) = 435.921023988	A4	69
B25	0x19.4	2^25*2^(3/12)=2^(25.25)	2^9*2^(3/12)=2^(9.25)=608.874042881	(2^25)/(60*60*24)*2^(3/12) = 461.842236971	Ais4/Bes	70
T25	0x19.5555	2^25*2^(4/12)=2^(25.3333)	2^9*2^(4/12)=645.079577546	(2^25)/(60*60*24)*2^(4/12) = 489.304805487	B4/Ces4	71
D25	0x19.6AAAA	2^25*2^(5/12)	2^9*2^(5/12)=683.438005335	(2^25)/(60*60*24)*2^(5/12) = 518.400383306	Bis4/C5	72
K25	0x19.8	2^25*2^(6/12)=2^(25.5)	2^9*2^(6/12)=724.077343935	(2^25)/(60*60*24)*2^(6/12) = 549.226074214	Cis5/Des5	73
G25		2^25*2^(7/12)			D5	74
F25		2^25*2^(8/12)=2^(25.6666)			Dis/Es	75
V25	0x19.C	2^25*2^(9/12)=2^(25.75)			E5/Fes	76
S25		2^25*2^(10/12)			Eis/F	77
Z25		2^25*2^(11/12)			Fis/Ges	78
M26	0x1A	2^26 = 0x 400 0000	2^10 = 1024 = 0x400	(2^26)/(60*60*24) = 776.722962963	G5	79
M30	0x1E	2^30 = 0x 4000 0000	2^14 = 16384 = 0x4000	(2^30)/(60*60*24) = 12427.5674074	G9	127
M31	0x1F	2^31 = 0x 8000 0000	2^15 = 32768 = 0x8000	(2^31)/(60*60*24) = 24855.1348148	G10
M32	0x20	2^32 = 0x1 0000 0000	2^16 = 65536 = 0x1 0000	(2^32)/(60*60*24) = 49710.2696296	G11

Length

Base unit: 1 earth equator.

m = milli as 1/65536, k as 65536

• 0x1 Q = 40 075 000 meter
• 0x1 mQ ~ 611 meter
• 0x0.1 mQ ~ 38.21849 meter
• 0x0.01 mQ ~ 2.3886 meter
• 0x0.001 mQ ~ 0.14929 meter
• 0x0.0001 mQ ~ 0.009330688 meter ~ 9.33 mm = 0.933 cm

• 1 AU = 149597870700/40075000 Q = 3732.94749095 Q ~ 0xE95 Q
• 0x10000 Q = 1 kQ = 2.6263552e+12 m = 17.5561 AU

• 1 light-year = 9460730472580800 meter = 9460730472580800/40075000 Q = 236075620.027 Q = 3602.22808879 kQ ~ 0xE12 kQ
• MQ = 0x10000 kQ = 1.7212081e+17 m = 18.193184436 ly

Speed

Equator moves with 1 Q/d, i.e. 611 meter/1.32 seconds ~ 463 m/s ~ 1670 km/h.

• .1 Q/d ~ 104 km/h
• .08 Q/d ~ 52 km/h
• .01 Q/d = 1 cQ/d ~ 6.52 km/h [c centi, as 1/256]

A precision 1 cQ/d should be sufficient for traffic signs, i.e. only two digits are needed.

Since 0.1 Q/d ~ 104 km/h, most signs will only need one digit. A speedometer in cars would count cQ/d [0.01 Q/d].

Light:

• 299792458*24*60*60/40075000 = 646339.822114 Q/d = 9.86236300832 kQ/d

Chemical elements

Element symbols are derived from the atomic number. The numbers run from 1 to 118, the latter currently is the highest number of known elements.

118 in hex is 0x76, i.e. two digits are sufficient.