The Dearth of Superlatitives

We now take a break from our investigation of the Singularity to discuss an approaching problem that gets very little attention.

The problem is Moore's law, or one of its many variations. For instance, consider computer performance. It doubles every 1.5 years. Or hard drive volume, it increases by 1000 times every 5 years. So right now we have can buy hard drives in the Tera-Byte(Tb) range, but 5 years ago, it was the top of the line was Giga-bytes (Gb), and 10 years ago, we were still in the Mega-byte range(Mb).

The system of SI units gives us prefixes for progressive powers of 1000. That means in 5 years, (baring truly major war, or disaster) we will have Peta-bytes (Pb) hard drives, then in 2018, Exa-byte(Eb), then 2023, Zetta-byte (Zb) and by 2028 Yotta-bytes (Yb). And then.... nothing.

The trouble is that math is a language and the venerable SI system of units, (aka metric), does not have any more pre-fixes, or words if you will, for larger numbers.

Borrowing from Wikipedia, we see that the both in terms of large and small, we are limited.

1000m	10n	Prefix	Symbol	Since[1]	Short scale	Long scale	Decimal
10008	1024	yotta-	Y	1991	Septillion	Quadrillion	1 000 000 000 000 000 000 000 000
10007	1021	zetta-	Z	1991	Sextillion	Trilliard	1 000 000 000 000 000 000 000
10006	1018	exa-	E	1975	Quintillion	Trillion	1 000 000 000 000 000 000
10005	1015	peta-	P	1975	Quadrillion	Billiard	1 000 000 000 000 000
10004	1012	tera-	T	1960	Trillion	Billion	1 000 000 000 000
10003	109	giga-	G	1960	Billion	Milliard	1 000 000 000
10002	106	mega-	M	1960	Million		1 000 000
10001	103	kilo-	k	1795	Thousand		1 000
10002/3	102	hecto-	h	1795	Hundred		100
10001/3	101	deca-	da	1795	Ten		10
10000	100	(none)	(none)	NA	One		1
1000−1/3	10−1	deci-	d	1795	Tenth		0.1
1000−2/3	10−2	centi-	c	1795	Hundredth		0.01
1000−1	10−3	milli-	m	1795	Thousandth		0.001
1000−2	10−6	micro-	µ	1960[2]	Millionth		0.000 001
1000−3	10−9	nano-	n	1960	Billionth	Milliardth	0.000 000 001
1000−4	10−12	pico-	p	1960	Trillionth	Billionth	0.000 000 000 001
1000−5	10−15	femto-	f	1964	Quadrillionth	Billiardth	0.000 000 000 000 001
1000−6	10−18	atto-	a	1964	Quintillionth	Trillionth	0.000 000 000 000 000 001
1000−7	10−21	zepto-	z	1991	Sextillionth	Trilliardth	0.000 000 000 000 000 000 001
1000−8	10−24	yocto-	y	1991	Septillionth	Quadrillionth	0.000 000 000 000 000 000 000 001

One suggestion would use all the upper and lower case numbers in the English alphabet, but this becomes problematic as the units these prefixes attach to are also English letters. That would lead to confusion (the first sin of any language). For instance, one proposed extension uses all of the English alphabet, starting with xona-, weka-, and vunda- for progressively higher powers of one thousand. So if we have VA, is that Vunda Amperes? or Volts times Amperes? Ambiguity is unacceptable.

Other approaches might be suggested by the mathematics of very large numbers. But this still struggles with the fact that learning more and more names for larger numbers is just putting the problem off. If you disagree, say 10^10000000000 is "ten tremilliamilliamilliatrecenttretriginmilliamilliatrecenttretriginmilliatrecentdotrigintillion" ten times fast.

Another solution would be to designate a new unit, like the Tera-Byte, as the BBoT, for lack of a better name. That would run out slower, lasting 4*5*8 = 160 years. That is good, but not perminent. Further, we would have to designate a new unit for every unit used.

If our growth is exponential, then if we should want a system that will scale in the same way. We have that for Earthquakes, for instance. It is called the Richter scale. Similar scales are used in apparent magnitude for astronomy and the decibel scale for sound. These all use base-10 logarithms, so that each time you increase by 1, the magnitude increases by 10 times. For instance, 5.4 on the richter scale is 10 times what 4.4 is. This system would last virtually forever. But implemenation is everything... and that is going to require more work.

Suggestions?