Exploring a Logarithmic Temporal Technology Scale

19 09 2013
Industrial archaeologist performing an underwater survey. (Credit: NPS)

Industrial archaeologist performing an underwater survey. (Credit: NPS)

In a previous, fairly soft-content post, I mused about the possibility of the existence of a logarithmic pattern in history that relates, in a predictable way, the subjective perceptions of technology within a civilization to their pace of technological advancement.  (In a sort of tongue-in-cheek gesture, I called it the McGee Scale of technological advancement.)

At the time, I based the scale itself on our civilization’s history and our historical understanding of the possibility of flight.  Then, I turned the scale around and anchored it to the present day to use it as a tool to make some tantalizing projections about the pace of our own future technological advancements.

However, while a fun, neuron-tickling exercise, after playing around with it a bit more, the scale has taken on something of a more serious light.  With this in mind, I thought I’d share the work and the resulting possibility that such a proposed relationship might actually be more than trivial.

Review: A Logarithmic Scale of Cultural Technological Achievement/Advancement

To begin, let me review what the scale looked like.  Being temporally-logarithmic in nature, it’s an intentionally coarse scale over time, which has the distinct benefit of smearing out statistical noise like wars, upheavals, disasters, and dark ages to provide an average pace of technological development in a civilization.

It’s admittedly subjective and tenuous in that we really only have one technological civilization’s history to base/test this upon (our own), but here’s what it looked like as compiled.  (Note: I also added an extra step at the end of the scale for grins.)

So, from any point in time for a given technological civilization, the scale defines the following general relationship in technological advancement, where “τ” (tau) is a reference moment in a civilization’s past or future technological history, and all units are in solar years:

  • Recent technological achievements at τ+1 year would have also been considered commonplace at time τ.
  • Recent technological achievements at τ+10 years would have been considered generally commonplace at time τ.
  • Recent technological achievements at τ+100 years would have been considered uncommon at time τ.
  • Recent technological achievements at τ+1,000 years would have been considered unachievable/fantasy at time τ.
  • Recent technological achievements at τ+10,000 years would have been considered unimaginable at time τ.
  • Recent technological achievements at τ+100,000 years would have been incomprehensible at time τ.

Granted, this all makes general sense, and the sentiment is a fairly logical one.  So, I’ll admit that at first this seems like an exercise that goes out of its way to justify something that is already straightforward or intuitive.  However, the intriguing and unique factor here is that this scale is based on actual historical information, and its utility is therefore a testable hypothesis.

Navigable balloon by Henri Giffard (1852). 19th century print.

Navigable balloon by Henri Giffard (1852). 19th century print.

Testing the Logarithmic Scale Looking Backwards: Practical Flight

It becomes easier to see how the scale might be tested if instead of working forward through time in the general case, the scale is anchored at the present moment but instead operates backwards through history.

With this conversion, the scale now becomes:

  • At τ-100,000 years, recent technological achievements at time τ are incomprehensible.
  • At τ-10,000 years, recent technological achievements at time τ are unimaginable.
  • At τ-1,000 years, recent technological achievements at time τ are considered unachievable and/or fantasy.
  • At τ-100 years, recent technological achievements at time τ are considered uncommon.
  • At τ-10 years, recent technological achievements at time τ are considered generally commonplace.
  • At τ-1 year, recent technological achievements at time τ are considered commonplace.

Now, let’s dive into specifics.  In my original thought-experiment, I evaluated the technology/science of flight.  So, where the above scale in the general form reads, “technological achievements commonplace at time t,” let’s insert the term, “practical human flight,” to refer to regular use of technological aircraft for transport between settlements.  Let’s also insert real year values, using 2013 as civilization reference time τ, and see what it all looks like:

  • In 97,987 B.C.E., practical human flight is incomprehensible.
  • In 7,987 B.C.E., practical human flight is unimaginable.
  • In 1,013 C.E., practical human flight is considered unachievable and/or fantasy.
  • In 1913 C.E., practical human flight is considered uncommon (but possible).
  • In 2003, practical human flight is considered generally commonplace.
  • In 2012, practical human flight is considered commonplace.

With this, we have real values and predictions, so let’s pick this list apart.

First, in the 98th millennia (or the 980th century) B.C.E., there is no historical information from humanity.  Originating in Africa, anthropological studies suggest humans (homo sapiens) became anatomically-modern roughly 200,000 years ago and began migrating to Eurasia ~100,000 years ago (our target period).  However, evidence suggests humans only became behaviorally modern, (meaning the development of language, music, and other cultural “universals,” such as personal names, leaders, concepts of property, symbolism, and abstraction, etc.)  some 50,000 years ago.  This means that our time period is nearly 90 millennia before the advent of agriculture and some 50 millennia before the widespread development of language and culture, where humans at the time operated only in nomadic groups known as “band societies.”  Therefore, it would have been impossible not only to convey the idea of practical, technological flight to them, but even describing the idea of a human settlement would have been problematic.  Therefore, this one is spot on; to these early humans practical human flight between settlements would have been incomprehensible.

Second, in the 8th millennia (or the 80th century) B.C.E., there is very little historical record to evaluate.  However, all we need to do to break (falsify) this logarithmic scale/model is demonstrate that practical human flight had been considered by that point.  Archaeologically, it can be demonstrated that the first steps toward technological civilization are being taken at this point in history.  Agricultural technology is being developed simultaneously in South America, Mexico, Asia, and Africa; stone tools, granaries, and huts are being developed in Africa; the creation of houses, carvings, stone tools, counting tokens and musical flutes made of bone are developed in Asia; statues, pottery, and evidence of ceremonial burials are found in Greece and the Mediterranean, along with wheat, barley, sheep, goats, and pigs, indicating a food-producing economy.  In all cases listed here, it seems that the problem of sustaining civilization, (i.e., food and shelter) is still paramount.  Of them, the early Greek civilization may have had the most technologically-developed system and therefore the most opportunity to consider technological advancement in the direction we’re considering.  Yet, based on a lack of both technology and historical/archaeological evidence, it appears safe to say that in this tumultuous time of antiquity practical human flight between settlements would have been plainly unimaginable.

Third, by the 11th century C.E., there are a few small-scale examples of individual flight attempts using kites, gliders, or even bamboo-copters across Asia and Europe.  None of them illustrated practical success.  At the specific time (11th century), of all civilizations on Earth, those of the Islamic world and of China had reached a technological and/or scientific peak.  So, in the interests of breaking this scale as a model, it is there that we’ll look for evidence that human flight might have been considered achievable in a practical sense.  Islamic contributions, insofar as history records them, are restricted largely to mathematics and not practical engineering.  Further, the year 1,013 C.E. preceded the birth of famous Islamic mathematician Omar Al-Khayyam by several decades, and neither he nor his predecessors offered any known discussion of technological flight. On the other hand, the existence of the Song Dynasty in China gives us the greatest run for our money.  There, the relatively advanced use of technology, including boating, magnetic compasses for navigation, horology, along with the development of art, literature, and sweeping advances in science (e.g., geomorphology, climate change,) push this boundary to the limit.  However, despite the sophistication of the civilization at the time as well as their notable use of hot-air Kongming lanterns for nearly a millennia prior(!), it seems that there is no evidence to suggest serious considerations or attempts concerning the development of a practical airship.  Hence, it is safe to say that globally, practical human flight would have been considered either unachievable or simple fantasy.

Fourth, the scale’s prediction for the year 1913 is not hard to corroborate, and further, is right on the money.  The successful invention of the manned, practical, but non-directional hot air balloon was made in the year 1793.  The first dirigible design that could have been utilized in the fashion described for this exercise (for practical transport between settlements) was invented in 1852.  The first commercial Zeppelin was launched in the year 1900, and the Wright brothers’ flight was performed in 1903.  So, yes, it is safe to say that while there was likely widespread belief by the year 1913 that flight was indeed possible, (graduating us out of the previous “bin”), such flights would certainly have been considered uncommon.

The rest, 2003-2012, is obviously correctly categorized – Success!

A printing operation as depicted on a woodblock ca. 1568.

A printing operation as depicted on a woodblock ca. 1568.

Testing the Scale Again: Electronic Text

Now, having gone through the first technical example, let’s attempt another and see if the agreement was a fluke.  This time, let’s leave the time scale intact from the previous example but shift to an entirely different sort of technology: printed language.  Working backwards, in order for this to work, we have to figure out what a “recent technological achievement” in “printed language” means at civilization reference time τ (now).

Well, for the purposes of this experiment, I’m drawn to consider so-called e-books, being digitally-formatted and distributed writings or texts to be displayed and read on electronic devices.   Hence, instead of inserting, “modern human flight,” let’s instead insert the term, “the use of electronic text” to refer to regular use of digital language technology and see what it all looks like:

  • In 97,987 B.C.E., the use of electronic text is incomprehensible.
  • In 7,987 B.C.E., the use of electronic text is unimaginable.
  • In 1,013 C.E., the use of electronic text is considered unachievable and/or fantasy.
  • In 1913 C.E., the use of electronic text is considered uncommon.
  • In 2003, the use of electronic text is considered generally commonplace.
  • In 2012, the use of electronic text is considered commonplace.

Again, since we have real dates and descriptions, let’s see how well they match up with history.

97,987 B.C.E. – Language has not yet been developed, hence this fits the scale’s definition of incomprehensible.

7,987 B.C.E. – Writing has been developed, but printing of any kind (stenciling was the earliest possible technology that qualifies) is still more than five millennia away at best; hence this fits the scale’s definition as unimaginable.

1,013 C.E. – The earliest example of printing with movable text was within a couple of decades of being first premiered in China.  So, the process of printing could be argued to be understood, but extending this to describe self-luminous text, single machines that can store entire libraries of information, and text that can change itself – Yes, this would clearly have been considered physically-impossible fantasy.

1913 C.E. – To start, history reveals that the pantelegraph, which can be considered an early version of a fax machine, was invented in 1865.  This leveraged technological advances to transmit printed text electronically, though it did not store said text, nor display or reproduce it electronically, only mechanically.  Next, electromechanical punch-card data storage was invented in 1880, so it can be truthfully claimed that the technological storage of numeric or text data was at least conceptually available by 1913, though again, this invention did not display any of the stored information electronically.  However, the technology gap regarding electronic displays began to close with the nearly simultaneous invention of the scanning phototelegraph in 1881, which allowed for the coarse electric transmission of imagery, (and at least hypothetically, visual text).  Finally, the invention of the Nipkow scanning disc in 1884 provided the first electromechanical means to scan and display imagery in real-time.  So, by 1913 we can reasonably claim that the existence of these inventions, used with greater prevalence over the course of at least three subsequent decades, implies that the key concepts necessary for using electronic text – electric scanning of visual information, the electromechanical storage of information, and electromechanical display of information – were all acknowledged realities.  Therefore, while perhaps a stretch to say that use of electronic text is merely “uncommon” in the year 1913, I would claim that the concept of electronic text would not seem unachievable or fantastic (the previous temporal “bin”).  Though there was admittedly no market for such a device, one could conceive of a large, hard-wired or wireless invention composed of a punch-card library, text-analogue mechanical counters for mechanically displaying lines of text (as stored on the cards), and a Nipkow televisor to transmit and display that text to a receiving/viewing station.  Highly uncommon, yes.  But clearly possible.  (I think we made it in right under the wire on this one.)

And again, the remaining categorical descriptions for 2003-2012 are obviously correct.  Success again!

The Antikythera Mechanism. (Credit: National Archaeological Museum, Athens, No. 15987)

The Antikythera Mechanism. (Credit: National Archaeological Museum, Athens, No. 15987)

Viewing the Scale in Both Time Directions: Testing the Wheel

First, readers may note that the “forward” and “backwards”-looking versions of the scale are actually two halves of a single scale with respect to arbitrary civilization reference time τ.  In complete form, note that the scale looks like this:

  • At τ-100,000 years, recent technological achievements at time τ are incomprehensible.
  • At τ-10,000 years, recent technological achievements at time τ are unimaginable.
  • At τ-1,000 years, recent technological achievements at time τ are considered unachievable and/or fantasy.
  • At τ-100 years, recent technological achievements at time τ are considered uncommon.
  • At τ-10 years, recent technological achievements at time τ are considered generally commonplace.
  • At τ-1 year, recent technological achievements at time τ are considered commonplace.
  • [τ = the current civilization/technology temporal reference point]
  • At τ+1 year, recent technological achievements would have also been considered commonplace at time τ.
  • At τ+10 years, recent technological achievements would have been considered generally commonplace at time τ.
  • At τ+100 years, recent technological achievements would have been considered uncommon at time τ.
  • At τ+1,000 years, recent technological achievements would have been considered unachievable/fantasy at time τ.
  • At τ+10,000 years, recent technological achievements would have been considered unimaginable at time τ.
  • At τ+100,000 years, recent technological achievements would have been incomprehensible at time τ.

Well, considering this now-complete scale (operating in both temporal directions) and presuming that the previous two examples demonstrated some general agreement between this scale and the history of technology, let’s explore what happens if we do not anchor time τ at the present-day.

For the following exploration, let’s consider advances in the technology of the wheel, but let’s set time τ instead to the height of Classical Civilization – smack in the middle of the scientific Hellenistic Period in the year 250 B.C.E. seems about right.  Where was the wheel then?  Well, the spoked wheel and chariot had been invented more than a millennia earlier.  So what was new then?

The answer, as it turns out, is the water-wheel, newly invented by the Greeks and used both for irrigation as well as for a mechanical power source in mining, milling, and other industrial activities.

So, including this in the scale as “the use of a technological water wheel,” the predictions in both directions are now:

  • In 100,250 B.C.E., the use of a technological water wheel is incomprehensible.
  • In 10,250 B.C.E., the use of a technological water wheel is unimaginable.
  • In 1,250 B.C.E., the use of a technological water wheel is considered unachievable and/or fantasy.
  • In 350 B.C.E., the use of a technological water wheel is considered uncommon.
  • In 260 B.C.E., the use of a technological water wheel is considered generally commonplace.
  • In 251 B.C.E., the use of a technological water wheel is considered commonplace.
  • τ = water wheel technology reference point in the year 250 B.C.E.
  • In 249 B.C.E., advances in wheel technology would have been considered commonplace.
  • In 240 B.C.E., advances in wheel technology would have been considered generally commonplace.
  • In 150 B.C.E., advances in wheel technology would have been considered uncommon.
  • In 750 C.E., advances in wheel technology would have been considered unachievable/fantasy.
  • In 9,750, advances in wheel technology would have been considered unimaginable.
  • In 99,750, advances in wheel technology would have been incomprehensible.

So, here we go:

100,250 B.C.E. – Language, agriculture, and settlements had not yet been developed amongst humans, and so technology like a water wheel for irrigation and mechanical power cleanly fits the scale’s definition of incomprehensible.

10,250 B.C.E. – While language and culture have been developed by this point, the world’s oldest known wheel dates back to roughly 5,300 B.C.E., which is five millennia into the future; hence the concept of a functioning water wheel fits the scale’s definition as unimaginable.

1,250 B.C.E. – The spoked wheel and the chariot had been invented a few centuries prior, yet it would still be seven or eight centuries before the first invention of the water wheel – essentially a giant wooden wheel powered by a stream to automatically deliver water to fields or grind grain.  The description in this context would likely have been considered unachievable/fantastic (in the technical sense), and therefore fits the scale’s definition.

350 B.C.E. – Being that the waterwheel was invented in in third century B.C.E., and we’re not quite there yet, the use of one certainly qualifies as “uncommon.”   Yet, is that too generous?  Would it have been considered unachievable or fantastic then?  To answer this, let’s look at the technological innovation going on at the time.  Hellenistic scholars of the 3rd century employed mathematics and dedicated empirical research to further technological and intellectual advances.  Specifically, there is evidence to suggest that finely-machined gear systems to represent the motions of the Sun, Moon and planets had been constructed (see: Antikythera Mechanism).  Thus, considering that 350 B.C.E. is just a century before the creation of such finely-tuned machines that their precision would not be reproduced for another two-thousand years, while a waterwheel might have seemed unusual prior to widespread adoption, it would certainly not seem impossible or fanciful.  Therefore, I would argue that its characterization is accurately predicted by the scale.

260, 251, 249, and 240 B.C.E. qualify with generally commonplace use of the water wheel and no major loss, upheaval, gains, or advances in wheel technology.

150 B.C.E. – Moving forward, this is where subjective decisions must be made about what the evolution of “water wheel technology” means in order to continue.  In my mind, what we’re really talking about is the mechanical use of the wheel – a circular disc – itself in technology.  From this generalized perspective, we now have the latitude to consider technological innovations that incorporate the wheel, but are not necessarily direct evolutions of a “water wheel,” as technological descendants of the technology under consideration at the reference point.  (This is doubly-reinforced by the reality that innovation is anything but linear.)  So, what wheel-based technologies came into being approximate a century after our reference point in 250 B.C.E.?  The astrolabe, which functioned as an analog calculator typically used in solving astronomical problems.  While precision technology using the wheel had been occasionally in existence for a couple of centuries prior to the reference time (250 B.C.E.), its use in this fashion would have definitely been considered uncommon.  This is accurately predicted by the scale.

750 C.E. – The early centuries of the Common Era are pretty tough on this scale, as coincidentally it is a period of particular turmoil and conflict… and therefore not much innovation.  However, a monk, astronomer, and engineer under the Tang Dynasty in China was notable for advancing the use of clockwork mechanisms with an escapement and integrating it with the movement of a large celestial sphere.  In common terms, he enabled the construction of an impressive, accurate, and automated astronomical display not unlike what is found in a modern planetarium.  Despite their relatively advanced technological achievements at the time, describing such a device to someone from the year 250 B.C.E. would have arguably seemed fantastic.  Therefore, the scale holds up.

9,750 C.E. and 99,750 C.E. – Now, here’s where we run out of data.  However, considering the many unbelievable technological achievements of even the last century that incorporate wheels or discs, including electrical dynamos, automobiles, two-wheeled personal transports (see: Segway PTs), electronic interface devices (e.g., Intellivision), etc., etc., all of which would have been either unimaginable or incomprehensible to someone from the year 250 B.C.E., it isn’t a stretch to say that technological innovation at these proposed times in the distant future would be even moreso.  And so, by convenient definition and temporal increments, the scale holds up here.

So – this makes three examples of using the scale with real-world data.  Is there any utility to it?

Assumptions (Weak Spots?)

Immediate objections amongst the astute may be that this scale is too coarse to be testable and/or of any meaningful value to us, (which may ultimately be true).  However, even this does not necessarily mean that the use or consideration of such a scale has no utility.  Perhaps where it fails can lead to even more interesting territory.

Of course, such a scale presumes human existence tens or hundreds of millennia into the future.  Is it too bold to be that optimistic? =)

Thoughts in general?

Relating Different Cultures via “τ-Power” Values

Used in another way, I propose that this scale may find its greatest utility in providing a means to compare the technological development within or between different cultures at separate stages of technological development.

Logarithmic scales may be thought of conveniently in powers of ten.  So, if we consider the technological time-position of a given reference culture to be the origin, or τ^0 power, the relationship of the technological level of a target culture to the reference culture may be simply described as a sequential power integer in either the positive or negative direction, as illustrated in the following converted scale:

  • Technology in use by the reference culture is incomprehensible to the target culture; (τ-100,000 years) = τ^-5 culture, or a negative-fifth-power culture.
  • Technology in use by the reference culture is unimaginable by the target culture; (τ-10,000 years) = τ^-4 culture, or a negative-fourth-power culture.
  • Technology in use by the reference culture is considered unachievable and/or fantasy by the target culture; (τ-1,000 years) = τ^-3 culture, or a negative-third-power culture.
  • Technology in use by the reference culture is considered uncommon by the target culture; (τ-100 years) = τ^-2 culture, or a negative-two-power culture.
  • Technology in use by the reference culture is considered generally commonplace by the target culture; (τ-10 years) = τ^-1 culture, or an order-of-magnitude culture.
  • Technology in use by the reference culture is considered commonplace by the target culture; (τ-1 year/τ+1 year) = τ^0 culture, or in other words are both considered to be technologically-equivalent cultures.
  • Technology in use by the target culture is considered generally commonplace by the reference culture; (τ+10 years) = τ^1 culture, or an order-of-magnitude culture.
  • Technology in use by the target culture is considered uncommon by the reference culture; (τ+100 years) = τ^2 culture, or a two-power culture.
  • Technology in use by the target culture is considered unachievable/fantasy by the reference culture; (τ+1,000 years) = τ^3 culture, or a third-power culture.
  • Technology in use by the target culture is considered unimaginable by the reference culture; (τ+10,000 years) = τ^4 culture, or a fourth-power culture.
  • Technology in use by the target culture is incomprehensible to the reference culture; (τ+100,000 years) = τ^5 culture, or a fifth-power culture.

Utility of the “McGee Scale”?

By considering the technological time-position of a reference civilization (which may itself possess different “t-power” values for different technologies within it), I believe the development of such a scale at least conceptually achieves or enables two objectives:

First, it provides an alternative means to describe, compare, and (at least roughly) quantify past cultures in terms of technological development.  This may yield new insight into both the relationship between evolving technologies and cultural change as well as the effects of introducing foreign technology (e.g., from a culture of a more advanced t-power) to the evolution of a given culture.

Secondly, gaining the ability to describe technological cultures in simple and quantifiable terms (based on human history of technology and not solely upon speculation, as is the case with the Kardashev Scale), also provides a more formalized method of evaluating the concepts underlying pursuits proposing non-terrestrial cultures and technology, such as the Search for Extra-Terrestrial Intelligence (SETI).

So – with all of that, I think I’ll fire this post off into the cyberwild.  Critical feedback is very welcome.  This whole concept scheme evolved organically, and if left to my own devices for much longer, I just might convince myself that this is worthy of a full write-up and submission to a journal – (perhaps Contemporary Archaeology?)…

Thoughts, anyone?

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One response

20 09 2013
roberthenryfischat

Reblogged this on robert's space and commented:
transcentalnumbers.

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