Deep Time
Time Logarithmic Time

Logarithmic Time

Time Main Page
   Cosmological time
   Geological Time
   Quaternary Time
   Historical Time
   Future Time

   Deep Time
   Logarithmic Timescale
   Cosmic Calendar
   Geological Timescales

Logarithmic Timeline by by Heinz von Foerster
Table of historical events by Heinz von Foerster, drawn on logarithmic paper. T=log(t0-t), where T=representational time; t0=asymptotic moment; and t=historical time. Asymptotic moment (Now!): t0=midnight, December 31, 1994. interview with Heinz von Foerster, by Stefano Franchi, Güven Güzeldere, and Eric Minch, SEHR, volume 4, issue 2: Constructions of the Mind.

The above diagram is an example of a logarithmic timeline, which is a timeline in which each unit or degree or level is ten (or some other predetermined number) times greater or smaller than the preceding one. These timelines are useful for portraying things like Deep Time, infinitesimal or vast (or both) size scales, wind strength, earthquakes, exponential technological or information acceleration (technological singularity), or other quantitative factors.

"The idea of presenting history logarithmically goes back at least to 1932, when John B. Sparks copyrighted his "Histomap of Evolution". Around the same time it was also explored by the cyberneticist Heinz von Foerster, who used it to propose that memories naturally fade in an exponential manner." (Wikipedia)

Heinz von Foerster (1911-2002) was an Austrian American scientist combining physics and philosophy. Together with Warren McCulloch, Norbert Wiener, John von Neumann, Lawrence J. Fogel, and others, Heinz von Foerster was an architect of cybernetics. (Wikipedia). From the interview from which the above diagram is taken:

"[Heinz von Foerster]: As I told you I was a very bad student in history, a bad student in geography, a bad student in all of these things where you have to memorize data. So I said to myself "History is absolutely catastrophic. I can't remember whether Caesar came before Augustus or after Augustus or aacchhh." So I thought I would make myself a table, a historical table. When I made this table I observed that the closer to the present you came, the more densely filled the paper was with data; conversely, the further you went back the thinner the table. As it went back to the fifteenth century there was almost nothing, a century or more with nobody to mention; then you go to Rome, of course there are a couple of wars, which you know. And then you go: 300 BC, 400 BC, empty. 500 BC you get one entry or something. This is a bad way of presenting things. The best way to represent such data is to shrink the extension of the graph the longer you go away, and the only method to do that -- or one elegant method to do that -- is to plot it logarithmically. Every decade, or every power of ten, covers the same distance and that means that, as you go further back into the past, ten years are as big as one year, and then one hundred years are as big as ten year, etcetera. Thousand years the same, ten thousand the same, hundred thousand, they're all the same size. With this kind of representation you get the same density everywhere. You can go back, and you have not only Caesar's assassination, you also have the extinction of the dinosaurs, and you have not only the extinction of the dinosaurs, you have the beginning of life, and a little bit further down you have the beginning of the solar system, and one step further you have the beginning of the universe. The whole thing fits in one table if you use a logarithmic time scale."

Although transhumanists and singularitans argue that the universe is characterised by exponentially accelerating change, and although this may well be the case, it is also undeniable that a logarithmic timescale simply reflects the fact that the further back in time one goes, the less information is preserved. So we could, if we were feeling particularly masochistic, in theory document for example modern print- and electronic mediated culture to mind numbing detail (every blog post or twitter tweet for example). With would still know an enormous amount of information about modern history, the history of the 20th century, say, thanks to newspapers, newsreel archives, and other documents, so each day could be described in great detail. By the time we get to the middle ages, information is getting scantier, and is mostly centered on the monarchy and the church. With the ancient Egyptians, we could think in terms of centuries, but not years. It's not that the ancient Egyptians did nothing for hundreds of years, it is just that the most of details have been lost to the sands of time. With the earlier Holocene and late Pleistocene we would pretty confident about climate fluctuations, what species were around, paleolithic tools, and so on. By the early Cenozoic land mammals can still be dated per million years or so, magnetic polarity, marine invertebrates, foraminifers and so on even better. With the Mesozoic, the fossil record has more gaps, though five million or so year intervals are probably reliable, as is paleogeography By the Precambrian, even with radiometric dating, inaccuracies creep in, and less is known about the organisms around then (being unicellular and soft-bodied) and geography is looking pretty sketchy. Prior to the formation of the Solar System we can think in terms of billions of years. Then with the Big Bang there is a reverse process of logarithmic acceleration, but this has nothing to do with archeology of the past (apart from things like Cosmic Background Radiation and the abundance ratios of light elements) and more with speculations based on equations on the blackboard and the results of particle accelerator experiments.

The following table, adapted and added to from Wikipedia, gives a nice overview of the rate of events at each power of ten increment, beginning from "now" and progressing backwards. I've also shown the type of timeline; each type would seem to span about four orders of magnitude. As more recent than Historical I have included three arbitrary levels of Current (years to days), Immediate (days to minutes) and Instant (minutes to fractions of a second). Deep time of course is precisely the opposite to instant or immediate time; instead of being present in immediate or contemporary experience and memory, it extends far beyond human history and socio-cultural, religious, and mythological memory. Transitional levels are indicated by alternating colours:

Logarithmic notation in
terms of Years Ago
Duration Type of timeline Field of knowledge Representative events
10-6 to 10-5 Minutes Instant / Immediate Live, online Whatever you are doing now...
10-5 to 10-4 an hour Immediate Live, online, breaking news What you've just been doing...
10-4 to 10-3 about 8 hours Immediate Breaking news What's happening today...
10-3 to 10-2 last 3 days Immediate / Current Current news Events and news of today, yesterday and the day before.
10-2 to 10-1 last 36 days Current Current affairs Recent news.
10-1 to 100 last year Current Current affairs Last year's current affairs.
100 to 101 last decade Current / Historical Current affairs War on Terror. Human genome sequenced. Subprime bubble bursts. Politics of climate change. Social networking. China begins to rival US
101 to 102 20th century Historical Modern History Car, flight, wireless radio, antibiotics, totalitarianism, world wars, nuclear power, end of colonialism, electronics, cold war, spacecraft, information revolution.
102 to 103 1000 to 20th century Historical World History Middle Ages, Renaissance, Printing press, Firearms, Colonialism, Little Ice Age, Industrial Revolution, steam engine, telegraph, telephone.
103 to 104 8000 BC to 1000 c.e. Historical / Quaternary World History, archeology, paleoclimatology, etc Holocene, Neolithic, Bronze Age, Iron Age, Cities, Empires, Writing, Wheel, Civilization, Religions, Philosophy.
104 to 105 Late Pleistocene to Holocene Quaternary Paleoclimatology, paleoanthropology, paleontology, etc Late Paleolithic, Music, Art, Cave paintings, Dance, Tally stick, Medicine, Neanderthal extinction, Ice age ends, megafauna extinction, Mesolithic, beginning of Neolithic, Domestication, Agriculture and Animal husbandry.
105 to 106 Pleistocene Quaternary Paleoclimatology, paleoanthropology, paleontology, geology, etc Pleistocene megafauna, Glacials and interglacials, Human (150 KYA), Language, fire, Tools (Paleolithic), Spirituality.
106 to 107 Miocene to early Pleistocene Quaternary / Geological Geology, paleontology, etc Tertiary mammals, hominids, global cooling, modern plants and invertebrates.
107 to 108 Late Cretaceous to mid Cenozoic Geological Geology, paleontology, etc Dinosaurs, flowering plants, Cretaceous-Tertiary extinction event, mammals, grasses.
108 to 109 Late Proterozoic, Paleozoic, Mesozoic Geological Geology, paleontology, etc Microbial life, Cambrian explosion, trilobites, land plants, insects, tetrapods, gymnosperms, Permian-Triassic extinction event, ammonites, dinosaurs, early mammals.
109 to 1.4×1010 Cosmology, Precambrian Geological / Cosmological Cosmology, astrophysics, geology, etc Big Bang, Stars and galaxies, Earth, Life.

Note that with a logarithmic timeline, each successive time unit follows the preceeding one. It is not the case that each larger increment includes the previous one, as with geological time, where eras include periods, which include epochs, and each pertains (generally) to a different scale of deep time. In a similar table on Deep Time, I have each exponentially larger increment include the preceeding one, so the resulting timescale is somewhat different.

Link: Scales of Reality - Modes of Being blog, posted on January 30, 2011 by Aaron - some useful comments and observations on experiencing or understanding spatial-temporal scales.

contact us

content by MAK110718, edited RFVS111109

Creative Commons License
Unless otherwise noted,
the material on this page may be used under the terms of a
Creative Commons License.