Vierordt’s Law and experimenting with time

Karl von Vierordt has a relatively short Wikipedia bio (compared, for instance, to this) for someone who pioneered the measurement of blood pressure, the measurement of lung function and – the activity that would link his name with a “law” for posterity, the experimental study of the time sense. Indeed, he seems to have been one of the first experimental psychologists.


This excellent set of slides gives an overview of Vierordt’s career and a very detailed discussion of the time experiments, their methodology, context, and implications. So what is Vierordt’s Law? As stated by Wearden in the talk:

the proposition that short intervals
of time are judged as longer than they are,
whereas long intervals are judged as
shorter, with an indifference point, where
intervals are judged correctly, somewhere
between the two

In 1868, Vierordt published Der Zeitsinn nach Versuchen
– “The Time Sense According to Experiments.” This was not the first study of time perception, but by had by far the most data. Wearden describes Vierordt’s experimental methodology:

The data collected in Der Zeitsinn come from
experimental studies in which Vierordt himself,
or sometimes his pupil Höring, was the sole
experimental participant
• Höring [Vierordt’s student] not only carried out time perception
studies to qualify for a medical degree, but his
thesis work has the oddity that Höring was the
participant and not the experimenter (who was
• The data were derived from very extensive
experimentation, often involving hundreds of
experimental trials carried out over many days

Two taps (on a glass plate) define a target
time interval and the participant must
make a response so that the time between
the second tap and the response is equal
to the time between the two taps

A very full account of the Vierordt effect (perhaps a better term than “law”) is given in Wearden’s paper linked to above. Wearden has an intriguing conclusion:

A potential conclusion is that the Vierordt effects
shown in different tasks don’t actually have any
common cause, and that different processes are
responsible in the different cases

• Here, unusually, theoretical analysis seems to
suggest that things that look the same aren’t
really the same at all, a kind of theoretical
“disintegration” rather than the usual theoretical
“integration” of different phenomena within the
same theoretical framework

He ends with two points that should give pause to those who see the science of today as inherently superior to the science of the past:

You can see that this 19th. Century work, in spite
of some peculiarities, not only produced reliable
data, but also has posed some problems which
are unsolved (and, it seems, quite difficult to
solve) even today in the light of many recent
advances in our understanding of time
• More generally, Vierordt seems to be a pioneer
of experimental Psychology who is unjustly
neglected….until now

In Space, No One Can Hear You Snore

Amazon Alexa informed me, as one of its “crazy facts” available on request, that astronauts do not snore because in zero gravity their airways do not collapse.

Sounds good, and plausible, but is it true? I decided to fact check Crazy Fact on this. And obviously one factchecks Alexa via Google.

First port of call was this 2008 piece, which informed me that :

Research on two space flights found some interesting sleep statistics. A 2001 study [1] conducted found that five astronauts actually stopped snoring completely while in space. As well, some who had suffered episodes of stopping breathing, called sleep apnea, had none when they were in space.

This was a breakthrough. They had proveN that gravity was indeed necessary to constrict the airflow, aggravate the throat and cause the vibrations along the soft palate and uvula. No gravity made it easier to breathe. Oddly they also learned that astronauts sleep fewer hours and use sleeps medications to assist them in sleeping.

An earlier study was done in 1998 aboard the shuttle Columbia to see how astronauts sleep in the artificial environment of a space shuttle. The result surprised many scientists and sleep specialists when microphones picked up snores from the crew. They were surprised because the feeling was that astronauts likely breathed less.

This led me to David Dinges who has the cool title “chief of the division of Sleep and Chronobiology and director of the Unit for Experimental Psychiatry in the Perelman School of Medicine at the University of Pennsylvania” and this 2001 editorial from the American Journal of Respiratory and Critical Care Medicine:

An excellent example of the latter outcome
is the investigation by Elliott and colleagues in this issue
of the American Journal of Respiratory and Critical Care Medicine
(pp. 478–485) (1). They recorded respiration and sleep
physiology in healthy astronauts during two National Aeronautics
and Space Administration (NASA) space shuttle flights
and compared these recordings to those made when subjects
were Earth-bound before and after flight. They found that microgravity
was associated with marked reductions in sleep-disordered
breathing, in time spent snoring, in arousals during
sleep, in respiratory rate during presleep waking, and in heart
rate during both presleep waking and slow wave sleep. The results
highlight not only the relative importance of gravity in
ventilatory mechanics during sleep, but also reveal that within
physically fit subjects there is a covariation between upper airway
resistance, snoring, and the likelihood of respiratoryrelated
arousals during sleep. It suggests Earth’s gravity has a
key role both in upper airway resistance and obstruction, and
in the relationship of these factors to arousals during sleep

So next to the paper “Microgravity Reduces Sleep Disorder Breathing in Humans” by Elliot and colleagues in that journal. Abstract:

To understand the factors that alter sleep quality in space, we
studied the effect of spaceflight on sleep-disordered breathing.
We analyzed 77 8-h, full polysomnographic recordings (PSGs)
from five healthy subjects before spaceflight, on four occasions
per subject during either a 16- or 9-d space shuttle mission and
shortly after return to earth. Microgravity was associated with a
55% reduction in the apnea–hypopnea index (AHI), which decreased
from a preflight value of 8.3 1.6 to 3.4 0.8 events/h
inflight. This reduction in AHI was accompanied by a virtual elimination
of snoring, which fell from 16.5 3.0% of total sleep time
preflight to 0.7 0.5% inflight. Electroencephalogram (EEG)
arousals also decreased in microgravity (by 19%), and this decrease
was almost entirely a consequence of the reduction in respiratory-related
arousals, which fell from 5.5 1.2 arousals/h
preflight to 1.8 0.6 inflight. Postflight there was a return to near
or slightly above preflight levels in these variables. We conclude
that sleep quality during spaceflight is not degraded by sleep-disordered
breathing. This is the first direct demonstration that gravity
plays a dominant role in the generation of apneas, hypopneas,
and snoring in healthy subjects.


All five subjects in this study showed some degree of snoring
from mild to moderate during preflight PSGs. Time spent
snoring ranged from 2.8 to 32.6% of the total sleep time. In
microgravity, snoring was almost completely eliminated in all
subjects. Importantly, the change in snoring habits of this
group correlated well with the changes in the number of respiratory
events per sleep period both on the ground and in space
(Figure 3). The correlation between snoring and AHI suggests
that the hypopneas were likely obstructive as opposed to central
in nature.

So truly, in space no one can hear you snore.