There are two halachic indivisible units of time. When it comes to interruption, or for defining a single statement (e.g. when correcting oneself in davening) the unit is tokh kedei dibbur — within the time it takes to say [“Shalom eilekha Rebbe uMori“], a greeting of 4 words consisting of 10 syllables. For calendrical calculations, the unit is the cheileq, 3-1/3 seconds. My instinct is that the two are intended to be equal — it takes around 3-1/3 sec to say 10 syllables, and for someone who isn’t timing themselves with a stopwatch, the tokh kedei dibbur definition is more useful.
Here is a possible explanation for the halakhah:
Hugs Follow a 3-Second Rule
by Rebecca Kessler on 28 January 2011, 1:23 PM
Ever wondered how long a hug lasts? The quick answer is about 3 seconds, according to a new study of the post-competition embraces of Olympic athletes. But the long answer is more profound. A hug lasts about as much time as many other human actions and neurological processes, which supports a hypothesis that we go through life perceiving the present in a series of 3-second windows.
Crosscultural studies dating back to 1911 have shown that people tend to operate in 3-second bursts. Goodbye waves, musical phrases, and infants’ bouts of babbling and gesturing all last about 3 seconds. Many basic physiological events, such as relaxed breathing and certain nervous system functions do, too….
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