# "mathematical" question

r norman rsnorman_ at _comcast.net
Wed Feb 12 08:52:33 EST 2003

```On Tue, 11 Feb 2003 16:20:37 +0100, "jakob ashtar"
<bamsefarogkyllingen at mailer.dk> wrote:

>Given 2 time-variables x>0 and y>0
>
>Given a lamp that has the following properties:
>
>A: The lamp is turned on for x seconds
>B : The lamp is turned off for y seconds
>
>Question 1:
>
>In an endless sequence of B-events where event A
>only occurs 1 time and y can be what ever, the question
>is:
>
>
>What is the minimum x=Xmin so that an observer who watches
>the sequence of events, will say that he saw that the
>lamp was turned on?
>
>Question 2:
>
>In an endless sequence of AB-events where x<Xmin, what
>is the maximum y so that an observer who watches this
>sequence of events, will say that he saw that the lamp
>was turned on?
>
>The background for the 2 above questions is based on
>the postulate (or fact?) that a human being detects
>events in discrete time (like a camera does). But
>events unfold in continuous time-space. Therefore,
>not all events can be detected during to their
>this not a problem for the scientific methods that
>we use today? There a natural boundaries to what
>we can detect and measure.
>
>Sincerely
>
>Jakob Ashtar
>Denmark
>
I am having trouble understanding exactly what you are
getting at.

Problem one -- what is the shortest light flash that you can
detect -- is not a question that makes sense.  You can clearly
see a strobe light that is "on" for only a fraction of a microsecond
and you can see laser flashes that are shorter than that.  I don't
know the limit, but it is probably as close to zero as you can
get and still have light!  The point is, if enough photons are
captured by the receptor cells, you can see the flash.  It doesn't
matter how long an interval the flash lasts.

Problem two seems to be talking about flicker fusion, but I am
not sure.  A sequence of light flashes, if separated by very short
intervals of darkenss, appears as a continuous light. That is the
way flourescent lights work and is the way most digital light
displays work.  It also underlies movies and television. Depending
on the light intensity and viewing conditions, flashes repeated
anywhere from twenty or thirty to seventy or eighty per second are
seen as continuous.

```