## Smoke Detector Intervals

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Buttons
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### Smoke Detector Intervals

At least, I think it's a smoke detector. Outside my apartment, something is making very short, piercing, intermittent beeps. This morning it was something like once every few hours, but they've since become more frequent. I decided to start timing the intervals between the beeps to figure out what was going on. (Because, you know, that makes more sense than buying new batteries for the smoke detector in the hallway.)

At first the data made sense, but it quickly devolved to the point that I don't see any pattern. Do you guys see something I don't see? Here are the times between beeps. Some might be off by a second or so, but I think in general I'm pretty consistent in my reaction times on the stopwatch button. I'm rounding to the nearest second because, well, why not.

1. 8'28"
2. 8'28"
3. 1'41" (Huh. Maybe it'll beep 8:28 after the previous one, though?)
4. 6'47" (Vindication!)
5. 2'50"
6. 6'11" (I give up.)
7. 12'26"
8. 1'42"
9. 1'07"
10. 0'34"
11. 5'05"
12. 3'57"

...at which point I get bored of holding onto the stopwatch. Any ideas?

Bassoon
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### Re: Smoke Detector Intervals

Well, I'd say what it is that is beeping, but that would ruin the fun.

Mathmagic
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### Re: Smoke Detector Intervals

Because it might make things a little clearer, I've converted the Min'Sec'' intervals into seconds:

508
508
101
407
170
371
746
102
67
34
305
237

Just off my first instinct, I'm going to divide each interval by the smallest interval on the list, which is 34 seconds. I'll also list the closest multiple of 34 in brackets, with the deviation from the recorded value.

14.94 (510, +2)
14.94 (510, +2)
2.97 (102, +1)
11.97 (408, +1)
5.00 (170, +0)
10.91 (374, +3)
21.94 (748, +2)
3.00 (102, +0)
1.97 (68, +1)
1.00 (34, +0)
8.97 (306, +1)
6.97 (238, +1)

Considering rounding errors and reaction time error (which would give an experimental error in the neighborhood of +/- 0.5 seconds, plus the self-admitted "second or so"), I think it's quite clear that the beeps *do*, or *would*, occur at regular intervals. For whatever reason, the alarm does not beep for some of the intervals.
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gorcee
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### Re: Smoke Detector Intervals

When processing data, your first question should not be "what is the pattern to this data?" Your first question should be, "are my assumptions that the data should be patterned in a certain way correct?"

Your expectation is that the smoke detector should beep in intervals. Why is that your assumption?

Buttons
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### Re: Smoke Detector Intervals

gorcee wrote:Your expectation is that the smoke detector should beep in intervals. Why is that your assumption?
Mostly religious reasons.

(EDIT: But really, that wasn't my assumption at first. I noticed the beeps were getting more frequent, so I decided to time them for a bit. After all, if they were decreasing with a constant ratio, I should probably hurry up and fix the damn thing before it became a constant drone.

But when I started timing, four of the first five beeps lay evenly spaced apart, one every 8'28" exactly. I figured that was too weird to be based on chance. Thus, the assumption that there's some pattern.)

Pathway
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### Re: Smoke Detector Intervals

The last 4 data points there sum to 507. You have:

508 508
508 508
101
407 508
170
371 541
746 746
102
67
34
305 507

Gather more data!
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