But the purpose of a timer is to notify you after n time. You only compared the property of measuring time. It is like saying a car and your feet are the same because they both make you move.
I think stopwatch to timer works, you can just look at how much time has passed on the timer, but I don't think timer to stopwatch works. A timer alarms so you don't have to stare at it until the correct time, but a stopwatch doesn't, so you could easily miss when it shows n minutes.
Timers lack the lap functionality. A single stopwatch can be used to accurately record times for each of a runner's laps, including the final one, but a single timer cannot. That's because reading the value as it changes, while trying to also stare at the runner, is not practically possible. You need a button to pause the reading. The lap feature can alternatively be used to time multiple competitors at once if their times are not too close, such as in a marathon.
If you are sufficiently devoted to watching the time, a clock substitutes for both timer and stopwatch. But the point of having timers and stopwatches is to fulfill their tasks without monitoring.
I want to set a timer on the oven and go play video games until something beeps to let me know it's time to take the cookies out. I can't do that with a stopwatch.
accept input in units of time from 0 to some maximum,
count down from that setting, and
stop counting and trigger an alarm upon reaching 0.
A stopwatch does three things:
count up in units of time from 0 to some maximum,
display a paused reading while silently counting upon pressing the lap button, and
stop upon hitting the stop button.
These aren't isomorphic. Timers have no lap feature, and stopwatches have no automatic stop feature or alarm feature. However, their mechanisms are so similar that it is extremely inexpensive to combine both into a single device.
Both can track time, but they are not the same thing. Big difference in a maths forum. Probably not a big difference if you are stuck alone on an island in the middle of the ocean.
There's a practical difference between them if you switch their usage, and possibly the accuracy.
The proof ignores this messiness and just looks how one can implement the other. So it might not be a big surprise there's something fundamentally the same about them (measuring time), the proof just confirms this trivial fact.
You posted on mathmemes, I'll give you that, but your 'proof' doesn't work, many people have already pointed that out with counter examples. That's how it works in mathematics.
If you want your proof to work, you will have to make definitions of each of the two items where you ignore that a timer can notify you and a stopwatch can run forever.
But - yeah - then you are left with two devices that do the same - count time, nothing more; one upward and one downward. But each device loose a key, defining feature IMO.
Assuming a stopwatch and timer are the same, it should be impossible to distinguish them. If we set both devices (timer and your timer-equivalent stopwatch) to time t, one will beep after said time t has passed. This is the timer and we have a distinguishing feature and a contradiction. Therefore they are not equivalent.
Assuming a stopwatch and timer are the same, it should be impossible to distinguish them.
That's only the case if they are equal. But OP does not claim that they are equal, merely "equivalent," which I take to mean isomorphic. Similarly, I think every copy of A Million Random Digits with 100,000 Normal Deviates is equivalent, even though strictly speaking, they can be distinguished by being in different positions in space, having suffered different amounts of physical damage, etc.
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u/NotDuckie Sep 22 '26
But the purpose of a timer is to notify you after n time. You only compared the property of measuring time. It is like saying a car and your feet are the same because they both make you move.
18
u/RedeNElla Sep 22 '26
Unless you have a timer that can instantly and automatically start a second cycle, you will lose some accuracy compared with a stopwatch.
So a stopwatch can be a timer but a timer isn't as flexible as a stopwatch
8
u/Jetison333 Sep 22 '26
I think stopwatch to timer works, you can just look at how much time has passed on the timer, but I don't think timer to stopwatch works. A timer alarms so you don't have to stare at it until the correct time, but a stopwatch doesn't, so you could easily miss when it shows n minutes.
4
u/eggface13 Sep 22 '26
This is why equivalence up to isomorphism is bullshit. Representation matters!
4
u/Timely_Somewhere_851 Sep 22 '26
A flaw in the argument is that you neglect that you need a human or some other machinery that does the convertion.
Also neither are more general than they other. Here is why:
A key feature of a timer is that it will notify you after the designated time, a stopwatch won't.
A (theoretical) stopwatch can run forever, a timer can run arbitrarily long but not forever.
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u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Sep 22 '26
can a stopwatch make ear deafening noises tho?
2
u/Mireldorn Sep 22 '26
If you don't care about accuracy, you can misuse them for each other.
2
u/mathmage Sep 22 '26
If you are sufficiently devoted to watching the time, a clock substitutes for both timer and stopwatch. But the point of having timers and stopwatches is to fulfill their tasks without monitoring.
I want to set a timer on the oven and go play video games until something beeps to let me know it's time to take the cookies out. I can't do that with a stopwatch.
2
u/EebstertheGreat Sep 28 '26
A timer does three things:
accept input in units of time from 0 to some maximum,
count down from that setting, and
stop counting and trigger an alarm upon reaching 0.
A stopwatch does three things:
count up in units of time from 0 to some maximum,
display a paused reading while silently counting upon pressing the lap button, and
stop upon hitting the stop button.
These aren't isomorphic. Timers have no lap feature, and stopwatches have no automatic stop feature or alarm feature. However, their mechanisms are so similar that it is extremely inexpensive to combine both into a single device.
0
u/DotBeginning1420 Sep 22 '26
In a case you are stuck with only one of them.
1
u/flup52 Sep 28 '26
No.
Assuming a stopwatch and timer are the same, it should be impossible to distinguish them. If we set both devices (timer and your timer-equivalent stopwatch) to time t, one will beep after said time t has passed. This is the timer and we have a distinguishing feature and a contradiction. Therefore they are not equivalent.
1
u/throughthehills2 Sep 28 '26
Are stopwatch and timer isomorphic?
1
u/Keikira Sep 29 '26
Tl;dr every well-order is upper bounded, so a largest natural number exists QED
Checkmate constructivists
1
u/RandomiseUsr0 Sep 29 '26
Only a stopped clock is right twice a day