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Changes from Version 9 to the current version
[…] clock makes no claim that the duration between $t_0$ and $t_1$ isequals the same asduration between $t_1$ toand $t_2$.
**This is not a shortcoming of the formulation.
This is the situation.**
The clock on its own cannot establish that its ticks are at […] = 0$.
Plotting the hourglass flips against the days gives:
```tikz Figure 1: hourglass flips against days
\begin{tikzpicture}[x=1cm,y=0.0417cm,>=stealth]
\draw[gray!45,very thin,xstep=1,ystep=24] (0,0) grid (7.4,192);
\draw[->,thick] (0,0) -- (8,0) node[right] {$d$};
[…] next post will briefly go through the history of standardizing the _second_ up to the day process for how we agree on time.
- Current versionJavier Nieto·
What is the Clock?
Changes from Version 11[…] next post will briefly go through the history of standardizing the _second_
up to the day process for how we agree on time. What is the Clock?
Changes from Version 10[…] = 0$. Plotting the hourglass flips against the days gives: ```tikz Figure 1: hourglass flips against days \begin{tikzpicture}[x=1cm,y=0.0417cm,>=stealth] \draw[gray!45,very thin,xstep=1,ystep=24] (0,0) grid (7.4,192); \draw[->,thick] (0,0) -- (8,0) node[right] {$d$}; […]
What is the Clock?
Changes from Version 9[…] clock makes no claim that the duration between $t_0$ and $t_1$
isequals thesame asduration between $t_1$toand $t_2$. **This is not a shortcoming of the formulation. This is the situation.** The clock on its own cannot establish that its ticks are at […]What is the Clock?
Changes from Version 8[…] of one kind fits together with a regularity of another kind. **Regularity is not a property of a clock. It is the relation between two.** Take $C': \mathbb{N} \to \mathbb{N}$ to be the function of hourglass flips with respect to the days, where the
counting of flipsflip count starts with thecounting of daysday count, i.e., $C'(0) = 0$. Plotting the hourglass flips against the days […]What is the Clock?
Changes from Version 7[…] flips starts with the counting of days, i.e., $C'(0) = 0$.
We can then havePlotting thefollowing graphhourglass flips against the days gives: ```tikz \begin{tikzpicture}[x=1cm,y=0.0417cm,>=stealth] \draw[gray!45,very thin,xstep=1,ystep=24] (0,0) grid (7.4,192); \draw[->,thick] (0,0) -- (8,0) […] (7,168); \draw[very thick,dashed] (0,0) -- (7,189); \draw[<->,very thick] (7,168) -- (7,189); \draw[thick,densely dotted,red!75,opacity=0.8] (0,0) .. controls (1.5,70) and (4,130) .. (7,150); \end{tikzpicture} ``` Linearity indicates _regularity_ between the two, where for every $d$ days we have $h$ hourglass flips. The dotted curve represents an irregular hourglass that varies greatly in its number of daily flips. The solid line represents our common notion of the day, where for every […] the history of standardizing the _second_ up to the day processonfor how we agree on time.What is the Clock?
Changes from Version 6[…] Both are consistent with everything we have observed. The next post
is aboutwill briefly go through the history of standardizing the _second_andup to the day process on how we agree on timetoday.What is the Clock?
Changes from Version 5[…] possibility for an hourglass $C''$: for every day, there are $27$ flips
of the hourglass. In this scenario, we cannot distinguish whether $C'$ is slow or […]What is the Clock?
Changes from Version 4[…] days, i.e., $C'(0) = 0$. We can then have the following
planegraph: ```tikz \begin{tikzpicture}[x=1cm,y=0.0417cm,>=stealth] \draw[gray!45,very thin,xstep=1,ystep=24] (0,0) grid (7.4,192); \draw[->,thick] (0,0) -- (8,0) […]What is the Clock?
Changes from Version 3[…] the next. We then have the clock as a sequence of
events_ticks_ (the passing of days), and a count of them. $$C = (e_0t_0,e_1t_1,e_2t_2, ...)$$ Note that the clock produces only the count and not _regularity_ in the increments. The clock makes no claim that thepassing of three days was of equalduration between $t_0$ and $t_1$ is the same as $t_1$ to $t_2$. This is not a shortcoming of the formulation. This is the situation. The clock on its own cannot establish that its ticks areevenat regular intervals, because there is nothingfor itto beevenregular against. The Feynman lecture gives an example of a man flipping […] days, i.e., $C'(0) = 0$. We can then have the followinggridplane: ```tikz \begin{tikzpicture}[x=1cm,y=0.0417cm,>=stealth] \draw[gray!45,very thin,xstep=1,ystep=24] (0,0) grid (7.4,192); \draw[->,thick] (0,0) -- (8,0) […] is how time becomes _standardized_. Nothing in the comparison forces the choice.WeFurther, we could fix the day and say it is $24$ flips, or […] is about the history of standardizing the _second_ and how wecome toagree on time today.What is the Clock?
Changes from Version 2[…] starts with the counting of days, i.e., $C'(0) = 0$. We can then have the following
imagegrid: ```tikz \begin{tikzpicture}[x=1cm,y=0.0417cm,>=stealth] \draw[gray!45,very thin,xstep=1,ystep=24] (0,0) grid (7.4,192); \draw[->,thick] (0,0) -- (8,0) […]What is the Clock?
Changes from Version 1[…] it to my summer research with [Category Labs](https://www.category.xyz/). Wikipedia defines the [clock](https://en.wikipedia.org/wiki/Clock) as "a device that measures and displays [time](https://en.wikipedia.org/wiki/Time)." As we will see, […]
What is the Clock?
Everyone knows what time it is. Most coordination in our everyday lives relies on it. Whether in our deadlines, schedules, or even cooking timers, we can take for granted that we share a common sense of time.
In this series, I want to investigate how we've come to agree on time and connect it to my summer research with Category Labs.
Wikipedia defines the clock as "a device that measures and displays time." As we will see, time itself is defined by clocks, so this definition is rather circular. So we will go the other way and start with the clock.
We will find more use in the physics definition of a clock (from The Feynman Lectures on Physics, Volume I, Chapter 5-2):
What really matters anyway is not how we define time, but how we measure it. One way of measuring time is to utilize something which happens over and over again in a regular fashion—something which is periodic.
Let's start with the day as something periodic. Count the days from one noon to the next. We then have the clock as a sequence of events (the passing of days), and a count of them.
Note that the clock produces only the count and not regularity in the increments. The clock makes no claim that the passing of three days was of equal duration.
This is not a shortcoming of the formulation. This is the situation. The clock on its own cannot establish that its ticks are even, because there is nothing for it to be even against. The Feynman lecture gives an example of a man flipping an hourglass as soon as the last grain of sand goes from the top to the bottom. He can then count how many flips occur in each day. However, how can he rule out that the hourglass is slow at night and fast during the day? Another passage from the lecture:
All we can say is that we find that a regularity of one kind fits together with a regularity of another kind.
Regularity is not a property of a clock. It is the relation between two. Take to be the function of hourglass flips with respect to the days, where the counting of flips starts with the counting of days, i.e., . We then have the following image:
Linearity indicates regularity between the two, where for every days we have hourglass flips. The solid line represents our common notion of the day, where for every day, there are flips of the hourglass. The dashed line represents another possibility for an hourglass : for every day, there are flips of the hourglass.
In this scenario, we cannot distinguish whether is slow or is fast. We must agree on which one to treat as correct, and calibrate the other to it. This is how time becomes standardized. Nothing in the comparison forces the choice. We could fix the day and say it is flips, or fix the hourglass and let the day be the one that varies. Both are consistent with everything we have observed.
The next post is about the history of standardizing the second and how we come to agree on time today.