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tock...</h1><div class="container_mt6G margin-vert--md"><time datetime=2016-04-06T12:00:00.000Z>April 6, 2016</time> · <!-- -->11 min read</div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><div class="avatar__intro authorDetails_lV9A"><div class=avatar__name><span class=authorName_yefp>Bradlee Speice</span></div><div class=authorSocials_rSDt><a href=https://github.com/bspeice target=_blank rel="noopener noreferrer" class=authorSocialLink_owbf title=GitHub><svg viewBox="0 0 256 250" width=1em height=1em class="authorSocialLink_owbf githubSvg_Uu4N" style=--dark:#000;--light:#fff preserveAspectRatio=xMidYMid><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 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2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"/></svg></a></div></div></div></div></div></header><div id=__blog-post-container class=markdown><p>If all we have is a finite number of heartbeats left, what about me?</p>
<p>Warning: this one is a bit creepier. But that's what you get when you come up with data science ideas as you're drifting off to sleep.</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=25-billion>2.5 Billion<a href=#25-billion class=hash-link aria-label="Direct link to 2.5 Billion" title="Direct link to 2.5 Billion">​</a></h2>
<p>If <a href=http://www.pbs.org/wgbh/nova/heart/heartfacts.html target=_blank rel="noopener noreferrer">PBS</a> is right, that's the total number of heartbeats we get. Approximately once every second that number goes down, and down, and down again...</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">total_heartbeats </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2500000000</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>I got a Fitbit this past Christmas season, mostly because I was interested in the data and trying to work on some data science projects with it. This is going to be the first project, but there will likely be more (and not nearly as morbid). My idea was: If this is the final number that I'm running up against, how far have I come, and how far am I likely to go? I've currently had about 3 months' time to estimate what my data will look like, so let's go ahead and see: given a lifetime 2.5 billion heart beats, how much time do I have left?</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=statistical-considerations>Statistical Considerations<a href=#statistical-considerations class=hash-link aria-label="Direct link to Statistical Considerations" title="Direct link to Statistical Considerations">​</a></h2>
<p>Since I'm starting to work with health data, there are a few considerations I think are important before I start digging through my data.</p>
<ol>
<li>The concept of 2.5 billion as an agreed-upon number is tenuous at best. I've seen anywhere from <a href=http://gizmodo.com/5982977/how-many-heartbeats-does-each-species-get-in-a-lifetime target=_blank rel="noopener noreferrer">2.21 billion</a> to <a href=http://wonderopolis.org/wonder/how-many-times-does-your-heart-beat-in-a-lifetime/ target=_blank rel="noopener noreferrer">3.4 billion</a> so even if I knew exactly how many times my heart had beaten so far, the ending result is suspect at best. I'm using 2.5 billion because that seems to be about the midpoint of the estimates I've seen so far.</li>
<li>Most of the numbers I've seen so far are based on extrapolating number of heart beats from life expectancy. As life expectancy goes up, the number of expected heart beats goes up too.</li>
<li>My estimation of the number of heartbeats in my life so far is based on 3 months worth of data, and I'm extrapolating an entire lifetime based on this.</li>
</ol>
<p>So while the ending number is <strong>not useful in any medical context</strong>, it is still an interesting project to work with the data I have on hand.</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=getting-the-data>Getting the data<a href=#getting-the-data class=hash-link aria-label="Direct link to Getting the data" title="Direct link to Getting the data">​</a></h2>
<p><a href=https://www.fitbit.com/ target=_blank rel="noopener noreferrer">Fitbit</a> has an <a href=https://dev.fitbit.com/ target=_blank rel="noopener noreferrer">API available</a> for people to pull their personal data off the system. It requires registering an application, authentication with OAuth, and some other complicated things. <strong>If you're not interested in how I fetch the data, skip <a href=#Wild-Extrapolations-from-Small-Data>here</a></strong>.</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=registering-an-application>Registering an application<a href=#registering-an-application class=hash-link aria-label="Direct link to Registering an application" title="Direct link to Registering an application">​</a></h2>
<p>I've already <a href=https://dev.fitbit.com/apps/new target=_blank rel="noopener noreferrer">registered a personal application</a> with Fitbit, so I can go ahead and retrieve things like the client secret from a file.</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token comment" style="color:hsl(230, 4%, 64%)"># Import all the OAuth secret information from a local file</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> secrets </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> CLIENT_SECRET</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> CLIENT_ID</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> CALLBACK_URL</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=handling-oauth-2>Handling OAuth 2<a href=#handling-oauth-2 class=hash-link aria-label="Direct link to Handling OAuth 2" title="Direct link to Handling OAuth 2">​</a></h3>
<p>So, all the people that know what OAuth 2 is know what's coming next. For those who don't: OAuth is how people allow applications to access other data without having to know your password. Essentially the dialog goes like this:</p>
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Application: I've got a user here who wants to use my application, but I need their data.</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Fitbit: OK, what data do you need access to, and for how long?</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Application: I need all of these scopes, and for this amount of time.</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Fitbit: OK, let me check with the user to make sure they really want to do this.</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Fitbit: User, do you really want to let this application have your data?</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">User: I do! And to prove it, here's my password.</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Fitbit: OK, everything checks out. I'll let the application access your data.</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Fitbit: Application, you can access the user's data. Use this special value whenever you need to request data from me.</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">Application: Thank you, now give me all the data.</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>Effectively, this allows an application to gain access to a user's data without ever needing to know the user's password. That way, even if the other application is hacked, the user's original data remains safe. Plus, the user can let the data service know to stop providing the application access any time they want. All in all, very secure.</p>
<p>It does make handling small requests a bit challenging, but I'll go through the steps here. We'll be using the <a href=https://dev.fitbit.com/docs/oauth2/ target=_blank rel="noopener noreferrer">Implicit Grant</a> workflow, as it requires fewer steps in processing.</p>
<p>First, we need to set up the URL the user would visit to authenticate:</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> urllib</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">FITBIT_URI </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'https://www.fitbit.com/oauth2/authorize'</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">params </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)"># If we need more than one scope, must be a CSV string</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'scope'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'heartrate'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'response_type'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'token'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'expires_in'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">86400</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)"># 1 day</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'redirect_uri'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> CALLBACK_URL</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'client_id'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> CLIENT_ID</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">request_url </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> FITBIT_URI </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'?'</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> urllib</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">parse</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">urlencode</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">params</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>Now, here you would print out the request URL, go visit it, and get the full URL that it sends you back to. Because that is very sensitive information (specifically containing my <code>CLIENT_ID</code> that I'd really rather not share on the internet), I've skipped that step in the code here, but it happens in the background.</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token comment" style="color:hsl(230, 4%, 64%)"># The `response_url` variable contains the full URL that</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token comment" style="color:hsl(230, 4%, 64%)"># FitBit sent back to us, but most importantly,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token comment" style="color:hsl(230, 4%, 64%)"># contains the token we need for authorization.</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">access_token </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">dict</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">urllib</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">parse</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">parse_qsl</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">response_url</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'access_token'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=requesting-the-data>Requesting the data<a href=#requesting-the-data class=hash-link aria-label="Direct link to Requesting the data" title="Direct link to Requesting the data">​</a></h3>
<p>Now that we've actually set up our access via the <code>access_token</code>, it's time to get the actual <a href=https://dev.fitbit.com/docs/heart-rate/ target=_blank rel="noopener noreferrer">heart rate data</a>. I'll be using data from January 1, 2016 through March 31, 2016, and extrapolating wildly from that.</p>
<p>Fitbit only lets us fetch intraday data one day at a time, so I'll create a date range using pandas and iterate through that to pull down all the data.</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> requests_oauthlib </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> OAuth2Session</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> pandas </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">as</span><span class="token plain"> pd</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> datetime </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> datetime</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">session </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> OAuth2Session</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">token</span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'access_token'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> access_token</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'token_type'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'Bearer'</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">format_str </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'%Y-%m-%d'</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">start_date </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> datetime</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">2016</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">end_date </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> datetime</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">2016</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">3</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">31</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">dr </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> pd</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">date_range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">start_date</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> end_date</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">url </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'https://api.fitbit.com/1/user/-/activities/heart/date/{0}/1d/1min.json'</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">hr_responses </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">session</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">get</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">url</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">d</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">strftime</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">format_str</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> d </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> dr</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">def</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">record_to_df</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">record</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">if</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'activities-heart'</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">not</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> record</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token plain"> </span><span class="token boolean" style="color:hsl(35, 99%, 36%)">None</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> date_str </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> record</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'activities-heart'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'dateTime'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> df </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> pd</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">DataFrame</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">record</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'activities-heart-intraday'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'dataset'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> df</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> df</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'time'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">apply</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">lambda</span><span class="token plain"> x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">:</span><span class="token plain"> datetime</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">strptime</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">date_str </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">' '</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">'%Y-%m-%d %H:%M:%S'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token plain"> df</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">hr_dataframes </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">record_to_df</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">record</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">json</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> record </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">in</span><span class="token plain"> hr_responses</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">hr_df_concat </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> pd</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">concat</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hr_dataframes</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token comment" style="color:hsl(230, 4%, 64%)"># There are some minutes with missing data, so we need to correct that</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">full_daterange </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> pd</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">date_range</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hr_df_concat</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> hr_df_concat</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> freq</span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token string" style="color:hsl(119, 34%, 47%)">'min'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">hr_df_full </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> hr_df_concat</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">reindex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">full_daterange</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> method</span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token string" style="color:hsl(119, 34%, 47%)">'nearest'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Heartbeats from {} to {}: {}"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'value'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">sum</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path 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<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Heartbeats from 2016-01-01 00:00:00 to 2016-03-31 23:59:00: 8139060</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>And now we've retrieved all the available heart rate data for January 1<sup>st</sup> through March 31<sup>st</sup>! Let's get to the actual analysis.</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=wild-extrapolations-from-small-data>Wild Extrapolations from Small Data<a href=#wild-extrapolations-from-small-data class=hash-link aria-label="Direct link to Wild Extrapolations from Small Data" title="Direct link to Wild Extrapolations from Small Data">​</a></h2>
<p>A fundamental issue of this data is that it's pretty small. I'm using 3 months of data to make predictions about my entire life. But, purely as an exercise, I'll move forward.</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=how-many-heartbeats-so-far>How many heartbeats so far?<a href=#how-many-heartbeats-so-far class=hash-link aria-label="Direct link to How many heartbeats so far?" title="Direct link to How many heartbeats so far?">​</a></h3>
<p>The first step is figuring out how many of the 2.5 billion heartbeats I've used so far. We're going to try and work backward from the present day to when I was born to get that number. The easy part comes first: going back to January 1<sup>st</sup>, 1992. That's because I can generalize how many 3-month increments there were between now and then, account for leap years, and call that section done.</p>
<p>Between January 1992 and January 2016 there were 96 quarters, and 6 leap days. The number we're looking for is:</p>
<span class=katex-display><span class=katex><span class=katex-mathml><math display=block><semantics><mtable rowspacing=0.16em columnspacing=1em><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mi>h</mi><msub><mi>r</mi><mi>q</mi></msub><mo>⋅</mo><mi>n</mi><mo>−</mo><mi>h</mi><msub><mi>r</mi><mi>d</mi></msub><mo>⋅</mo><mo stretchy=false>(</mo><mi>n</mi><mo>−</mo><mi>m</mi><mo stretchy=false>)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding=application/x-tex>\begin{equation*}
hr_q \cdot n - hr_d \cdot (n-m)
\end{equation*}</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:1.2em;vertical-align:-0.35em></span><span class=mord><span class=mtable><span class=col-align-c><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.85em><span style=top:-3.01em><span class=pstrut style=height:3em></span><span class=mord><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.1514em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.03588em>q</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>⋅</span><span class=mspace style=margin-right:0.2222em></span><span class="mord mathnormal">n</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>−</span><span class=mspace style=margin-right:0.2222em></span><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>⋅</span><span class=mspace style=margin-right:0.2222em></span><span class=mopen>(</span><span class="mord mathnormal">n</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>−</span><span class=mspace style=margin-right:0.2222em></span><span class="mord mathnormal">m</span><span class=mclose>)</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.35em><span></span></span></span></span></span></span></span></span></span></span></span>
<ul>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>h</mi><msub><mi>r</mi><mi>q</mi></msub></mrow><annotation encoding=application/x-tex>hr_q</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.9805em;vertical-align:-0.2861em></span><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.1514em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.03588em>q</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span></span></span></span>: Number of heartbeats per quarter</li>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>h</mi><msub><mi>r</mi><mi>d</mi></msub></mrow><annotation encoding=application/x-tex>hr_d</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.8444em;vertical-align:-0.15em></span><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span></span></span></span>: Number of heartbeats on leap day</li>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>n</mi></mrow><annotation encoding=application/x-tex>n</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.4306em></span><span class="mord mathnormal">n</span></span></span></span>: Number of quarters, in this case 96</li>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>m</mi></mrow><annotation encoding=application/x-tex>m</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.4306em></span><span class="mord mathnormal">m</span></span></span></span>: Number of leap days, in this case 6</li>
</ul>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">quarterly_count </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'value'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">sum</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">leap_day_count </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">month </span><span class="token operator" style="color:hsl(221, 87%, 60%)">==</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">&</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">day </span><span class="token operator" style="color:hsl(221, 87%, 60%)">==</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">29</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'value'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">sum</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">num_quarters </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">96</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">leap_days </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">6</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">jan_92_jan_16 </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> quarterly_count </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> num_quarters </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> leap_day_count </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">num_quarters </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> leap_days</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">jan_92_jan_16</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> 773609400</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>So between January 1992 and January 2016 I've used <span class=katex><span class=katex-mathml><math><semantics><mrow><mo>≈</mo></mrow><annotation encoding=application/x-tex>\approx</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.4831em></span><span class=mrel>≈</span></span></span></span> 774 million heartbeats. Now, I need to go back to my exact birthday. I'm going to first find on average how many heartbeats I use in a minute, and multiply that by the number of minutes between my birthday and January 1992.</p>
<p>For privacy purposes I'll put the code here that I'm using, but without any identifying information:</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">minute_mean </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'value'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">mean</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token comment" style="color:hsl(230, 4%, 64%)"># Don't you wish you knew?</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token comment" style="color:hsl(230, 4%, 64%)"># birthday_minutes = ???</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">birthday_heartbeats </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> birthday_minutes </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> minute_mean</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">heartbeats_until_2016 </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">int</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">birthday_heartbeats </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> jan_92_jan_16</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">remaining_2016 </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> total_heartbeats </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> heartbeats_until_2016</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Heartbeats so far: {}"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">heartbeats_until_2016</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Remaining heartbeats: {}"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">remaining_2016</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Heartbeats so far: 775804660</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Remaining heartbeats: 1724195340</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>It would appear that my heart has beaten 775,804,660 times between my moment of birth and January 1<sup>st</sup> 2016, and that I have 1.72 billion left.</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=how-many-heartbeats-longer>How many heartbeats longer?<a href=#how-many-heartbeats-longer class=hash-link aria-label="Direct link to How many heartbeats longer?" title="Direct link to How many heartbeats longer?">​</a></h3>
<p>Now comes the tricky bit. I know how many heart beats I've used so far, and how many I have remaining, so I'd like to come up with a (relatively) accurate estimate of when exactly my heart should give out. We'll do this in a few steps, increasing in granularity.</p>
<p>First step, how many heartbeats do I use in a 4-year period? I have data for a single quarter including leap day, so I want to know:</p>
<span class=katex-display><span class=katex><span class=katex-mathml><math display=block><semantics><mtable rowspacing=0.16em columnspacing=1em><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mi>h</mi><msub><mi>r</mi><mi>q</mi></msub><mo>⋅</mo><mi>n</mi><mo>−</mo><mi>h</mi><msub><mi>r</mi><mi>d</mi></msub><mo>⋅</mo><mo stretchy=false>(</mo><mi>n</mi><mo>−</mo><mi>m</mi><mo stretchy=false>)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding=application/x-tex>\begin{equation*}
hr_q \cdot n - hr_d \cdot (n - m)
\end{equation*}</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:1.2em;vertical-align:-0.35em></span><span class=mord><span class=mtable><span class=col-align-c><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.85em><span style=top:-3.01em><span class=pstrut style=height:3em></span><span class=mord><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.1514em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.03588em>q</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>⋅</span><span class=mspace style=margin-right:0.2222em></span><span class="mord mathnormal">n</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>−</span><span class=mspace style=margin-right:0.2222em></span><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>⋅</span><span class=mspace style=margin-right:0.2222em></span><span class=mopen>(</span><span class="mord mathnormal">n</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>−</span><span class=mspace style=margin-right:0.2222em></span><span class="mord mathnormal">m</span><span class=mclose>)</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.35em><span></span></span></span></span></span></span></span></span></span></span></span>
<ul>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>h</mi><msub><mi>r</mi><mi>q</mi></msub></mrow><annotation encoding=application/x-tex>hr_q</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.9805em;vertical-align:-0.2861em></span><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.1514em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.03588em>q</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span></span></span></span>: Heartbeats per quarter</li>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>h</mi><msub><mi>r</mi><mi>d</mi></msub></mrow><annotation encoding=application/x-tex>hr_d</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.8444em;vertical-align:-0.15em></span><span class="mord mathnormal">h</span><span class=mord><span class="mord mathnormal" style=margin-right:0.02778em>r</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.0278em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class=vlist-s>​</span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span></span></span></span>: Heartbeats per leap day</li>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>n</mi></mrow><annotation encoding=application/x-tex>n</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.4306em></span><span class="mord mathnormal">n</span></span></span></span>: Number of quarters = 16</li>
<li><span class=katex><span class=katex-mathml><math><semantics><mrow><mi>m</mi></mrow><annotation encoding=application/x-tex>m</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.4306em></span><span class="mord mathnormal">m</span></span></span></span>: Number of leap days = 1</li>
</ul>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">heartbeats_4year </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> quarterly_count </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">16</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> leap_day_count </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">16</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">heartbeats_4year</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> 128934900</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>Now, I can fast forward from 2016 the number of periods of 4 years I have left.</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">four_year_periods </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> remaining_2016 </span><span class="token operator" style="color:hsl(221, 87%, 60%)">//</span><span class="token plain"> heartbeats_4year</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">remaining_4y </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> remaining_2016 </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> four_year_periods </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> heartbeats_4year</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Four year periods remaining: {}"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">four_year_periods</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Remaining heartbeats after 4 year periods: {}"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">remaining_4y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Four year periods remaining: 13</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Remaining heartbeats after 4 year periods: 48041640</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>Given that there are 13 four-year periods left, I can move from 2016 all the way to 2068, and find that I will have 48 million heart beats left. Let's drop down to figuring out how many quarters that is. I know that 2068 will have a leap day (unless someone finally decides to get rid of them), so I'll subtract that out first. Then, I'm left to figure out how many quarters exactly are left.</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">remaining_leap </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> remaining_4y </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> leap_day_count</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token comment" style="color:hsl(230, 4%, 64%)"># Ignore leap day in the data set</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">heartbeats_quarter </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">month </span><span class="token operator" style="color:hsl(221, 87%, 60%)">!=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">&</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hr_df_full</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">index</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">day </span><span class="token operator" style="color:hsl(221, 87%, 60%)">!=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">29</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token string" style="color:hsl(119, 34%, 47%)">'value'</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">sum</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">quarters_left </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> remaining_leap </span><span class="token operator" style="color:hsl(221, 87%, 60%)">//</span><span class="token plain"> heartbeats_quarter</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">remaining_year </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> remaining_leap </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> quarters_left </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> heartbeats_quarter</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Quarters left starting 2068: {}"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">quarters_left</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">print</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token string" style="color:hsl(119, 34%, 47%)">"Remaining heartbeats after that: {}"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">format</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">remaining_year</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Quarters left starting 2068: 8</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Remaining heartbeats after that: 4760716</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>So, that analysis gets me through until January 1<sup>st</sup> 2070. Final step, using that minute estimate to figure out how many minutes past that I'm predicted to have:</p>
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> datetime </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> timedelta</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">base </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> datetime</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">2070</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">minutes_left </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> remaining_year </span><span class="token operator" style="color:hsl(221, 87%, 60%)">//</span><span class="token plain"> minute_mean</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">kaput </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> timedelta</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">minutes</span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain">minutes_left</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain">base </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> kaput</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> datetime.datetime(2070, 2, 23, 5, 28)</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
<p>According to this, I've got until February 23<sup>rd</sup>, 2070 at 5:28 PM in the evening before my heart gives out.</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=summary>Summary<a href=#summary class=hash-link aria-label="Direct link to Summary" title="Direct link to Summary">​</a></h2>
<p>Well, that's kind of a creepy date to know. As I said at the top though, <strong>this number is totally useless in any medical context</strong>. It ignores the rate at which we continue to get better at making people live longer, and is extrapolating from 3 months' worth of data the rest of my life. Additionally, throughout my time developing this post I made many minor mistakes. I think they're all fixed now, but it's easy to mix a number up here or there and the analysis gets thrown off by a couple years.</p>
<p>Even still, I think philosophically humans have a desire to know how much time we have left in the world. <a href="https://www.biblegateway.com/passage/?search=psalm+144&version=ESV" target=_blank rel="noopener noreferrer">Man is but a breath</a>, and it's scary to think just how quickly that date may be coming up. This analysis asks an important question though: what are you going to do with the time you have left?</p>
<p>Thanks for sticking with me on this one, I promise it will be much less depressing next time!</div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Blog post page navigation"><a class="pagination-nav__link pagination-nav__link--prev" href=/2016/03/tweet-like-me><div class=pagination-nav__sublabel>Older post</div><div class=pagination-nav__label>Tweet like me</div></a><a class="pagination-nav__link pagination-nav__link--next" href=/2016/05/the-unfair-casino><div class=pagination-nav__sublabel>Newer post</div><div class=pagination-nav__label>The unfair casino</div></a></nav></main><div class="col col--2"><div class="tableOfContents_bqdL thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href=#25-billion class="table-of-contents__link toc-highlight">2.5 Billion</a><li><a href=#statistical-considerations class="table-of-contents__link toc-highlight">Statistical Considerations</a><li><a href=#getting-the-data class="table-of-contents__link toc-highlight">Getting the data</a><li><a href=#registering-an-application class="table-of-contents__link toc-highlight">Registering an application</a><ul><li><a href=#handling-oauth-2 class="table-of-contents__link toc-highlight">Handling OAuth 2</a><li><a href=#requesting-the-data class="table-of-contents__link toc-highlight">Requesting the data</a></ul><li><a href=#wild-extrapolations-from-small-data class="table-of-contents__link toc-highlight">Wild Extrapolations from Small Data</a><ul><li><a href=#how-many-heartbeats-so-far class="table-of-contents__link toc-highlight">How many heartbeats so far?</a><li><a href=#how-many-heartbeats-longer class="table-of-contents__link toc-highlight">How many heartbeats longer?</a></ul><li><a href=#summary class="table-of-contents__link toc-highlight">Summary</a></ul></div></div></div></div></div><footer class=footer><div class="container container-fluid"><div class="footer__bottom text--center"><div class=footer__copyright>Copyright © 2024 Bradlee Speice</div></div></div></footer></div>
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