Using Algebra to Finish Five Books
Outline
In this piece, we will explore integrating a quantitative-based strategy within your schedule in order to complete one or multiple books. If you do not wish to read the math, you can stop after reading Section 2 below (which contains the tool’s link and the guide on how to use it).
Why It Matters
The Tool and How To Use It (TOOL IN FORM OF GOOGLE SHEET HERE)
Columns to Fill Out
Columns to Interpret & Act Upon
Recommended Strategy
Math Behind-The-Scenes (BTS)
Units
What We Start With
Pages Per Day (PPD)
Today’s Target Page (TTP)
Daily Minutes Needed (DMN)
Formal Topics
Why It Matters
This tool provides you quick, straightforward, time-based guidance on how to finish what you wish to read. This will easily support a variety of situations, but if at least 1 of these 4 reasons resonate with you, this could definitely help you.
You are tired of not finishing the books that you start.
This is only referring to books that you actually want to finish. There is nothing wrong with starting a book, but realizing you don’t like it nor want to continue reading it.
You want to be a habitual reader.
You want to be able to read multiple books at once.
You need to read multiple books/book-excerpts at once.
example: you are a student or professional with a variety of reading assignments (textbooks, novels, research, etc.)
The Tool and How To Use It
The tool is a human readable table (TOOL IN FORM OF GOOGLE SHEET HERE) that serves like a bookmark and a planning companion. Some key things it will do is:
keep track of where you left off on a book
tells you when you’re reading deadlines are, whether you decide these deadlines for yourself, or if they are imposed on you (like a library due date or when your colleague made need the book back by).
dynamically tells you how much “daily” time you need to read, as well as the page you need to reach, in order to complete that book or reading by the deadline.
Each row in this table represents one particular book/reading. So we will move on to what columns you’ll need to fill out, and what columns provide you info to act on.
Columns To Fill out
Note: I care about your time, as it is a common sentiment that many of us do not get to read because we feel that we don’t have time. So my instructions/design consider a balance between speed and accuracy.
- Title - name of the book
- deadline – the date you want, or have, to complete this book by.
Total pages – provide the total number of pages you’ll be reading. This does not need to be an exact number.
If you’re starting a book: $$ \text{Total Pages} \approx [\text{Last Page Number in Book}] + 10.$$ the 10 is for the introduction that may be in roman numerals
If you’re reading an excerpt or book section: $$ \text{Total Pages} = [\text{Ending Page Number}] - [\text{Starting Page Number}]$$
- Current Page – the page number you’re currently on
- If you’re starting a book at the beginning, just put 1 (don't worry about the roman numerals as you can account for them in the "Total Pages" column).
Minutes Per Page – How long it takes you to read one full page. The full part is important because this will inform you how long it takes to read the pages that will probably take you the longest. Luckily, most books’ pages differ; some are half a page (especially if you’re starting or ending a chapter, or if the book has images). To get this Number, it will take a 1-5 min experiment on you’re part. If you do not feel like doing this, or feel as though you don’t have time, put a ‘2’ for non-textbooks, and a '4' for textbooks or word-intensive books (like Harry Potter). Instructions are:
- Pick any page that has words on it from top to bottom
- Start a stopwatch and read the page until you finish it.
- Stop the stopwatch once you finish the page.
- If the time is in seconds, divide by 60 and round up to the nearest minute (ex: If you're time \( = 80 \) seconds, then \( \text{Minutes Per Page} = \frac{80}{60} = 1.3 \xrightarrow{\text{round } \uparrow} 2 \) )
- If the time is in minutes and seconds, take the number of minutes and add 1 (ex: if the time = 1 min 25 seconds, then Minutes Per Page = 1 + 1 = 2 minutes. The first '1' came from the '1 min' from the 1 min 25 seconds.)
- Note: If you wish, you can put fractional times here. I just wanted to make it easier/quick calculation for you. Just note that your fractional time needs to be in the form of minutes. So let's say your time is in mins and seconds. Then; $$ \text{Minutes Per Page} = \text{minutes_part}\left(\text{your time}\right) + \left( \frac{ \text{seconds_part}\left( \text{your time} \right) }{60 \frac{\text{sec}}{\text{min}} } \right)$$
- Note: If you wish, you can also get an average by reading 2 or 3 pages as well and get the average minutes across each page.
Columns Interpret & Act Upon
Today’s Target Page (TTP) – the page you need to reach today in order to stay on schedule to reaching your goal by the deadline
Daily minutes needed (DMN) – an estimate (in minutes) of how long it’ll take you to reach today’s target page.
Pages Per Day (PPD) – an estimate of how many pages you’ll need to read daily to complete your reading by the deadline.
Recommended Strategy
The TTP will be your main guide, with the DMN and PPD playing supporting roles. You get an actionable, hopefully doable number from the TTP; you know exactly what you have to reach.
The DMN or PPD gives you an estimated amount of effort to reach the TTP. Focusing on the DMN, this particular field will allow you to quickly or thoughtfully plan. If you see that it says something like 20 minutes, then:
You may be able to do that while you’re eating a snack
You could take some of the time you were using to watch something (YouTube, movie, etc.) to read. Then you could reward yourself by continuing with whatever you were watching.
Putting it into your night routine before you go to sleep
I know you are a busy person, so this isn’t about you adding yet another thing into your already tight day; it’s about finding moments that you can integrate reading. Sometimes focusing on your time – in conjunction with your intentions – causes more available time to appear to you.
Similarly if you see the DMN looks unrealistic for your schedule, such as saying you need to read 3 hours a day, do not be discouraged. Read what you can, as that's better than nothing. This also serves as an indicator to inform you may need to figure out a new plan in order to complete the reading. See if you can extend the due date (library renewals, asking the Deadline-Imposer for some more time, or just extending the deadline if you created it). If there is no way of extending it, then you may be in one of 2 situations:
You HAVE to finish it
If you are in this boat, then at least you know just how much effort you’ll need to put in, and you can plan accordingly (block scheduling may be you’re friend in this case). Grab whatever you use to stay up (coffee, smoothie, shear will) and good luck!
You Don’t Necessarily HAVE to finish it
keep reading as much as you can, but start figuring out how you get the book back after the deadline. Once you get it back, just continue where you left off!
The same mode of thinking can be done with the PPD, but we focused on DMN because it provides you a more helpful way to plan than PPD since the DMN is time-based.
You may not read every day, nor reach your targets every day. Other days, you may be able to surpass your targets. If you can, that’s great; and will serve as a positive-reinforcement feedback loop, pushing you to read more and more! It’s about guiding your habitual effort to “average-out” causing you to finish what you’re reading.
Although this may seem like that it’s about reaching a goal, it’s not. This tool is focused on a systemic/habitual approach to reaching those goals.
Now, we’re ready to pivot and focus on the Sauce behind the tool. The Math behind the Antics!
Math BTS
We will explain the math riddled through this tool to determine the 3 decision-supporting numbers (TTP, DMN, and PPD). The order of thinking will be:
The importance of units in the calculation process
Pulling together the non-calculated variables that we’ll start with.
PPD Motivation and calculation
TTP Motivation and calculation
DMN Motivation and calculation
Units
When running calculations to measure things in real life, numbers don’t mean anything tangible until we include units. To be clear, we are saying units for brevity; we are actually referring to units of measurement (as units can mean something else). You can think of units as a description that, when associated with a numerical value, helps measure something (like the units minutes measuring time).
Units can be made of other units; rates are an example. Minutes is a unit measuring time. Pages is a unit measuring a physical quantity (literally the pages in a book). Creating the new unit \( \left[ \frac{\text{mins}}{\text{page}} \right] \) (minutes per page), helps measure reading speed (this is not a conventional way to write speed, as usually the time-based unit is on the denominator of the fraction). This is possible because you can treat units somewhat like numbers. Consider the following:
- \(1[unit_a]+1[unit_a]=2[unit_a] \)
- \(1[unit_a]\times1[unit_a]=1[unit_a]^2 \)
- think of \( m^2 \) representing meters squared that is a unit that measures area
- \(1\left[\frac{unit_a}{unit_b}\right]\times1[unit_b]=1[unit_a] \)
- unit b was cancelled out like when doing fraction arithemetic
This can be done because of a (plot twist):
PLOT TWIST
a unit is actually a description with a “hidden 1” (as a form of standardization).
For example, The mins units = 1 mins. This allows that “numerical” value to actually serve as a multiplier to the units:
- \(45[\text{mph}]=45\times1[\text{mph}]\)
- \(2.5\left[\frac{\text{mins}}{\text{page}}\right]=2.5\times1\left[\frac{\text{mins}}{\text{page}}\right] \)
Our calculations are going to require units (and mathematical manipulations of them) to make sense of things. You might have noticed already, but to be clear, we will write our units in brackets beside the number they go with . So let’s move on to the actual calculations.
What We Start With
The first thing we’re going to do is list our assumptions and what we already know/have. Why would we assume anything? Well, that’s because our instructions above stated that in order to use this tool, you must gather a set of numbers needed to make the tool run properly. In general, whenever working with calculations, you should start with what you already know, or what you will assume to be true. So our assumptions/what-we-know are:
| # | Assumption/ What We Know | Symbol | Unit |
|---|---|---|---|
| 1 | The book we're reading | \(B \) | N/A |
| 2 | Total pages of \(B\) | \(T\) | [pages] |
| 3 | You're reading "speed" | \(r\) | \(\left[\frac{\text{mins}}{\text{page}}\right] \) |
| 4 | Your deadline | \(t_{end}\) | Date* |
| 5 | Today's date | \(t_{now}\) | Date* |
| 6 | Page you're currently on | \(c\) | [page] |
Let it be clear that the units page and pages are the same unit, just like how those two words are the singular and plural versions of the same noun. Sometimes the word to describe a particular unit has a plural version for the sake of literal clarity (like minute and minutes refer to same time-unit).
* Date is not technically a unit, but we will treat it like “semi-unit” (more to be explained later).
Pages Per Day (PPD) and Motivation
With our goal, and the deadline in mind, one of the 1st questions we ask is: “ Just How much reading would we need to do daily to reach our goal on time?”
Aside (Side Note): You might wonder “why daily?” There is a philosophical reason. I am a believer of systems (habits, routines, feedback loops) to produce results. We technically can’t control outcomes; what we can control is our behavior in hopes that it produces desired outcomes. The day is a unit of time that is a good balance between a period of time you have immense control over, and “realistic repeatability” (it’s more realistic that you could read once every day over once every hour).
We can answer this question in terms of pages. To reform the question, we are asking “How many pages a day will we read in order to finish the reading on time?”
So let’s think of the answer in a conversational tone first before we build a formula. This is a helpful approach in general to build intuition around the formulas you create:
Conversational Answer:
Once we figure out how many pages left you need to read, and then split that across whatever days you have between now and the deadline then that should be the answer.
This translates to:
$$PPD=\frac{T[\text{pages}]-c[\text{pages}]+1[\text{pages}]}{\text{days}(t_{end}-t_{now})}$$
PPD Numerator Explained
- “\(T[\text{pages}]-c[\text{pages}]\)”: represents the number of pages to get from page \(c\) to page \(T\).
- “\(+1[\text{pages}]\)”: This includes 1 more page. Particularly the actual page you are on (which is \(c\) ). We can think of it like this: \(4-1=3\). The 3 represents 3 steps to get from 1 to 4; those steps are “2”, then “3”, and then finally “4”. You can see how “1” is not included in that calculation. If you wanted to include you’re starting number (as this is often needed in real life problems), than you’ll need to add 1. Coming back to our particular problem, when people place a bookmark to indicate a page they left off on, it is expected that they are going to read that page as well. So we need to consider the current page \(c\) as an additional page that we need to read.
PPD Denominator Explained
“\(\text{days}(t_{end}-t_{now})\)” will be a dynamic difference because “today’s” date will change. Also, since this is 2 dates, the difference is ambiguous (we don’t know if we care about the difference in weeks, months, etc). This is why we make it clear by writing a “psuedofunction” wrapping our difference with “days” to clarify what kind of subtraction we are doing.
Now after that whole “+1” thing from the numerator, you might ask why don't we add “+1” to here since we're waiting on today as well? The reason is a combination between reality and math. We want to make sure that we create these numbers while hopefully accounting for some of the uncertainty of life, which in this form may be days where you can’t read or can’t read enough. So we focus on the edges of the time-range (the potential first and last day of reading). There were several scenarios to consider before we decided on 1. First recall that "\(\text{days}(t_{end}-t_{now})\)" does include reading on the deadline date. 2nd, we will be excluding the “days” psuedofunction from the formulas we write below, but just know that all these calculations are around calculating a number of days:
| # | Scenario | Formula |
|---|---|---|
| 1 | I want to include reading today and expect to read on the deadline | \(t_{end}-t_{now}+1[\text{day}]\) |
| 2 | I don’t expect to read today or on the deadline | \(\left(t_{end}-1[\text{day}]\right)-t_{now}\) |
| 3 | I expect to read today and don’t expect to read on the deadline | $$\begin{align*} &=\left(t_{end}-1[\text{day}] \right)-t_{now}+ 1[\text{day}]\\ &= \left(t_{end}-t_{now} \right)-1[\text{day}]+ 1[\text{day}] \\ &= \left(t_{end}-t_{now} \right) \end{align*}$$ |
Thinking about the scenarios:
Scenario 1 is pretty optimistic. Slightly unrealistic (for some) that you will be able to read on the day your goal is due (you may have a tight schedule where all have time to do is just return the book to where it is supposed to go until it can be in your possession again).
Scenario 2 is the most pessimistic.
Scenario 3 sits somewhere in the middle between Scenarios 1 and 2. This is also a relatively realistic scenario. It also happens to match up with just getting the difference between now and the end date. Since this scenario is kind of like an “average between optimism and pessimism” we will go with this one.
Units
With the numerator being pages, and the denominator being days, the unit for PPD is: \(\left[ \frac{\text{pages}}{\text{day}} \right]\)
Today’s Target Page (TTP) and Motivation
Now that we have pages per day, we can focus on what we can do right now (or “today”). By knowing how many pages we need to reach each day, we now can ask the following question: What page do I need to reach today to adhere to that daily quota?
Conversational Answer:
if we read a total of pages equal to the pages per day from wherever we left off at, that will be page to reach today.
This translates into Today’s Target Page (TTP):
Now this may look like a lot of gook just to write \(c+PPD\), but this is an important formality that we don’t want to ignore. The PPD is like a rate, so we need to convert that into just a quantity (number of pages). Since we are asking for how many pages to read today only, we are only considering the number of pages we read in 1 day. So we multiply our PPD by 1 day. (Similarly, if you wanted to know how many pages you needed to read in a week – 7 days – than that would be \(PPD\times7\) ).
Daily Minutes Needed (DMN)
So now we know what page to reach, but that’s only half the battle. It’s helpful to know what to reach, but action requires effort and we’re more likely to act and plan accordingly by knowing how much effort. In our case, we will measure that effort in terms of time (minutes particularly). Our question becomes:
How much time do you need to read each day to reach your daily page quota?
Hmm, this sounds like it will be a rate.
Conversational Answer:
If we consider our reading rate, and how many pages per day, we can probably convert our pages per day to minutes per day.
This translates into:
Recall that we can manipulate units like numbers as well.
THAT’S IT! CONGRATS ON MAKING IT TO THE END!!!
Formal Topics (If Interested)
If you are interested in formal topics, related to the math in this article, please consider researching these topics I have provided some links, but please feel free to explore beyond the ones below:
1. Dimensional Analysis (units)
2. Descriptive Statistics (Expected Values/Averages)
3. Algebra
