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English
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Part 37 of Mathematical Proof
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Published:
2012-11-13
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1,235
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1/1
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A Personal Account of a Scientific Study of the Helpfulness of Dr. John Hamish Watson by Sherlock Holmes

Summary:

A combination of increasing familiarity with the subject, John Watson, and knowledge of the general predictability of humans (even including John Watson) have led me over time to the impression that John’s behaviors vary in a fashion that can be predicted by a certain set of factors. In particular, in this study I wish to capitalize upon the factor of John’s helpfulness to me.

Notes:

(1) Yes, I know "Sherlock keeping tables of things" has been done before (lots), better (definitely), and etc. (I guess I've actually already had him do it once or twice myself, i.e. in "Fuzzy Measures," not that the table was shown.) But I couldn't resist.

(2) No math background from me because Sherlock is your teacher today, here to help you learn a lesson about collinearity. (Good luck.)

(3) (But if you feel he's being too opaque, see end notes for "translation" of his final finding.)

(4) Yes, data totally fabricated and manipulated to fit my needs. Mwahahaha.

(5) I hope the formatting doesn't look too horrendous on your screen of choice, and I hope the images aren't a nuisance. Trust me, it was way better than trying to make the HTML tables look even vaguely presentable.

(6) I was going to do SO much more with this, but making up the data took longer than I thought it would and I have a big test tomorrow. Need to go to sleep now so that I can study before class...

(See the end of the work for more notes.)

Work Text:

The Science of Deduction

A Personal Account of a Scientific Study of the Helpfulness of Dr. John Hamish Watson by Sherlock Holmes (Currently In Progress)

Introduction, Experiment Setup, and Definition of Parameters

            A combination of increasing familiarity with the subject, John Watson, and knowledge of the general predictability of humans (even including John Watson) have led me over time to the impression that John’s behaviors vary in a fashion that can be predicted by a certain set of factors. In particular, in this study I wish to capitalize upon the factor of John’s helpfulness to me. That is, what parts of John’s daily life and behaviors can be used to predict the extent to which John will be agreeable and helpful in assisting me in my work? I hope to use this data to better manipulate the factors over which I have control, thereby maximizing the extent to which John can help me with my work and thereby increasing the quantity and quality of work done overall.

            To this end, I have selected an array of habits, which I shall study over the next two months (60 days) in order to determine which of these have an impact on John’s helpfulness (as perceived by myself) and which do not. Here, “helpfulness” will be defined quantitatively on a scale of 1 to 100 (although the value will be selected by me based on qualitative data). For optimally usable results, there must be some reasonably well-defined scale against which to measure the helpfulness; therefore, some variety of “test question” must be designed to ensure that helpfulness is judged based on the same general difficulty of request from day to day. However, it is also necessary to ensure that John not discover that this is an experiment, so the same question cannot be used on a daily basis; rather, several test questions of roughly similar nature must be selected from such that suspicion of repetition can be avoided. I intend to use the following:

(1) Would you go acquire [common item] for me?

-          This would be an item that could easily be gotten from Tesco or the like.

-          To be asked in a context easily interpreted as being related to an experiment.

-          Helpfulness rating based on whether he acquires the item, how quickly, whether he has reason not to if he does not, and general attitude in response to request.

(2) Please hand me [item].

-          To be used in the context of doing an experiment.

-          To balance the difficulty of (1), should be an item that it would be slightly inconvenient or unpleasant to acquire, given that it is already in close proximity.

-          Helpfulness rating based on willingness, speed, whether he has a reason to if he refuses, general attitude.

(3) Accompany me to [place].

-          To balance difficulty with (1) and (2), may be location or timing to which John would not readily agree (i.e. when he is somewhat busy, has other engagements), or may entail significant time commitment.

-          To be used in context of case or research.

-          Helpfulness rating based on willingness, whether he has a reason to if he refuses, general attitude, attitude upon arrival at location, willingness to stay/frequency of mention of reason(s) to leave.

 

This should cover a wide enough range of possibilities that the question can be used daily without arousing suspicion. Similar questions can be used in their place provided difficulty of the request or task is taken into account. Any questions not of the above format will be noted over the course of the experiment.

            Factors to be tested for over the course of the experiment shall cover a wide variety of possible influences. They can be seen in the headers of Table 1.1. Since of particular concern is factors over which I have control, those shall be the focus of the data collection.

            In the interest of ensuring that I do not make predictions before observing all the facts, for the duration of the experiment I shall hide all previous data from myself by changing the font color in the table (stored on my laptop, to be posted in this location after the completion of the experiment) and shall delete any memory of it after recording and hiding it. When collection is complete, the table will be shown in full below.

            The experiment shall commence tomorrow, the sixteenth of August, and proceed through October the fifteenth.

 

Data

 

Data Analysis and Conclusions

            Upon careful analysis of the data, it would appear that John’s helpfulness to me is most likely dependent on the number of hours he spends assisting me with my work (so, he is most helpful when we are on a case), his masturbatory habits and watching telly (in particular, here, with me, as I have no idea what he does while I am not at the flat), sensible possibilities as they typically indicate general mood and presence of free time, physical contact with me (perhaps because this occurs most frequently when we are on a case or watching telly together), and, to a lesser extent, the number of meals he eats and amount of sleep he gets (perfectly reasonable, as a hungry or tired John is much more likely to antagonize me). Figure below shows analysis of a model of the data.

 

 

 

            My initial evaluation of the data led me to the conclusion that by, whenever possible, including John in my work, and in return attempting to ensure that he occasionally has time to subject me to his horrid taste in films, I might most easily maximize his helpfulness to me on a day-to-day basis.    

            However, one particularly interesting and noteworthy result occurred in the correlation between two of the variables which has modified my approach slightly. I tested each variable for collinearity in an effort to ensure that none of the variables was strongly affected by the other, and found, in fact, that two of the variables were quite related to one another, as determined by a regression of one x variable on all others (note the very high R-squared value listed at the bottom of the summary of the third regression, indicating the high correlation between the two variables in question). I leave the results here for your viewing, and leave you to your deductions.

 

 

 

 

Latest Forum Posts

 

John Watson
Sherlock, that is completely inappropriate to post up online. Please take it down.

 

            SH
          I can’t imagine I know what you’re talking about.

 

                        John Watson
                       You can, you do, and you know.

 

                                    SH
                                    Everyone who visits here is an idiot anyway, John. They won’t reach the obvious conclusion.

 

                                             John Watson
                                             What obvious conclusion?

 

                                                            SH
                                                            Oh. I see.
                                                            I had imagined that was why you had wanted it taken down.

 

                                                                      John Watson
                                                                      Not everyone wants their wanking habits posted for the world to see.
                                                                      (Or anything else you’ve got on that chart, for that matter, but especially that.)

 

                                                                                      SH
                                                                                      Oh, so you do follow.

 

                                                                                                     John Watson
                                                                                                     Sherlock, just take it down.

 

                                                theimprobableone
                                                someone’s got a widdle crush…

 

                                                            John Watson
                                                            [comment deleted]

 

                                                            theimprobableone
                                                            [comment deleted]

 

                                                                        SH
                                                                        [comment deleted]

 

                                    John Watson
                                    I think I just reached the obvious conclusion.

 

                                                SH
                                                Funny, it sounded like you reached it hours ago.

 

                                                            John Watson
                                                            Shut up.

 

                                                                        SH
                                                                           Unlock your door.

 

                                                                                    G Lestrade
                                                                                     Jesus Christ, you two, get a room.

 

                                                                                                SH
                                                                                                Why do you think I told him to unlock his door?

 

                                                                                                             John Watson
                                                                                                             [comment deleted]

 

                                                                                                            G Lestrade
                                                                                                            [comment deleted]

Notes:

As you can see in the second figure, toward the top, we have a regression of John's time masturbating over all the other variables. This would be one instance of Sherlock seeing if any of the variables depend on the others (which is generally regarded as bad); in this case, does the variable for John's masturbatory habits vary as any of the other variables vary? (In other words, could we use some of the other variable(s) Sherlock measured to predict how long John's going to spend wanking each day?) Anything with a symbol over on the right-hand side is significant; the key tells you how much. (It's actually a measure of how likely it is that that particular variable doesn't affect the outcome.) So we can see that the chances that John's masturbation is not influenced by John's physical contact with Sherlock are astronomically tiny. (We also see, weirdly enough, that there's the distinct possibility that Sherlock's violin-playing affects it as well...)

The second half, starting with "m3," shows a more in-depth analysis of what's going on with these two particular variables. You can see that there is essentially no way in hell you couldn't use John's amount of physical contact with Sherlock to predict how much he's going to wank tonight. (Again I should point out that this is because I manipulated the data to make it that way...) This is more formally measured by the R squared value. It's very, very close to one, so that means that these two variables are collinear. If we were trying to fit the best model possible to predict John's helpfulness, we would either leave out his masturbation habits, or his physical contact with Sherlock, because what the high R squared value says is that you get the same information from one as you get from the other, and there's no reason to have the same information in your model twice.

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