"Impossible" vs. "Improbable"

[Carol the Dabbler]

Sherlock Holmes has long been noted for quotes such as these (thank you, Wikiquote!):

 

How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth? [The Sign of the Four]

It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth. ["The Adventure of the Beryl Coronet"]

That is the case as it appears to the police, and improbable as it is, all other explanations are more improbable still. ["Silver Blaze"]

It is impossible as I state it, and therefore I must in some respect have stated it wrong. ["The Adventure of the Priory School"]

We must fall back upon the old axiom that when all other contingencies fail, whatever remains, however improbable, must be the truth. ["The Adventure of the Bruce-Partington Plans"]

When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth. ["The Adventure of the Blanched Soldier"]

What I would like to know is, how does Holmes propose to distinguish the impossible from the merely improbable? It seems to me that a good many "impossible" things merely represent ignorance on the part of the observer (and Holmes's ignorance is "remarkable" -- though apparently not "spectacular" -- according to Watson's observations in A Study in Scarlet).

 

Can someone please defend the poor man from my vicious attack?

[Bakerstreet Irregular]

The think one of the problems is or was....that Watson hadn't known Holmes for very long when he set about making his list and, as we all know, if Holmes didn't want you do know something about him....you never learned it no matter how long you might live with him and no matter how deeply Holmes regarded your friendship. He was well rounded he just didn't clutter up his "lumber room" with useless information. He had plenty of reference books and such to use and refer to.

 

As to his thought processes.....he seldom gave them away as well. He would be up and about....in and out of the flat and poor Watson and Lestrade none the wiser to what he was up to. He would finally throw out his deductions and conclusions but never give the steps A to Z as how he come to them in many cases.

[Carol the Dabbler]

As to his thought processes.....he seldom gave them away ... and poor Watson ... none the wiser ... in many cases.

From a real-world perspective, of course, that's exactly what Watson was there for -- to keep us readers in the selective dark.

 

But from an in-universe viewpoint, I'm hoping someone can give even one example of Holmes explaining (or hinting) how he knew something was impossible, while something else was merely improbable.

[Bakerstreet Irregular]

I may be wrong, but "Silver Blaze" which you give as an example above comes to mind as how he actually give out his train of thought. Like why he stretched himself out on the blanket in the mud and what he found in the mud. The strange action of the dog in the nighttime and all that?

[Carol the Dabbler]

OK, that's the "That is the case as it appears to the police, and improbable as it is, all other explanations are more improbable still" quote -- which deals with degrees of improbability (rather than impossible vs. improbable). But if Holmes explains even that, it should shed some light on his technique. And that's the one with the famous nighttime dog too? Yeah, I'll read that. Thanks!

[Bakerstreet Irregular]

I was beginning to think that I was missing the point of your question altogether.

[Shangas]

"Impossible".

 

Nailing jello to a brick wall is impossible.

 

"Improbable".

 

It is improbable that the Queen will accept a flyswat made of bread-dough as a Christmas present.

 

The difference is that one is clearly unobtainable, while the other has an element of chance, or the unknown, involved.

 

Holmes would differentiate between the two by deciding how likely each one of these scenarios would be.

 

I've done a few 'deductive puzzles' myself, and when you really think about it, it's not TOO difficult. Granted, some of the things I practiced on were fairly easy...

 

It helps, I think, to have a big imagination. If you can't imagine, and think outside the box, deduction is extremely difficult.

 

In another Sherlock Holmes board, of which I was a member before it went belly-up, I initiated a Deductions Game thread which was very well-received. To start off with, ironically, just as Holmes had started off with - I used a pocketwatch!!

[Bakerstreet Irregular]

Very appropriate too. I wonder if it would work as well with a mobile phone, of course the inscription helped but it is fun to watch him run through it. Nailing gello may be a challenge for sure, but impossible? I can see the experiments on just how firm could one get the stuff to set up before it would stick?

[Carol the Dabbler]

That's my point exactly, Fox.

 

Shangas, your explanation and your examples are perfectly logical. It's just that people become so attached to their own idea of "common sense" that it can get in the way of, as you say, thinking outside the box. In fact, I suppose common sense is the box.

 

Would love to hear Holmes himself explain how to tell the impossible from the merely improbable -- too bad we don't have his monograph on that subject!

[Shangas]

That's my point exactly, Fox.

 

Shangas, your explanation and your examples are perfectly logical. It's just that people become so attached to their own idea of "common sense" that it can get in the way of, as you say, thinking outside the box. In fact, I suppose common sense is the box.

 

Would love to hear Holmes himself explain how to tell the impossible from the merely improbable -- too bad we don't have his monograph on that subject!

 

Common sense is not the box. The box is the limits of conventional thought. Imagination is what exists beyond the box. Common sense is the lid on top of it. How much imagination (and therefore, deductive ability, arguably) one would have, is determined by how much we can override common sense. To throw off the lid, and have our minds spill outside the box into the realms of imagination and fantasy, and to what extent. The more we can do that, the better we'd be at deduction.

[Bakerstreet Irregular]

The brilliant thing about being a high functioning sociopath and on the spectrum, the box pretty much doesn't exist anyway. These people have no problem throwing over the traces of the social norm. One expert in this field considered it an up side. They can be as creative and free thinking as they want and the torpedoes be damned.

 

When Sherlock tells John that he is a Consulting Detective and the only one in the world because he created it, that is text book sociopathic behavior. They can, will, and do create their own niches a true blessing beyond the curse.

 

For Sherlock Holmes nothing is impossible unless or until he can prove it to be so by his own methods and understanding.

[Carol the Dabbler]

Common sense is not the box. The box is the limits of conventional thought. Imagination is what exists beyond the box. Common sense is the lid on top of it.

At least we agree that common sense is one of the limits on imaginative thought.

 

You're apparently using "common sense" as a technical term. Unfortunately, most people use the term more loosely, to mean something like "well, everybody knows that ..." In other words, the limits of conventional thought. In order to communicate effectively, we are, alas, kind of stuck using words the way most people use them, unless we explicitly define them otherwise.

 

 

For Sherlock Holmes nothing is impossible unless or until he can prove it to be so by his own methods and understanding.

That does sound like Sherlock Holmes. I hate to "insult" the man (as he would see it), but to my way of thinking, what he does is more of an art than a science. He's so effective at what he does simply because his insights tend to be accurate. Even though he sometimes explains what he did (i.e., what steps he took), there's no way that he can explain how, because his thought processes consist of right-brain insights strung together with left-brain logic. In short, he's a creative artist.

 

How does that sound?

[Bakerstreet Irregular]

what he does is more of an art than a science.

Hence the term "the art of deduction".

[Carol the Dabbler]

Right, it does seem like that would have been a more accurate name for Sherlock's blog. But he insists on seeing what he does as "The Science of Deduction."

 

However, Google brings up a number of fan sites that apparently like the term "Art of Deduction."

[Bakerstreet Irregular]

I guess Sir Arthur Conan Doyle used the term science but it seems like there is a reference to art as well. I'll have to go through the annotated books and see what I can come up with.

[Carol the Dabbler]

Oh, sorry, I switched lanes without signaling -- I was referring to Sherlock just then. I'm not sufficiently familiar with the canon to have a clear idea of the terminology Holmes used there. Sorry for the confusion -- maybe I'd better go to bed now, and continue posting in the morning when my head is clearer!

[Bakerstreet Irregular]

That's okay. The mind hates to shut down now that it is officially the weekend. Pretty drifty myself.

[Julia Mae]

John's Blog is Wrong or the Solar System is explains why it is impossible for Sherlockk and John to have met outside 221B Baker street at 7 o'clock the day after their meeting at Saint Bart's, which is the reality of the show. It is, at least, the time and day Sherlock gave John in the lab. But that wasn't the correct time if you check the date on John's blog. Eitrher the date on the blog is wrong, or Sherlock and John live in an alternate universe or on an almost exact duplicate of earth.

 

I think it's less probable that they are shipping Sherlock from an alternatre universe, than I do that the date got messed up on John's blog.

 

To Sherlock Holmes, in either the Canon or show, the terms are used with their mathematical implications: what is the probabality of an event having occurred? If it is 0, that is an impossible event. If it is even 1 in a million, that is an improbable, but still possible, event.

 

Most of Sherlock's conclusions involve what is probable, rather than what is impossible. Like when he solved the "code" on Irene Adler's camera-phone.

[Carol the Dabbler]

I agree with you regarding John's blog, but for a somewhat different reason, namely that I consider John's blog (the portions of it not included in the show) to be only semi-Sherlock-canon. If there's a discrepancy between the blog and the show (as there seems to be here), then I'll go with the show.

 

I understand the basic concept of mathematical probability, but I don't see how it would often be of much help in detective work, because very few things in life have a mathematically-calculable probability. To continue with your example, how could anyone calculate the probability that Irene Adler used "SHER" as her telephone password? I suspect that Sherlock was going on more of a [perish the thought] hunch there. As I said earlier, it seems to me that he actually practices a combination of art and science, though my head says it's bedtime, so I could be overlooking something.

[Bakerstreet Irregular]

I think Irene gave him the clue about her using "SHER" when she and Mycroft was talking at the table behind. Something about "He is good, isn't he. I should have him on a leash in fact, I might."

[Carol the Dabbler]

I think Irene gave him the clue about her using "SHER" when she and Mycroft was talking at the table behind. Something about "He is good, isn't he. I should have him on a leash in fact, I might."

That may indeed have been the final clue -- or it could have been merely the last straw, the insult that prodded Sherlock to reach for one more deduction.

 

But in any case, there doesn't seem to be any mathematical precision involved. This doesn't seem to be a case of "eliminating the impossible."

[Bakerstreet Irregular]

-- or it could have been merely the last straw, the insult that prodded Sherlock to reach for one more deduction.

This younger, more modern Sherlock may not be the patriot that the original Holmes was, but to see Mycroft ruined and England bankrupt by this woman...then humiliated by her......even though she did say that what she had said wasn't true...she was just playing the game.....I can see how that would gall him. He was looking for a partner....a brain and intellect to match and complement his own....not a competition or a tug of war over who could best who. He was not looking to dominate nor to be dominated.

[Julia Mae]

 

 

I understand the basic concept of mathematical probability, but I don't see how it would often be of much help in detective work, because very few things in life have a mathematically-calculable probability. To continue with your example, how could anyone calculate the probability that Irene Adler used "SHER" as her telephone password? I suspect that Sherlock was going on more of a [perish the thought] hunch there. As I said earlier, it seems to me that he actually practices a combination of art and science, though my head says it's bedtime, so I could be overlooking something.

----------

 

Sherlock assumes the killer in SiP is a man because it's statistically more likely, so that's one example.   In TRF, he identifies that glycerine molecule by what we would call hunch, but to a trained scientific mind is more: probability.  The Hansel and Gretel clue combed with the molecule led him to candy factory.  He didn't have proof though.    But in actual detective work, or just police work, I can tell you (as I was a cop in my youth in a major city) you use probability even though you don't calculate mathematically.  For instance, some convenience store gets stuck-up and you get 5 descriptions from 5 witnesses.  They will vary, often in such things as height, build and clothing, and also sometimes in race and other basic descriptors.

 

So, what description am I broadcasting over the radio for officers to be on the lookout for minutes after the crime?  The "average" or most probable description.   So if three people say he was wearing a baseball cap, 1 says a knit hat and 1 says no hat, I say wearing a baseball cap. 

 

I suggest you use probability every day and just don't think of it that way.  If there are two routes to the Mall, you probably choose the one you think most likely to be faster.  You might go one way in the middle of the day, but not go that way at rush hour.  Human beings (and some other animals) are born able to to these calculations without any training or knowing the names of numbers or being conscious they do them.

 

If you are leader in a group of volunteers, you tell Fred to put away the chairs, not George because you know George is likely to leave early, not get all the chairs or put them away haphazardly.  The probability is Fred will do a better job.  A statistician, with enough data from previous Fred/George experiences, can develop a model to predict the likelihood each will perform the duty satisfactorily.  But you don't need it, because you have the experience, you just don't consider it doing a  a calculation.  But it still is.

 

As Roger Penrose says in Hawking:  "You don't need words to think about mathematics.  In fact, words get in the way."

[Julia Mae]

I think Irene gave him the clue about her using "SHER" when she and Mycroft was talking at the table behind. Something about "He is good, isn't he. I should have him on a leash in fact, I might."

---------------------

Mr. Cumberbatch, in every role I've seen him in (admittedly not nearly enough) does this thing when his characters are thinking where his eyes move.  He does a pronounced version of that in Sherlock, who is bigger than life.  In this scene, he isn't doing that.  He is just listening, but he comes to life when she says, "Jim Moriarty sends his love."

 

Jim Moriarty?

 

That's when the head comes up and the eyes start moving.  Sherlock didn't know he was involved, so now he has a train of thought:  She's not just there for her own purposes, Moriarty is pulling the strings.  He had trouble reading her, but she did show him something, her body.  What else does he know about her body?  When her pulse becomes elevated and her pupils dilate.  Moriarty can't tell her to do that, obviously.  So what is her purpose, beyond getting money out of Mycroft?  Mycroft says "Bond air" and he much later connects it to 007.  Adler's phone says locked, personal combination on the safe, the only thing he could read was her body, locked phone the only thing he can read is her pulse, her pupillary response -  personal motives.... she wants him on a leash... to have him on the desk.... she didn't need any of that to do what Moriarty wanted, or get money from Mycroft.  So it's personal, like her body, her feelings.  Sentiment.  Her feelings were about him, Sherlock. 

 

I think without her mentioning Moriarty, he never gets there.  But he needed all those pieces.

[Carol the Dabbler]

Sherlock assumes the killer in SiP is a man because it's statistically more likely, so that's one example.

 

Although it would be possible to calculate a probability that the killer is a man, it wouldn't be exact, due to the percentage of unsolved murders, etc.  And even if it were exact, Sherlock doesn't claim that the statistics prove the killer is a man, merely that it's (as you quoted him) "statistically more likely" -- a first-order working hypothesis, a good starting place.

 

 

To Sherlock Holmes, in either the Canon or show, the terms are used with their mathematical implications: what is the probabality of an event having occurred? If it is 0, that is an impossible event. If it is even 1 in a million, that is an improbable, but still possible, event.

 

Going back a few days, that's how we got into probability in the first place.  Again, what you say is true, but it seems to me that the only way to calculate a precisely zero probability would be to know already that the event was impossible.  If the zero came from unbiased calculations, how would one know whether it was truly zero, or merely very, very small?

 

Which gets us back to my original question -- how does Sherlock determine whether something is truly impossible or merely highly improbable?  In fact, can anyone actually do that?  I still contend that we often label something as "impossible" merely because we lack the knowledge and/or the imagination to see how it could happen.