Can We Agree On How To Measure The Similarity Of Dive Profiles?

[kr2y5]

There have been a number of heated debates spanning over countless threads, in which people have violently argued various points, most of which ultimately boiled down to a disagreement on whether certain dives profiles were similar or not, how much they were similar, or whether X is more similar to Y than to Z. On the basis of the supposed similarity (or lack thereof), people have drawn a variety of conclusions, such as that some profiles are representative (or not) of real diving, that some decompression strategies produce equivalent results, and so on.

I don't recall reading any proposed definition of "similarity" that all the opponents in a discussion would be able to accept. Maybe there was one that I missed, or that I don't remember.

If there is no agreement on what it actually means to be "similar" in a somewhat concrete sense, any discussion on whether things were similar (or representative, or equivalent, or whatever) is unlikely to lead to a constructive outcome: on one hand, a consensus would not be very meaningful, and on the other hand, if the true reasons for the disagreement lie in the different ways, in which people define similarity, it will probably be more productive to elevate the whole discussion, and debate the true source of the apparent disagreement, rather than debating its consequences.

With this said, I have a few specific questions:

1) What is "similarity"? How would you define this concept for a pair of dive profiles, in concrete terms?

2) What does "more similar" mean? If we have dive profiles X, Y, and Z, on what basis could we possibly claim that X is more similar to Y than it is to Z? Could we take that further and say that similarity between dive profiles A and B is greater than similarity between C and D? How would we decide that?

3) What does "similar" mean? On what basis could we possibly attempt to draw a boundary between "similar" and "not similar"? Could we, for example, define a number, such as, to say that similarity of X and Y is 0.58, whatever that might mean, and apply a threshold, beyond which things are to be considered "similar"? If not a number, then on what other basis can we possibly hope to distinguish "similar" from "dissimilar"?

Thanks!

 

[kr2y5]

Let me seed the discussion with one concrete proposal based on a recent thread. What I think was postulated there is that, we can define similarity in terms of the largest difference in time spent at any specific depth. For example, if both profiles had the same bottom time, but one had 20 minutes more deco at one of the stop depths compared to the other, then "20 minutes" would be one possible measure of how much the profiles are dissimilar. The answers to all the above questions follow in the obvious way from this characterization.

Does everyone agree with such definition of similarity? Does it agree with intuition? Are there any pitfalls there, could it lead to bogus results? Is it reasonable, for example, to attach the same weight to a 5-minute difference at 100 feet, as compared to 5-minute difference at 10 feet? How does this approach generalize to profiles that include gas switches at different depths? Can you try to think of anything that you feel works better (however you choose to define "better")?

 

[dlofting]

I wasn't a participant in any of the threads you referenced......what is the reason or reasons that you want to quantitatively compare dive profiles ?

 

[kr2y5]

I wasn't a participant in any of the threads you referenced......what is the reason or reasons that you want to quantitatively compare dive profiles ?

One of the debates is actively going on in this thread, and it currently involves trying to determine whether two ascents are similar. There have been other instances of the question earlier in this and related threads on deeps stops, and one of the things that seems concerning is that the decision is always made on a case-by-case basis, which invites subjectivity into the discussion.

 

[rjack321]

There's mathematically similar, biologically similar, clinically similar, and having similar risk. There's 4 features alone (there are probably more) which may or may not be mutually exclusive with dissimilar. E.g. a profile might be statistically similar in terms of it curvature and duration (e.g. the quadratic function defining it) but despite this mathematically "identicalness" present a very different risk profile.

So the answer to your question is no, there's never going to be agreement. Define your terms, state your evidence. Ignore or block the evidence-less pontificators and go diving.

 

[kr2y5]

I agree, it seems that people are coming at it from very different angles, which is a part of the reason for disagreements. While it might not be possible to reach consensus, perhaps it would make sense to at least try to arrive at a more concrete definition for each of the possible alternatives, and to clarify, when one is making an argument, which is the perspective they have adopted. I, for one, would like to understand how an assessment of mathematical vs. biological vs. clinical vs. risk-wise similarities can differ, it would help me better understand why person A disagrees with person B. As you say, "define your terms": when we assert something to be true, we should be able to at least state the principles and assumptions, based on which we reached whatever one claims to be true, if nothing else then to help others better appreciate what's being communicated. I'd love to see some specific examples of how different people approach this, and, more importantly, the reasons why someone chooses A over B.

 

[rjack321]

Ask them what they mean by similar and deduce their usage from peer reviewed published work. SB doesn't count as publication

 

[kr2y5]

Ask them what they mean by similar

Yup, that's why we're here

and deduce their usage from peer reviewed published work. SB doesn't count as publication

I'm in the camp that believes ideas can be judged on their own merit, and can be communicated in a number of different ways. As long as someone can state their claims and assumptions somewhat clearly, no reason why they can't be shared even in a casual conversation. Since we're in the realm of definitions, and we don't need to prove or disprove anything, I think there's no reason we can't have this discussion.

 

[rjack321]

Yup, that's why we're here



I'm in the camp that believes ideas can be judged on their own merit, and can be communicated in a number of different ways. As long as someone can state their claims and assumptions somewhat clearly, no reason why they can't be shared even in a casual conversation. Since we're in the realm of definitions, and we don't need to prove or disprove anything, I think there's no reason we can't have this discussion.

Good for you but there's a whole pile of deco BS on SB. Some with no evidence at all, contradictory evidence, and just a good sounding argument. How many deco dives have you done? What frame of reference are you evaluating these "differences" (or similarities) from?

You still seem to think there are definitions for similar and different - they don't exist.

 

[kr2y5]

Good for you but there's a whole pile of deco BS on SB. Some with no evidence at all, contradictory evidence, and just a good sounding argument. How many deco dives have you done? What frame of reference are you evaluating these "differences" (or similarities) from?

Sure, there is a risk of misunderstanding when sharing thoughts on SB, in that those thoughts can enter minds of people with less experience and a different frame of reference, and invite unfair criticism, or what you refer to as deco BS. It seems to me that the people, who chose to participate in all those other threads, have already accepted that risk, and have not exactly been shy to share their opinions and face disagreements.

Presumably, the reason is because there is the upside: sometimes, useful ideas come from people with less experience, and a different frame of reference, and the number of dives is not a perfect predictor of someone's ability to understand or contribute. In my mind, the value of a place like SB is the ability to be exposed to different perspectives, that's what I come here for anyway. I think most of us realize that you need to approach things with a healthy dose of skepticism, and quite frankly, that also includes credentials. At least, ideas we can debate without hurting anyone in the process.

If anything, the goal of this thread is to reduce the amount of misunderstanding: we seem to be using the same words to mean different things, perhaps we can try to at least explore those differences to see what is their nature, and the underlying reasons for people having different preferences.

You still seem to think there are definitions for similar and different - they don't exist.

I assume by this you mean there are too many definitions to hope for a single one of them to be universally accepted. As I said earlier, I am happy with this as the outcome if it comes to it: if nothing else, many of us would learn something in the process. But, until we actually have multiple somewhat concrete proposals on the table, I'd be inclined to suspend judgment, and hear what everyone else thinks.

I realize this isn't a forum of physicians-mathematicians, and I'm not necessary expecting anyone to pull out a handy formula like a rabbit out of their pocket. But, a lot of people have expressed strong opinions, and presumably behind each of those opinions lies a certain mental model based on that person's intuition or their experience, be it in diving, physiology, or whatever.

Perhaps we could, then, try to explore those intuitions, throw some ideas on the table, kick them around, and see what comes out. I see no harm in trying.