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Comment by learnstats2 | Hacker News Reader

The author of this blog post is wrong to say this is 'integration'[0], and is also later wrong to say it's the 'trapezoidal rule'[1].

It seems to me that it's diagnostically useful to have a standardised method for estimating the area under the curve, rather than everyone inventing their own method.

[0](since you don't know the whole function, you only know point estimates at particular moments in time)

[1] (trapezoidal rule is normally defined by having equal intervals - here, measurements are often taken at irregular intervals)

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This comment is just wrong. It's still integration even if you only have enough data to approximate the integral. Also, Wikipedia's definition of the trapezoidal rule permits intervals with different sizes.[1]

I don't know why you'd defend a researcher who lacked basic math knowledge, and more damningly refused to acknowledge her mistake once it was brought to light.

[1] https://en.m.wikipedia.org/wiki/Trapezoidal_rule

> It's still integration

In my view integration is by definition part of calculus, and requires the concept of the infinitesimal. (This is maybe semantic, but Wikipedia agrees with me in this case).

The paper shares one of the many goals of integration, which is to find the area under the curve, but you literally cannot use integration as the tool to do this here.

So, it's not integration.

A comment below calls this "numerical integration" - which I also find dubious. Numerical integration is still using calculus - you have to know the whole function - but without getting to a closed form answer.

Is this something that could be applied in general mathematics? If so, is it truly novel and worthy or a trivial derivation? I’m asking because I don’t know, not rhetorically.

I agree that someone shouldn’t be publicly made fun of in-general for sharing something novel and non-trivial that others didn’t already know, and if it highlights a problem in inadequate reviews, maybe it should’ve been presented to the journals that published it with that info.

This is kind of where grand parent's thesis (that the paper is in fact novel and useful) falls down.

I'd be stunned if the concept of integrating an unknown function that needs to be guessed based on measurements taken at irregular points in time hasn't been studied rigorously from a generalized mathematical point of view. What such study would likely do (that a medical treatment would not) is discuss tradeoffs of different approximation methods, probably explore things like error bounds and behaviours with different unknown functions, and selection of the best integration method.

GP is right in that I'm sure it's useful to have a standardized method that allows for comparison between doctors and patients. But I think it's naive to assume that the findings in this paper are mathematically novel, and further, that mathematicians couldn't do a more rigorous job of deducing an accurate 'standard' way of measuring this.

If you look close enough, you see this kind of thing quite often, eyperts in one field "discovering" the basics of another, non related, field. And then praising themselves for discovering it. No idea if people looked at that, but I sometimes have the impression, that our hyper specialization isn#t helping.

I see this at the moment a lot with supply chain management. Best example used to be masks, and no vacinations. It is kind of funny to see in real time people dicovering, and trying to cope with, the time axis coming with purchase orders, volumes and delivery dates. It is also quite saddening to watch. A medical researched discovering maths I learned already before entering university falls into kind of the same category.

I don’t think there’s anything here for mathematicians. The only nontrivial fact in the paper is that the approximation works well in medical practice (which is not something that Leibniz or Newton would have been able to tell you since there could be complicated biological factors confounding it - what if the ‘real curve’ has a bunch of spikes that don’t show up in measurements?).

However, the original paper really is incomplete because of its seeming ignorance of the real “trapezoidal rule.” It really needs a discussion along the lines of “the trapezoid rule from ordinary calculus can be used by diabetes practitioners with surprising accuracy” and explained that sources of error, discontinuity, etc., aren’t likely to affects the approximation.

But don’t worry about M.M. Tai’s feelings too much :) The paper is almost 30 years old and it’s world-famous for the silly error, Tai has already been throughly roasted.

It most certainly is still (numerical) integration.

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