Jamie123 Posted September 8, 2022 Report Share Posted September 8, 2022 As a young postdoc who had recently transferred from one field of research (semiconductors) to another (telecommunications), I independently "discovered" the Erlang-B formula and Bayes' Scolium. Fortunately I was disillusioned by "older, wiser and better people" before making an ass of myself in the literature, but other people have not been so lucky. Like Mary M. Tai. You can read her paper here: TaisMethod.pdf (berkeley.edu). You'll notice at once that "Tai's Mathematical Model" (as she calls it) is nothing but the trapezoidal rule. I could understand it if Tai didn't take calculus (or even pre-calculus) at school, but can this be true? Her mathematical notation is immaculate and she uses the sigma notation for addition perfectly. She even uses the word "abscissa" correctly! So how can she think that she "invented" (and gets the honour of naming!) a technique familiar to every 16-year-old? I read somewhere that this paper has over 400 citations - so she's clearly doing well out of it! Vort 1 Quote Link to comment Share on other sites More sharing options...

Vort Posted September 8, 2022 Report Share Posted September 8, 2022 And it got past peer review... Quote Link to comment Share on other sites More sharing options...

Carborendum Posted September 8, 2022 Report Share Posted September 8, 2022 (edited) 5 hours ago, Jamie123 said: You'll notice at once that "Tai's Mathematical Model" (as she calls it) is nothing but the trapezoidal rule. ... I read somewhere that this paper has over 400 citations - so she's clearly doing well out of it! I'm going to defend this paper. Hear me out. BACKGROUND: I was never taught the "trapezoidal rule" for calculus. I was taught the "rectangular rule". Actually, various instructors never gave it a name. They just described the method. Maybe my instructors all sucked. I dunno. And TBH, I never really read any math books. Maybe it was in there, maybe it wasn't. Regardless, when working with differential elements, the difference between a rectangular method vs a trapezoidal method is trivial. That said: I believe the trapezoidal rule is traditionally about describing the logic behind calculus. (Let me know if I'm wrong). The description in the paper is not about calculus. It is about using this same logic that was used for calculus in a different application and a different level. That same logic was used to help determine an approximate function based on statistical data points. I have no idea what her motivation was in creating this paper. It may simply be "this is the method I'd use..." And others decided to copy her. So, more background would be helpful. Maybe she wasn't trying to make a name for herself. She may have seen it as publicly, formally stating the obvious because she saw so many people faltering. Who knows? EXAMPLE: Most of my projects have cookie-cutter math and analysis. But a lot of them have at least one or two items that don't fit into the standard methods that are industry standard. So, when I have to analyze something that doesn't fit into any code-approved method, then I have to come up with something out-of-the-box. At that point, I can come up with some fanciful mathematical model that seems to have all the technical merits that a mathematical proof would have. But if it is not an approved standard, a reviewer can reject it simply because he is not familiar with anyone using it. However, if you have a white paper from a University that says this is a valid method of analysis, that can sway the reviewer's opinion. So, I'd really like to hear MOE's opinion on this (@MarginOfError?) . Is this an OLD method for statistics? It was from 1993. A 30-year-old paper. I wonder if this method was commonly used in statistical analysis prior to that time. ... I'd also agree with @Vort that peer-review at woke universities is almost non-existent. They pretty-much just rubber-stamp everything. And anything from Berkeley is considered God's word regardless of the merits. Edited September 8, 2022 by Carborendum Vort 1 Quote Link to comment Share on other sites More sharing options...

mikbone Posted September 8, 2022 Report Share Posted September 8, 2022 (edited) So, someone has diabetes? Edited September 8, 2022 by mikbone Just_A_Guy 1 Quote Link to comment Share on other sites More sharing options...

MrShorty Posted September 8, 2022 Report Share Posted September 8, 2022 I sometimes wish I had chosen a career in math pedagogy or similar so I could talk more intelligently about things like this. A few thoughts Yes, it is obvious this is a simple Riemann sum approach (https://en.wikipedia.org/wiki/Riemann_sum) to integration. The basic methodology (break up an integral into "slices" that you can easily find the area of, then sum up the area of the slices) is attributed to Riemann in the 19th century. I learned them as Riemann sums in my second full calculus class (I do not recall them being mention in pre-calculus or my first, simple calculus class). It appears to me (decades after graduation) that not every calculus class taught these methods, and not all of them attributed the method to Riemann. The first thing I notice in Tai's paper is that this is a medical application (Glucose tolerance and metabolic curves). It is not clear what Tai's credentials are, but I would guess she (assuming someone named Mary is female) is well studied in medicine. I don't recall (if I ever knew) the math ed requirements for pre-med, nursing, and other "practical" medical degrees and certification. What medical fields (if any) expect a solid course in calculus? Looking at the references Tai used in preparing the paper, I notice that all references are medical in nature. The only mathematical reference appears to be a geometry text. I could be wrong, but I wouldn't expect a geometry text to cover Riemann sums and definite integrals. Speaking of definite integrals, I notice that Tai never uses that term in the paper (unless I missed it). She always uses "area under the curve." I also notice that she refers to other methods by various names, but I would suspect that those methods are also Riemann sums (perhaps, left, right, or midpoint rules with the predictable errors from those rules -- especially if you don't know the calculus behind the rules). Reading between the lines, I infer that Ms. Tai has not had a calculus class, and perhaps none of her immediate colleagues or reveiwers/editors have had a calculus course, either. Within the narrow confines of her medical field, she has independently developed a method developed by others long ago. Climbing on my soapbox, assuming that someone in her field has had calculus, it shows the grand weakness in our math ed -- practical application. How many math teachers from middle school on up to college struggle to answer the "When am I ever going to use this?" question from students. It is also possible that Ms. Tai and/or her colleagues had calculus classes, but saw them as unnecessary hurdles to jump. "I'm never going to need to find the area under a curve, so I don't need to really know how to find definite integrals. I just need to get through the class, but this will never apply to my medical career." In some ways, this is why I wish I had chosen a career in math pedagogy. I would like to have been a part of figuring out how to make math ed applicable to real life. Of course, perhaps I do sin in my wish, because many very smart people have been trying for years and generations to figure out how to help students see the applicability of math to real life. That's probably more than the issue deserved, but this is the internet where random people go on all kinds of rants about trivial things all the time. Vort 1 Quote Link to comment Share on other sites More sharing options...

Jamie123 Posted September 8, 2022 Author Report Share Posted September 8, 2022 (edited) 3 hours ago, MrShorty said: That's probably more than the issue deserved, but this is the internet where random people go on all kinds of rants about trivial things all the time. I'm not the right person to judge the medical quality of the paper, but it may be fine in that regard - particularly if researchers had been using cruder methods and could gain greater precision using trapezoids (though Simpson's rule would be better still). But you must admit it's comical that in the very first sentence of the abstract she names a method known for millennia after herself. No one unilaterally names their own discoveries anyway. (Well almost no one: the only other example I can think of is the "Hovind Theory" - named by Kent Hovind - that the ice age was caused by an "ice meteor" breaking apart in the earth's atmosphere and falling as "super-cold snow".) Most scientists have the humility to let others decide whether they deserve the accolade of an equation named after them. Edited September 8, 2022 by Jamie123 Vort and MrShorty 2 Quote Link to comment Share on other sites More sharing options...

Ironhold Posted September 8, 2022 Report Share Posted September 8, 2022 I often write fiction on the side, with numerous "sandbox" projects to test out concepts and various projects seriously intended to be solicited. It frequently happens that I'll come up with something I think is unique and novel, only to later find out that I wasn't the first one. One of the more frustrating moments was naming a central character "James Longstreet" because I figured it would stand out, only to find a full month *after* developing everything out that there was a real-life Confederate general with that name. I basically scrapped everything entirely because I judged it too much work to come up with a new name for the character and redo all of my notes & paperwork accordingly. Quote Link to comment Share on other sites More sharing options...

Jamie123 Posted September 8, 2022 Author Report Share Posted September 8, 2022 (edited) 6 hours ago, Carborendum said: I believe the trapezoidal rule is traditionally about describing the logic behind calculus. (Let me know if I'm wrong). You're partly right, but it's also a method of evaluating definite integrals of functions with no analytical integral, or indeed any equation form at all. (Though Simpson's rule is usually more accurate since it is based on a parabolic rather than linear interpolation.) Edited September 8, 2022 by Jamie123 Quote Link to comment Share on other sites More sharing options...

Vort Posted September 9, 2022 Report Share Posted September 9, 2022 8 hours ago, MrShorty said: The basic methodology (break up an integral into "slices" that you can easily find the area of, then sum up the area of the slices) is attributed to Riemann in the 19th century. I learned them as Riemann sums in my second full calculus class (I do not recall them being mention in pre-calculus or my first, simple calculus class). First semester calculus is generally devoted to differentiation. Integration is typically introduced in the second semester. I'm guessing this is why you were taught it in your second calculus class. MrShorty 1 Quote Link to comment Share on other sites More sharing options...

Vort Posted September 9, 2022 Report Share Posted September 9, 2022 5 hours ago, Ironhold said: It frequently happens that I'll come up with something I think is unique and novel, only to later find out that I wasn't the first one. The story of my life. I have come up with a dozen "novel" ideas, only to find out that they had already been thought up and patented decades earlier. I'm reminded of an old economics joke: Two economists notice a $20 bill on the sidewalk. One stops to pick it up. The other says, "Don't bother. If it were a real $20 bill, someone else would have picked it up already." This is funny not only because the attitude is uselessly cynical, but because it's also true. How many people have brilliantly stumbled onto the idea of real-time computer-driven stock or commodities trading based on historical analysis of trade patterns, only to discover that it has been developed and used since the 1960s? There is nothing new under the sun—a lesson that our exceedingly shortsighted and presentist generation would do well to learn before crowing in self-congratulations about, well, anything and everything. 5 hours ago, Ironhold said: One of the more frustrating moments was naming a central character "James Longstreet" because I figured it would stand out, only to find a full month *after* developing everything out that there was a real-life Confederate general with that name. I basically scrapped everything entirely because I judged it too much work to come up with a new name for the character and redo all of my notes & paperwork accordingly. Search & Replace is your friend. Quote Link to comment Share on other sites More sharing options...

MarginOfError Posted September 9, 2022 Report Share Posted September 9, 2022 Since @Carborendum is going to pull me into this, I'm going to suggest that the incredulity might be somewhat misplaced. It doesn't look to me that Tai is trying to reinvent calculus, because her notational development doesn't include any attempt to generalize to formulae. Her method is focused on curves. The difference being that a formula has a known and well define structure. A curve may just be the line that goes through a set of observed data. When looking for the area under an empirical curve for which you have no defined structure, your options are to estimate a curve or to break the curve into shapes and add up the areas of the shapes. The two general approaches both have advantages and disadvantages with respect to what kinds of biases they introduce. (bias being the mathematical term for "difference from the true value"). When measuring something like glucose tolerance, the end point can be affected by diet, enzyme activity, food and liquid intake, etc. And with inconsistencies in when a person eats from day to day, you might have to develop a new equation for each person every single day. It would be absurd to do this for a lot of reasons, so working with the empirical curve is the most practical thing to do here. Tai's method, then, is an approach to getting the area under the empirical curve (as opposed to the theoretical curve). Her approach is an algorithm for forming the regions, areas, and their sum from a set of known points on a cartesian coordinate system. That is to say, she isn't proposing the trapezoidal rule as being novel, but the algorithm for processing it may be novel. Objectively, her algorithm is working better than the algorithms she compares against. Therefore, it would appear to have some interest in the field. Why would it have interest in the field? Probably because the software available to people in this field is limited in what it is able to do. (you can complain about this if you like. Certainly, there is software in the world that can do these calculations already. But a lot of them require programming experience, which may not be accessible to physicians or the software programs being used). So here's the point I'm trying to make. It looks like Tai is trying to solve an industry problem, not a mathematical problem. Side note: There was some talk about the difference of trapezoidal rule vs rectangular rule. The difference between the two only matters with empirical curves. But once you start taking the limit as the width of the shape goes to zero, then the solutions converge to each other. MrShorty and Carborendum 2 Quote Link to comment Share on other sites More sharing options...

Jamie123 Posted November 12, 2022 Author Report Share Posted November 12, 2022 (edited) I just published another paper on the "numbers of words in books" thing, which included this rather neat formula for the number of words n(f) appearing exactly f times in a book: But now it's in print, I suddenly discover an obscure 1961 paper by Benoit Mandelbrot with exactly the same result (at least for the unlimited types case). His derivation is identical to mine - all that's different is the symbols he uses. (His A is my 1/alpha, and his i is my f.) In my defence, this result seems to have been largely ignored in the literature. I only just discovered it in the references of a paper published in 2020, where it's described as "a notable exception" (to commoner and wronger methods). Well, at least I didn't call it the "Jamie Model". But go ahead ... call me Mary! Edited November 12, 2022 by Jamie123 Vort, MrShorty and mordorbund 3 Quote Link to comment Share on other sites More sharing options...

mirkwood Posted November 12, 2022 Report Share Posted November 12, 2022 3 hours ago, Jamie123 said: I just published another paper on the "numbers of words in books" thing, which included this rather neat formula for the number of words n(f) appearing exactly f times in a book: But now it's in print, I suddenly discover an obscure 1961 paper by Benoit Mandelbrot with exactly the same result (at least for the unlimited types case). His derivation is identical to mine - all that's different is the symbols he uses. (His A is my 1/alpha, and his i is my f.) In my defence, this result seems to have been largely ignored in the literature. I only just discovered it in the references of a paper published in 2020, where it's described as "a notable exception" (to commoner and wronger methods). Well, at least I didn't call it the "Jamie Model". But go ahead ... call me Mary! Thanks for the migraine. Jamie123 1 Quote Link to comment Share on other sites More sharing options...

mordorbund Posted November 12, 2022 Report Share Posted November 12, 2022 7 hours ago, Jamie123 said: Benoit Mandelbrot The “B.” in Benoit B. Mandelbrot stands for “Benoit B. Mandelbrot”. Vort, Jamie123 and Carborendum 3 Quote Link to comment Share on other sites More sharing options...

Vort Posted November 13, 2022 Report Share Posted November 13, 2022 (edited) 16 hours ago, mordorbund said: The “B.” in Benoit B. Mandelbrot stands for “Benoit B. Mandelbrot”. Here's a link to a self-referential post. Edited November 13, 2022 by Vort Jamie123 and mordorbund 2 Quote Link to comment Share on other sites More sharing options...

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