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You say "There's a formula with a triangle ..." without telling me where. That's not real helpful, and you're making me do the work to find out what you're tal

You say "There's a formula with a triangle ..." without telling me where. That's not real helpful, and you're making me do the work to find out what you're talking about. If you want assistance to get started, you need to be more explicit. However, I have done that work, so I've looked, and in the second column of page 210 there's a "formula with a triangle": t_c = 5 \middot 10^{-5} \sqrt( V / Dt ) ... where the "D" I've used is where the triangle appears in the formula. But that can't be it, because just two lines above it we have: "For a pulse of width Dt, the critical time ..." So that's stating that "Dt" is the width of the pulse, and should be thought of as a single term. So maybe that's the wrong formula, or maybe it was just a bad example. So trying to be more helpful, the "triangle" is a Greek capital delta and means different things in different places. However, it is often used to mean "a small change in". https://en.wikipedia.org/wiki/%CE%94T https://en.wikipedia.org/wiki/%CE%94T FWIW ... at a glance I can't see where that result is derived, it appears simply to be stated without explanation. I might be wrong, I've not read the rest of the paper.

tomerv 5y ago
I think that this is indeed the formula in GP's question. And indeed sometimes math notation is obtuse like that. It looks like 2 terms, but the triangle goes together with the t as a single term. At other times it might be called "dt" and despite looking like a multiplication of 2 variables (d and t, or triangle and t in this case) it's just a single variable with a named made of 2 characters. The important thing here is that "For a pulse of width Dt" is the definition of this variable, but this can be easily missed if you're not used to this naming convention.
- enriquto 5y ago
  > it's just a single variable with a named made of 2 characters. I have this same problem with programming, when I have to deal with code written by non-mathematicians. They tend to use all these stupid variables with more than one letter and that confuses the heck out of me.
- kergonath 5y ago
  That’s because “Δ” means “a change of” or “an interval of”. So, Δt is “an interval of time”. It is like a compound word, really. It conveys more information than giving it an arbitrary, single-letter name. This convention is used in a whole bunch of scientific fields, like quantum mechanics, chemistry, biology, mechanics, thermodynamics, etc. It’s also very useful in how it relates to derivatives, which is a crucial concept in just about any kind of science you could care to mention. So yes, there is a learning curve, but we write things this way for good reasons, most of the time. Multiplication should be represented by a (thin) space in good typography, to avoid this sort of things. Not doing it is sloppy and invites misreading. Same with omitting parenthesis around a function’s argument most of the time (e.g. sin 2πθ instead of sin(2 π θ) ).
rullopat 5y ago
Sorry I didn't mean to make you work for me, but it's a PDF and I didn't know how to explain better the position (maybe I should have told you the first formula on page X). For you it was a D, for me it was a triangle and I didn't get the meaning of that Dt. Maybe it's just a too advanced paper for my knowledge.
- ColinWright 5y ago
  I'm just saying "D" because I can't immediately type the symbol here and it was easier just to use that. Not least, I didn't know if that was the formula you meant. But as I say, immediately above the formula it says: "For a pulse of width ∆t, the critical time ..." So that really is saying exactly what that cluster of symbols means. There will be things like this everywhere as you read stuff. Things are rarely completely undefined, but you are expected to be reading along. And you need to work. I just typed this into DDG: "What does ∆t mean?" The very first hit is this: https://en.wikipedia.org/wiki/Delta_%28letter%29 https://en.wikipedia.org/wiki/Delta_%28letter%29 That gives you a lot of context for what the symbol means, and this is the sort of thing you'll need to do. You need to stop, look at the thing you don't understand, read around in the nearby text, then type a question (or two, or three) into a search engine.
- gspr 5y ago
  I'll use this as an example for the point I'm trying to make in my comment https://news.ycombinator.com/item?id=29341727 https://news.ycombinator.com/item?id=29341727 Please don't take this the wrong way. It is not meant to be demeaning, and it is not meant to be gatekeeping (quite the contrary!). But: If you do not know what a derivative is, then learning that that symbol means derivative (assuming that it does, I have not actually looked at what you link to) will help you next to nothing. OK, you'll have something to google, but if you don't already have some idea what that is, there is no way you will get through the paper that way. I hope you take this as motivation to take the time to properly learn the fundamentals of mathematics (such as for example calculus for the topic of derivatives).
  - deleted 5y ago
    [deleted]
NamTaf 5y ago
I feel you're coming at this without appreciating your body of prior knowledge. Intended or not, your statment "But that can't be it, because just two lines above it we have..." assumes a whole lot of knowledge. You and I both know that it reads as one term, but for someone unfamiliar with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items, because the algebraic 'multiply' is so often implied, e.g. 3x = 3 * x as two individual 'things'. I think there's merit in explaining the concept of delta representing change, because it's not obvious. For example, when I was taught the concept in school, my teacher explicitly started with doing a finite change with numbers, then representing it in terms of 'x' and 'y', then merged them into the delta symbol. That's a substantial intuitive stepping stone and I think it's pretty reasonable that someone may not find this immediately apparent.
- ColinWright 5y ago
  I agree completely that I'm coming at this with a lot of background knowledge, but if I'm reading in an unfamiliar field and I see a symbol I don't recognise, I look in the surrounding text to see if the symbol appears nearby. As I say, "Δt" appears immediately above ... that's a clue. As you say, it's drilled in at school that everything is represented by a single glyph, and if these are juxtaposed then it means multiplication, and that is another thing to unlearn. But I think the problem isn't the specifics of the "Δ", it's the meta-problem of believing that symbols have a "one true meaning" instead of being defined by the scope. I agree that explaining the delta notation would be helpful, but that's like giving someone a fish, or making them a fire. They are fed for one day, or warm for one night, it's the underlying misconceptions that need addressing so they can learn to fish and be fed, or set on fire and be warm, for the remainder of their life.
  - NamTaf 5y ago
    I absolutely agree with your comments regarding teaching the underlying approach to digesting a paper. You definitely raise good points, especially the 'one true meaning' comment. I should state that I'm not discounting the value of your point, especially given this clarification, however I guess that when I reflect on my experience in my time learning this, the time I best learnt was via initial expalnation, then worked example, then customary warning of corner-cases and here-be-dragons. e: I also think, on reflection, that a signfigicant part of your ability to grok a new paper per your comments is your comfort in approaching these concepts due to your familiarity. Think of learning a new language - once you have a feel for it, you're likely more comfortable exploring new concepts within it, however when you're faced with it from the start you probably feel very lost and apprehensive. I feel that understanding calculus is a fairly fundamental step in the 'language of maths', teaching that symbols don't necessarily represent numbers but can represent concepts (e.g. delta being change). This isn't something you encounter until then, but once you do you begin to understand the characters associated iwth integrals, matricies, etc. in a way that you may not have previously with algebra alone.

tomerv 5y ago

I think that this is indeed the formula in GP's question. And indeed sometimes math notation is obtuse like that. It looks like 2 terms, but the triangle goes together with the t as a single term. At other times it might be called "dt" and despite looking like a multiplication of 2 variables (d and t, or triangle and t in this case) it's just a single variable with a named made of 2 characters. The important thing here is that "For a pulse of width Dt" is the definition of this variable, but this can be easily missed if you're not used to this naming convention.

enriquto 5y ago
> it's just a single variable with a named made of 2 characters. I have this same problem with programming, when I have to deal with code written by non-mathematicians. They tend to use all these stupid variables with more than one letter and that confuses the heck out of me.
kergonath 5y ago
That’s because “Δ” means “a change of” or “an interval of”. So, Δt is “an interval of time”. It is like a compound word, really. It conveys more information than giving it an arbitrary, single-letter name. This convention is used in a whole bunch of scientific fields, like quantum mechanics, chemistry, biology, mechanics, thermodynamics, etc. It’s also very useful in how it relates to derivatives, which is a crucial concept in just about any kind of science you could care to mention. So yes, there is a learning curve, but we write things this way for good reasons, most of the time. Multiplication should be represented by a (thin) space in good typography, to avoid this sort of things. Not doing it is sloppy and invites misreading. Same with omitting parenthesis around a function’s argument most of the time (e.g. sin 2πθ instead of sin(2 π θ) ).

rullopat 5y ago

Sorry I didn't mean to make you work for me, but it's a PDF and I didn't know how to explain better the position (maybe I should have told you the first formula on page X). For you it was a D, for me it was a triangle and I didn't get the meaning of that Dt. Maybe it's just a too advanced paper for my knowledge.

ColinWright 5y ago
I'm just saying "D" because I can't immediately type the symbol here and it was easier just to use that. Not least, I didn't know if that was the formula you meant. But as I say, immediately above the formula it says: "For a pulse of width ∆t, the critical time ..." So that really is saying exactly what that cluster of symbols means. There will be things like this everywhere as you read stuff. Things are rarely completely undefined, but you are expected to be reading along. And you need to work. I just typed this into DDG: "What does ∆t mean?" The very first hit is this: https://en.wikipedia.org/wiki/Delta_%28letter%29 https://en.wikipedia.org/wiki/Delta_%28letter%29 That gives you a lot of context for what the symbol means, and this is the sort of thing you'll need to do. You need to stop, look at the thing you don't understand, read around in the nearby text, then type a question (or two, or three) into a search engine.
gspr 5y ago
I'll use this as an example for the point I'm trying to make in my comment https://news.ycombinator.com/item?id=29341727 https://news.ycombinator.com/item?id=29341727 Please don't take this the wrong way. It is not meant to be demeaning, and it is not meant to be gatekeeping (quite the contrary!). But: If you do not know what a derivative is, then learning that that symbol means derivative (assuming that it does, I have not actually looked at what you link to) will help you next to nothing. OK, you'll have something to google, but if you don't already have some idea what that is, there is no way you will get through the paper that way. I hope you take this as motivation to take the time to properly learn the fundamentals of mathematics (such as for example calculus for the topic of derivatives).
- deleted 5y ago
  [deleted]

NamTaf 5y ago

I feel you're coming at this without appreciating your body of prior knowledge. Intended or not, your statment "But that can't be it, because just two lines above it we have..." assumes a whole lot of knowledge. You and I both know that it reads as one term, but for someone unfamiliar with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items, because the algebraic 'multiply' is so often implied, e.g. 3x = 3 * x as two individual 'things'. I think there's merit in explaining the concept of delta representing change, because it's not obvious. For example, when I was taught the concept in school, my teacher explicitly started with doing a finite change with numbers, then representing it in terms of 'x' and 'y', then merged them into the delta symbol. That's a substantial intuitive stepping stone and I think it's pretty reasonable that someone may not find this immediately apparent.

ColinWright 5y ago
I agree completely that I'm coming at this with a lot of background knowledge, but if I'm reading in an unfamiliar field and I see a symbol I don't recognise, I look in the surrounding text to see if the symbol appears nearby. As I say, "Δt" appears immediately above ... that's a clue. As you say, it's drilled in at school that everything is represented by a single glyph, and if these are juxtaposed then it means multiplication, and that is another thing to unlearn. But I think the problem isn't the specifics of the "Δ", it's the meta-problem of believing that symbols have a "one true meaning" instead of being defined by the scope. I agree that explaining the delta notation would be helpful, but that's like giving someone a fish, or making them a fire. They are fed for one day, or warm for one night, it's the underlying misconceptions that need addressing so they can learn to fish and be fed, or set on fire and be warm, for the remainder of their life.
- NamTaf 5y ago
  I absolutely agree with your comments regarding teaching the underlying approach to digesting a paper. You definitely raise good points, especially the 'one true meaning' comment. I should state that I'm not discounting the value of your point, especially given this clarification, however I guess that when I reflect on my experience in my time learning this, the time I best learnt was via initial expalnation, then worked example, then customary warning of corner-cases and here-be-dragons. e: I also think, on reflection, that a signfigicant part of your ability to grok a new paper per your comments is your comfort in approaching these concepts due to your familiarity. Think of learning a new language - once you have a feel for it, you're likely more comfortable exploring new concepts within it, however when you're faced with it from the start you probably feel very lost and apprehensive. I feel that understanding calculus is a fairly fundamental step in the 'language of maths', teaching that symbols don't necessarily represent numbers but can represent concepts (e.g. delta being change). This isn't something you encounter until then, but once you do you begin to understand the characters associated iwth integrals, matricies, etc. in a way that you may not have previously with algebra alone.