Timeline for What are the units of $f/f_s$?
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| Sep 22, 2020 at 16:46 | comment | added | Cedron Dawg | Funnier yet, reverse "Ced" phonetically. Oh so many layers. "If you get down and you quarrel everyday You're saying prayers to the devils, I say, wooh ", Bob Marley. | |
| Sep 21, 2020 at 3:10 | comment | added | robert bristow-johnson | You said: "spoken by the guy who can't comprehend the difference between..." (and some math that i am not going to punch in). Now, what is it that I said that is demonstrative of something that you need also cite in your claim of something I "can't comprehend"? Again, you also need to account for what you say. You don't get a pass. | |
| Sep 21, 2020 at 3:02 | comment | added | Bob K | I just did that... it's all on the record. I would need to check with Fat32 before a 3rd repetition, because he/she chastises me for my affinity for redundancy. Fun times here! | |
| Sep 21, 2020 at 2:51 | comment | added | robert bristow-johnson | @BobK, you're full of shit. And you're making a few people other than me laugh. Now I can be expected to account for things that I say. But I will not account for things that I don't say, nor about ambiguous insinuated references. In your comment above, what is it that I said in the cited post (or any other post of mine that you cite) that you expect me to account for? That implies a lack of comprehension? You need to account for what you say. | |
| Sep 21, 2020 at 2:38 | comment | added | Bob K | If you are finally ready to abandon that indefensible position, great! Follow the link (above) to the comments under my Aug 25 14:04 answer, and apologize for being adamantly incorrect for the last 6 years. | |
| Sep 21, 2020 at 1:56 | comment | added | robert bristow-johnson | who are you quoting? and what is the quote? | |
| Sep 21, 2020 at 1:14 | comment | added | Bob K | ...spoken by the guy who can't comprehend the difference between $\ \sum_{k=-\infty}^{\infty} x[n + kN]\ $ and $x[n \bmod N]$ (see dsp.stackexchange.com/questions/18144/…) | |
| Sep 19, 2020 at 20:18 | comment | added | robert bristow-johnson | reverse the spelling of both words. Ced has some history with comp.dsp. BobK has history with Wikipedia. both grossly overesteem their own competence and expertise. | |
| Sep 19, 2020 at 19:10 | comment | added | Bob K | @robertbristow-johnson //you're also saying that $f$ and $f_s$ have different units?// At the risk of the dreaded redundancy, yes. In terms of a continuous sinusoid (for instance), $f$ (in Hz) is the average number of periods it completes per second. When we sample it at intervals of $T$ sec/sample, $f_s = 1/T$ samples/sec is the average number of samples taken per second. periods/sec and samples/sec are different units. //We remember "Nordic God". May I add BobK to the mix?// Whatever that is, no thanks. | |
| Sep 19, 2020 at 18:43 | comment | added | Fat32 | @robertbristow-johnson don't know what to say... I beleve this thread should totally be deleted... And if necessary (which I don't think so) it could be reposted with a clean and focused style... and providing only cited answers instead of personal views (ad hominem!)... Besides, I believe this (dsp.se) is not the place to discuss a revolutionary invention, rather a place to provide answers based on the current state of the field ... | |
| Sep 19, 2020 at 18:26 | comment | added | robert bristow-johnson | for uniform rotation, Mills correctly defines the revolution frequency as the number of complete revolutions, N, divided by the time interval, he takes the unit for N to be ‘cycle’ (which he defines as one revolution) rather than the correct unit: the number one. The unit for ‘frequency’ then appears to be ‘cycle per second’ (i.e. revolution per second), whereas it should be one per second, correctly called hertz. .. | |
| Sep 19, 2020 at 18:23 | comment | added | Fat32 | @BobK pure mathematician had a kind of humor in it, in the sense that he's somone who spends his entire time on "unitless" quantities so much to the extend that at some point he gets crazy and makes up his own units to associate even with summation indices, as they are the main objects he is dealing with... ;-) I must attach a unit to my numbers !!! | |
| Sep 19, 2020 at 17:30 | comment | added | robert bristow-johnson | $$\begin{align} x_\mathrm{s}(t) &\triangleq T \sum\limits_{n=-\infty}^{\infty} x(nT) \delta(t-nT) \\ \\ X_\mathrm{s}(f) &= \sum\limits_{k=-\infty}^{\infty} X(f - k\,f_\mathrm{s}) \qquad \text{where} f_\mathrm{s} \triangleq \frac{1}T \\ \end{align}$$ are there objections to that? do we agree on the definition of the continuous Fourier Transform that relates all the x's together? And @BobK, you're also saying that $f$ and $f_\mathrm{s}$ have different units? (BTW, we old timers are joking a little about this on Facebook. We remember "Nordic God". May I add BobK to the mix?) | |
| Sep 19, 2020 at 17:04 | comment | added | Bob K | //No need to discuss this.// Happily, because we live in different worlds. In mine, things like samples and cycles actually exist, as they also do in EE textbooks. And redundancy (as you call it) is actually a helpful thing. And BTW I've never been mistaken for "a pure mathematician" before. I think of that as someone who would rather not associate k with a unit. | |
| Sep 19, 2020 at 15:33 | comment | added | Fat32 | @BobK I don't take it. Associating a unit with a summation index is the first of a kind I heard from you... Your units are redundant. It's sufficient to associate units of f with 1/s, T = 1/f = seconds and k is a unitless summation index number. You lose nothing by the simplicty and you gain nothing by your redundancy... No need to discuss this. Pew associating k with a unit ! :-)) Only a pure mathematician could do that :-) | |
| Sep 19, 2020 at 15:25 | comment | added | Bob K | @Fat32://Throughout sampling theorem $f+f_s$ or $f-f_s$ are arithmetically added with no conversion factors.// No. In general, you are referring to something like $\sum_{k=-\infty}^{\infty} X\left(f - \frac{k}{T}\right)$, where $T$ has units of sec/sample, and therefore $k$ has units of cycles/sample. Choosing the case $k=1$ to make it invisible does not change its invisible units. | |
| Sep 17, 2020 at 12:02 | comment | added | Fat32 | @CedronDawg answer: 1+0=1 is the first step in Real Analysis. 0/0 is covered extensively, from all directions. No need for me to explain it. If this accounts for an answer , then f/fs is first step in DSP and covered across all textbooks as unitless is just a legitimate answer too :-)) So the topic is closed! well-done; -) have a nice day too Ced. | |
| Sep 17, 2020 at 11:59 | comment | added | Cedron Dawg | @Fat32 1+0=1 is the first step in Real Analysis, not my favorite (by far) branch of Mathematics. 0/0 is covered extensively, from all directions. No need for me to explain it. Have a nice day! (My second mandate) Don't expect any more replies here. | |
| Sep 17, 2020 at 11:55 | comment | added | Fat32 | @CedronDawg Real Analysts cannot even answer the question how come the algebraically (and arithmetically) illegal statement 0/0 produce anything valid or meaningful in the mystery of the non-mathematical thing called limit. Mathematicians should answer their very own fundamental philosophical problems, (or abondon calculus all together ) before trying to deal with others'... ;-) | |
| Sep 17, 2020 at 11:26 | comment | added | Cedron Dawg | @Fat32 The answer isn't "Because Ced said so." Real Analysts would disagree about the importance. I'm done here. | |
| Sep 17, 2020 at 11:18 | comment | added | Fat32 | @CedronDawg You cannot even determine that 1+0=1 unless you accept some unprovable postulates which are accepted to be true by their own. This is not such an important topic. Numbers are unitless mathematical things and when they refer to physical quantities they will have units based on the nature of the quantity. Throughout sampling theorem $f+f_s$ or $f-f_s$ are arithmetically added without no conversion factors. | |
| Sep 17, 2020 at 3:20 | comment | added | Cedron Dawg | @Fat32 Okay. How did you determine that the quantities could be added without a conversion factor? | |
| Sep 16, 2020 at 22:38 | comment | added | Fat32 | @CedronDawg I know it's weird but I have to repeat RBJ's comment here: but where Ced is wrong and always had been (we had argued about stuff like this on comp.dsp as recently as 2017) is that there are units attached to dimensionless numbers and that sample rate is not compatible with Hz. whenever you can add, subtract, or compare commensurate quantities, they are the same dimension. and if you can correctly add them without a numerical conversion factor, then they have exactly the same units. | |
| Sep 15, 2020 at 8:40 | comment | added | Cedron Dawg | now RB-J, when are you going to answer my question? What are the units, not dimensions, or translation to common units, the actual units of $f/f_s$? If I were you I would delete this answer and answer again without the distraction. I don't mind all these comments disappearing. (Seems you like to Karen the comment policy at Physics.SE too). You don't seem to be the type to say "Uncle, I'm sorry." Even after being incorrect all these years. The misperceptions belong to you, and the unlearning is yours to do. Yeah, it can be difficult, but I'm rooting for you. | |
| Sep 14, 2020 at 19:51 | comment | added | Fat32 | @CedronDawg I'm out of this discussion. I will use the notation found in the standard DSP texts, and IEEE standards. You know it's all about standards. Units do not have absolute meanings. Only relative. And I think that's the onto-epistemological-metaphysical mistake we are making here: trying to attach absolute meanings to things which only have binding-relations to objects/purpose they represent. What's the absolute meaning of the word apple? The only meaning is it represents a fruit which we agreed to call an apple. So keep up the standards and avoid useless discussions :-)). | |
| Sep 14, 2020 at 19:01 | comment | added | Cedron Dawg | Finally, did Ted's wife divorce him? And quit using "neanderthal" in a disparaging manner. (There's my first mandate compared to many from you.) | |
| Sep 14, 2020 at 19:00 | comment | added | Cedron Dawg | (con't) Also from the article, "Then when adding two quantities of like dimension, but expressed in different units, the appropriate conversion factor, which is essentially the dimensionless 1, is used to convert the quantities to identical units so that their numerical values can be added or subtracted." Yeah, that's what I said, and you denied. Guess what, sometimes the conversion factor has a magnitude of 1. That doen't make it disappear until you categorize from the unit level to the dimension level. | |
| Sep 14, 2020 at 18:59 | comment | added | Cedron Dawg | Nothing I have said violates the "The factor-label method for converting units" section of en.wikipedia.org/wiki/Dimensional_analysis. (@Fat32, is a kg of NOx like a kilo of apples?) Furthermore, the Huntley and Siano extensions in the end bring DA definitions of dimension more in line with math ones. And the biggest annoyance is your continued insistence that "units are being attached to a number". What units did I attach to 12? | |
| Sep 14, 2020 at 16:02 | comment | added | Fat32 | @CedronDawg so yo call "n" as a potential function ! :-) Never heard that before. Let me visit my electromagnetic books for that :-). I cannot get the slick trick on wikipedia. I have no idea of why it should be that way true or useful...:-)) | |
| Sep 14, 2020 at 15:53 | comment | added | Cedron Dawg | Oh, the potential function is the value of the index of refraction (fluff density on the log scale) at every point. It has a gradient which is a conservative vector field. | |
| Sep 14, 2020 at 15:47 | comment | added | Cedron Dawg | @Fat32 No worries, you can email if you want to discuss it further, or post in Physics.SE and notify me. (6) is part of the definition of the "Calculus of Variations". This was my first real deep dive into it, and it confirmed my earlier Newtonian approach. (7) The nature of the "slick trick" (the product has to be constant, but not the constituent factors within their respective frames) is the nature of the slick trick and does indeed take some pondering to wrap your head around. I have not found (13) and (18) anywhere else. Nobody has refuted them yet. | |
| Sep 14, 2020 at 15:37 | comment | added | Fat32 | @CedronDawg I cannot justify by myself why Eq. 6 & 7 should be true, I think they are but don't know why. Also there's a potential function you talk about, what potential function is that, I can't see as well.Finally is really true that if F = 1, F is a constant, then how & why do you set its derivative ? I mean isnt it dF/dx = 0 ? But Eqs. 8 & 9 say dF/dq is nonzero ? So how come F = 1 for all q ? There are various such puzzles that I cannot find their justification... | |
| Sep 14, 2020 at 15:32 | comment | added | Cedron Dawg | (con't) I had to throw away half of the article due to the concept of anisotropism. The speed of the particle under the definition "c/n" is isotropic, the same in all directions. I derived the solution for the Schwarzschild Solution in the radial direction (and it is similar) and thought I had it made, but it turned out not to be that simple. Still a work in progress. The equation can also be applied, with some tweaking, to the propagation of sound waves in water with varying salinity conditions. So it is a general principle. I don't know if it could be considered solving anything unsolved. | |
| Sep 14, 2020 at 15:29 | comment | added | Cedron Dawg | @Fat32 Brief explanation: (6) is part of the E-L definition. (7) Is the "slick trick", (18) is the crown jewel and is the result of a unit conversion from (13). (13) and (18) say that the acceleration of the particle occurs in a plane (or line) defined by the gradient of the index of refraction and the velocity of the particle. I was motivated by considering that Snell's law was physically impossible, there had to be a little curvature to that bend. So you can think of (13) and (18) as the vector differential form of Snell's law. "n" is assumed to be real as a simplifying assumption. | |
| Sep 14, 2020 at 15:24 | comment | added | Cedron Dawg | RB-J, you have yet to demonstrate that anything I have said is erroneous, only loudly proclaiming it is heretical and must be vanquished else others may be tainted. Tighter integrity checking requires higher informational content, no way around that. How "complicated" that is remains in the eye of the beholder. I deleted the comments because they seemed too "braggish" upon rereading. The discussion should be about the message, not the messenger. I'm tired of your heckling and proselytizing. | |
| Sep 14, 2020 at 14:37 | comment | added | robert bristow-johnson | @Fat32, //making things more complex than they actually are// -- it's actually worse than making things more complex than they actually are. it's erroneous which becomes obvious when Ced says that pure mathematical numbers like $2$ or $2\pi$ have units. or that $f_\mathrm{s}$ has different units than $f$ when we are adding them directly together. that pendantry will lead other pendants down the wrong path and they will later have to unlearn crap they picked up from Ced. | |
| Sep 14, 2020 at 14:35 | comment | added | Fat32 | @CedronDawg I read your article. It sounds fine.Iignoring several points (cal of variations, Euler-Lagrange eq.), I see that you apply vector calculus operators to solve some classical equtions to find the shortest path for the light in non-isotropic medium. Recall that "n" is a Tenor of rank-2, but I can't see if you have utilized this. Also I can't make much sense of Eqs 6,7,13,and 18. Also I can't see what's accomplished in your solution? Did you solve an unsolvable problem in physics? It's not stated clearly. But otherwise, yes that's a good amount vector calculus of variations :-) | |
| Sep 14, 2020 at 13:53 | comment | added | Cedron Dawg | @Fat32 To me, this means that matter is composed of "photons" captured in each other's "fluff wakes". I haven't gotten to the point where I can rectify this interpretation with contemporary theory but I conjecture that is possible. I do note that CERN recently announced it had produced particles (stable flow configuration) from light. Studying the eigenvector of the DFT vs the Hermite-Gaussian functions is part of that quest. | |
| Sep 14, 2020 at 12:39 | comment | added | Cedron Dawg | Simply put, you can't add samples and cycles unless you recognize that there is one sample per cycle. | |
| Sep 14, 2020 at 12:16 | comment | added | Cedron Dawg | @Fat32 I've added a followup to my question. I hope I have explained things clearly enough that I can step away without any more heckling. If you want to see my contribution to physics, check out dsprelated.com/showarticle/1190.php (Shameless self-promotion). | |
| Sep 14, 2020 at 8:59 | comment | added | Fat32 | @CedronDawg ok but I thing being a mathematician you should step back a little on this topic of physics and engineering... When you say I bought 2 kgs of apples, apples is not a unit right ;-) at least in the sense that we tend to associate within the physical science... Defining a rate such as how many apples per dollar will you get, is not about considering apples as a unit in the sense that I tend to use it. It's just a mathematical rate. Otherwise yes, apples and oranges are different things of their own nature and we can attach their type names as units in computations. | |
| Sep 14, 2020 at 8:52 | comment | added | Fat32 | @robertbristow-johnson yeah we agree here... don't know about your past with Ced on comp.dsp :-)). I find his way of attaching units to everything in DSP as making things more complex than they actually are... At one point I fear if units of units will appear such as : velocity = meter / s = meter per coordinate scale / second per coordinate scale... where coordinate scale is a relativistic concern :-) | |
| Sep 14, 2020 at 3:05 | comment | added | robert bristow-johnson | but where Ced is wrong and always had been (we had argued about stuff like this on comp.dsp as recently as 2017) is that there are units attached to dimensionless numbers and that sample rate is not compatible with Hz. whenever you can add, subtract, or compare commensurate quantities, they are the same dimension. and if you can correctly add them without a numerical conversion factor, then they have exactly the same units. | |
| Sep 14, 2020 at 3:01 | comment | added | robert bristow-johnson | @Fat32 , i think we are on the same page. "cycles" or "samples" or "ticks" are things that we count. when we count them in time, there is a rate. whether it's "Hz" (or "cycles/sec") or "samples/sec" or "ticks/sec", the dimension is $\mathrm{T}^{-1}$ and the common unit is "$\frac{1}{\mathrm{s}}$" or "$\mathrm{s}^{-1}$". it may be wrong, but it is meaningful to add "ordinary frequency" to "angular frequency" because they are the same dimension. it would be like adding the number of km to the number of miles. but it's usually wrong unless you put in a conversion factor. | |
| Sep 14, 2020 at 2:51 | comment | added | robert bristow-johnson | i have deleted no comments in this thread and consider the deletion of a comment to be on the spectrum of disingenuous. (unless one is asked to delete a comment that someone finds offensive or similar.) we should all stand by what we say and if we figured out that we said something incorrect or wrong or foolish, just correct yourself and move on. | |
| Sep 14, 2020 at 0:54 | comment | added | Cedron Dawg | @Fat32 The links have sufficient coverage of this topic and I don't have that much interest. I'll say this: There are $2\pi$ radius lengths in a circumference. There are 12 inches in a foot. Anything you count, you are counting units of it. (Unit means "one" essentially). Some things come in fractional quantities, yet the scale remains in units of those things. "More or fewer", "greater or less", whether discrete or continuous, comparisons can only be made along the same dimension in the same units, likewise with sums. | |
| Sep 14, 2020 at 0:42 | comment | added | Fat32 | @CedronDawg yes I realized it after posting my comment, sorry for that. Now my final words on units/dimensions is this : $2\pi$ is a number (quantifically 6.28..) without a unit. Angles do have units such as Degree, Grad, Radian. When your numbers refer to an angle, then their unit (actually a scale) is, say, radian: 3 radians, 5 radians or $2\pi$ radians. I find the cycles thing as quite unnecessary. Never seen it in any math,physics, eng book. But as long as it works for you. Thats ok. | |
| Sep 14, 2020 at 0:37 | comment | added | Cedron Dawg | @Fat32 Yes, I made that point earlier to RB-J but deleted the comment. There is a one to many between Dimensions and Units. So, my naming comment above really came from database normalization principles. It's why I also did both "time" (dimension), and "sec" (unit) in my equation example. And I made the smarmy statement "Also, the application is not always in seconds, or time for that matter." at the end of the original post of dsp.stackexchange.com/questions/69186/… | |
| Sep 14, 2020 at 0:27 | comment | added | Fat32 | @CedronDawg actually a dimension is more general than a unit. So length is a dimension, but it has many different units such as meter, foot, yard, inch etc. Mass is a dimension and it also had many units throughout history. Time also had different units untill the second was adopted universally. So dimensional analysis is more general than the one with explicit units and conversion factors. I'm reading these from Ohanian Physics 2E expanded,ch1: Measurement of Space, Time , and Mass... I highly suggest this book for any scientist or engineer. | |
| Sep 14, 2020 at 0:23 | comment | added | Fat32 | @robertbristow-johnson yes I was unfortunately restrictive about units there. However when I said they are physical, I didin't mean they have phsyical existance :-) but instead I meant they are used to scale physical quantities. So we have non-physical units of bits, bytes, and MACs, samples, etc. And yes units is an abstract (anthropometric) construct without a physical existance on their own :-) | |
| Sep 13, 2020 at 23:44 | comment | added | Cedron Dawg | (con't) I did a little more searching and came across these discussions, which are very much on this topic and interesting, from quite a while back. golem.ph.utexas.edu/category/2006/09/dimensional_analysis.html golem.ph.utexas.edu/category/2006/09/… RB-J makes an appearance as well which made me chuckle a little. The postings are actually on someone's blog (John Baez) and he seems to be reading the same playbook as me but several chapters ahead. | |
| Sep 13, 2020 at 23:44 | comment | added | robert bristow-johnson | sorry, @Fat32, but while i think we both realize there's a bunch of poppycock in this whole question (it should have been obvious when Ced says that pure numbers such as $2$ or $2\pi$ have units or when Ced said that there was an implicit conversion factor applied to $f_\mathrm{s}$ when it is added to $f$, all this is pedantic bullshit that engineering professors would have to unteach students), the fact is that "Units" are themselves also only a anthropometric construct. Units are not physical. Physical quantity is physical, but units are not. | |
| Sep 13, 2020 at 23:44 | comment | added | Cedron Dawg | (con't) One big criticism of DA is that the dimensions are labeled/identified by their default units as you just demonstrated. So, is "Dimensional Analysis" really "dimensional analysis", or is it really "unit analysis" in disguise? This naming restriction really makes the dimensionless case really problematic. Do you disagree with how I either carried the units or did the Dimensional Analysis of the $2\pi f t = \theta$ formula? | |
| Sep 13, 2020 at 23:43 | comment | added | Cedron Dawg | @Fat32 "Dimensional Analysis" is a title. "unit analysis" is a descrtiptive phrase (better known as "carry they units"), "Unit Analysis" isn't serious. I grew up on carrying the units (should be a common experience) and was only introduced to DA the first time RB-J tried to teach me his religion. That's why I put the "this ain't about DA" in my question itself. I read up on it, decided it was inferior, and didn't take it much further. Mind your units and the dimensions will take care of themselves. | |
| Sep 13, 2020 at 23:07 | comment | added | Fat32 | @CedronDawg and finally I never heard of something called a unit analysis before... It's probably same thing as a dimension analysis with conversion factors. | |
| Sep 13, 2020 at 23:01 | comment | added | Fat32 | @CedronDawg your mass has a unit of kg. Your height has a unit of m, your velocity has a dimension and derived unit of m/s. Your momentum has a derived unit of kg*m/s which is the dimension of it as well... etc... | |
| Sep 13, 2020 at 22:47 | comment | added | Fat32 | @CedronDawg I had put this in my answer but removed, let me add it here: dimensional analysis and units are physical things. Dimensional analysis: if LHS of an equality has the following dimension $ \frac{ V^2 \cdot m^3 \cdot kg}{s^2 \cdot C }$ then the RHS must also have the same dimension. Checking the validity of this is called a dimensional analysis. Units (SI units, fundamental or base units) are accepted as: m, kg, s, A, K, mole,cd... two supplementry defs are: radian and streradian. Also it's noted that K,cd and mole could be eliminated... | |
| Sep 13, 2020 at 20:48 | comment | added | Cedron Dawg | In dimensions, it's: $$ \text{none} \cdot \text{time}^{-1} \cdot \text{ time } = \text{ none } $$ In Dimensional Analysis default units, it's: $$ \text{none} \cdot \text{sec}^{-1} \cdot \text{ sec } = \text{ none } $$ Okay, it tests true, but it isn't very powerful a test. | |
| Sep 13, 2020 at 11:36 | comment | added | Cedron Dawg | Dimensional analysis is a generalization and pedantic formalization of this. Less specific = weaker. $$ $$ Other conversion factors carrying units: $$ 1 = 12 \frac{\text{ Eggs }}{\text{ Dozen }} = 12 \frac{\text{ Persons }}{\text{ Jury }} = 12 \frac{\text{ Months }}{\text{ Year }}$$ The "1" is what is unitless. It can be multipied into any term in any equation. Not that hard to understand. $$ $$ In the NASA's Mars Climate Orbiter crash, the dimensions matched, but not the units. | |
| Sep 13, 2020 at 11:36 | comment | added | Cedron Dawg | Here is an equation that should be familiar to you: $$ 2\pi \cdot f \cdot t = \theta $$ Here it is carrying units: $$ 2\pi \frac{\text{ Radians }}{\text{ Cycle }} \cdot f \frac{\text{ Cycles }}{\text{ Second }} \cdot t \text{ Seconds } = \theta \text{ Radians } $$ Carrying units was taught in Junior High School for me, not self-taught. Same was used in High School. Same was used in College. It works. It is very useful for integrity checking formulas, and in performing calculations. | |
| Sep 11, 2020 at 18:53 | comment | added | robert bristow-johnson | the term "radian" is a semantic. angles measured as "radian" are dimensionless quantities that are the ratio of two like-dimensioned lengths: the arc-length divided by the radial arm length. there is no unit. | |
| Sep 11, 2020 at 18:50 | comment | added | Cedron Dawg | Once you go ad hominem, I'm done. I was going to say if you concede that a radian is a unit, what is its dimension, but don't bother replying, I'm done. | |
| Sep 11, 2020 at 18:04 | comment | added | robert bristow-johnson | and Ced, you are a lousy judge of your own expertise. | |
| Sep 11, 2020 at 18:02 | comment | added | robert bristow-johnson | i don't know for sure what you're thinking but if my guess is correct, the "dimensionless units" such as *percent (%) or degree (°) or even the decibel ($\mathrm{dB}$), all those "units" are, are a convention in that the symbol is equal to a dimensionless conversion factor. ... "%"$=\frac{1}{100}$. ... "°"$=\frac{\pi}{180}$. ... and "$\mathrm{dB}$" $=\frac{\log(10)}{20}$ and those are just numbers. | |
| Sep 11, 2020 at 17:39 | comment | added | robert bristow-johnson | i'd like to see you persuade any mathematician that either $2$ or $\pi$ are anything other than dimensionless numbers. or that radians are anything other than a dimensionless measure. it's a silly position to take. one that i am sure is self-taught. $$ $$ i know it's hard to unlearn things. | |
| Sep 11, 2020 at 13:12 | comment | added | robert bristow-johnson | I'm sorry Ced. but while units are a thing, "unit analysis" is not a thing. There are no units attached to $2$ or $2 \pi$ or the like. The are just pure numbers. Dimensionless numbers. It's possible that when someone is self taught, that there are no checks on when they taught themselves a false thing. | |
| Sep 11, 2020 at 8:30 | comment | added | Cedron Dawg | This is not a question about dimensional analysis, it is about unit analysis. They are not the same thing. Dimensional analysis is much weaker, it can't even tell the difference between an inch and a mile as both are units of distance. More germane, it can't tell the difference between a sample and a cycle. Notice the question has "units" in it, not "dimension". You seem to have missed that point when made in the main section as well. Both are intended as integrity checks for formulas and calculations, unit analysis is better at that. Search on "NASA's Mars Climate Orbiter". | |
| Sep 11, 2020 at 2:33 | history | answered | robert bristow-johnson | CC BY-SA 4.0 |