5 ms·

Do you really think > speed = distance / time is less clear than > speed is the ratio of distance over time ? To me the first equation is genuinely easier t

Do you really think > speed = distance / time is less clear than > speed is the ratio of distance over time ? To me the first equation is genuinely easier to read for the purposes of understanding, not just for formal manipulation. For larger equations the difference is only more stark, not less. I have a maths PhD so your comment about symbols being for novices doesn't apply. I suppose the beauty of the first equation is that the objects (speed, distance, time) are visually very distinct from the operations and relationships. In the second form, there's a bit of a word soup so you need to "manually" parse the sentence rather than letting your eyes (really the visual cortex) do that bit of the processing for you.

auggierose 6y ago
The problem is when it is not quite clear what the symbolic notation stands for. With division, that tends to be less of a problem.
- quietbritishjim 6y ago
  * I find it quite unusual in practice for genuinely new symbolic notation to be used by an author. Maybe that just reflects the fields I read about most (information theory, Bayesian modelling, harmonic analysis). * Usually you don't come across a journal article or even blog post with a single isolated equation. So any new or unusual notation can be explained once and reused many times. * Even if you did have an isolated equation with unusual notation, I still think it's more clear to define the notation and then show the equation rather than spelling it out it words! (I'm sure you could find terrible counterexamples!) The visual benefit seems so great to me that it would be worth splitting it into two parts. A bit like a diagram or a graph can make things clearer even if it needs a bit of explanation.
  - throwaway744678 6y ago
    > * I find it quite unusual in practice for genuinely new symbolic notation to be introduced by an author. This sentence seems to contradict the rest of your comment; did you mean "I find it quite unusual in practice for genuinely new symbolic notation to NOT be introduced by an author."?
    - quietbritishjim 6y ago
      Thanks, that was ambiguous and the way you read it wasn't what I intended. I meant it was unusual for an author to use a new symbolic notation at all, without saying anything about whether they define it in those cases where they do use something new. I've edited "introduced" to "used".
  - nicoburns 6y ago
    It doesn't need to be genuinely new to be confusing. It just needs to be unfamiliar to the reader. At the very least, one should point the reader to a resource where they can read about the notation.
erezsh 6y ago
That's not a genuine example. Most academic texts I've read will use something like s = d/t And sometimes not even explain what the components mean, because obviously 't' stands for time. That's what all their lecturers used, so why bother explain it. Some will even make up their own notation: s = d(t) And somewhere will say "f(x) in this article describes an inverse multiplicative relation", without explaining that it's actually simple division, so other academics won't find them too obvious or boorish. Some even take it a step further and use random greek letters (without exhausting the English alphabet first ofc.), where small gamma and big gamma mean completely different and unrelated things.
- HPsquared 6y ago
  That sounds more an issue of unclear naming, than with notation itself. Edit: Though I agree, mathematical notation lends itself to using single letters to denote objects. This can of course be problematic. I'm a fan of 'pseudocode' - somewhere between natural language and rigorous notation - where possible.
- swilliamsio 6y ago
  >s = d/t Slightly worse than that. That equation is always written as v = s/t. v represents velocity and s represents distance, for some reason.
  - Sharlin 6y ago
    I would assume that the "s" comes either from Latin spatium or German Strecke.
  - abenga 6y ago
    This is (velocity) = (displacement) / (time). s is used because of the Latin word _spatium_ for space. If I remember correctly, there was a difference between distance and displacement. (displacement is "net").
    - quietbritishjim 6y ago
gjulianm 6y ago
But that example is a little bit artificial, isn't it? A lot of mathematical concepts are more complex than that and sometimes symbols are not the best option. Say, for example the definition of Hausdorff space, in words and symbols: - Any two distinct points in the space have disjoint neighbourhoods. - ∀x,y ∈ X with x ≠ y, ∃U,V ⊂ X s.t. x ∈ U, y ∈ V and U ∩ V = ∅. Another example would be Navier-Stokes equations, where they're much easier to understand in words than in symbols. Symbols are ok when you don't have to search too much to see what they mean and when the idea you're trying to transmit with them is relatively simple, but trying to build complicated phrases and definitions with symbols, for me, ends up being a mess. edit: fixed hausdorff space definition, points should be distinct
- toxik 6y ago
  Curiously, you have been ambiguous in the mathematical notation. Counterproof: let x = y.
  - nicoburns 6y ago
    Unfortunately that's not uncommon in mathematical texts either!
  - Bootvis 6y ago
    IMO It should be "Any two distinct points in..." in English as well. Precisions is hard!
  - gjulianm 6y ago
    You are indeed right!
- andrepd 6y ago
  You are comparing apples to oranges. Your English definition is missing the definition of neighborhood. To actually be an accurate comparison you'd need to add ", where a neighborhood is a set that contains an open ball that contains the point." But now, you're also missing the definition of open ball...
contravariant 6y ago
The first one isn't really symbolic though. So really you should compare: - speed is the derivative of position with respect to time. and - Let x(t) be the position of an object at time t then its speed v(t) is: v(t) = (dx/dt)(t) Also note that most of the time I'm just putting the symbols after the word explaining what it means, while this does allow me to use the symbolic notation for differentiation it doesn't really make the first part any shorter. Also it would be a mistake to introduce speed by just 1 specific formula (even if I didn't specify the types of the object involved) since speed is a far more general concept.
Smaug123 6y ago
I'm certainly not saying that symbols are always bad. Rather, I am attempting to argue that the parent is false in asserting that "mathematician[s]… just wish it would be written with symbols so that they could know precisely what the book is trying to say". The Hausdorff space example is a good one: it's very easy to say what a Hausdorff space is, but if you have to spell it out formally then the definition is kind of big and ugly.

auggierose 6y ago

The problem is when it is not quite clear what the symbolic notation stands for. With division, that tends to be less of a problem.

quietbritishjim 6y ago
* I find it quite unusual in practice for genuinely new symbolic notation to be used by an author. Maybe that just reflects the fields I read about most (information theory, Bayesian modelling, harmonic analysis). * Usually you don't come across a journal article or even blog post with a single isolated equation. So any new or unusual notation can be explained once and reused many times. * Even if you did have an isolated equation with unusual notation, I still think it's more clear to define the notation and then show the equation rather than spelling it out it words! (I'm sure you could find terrible counterexamples!) The visual benefit seems so great to me that it would be worth splitting it into two parts. A bit like a diagram or a graph can make things clearer even if it needs a bit of explanation.
- throwaway744678 6y ago
  > * I find it quite unusual in practice for genuinely new symbolic notation to be introduced by an author. This sentence seems to contradict the rest of your comment; did you mean "I find it quite unusual in practice for genuinely new symbolic notation to NOT be introduced by an author."?
  - quietbritishjim 6y ago
    Thanks, that was ambiguous and the way you read it wasn't what I intended. I meant it was unusual for an author to use a new symbolic notation at all, without saying anything about whether they define it in those cases where they do use something new. I've edited "introduced" to "used".
- nicoburns 6y ago
  It doesn't need to be genuinely new to be confusing. It just needs to be unfamiliar to the reader. At the very least, one should point the reader to a resource where they can read about the notation.

erezsh 6y ago

That's not a genuine example. Most academic texts I've read will use something like s = d/t And sometimes not even explain what the components mean, because obviously 't' stands for time. That's what all their lecturers used, so why bother explain it. Some will even make up their own notation: s = d(t) And somewhere will say "f(x) in this article describes an inverse multiplicative relation", without explaining that it's actually simple division, so other academics won't find them too obvious or boorish. Some even take it a step further and use random greek letters (without exhausting the English alphabet first ofc.), where small gamma and big gamma mean completely different and unrelated things.

HPsquared 6y ago
That sounds more an issue of unclear naming, than with notation itself. Edit: Though I agree, mathematical notation lends itself to using single letters to denote objects. This can of course be problematic. I'm a fan of 'pseudocode' - somewhere between natural language and rigorous notation - where possible.
swilliamsio 6y ago
>s = d/t Slightly worse than that. That equation is always written as v = s/t. v represents velocity and s represents distance, for some reason.
- Sharlin 6y ago
  I would assume that the "s" comes either from Latin spatium or German Strecke.
- abenga 6y ago
  This is (velocity) = (displacement) / (time). s is used because of the Latin word _spatium_ for space. If I remember correctly, there was a difference between distance and displacement. (displacement is "net").
  - quietbritishjim 6y ago

gjulianm 6y ago

But that example is a little bit artificial, isn't it? A lot of mathematical concepts are more complex than that and sometimes symbols are not the best option. Say, for example the definition of Hausdorff space, in words and symbols: - Any two distinct points in the space have disjoint neighbourhoods. - ∀x,y ∈ X with x ≠ y, ∃U,V ⊂ X s.t. x ∈ U, y ∈ V and U ∩ V = ∅. Another example would be Navier-Stokes equations, where they're much easier to understand in words than in symbols. Symbols are ok when you don't have to search too much to see what they mean and when the idea you're trying to transmit with them is relatively simple, but trying to build complicated phrases and definitions with symbols, for me, ends up being a mess. edit: fixed hausdorff space definition, points should be distinct

toxik 6y ago
Curiously, you have been ambiguous in the mathematical notation. Counterproof: let x = y.
- nicoburns 6y ago
  Unfortunately that's not uncommon in mathematical texts either!
- Bootvis 6y ago
  IMO It should be "Any two distinct points in..." in English as well. Precisions is hard!
- gjulianm 6y ago
  You are indeed right!
andrepd 6y ago
You are comparing apples to oranges. Your English definition is missing the definition of neighborhood. To actually be an accurate comparison you'd need to add ", where a neighborhood is a set that contains an open ball that contains the point." But now, you're also missing the definition of open ball...

contravariant 6y ago

The first one isn't really symbolic though. So really you should compare: - speed is the derivative of position with respect to time. and - Let x(t) be the position of an object at time t then its speed v(t) is: v(t) = (dx/dt)(t) Also note that most of the time I'm just putting the symbols after the word explaining what it means, while this does allow me to use the symbolic notation for differentiation it doesn't really make the first part any shorter. Also it would be a mistake to introduce speed by just 1 specific formula (even if I didn't specify the types of the object involved) since speed is a far more general concept.

Smaug123 6y ago

I'm certainly not saying that symbols are always bad. Rather, I am attempting to argue that the parent is false in asserting that "mathematician[s]… just wish it would be written with symbols so that they could know precisely what the book is trying to say". The Hausdorff space example is a good one: it's very easy to say what a Hausdorff space is, but if you have to spell it out formally then the definition is kind of big and ugly.