4 ms·

"goobledegook = e + 5.6. Wow you didn't know about goobledegook? Let me teach you about this revolutionary concept." I majored in mathematics and can say I've

"goobledegook = e + 5.6. Wow you didn't know about goobledegook? Let me teach you about this revolutionary concept." I majored in mathematics and can say I've never heard of versine and have probably used it many times without knowing. I don't think everything needs a name.

desertrider12 6y ago
I think the point of these was for when they read low-precision values out of a printed table and then multiplied them using slide rules. Even though the article doesn't say it, I can't think of any other practical reason to multiply by adding logarithms.
- todd8 6y ago
  Generally, slide rules were only good for rough calculations (3 significant digits if you were lucky), but they did contain multiple scales providing multiplication, division, exponential, log10, ln, roots, sin, cos, tan, and hyperbolic trig functions. Notably one couldn’t do addition or subtraction with a slide rule; we used pencils for that. When more precision was needed, I and my fellow engineers would break out our copies of CRC’s reference tables. The better log tables allowed calculations to 5 or 6 significant digits. Using these were not unusual and all of us learned to use them in high school (before 1970 at least).
  - lmm 6y ago
    > Notably one couldn’t do addition or subtraction with a slide rule; we used pencils for that. Huh? It's trivial to make a slide rule that you can add and subtract on, you just rule linear scales on it.
    - todd8 6y ago
      Of course you are right, the slide rule works with logarithmic scales that are “added” together to do multiplication. Linear scales could be used to add, but the low number of significant digits (no more than three on standard slide rules) meant that it wasn’t worth it, and no engineering slide rule that I ever saw had scales for addition.
  - gshubert17 6y ago
    Back in the 1970s I used a slide rule when 2-3 place accuracy was enough; or 5-place or 7-place log tables and a pocket mechanical adding machine (rather than by hand) when more accuracy was required. I found a 2-minute video of the sort of pocket adding machine I used, https://www.youtube.com/watch?v=ryST18JJ7VU https://www.youtube.com/watch?v=ryST18JJ7VU (The device is actually easier to use than shown. Using the colors next to the digits: if silver, pull the stylus down; if red, pull up and over the curve at the top of the column to the next digit. No extra or wasted motions are needed.) Five places were usually enough, but seven places were needed for some astronomical calculations such as eclipses. The $7 I paid for the log tables in the late 1960s would purchase about $50 today; and the adding machine was probably a couple of dollars back then.
- stan_rogers 6y ago
  The log tables let you work without slide rules, which were themselves horribly expensive not too terribly long ago in the grand scheme of things. But yes, this was all about practical calculation, not mathematics for its own sake, that needed to be carried out quickly by people who wouldn't have handy access to machines that keep the dirty arithmetic details (and potential for error) hidden from the operator, whether that's your ship's navigator or the machinist with nothing but a sine bar and gauge blocks setting up a precision operation, and if you needed precision using a four-figure table book, the only way you were going to get it was if the derived operations were in the tables.
  - bregma 6y ago
    The converse is true: slide rules let you do calculations quickly and easily (since they hang in the leather holster on your belt) without having to carry an expensive and heavy copy of the rubber bible or similar work and stop and look up numbers then scratch the values down on paper and work the problem.
    - stan_rogers 6y ago
      Again, you're thinking of an era where slide rules were relatively affordable. That's mid-twentieth century stuff (although the key word is relatively; my first good slide rule cost more than a month's rent at the time).
- gumby 6y ago
  Slide rules are literally the physical embodiment of a log table (or several, if you had a multilog rule). You used them by physical addition.
- desertrider12 6y ago
  OK, now I understand that the logs of these values are for pencil+paper addition and subtraction, not slide rules.
Waterluvian 6y ago
It kind of helps a non Mathie like me doing trig. But I'll ask fof one better: I would love an application that lets me plug in what I have (coords and angles), what I want, and for it to show me how to get it.
- anonytrary 6y ago
  Does it? No one does this: var STRAWBERRY_PI = 1 + Math.PI; For example, no one doing math will use τ (2𝛑) and 𝛑 simultaneously. Choose one or the other, otherwise you are increasing the number of symbols someone has to learn to understand your math. Naming everything is overwhelming. Mathematics is about similarities, not differences. If the transformation is trivial, then don't bother creating a new symbol. It will just confuse you more.
  - exmadscientist 6y ago
    I don't agree at all. This happens all the time. For example, electrical engineering has f, ω, and s, all only differing by basic factors of 2π or i. As far as I can tell, the main reason this gets done is to give commonly recurring quantities single symbols, to reduce errors in lengthy calculations. When those recurring quantities are meaningfully different, in ways that help prime one's intuition, that's all the more reason to do it.
    - unishark 6y ago
      You also save clock cycles by avoiding the extra calculation each time you compute 2pi or whatever by defining TWO_PI once. So it was lot more common in Fortran and C programming days.
    - trevortheblack 6y ago
      As an electrical engineer you'll typical use f, ω, and s, in different contexts and you'll learn each of those contexts separately. f: consumer electronics ω: circuits s: frequency response Having multiples of terms for each is definitely a hindrance to education. It makes switching between each use a mental headache.
framecowbird 6y ago
versine clearly needed a name once when it was in common usage. As in, "Hey Greg, can you help me? I can't find this computation in these tables. --- Oh, try the versine".
- deleted 6y ago
  [deleted]
Sharlin 6y ago
The article explains pretty well why these named functions (or at least some of them) were once useful and thus had common names.
acqq 6y ago
> I don't think everything needs a name. And you are wrong, at least historically: The article points that without the access to the computers and to achieve numerical precision having precalculated tables of such functions was of direct practical use. Even if you personally and more recently didn't need that, the said names were needed and used, and that's why they exist. Had you been you born, for example, more than 100 years ago, you could have been one of the persons assigned to spend maybe years just carefully calculating (or just verifying) the tables of one of those functions which today are seldom referenced by a name. Or at least with a job which involved using such tables (and the names too). Also, in current computing practice, one can still write programs which produce wrong results if one is not aware of the limits of the partial numerical calculations, including these named. One doesn't have to know the names, but in some specific cases it could be needed to have separate functions calculating exactly the values of the functions named. As we start to discover again that the custom processors could calculate more with less binary digits, knowing this becomes even more important compared to the times where "just use doubles" was enough.

desertrider12 6y ago

I think the point of these was for when they read low-precision values out of a printed table and then multiplied them using slide rules. Even though the article doesn't say it, I can't think of any other practical reason to multiply by adding logarithms.

todd8 6y ago
Generally, slide rules were only good for rough calculations (3 significant digits if you were lucky), but they did contain multiple scales providing multiplication, division, exponential, log10, ln, roots, sin, cos, tan, and hyperbolic trig functions. Notably one couldn’t do addition or subtraction with a slide rule; we used pencils for that. When more precision was needed, I and my fellow engineers would break out our copies of CRC’s reference tables. The better log tables allowed calculations to 5 or 6 significant digits. Using these were not unusual and all of us learned to use them in high school (before 1970 at least).
- lmm 6y ago
  > Notably one couldn’t do addition or subtraction with a slide rule; we used pencils for that. Huh? It's trivial to make a slide rule that you can add and subtract on, you just rule linear scales on it.
  - todd8 6y ago
    Of course you are right, the slide rule works with logarithmic scales that are “added” together to do multiplication. Linear scales could be used to add, but the low number of significant digits (no more than three on standard slide rules) meant that it wasn’t worth it, and no engineering slide rule that I ever saw had scales for addition.
- gshubert17 6y ago
  Back in the 1970s I used a slide rule when 2-3 place accuracy was enough; or 5-place or 7-place log tables and a pocket mechanical adding machine (rather than by hand) when more accuracy was required. I found a 2-minute video of the sort of pocket adding machine I used, https://www.youtube.com/watch?v=ryST18JJ7VU https://www.youtube.com/watch?v=ryST18JJ7VU (The device is actually easier to use than shown. Using the colors next to the digits: if silver, pull the stylus down; if red, pull up and over the curve at the top of the column to the next digit. No extra or wasted motions are needed.) Five places were usually enough, but seven places were needed for some astronomical calculations such as eclipses. The $7 I paid for the log tables in the late 1960s would purchase about $50 today; and the adding machine was probably a couple of dollars back then.
stan_rogers 6y ago
The log tables let you work without slide rules, which were themselves horribly expensive not too terribly long ago in the grand scheme of things. But yes, this was all about practical calculation, not mathematics for its own sake, that needed to be carried out quickly by people who wouldn't have handy access to machines that keep the dirty arithmetic details (and potential for error) hidden from the operator, whether that's your ship's navigator or the machinist with nothing but a sine bar and gauge blocks setting up a precision operation, and if you needed precision using a four-figure table book, the only way you were going to get it was if the derived operations were in the tables.
- bregma 6y ago
  The converse is true: slide rules let you do calculations quickly and easily (since they hang in the leather holster on your belt) without having to carry an expensive and heavy copy of the rubber bible or similar work and stop and look up numbers then scratch the values down on paper and work the problem.
  - stan_rogers 6y ago
    Again, you're thinking of an era where slide rules were relatively affordable. That's mid-twentieth century stuff (although the key word is relatively; my first good slide rule cost more than a month's rent at the time).
gumby 6y ago
Slide rules are literally the physical embodiment of a log table (or several, if you had a multilog rule). You used them by physical addition.
desertrider12 6y ago
OK, now I understand that the logs of these values are for pencil+paper addition and subtraction, not slide rules.

Waterluvian 6y ago

It kind of helps a non Mathie like me doing trig. But I'll ask fof one better: I would love an application that lets me plug in what I have (coords and angles), what I want, and for it to show me how to get it.

anonytrary 6y ago
Does it? No one does this: var STRAWBERRY_PI = 1 + Math.PI; For example, no one doing math will use τ (2𝛑) and 𝛑 simultaneously. Choose one or the other, otherwise you are increasing the number of symbols someone has to learn to understand your math. Naming everything is overwhelming. Mathematics is about similarities, not differences. If the transformation is trivial, then don't bother creating a new symbol. It will just confuse you more.
- exmadscientist 6y ago
  I don't agree at all. This happens all the time. For example, electrical engineering has f, ω, and s, all only differing by basic factors of 2π or i. As far as I can tell, the main reason this gets done is to give commonly recurring quantities single symbols, to reduce errors in lengthy calculations. When those recurring quantities are meaningfully different, in ways that help prime one's intuition, that's all the more reason to do it.
  - unishark 6y ago
    You also save clock cycles by avoiding the extra calculation each time you compute 2pi or whatever by defining TWO_PI once. So it was lot more common in Fortran and C programming days.
  - trevortheblack 6y ago
    As an electrical engineer you'll typical use f, ω, and s, in different contexts and you'll learn each of those contexts separately. f: consumer electronics ω: circuits s: frequency response Having multiples of terms for each is definitely a hindrance to education. It makes switching between each use a mental headache.

framecowbird 6y ago

versine clearly needed a name once when it was in common usage. As in, "Hey Greg, can you help me? I can't find this computation in these tables. --- Oh, try the versine".

deleted 6y ago
[deleted]

Sharlin 6y ago

The article explains pretty well why these named functions (or at least some of them) were once useful and thus had common names.

acqq 6y ago

> I don't think everything needs a name. And you are wrong, at least historically: The article points that without the access to the computers and to achieve numerical precision having precalculated tables of such functions was of direct practical use. Even if you personally and more recently didn't need that, the said names were needed and used, and that's why they exist. Had you been you born, for example, more than 100 years ago, you could have been one of the persons assigned to spend maybe years just carefully calculating (or just verifying) the tables of one of those functions which today are seldom referenced by a name. Or at least with a job which involved using such tables (and the names too). Also, in current computing practice, one can still write programs which produce wrong results if one is not aware of the limits of the partial numerical calculations, including these named. One doesn't have to know the names, but in some specific cases it could be needed to have separate functions calculating exactly the values of the functions named. As we start to discover again that the custom processors could calculate more with less binary digits, knowing this becomes even more important compared to the times where "just use doubles" was enough.