EEVblog 1479 - Is Your Calculator WRONG?

[TimFox]

I suggest that careful workers either use sufficient parantheses/brackets to make their expressions unambiguous, or revert to variations on Łukasiewicz (Polish) notation where parantheses are not needed and there are no ambiguous formations.

[Scherms]

I suggest that careful workers either use sufficient parantheses/brackets to make their expressions unambiguous, or revert to variations on Łukasiewicz (Polish) notation where parantheses are not needed and there are no ambiguous formations.

This leaves me wondering how much screwed up software is out there.

That's where HP RPN comes in! It eliminates the confusing 'implicit' schemata... 

6 / 2(2 + 1)

Enter numbers onto stack:
6 ENTER, 2 ENTER, 2 ENTER, 1 ENTER



Enter operator:
+, x, /

= 1.0000

 

[Vtile]

...or eg. instruction list:

L 2.0
L 1.0
+R
L 2.0
*R
L 6.0
TAK
/R
T #RESULT

There is RPN outside HP Calcs.

[Scherms]

The DM41X, another member of our flagship line-up of RPN calculators, is a faithful recreation of the software environment of the HP-41CX, one of the most versatile calculators ever created and the first alphanumerical calculator, in a modern hardware architecture. Easily share or back up your programs or your entire DM41X environment and use hundreds of existing, professionally developed software applications with this rugged calculator sporting a stainless steel case and a Gorilla Glass screen.

Like all SwissMicros calculators, the DM41X uses the efficient and time-tested RPN logic.

[gnuarm]

The expressions to evaluate shown in the video thumbnail are not the same (pocket calculator screen vs. the Wolfram webpage), notice the extra parentheses in the calculator's LCD.

Thanks Captain Obvious. However if you watched the video for at least a few minutes, you would know why.

Why the need to be rude?  The real question is "why" do they use the two methods?  I didn't see that explained in the ever annoying video.

[Scherms]

The real question is "why" do they use the two methods?  I didn't see that explained in the ever annoying video.

There is no two methods, one is structurally wrong and can't be used!

eg: WRONG




eg: RIGHT



 

[Nominal Animal]

The real question is "why" do they use the two methods?

Because humans and their languages.

(Why are lead, lead, and lead pronounced differently in English?)

It is like standards.  One is never sufficient, because humans.

Specifically, here the problem is that some humans think that it is acceptable to omit multiplication operator in certain situations, but do not think it is necessary to define the priority of (operator order for) said implicit multiplication.  Purely a human foible.

[gnuarm]

The real question is "why" do they use the two methods?

Because humans and their languages.

(Why are lead, lead, and lead pronounced differently in English?)

I know how lead and lead are pronounced, but what is lead?  I've never heard of that word.

It is like standards.  One is never sufficient, because humans.

Specifically, here the problem is that some humans think that it is acceptable to omit multiplication operator in certain situations, but do not think it is necessary to define the priority of (operator order for) said implicit multiplication.  Purely a human foible.

I think the priority is established, the question is, why are the two multiply operators handled differently?

[Nominal Animal]

I know how lead and lead are pronounced, but what is lead?  I've never heard of that word.

IPA /lɛd/, /liːd/, /lid/.  It turns out one of those is American pronunciation, the other two English.  Dunno about aussies, though; there could be more (/lɛ:d/?)

I think the priority is established, the question is, why are the two multiply operators handled differently?

For the same reason a pint is approximately 568 ml, or approximately 551 ml, or approximately 473 ml, depending on who you ask and in which context: because humans.

Would it be so odd to have two different multiplication operators, × and ·, that have a different priority?  After all, - and - do: one is unary negation, and the other is binary subtraction, both using the same character/glyph.

[gnuarm]

I know how lead and lead are pronounced, but what is lead?  I've never heard of that word.

IPA /lɛd/, /liːd/, /lid/.  It turns out one of those is American pronunciation, the other two English.  Dunno about aussies, though; there could be more (/lɛ:d/?)

I don't know what LEAD /lid/ is.  The pronunciation of this is like the word "lid".  I can't find any reference that indicates this is a pronunciation of LEAD. 

I think the priority is established, the question is, why are the two multiply operators handled differently?

For the same reason a pint is approximately 568 ml, or approximately 551 ml, or approximately 473 ml, depending on who you ask and in which context: because humans.

That is not a reason.  This is math, with rules and structures.  Without that, math literally doesn't exist.

Would it be so odd to have two different multiplication operators, × and ·, that have a different priority?  After all, - and - do: one is unary negation, and the other is binary subtraction, both using the same character/glyph.

The character does not matter.  They clearly have different functions.  This is a false analogy. 

Having two operators with the same functionality is silly and pointless.  There must be a usage that makes a higher priority for the implied multiplication significant, even if it's only convenience.  But there has to be a use case where it makes a difference.

[Nominal Animal]

I know how lead and lead are pronounced, but what is lead?  I've never heard of that word.

IPA /lɛd/, /liːd/, /lid/.  It turns out one of those is American pronunciation, the other two English.  Dunno about aussies, though; there could be more (/lɛ:d/?)

I don't know what LEAD /lid/ is.  The pronunciation of this is like the word "lid".  I can't find any reference that indicates this is a pronunciation of LEAD. 

Here, with audio.

I think the priority is established, the question is, why are the two multiply operators handled differently?

For the same reason a pint is approximately 568 ml, or approximately 551 ml, or approximately 473 ml, depending on who you ask and in which context: because humans.

That is not a reason.  This is math, with rules and structures.  Without that, math literally doesn't exist.

It is, because we have two layers of definitions here.

The surface layer is the words, acronyms, symbols, and glyphs we use.  These mutate, change, and evolve constantly.  These are the ones you are fully allowed to play with; the only requirement in science and math is that you define them.  In math, this is notation.  There are many valid notations, and if you do complex work, you often end up inventing your own if a suitable one does not yet exist.

The deep layer is the things and rules being described.  These are not to be messed with willy-nilly, because we've discovered them only through hard work and critical peer review.

Math is the deep layer.  What we are talking about is the notation, the surface layer, that is completely up to humans to define.

It is no different than defining "elektroni" = "electron" and "sähkälehitu" = "electron" (which does imply "elektroni" = "sähkälehitu").
Or what base (radix) we use when writing numbers.

The answer to the question "Why would implicit multiplication have a different priority than explicit multiplication?" is that the human surface layer, the notation layer, is always in flux, and not something you can blindly rely on.  (Well, currently, we can somewhat rely on the priorities of explicit operators, and use parentheses to ensure a specific order, as many have pointed out earlier in this thread.)

Personally, I only use implicit multiplication between numeric constants and variables.  This is because I find \$2 \pi x\$ easier to read than \$2 \times \pi \times x\$.  I do believe that human perception detail is at the core of why two different notations for multiplication exist.  I also believe that it is most likely human shortsightedness –– specifically, "out of sight, out of mind" –– that has caused implicit multiplication being omitted when humans have agreed upon the priorities of operators.  The priorities of the operators being just another notational detail: the math itself does not change, even if the notation does.

Having two operators with the same functionality is silly and pointless.  There must be a usage that makes a higher priority for the implied multiplication significant, even if it's only convenience.  But there has to be a use case where it makes a difference.

That assumes humans are rational beings.  Evidence suggests otherwise.

[IanB]

IPA /lɛd/, /liːd/, /lid/.  It turns out one of those is American pronunciation, the other two English.  Dunno about aussies, though; there could be more (/lɛ:d/?)

There are only two standard pronunciations. One is with short 'e' sound, as in 'led', the other is with a long 'ee' sound, as in 'leed'.

If you consider regional accents, these two pronunciations can have varying vowel sounds, but they still correspond to one or the other of the two. For example, in New Zealand, 'led' can sound like 'lid', but that is just the common pronunciation of 'e' in that part of the world.

Things get really complicated if you start considering regional accents. For example, the standard British pronunciation of 'a' in 'cat' is a different sound from the American 'a' in the same word. And then the American 'a' sound, while different from British, also varies itself in different parts of the USA.

[gnuarm]

I know how lead and lead are pronounced, but what is lead?  I've never heard of that word.

IPA /lɛd/, /liːd/, /lid/.  It turns out one of those is American pronunciation, the other two English.  Dunno about aussies, though; there could be more (/lɛ:d/?)

I don't know what LEAD /lid/ is.  The pronunciation of this is like the word "lid".  I can't find any reference that indicates this is a pronunciation of LEAD. 

Here, with audio.

Zero help.  There were THREE pronunciations provided with THREE definitions.  The above link is very hard to follow, but I only see two. 

I think the priority is established, the question is, why are the two multiply operators handled differently?

For the same reason a pint is approximately 568 ml, or approximately 551 ml, or approximately 473 ml, depending on who you ask and in which context: because humans.

That is not a reason.  This is math, with rules and structures.  Without that, math literally doesn't exist.

It is, because we have two layers of definitions here.

The surface layer is the words, acronyms, symbols, and glyphs we use.  These mutate, change, and evolve constantly.  These are the ones you are fully allowed to play with; the only requirement in science and math is that you define them.  In math, this is notation.  There are many valid notations, and if you do complex work, you often end up inventing your own if a suitable one does not yet exist.

The deep layer is the things and rules being described.  These are not to be messed with willy-nilly, because we've discovered them only through hard work and critical peer review.

Math is the deep layer.  What we are talking about is the notation, the surface layer, that is completely up to humans to define.

It is no different than defining "elektroni" = "electron" and "sähkälehitu" = "electron" (which does imply "elektroni" = "sähkälehitu").
Or what base (radix) we use when writing numbers.

The answer to the question "Why would implicit multiplication have a different priority than explicit multiplication?" is that the human surface layer, the notation layer, is always in flux, and not something you can blindly rely on.  (Well, currently, we can somewhat rely on the priorities of explicit operators, and use parentheses to ensure a specific order, as many have pointed out earlier in this thread.)

Personally, I only use implicit multiplication between numeric constants and variables.  This is because I find \$2 \pi x\$ easier to read than \$2 \times \pi \times x\$.  I do believe that human perception detail is at the core of why two different notations for multiplication exist.  I also believe that it is most likely human shortsightedness –– specifically, "out of sight, out of mind" –– that has caused implicit multiplication being omitted when humans have agreed upon the priorities of operators.  The priorities of the operators being just another notational detail: the math itself does not change, even if the notation does.

Having two operators with the same functionality is silly and pointless.  There must be a usage that makes a higher priority for the implied multiplication significant, even if it's only convenience.  But there has to be a use case where it makes a difference.

That assumes humans are rational beings.  Evidence suggests otherwise.

If you say so. 

[Nominal Animal]

I know how lead and lead are pronounced, but what is lead?  I've never heard of that word.

IPA /lɛd/, /liːd/, /lid/.  It turns out one of those is American pronunciation, the other two English.  Dunno about aussies, though; there could be more (/lɛ:d/?)

I don't know what LEAD /lid/ is.  The pronunciation of this is like the word "lid".  I can't find any reference that indicates this is a pronunciation of LEAD. 

Here, with audio.

Zero help.  There were THREE pronunciations provided with THREE definitions.  The above link is very hard to follow, but I only see two. 

You wrote you cannot find any reference to IPA /lid/.  (The same page contains the two other IPA pronunciations, if you look carefully.)  I posted a link to the etymology and to the audio file matching the IPA pronunciation.  If that's zero help, well, you're welcome.

That assumes humans are rational beings.  Evidence suggests otherwise.

If you say so.

Who cares what I say?  Go read a blog post describing some of that evidence with references instead.

[IanB]

You wrote you cannot find any reference to IPA /lid/.  (The same page contains the two other IPA pronunciations, if you look carefully.)  I posted a link to the etymology and to the audio file matching the IPA pronunciation.  If that's zero help, well, you're welcome.

You provided a link to this page: https://en.wiktionary.org/wiki/lead

It describes TWO English pronunciations. One that sounds like "led" and one that sounds like "leed".

[Scherms]

...in the real world of mathematics and engineering, adjacent terms bind more tightly than operators. Therefore a/bc is understood to be \$\frac{a}{bc}\$

Similarly, 6/2(2+1) would be read as \$\frac{6}{2(2+1)}\$

Yes, there is only one FORM solution to this equation...

6/2(2+1) would be read as \$\frac{6}{2(2+1)}\$ = [6 / [2 x [2 + 1]]] = 1

[gnuarm]

I know how lead and lead are pronounced, but what is lead?  I've never heard of that word.

IPA /lɛd/, /liːd/, /lid/.  It turns out one of those is American pronunciation, the other two English.  Dunno about aussies, though; there could be more (/lɛ:d/?)

I don't know what LEAD /lid/ is.  The pronunciation of this is like the word "lid".  I can't find any reference that indicates this is a pronunciation of LEAD. 

Here, with audio.

Zero help.  There were THREE pronunciations provided with THREE definitions.  The above link is very hard to follow, but I only see two. 

You wrote you cannot find any reference to IPA /lid/.  (The same page contains the two other IPA pronunciations, if you look carefully.)  I posted a link to the etymology and to the audio file matching the IPA pronunciation.  If that's zero help, well, you're welcome.

Calm down.  Relax.  Take a deep breath and exhale. 

I saw a claim of three separate words that are spelled the same.  I got the IPA pronunciation notation mixed up.  Ok?  I'm looking for someone to tell me what the third word is.  I know what lead and lead are, now what is lead?

That assumes humans are rational beings.  Evidence suggests otherwise.

If you say so.

Who cares what I say?  Go read a blog post describing some of that evidence with references instead.

If you say so.

[gnuarm]

You wrote you cannot find any reference to IPA /lid/.  (The same page contains the two other IPA pronunciations, if you look carefully.)  I posted a link to the etymology and to the audio file matching the IPA pronunciation.  If that's zero help, well, you're welcome.

You provided a link to this page: https://en.wiktionary.org/wiki/lead

It describes TWO English pronunciations. One that sounds like "led" and one that sounds like "leed".

I was asking what the third word is.  It's not about pronunciations.  I'm asking what the word is. 

[IanB]

I was asking what the third word is.  It's not about pronunciations.  I'm asking what the word is.

There are more than three.

As a noun:
1. The metal
2. An inside track or a prospect, as in a sales lead
3. A position at the front, as to be in the lead
4. A cord or a cable, as in a power lead

As  a verb:
1. To be in front, as in to lead the field
2. To go somewhere, as in the path leads to the village
3. To draw along, as in to lead a bull by the nose

As an adjective:
1. Being made of lead, an in a lead weight
2. Being ahead of others, as in the lead position

I'm sure there may be others, but these are the first that come to mind.

[gnuarm]

I was asking what the third word is.  It's not about pronunciations.  I'm asking what the word is.

There are more than three.

As a noun:
1. The metal
2. An inside track or a prospect, as in a sales lead
3. A position at the front, as to be in the lead
4. A cord or a cable, as in a power lead

As  a verb:
1. To be in front, as in to lead the field
2. To go somewhere, as in the path leads to the village
3. To draw along, as in to lead a bull by the nose

As an adjective:
1. Being made of lead, an in a lead weight
2. Being ahead of others, as in the lead position

I'm sure there may be others, but these are the first that come to mind.

Your examples come down to two words:

1) Lead, the metal itself or relating to it's properties.  Pronounced like "led"

2) Lead, in some manner, referring to ahead of others or being pulled by something ahead of you, pronounced with a long e, "leed". 

While there are multiple definitions of these two words, they are still only two words.  Words often have multiple definitions, but are still only one word. 

Still, someone posted that there were three words, with three pronunciations, all spelled "lead". 

I suppose this has dragged out as much as is meaningful.  I'm happy to say you are right and there are an unlimited number of words spelled lead.

[Nominal Animal]

I was asking what the third word is.  It's not about pronunciations.  I'm asking what the word is.

If you say so.

[IanB]

Your examples come down to two words:

1) Lead, the metal itself or relating to it's properties.  Pronounced like "led"

2) Lead, in some manner, referring to ahead of others or being pulled by something ahead of you, pronounced with a long e, "leed". 

While there are multiple definitions of these two words, they are still only two words.  Words often have multiple definitions, but are still only one word.

You are absolutely right, and we are both agreed on this. One word is related to the metal, and generally sounds like "led"; the other word is related to the action, and generally sounds like "leed".

Still, someone posted that there were three words, with three pronunciations, all spelled "lead". 

That someone is mistaken, and there are not three different words, nor are there three different pronunciations.

[gnuarm]

I was asking what the third word is.  It's not about pronunciations.  I'm asking what the word is.

If you say so.

I dug back and it was YOU!  lol

[Nominal Animal]

That someone is mistaken, and there are not three different words, nor are there three different pronunciations.

If you say so.

It's not like I'm a native English speaker myself, you see.

I dug back and it was YOU!  lol

lol

[IanB]

That someone is mistaken, and there are not three different words, nor are there three different pronunciations.

If you say so.

I do say so.