# Mathematics is NOT a Universal Language



## Jonmo1 (Dec 31, 2015)

I say that Mathematics is no more universal than any other language like English, Spanish, French, German, or ANY other language.

I recently came across a meme on Facebook that posed a simple math question and asked the readers to solve it.

2+2*2+2

For this rant, it doesn’t matter what the correct answer is (8).  And I’m not actually posing this question to this forum.
What matters is that not everyone gives the same answer.  

I noticed that the responses were split about 50/50 between the answers of
2+(2*2)+2 = 8
And
((2+2)*2)+2 = 10
A small fraction even answered like this
(2+2)*(2+2) = 16

So I posted my opinion, If Mathematics is the only Universal Language, then I think we are all screwed.  This kicked off a lengthy discussion with a few friends and family.

I read up a little and found basically that Math is considered Universal because 2+2=4 no matter whom in the world you’re talking to.  I argued that this is clearly not the case when the problem is more complicated like the posted example 2+2*2+2.  A vast majority of people give different answers.  The usual response is “Well if someone gives the wrong answer, then they are not speaking Math”.

Well, that is true of ANY language, say English for example.  If I say “I’m Hungry” in English, then that means “I need food”.  No matter whom I’m talking to.  As long as the speaker and listener are both speaking English.  If I say “I’m Hungry” and you think I’m saying "the sky is blue", then you are not speaking English.

I then argued that if the language must be learned, and it has rules that must be followed (Like multiply before add), then that language is NOT Universal.  Clearly NOT everyone has learned it the same way.  The response is “That is true of any language, All languages must be learned”. 

Well, that’s exactly my point.

To me, calling a language Universal means that I can walk up to a complete stranger and start speaking it.  And that person would understand me.  That is clearly not a true condition of Math as a language.

So in conclusion, I say that Mathematics is no more universal than any other language like English, Spanish, French, and German etc.


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## Joe4 (Dec 31, 2015)

The fact that different people get different answers is because they are not following the rules.  Of course it needs to be learned.  We are not born with the full knowledge of any method of communication, or have any in-born knowledge of "rules".

I think you are misunderstanding what is meant by "universal".  It does not mean it does not have to be learned.  It is universal in the sense that there is only one mathematical language (do you know of any alternative mathematical languages?).  A mathematician in Germany who speaks no English could communicate in "mathematics" to an English speaking mathematician who knows no German.  That is how it is universal.


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## mole999 (Dec 31, 2015)

interesting, I didn't learn PEDMAS at school, though i have vague recollections that it was trying to be taught.

I thought ESPERANTO was to be the universal language, at some stage. 

Where would we be if we all understood everything the same


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## Jonmo1 (Dec 31, 2015)

My point is How is Math any different from any other language like English?
If both parties speak the same language and follow the same rules, then they can effectively communicate in that language.
That is true of ANY language.


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## Joe4 (Dec 31, 2015)

Here are some explanations on why math is considered a universal language:
Math in Daily Life -- The Universal Language
Why Is Math the Only True Universal Language?


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## Jonmo1 (Dec 31, 2015)

I get 'why' they say it's Universal.
My point is, the reasons they say Math is universal are true of ANY language.


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## Jonmo1 (Dec 31, 2015)

If Math is Universal, why does my computer get it wrong?
On a Windows based computer, open up the calculator application.
Enter the equation
Press 2
Press +
Press 2
Press *
Press 2
Press +
Press 2
Press =

Shows 10.


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## mole999 (Dec 31, 2015)

Jonmo1 said:


> If Math is Universal, why does my computer get it wrong?
> On a Windows based computer, open up the calculator application.
> Enter the equation
> Press 2
> ...




because each entry is evaluated as typed, its the right logic, switch to scientific to get the real answer

BTW most know they have a calculator on their smart phones, did you know if you rotate the phone 90 degrees, many change to scientific mode


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## Jonmo1 (Dec 31, 2015)

mole999 said:


> because each entry is evaluated as typed, its the right logic, switch to scientific to get the real answer


So _another_ rule to follow, must use the scientific version.

Well, a person doing it that way in their head is the correct logic as well, right?


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## Jonmo1 (Dec 31, 2015)

The calculator on my iPhone gets it right.

Clearly Windows and iPhone were created by educated people right?
Why are the answers different ??

So from this I conclude that people of higher education (who clearly speak math) disagree on the rules of math.
Or at least they don't apply the rules in the same way.
Therefore it's NOT universal.


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## Eric W (Dec 31, 2015)

It is true that the math "language" must be learned.  Two people must agree on what a plus sign is.  And if you look at math history, that took a lot of doing.  And of course eventually agree on the other rules of the language, order of operations, etc. etc.  But once those rules are agreed upon, when the language is spoken correctly, both sides will always get the same answer. 

But for a spoken language, that's not always the case.  There is cultural bias, idioms, past history, all encompassed within the language.  It's possible to create a statement that entirely follows the rules of the language, which is incomprehensible to another speaker.  As a very minor example, in English we'd say "I'm full" when we're done eating.  In Spanish, the exact translation of that would be "Estoy lleno."  Which would make no sense to a native Spanish speaker.  They would say "Estoy satisfecho" (I'm satisfied) instead.

So yes, both parties (speaker and listener) must still learn the language of mathematics, but when properly "spoken", it is more easily understood than other languages.  You could say "a bird in the hand is worth 2 in the bush" to an alien, but he'd probably just wonder what a bird or a bush is.  But he could comprehend  2 > 1.

That's my 2 cents.


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## mole999 (Dec 31, 2015)

Eric W said:


> But he could comprehend  2 > 1.



really ? if the constants have not been agreed the very words that produce them could lead to a misunderstanding. 

Then again to discover why one is better than two begs a question


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## Eric W (Dec 31, 2015)

mole999 said:


> really ? if the constants have not been agreed the very words that produce them could lead to a misunderstanding.


I was very pointed in saying that the language of math must be learned, which would include what the constants are.  I can imagine trying to communicate with an alien across light years with only a binary code, and eventually build up a math language.  But would you want to teach him the verb "walk" when he may not even have legs?  Yet every Earth language has that verb.  If you were to receive a signal from outer space, how would you try to communicate?


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## Jonmo1 (Dec 31, 2015)

Eric W said:


> It is true that the math "language" must be learned. Two people must agree on what a plus sign is. And if you look at math history, that took a lot of doing. And of course eventually agree on the other rules of the language, order of operations, etc. etc. But once those rules are agreed upon, when the language is spoken correctly, both sides will always get the same answer.


That is True of ANY language



Eric W said:


> But for a spoken language, that's not always the case. There is cultural bias, idioms, past history, all encompassed within the language. It's possible to create a statement that entirely follows the rules of the language, which is incomprehensible to another speaker. As a very minor example, in English we'd say "I'm full" when we're done eating. In Spanish, the exact translation of that would be "Estoy lleno." Which would make no sense to a native Spanish speaker. They would say "Estoy satisfecho" (I'm satisfied) instead.


I don't see how that is relevant to this discussion.
You're posting an example of two people speaking two different languages.
I'm talking about two people speaking the same language.. Math.
But anyway, if your Translator truly understood Both the English and Spanish languages, then the meaning would be correctly expressed to/from either party.



Eric W said:


> So yes, both parties (speaker and listener) must still learn the language of mathematics, but when properly "spoken", it is more easily understood than other languages. You could say "a bird in the hand is worth 2 in the bush" to an alien, but he'd probably just wonder what a bird or a bush is. But he could comprehend 2 > 1.


Again, This is true of ANY language.

If to be called Universal it means that both speaker and listener must abide by the same rules, symbols and syntax, then Math is no more Universal than Any other language.


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## Joe4 (Dec 31, 2015)

> So from this I conclude that people of higher education (who clearly speak math) disagree on the rules of math.
> Or at least they don't apply the rules in the same way.
> Therefore it's NOT universal.


Bad programming.  I have seen a lot of it.  One would like to think people with "higher education" would know better, but laziness abounds!
FWIW, I have also seen plenty of people with higher education butcher the English language (when it is their native tongue).



> If to be called Universal it means that both speaker and listener must abide by the same rules, symbols and syntax, then Math is no more Universal than Any other language.


If you look at those links I provided on the previous page, one plainly states how it is universal.    It is the concept, not the language or symbols one chooses.  If you have ten of something and add another ten, you will have twenty.  Regardless of what language or symbols you use, the actual number of objects is not different because of the language or symbols used.  You would never have 19 objects because you used a different language or symbols.


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## Eric W (Dec 31, 2015)

Maybe it's just the word "Universal" that's the problem.  I agree, a language of whatever type must be learned by both sides to be useful.  And mathematics is not "spoken" universally by everyone, hence the difference of opinion about what 2+2*2+2 is.

Maybe a better word would be elementary, or "context-free" language.  Mathematics is a self-contained subset of the methods we use to communicate.  (Let's not quibble about self-contained and Godel right now.)  1 + 1 means the same thing in Japan or New Orleans.  1 pagoda + 1 pagoda does not mean the same as 1 jazz club + 1 jazz club.  But if you strip out history, cultural bias, context, idioms, etc. etc. you're left with . . . math?


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## DocAElstein (Dec 31, 2015)

Cross Posted here:
http://www.mrexcel.com/forum/lounge-v-2-0/911516-mathematics-not-universal-language.html
Mathematics is NOT a Universal Language - Page 2



Jonmo1 said:


> I say that Mathematics is no more universal than any other language............ like English, Spanish, French, and German etc.





Joe4 said:


> The fact that different people get different answers is because they are not following the rules.  Of course it needs to be learned.  We are not born with the full knowledge of any method of communication, or have any in-born knowledge of "rules"........ A mathematician in Germany who speaks no English could communicate in "mathematics" to an English speaking mathematician who knows no German.  That is how it is universal.



Just a small German / English contribution...

Sometime it can help get over language differences ( non universalability ) to go the extra mile, adding extra, not always necessary steps. But that can irritate those that do not need the extra Info.    Parenthesis can both have a similar Mathematical significance as well as generally being interpreted as indicating an order..  Helps to bridge the gap, maybe make it a “ bit more Universal “
So, maybe write always:
2  + _(  2 * 2  )_  +  2​
As Jonmo1 reported half the people thought that anyway, most of the rest would get the meaning of the Parenthesis.
___o00o__`(_)`___o00o___
2  + __(  2 * 2  )__         +  2


Happy New Year​
So what I am saying,  if you have the time, go the extra mile to explain it a bit clearer. There are no easy way to bring together differences in Languages and cultural ways of thinking built up over the years.... But it can help..  To Work together to help make it ( more ) universal

Alan


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## shg (Dec 31, 2015)

The fact that two systems evaluate an expression differently doesn't mean that the math is not universal; it means that the systems have not agreed on the meaning or precedence of symbols. 

The meaning of symbols changes depending on the conversation, and operator precedence is just a convenience for making written expressions more compact, to avoid a proliferation of parens -- but requires prior agreement. Witness the tempest in a teapot about Excel's evaluation of -2^2.

NASA thought it was universal enough to put some basics on the Voyager spacecraft in 1977: http://voyager.jpl.nasa.gov/spacecraft/images/image003.gif


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## DocAElstein (Dec 31, 2015)

DocAElstein said:


> ...
> Sometime it can help get over language differences ( non universalability ) to go the extra mile, adding extra, not always necessary steps. But *that can irritate *those that do not need the extra Info.  .......





shg said:


> ....... and operator precedence is just a convenience for making written expressions more compact, to *avoid a proliferation of parens* -- but requires prior agreement. .....


Sorry   Somehow I thought you would reply just after me...( I assume you mean Parenthesis by parens  - I could not find a reference to that abbreviation – you introducing a new language ? ). Happy New Year shg.   ?


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## shg (Dec 31, 2015)

Sorry about what?


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## Jonmo1 (Dec 31, 2015)

Joe4 said:


> If you have ten of something and add another ten, you will have twenty.  Regardless of what language or symbols you use, the actual number of objects is not different because of the language or symbols used.  You would never have 19 objects because you used a different language or symbols.


The same is true of English.
If both parties must learn the language and it's rules, then if the speaker says "I'm Hungry", then the listener would never hear "Jelly Fish"


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## Jonmo1 (Dec 31, 2015)

From Post #6 in the same thread on the other forum

Now that I can agree with.  Anyone/Everyone will have a need to use Math.  That makes sense.

I still think Universal is the wrong word for it though....I'm pondering what the correct word would be..


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## mole999 (Dec 31, 2015)

English is not good to cite, consider

To, Too & Two

You Are, Your, Your'e, Yaw

it easy for us to be confused

Lead (to escort forward / a base metal)

Or the confusion over Cinderellas Glass Slipper, which failed to make the transition from Fur in the original French


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## Jonmo1 (Dec 31, 2015)

What's you're point?


mole999 said:


> English is not good to cite, consider
> 
> To, Too & Two <- I see 3 distinctly different words
> 
> ...


All languages, even Math, have similar looking words/symbols.  All languages, even math, have rules to follow.

If a speaker says one thing, but the listener hears something different, then they are not speaking the same language.
A common argument used to support Math as Universal.
If 2 people get different answers from the same problem, then one of them is not speaking math correctly.


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## Joe4 (Dec 31, 2015)

> I still think Universal is the wrong word for it though....I'm pondering what the correct word would be..


So what we are really talking about here is semantics.  That's a slippery slope I do not wish to go down.  Just ask Bill Clinton: https://www.youtube.com/watch?v=j4XT-l-_3y0



> From Post #6 in the same thread on the other forum


But are the rules for Cross-Posting the same in all forums!


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## mole999 (Dec 31, 2015)

Jonmo1 said:


> If a speaker says one thing, but the listener hears something different, then they are not speaking the same language.


To, Too & Two, you must be tonally pitch perfect, they sound the same to me, its only their context that separates them out


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## Jonmo1 (Dec 31, 2015)

Joe4 said:


> But are the rules for Cross-Posting the same in all forums!


But not so strictly enforced here as they are over on that other forum.




mole999 said:


> To, Too & Two, you must be tonally pitch  perfect, they sound the same to me, its only their context that  separates them out


Right, Context.
It's a rule that needs to be followed when speaking English.
Just like order of operations is a rule that needs to be followed in Math.
All languages have them, so I see Math as no different from (no more Universal than) English in that regard.


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## J.Ty. (Jan 1, 2016)

Mathematics is not a universal language, because it is not a language at all. Mathematics is one of the sciences. Certain parts of mathematics are considered to be truly universal. It is widely believed, that any civilization (on Earth or elsewhere) that starts dealing with mathematical thinking, will eventually discover the concept of prime numbers, the constants PI() and EXP(1) (here written in Excel's notations), etc.  


Of course, there must be a language, which is used to express mathematical statements. Its construction and principles are very much the matter of convention, and it is to some extent external to the mathematics itself. The one we use on Earth is rather uniform in its basics, but still permits a lot of diversity. E.g., in my home country we use the decimal comma, while most of the readers here use the decimal point instead. 


The initial puzzle of 2+2*2+2 is an example of an expression, whose meaning depends on the conventions of dealing with operations witout explicitly declared order of operations. The answer to this problem is the common idea of providing a proof for mathematical statements.  


So for me any of the statements
2+2*2+2 = (2+2)*(2+2) = 16
2+2*2+2 = (2+(2*2))+2 = 8
2+2*2+2 = ((2+2)*2)+2 = 10
is perfectly correct, providing the value and the way it was achieved. If it is not what I expected, it is due to a misunderstanding, but not a mistake.


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## mole999 (Jan 1, 2016)

Languages adjust and evolve

I used x and ÷ when at school, then these computer people came along and changed the convention to be represented as * and /. The principle is sound, but the language changed


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## DocAElstein (Jan 2, 2016)

J.Ty. said:


> Mathematics is not a universal language, because it is not a language at all. Mathematics is one of the sciences. Certain parts of mathematics are considered to be truly universal. It is widely believed, that any civilization (on Earth or elsewhere) that starts dealing with mathematical thinking, will eventually discover the concept of prime numbers, the constants PI() and EXP(1) (here written in Excel's notations), etc.
> .......
> So for me any of the statements
> 2+2*2+2 = (2+2)*(2+2) = 16
> ...



One  of my New Year’s resolutions is: I am going to use a lot more Brackets ( Parenthesis, Parens ) from now on. That seems to be almost universally understood. I hope that does not irritate too much. If anyone asks why I will just refer them to this Thread.
Alan

P.s. 
Maybe some Mathematics ( Maths ) experts can suggest some other ideas to help making both mathematical code lines ( or any other code lines for that matter ) more universally readable... Extra use of   Brackets ( Parenthesis, Parens ) seems a good idea,.. to me! Maybe a few extra empty spaces as well helps sometimes, colours , like the MrExcel Screen shot tools does in formulas can also help. 
..___ o00o__`(_)`___o00o__..
..(__ (2+__(2*2)_)__+2_).. 
Not relying on the Implicit, could also be a good new resolution , IMHO, even for some experts..
P.P.s.
( I guess maybe VBA, though, is a language, and un______in that? (  not universally understood…so maybe not universal…  maybe unequivocal…





Pepe Le Mokko said:


> Definition of "Universal" in the Collins dictionary :"(esp of a language) capable of being used and understood by all"........


  ..VBA has only been written in English, so there is no confusion in what is meant, if you have understood the single set ( one language version as yet ) of Rules for interpretation. Even, the different *__  , __ .__ ;__ \ __* conventions in Excel are not apparent in VBA, but they always seem to give problems when interacting with the Sheets, ( at least as far as I know with Worksheets ( Spreadsheets ) . I wonder why they did not just do Excel in English: I guess they just did not think they would get away with forcing non English users to use Excel in English ?


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## mole999 (Jan 2, 2016)

if persons have not understood PEDMAS/BODMAS this may help http://www.thecalculatorsite.com/articles/units/pemdas-bodmas-order-of-operations.php


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## DocAElstein (Jan 6, 2016)

*Maybe we could try this one:*

 We say Mathematics is a Science as we use that word for the study of “it”,  - where here “it” is referring to Mathematical things. Mathematical is what we refer to as the various concepts which start at the simplest addition and then go on to encompass the concepts, ideas and everything as yet the people studying Mathematics have up until now come up with.  
 ( Sometimes Math or Maths is used as a slang or quick way of saying either mathematics or to refer to mathematical Things. )
 So this





J.Ty. said:


> Mathematics is not a universal language, because it is not a language at all. Mathematics is one of the sciences. …


 sounds OK.
  From all we know about the Universe up until now we can use a Theory  ( based on the ideas, for example, that if I am given and take / accept something, and then do the same again I have two of those things ). This Theory to prove that the Mathematical things, here for example addition, are universal, or appears to be so as far as we know.-  We could extend the idea or Theory here to that of “Addition” to “Counting”, saying the two are related. ( I mean the Theory of “If I give or add something of the same type 2 times, then the count of the things I have is "2”, etc.. ) In the above example the count was 2 after I had taken and accepted 2 things of the same sort. For now that total concept  is taken as Universal

  I guess if we found somewhere where that did not work we would have to think again. Maybe somewhere in the Universe having / accepting something could be governed by a similar rule to the Microsoft Scripting Runtime Dictionary, and no matter how many times I take a particular thing I would still be left with just one of it. I might need to modify my concept of count then to give different Count Concepts. I could have two counts then, One of how many things I have, and one of how many things were given to me. It sounds absurd, but only because we have either not experienced that yet, or have not got a Theory to cover it. 
 Maybe God or the maker of the universe or Wotever ( Whatever )  just never got around to documenting it properly… or it got lost in the ever increasing ( if it does ) Universe. ( And BTW, if the universe is ever increasing then nothing I guess can be sure to be universal as the universe ‘aint ( isn’t ( is not ) ) finished yet, so we cannot be sure ‘till ( until ) it is.

_ ……………………………………….

As this is a VBA Forum and the Lounge at that, just a fun example of something similar. This code confused me for a while, still does a bit..


```
' ‹(o¿o)›
Option Explicit
'http://www.mrexcel.com/forum/lounge-v-2-0/911516-mathematics-not-universal-language.html  Count Wonk Doc.AElstein "wbcodes.xlsm"
Sub ModuleSheetsAddDelete() 'Different Count Concepts in universe
10 Dim CntS As Long, CntW As Long '
20 Let CntW = ThisWorkbook.Worksheets.Count: Let CntS = ThisWorkbook.Sheets.Count 'Both counts are the same originally ( If I have not added charts or diagrams )

' Add "Modules"
30 ThisWorkbook.Modules.Add 'A "Module" appears in the VB Editor VBAProject Window
40 ThisWorkbook.Modules.Add 'Another "Module" appears in the VB Editor VBAProject Window
50 Let CntW = ThisWorkbook.Worksheets.Count: Let CntS = ThisWorkbook.Sheets.Count 'Worksheets count stays the same: Sheet count goes up by 2

'Delete "Modules"
60 ThisWorkbook.Modules.Delete 'Seems to delete all the "Modules" we added.
'70 Application.DisplayAlerts = False 'Option to Stop me being warned about deleting a "Worksheet"!!!? ! - no worries - it only deletes the "Modules" that I just added
80 Let CntW = ThisWorkbook.Worksheets.Count: Let CntS = ThisWorkbook.Sheets.Count 'The "Counts" are back to the original
90 Application.DisplayAlerts = True

'Try to Delete "Modules" again
100 ThisWorkbook.Modules.Delete 'This errors, so presumably "Modules" Object is a "Code module"??_(o¿o)_** and we have none there to be deleted
End Sub
'
'Referrences used:	
'http://www.vbforums.com/showthread.php?512860-Worksheets-vs-Sheets
'http://www.mrexcel.com/forum/excel-questions/441155-what-difference-between-worksheets-sheets.html
'http **-??_(o¿o)_// -  Thread where shg and Rompry discussed old  Code Modules...
'Count Wonk Doc.AElstein "wbcodes.xlsm"
```


 The code I ran on a . xlsm Workbook with just a few Worksheets in it. I also had a few of what I thought we call “Modules” in it, ( - At least I put them there by “inserting” a “Module” )

 Lines 30 and 40 result in something being shown in the VB Editor VBAProject Window that looks like a Module. ( twice in total ). Line 60 appears to delete “them” “2” things. Interestingly line 100 then errors even if I have lots of other “Modules” shown. 

 The answer seems to lie in the different “Count” Concepts I have in code “ Lines “ 20, 50 and 80. Modules seems to be an Object of a collection of things. These are in turn all within the collection Sheets object. Misleadingly these “Things” are shown identical to what most of us think is a “Module” like one wot ( What ) we insert. Misleadingly again, ( at least in my Excel,  ( XL 2007 ( German )  )  ) the warning thrown up before I attempt to delete these “Things” refers to the “Things” as “Worksheets”. ( I guess it should refer to them as sheets, or wotever ( Whatever ) they are.

 Maybe Bill gates or whoever never got around to documenting it properly or it got lost in the ever increasing universe of VBA. Unfortunately I lost the MrExcel Thread I lurked, ( where Rory explained this one to do with a throw back to old Code Modules ) in the ever increasing Universe of MrExcel Threads. 

Alan Elston  _(o¿o)_
( Doc AElstein ) ---o00o---`(_)`---o00o---    ___o00o---`(_)`---o00o___      ஜ۩۞۩ஜ ..  ‹(•¿•)›..

P.s.
 Similarly bad explained the___ : ___ for putting 2 “ Lines “ of code on 1 “ Line “. I seem to have two  concepts of lines here. In each of my code “ Lines “ numbered 20, 50 and 80 I have  2 code “ lines “ looking from the point of view of how the code is executed. But looking at how I am able to number the “ Lines “ I have only one code “ line “ per code “ line “. I mean this will not work

```
20 Let CntW = ThisWorkbook.Worksheets.Count:25 Let CntS = ThisWorkbook.Sheets.Count
```
( And note the whole “Line”, that is to say both “lines” !? turn Red indicting where the error is,  – again misleading as clearly the second bit of the “Line” or second “line” is in error ) 

 So my concept of count must be modified to allow for two Line Count Concepts which will give me counts allowing for a difference in 3 in total for the entire code.


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## Richard U (Jan 26, 2016)

Do not confuse a universal language with the infinite diversity of ignorance.

math is indeed a universal language, regardless of how many people can accidently or deliberately throw a spanner in the works.


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