## The alligator eats the big number

## The alligator eats the big number

(OP)

I keep lurking on an editor's Facebook page, and somebody posted this. How to keep track of what

Some engineering type replied with righty tighty, lefty loosey.

*greater than*and*less than*mean.*A*>

*B*,

*C*<

*D*

Some engineering type replied with righty tighty, lefty loosey.

--

JHG

## RE: The alligator eats the big number

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: The alligator eats the big number

Just to soap-box on the failure in math teaching, and what isn't taught and should be -

Mathematics is discovered and has to be discovered independently by everyone who wants to use it, though that discovery process can be helped with a lot of hinting. What is taught in math class isn't mathematics. It is tools that are invented to describe the mathematical discoveries. And symbols like "<" and ">" typify that sort of invention. So what a math teacher is often doing is teaching the invention, which is often unclear to students who haven't discovered what the invention is for.

Parents (usually) teach children to count - the sounds and shapes related to that are arbitrary inventions as demonstrated by the wide variety in various cultures and languages. However it is up to the child (and eventually adult) to eventually discover the underlying math that the invention is used to externalize. I think the breakthrough must be the realization that one scoop of ice cream isn't as good as two.

Order of evaluation rules - an invention, arbitrary though convenient. Matrix representations - wonderful invention, and so on.

The sad part is that it is difficult to evaluate students on anything except mastery of the invention. Even so called Common Core/New Math, intended to fix this problem, is just another pile of arbitrary inventions which many students can use without discovering what they are for.

What I can say is that discovery doesn't happen just because a teacher is more insistent or gives a poor grade. It doesn't happen because the student is even more desperate. In this many math courses resemble the Saw movies where those trapped in the machine have to already know the way it all works to avoid injury. Small wonder that, in one book on teaching math, the author wrote that when he tried to figure out what goes wrong by asking adults about math classes the general response was a look of horror and a great desire to change the subject.

## RE: The alligator eats the big number

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: The alligator eats the big number

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

## RE: The alligator eats the big number

The Order of Operations isn't arbitrary...mostly. The OoO comes from the logic of mathematics, and is organized based on how we write equations and how most languages read. Kids are first taught (around 3rd grade, IIRC) that multiplication and division precede addition and subtraction, then later they are introduced to parenthesis and exponents and where they fit into the OoO. In the USA, they learn the acronyms MDAS, then PEMDAS. Unary operations such as factorial are left out because most students will never use them. They fit in between parenthesis and exponents.

Here is how the combination of logic and language leads to the OoO:

The most basic two-number operation in mathematics is addition. Subtraction is simply the opposite of addition (and is often thought of as adding a negative number), so it makes sense that neither addition nor subtraction have priority over the other. These two operations are thus performed left to right, in order, because most languages read left to right.

Multiplication represents repeated addition, and multiplications can be expanded into a series of additions, so it makes sense to evaluate multiplications before additions and subtractions. Division is simply the inverse of multiplication (and can be thought of as multiplying by the reciprocal), so it makes sense that neither multiplication nor division have priority over the other. These two operations are also performed left to right, in order, before additions and subtractions.

Exponents represent repeated multiplication, and exponents can be expanded into a series of multiplications, so it makes sense to evaluate exponents before multiplications and divisions.

Parentheses are used to modify the normal order of operations and get attention first.

There are some disagreements among mathematicians about how to handle certain things (e.g. is 6/2y equivalent to [6/2]*y or 6/[2y]?), but for the most part the OoO that people need for their everyday lives (and they do need it) is pretty simple and not subject to disagreement.

So, how do people use the OoO in real life? For starters, adding up the total value of a bunch of coins of different denominations or finding the total square footage of several rooms for calculating the amount of flooring to buy. The only way to get the correct answer, of course, is to multiply before adding.

Fred

============

"Is it the only lesson of history that mankind is unteachable?"

--Winston S. Churchill

## RE: The alligator eats the big number

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: The alligator eats the big number

The area operation is exceptional as the units matter. Adding feet to square feet makes little sense. but for non-dimensional calculations: 5+4*4 could be interpreted as 5 enter, 4, plus, 4, times in a RPN variation to result in 36 rather than 21.

Or there could be a system that has no subtraction and depends on adding the 2s complement.

Thinking more on it - consider this progression

2 TIMES 2 IS 4.

2 X 2 = 4

2*2 = 4

2x = y

As the math gets more complicated the invention of symbols and meanings varies according to a mutually agreed upon basis. So 2x is somehow different from 23; the multiplication symbol has evaporated, having shrunk in each stage. I skipped the one where it's s dot; that dot is sometimes simple multiplication or represents the vector dot product, which makes no sense applied to a scalar value.

People are familiar with some invention so they think that it's the same as the math it is intended to represent or that it's the only way to do so.

## RE: The alligator eats the big number

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: The alligator eats the big number

3DDave, 5+4*4 = 21, not 36.www.PeirceEngineering.com

## RE: The alligator eats the big number

## RE: The alligator eats the big number

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: The alligator eats the big number

For sure. We never stayed the course, so I don't know what would have happened. Certainly, one concern I had was the hard association with physical things might make it more difficult to deal with the abstractness of the later math, like algebra, etc.

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

## RE: The alligator eats the big number

I will repeat, the OoO is not arbitrary, but comes from the logic of mathematics. Math is not ever done strictly left-to-right. Also, I have been using RPN since 1974 and I apply the OoO every time I work out a problem.

Fred

============

"Is it the only lesson of history that mankind is unteachable?"

--Winston S. Churchill

## RE: The alligator eats the big number

John R. Baker, P.E.(ret)EX-'Product Evangelist'

Irvine, CA

Siemens PLM:

UG/NX Museum:

The secret of life is not finding someone to live withIt's finding someone you can't live without

## RE: The alligator eats the big number

The examples chosen here are simplistic, but OoO follows the rules applied from evaluation of polynomials:

A*x^3 + B*x^2 + C*x + D

Think of the algebraic chaos if everyone did OoO differently, i.e., if exponentiation was trumped by multiplication, and addition trumped multiplication or exponentiation. No parentheses are required for the polynomial above, because OoO is automatically understood and applied. Therefore, no parentheses should be needed if the variables are replaced with actual numbers.

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

## RE: The alligator eats the big number

John R. Baker, P.E.(ret)EX-'Product Evangelist'

Irvine, CA

Siemens PLM:

UG/NX Museum:

The secret of life is not finding someone to live withIt's finding someone you can't live without

## RE: The alligator eats the big number

All these arguments do demonstrate that the invention can completely overwhelm the underlying discovery.

"Math is not ever done strictly left-to-right." says someone who has never programmed in Postscript.

## RE: The alligator eats the big number

You need to try APL. There is no math hierarchy whatsoever, beyond brackets.

--

JHG

## RE: The alligator eats the big number

Haskell is the way to go, just ask the Haskell programmers.

By the by - my father was a systems programmer for IBM from the late 1950s. Plenty of wayside languages in his library. JOVIAL*, VULCAN, PL/1. But APL really stood out by needing a custom terminal to program in it (no GUIs to have virtual keyboards.) Though IBM did have some cryptic keys on their terminals anyway.

*not JUPITER - too many languages. crossed wires with recent Jupyter thread of Python.

## RE: The alligator eats the big number

Interesting. I’ve never seen a term split arbitrarily like that, the use or lack of an operator is important as my 7th grade algebra teacher used to say. 6/2y = 6/(2*y).

## RE: The alligator eats the big number

I’ll see your silver lining and raise you two black clouds. - Protection Operations

## RE: The alligator eats the big number

2

y

mul

div

## RE: The alligator eats the big number

TTFN (ta ta for now)FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

## RE: The alligator eats the big number

If you're hand solving your own equation, go for it. Otherwise use parens to disambiguate it. Even if there's no ambiguity about it in the first place.

I’ll see your silver lining and raise you two black clouds. - Protection Operations

## RE: The alligator eats the big number

www.PeirceEngineering.com

## RE: The alligator eats the big number

-Dik

## RE: The alligator eats the big number

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

## RE: The alligator eats the big number

BUT the image that comes to mind immediately is that the vertical distance between the two lines corresponds to the relative size of the operands. The side of the operator where the vertical distance is big corresponds to the big operand and the other side where the vertical distance is little/zero corresponds to the little operand.

I wonder if that's something that was taught to me way back in grammar school and faded into my subconscious. I'm guessing it probably was.

At any rate that seems way more intuitive than righty-tighty / lefty loosie. I'm not even sure how RT/LL helps us remember anything (outside of valves, fasteners, and most importantly... beer bottle caps!). Maybe you're supposed to focus on the L's in lefty-loosie and think "Less than"? Or maybe it was just a wise-crack making fun of the person who asked the question?

=====================================

(2B)+(2B)' ?

## RE: The alligator eats the big number

I have solved part of this problem by carrying a pocket knife with a bottle opener, and by not buying beer with twist-off caps. I am a beer snob. I prefer micro-breweries, especially if they are in walking distance of where I live.

--

JHG

## RE: The alligator eats the big number

A beer connoisseur, I ain't.

I won't admit to drinking Bud... but Blue Moon with a slice of orange is nice.

=====================================

(2B)+(2B)' ?

## RE: The alligator eats the big number

John R. Baker, P.E.(ret)EX-'Product Evangelist'

Irvine, CA

Siemens PLM:

UG/NX Museum:

The secret of life is not finding someone to live withIt's finding someone you can't live without

## RE: The alligator eats the big number

The newspaper says the answer is 5... go figgure?

-Dik

## RE: The alligator eats the big number

But, it does violate PEMDAS

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

## RE: The alligator eats the big number

-Dik

## RE: The alligator eats the big number

## RE: The alligator eats the big number

-Dik

## RE: The alligator eats the big number

## RE: The alligator eats the big number

-Dik

## RE: The alligator eats the big number

230 - 220 / 2 .... PEMDAS tells me 120 (230-110), just like dik said 21 Sep 21 19:36.

Then my confusion started with dik's post 22 Sep 21 02:10

> I got caught...

In what way? I thought 120 was right.

> although the answers are 120 and 5... the pHD guy answers 5!, which is also 120.

How is 5 also 120?

> The allowable answers do not show 5!

5 is an allowable answer on the graphic posted 21 Sep 21 19:36. But why do you want it as an allowable answer?

> I am reminded the "F" in PEMDAS covers this contingency.

wut?

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(2B)+(2B)' ?

## RE: The alligator eats the big number

I missed it... the exclamation mark is 5 factorial which is 120 (5x4x3x2x1). Fortunately the permissable answers did not include the '!' mark, but the question did.

was humour... that's why I added the DONUT comment... Dave started it.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: The alligator eats the big number

I like it. That's a pretty sly setup. One can easily interpret the ! as exclamation as posted, rather than interpretting it as factorial. Now I see why you said the allowable choices 120 and 5 (not 5!) further obscure the situation....

Someone had to set up those numbers pretty carefully so that the two answers resulting from two choices of OoO (PE-MD-AS or PE-AS-MD) are related to each other through a factorial. That didn't happen by accident! (good thing "accident" isn't a number, I don't have to clarify my meaning).

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(2B)+(2B)' ?

## RE: The alligator eats the big number

## RE: The alligator eats the big number

pete... I don't know if it was intentional...

-Dik

## RE: The alligator eats the big number

## RE: The alligator eats the big number

I dunno. It's not like you can pick some random expression like

2 x 22-20

or

-714+717 x 2

...and expect the right OoO to yield an answer which is the factorial of the answer you'd get from applying the wrong OoO.

Right?

oh, wait...

I know a phd who said the answer to the first is 4!

And the answer to the second was 6!

Maybe I succeeded in undermining my own point.

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(2B)+(2B)' ?

## RE: The alligator eats the big number

-3628790 + 3628795 x 2 = 10!

Sorry, now that I finally got the joke, I just can't stop.

The 6!, 8!, 10! all follow the same pattern, I could keep going with the same approach with even integer factorials ad infinitum.

But I admit it's not quite as funny the 4th and 5th time (and when you have to get out your computer / calculator to figure it out!)

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(2B)+(2B)' ?

## RE: The alligator eats the big number

Another OoO problem

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

## RE: The alligator eats the big number

Apart from this if you want to learn something new then the DevOps course will boost your knowledge.

## RE: The alligator eats the big number

My glass has a v/c ratio of 0.5

Maybe the tyranny of Murphy is the penalty for hubris. - http://xkcd.com/319/

## RE: The alligator eats the big number

## RE: The alligator eats the big number

It's 120.

## RE: The alligator eats the big number

Maybe 'penalty for hubris' is just a moralistic way of describing entropy.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

## RE: The alligator eats the big number

Hey wait a minute, is this SPAM?

Reported.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

## RE: The alligator eats the big number

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

## RE: The alligator eats the big number

"Splunk" or "Spelunk"? I use the word "nutate" whenever I can.

--

JHG