# It's not just the illiteracy, it's the innumeracy!

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#### Blast it Tom!

##### Well-Known Dweeb
TRF Supporter
You guys have said it all. The curriculum we used for our kids required writing checks and making change and balancing your checkbook and properly writing out numbers - real world math. And yeah - downsizing packages and keeping the price the same is insidious. But my wife & I are wise to their wiles!

#### stealth6

##### insert witty tagline here
Umm, more like $1.53 each. Ummmm, except then he wouldn't "have money left over". In fact he would be out$310,000.
Now if he gave everyone $1.52 each, then he would some left ($2,960,00 in fact).
Basic math.

ssixsixsix

#### Blast it Tom!

##### Well-Known Dweeb
TRF Supporter
I just thought about that time a news network reported that Columbia was travelling 18x the speed of light when it broke up over Texas... You just don't even have the rudiments of basic physical understanding of the world you live in to let that one go by...

#### Bat-mite

##### Rocketeer in MD
I'm having trouble even getting my kids to use a calculator. They just want to ask Siri.
This is part of the reason why we home school and limit kids' screen time to 40 minutes a day.

#### Blast it Tom!

##### Well-Known Dweeb
TRF Supporter
This is part of the reason why we home school and limit kids' screen time to 40 minutes a day.
AND BUILD GIANT ROCKETS! Wow, your profile pic!

#### Bat-mite

##### Rocketeer in MD
Here's a stumper that requires either a calculator or pencil and paper.

If watermelons cost $12 a dozen, how much are a 100 watermelons? #### Blast it Tom! ##### Well-Known Dweeb TRF Supporter$100

ETA: I had to set that up using quaternions....

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#### stealth6

##### insert witty tagline here
Here's a stumper that requires either a calculator or pencil and paper.

If watermelons cost $12 a dozen, how much are a 100 watermelons? Ummmm......no real need for a calc/pencil/paper - that one was pretty simple to do in the head. BUT! - The real problem is that the second sentence is problematic grammatically. The way it's written, there is no actual correct answer. The closest would actually be that there are 100 watermelons, (not that they would cost$100).

ssixsixsix

#### Blast it Tom!

##### Well-Known Dweeb
TRF Supporter
Ummmm......no real need for a calc/pencil/paper - that one was pretty simple to do in the head.
BUT! - The real problem is that the second sentence is problematic grammatically. The way it's written, there is no actual correct answer. The closest would actually be that there are 100 watermelons, (not that they would cost $100). But this thread is about innumeracy, not illiteracy. ssixsixsix I'm a show-offy engineer, not a grammarian! (but you are correct!) #### Donnager ##### Well-Known Member Our behavior with regard to this pandemic is as much evidence to the innumerate nature of our public as anything I've ever seen. #### cbrarick ##### Wildman CT I just thought about that time a news network reported that Columbia was travelling 18x the speed of light when it broke up over Texas... You just don't even have the rudiments of basic physical understanding of the world you live in to let that one go by... the dilithium crystals must have given up. Poor Scotty! #### BABAR ##### Builds Rockets for NASA TRF Lifetime Supporter TRF Supporter There are three types of ‘Mericans. Those who can count and those who can’t. #### Bowman ##### Well-Known Member My wife is a nurse and consequently I am very good at drug calculations . She asks me from time to time to check her calcs. Right all the time I think, but she likes to check answers sometimes if the answer is unusual. Trainee nurses have to score 100% on the calculations exam. My wife teaches that subject. Nurses work under a terrible load and sometimes have to make those calculations at bedside in emergent situation and possibly 14 hrs into a 12 hr shift. It's scary when you think about the chain of events that must go right in order to ensure that you receive the proper dose of some drug. From the tired and over-worked doc placing the order, to the pharma company properly labeling and filling the product vial, to the pharmacy (rare) or pyxis being loaded and working correctly, to the nurse at the bedside interpreting the order, verifying the dose and administering the med. There's a lot of opportunity for error. Considering the possible problems I am astounded that there are not legal restrictions on shifts worked and hrs worked for some medical professionals. There is for truck drivers but not for those who literally have our lives in their hands. I know the claim is that statistically the hours aren't a significant factor in negative outcomes but I find it hard to believe. #### Blast it Tom! ##### Well-Known Dweeb TRF Supporter Nurses work under a terrible load and sometimes have to make those calculations at bedside in emergent situation and possibly 14 hrs into a 12 hr shift. It's scary when you think about the chain of events that must go right in order to ensure that you receive the proper dose of some drug. From the tired and over-worked doc placing the order, to the pharma company properly labeling and filling the product vial, to the pharmacy (rare) or pyxis being loaded and working correctly, to the nurse at the bedside interpreting the order, verifying the dose and administering the med. There's a lot of opportunity for error. Considering the possible problems I am astounded that there are not legal restrictions on shifts worked and hrs worked for some medical professionals. There is for truck drivers but not for those who literally have our lives in their hands. I know the claim is that statistically the hours aren't a significant factor in negative outcomes but I find it hard to believe. My daughter is an ER nurse and I couldn't agree with you more! I'd give you all 10 of my thumbs up if I could! Yet despite what for me would be a debilitating lack of sleep, working and caring for 3 little ones, she hasn't made that kind of an error yet. Still, as you note, it just seems like a cord stretched really thin. #### DuctTapeandRocketFuel ##### Well-Known Member Most convenience stores don't give you a receipt any more, unless you ask. They don't want you tracking how much money you are spending. #### prfesser ##### Lifetime Supporter TRF Lifetime Supporter The message I took from that was even when using a computational aid (spreadsheet, computer, calculator, whatever) it was very useful to be able to think through the math as a sanity check and make sure the answer makes sense. It helps prevent GIGO (Garbage In, Garbage Out). Oh yeah!!!! In my gen chem lectures/problem solving I emphasized that the answer MUST agree with physical reality. On examinations especially, the ability to put together your calculator answer and the knowledge from the course was required. Instead, I saw answers to questions like "How many atoms are in 13.3 grams of sodium?" that ranged anywhere from 1.24E-17 (REALLY?!? a tiny fraction? Them's BIIIIG atoms!) all the way up to the correct answer, 3.48E+23. And beyond, of course. "But...but... that's what the calculator said." "Your calculator is an idiot." But my approach saved thousands, tens of thousands, possibly hundreds of thousands of lives! It kept the idiots out of medical school. Best -- Terry #### Antares JS ##### Professional Amateur I saw answers to questions like "How many atoms are in 13.3 grams of sodium?" that ranged anywhere from 1.24E-17 (REALLY?!? a tiny fraction? Them's BIIIIG atoms!) And the aforementioned cancer just came out of remission... Ugh... #### modeltrains ##### Well-Known Member And yeah - downsizing packages and keeping the price the same is insidious. But my wife & I are wise to their wiles! And speaking of their wiles, how about this from Harvard Business Review, But does supersizing make sense in more typical contexts? Actually, no. It turns out that the smart strategy can be to do just the opposite. To begin with, reducing product size for a given (or less than proportionally reduced) price can be a great cost-cutting strategy when most of the costs are variable rather than fixed, when the production and transaction costs of selling more units are low, and when the cost of packaging increases with product size. In this context, downsizing can increase perceived benefits by appealing to: • Consumers who need smaller quantities, such as the expanding number of single households, or to those who concerned about perishability and storage costs. • Consumers with liquidity constraints, who need sizes that fit their budget constraints, whether it is single-usage packs or phone services priced by the second. • Consumers who want to better control their consumption and who recognize the limits of their willpower and are prepared to pay a premium in order to reduce temptations, whether in the form of chocolate candies or internet access. • Consumers whose unit of value differs from the producer’s. For example, consumers treat the roll as the basic unit when buying toilet paper and usually don’t pay much attention to the size of each roll, let alone each sheet. But from the manufacturer’s perspective, the issue is simply how much paper they can sell. There is an opportunity, therefore, to sell less paper for a given price simply by offering more but smaller rolls, with smaller sheets, which explains why the sizes of rolls and sheets have shrunk considerably over the years. • Consumers who take smaller sizes as a signal of quality and scarcity, which is common in luxury goods. #### modeltrains ##### Well-Known Member Related content to previous post, Larger packaging does not always equal lower prices Published in Food on 15-01-2018 Yoni Van Looveren Many supermarket items in large packaging are cheaper by the kilo or the liter than small packages, but in some cases, the reverse is true. Much depends on the standard packaging. Many approaches On average, it is cheaper to buy larger quantities in supermarkets, but if a certain type of packaging does not sell too much, the reverse is often true. Whenever that happens, it is cheaper to buy smaller quantities. “The consumer did not have any information back in the day, but now he has all the tools to compare prices”, Snoeck said. “Manufacturers and supermarkets realize that and that is why there is a conscious move to change packaging to avoid that the consumer has an easy one-on-one comparison. The more packaging and quantities there are, the more difficult it is for the consumer to check which one is actually the cheapest.” A remarkable fact is that plastic packaging is usually more expensive than other types, although it is cheaper to manufacture. “The entire industrial world is trying to limit the environmental impact its products have during their entire cycle. I do not exclude the idea that they therefore increase the price of their plastic version compared to other packaging options”, Fost Plus’ Fatima Boudjaoui said. #### Funkworks ##### Well-Known Member I remember reading a summary of a study that compared the types of mistakes people made when doing math in their heads, vs doing math on a calculator. I forget the specifics, but when asked to calculations in their heads, any mistakes these folk made were in the less significant parts of the answer. But when doing calculations on a calculator, the errors were much larger, like orders of magnitude errors. When using a calculator, it was easier to fat finger an extra digit, or get the decimal in the wrong place. The message I took from that was even when using a computational aid (spreadsheet, computer, calculator, whatever) it was very useful to be able to think through the math as a sanity check and make sure the answer makes sense. It helps prevent GIGO (Garbage In, Garbage Out). Not aware of these studies but I'd say if orders of magnitudes are involved, that's when computers are more likely to be used. In any case, double check everything in as many different ways possible, for sure. #### Cape Byron ##### The BAR formerly known as Skippy-2 TRF Supporter Of course, the pandemic pretty much killed use of cash here in the states. I haven't used cash for a single purchase in 14 months. I use it to give my younger son his allowance; that's about it. When he buys something I use a credit card and he pays me the cash. This summer he turns 14, gets a bank account and wi rarely touch cash again... Yeah I rarely touched cash after having kids but, I think for a different reason... #### Jimmy ##### Well-Known Member TRF Supporter Innumeracy is just like illiteracy, except it's with numbers and not reading/writing. Went to Taco Bell for some cheap takeout; two tacos, one bean burrito, no sides, no drinks. Bright-eyed cashier blithely says$10.24". whaaaAAAAAT?? for THREE cheap items?

She finally figured out that it was wrong, new total was $6+. Still sounded high. Looked at the receipt; no, I didn't want the SUPREME burrito, wanted the BEAN burrito. Second gal, assistant manager I guess, came out to fix it. Apparently she couldn't figure the difference between the two items, so she just refunded me a supreme, then sold me the bean. The calculator was a wonderful tool when it came out, but now the downside really shows its face. The first gal didn't even recognize that the price was about three times what it should have been, and the second apparently couldn't do that advanced math. You know....percentages. Not just the general public; even college students. In an attempt to generate some thinking, I asked a first-year chem student what 4x7 was. Poor gal just sat there. Dropped the course shortly thereafter. Some guys can't count past 10 unless they take off their shoes, and they're stumped past 20 unless they take everything else off. And if anyone thinks that it's bad now, just wait until retailers figure out just how little consumers know about prices and money. You will see "Just 49 cents per can, or SAVE and get a dozen for just 7.50!!" in every possible anti-consumer advertisement. And as most transactions are electronic these days, people will toss the receipt into the trash, never knowing that the cashier charged$10 for the can of Coke HE'S drinking. And kept the change.

Best -- Terry

#### les

##### Well-Known Member
TRF Supporter
Oh yeah!!!! In my gen chem lectures/problem solving I emphasized that the answer MUST agree with physical reality. On examinations especially, the ability to put together your calculator answer and the knowledge from the course was required.
One of my engineering college courses, the professor would take off credit for a wrong answer, and subtract additional credit if the answer was way off. If you added a note that the answer did not look reasonable, but you didn't know where the mistake was, he wouldn't take the additional credit off.

Many students complained, but he explained that "you need to know if the answer makes sense or not"

Another course gave you a problem without all the variables, such as "What is the weight of the air in this classroom" or "How many acres are trees are required for the printing of the Sunday Times". We had to document our assumptions, go through the math, and then discuss if our answers seemed reasonable. One of the greatest classes to handle real world engineering where everything is not neatly defined......

#### OverTheTop

##### Well-Known Member
TRF Supporter
We used to play Monopoly with our daughter from an early age and she was the banker most of the time. That encouraged her to be able to add and subtract quite well.

#### Alan Whitmore

##### Well-Known Member
There was a time before the invention of the calculator (first the desk-top and then the battery-powered hand-held) when those of us who were technically inclined used a slide rule. My father was an engineer, and he taught me how to multiply and divide using a slide rule before I entered first grade. The slide rule was really only accurate to about 3 significant figures, but that was usually good enough, and you could use it anywhere, with or without electricity of any sort. The important point about slide rules in this discussion is that they only gave you the digits of the answer: it was up to your good sense to put the decimal point where it belonged.
For example, you could divide 17 by 3 and get the digits "5666". To get the correct answer, you needed some practical sense of where the answer should be. Most people could quickly recall that 15 divided by 3 was 5.000, so you could immediately sense that the actual answer you were looking for was 5.666.
Innumerate people never could figure it out, and now, when their electronic devices give them something absurd, they don't see the error.
Arithmetic is one of the hardest of the "hard sciences" but it is still possible for YOU or anybody ringing up your bill to make a mistake, and that's when a certain subjective "feel" for the data comes in. All rational humans need the ability to evaluate a figure, a sum, or a statement and say (or think) "That's not right." Immediately. Then, the process of skeptical evaluation comes in.
That's a sermon for another Sunday.......

#### prfesser

How about the fact that many products are no longer sold in their typical size.
Coffee used to come in 1lb packages (or larger), other things as well, Triscut crackers for example.
Why? Because the vendors know that most people won't pay enough attention to know that they just paid the same price for less goods.
So instead of simply being honest and pricing the item based on cost and of course margin, they prefer to take the deceptive approach and count on us not noticing. Of course if you ask they will come up with some absurd reason like "the smaller package is more efficient to ship and stock.."
How dumb do they know we are?
The usual approach is to downsize the item, a little at a time, at the same price. Then "30% bigger!!" for twice the price. Candy bars...I watched through the years as a plain Hershey bar got a little smaller, then a little smaller. Then it went back to the original size but it was a dime instead of a nickel. And so on.

I trust most companies to behave ethically about as far as I can throw Jeff Bezos.

Best -- Terry

#### OverTheTop

##### Well-Known Member
TRF Supporter

 Just bought one on eBay

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#### Funkworks

##### Well-Known Member
The usual approach is to downsize the item, a little at a time, at the same price. Then "30% bigger!!" for twice the price. Candy bars...I watched through the years as a plain Hershey bar got a little smaller, then a little smaller. Then it went back to the original size but it was a dime instead of a nickel. And so on.
And that would explain inflation at least partly: when every company tries getting more $for their product, every product ends up cost more (which is the same as a dollar losing value). #### jqavins ##### Helpful Smartass TRF Supporter Went to Taco Bell for some cheap takeout; two tacos, one bean burrito, no sides, no drinks. Bright-eyed cashier blithely says$10.24". whaaaAAAAAT?? for THREE cheap items?

She finally figured out that it was wrong, new total was $6+. Still sounded high. Looked at the receipt; no, I didn't want the SUPREME burrito, wanted the BEAN burrito. Second gal, assistant manager I guess, came out to fix it. Apparently she couldn't figure the difference between the two items, so she just refunded me a supreme, then sold me the bean. Innumeracy is bad, but only part of the problem. The innumeracy is growing worse, but the stupidity is and has always been our constant companion. Agree with the blank stares from sales clerks. I had a purchase that was$4.87. I had some loose change so I gave the clerk \$5.12. They balked because I gave them too much. I responded I didn't want a lot of change in my pocket. They we still puzzled so I told the person to just enter the amount. I finally got a single quarter to replace the 5 pennies, 2 nickels, and dime I would have ended up with.
I had a similar experience once. In my case the cashier didn't balk, but just put the amount tendered into the register then looked at the answer. Then she looked at me, looking somewhere between merely impressed and awed and said "How did you do that?" I quoted Terry Pratchet: "We used to have a thing called education."

Kids these days don't even know how many pence to a shilling, for shame!
And they don't even know how many hands high their horses are.

I do agree that innumeracy is a real problem, but rememner that skills one generation considers essential become obsolete quite often. Arithmetic shouldn't be one of them, if you ask me, but this is really not a surprise, and not a historical outlier.

Of course, the pandemic pretty much killed use of cash here in the states.
I've lost count of all tne things that have killed cash in the last few decades.

I just thought about that time a news network reported that Columbia was travelling 18x the speed of light when it broke up over Texas...
Wow, I'm really glad that wasn't true! Imagine the damage when a superluminal object weighing many tons hits the atmosphere.
the dilithium crystals must have given up. Poor Scotty!
But Scotty was the engineer on the Enterprise, NCC-1701. I don't know who the engineer was on the Columbia (NX-02).

The real problem is that the second sentence is problematic grammatically. The way it's written, there is no actual correct answer.
An old chestnut asks "Is it seven and six is twelve, or seven and six are twelve?" Of course, neither is correct; seven plus six equals thirteen. But falling for that one is nothing new.

Our behavior with regard to this pandemic is as much evidence to the innumerate nature of our public as anything I've ever seen.
The two factors that most affect the spread of COVID19 are the density of the population and the density of the population. I don't think innumeracy has anything to do with it; most people who don't want to wear a mask or get vaccinated are not looking at the numbers, whether they would be able to understand those numbers or not.