Reader cesar sent this astounding example of innumeracy with a note:
This is for real…..The dramatis personae are Brian Williams and Mekita Rivas, member of the NYTimes editorial board. (Apparently somebody at NPR also fell for it.)
You can spot the error immediately if you know that a million million is a trillion.
But, but, but . . . it was in a tweet, so it must be true. Right?
I am now reading that apparently what she said had been checked, or “checked”, by several people in the newsroom??????????
“Eric Weinstein
@EricRWeinstein
So MSNBC, The New York Times, & the Washington Post are directing our national conversation. I don’t think I know anyone like @BWilliams MaraGay & @MekitaRivas in our podcasting movement.
We all make dumb mistakes. But this propagated frictionlessly within a staffed news room.”
Frictionless? Perhaps the newsroom is staffed with Coleridge’s ‘thousand thousand slimy things’.
A million million is a billion and a billion billion is a trillion. What USians call a billion is actually a Millard.
The UK has adopted the US terminology.
Hi Graham, been a long while since I have seen a post from you on a forum, glad you are still about.
Also glad there is still someone around who knows the difference between a billion and a milliard. It is a pity the UK decided to take on the incorrect usage of the term million.
My post would have made more sense if I had finished with the correct word, ie billion, not million.
Milliard.
I’m rather attached to the old term for ten thousand – a myriad.
How much is a brazilian?
$6,000CDN if your name is Jessica Yaniv.
Yeah that always confuses me. I can never remember who is talking about what when. Same with gallons.
Alas, UK and US, divided by a common language. But this was about American finances, not British, so you’ll just have to translate.
+ 1
🙂
I sympathize with the old Brit method because it saves needing new names for awhile.
But it’s inconsistent and can be bettered. To be consistent, call:
ten tens = a hundred = 10**2 (as usual)
hundred hundreds = a thousand = 10**4 (i.e. ten ten ten tens, as nobody does)
thousand thousands = a million = 10**8 (going way up!)
million millions = a billion = 10**16
billion billions = a trillion = 10**32
So both the USian trillion and the old British trillion are, pardon me, FA, compared to my trillion.
All the others in between and for a fair ways above have perfectly sensible names, such as
ten thousand billion trillion is !0**53
as long as 1+4+16+32=53, which it is.
We can get all the way up beyond the number of elementary particles in the visible universe without strain, as long as you hate powers of 10, which however is the right way to do it.
ERROR : 53 should be 57
ERROR is an error. C’mon, don’t expect me to get arithmetic correct.
There are three kinds of people in the world. Those who can do math and those who cant.
LOL!!!
There are 10 kinds of people in the world, those who understand binary and those who don’t.
That one makes sense.
There are two kinds of people in the world. Those who believe there are two kinds of people in the world, and those who don’t.
I’m reminded of, “Those who know they don’t know, and those who don’t know they don’t know.”
In 10% of relationships, one person is unfaithful.
I’m just trying to work out if it’s my wife or my girlfriend.
tish boom!
No, there are 53 kinds of people in the world:
Those who can do math as well as arithmetic, those who can do math but get their arithmetic wrong usually, those who can do arithmetic and have no idea what math really is, and those who vote for Drumpf despite it being against their interests (as well as that of the entire human species).
Correction to the post…I believe that person in the video is not Mekita Rivas, but Mara Gay, who is on the NYTimes editorial board.
And she is repeating a tweet sent out by Mekita Rivas..who is also a journalist.
So, it’s actually worse than at first blush, so to speak.
https://www.washingtonpost.com/politics/2020/03/06/no-michael-bloomberg-couldnt-give-every-american-1-million/
🙀
“You can spot the error immediately if you know that a million million is a trillion. ”
You can also spot the error if you have some sense of proportion. The idea that Bloomberg could make instant millionaires of everyone in the US with just the money he spent on his failed campaign should set off alarm bells and exclamations of “Wait! That can’t be right!” Innumeracy is rampant here in the US. I can see where the on-air people have a reasonable excuse as, presumably, most stuff is prepared by others and they just read it. I could easily make that mistake if I was reading it off a teleprompter. It’s the people in the back that really screwed up.
For some reason I’m reminded of U.S. Commerce secretary Wilbur Ross in an interview describing the scope of a certain trade agreement as “intergalactic.”
All you have to do to spot the error is notice that both $500,000,000 and 327,000,000 have two commas, the first of which is followed by six zeros. Take ’em away and it’s clear Bloomberg could’ve given Americans the equivalent of $500 split between 327 people, or a buck and some change apiece.
Speaking of which, I’m still waiting for my check from George Soros for going out and protesting Donald Trump’s local visit. It’s been damn near two years now, George; shake a leg already, willya?
Yep, the numbers were on consecutive lines, 500 million, and
375 million.
Cross off the million and there it is.
I just use the unit “gazillion.”
Didn’t Dubya say that’s the number that comes right before a Brazilian? 🙂
😂
And when he ordered a quiche he pronounced it a quickie…
If you have five hundred million dollars, or apples, or cookies, how many people could you give a million dollars, or an apple, or a cookie to?
Five hundred.
It is a stretch to regard the various names for large numbers as being “math”.
That is not to excuse those talking, but empty, heads, or detract from the mirth and hilarity here.
Teaching kids elementary manipulations with certain numbers written as powers of 10 is certainly important. Remembering which one is called a hundred, or million, or billion, or trillion is like which one is called NY, which LA etc. Math as a language consists of assertive sentences (facts), interrogative sentences (equations) imperative sentences (algorithms or programs or apps) in a simplistic but useful ‘philosophy’ of math.
I hope Brian Williams isn’t another one of those Canucks who ‘made it’ in the US as TV talking heads. The effect on the brain of living south of the border for awhile surely isn’t that bad.
A propos nothing too much: aren’t some equations assertions (propositions)? (E.g., an identity.) I seem to remember this ambiguity coming up in grade 11 trig for some reason.
I guess I’d just say that
(x+1).(x+2)=x.x + 3.x + 2
is not an equation, it’s an assertion, and should be preceded by ‘For all x,…’ assuming high school level of generalities. And it happens to be a true statement.
And
(x+1).(x+2)=17
is an equation, should be preceded by “What are all numbers x such that…” followed by a question mark.
I wonder how many high school teachers ever think about this, instead of thinking about learning math, say algebra, as some kind of memorization/knee-jerk response to words like ‘identity’ or ‘solve by the following thoughtless sequence of moves’?
It never even occurred to me before going to university for example that, when someone (even maybe a math teacher in spare time) gave you a puzzle to think about, the actual answer might be a proof that it cannot be done. Nor occurred to the questioner. But I’m from the boonies, and my final pre-university math teacher was actually very successful at getting very marginal students through Grade 13 math with some kind of a pass. More than one of the latter ended up teaching that very same math (along with coaching the high school hockey team, maybe).
People in math don’t usually quibble over the fact that many expressions called “equation” that are not really equations. I suppose if you are writing a book, it would be worth getting right. Describing expressions with something more specific, such as “equation” or “inequality”, runs out of gas quickly as the number of such categories are limited only by mathematicians’ imagination. You also run up against other problems. If the first expression in a book is labelled “Equation 1”, what do you call the next one if it’s an inequality? Is it “Equation 2” or “Inequality 1”? “Expression” is suitably vague but, as far as I know, it isn’t used this way.
Working backwards:
An expression is a noun. Equations and inequalities and identities are sentences of various grammatical kinds, as I said earlier.
Labelling is never any problem at all.
“I suppose if you are writing a book, it would be worth getting right.” It is utterly worthless or worse if you are teaching math and get it wrong, so I’d strongly dispute your cavalier attitude there, if I understand.
People who know math do indeed quibble. Your “people in math” sound like a bunch anti-intellectual nitwits wishing to preserve ignorance, for whatever reason.
At a higher level, if, say, you come to General Relativity and Einstein’s equation, the first thing you have to know is: What is it an equation for? The same thing at lower levels in physics and also in math.
Same for inequalities: if they are there to constrain something, you want to know what is being got at before even puzzling out the specifics.
But being more analogous to an identity so an assertive sentence is different. ‘3<2' is a perfectly formed inequality; the sentence just happens to be false.
Math is not fundamentally different from just plain accurate attempts to think, just usually more precise and more notationally involved so needs hard work for most of us.
I think what you are saying comes under the category of pecksniffery. I said that the choice of word matters in some contexts but the use of the word “equation” to refer generally to mathematical expressions of all kinds is perfectly fine. Stephen Hawking once said:
“Someone told me that each equation I included in the book would halve the sales.”
https://www.brainyquote.com/quotes/stephen_hawking_163498
Do you think Hawking was only talking about true equations, and that adding inequalities to his book might be ok? Do you think we should have corrected him that he really meant “expressions” and not “equations”? Of course not.
This kind of thing happens a lot in natural language. Better to make students aware that they will encounter this in the wild and have them think it through.
Hawking, to make his point, had no need at all to enumerate other things which might drastically reduce his book sales. His great abilities, in this case being able to express difficult ideas without technicalities, are not a talent many people have. Despite that, it was a common conjecture that his book sales probably had the worst ratio ever to books actually read!
Many bright people who have or had trouble with math, especially at an elementary level, tend to blame themselves. I suspect it’s more often than not the teaching they suffered through which caused it.
Trying to help fix that might to you be pecking, or nose picking, or sniffing, or sniffling, or whatever you think it to be, but that kind of insult just runs right off me like the rain does. Direct answers to specific points are all that interest me.
Really bad use of words by teachers is not something a young student can solve by “thinking it through” as you say, at least not until many years later, often too late, and especially not in math or physical science.
Perhaps the whole point is that this is not and cannot be entirely natural language. Why don’t you get down to work to see if you can write a useful text in elementary algebra in natural language and your slipshod definitions. If any use at all, I’d be very interested to see it.
“Why don’t you get down to work to see if you can write a useful text in elementary algebra in natural language and your slipshod definitions. If any use at all, I’d be very interested to see it.”
I never suggested that it didn’t matter what words one used in a textbook. In fact, I said exactly that. Go argue with yourself because I’m done with you.
Z/2 symmetry is, as usual, more than welcome.
I find this extremely disconcerting.
Hell, even if Bloomberg gave his entire $40 billion fortune to the American people (for the sake of this post, we’ll pretend that it would come out to $40 billion in cash if he immediately liquidated all his assets), he would be able to give each person about $122 and change.
Also, nothing on a news report should start with the words “somebody tweeted,” though so many do nowadays.
‘Also, nothing on a news report should start with the words “somebody tweeted,” though so many do nowadays.’
The same with (e.g., NY Times) news “ledes” that start with the likes of, “You might think . . . .” or “It might seem odd (or “unlikely”) . . . .”
I thought the UK convention is to call a thousand million a “billiard”, like the game Americans call “pool”, or the Brits call “snooker”. Brian Williams in the video
clip probably was the beneficiary of “new math” in his school days, and his younger colleagues perhaps of the still newer fashions in “de-colonized” math.
Billiards, pool and snooker are three different games. Although they all involve similar principles they are played with different numbers of balls, on different sized tables and with different rules.
We largely go with the US convention regarding the -illions nowadays.
One sure doesn’t need arithmetic skills to make millions. Williams has made many kids feel so much better now. 🙁
Maybe it’s in Dr. Evil money.
If it’s a tweet, no need for checking it. It’s twitter, Jake.
As a mathematician, I’m afraid I don’t find this surprising at all. Inability to do basic arithmetic is something that otherwise educated people actually boast about. Try introducing yourself as a mathematician to a room full of college-educated people, and you’ll see what I mean. “Oh, I could never do maths at school” is an acceptable response in a way that “Oh, I could never read” isn’t.
And we *are* talking about basic arithmetic here, not mathematics. Confusing millions, billions and trillions is an inability to do the basics, like not knowing a verb from a noun.
I concur, the fact that so many well-educated adults cannot perform basic arithmetic is shocking, and pretty depressing. It’s certainly nothing to be proud and shouldn’t be so casually accepted. What’s worse is the sort of thing that this example demonstrates – no comprehension of scale and orders of magnitude, and no critical analysis of whether it is a realistic claim. Before you even get to the maths it should strike an educated person as unrealistic. Common sense means he first has to obtain that money, even ignoring his costs, that’s $1,000,000 from every person in the US!
This highlights a general problem in education. Here in the UK kids are not taught how to calculate, estimate or even appreciate scale. Understanding scale and being able to solve basic back of the envelope problems are crucial skills as an educated adult, but they are only covered briefly in passing.
I’m a maths fan, I have a good mathematical education and genuinely love the subject. However, when I help my daughters with their maths schoolwork I am bored to tears, it’s painfully, drearily dull. It’s no wonder kids learn to dislike the subject. Obviously, learning the basics is critical, but kids need to be shown the beauty and wonder of numbers too. They need to experience the fun of solving interesting problems that are relevant to their lives.
There is no imagination put into maths teaching in the UK, no attempt to show the beauty in numbers and the amazing patterns that lie just below the surface. It’s a crying shame and our kids are being let down massively; they are turned off the subject by their schools at the first opportunity. I can’t see it changing any time soon though, the material appears to be just as boring and unimaginative as it was when I left high school 30 years ago.
+many from another mathy.
Are the wrong people going into teaching? Who should teach? And not a few would ask, why would anyone want to teach, not just K-12 (U.S.) but also university level, what with all the nonsense, pedagogical and social, currently obtaining there?
FWIW, pedagogical regimens – scripted lessons – are often imposed on teachers by their educational administrator masters. IIRC, in the U.S. 50% of newly-minted teachers leave the profession by the five-year point.
And, FWIW, not every short attention-spanned human primate is predisposed to submit to the focus and discipline required to understand and appreciate the beauty of mathematics and other academic subjects.
(And I confess that my eyes were glazed over with dealing with the austere pedagogy. First explain it in a way a third grader could understand and appreciate it, and then lets gingerly approach the more formal f(x) and g(x) and f(g(x)), or whatever. Let’s first give the analogy of “domain” being at “home,”[“domus,” “domicile”, from Latin] and “range” being some distance away from home.)
Some are unable or unwilling to appreciate mathematics for its own sake. (I gather that the university continues to exist to pursue knowledge for its own sake, the currently-obtaining corporatista MBA/JD/Ed D worldview notwithstanding.) Some STEM enthusiasts out there advocate for teachers’ appealing to students’ pop culture interests to get them interested in STEM. (E.g., Neil de Grasse Tyson) No one had to appeal to my fatuous,piffle pop culture interest to prompt my interest in learning.
(Re: Richard Hofstadter’s “Anti-Intellectualism in American Life” and Susan Jacoby’s “The Age of American Unreason”.)
I may be wrong but I get the impression that you believe I hold the teachers responsible for the state of maths teaching. That’s not true at all, the fault is with the system, not the teachers. In the UK everything is now about passing exams and building a school’s official ratings, teaching autonomy is therefore limited and lessons are precsriptive. Teaching these days is a tough gig and definitely not something I would want to do.
It is indeed true that ‘Some are unable or unwilling to appreciate mathematics for its own sake’. And many people do not especially want to, which is perfectly fine, but that doesn’t mean we should deprive all students of that appreciation. I don’t enjoy poetry myself, I don’t see the point and I rarely get anything out of it. That doesn’t mean we should never teach about beauty in poetry to others, but that is what we do with maths, even though maths is demonstrably more important for the vast majority of individuals and occupations.
My main argument isn’t about beauty though, it’s about real-life practical skills. The most important of these being the ability to assess situations with numerical literacy and an idea of scale. Being able to calculate and estimate is an absolutely crucial skillset in modern life. You can grasp very little about how the world works – or of economics and how incentives affect individuals – without numeracy and appreciation of the size of numbers. You have little chance of intuiting anything quantitively about the world if your knowledge is so limited.
Your point about pop culture piffle is misplaced in my opinion. When teaching maths, involving children in things they personally understand makes their learning more effective and interesting. You dont have to talk about the X Factor or the Kardashians to gain their attention. There are many things that will help them. With my daughter I used the number of pixels in different sizes of iphone to demonstrate and explain the inverse square law of electromagnetic radiation. Another in basic probability – when will your iphone likely repeat a song if you set it to random? She loved these tasks and learned too – they certainly are not piffle.
Also, the fact that no-one had to appeal to your ‘fatuous piffle’ to enthuse you in your learning makes you a very lucky person. Unfortunately it doesn’t happen like that for everyone, nevertheless we owe these crucial life skills to our kids. If they do not have the ability or enthusiasm to ‘Just Do It’ we need to find better ways of teaching kids maths. What else can we do? Shrug our shoulders and leave them to struggle?
I think a POTUS candidate should be able to do a two-step algebra problem at a minimum (not to mention deriving the quadratic formula from y = ax^2 + bx + c), and perhaps balance a simple chemical equation, in order to so run for office. I’d be reasonably impressed by a competent explanation of the relationship between Fahrenheit and Centigrade temperature scales.
i’m sure Pete could do all of those, and ofcourse MATH Yang,and probably Bloomberg.
That’s the thing I find really sad. People wear their inability to do basic arithmetic like a badge of pride.
😖 agreed
Schools, at least when I was there, didn’t care that a girl like me struggled with math. I worked very hard to cope on my own. It is truly atrocious how I was treated and I most likely have a learning disability but there wasn’t even a class to help me though there were plenty of reading classes. It also is still considered socially acceptable to laugh out loud at me and call me stupid for my disability but not for dyslexia.
There really doesn’t seem to be any need to worry about which power of ten a billion or a trillion is. If you have $500 million it is as clear that you could not give 327 million people one million dollars each as it would be that owning 500 pieces of cake would not permit you to give a piece of cake each to a population of 327 million.
The real number would have been to give 327 billionaires a million, just like the government does every so often.
I don’t know whether I should put a winky face or a sad face at the end of this comment, so….
¯\_(ツ)_/¯
My anecdotal experience of journalists is that they have difficulty discerning million-billion-trillion.
They should just do what I do & say “A lot” and if anyone gives you shit say “Who cares I’m not putting a guy on the moon”.
Which is not to say that you do not give due credit to those who can successfully land a Spirit or Pathfinder (and the upcoming Perseverance) on Mars 35,000,000 miles (v. 240,000) miles away). 😉
Yes. Just nothing in my life needs that level of accuracy. I can probably get away with 1 sigma most of the time. 🤣
Math isn’t my strong suit so when things like this happen I assume I’ve got it wrong and then ask a math friend if I’m wrong or they’re wrong.
This isn’t maths, it’s basic arithmetic. Being unable to understand that 500 million and 328 million are not different by a million times is a bit like not being able to spell Bloomburg.