One of my Facebook friends commented on this simple, apparently long-circulating, arithmetic problem and so it prompted many other of my Facebook acquaintances to also weigh in. The statistics of this FB post, as a whole, captured my attention. With 516K votes (“likes” I suppose) and 5.5M comments that is almost too impressive.
I don’t think the interest in this question would have been so high if everyone had arrived at the same answer. Since some did not, from the few answers I’ve seen, it seems many were prompted not only to correct the errors, but to also provide detailed explanations on the order of precedence rules in arithmetic.
Now, I’m naturally skeptical and suspicious (not always a good trait) and so I could not help suspecting that some of the wrong answers presented with conviction were nothing more than “click bait” and perhaps led to the phenomenal response to this simple post.
As a tutor in chemistry and physics this discussion provoked some interesting thoughts …
- In any math problem that involves a mathematical expression, the expression is a language that connects the person who set up and solved a math problem and someone else who uses the solution to find the correct answer to a similar problem. The conventions around the rules of precedence, that is to say: “multiplication and division must be done before addition and subtraction” are established so that the users of the equation understand how they are to perform the various operations correctly to get the right answer. If they are not followed, then using hyperbole, bridges will fall down, planes won’t leave the runway, and patients will received incorrect dosages. The rules involve shorthand (default rules that everyone is supposed to know) that make the expression as compact as possible.
- since multiplication is done first, as most respondents noted, the expression simplifies to:
- 50+50+0+2+2=? and so the answer is 104
- If the person who set up the expression wanted a different outcome, then brackets would be used to change the order of operations … (50+50-25)x0+2+2=? … this answer would be 4
- The conventions communicate from the person who set up the equation to the user. Like all conventions of this sort, they are only effective if we all agree to the same ones.
- The second interesting point has to do with calculators. Depending on the calculator, a person who has not bothered to learn the order of precedence conventions can easily get the wrong answer. Using a calculator is no guarantee of accuracy.
- For an older, simpler calculator that forces you to enter a number and an operation and another number to complete the operation, going from left to right will give the incorrect answer. By beginning at the left the user imposes an incorrect order of operation on the whole equation. You will in effect solve … (50+50-25)x0+2+2=?
- A more sophisticated calculator that lets you enter the whole expression will follow the rules of precedence
Bottom line: having a calculator does not necessarily keep you from making mistakes if you don’t learn the rules.
For your convenience I have also reproduced the questions and answers here. I welcome any questions you might have. Thank you Andrea!
Why do you write?
I love to read Fantasy and Science Fiction. First and foremost then, I write books that I would like to read, but no one else has taken the trouble to write them. Specifically, I like books that are plot-driven and keep me riveted wondering what happens next. But I also like books that ask the Big Questions, as people do in real life. Why are we here? What does it mean to be human? Why should I try to be good?
When did you decide to become a writer, and what was that process like?
For a large fraction of my life, I was a researcher in chemistry and much of my writing appeared in technical journals or as patents. My career as a novelist had a curious start. I was a member of a book club and during one of our sessions I mused how I would love to write a novel. One of my friends said, “Well why don’t you do it?” The gauntlet was thrown down and I had to do something about it. It took me four years of attending writer’s conferences, and writing in my spare time while still holding a full time job before my first book came out, the first edition of the colonization epic The Halcyon Dislocation.
So, what have you written? (Include everything you have published)
As I mentioned I have more than sixty technical publications on chemistry and about 175 US patents, but I’m sure your readers are not that interested in them. In terms of novels I have written three (in the order of publication):
- The Halcyon Dislocation (two editions)
- Questioning Your Way to Faith
- The Battle for Halcyon
The Halcyon Dislocation and The Battle for Halcyon are the first two books of a four part series that I call The Halcyon Cycle. They deal with a science experiment that transports the island University of Halcyon to a parallel world. In the story we experience how various members of the university deal with the trauma of the dislocation and the challenges of surviving in a new world.
Questioning Your Way to Faith is a much shorter book that arose because of requests I received from some of my readers. In terms of a time line, Questioning Your Way to Faith is set before the dislocation and involves two university friends having an extended discussion about whether or not Christian belief is reasonable.
Where can we buy or see them?
My books are available as either e-books or as trade paper backs at most major bookstores and online outlets. In alphabetical order here are some links:
- Amazon/Kindle http://tinyurl.com/qbyw5b8
- Chapters-Indigo/Kobo http://tinyurl.com/odmn6j6
- Google Store http://tinyurl.com/qbnxs6j
- iTunes http://tinyurl.com/pkteyj5
What genre are your books?
My books are Science Fiction that read a bit like Fantasy. I say that because my books have a strong science component and I worry a lot about whether events like the dislocation are feasible. Having said that, once the University of Halcyon is in the new world, technologies begin to fail (because modern technology requires enormous infrastructure) and then one has much more of a Fantasy-style landscape.
Do you do any research for you books?
I try hard to get the details right in my books, so I do quite a bit of research to make sure that the phases of the moon are correct, the fish found off the island of Halcyon are correct for that locale and that events like the dislocation are not unreasonable from a physics perspective.
Are you working on at the minute?
I’m working on the next book in The Halcyon Cycle which I have provisionally called Descent into Abaddon.
Do you mind telling us about it?
Not at all. I listened to a wonderful lecture a few years ago that described how our relatively low atmospheric pressure limited the size of land mammals and also the size of flying birds. My next book is centered on a continent so far below sea level that the high atmospheric pressure removes these constraints.
What is your favorite book that you have written so far and why?
I would probably say The Halcyon Dislocation. I like the Crusonian aspects of being marooned in a new world and all of the discovery that entails.
How often do you write a week?
I write in fits and starts. When one has several books in print, one has many duties. I work better when I work at something for a concentrated period of time.
Do you aim for a set amount of words/pages per day?
No I don’t set pages per day. I like long books, so I aim for more than 100,000 words for my books.
What do you find is the easiest thing about writing?
There’s nothing easy about writing well. Of all the hard things that must be done to produce a good novel, I find imagining new worlds and new inhabitants of those worlds easiest.
How long on average does it take you to write a book?
I suppose it takes me roughly four years from start to finish to write a book. However that’s highly misleading since I start the next book right after the first draft is complete, so there is a good deal over overlap when I’m writing the first draft of one book and editing the last.
Do you ever get writer’s block and if so do you have any tips on how to get through it?
Writer’s block, in the sense of reaching an impasse in a story is not usually my problem. My problem is sheer laziness. I have many duties to complete and I get caught up in all of these urgent matters and let my writing time slip.
What is your editing process like?
I have friends who have taken a great deal of time as “beta readers” who critique my book and often see blind spots that I as a writer have missed. I always enlist the services of a professional editor to complete the edits. I can’t stress how important it is to find an editor who is not only technically competent, but has a genuine love for your books.
Self-publishing is a very broad term that includes vanity publishing. I prefer the term micro-publishing. By that I mean running a very small publishing business with an emphasis on the quality of the books produced and a severe eye on the costs.
Why self-publish or micro-publish? In my journey, I have seen many writers who spend years producing a novel and then spend years writing to acquisition editor after acquisition editor trying to interest them in their work. Often the writers eventually give up in discouragement without ever having provided their book to the people who really matter—their reading public. [For more on micro-publishing check my blog http://wp.me/p4cZo4-1l .]
What advice would you give to aspiring writers?
Force yourself to be a “finisher.” Make sure you sell some version of your book to your reading public to get feedback from them.
Where do you see publishing going in the future?
In my role as a research scientist I had a chance to see the Print-On-Demand technology develop. I think this trend will continue and will favor the smaller publisher. Traditional publishing will not disappear but will continue to be under increased cost pressure because of their extensive infrastructure.
Is there anything else you would like to add that I haven’t included?
- The best books become part of our intellectual scaffolding. Remember as a writer you are an artist first. You want your books to be entertaining, but also to make a difference in your readers’ lives.
- Don’t mistake sales as the primary indicator of your success.
[On re-reading this second point, I realized that my brief comment could lead to misunderstanding. Sales as a primary indicator for success can be highly misleading for an author starting out for two reasons. First of all, selling books is an annuity business and so sales build over time. That is to say, you have many upfront costs (Realistically one should charge at least minimum wage for all the time one invests writing and setting up one’s business. Many writers mistakenly think they are getting as bargain if they can find a traditional publisher that will pay them an advance and a royalty. Often these writers haven’t accounted for the enormous time they invested in preparing the manuscript for consideration by the traditional publisher.), but sales only begin once your book lists. However, once your book lists, it stays listed for a long time and generates an annuity stream. Secondly, there may be two reasons why a book doesn’t sell: (1) the book is poorly conceived and written; (2) the author is not well-known and so few readers get as far as even trying the book and so they never find out if it’s good or not. Unless one is well-known for other reasons (e.g. you’re a U.S. President), being unknown will always be an impediment when you start out. To distinguish these two barriers to sales, one needs to get the book into the hands of readers and get feedback.]
What is your favorite book and why?
My favorite books (on an equal footing) are C. S. Lewis’ Narnia series and J. R. R. Tolkien’s Lord of the Rings. I re-read the Narnia books because of the profound spiritual insights that Lewis offers. I re-read The Lord of the Rings because of the sheer beauty of the work. Even though I know the plot almost line for line, I love the beauty of walking through the vale of Ithilien and the terror of the Mines of Moria.
How can readers discover more about you and you work?
I’m always delighted to hear from my readers. They can contact me by email directly or leave a comment on my blog.
Amazon Author Page: http://www.amazon.com/-/e/B00JB0IWE6