Saturday, June 16, 2007

LIES, DAMNED LIES, AND STATISTICS (Part 1)

All about the abuse of anecdotal math to falsify the truth and truthify falsehood.

Mark Twain famously wrote:

Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: "There are three kinds of lies: lies, damned lies and statistics." [from the Autobiography of Mark Twain]


He was implying that, of the three classes of lies, statistics were the worst. Others have added to the list, in order of falseness:

  1. Lies
  2. Damned Lies
  3. Statistics
  4. Politicians Quoting Statistics
  5. Journalists Quoting Politicians Quoting Statistics

This new topic posting (like a presentation at a physical club meeting) gives some examples of how anecdotal math and statistics are used to confuse the public.

A large percentage of the population is “mathematically challenged.” Their eyes glaze over like deer caught in headlights whenever someone uses numbers and mathematics to argue for their version of the truth. Some even proclaim their innumeracy as if it was a badge of honor!

The result is that many educated people are convinced to accept falsehoods as truth and to discard truths as falsehoods.

This first example has to do with the need for reason as well as mathematics.

Please read this poem:


When I was going to St. Ives,
I met a man with seven wives,
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits,
Kits, cats, sacks, wives,
How many were going to St. Ives?


Can you figure out the answer? If you think you know the answer, or how to figure it out, write it down on a scrap of paper. Then, please scroll down and continue reading.




















OK. Here is one approach. The poem says: I met a man with seven wives, so at least seven wives are going to St. Ives. Right?

The poem continues: "Each wife had seven sacks," so, that would be 7 x 7 = 49 sacks. But, should we count sacks in our total? The last line of the poem asks: How many were going to St. Ives? It does not ask how many people or how many living things are going, just "how many".

Therefore, let's count the sacks. We have 49 sacks going to St. Ives.

The poem goes on: Each sack had seven cats, so, that would be 49 x 7 = 343 cats going to St. Ives.

The poem adds more information: Each cat had seven kits, so, that would be 343 x 7 = 2401 kits going to St. Ives.

Adding them all together, Kits, cats, sacks, wives, we get 2401 + 343 + 49 + 7 = 2800 total items going to St. Ives. OK, so that is the answer. Right?

Think about it, then scroll down and continue reading.



OOPS, we forgot the man! We were so engrossed in mathematics we only figured the Kits, cats, sacks, wives and forgot all about the man who had the seven wives. So let us add him, and we get 2800 + 1 = 2801. OK, so that is the answer. Right?

OOPS again! The first line of the poem says: When I was going to St. Ives, so we need to add the author of the poem to get the answer to "How many were going to St. Ives?" We get 2801 + 1 = 2802 people and sacks and cats and kits going to St. Ives. OK, so we finally have the answer! Right?

Think about it, then scroll down and continue reading.



2802? No we don't! Read the poem again. All it says is When I [the author of the poem] was going to St. Ives. That is just one person we know of who is going to St. Ives.

All the others, including the man, his wives, the sacks, the cats and the kits could be coming from St. Ives or coming or going to or from any other place!

So, the correct answer, based on the facts in the poem, is ONE is going to St. Ives. All the rest is unsupported conjecture.

THE LESSON: Don't jump in and work the mathematics until you understand the logic and reason!

Please comment on this posting!

I plan to post the next part of "Lies, Damned Lies, and Statistics" in a week or so.


Ira Glickstein

8 comments:

JohnS said...

You state: “A large percentage of the population is “mathematically challenged.” Their eyes glaze over like deer caught in headlights whenever someone uses numbers and mathematics to argue for their version of the truth. Some even proclaim their innumeracy as if it was a badge of honor!”

I would expand the above to state that a large percentage of the population is rationally challenged or simply intellectually lazy. That is they accept that which conforms to their version of the truth regardless of its validity while ignoring or even denying truth if it does not conform.. Thus they are the gullible tools of those who would distort reality to obtain their personal goals..

Kerensa said...

Similar lies and statistics come from the medical community. Having recently given birth to a healthy babe, I can't begin to tell you the scare tactics they use. They even have numbers to back them. They forget one thing...humans thrived before modern western medicine and being told how we need to do things by doctors (We even might have had fewer side effects). A little bit of commonsense and trust in yourself goes a long way, like the value of a good question as Steve stated.

Johntruth said...

Who in there right mind would want to go to St Ives in the first place?

Ira said...

All:

Somehow we got into a pattern of posting comments related to this topic ("Lies...") under the first main topic ("Welcome...").

To help the "newbies" who may be joining us, I've posted this comment here (under the "Lies..." thread) and I hope some of the other Commenters (and Lurkers who'd like to "upgrade" and become Commenters) will add more comments.

I was impelled to post the "St. Ives" puzzle poem because my wife has a bottle of "St. Ives Soothing Lotion" that sits on our bathroom sinktop and I see it a few times each day.

Like Stu and probably others, I remembered the poem from long ago. However, I have the impression that the last time I saw it was in a math or programming class where the teacher used it to develop an iterative algorithm for the sum of successive multiplications by the same number. (I remembered the poem but not the algorithm :^)

If any of you have similar memories of interesting math-related puzzles, you can post them as comments to this thread or, if you "upgrade" and become an Author, you could post a new main topic about it.

Let's keep this Blog active and please feel free to invite others who may be interested.

Ira

Ira said...

to JohnS, Kerensa, and JohnTRuth:

Sorry I did not reply to your Comments earlier, but I was outwitted by my misunderstanding of this Blog setup.

JohnS, Yes, a large percentage of the population is rationally challenged (apparently including me by my example of not understanding my moderating duties).

Lincoln said "You can fool some of the people all of the time, and all of the people some of the time, but you can't fool all of the people all of the time."

However, some politicos and pitchmen (and -women) sure try to do it all of the time, don't they?

Kerensa, Great your baby came out OK. Enjoy it! Our daughters and granddaughters and soon-to-be born grandson are the joys of our lives.

I guess it the "scare tactics" doctors use are a vain attempt to protect themselves from the lawyers. One of our daughters is now recovering nicely from a serious operation and some of the things her doctor told her about what *might* happen would fall into that category.

Much of the medical care burden is due to overly protective medicine, unnecessary tests, and so on that protects against malpractice claims. The problem is that a seriously "abnormal" baby or, for that matter, an adult who has a bad outcome from an operation, is so appealing to the average juror that the awards can sometimes be millions, unjustly enriching the trial lawyers, clogging the courts, discouraging some doctors from working in high-risk areas such as emergency rooms and gynecology, and raising the costs for everyone involved.

[Of course, that is just *my* opinion. Anyone is entitled to yours -- and I wish they would express it (courteously) on this Blog!]

Ira Glickstein

PS: Anyone know where St. Ives is? All I know about it is that old poem and the fact it is the brand name on the label of "soothing lotion" my wife keeps on our bathroom counter. (JohnTRuth: After all this talk about it, I would like to go there, assuming all the cats and kits are gone by now :^)

wwp07 said...

who said these wives are his?

(my first posting to any blob)

Ira said...

To WWP07 (who happens to be my next-door neighbor :^):

True, they may not be the man's wives.

I suppose they could be any seven wives who fancy cats and kittens, not necessarily his.

Therefore, some *could* be going to St Ives and some might be coming from St. Ives and some might be going or coming from anywhere else and some may live where he met them.

Statistics can be used to "complexify" as well as to truthify or falsify.

Ira Glickstein

PS: Notice my photo with this Comment. Kerensa's Comment with her photo lead me to complete my "profile" on Google Blogger and include my photo. You may do the same. If you have a problem posting the photo (it is not easy) send me an email at ira@techie.com and I will tell you how to do it.

PPS: This is a "Blog" not a "Blob" -- or at least it was until you posted your Comment. THANKS for posting!

Timothy said...

I completely agree that you should first understand the logic of a problem before completing the math. Unfortunately, the approach of always trying to understand the logic before doing the math has stifled my progress in studying mathematics. I always hated it when I used the sin() or cosin() trignometric functions without understanding how to compute their results by hand.

Tim