My recent Decoded Science article, “Repercussions from the Richard Paradox” explains Richard’s Paradox and tells of some responses that helped keep mathematics on a stable footing.

Richard’s Paradox as well as Richardian Numbers

"For All x, the Function of x", image by Mike DeHaan

French mathematician Jules Richard actually developed a pair of paradoxes. They were important because he avoided one of the disputed issues that clouded certain previous paradoxes.

Among others, Bertrand Russell addressed Richard’s Paradox in his first book about the foundations of mathematics.

Let me tip my hat to Andrea Cantini for her article “Paradoxes and Contemporary Logic“, one of my references.

Publicity for Richard’s Paradox

As always, I also promote my article in my Xanga blog (“The Paradox of Richardian Numbers”). My Blog of Writing article, “Preview of the Richard Paradox” also provides a free writing tip.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in articles in Decoded Science, Environmental Graffiti, Squidoo and Suite 101. That’s why we highlight articles on this blog page.

To only see our posts about Toronto events or fitness, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin. Thank you.

Thanks to an alert reader and commentator (”Impress Your Date”; see the comments in “Introducing the Math of Conditional Probability“), I just researched and installed a “Captcha” plug-in for this WordPress site.

Why Add a Captcha to the Comments?

The reason for adding Captcha to the comments is simple: while I appreciate my readers and the fact they make comments, my settings require me to approve or delete each comment.

"Captcha in DeHaan Services", image by Mike DeHaan

As much as I love my readers, it is tiresome and time-consuming to weed through the spam comments. Yes, you get a link and your message in the sidebar. No, I do not approve every comment. (Believe it or not)!

The Captcha should ensure that I’m not receiving automated spam comments. It should also be annoying for humans to generate more than one or two self-serving comments, too.

Time alone will tell. Will I tell too?

Planning for the Future

I plan to write a more complete description of the process in my Blog for Writing soon, but at the moment I have other irons in that fire. In the meantime, you can begin your journey by checking the main Captcha site.

My latest post, “Weight Loss Risks for Toronto Mayor Rob Ford” presents my viewpoint in my DeHaan Fitness and Weight Control blog.

Just a hint: I do think he runs some risks, especially if he treats this as a “crash diet”; but it may be worth it for the health benefits.

Good Luck to His Honour, Mayor Rob Ford

"Mayor Rob Ford in David Pecaut Square, Toronto" image by West Annex News.

Let’s call this a “before” picture, and hope to see the difference in an “after” picture in the summer of 2012.

His goal is to lose approximately two pounds per week, achieving a fifty pound loss over six months. It is a challenging task, and I sincerely hope he succeeds and stays healthy doing so.

My article also gives a link to a site where anyone can participate, follow his progress, or donate to a charity “of your choice”.

The first weigh-in was quite a “Toronto event” and well-covered by the local media. Mayor Ford’s starting weight was 330 pounds. As my main article notes, this almost guarantees health problems in later life. Mayor Ford made the same point at that inaugural event.

One hopes that the media will keep us well-informed and track his progress over the course of the next six months.

Is it true that our former mayor, David Miller, also managed to lose weight and become fitter while serving Toronto? This might be the only policy agreement between those two gentlemen.

Self Promotional Notes

As always, I also promote my article in my Xanga blog (”Can Crash Diets be Risky?“).

In my Blog of Writing, “A Local Toronto Angle for Diet Risks” puts the focus on writing universal truths by starting with a specific local instance.

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Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in articles in Decoded Science, Environmental Graffiti, Squidoo and Suite 101. That’s why we highlight articles on this blog page.

To only see our posts about Toronto events or fitness, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin. Thank you.

My latest DeHaan Fitness article, “Marathon Training Unlikely to Increase Risk of Heart Attack“, actually presents a bit more of a balanced view than the title indicates.

The much larger of the two research papers that I reference, provides results from about a decade of organized marathon events in the USA. They counted both full and half marathon races.

One of their conclusions was that having spectators and professional medical people available reduced the mortality rate in the few heart attacks that occurred.

Both studies showed that there are, indeed, risks in exercising. Nonetheless, the title reflects my sincere belief that most people would be healthier if they would train at a not-too-intense, recreational level for endurance sports such as running or bicycling.

The Toronto Connection for Heart Attacks During Organized Marathon Events

"Heart with Anterior Wall Dysfunction", image by Patrick J. Lynch

Toronto has hosted, on average, two marathon events a year for quite a few years. Each event includes a full marathon run of 42.2Km (26 miles, 385 yards for our American friends), as well as a half-marathon (21.1Km, “duh“).

If memory serves, from what I remember from our local news in the last six to ten years, Toronto has averaged about one death every two years across all these full and half marathon races.

Although participation has grown over the years, let’s just use the 2011 entrant numbers to get a rough estimate. The Toronto Scotiabank Waterfront Marathon, held in the autumn, had about 12,750 runners across the two races. The Goodlife Fitness Toronto Marathon, now a spring event, had about 5,300 participants. If these numbers were consistent across all the years, we would have seen about 1 death for every 36,000 entrants.

If my numbers are off…and certainly participation has grown over the years…I would still guess that one death for 25,000 entrants would be somewhat pessimistic.

Disclaimers All Around

Let’s note that the news would not report every cardiac arrest, nor every ailment treated on-scene or at hospitals. So I don’t have a firm comparison with the “Participating in marathons, half-marathons not found to increase risk of cardiac arrest” article from Medical Xpress (based on a report in the New England Journal of Medicine).

Let me repeat, I also did not go back to research the news archives for the Toronto deaths. I had begun paying attention around 2003 or so, when my own endurance training had started.

Nonetheless, another real problem (especially for anyone who shovels snow) is that cardiac arrests can occur to anyone; and lack of regular exercise is one of the contributing factors.

Also Promoting my Article about Marathon Training and Heart Attacks

As always, my Xanga blog (”Have a Heart for Marathon Training“) promotes my article. So does my Blog of Writing, where “My Disclaimer for Marathon Training” provides a writing tip about disclaimers, such as:

Disclaimer: The information contained in this article is for educational purposes only and should not be used for diagnosis or to guide treatment without the opinion of a health professional. Any reader who is concerned about his or her health should contact a doctor for advice.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in articles in Decoded Science, Environmental Graffiti, Squidoo and Suite 101. That’s why we highlight articles on this blog page.

To only see our posts about Toronto events or fitness, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin. Thank you.

Don’t confuse the “given” event with the final combined conditional event, or you will have fallen victim to a conditional probability pitfall.

Find the facts in “The Pitfall that Conditional Probability is Not Commutative“, my latest article in Decoded Science.

Do We Even Use Conditional Probability?

Yes, we do. Especially those of you who raise your bets when the cards are going your way. Or, every time you think, “I need to make a good first impression to improve my chance of landing that job”.

"Probability of the Intersection Sum of Two Dice", image by Mike DeHaan

This article stands alone, but is part of a series about probability theory that I’m writing for Decoded Science.

Although I had to make some of my own images, there are more enjoyable pictures in the main article.

I used Eric W Weisstein’s “Conditional Probability“, in MathWorld-Wolfram, as my reference material; but contributed my own examples and explanations.

As always, I also publicize the main article, both in my Xanga blog (”Take Care with Conditional Probability“) and in my Blog of Writing, where “Preview of Non-Commutative Conditional Probability” includes a bonus writing tip.