The Human Body: Bad Design?

In December, I went to see a physiotherapist because of a sore arm. The actual problem was a nerve in my neck. I got an exercise to do to deal with the problem.

Monday, I went to see her again. I pushed out my other arm very fast to avoid falling when slipping. I would have been better off falling as I wrenched my arm badly. The actual problem was a muscle that is in the arm but also the chest. I now have exercises to do. One involves massaging the actual part that needs it: on my chest.

Who designed the human body anyway?

If you have some odd aches and pains that are not going away, consider seeing a physiotherapist.

I live in Kamloops, British Columbia, Canada. My physiotherapist is Lucki Khurana who works for Kamloops Physiotherapy. Highly recommended and professional.

Puzzle #248: Blended Pets

Tom and Sabrina just got married. It is a blended family including the pets. There are three cats and two dogs. Tom and Sabrina each had had at least one pet. How many combinations of the premarital distribution of the numbers of cats and dogs are there?

[Note: This puzzle is not asking about specific cats and dogs but the number of them. For example, if Tom had had one cat and one dog and Sabrina had had two cats and one dog, that would be one combination. Who had had which pets is not relevant here.]

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, March 7, 2018 at noon Pacific Time. I will post the answer shortly after.

Puzzle #246 Solution: Chocolates

Spoiler Inside: Solution to Puzzle SelectShow

Solving the Right Problem Right

Presh Talwalkar recently wrote a blog post about people trying to solve problems with no solution.

I want to add something to this.

The numbers in a real world problem have meaning. You can not just do arithmetic operations without regard for what the numbers mean and expect to get a correct answer except by fluke.

Mathematical tools have requirements for their use. For example, if one has two of voltage, current, and resistance for some types of electrical circuits, one can compute the third using the formula E=IR. BUT you must have two of the values. If you only have one of them, you do not have enough information.

In a real world problem, you may have to hunt down the missing information. Sometimes, you can compute a missing value from other information given in the problem.

For example, in the problem “Albert has 25 marbles more than Carl does. Beth has 45 marbles. Carl has 15 fewer marbles than Beth. How many marbles does Albert have?”, Albert has c + 25 marbles. We do not know the value of c, but we do know that c = b – 15. That still is not enough, but since we know b = 45, we can substitute 45 for b to get c = 45 – 15 = 30 and then for c in a = c + 25 to get a = 30 + 25 = 55. Thus, Albert has 55 marbles.

Note that it was necessary to do something else before c could be computed. This is not a trick question. It is simply that one must have the necessary pieces before one can proceed.

Odd Language #244: Dispatching

This story by L. E. Modesitt, Jr. has the sentence in paragraph 2: “Is there a glow from the single lamp, illumining the high-backed reading chair last occupied by his wife before he dispatched her with their children, and all others within and without the City, to the highlands west of the Ramparts of the Sky?”

The issue: “dispatched” could mean sent or killed. Until the “… to the highlands …”, it is uncertain, and I first thought it was the latter which is considerably darker.

Puzzle #247: Full House

From an ordinary 52-card deck of playing cards, you have just been dealt the ace of diamonds and the king of hearts. What is the probability that the remaining three cards will complete a full house? Answer to the nearest 0.01%.

[A full house is a poker hand of three of a kind and a pair.]

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 28, 2018 at noon Pacific Time. I will post the answer shortly after.

Puzzle #245 Solution: Treasure

Spoiler Inside: Solution to Puzzle SelectShow

How YouTube and Others Shape Opinion

Do you watch YouTube videos? I do.

As I have watched different videos, what YouTube offers me for more to watch has changed. I watched some Jordan Peterson videos, and so I get offered more of the same. More Jordan Peterson and also Ben Shapiro and Dinesh D’Souza. They are very good speakers. There might be some leftist speakers who also are good speakers, too, but YouTube does not offer me any of those.

I am pretty much non-leftist, but that does not mean that I do not want to hear well-stated leftist thought. I do like to learn from other viewpoints.

It is hard to avoid the idea that I might be missing something. Polarisation is ugly.