Making everyday conversation less fuzzy

February 18, 2018

In everyday conversation we use words and phrases that are, at best, ambiguous and vague. Yet, despite the fuzziness we somehow manage to communicate with each other and get things done.

A cool thing about mathematicians is that they work really hard to give words and phrases precise meaning. Today I learned how they give precision to the phrase infinite set. I think it’s mind-blowing.

Consider the set of positive integers, 1, 2, 3, 4, …

Clearly it is an infinite set. But wait! What does “infinite set” mean? That’s one of those ambiguous, vague phrases. So, how to define it? Let’s approach the problem by identifying a characteristic of infinite sets.

Notice that each positive integer can be mapped to an even integer by multiplying the positive integer by 2:

 

 

 

 

 

 

 

 

For every positive integer there is a corresponding even integer. There is a 1-for-1 correspondence between the two sets.

Therefore the two sets have the same number of members!

This result is surprising in view of the fact that the set of even integers is a proper subset of the set of positive integers (3, for example, is in the positive set but not the even set). We are accustomed to thinking of a set as being “larger” than any of its proper subsets, but here we are inescapably led to conclude that sometimes a set and a proper subset of that set may have the same number of members.

That is really unusual behavior!

When we examine the sets that exhibit this unusual behavior, we find that they are just the ones that we would intuitively call infinite.

DEFINITION: A set is infinite if and only if it is equivalent to a proper subset of itself.

Wow!

 

A New Goal: Aim to Be Less Wrong

February 16, 2018

At a conference last week, I received an interesting piece of advice:

“Assume you are wrong.”

The advice came from Brian Nosek, a fellow psychology professor and the executive director of the Center for Open Science. Nosek wasn’t objecting to any particular claim I’d made — he was offering a strategy for pursuing better science, and for encouraging others to do the same.

When Nosek recommended that I and other scientists assume that we are wrong, he was sharing a strategy that he’s employed in his own lab — a strategy for changing the way we offer and respond to critique.

Assuming you are right might be a motivating force, sustaining the enormous effort that conducting scientific work requires. But it also makes it easy to construe criticisms as personal attacks, and for scientific arguments to devolve into personal battles. Beginning, instead, from the assumption you are wrong, a criticism is easier to construe as a helpful pointer, a constructive suggestion for how to be less wrong — a goal that your critic presumably shares.

https://www.npr.org/sections/13.7/2018/02/12/585057058/a-new-goal-aim-to-be-less-wrong

With my mind I shall heal my body

February 6, 2018

When I was growing up my parents didn’t have money. When one of us kids got injured there wasn’t the option of going to a physical therapist or a massage therapist or a chiropractor or an acupuncturist. I read a lot of books on the power of the mind, so when I got injured I used my mind to heal myself. And it worked. I successfully healed myself of a heart murmur. When I was young, my mind was powerful and strong.

Now that I am an adult, I can afford to hire physical therapists and massage therapists and chiropractors and acupuncturists. 3 months ago, I injured my shoulder. Since then I’ve undergone physical therapy, massage therapy, chiropractic, and acupuncture. I’ve given them a lot of my money and time. The pain in my shoulder remains. Recently I remembered how, as a child, I used my mind to heal myself. Sadly, I’ve come to realize that my mind has become weak in terms of its power to heal myself. But, I am determined, my mind will be powerful again! Deep inside, I know how to heal my shoulder – do the deep relaxation that I used to do as a child. I have started doing this and my shoulder is already improving.

Hello darkness my old friend …

February 4, 2018

Hello darkness my old friend
I’ve come to talk with you again

That song was written by Art Garfunkel in honor of his friend Sanford Greenberg, who he befriended at Columbia University in the 1950s. The two made a pact that they would always help each other in times of need. During the school year Greenberg contracted an eye disease and went blind. Garfunkel helped him through that period, reading his school assignments, encouraging him. Greenberg graduated and moved to London. One day he got a call from Garfunkel who told him that he had been writing music with a fellow by the name of Paul Simon and needed $400 to record their first album. Greenberg had $404 in his bank account, wrote out a check for $400 and sent it to Garfunkel.

It is a wonderful story, well worth listening to:

At 15 minutes, 56 seconds: http://www.bbc.co.uk/programmes/p05wxfkh

What is the meaning of life?

February 2, 2018

What is the meaning of life? I think people ask that question out of the assumption that meaning is something you can look for, “Oh I found it. Here’s the meaning. Here’s what it is. Here’s what I’ve been looking for.” But that doesn’t consider the possibility that, maybe, meaning of life is something that you create, you manufacture for yourself and for others. When I think of meaning in life, I ask, “Have I learned something today that I didn’t know yesterday?” Bringing me a little closer to knowing all that can be known in the Universe. Just a little closer. However far away all the knowledge sits, I am a little closer. If I live a day and I don’t know a little more that day than the day before, then I think I wasted that day.

— Neil deGrasse Tyson (6:53) https://www.youtube.com/watch?v=ltJbyS_DWIo

The knowledge that I am going to die brings focus and urgency to my life

January 28, 2018

It is the knowledge that I am going to die that creates the focus that I bring to being alive. The urgency of accomplishment, the need to express love – now, not later.

If we live forever, why ever get out of bed in the morning, because you always have tomorrow? That’s not the kind of life that I want to lead.

Larry King: Don’t you fear not being around?

Neil de Grasse Tyson: I fear living a life where I could have accomplished something and I didn’t. That’s what I fear. I don’t fear death. I want this written on my tombstone: Be ashamed to die until you have won some victory for humanity. [Horace Mann]

— Neil de Grasse Tyson (https://www.youtube.com/watch?v=Ndj5KjKyr3E) starting at 3 minutes, 20 seconds into the video

Why do Chinese, Koreans, and Scandinavians save money better than Americans?

January 21, 2018

If I’m speaking in English, I speak grammatically differently if I’m talking about past, present, and future. It rained yesterday. It is raining now. It will rain tomorrow. Notice that English requires a lot of information with respect to the timing of events.

It’s simply not permissible in English to say it rained tomorrow. In contrast, that’s almost exactly what you would say in Chinese. They would say yesterday it rained, now it rained, tomorrow it rained. The Chinese language doesn’t divide up the time spectrum in the same way that English does.

Chinese is a futureless language. English, on the other hand, is a futured language, which means that time constantly intrudes into our speech in all kinds of ways.

That difference led UCLA professor of economics Keith Chen to an intriguing hypothesis – could how you speak about time affect the way you think about money?

You speak English, a futured language, and what that means is that every time you discuss the future or any kind of a future event, grammatically, you’re forced to cleave that from the present and treat it as if it’s something viscerally different. Now suppose that that visceral difference makes you suddenly disassociate the future from the present every time you speak. If that’s true, and it makes the future feel like something more distant and more different from the present, that’s going to make it harder to save.

If, on the other hand, you speak a futureless language, the present and the future, you speak about them identically. If that suddenly nudges you to feel about them identically, that’s going to make it easier to save.

More … https://www.npr.org/templates/transcript/transcript.php?storyId=295356139

Stop stretching

January 14, 2018

I hear this advice all the time: Do stretching. Get flexible.

That is bad advice.

Your muscles are like springs. Kind of like the springs in your car. Do you want loose springs in your car? Of course not. You want firm springs.

When you bend down to pick up an object, you want tight hamstrings (ham-springs) to firmly move you back up to the standing position.

The back is not designed to bend or twist. It is designed to stop motion and hold your torso stiff. Stop doing crunches, sit-ups, bends, and twists. They will ultimately harm your back.

Last night I taped my mouth shut

January 10, 2018

I heard that taping the mouth shut will yield deeper sleep. Supposedly, mouth-breathing (and snoring) while sleeping is not conducive to deep sleep. I slept well, I think. I seemed to be more aware of my dreams. The tape that I used is called Somnifix. A good thing is the tape came right off, painlessly, in the morning. And it wasn’t uncomfortable to wear at night.

I no longer feel the need to know everything

December 27, 2017

As I’ve gotten older, I’ve gotten a bit wiser. One thing that I am very pleased with is that I no longer feel that I must be an expert at everything. I’m okay with releasing control and letting others who have the expertise tell me how to do something. I will contribute my limited knowledge and expertise.  Perhaps working together, we can create great things.