Archive for February, 2014

A firsthand experience at a different, non-reductionist thought process

February 26, 2014

I would like to share with you an experience I had today.

I am working with two other people to write a paper that summarizes some work we did. One of the persons was born and raised in Taiwan, i.e., he is Chinese.

In today’s discussion I said to my colleagues, “We need to show how all the rules fall into five separate categories.”

The problem, however, was that the rules didn’t really fit into five neat categories.

The Chinese guy said, “No, the rules have some of this set of properties and some of this other set properties; we need a matrix which shows the rules are part this, part that.”

What a radical difference of mindset.

The third person explained to me: “In the Western culture we try to break everything down into tidy, independent categories. For example, in grade school we are told that the human body is composed of a liver, a heart, lungs, and so forth, and each works pretty much independently. This is called the reductionist approach. But in the Asian culture they don’t think this way. They are taught that everything is interconnected, e.g., depression in the brain affects digestion in the stomach, digestion in the stomach affects depression in the brain.”

This was a huge wakeup call for me. I feel very privileged to have had this experience. My tiny view of the world got shattered.

Ways To Specify Things Precisely And Clearly

February 23, 2014

I am interested in hearing your thoughts on this:

Need Precision And Clearness

In work and in daily life it is important to be precise and clear. Mathematics is one way to achieve precision and clearness, if the problem is numerical in nature. However, there are many problems that require precision and clearness and are not numerical in nature. I think our educational system devotes too much time to mathematics as a way to express precision and clearness, and not enough time to the other means to express precision and clearness.

Allow me to explain please…

My Kitchen Has 10 Pieces Of Fruit

In my kitchen I always keep 10 pieces of fruit on hand. Of the 10 pieces of fruit I always have two varieties: bananas and oranges, pears and kiwis, etc. If I wanted to rigorously specify this, I could create a mathematical equation:

x + y = 10

where x represents one kind of fruit and y the other.

Equations are great for precisely and clearly specifying things that are numerical, such as the count of pieces of fruit in my kitchen.

Being able to specify things precisely and clearly is important. Mathematical equations are great for this: they are succinct, they are abstract (free of irrelevant details such as the fruit’s color, shape, and texture), and they avoid the clumsiness of the English language (“I have 10 pieces of fruit and of them I have two varieties” is clumsy compared to “x + y = 10“).

Non-Numerical Problems Need Precision And Clearness

Not everything that we want to specify precisely and clearly is numerical. For instance, it would be useful to precisely and clearly specify the format of a Web page (i.e., HTML): an HTML document must have html at the beginning (the root element) and it must contain a head element followed by a body element; the head must contain zero or more meta elements and a title element, and so forth. Some very smart people have developed a succinct, precise way of specifying the HTML format, using something called a “BNF grammar.”  A BNF grammar contains “rules” and each rule specifies the content of each element, e.g.,

<html> ::= <head> <body>
<head> ::= <meta>* <title>
<body> ::= …

That notation might look strange. That illustrates my point. Here we have something that is non-numerical and needs a precise and clear specification. The BNF grammar notation is something that our educational system should expose to students early in their education.

Students need to see that (1) things need to be specified precisely and clearly, (2) not everything is numerical, and (3) non-numerical things can be expressed as precisely and clearly as numerical things.

There are many other non-numerical things that would benefit from a precise and clear specification. For example, think about the shipping requirements of Fedex and UPS. In order to ship a package from point A to point B it may have to go through point C. But if point C is unavailable (heavy snow storm there) then the package needs to be re-routed to point D and then E. You get the idea. A precise and clear specification of the routing problem is needed. It is not a numerical problem and so mathematical equations are of limited use. Some very smart people have developed a succinct and precise formalism for this type of thing, called graphs. I won’t go into an explanation of them. The point to be made here is that this is another example of a non-numerical problem for which we need precision and clearness, and students should learn at an early age these formalisms.

Summary

Mathematical equations are great for expressing numerical problems precisely and clearly. Our educational system exposes students early to this way of specifying problems. But there are other problems that are not numerical, require precision and clearness, and for which ways have been created for  specifying them. I think that our educational system should expose students early to these other ways. I think that by the time a student is 10 years old he/she should have been exposed to BNF grammars, graph theory, Turing machines, finite automata, and probably several other things.

Frozen versus fresh vegetables

February 16, 2014

British researchers found that 66 percent
of the time, frozen produce had more
vitamins and antioxidants than fresh did
after three days of refrigeration.

Successful people are those with a great love for their craft

February 9, 2014

Yesterday I was listening to an interview of Malcolm Gladwell. The interviewer asked Malcolm why he didn’t believe in genius. Malcolm said that successful people are those with a great, all-consuming love for what they are doing, not because of some genius quality.

He gave an example: When Wayne Gretsky was 2 years old his parents would let him watch hockey games on TV; after each game ended he cried because he loved the game so much he didn’t want it to end. This love for hockey consumed him and he went on to become arguably the greatest hockey player of all time.

Albert Einstein was great because he had a tremendous curiosity. He didn’t strive to become the greatest scientist in the world. He simply wanted to understand how the universe worked. As a side-effect of his great curiousity he became arguably the greatest scientist of all time.

This is what I learned: Don’t strive to be a great hockey player (or scientist or teacher or researcher or whatever). Instead, be filled with a tremendous love for hockey (or science or teaching or research or whatever). If you do that, then you will become great without even trying to become great.

What time do birds go to bed?

February 5, 2014

I got a bird feeder for Christmas. (Yea!)

Since hanging it outside I have observed that the birds come to eat at the feeder between roughly 8 am and 4 pm. I infer from that that they are asleep the rest of the time. Is that true?

I got the following message from a friend. It is both amusing and thought-provoking:

OK…but why do you infer that if a bird must be sleeping if it is not eating at your feeder? Might a bird have other activities to do during its waking hours?

And maybe the time a bird comes to your feeder has as much to do with when it is safe/convenient to do so as when the bird is awake/hungry. If I were a bird and I were awake and hungry, I still might avoid your feeder if there was a hungry cat nearby.

And what does it mean for a bird to sleep? Why assume that birds sleep is similar to humans sleep. I have read that birds sleep in short bursts. I have also read that birds can let parts of their brain sleep while other parts of their brain remain active. And I have read that birds can control their brain activity and effectively shut down parts of their brain (“go to sleep”) at will. That would be a pretty neat trick.