Summer Teaching

I'm looking forward to teaching pre-calculus this summer. I've been teaching some of the lower level math courses which has given me a re-found appreciation for more fundamental mathematics concepts; especially rational, irrational and prime numbers. What is really nice is passing on the passion of a known, new or learned concept to others - i.e. teaching. It will be nice to re-visit and pass on my passion for the next level and teach college algebra; matrices; and algebraic, exponential and logarithmic functions in the pre-calculus course.

Tracking Joy

With so many uncertanties in the world today and in life in general, the "what if's", "but's", deadlines, etc. can unfortunately creep forwards as we proceed through life's work and play and be used to dampen the feelings of Joy or Happiness that might be felt over an achievement or even over a momentary thought or feeling.
When we have a moment of happiness or joy, we need to make sure we do not follow it up with a dampening thought.
If we do not learn to recognize, allow ourselves to feel and hold on to the moments of happiness or joy, then when things get tough there will be nothing positive to hold on to to help you make it through the uncertain times. If you are religious, I suppose you can "look to God"; but I prefer to focus on something more tangible.

As an example, I was working this morning and quickly got a login procedure working in a large web application. It felt good when done; as how to best make it work was alluding me yesterday. I could have easily dampened the good feeling by thinking of how much more work there is and deadlines but I didn't. A few minutes later I had an email for a support issue that started yesterday. I resolved it in about an hour. It felt good. I could have dampened it by thinking about the entirity of the application that the support was needed for. But I didn't.
So Hopefully, I'm learning to Track the Joyous moments.

Well. Back to work and tracking the joy.

Numbers with 4

Every number between 1 and 100 can be created by combining 4's.
1= 4^0 (where ^ is "power". 4 to the 0th power)
2=(4+4)/4
3=(4-(4/4))
5=(4 + (4/4))
Note. There may exist more than one solution. For example, 5=4+(4^0) or 4+(4/4)
6=((4 *4) + (4+4))/4
...
Try some others.

Numbers2

Other than minimal thought, I have not worked on my previous problem of having a number (not necessarily prime) but who's decimal expansion is made up of only primes.

3/4 is an example. It is a Rational Number, 0.75, but it's digits are all prime.
2/3 is not an example, it a a Rational Number, 0.6666... but none of the digits are prime.

We can construct Integers, Rational, Irrationals, Primes, etc, but is there a way to construct what I will call "prime expansions" for now?

More later as some part of my Gray cell collection works on it.

Moderate Muslims?

Muzzammil Hassan started a cable TV network after 9/11 in New York state to prove to America that American Muslims are a moderate, peaceful people. Today he is charged with killing his wife, Aasiya, by beheading after she served him with divorce papers and a restraining order. Blogger Debbie Schlussel wonders why Hassan has only been charged with second-degree murder. "It's not that easy to behead someone, and it was likely planned in advance 'with malice aforethought,'" she writes.

Schlussel notes that such killings are not rare among Muslims. Known as honor killings, they are typically directed by a male head of household against his spouse or other female family members for violating the honor of their family.

From http://advanceindiana.blogspot.com/2009/02/moderate-american-muslim-tv-executive.html

Numbers

Teaching the Real Number line is fascinating. How dense is it? Are there any holes?
I start off teaching the Natural or Counting numbers. These are easy. They are the numbers you naturally count with, 1, 2, 3, ... where the ... means keeps going to infinity. We can also have the opposites of these, the negative counting numbers,-1, -2, -3, ... off to negative infinity. We can also add in the number 0. It turns out 0,1,2,3... has a special namec alled the Whole Numbers. And if we take the whole numbers and negative counting numbers we get the Integers. So, now we have a nice set of numbers called the Integers that looks like
...-3,2,1,0,1,2,3...
But what's between 0 and 1? 1/2 or 0.5; 2/3 or 0.666... are examples. And, as before, their opposites or the negatives of these. So we can really pack them in. The Integers and all the stuff in between the integers.
The problem is numbers like 1/2, 3/4, 2/3 are very well behaved. They act rationally. As a matter of fact, they are called Rational Numbers. By definition, the Rational Numbers are numbers of the form p/q where p and q are Integers and q cannot be zero.What throws alot of people is that 5, for example, is a Rational Number because 5=5/1 and so fits the definition. An interesting property of the Rational Numbers is that their decimal versions either Terminate (3/4=.75) or Repeat (2/3=.666...)
So our Number line is filling up with the Integers and these things called Rational Numbers between the Integers (and actually including the Integers - as seen before 5=5/1)
What else is there? What about numbers whose decimal expansion do not repeat and do not terminate. For example, 3.1415926536897... These have a name also. They are the Irrational Numbers.
So finally, once we put in the Integers, Rational and Irrational numbers we end up with a verydense set of numbers, the Real Numbers that make up the Real Number line:
As an example ...-3,-2,-1,0,0.5,0.666..., 0.75,1,2,3,3.14159...,3.5,4... Hopefully you get the picture. Between any two numbers, Integer, Rational or Irrational, are more numbers.

There is an Infinite number of Integers
There is an Infinite number of numbers between any two numbers
There is an infinite number of even numbers {2,4,6,...}
There is an Infinite number of odd numbers {1,3,5,7...}
There are even special numbers called prime numbers divisible only by 1 and themseleves:{2,3,5,7,11,13,17...}
There is an infinite number of primes also.

Are we missing any numbers? or are we as dense as can be? Any holes?

You think about it.

Oh, one last thing. Are there any numbers whose digits are all primes? There must be beut how can we construct them?

A horse of a different color

So the US will get rid of GITMO and not engage in torture but they will allow RENDITION. What this means is that we can send suspected terrorists to countries that do believe in torture. So how is this different from the US just doing it? Got me.

Ask yourself a question.
If your child was being held by terrorists, and they knew where they were, wouldn't you do anything to get back your child? This includes torture to extract the information on the whereabouts of your child? (maybe you would just talk to the terrorist or wait for the Judicial system to do their job -- I'm sorry but your child would be dead in the six months it takes to go to trial.

This scenario is no different than the "child" being the US and its citizens.

Let the pro's do their job.

Ya Think?

According to the Times, "The provision illustrates that the president's order to shutter foreign-based prisons, known as black sites, is not airtight and that the Central Intelligence Agency still has options if it wants to hold terrorist suspects for several days at a time."
More change we can believe in?

The Times notes: "The exception is evidence that the new administration, while announcing an end to many elements of the Bush 'war on terror,' is leaving itself wiggle room to continue some of its predecessor's practices regarding terrorist suspects."

Imagine that. There must be some dangerous people out there after all.

Quoted from Gather News

Torture? Hmmm...

What constitutes torture? Are you for it or against it?

Let's think this way:
Suppose your child, spouse or loved one has been taken hostage. The hostage taker will have them killed. You capture the hostage taker but they refuse to talk.

To what lengths would you go to get your child (or loved one) back? At what point would you say "that's torture, let my child (or loved one) die?"

What if it were you who was taken hostage?

Now, let's take that child, loved one or yourself and make it America (of which you and your loved ones are a part by the way.) How do you feel now? I cannot answer that. It is up to you.

There are fine lines no doubt. But we should think before we damn something.

Change? Less than you might think

As some of us who do not wear blinders are becoming aware, Obama is not "changing", the way he said he would.

In particular, the ways of keeping our nation safe. As is quoted,
"Obama will be loath to throw away the tools that have kept the homeland safe. Just as he will be loath to jeopardize the remarkable turnaround in American fortunes in Iraq. Obama opposed the war. But the war is all but over. What remains is an Iraq turned from aggressive, hostile power in the heart of the Middle East to an emerging democracy openly allied with the United States. No president would want to be responsible for undoing that success."

Obama is learning the truth about the economy, terror and what it means to be President, etc. It is a shame that he waited until he was elected to learn these things.
Hopefully his learning curve will be short and he will rely on "those in the know."

I'll back whoever becomes President, because that what Americans do (to a point. Clinton should have been impeached.) That's what people do who love America (hey Michelle) and want the best for the next generation.

Please, future Presidential candidates, have more experience and less naivety.

Good luck Obama, and I mean that!

A lesson learned for young voters

For all young voters, looking to Obama for change. You may be disappointed. I'm not saying you shouldn't have voted for Obama, but politics is about promises often not kept. Us "old people" know this and are not surprised by the following.

Excerpt from Lionel Beehner (italics are mine)
Pardon the metaphor, but Obama is trying to put lipstick on the pig that is US foreign policy. His national security team looks no less hawkish than the team assembled during Bush's second term. If I may ask, how is Hillary Clinton signing a communiqué or Robert Gates asking for more defense funding a "new dawn" exactly?
Ah, but the buck stops not with them but with Obama. The 3am call is his, not Clinton's, to make (even though one can almost hear her rehearsing Alexander Haig's famous "I'm in charge now" line in her head). Still, Obama's familiar-looking team of national security fixer-uppers does not inspire confidence. Nor do his vague answers to detailed questions on specific policies. "We're going to have to bring the full force of our power, not only military but also diplomatic, economic and political, to deal with those threats not only to keep America safe, but also to ensure that peace and prosperity will exist around the world," he told reporters. Obama seems to think he can wish away the world's evils with his eloquence and charm.
But his statements to date, whenever issues of substance are involved, have been lacking in specifics -- the kind of fluff that goes good with peanut butter but not with issues of war and peace. To wit: He says he will close Guantanamo. Great, a symbolic blow to terrorism recruiters' kneecaps, but what about Bagram Air Base in Afghanistan, which is even larger (with over 1,000 detainees), more secretive, and even houses juveniles? Obama promises to send more troops to Afghanistan but to what end: What are our goals there? And more troops will do nothing to improve the aid-distribution mess there or rid Kabul of corruption.
and it goes on ...
I hate to say it, but in terms of U.S. foreign policy, I don't see a whole lot changing under Obama, especially with the national security team he has assembled. The biggest thing I fear is that when Obama gets that 3am phone call, his voice will sound an awful lot like Bush's.

This is what us "old people" already knew. A lesson learned for the young.

Happy Birthday to me

I recently had a birthday. My immediate family recognized it and, although the importance of birthdays has lessened over the years, it is still enjoyable to be recognized.

It is dissapointing that other extended family members, as they call themselves, cannot bring themselves to remember, and if they do, said nothing; with the exception of one person(of a dozen or more people). Thanks to that one. It was an email and it meant a lot. A kind gesture. That person gave away nothing and enhanced someone else's life. I think that is great. It's like a compliment: "thanks for living one more year." It means no more and no less; no hidden agenda.

Others claim to care, but when even a simple birthday does not get honored by a card, email, phone call, whatever; that is saying something other than caring (actions matter.) They are thinking of self only. I've been guilty of that myself so I recognize it. That does not excuse it. And believe me, one can come up with all kinds of lame excuses if one tries.

Shame on those people. But more importantly shame on them for not even trying to change their behavior.

I guess for them, other things are more important. But I will tell you, it sure does not feel that way on the receiving end, no matter the reason.

P.S. What's even more ludicrous is some of these people are saddended by the fact we are growing apart -- big surpriser there uh!

Oh well. Happy birthday to me and thanks to the three who cared.

P.S.S: A recent study showed a direct correllation to the number of birthdays and length of life. In short, the more birthdays you have the longer people tend to live.

Three Legged Chicken

A man was driving along a freeway when he noticed a chicken running alongside his car. He was amazed to see the chicken keeping up with him, as he was doing 50 mph. He accelerated to 60, and the chicken stayed right next to him. He sped up to 75 mph, and the chicken passed him. The man noticed that the chicken had three legs. So he followed the chicken down a road and ended up at a farm. He got out of his car and saw that all the chickens had three legs. He asked the farmer, "What's up with these chickens?" The farmer said "Well, everybody likes chicken legs, so I bred a three-legged bird. I'm going to be a millionaire." The man asked him how they tasted. The farmer said, "Don't know, haven't caught one yet." (Molly - Ohio/USA)

Child Abuse

Those are words no parent wants to hear. There is a type of child abuse though called covert child abuse. We have to be careful because many times this is associated with "Munchhausen by proxy". However, there is another form. This other form has the form that the child is ignored, totally. Lets take an example. Suppose Johnny was in first grade and did not do his first home work assignment. What does that really mean. Nothing. It means Johnny did not do his first home work assignment. No more; no less. Now add in the following. No parent even knew there was home work, no parent asked to look at it, check to see if it was done, or anything. How does Johnny feel? Good question. I do not know. He's six. He feels but does not know how to analyze feelings or even what to do with them. It's covert; no overt like "I feel hungry." He does not know enough to go to his parents and say "parent me." Now Johnny goes to school, does not have his homework so he lies, my dog ate it or whatever. The lying worked, or so he thinks - it does not matter, it now becomes a tool for his covert life. "If I'm ignored, I can lie and no-one will know, I can do things and no-one will pay attention and know, I can become whoever I want (falsely)" plus a host of other behaviors.
Now fast forward a few years to a project Johnny is working on. It's been a few years, Johnny developed an interest on his own in third grade and learned what he could. But of course no-one else knew, why bother even telling them at this point. As a matter of fact, the thought does not even cross his mind. He tells other children but they do not understand. That's okay though, they are not his parents. He is disappointed but associates "with a child's mind" that no-one, even his peers care. No-one asks, cares or inquires in anyway about it. Johnny by this time cares but does not care. He has learned to manufacture a bubble around him so that even if someone cared, he would not trust it.

However, Johnny's feelings are not totally dead, at the school wide showing of the projects, his parents go through the motions of attending, but they are just the required motions and the minute they can leave they do. Maybe Johnny gets asked a question about his project which he answers incorrectly. Although he knew a lot and had interest, this is met not with parental interest in explaining the mistake, and patience; but simply criticism. Now Johnny feels stupid too.

Of course these are two things which Johnny remembers. There are probably hundreds; but the mind can't handle that as a child or adult and rolls it in to a form it can remember best; a couple of instances. But the baggage: slews of learned or figured or behaviors-real or not; correct or not.

So by the age of 10 Johnny feels others do not really care, he feels dumb and he has learned to trust the covert world of lying and distrust others. Through watching his peers, he starts to understand that this is not what other's lives are like and that it must be him. He sees the overtly abused child and feels bad about himself for having his feelings; he is not beaten. He feels shame and self loathing. He must be wrong and bad; why else would no-one care?

It does not really matter why Johnny's parent's are so ignoring of Johnny. Why they only care about themselves. What matters is what Johnny is learning. Maybe they are alcoholic, recovering alcoholics, maybe they are over compensating for their childhood; whatever. But they do not have time for Johnny; not real time. They might fake it. By now Johnny can see right through, does not trust it, and it simply reinforces his feelings; which are no longer feelings; they are beliefs that really he is a piece of sh_t. It's okay though (not really). He has a covert life and can pretend all is okay. He can lie and make others believe what he wants (actually just those who don't really pay attention.)

At some point in a child's life, 14 or so, when they start to become their own person they begin to understand that something is not right. Two paths are typically taken. One path leads to the child who acts out by getting in trouble to force attention and caring; positive or negative. The other simply recedes in to the shadows and has learned how to make everything appear okay.

What happens to that child when they grow up? I do not have an answer other than to say that grown up Johnny is still the 6 year old who did not do his first home work assignment and no-one knew, cared or paid any attention.

Johnny, being the "okay" teen may even be put in charge of the ignored other sibling who took a different path. Johnny learns fear and power. More tools. If he succeeds, it is because he faked it (at least that is what he believes deep down inside.) He is praised but he knows it he faked it and it reinforces his feelings (which have now become behaviors) of his own "covertness". If he fails, that's even worse. Now he knows he cannot fail. He fears failure. He fears the loss of control that he has learned to embrace.

What happened before 6? Between 6 and 10; and thereafter. Many things I'm sure. I do not have answers.

This is all just food for thought; fraught with gaps and questions but also of the beginning of important understanding.

None of us is perfect parents (I don't think) but we need to parent as best we can. At least let our children know that we know about them, what they are doing and give them the attention that steers them towards what we feel is correct behavior. They need to know we know.

Johnny did not have that and probably still does not. Even if he does, he has learned to not trust it.

Sleep Disorders

It is interesting. In the latest issue of Discover magazine (Dec. 2008) they discuss a sleep disorder called REM sleep Behavior Disorder (RBD). Some indictation of this disorder is activity during REM sleep such as vivid dreams that result in bodily movement, dreams of choking so real that the person wakes up coughing and in some cases may even try to hurt their bed partner if the dream invokes it. During REM sleep the body is supposed to be essentially paralyzed. The solution to RBD is a simple medicine called Clonazepam.

Advice to the president

Not from me but I endorse it (no matter who is president):

Read The Origin of Species and understand evolution.
This is an excerpt by Jack Horner in Discover Magazine.


Lincoln read Euclid's Elements. He did this not to widen his knowledge of Geometry but sharpen his logical thinking skills. Of course, I'm sure he learned some geometry too.

Work on Primes-a work in Progress

No. No headway yet. Hard work and persistance is the key; and, of course, it's fun.

As Edison said: I did not fail 2000 time (approx.) to create a lightbulb, I learned 1,999 ways not to create one.

Primes

Among several of my mathematics research projects, I am, like most mathematicians, venturing in to the world of Prime Numbers.

For those not in the know, Prime Numbers are those that are divisible by only the number 1 and the number itself. For example, 17 is only (evenly) divisible by 1 and 17.

The long standing problem is a "formula" for predicting primes. There isn't one (yet).

Since Primes are the building blocks of all other natural numbers (every number is the product of prime numbers), I see them as important.
As an example, the number 15 is the product of 3 and 5, both prime.
The number 26 is the product of 13 and 2 - both prime .
and so on for all Natural numbers.

Oh No...Politics is creeping in to my blog

I do not want politics on my blog but I have to say, regarding Obama's plan of extra taxes for those over $250,000 and "Spread the wealth", the following:

Spreading the wealth is a socialist idea. Although many countries employ socialism, it does not work very well. Ask yourself, "who is going to spread their wealth to you anyway? and who is doing the spreading?

The $250,000 idea is ridiculous. In some states that's a lot of money, in others, it's the bare necessity. How is he reconciling this fact?

Well, that's my two cents worth (am I taxed on two cents?). I'm not telling who I am voting for because, as always, their are positives and negatives. We seem to always have to choose "the lesser of two evils". But I do see one as much less capable of "evil."

We really need a third party for checks and balances (that our government is so proud of) and to offer a 3rd party perspective. Maybe this 3rd party would take the best of both parties.

Evolution Conundrum

Evolution to me is just plain obvious. However, there is an oddity that keeps me thinking. Humans do not manufacture vitamin C. We have to get it or die of scurvy. Most animals manufacture it in their bodies. But focusing on just humans I would think that we would have evolved to create our own vitamin C. In other words, during the process of evolving, I would think that the group that could not manufacture vitamin C would have die out in favour of those who could manufacture it. So this begs a couple of questions. Has the mutation to create vitamin C just never occured in humans so it never became a factor in the evolutionary process? Or maybe at one time we did manufacture vitamin C and evolved out of it as vitamin C bearing foods became abundant and other evolutionary survival traits became more important.

Maybe this is what happened to the Neandertals. Maybe they all died of scurvy in the end while the cro-magnon was able to gather the necessary foods to survive.