Just a spectacular graphic! Unknown source. Found on someone's blog.


Finally I decided to go ahead and explain this the way I see it.

Remember, Romney was pushed through by the elite of the party, which disconcerted many, with the goal of ridding the White House and country of Obama. Here the analogy is to the Trojan Horse in this case  built to fool the voters to let the Republicans who caused the financial mess back into power.  Once in power they fully intend to control Romney so he is basically a non-entity, a facade. Remember the quote about not needing a candidate that could think but one who would get elected? They would do the thinking and he would have to tag along for the ride. Remember, these are people who do not compromise, who do not back down regardless of a country in dire need of help. They are willing to go the edge of doom to get things exactly their way. They are willing to play chicken with a car speeding at them until the other guy develops the sanity of pulling to the side. The other guy has no way to stop them without sacrificing everything.

Point, well, taken.

Assumptions, or postulates, are pretty much standard stuff in many fields of knowledge, including mathematics. They are seldom made clear or obvious and I feel that their importance is shoved to the back burner, when they should not be.

I often bore people with the personally startling story of when I learned that these life assumptions were extremely important and that the knowledge subsequently derived from such baseless but expedient assumptions was knowledge not to be fully trusted as truth but more on an intuitional basis.

When just a young man, the significant moment occurred as I was confronted with one of Zeno’s paradoxes. Zeno was a Greek philosopher from the 5^th century B.C. There was a grade school level cartoonish article on the bulletin board in my elementary math class which I am fairly certain did not mention Zeno by name. I did not know that there was a great thinker behind the thing. I would love to have that little piece of paper now because it began a lifelong healthy doubt in all established thought. Zeno needs to be added to my list of heroes.

An adult version of his paradox is as follows:

The Dichotomy Paradox

“That which is in locomotion must arrive at the half-way stage before it arrives at the goal.”Aristotle, Phisics

Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

The resulting sequence can be represented as:

This description requires one to complete an infinite number of tasks, which Zeno maintains is impossibility.  -Wikipedia

When I tell this story I often tell of how much it disturbed me at the time. I was ever the worrier. Even without an impressive authority to back it, this thing on the bulletin board was not striking me as particularly humorous as intended, but was an attack on the “number line” itself which was posted above the black board of every elementary math class I can remember. Its importance was preeminent to the class. Do not attack my number line!

Further along in my education, with Zeno nagging me constantly, I found that our numbering system, or rather numbers in and of themselves, were derived from one important assumption or “postulate.” This was the concept of the “spatial point.” Between the point marked “Zero” and the point marked “One” is an infinite number of divisions. This is because, as I learned later in geometry, each point on the number line is infinitely small. Add these infinitely small points together and get an infinitely thin line. I promise I am not making this up from whole cloth but you should be suspecting me, because you should suspect everything you believe that you know. Zeno should be sitting on your shoulder when making any decision.

My mind raced as a young man. If the points are infinitely small, they cannot really connect together. I have fairly good “spatial reasoning,” I think. So, from this hazy notion I concluded that the “number” part of the number line was pretty much based on something called “the point.”  They actually tell you these things in the beginning but you pass over them and go on to build huge structures of elegant thought based upon them. It would be different if the teacher came in every day and stated what needs to be said: “Accepting the postulate that there is such a thing as a number, let us proceed with the class.”

After further research to make sure once again that I was not dreaming in elementary school when they told me that mathematics itself was fairly a guess, it seems that this postulate has further degraded in its ability to convince me.

In Wikipedia, the entry on “point”:

In geometry, topology and branches of mathematics, a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero dimensional, they do not have volume, area, length or any other higher-dimensional analogue. [emphasis mine]

And the entry on “primitive notion”:

In mathematics, logic and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience.

If I were to start with a notion like “Let’s assume there is a God…” or “Let’s assume no God…” well, you get the point, which is infinitely large as well as infinitely small, being zero dimensional as it is, or was, or whatever.

Cutting Edge Intelligence

By accident, Fox News (the channel which the TV set was left on by the previous occupant of the condo we are using for vacation) played for about 20 minutes and the two most air headed "contributors" from right and left traded commentaries about President Obama's convention speech of the previous night. At first I thought that the liberal lady (model type beauty) was chosen simply because she looked good and was air headed. She talked only in platitudes like "played to the base" that could have been said after any political speech ever given. But, then, just as I was about to change the channel thinking Fox News had obviously and intentionally provided a bad spokesperson for the left, a twin air headed person speaking for the right (same model type beauty) said things even more platitudinous and devoid of intelligent thought. It was worth about five more minutes before I turned the channel and landed on a local area public access channel. I watched two very youthful Orange Beach girls teach me how to make mini pizzas and how to slice various vegetables correctly and with safety. Hold the knife like this so that it doesn't slip; slice onions like this; slice bell peppers like this; and remove this funny looking piece and throw it away. These girls were brilliant. They made smiley faces out of the vegetables on the tomato sauce covered dough they had already taught me to roll out and stretch. As one dropped a pizza round after trying the on "top of the knuckle" method that professionals use to stretch the dough, she said, "It's okay if you drop it as long as it doesn't go on the floor. Obviously this method is not working out for me so I will use the rolling pin some more." It was quite enjoyable to see how well they had prepared for the show. "This is the part of the onion where the roots come out, and this is the part where the green growth comes out, because onions grow underground." Mom was called in to put the pizzas in the oven for safety. Really cute AND thoughtful stuff. I loved it! Oh yes, do not wash the mushrooms in water but use a dry paper towel to clean them. Mushrooms soak up water like a sponge. These budding TV personalities and intelligent girls were clearly not destined for the likes of Fox News.

Mitt's Flaws, Not Clint's

I have been kind of wondering why some people think all of the jokes about "the chair" are somehow mean spirited and cruel. The reason the speech seemed so odd was precisely the cruelty and disrespect Clint Eastwood showed towards the President. There were snarky remarks, remarks that blamed a war from President Bush on President Obama, and worse, two remarks that basically said the President (with no way to respond) had asked Romney and Clint to go F themselves.

It is not uncommon for a mob to create an effigy of a hated figure and do terrible things to it. It is not so common at a convention. The Romney, or GOP people, responsible did not vet the speech, trusting Clint Eastwood for some reason, to ad lib without teleprompters. The jokes about "the chair" are mostly not pointed at Clint Eastwood's personal character but at the incompetence of the Romney "kiss my a**" people who all let Clint Eastwood twist in the wind.

Not unlike every other touchy situation, they found other people to blame and swallow what should have been their responsibility. For those who have made this some kind of mean spirited attack on Clint Eastwood, I even hesitate to criticize them. Clint Eastwood burned an effigy of Obama in one of the most public of places and, despite what some people think about some imagined infirmity on his part, he is a highly intelligent man capable of writing, directing, and acting. His weakness is in having the ego of a man who believes he knows better than those around him and overestimates his own ability to create a spontaneous stage presence.

Comedy aside, the whole affair was such an accurate metaphor for the GOP, it is hard to overstate it. In attacking people with meanness, making untrue accusations, creating an evil Obama out of thin air, and treating those of us who respect the President to a sorry display of utter hatred, THEY cross the line. The Democrats have, for all too long, rolled over in the face of things like this, the dehumanizing of us all. In general liberal folks do not display the type of hatred that, say, the tea party folks, display without reserve. Liberals generally do not even do this in response to the hatred they receive. But times have changed as hatred has piled upon hatred, often by those who act morally superior, and now the liberal side is actually fighting back. And enough IS enough. Eventually you punch the boy in the nose who constantly steals your lunch money.

For further reading on the "chair" incident and the flaws it illustrates:

http://www.slate.com/articles/news_and_politics/scocca/2012/08/clint_eastwood_gop_convention_the_romney_campaign_sells_out_its_surprise_speaker_.html

 

This is brilliant, i.e. not mine. :)  I wish I had time to be more aimless.