Author Topic: Elegant demonstration of Bertrand Russell sets of sets idea.  (Read 1023 times)

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Plane

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Elegant demonstration of Bertrand Russell sets of sets idea.
« on: August 29, 2014, 11:59:53 PM »



Bertrand Russell discovered that a set of sets may not be equal to itself.

His head did not explode .

Xavier_Onassis

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #1 on: August 30, 2014, 09:12:51 AM »
interesting.

Have you noticed that computers do not explode and  self-destruct when there is no logical answer?

My calculator simply posts an "E".

My computer does "file not found" or "division by zero error".

Kirk and Spock would somehow seem less heroic in these real life situations.
"Time flies like an arrow; fruit flies like a banana."

Plane

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #2 on: August 30, 2014, 02:04:34 PM »
  I have seen electronic devices smoke or even explode, but this never happens due to logic error.

    Sophisticated machines reset themselves.

       This is a dramatic hyperbole, logic machines can fail, but they don't even overheat due to logic contradiction.

          On the other hand I have heard of virus that can activate devices out of sequence and potentially do permanent damage.


[][][][][][][][][][][]

What I think is cool is that in special circumstances there are certain things that truly do not equal themselves .

Wipes out a basic axiom.

Xavier_Onassis

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #3 on: August 30, 2014, 02:19:00 PM »
I bought a USB charger cord from Yugster that charged rapidly and at the same time showed a moving image of blue dots that looked like electricity flowing into my Kindle. I realize that the image really had little to do with the speed of electricity, but it did look very cool, Everyone was most impressed. Then one afternoon there was this horrible smell, like a garbage dump on fire, and my device was melting, with plastic actually burning. I have  another one, and so far it works fine. The USB was plugged into a currency stabilizer that I bought for the TV, since in the Dominican Republic, electricity is unpredictable. So I guess my charging cable was defective. Teh image of the electricity flowing was bogus, but impressive. It did this for about 5 minutes, and continued charging.

I bought a different model that has a wire that just glows blue when it is plugged in.

=======================================================

Under what circumstances do things not equal themselves?

Like 2+2=5 for extremely large values of 2?
"Time flies like an arrow; fruit flies like a banana."

Plane

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #4 on: August 30, 2014, 05:25:02 PM »
The display of a charger just demonstrates that it is on , most of them do not indicate more than that .

I have some bad experience with the Kindle , which can destroy a normal cell phone charger. The Kindle can allow a charging rate that overheats and ruins the control circuit. You need a charger built for the Kindle to get dependability.

If you are willing to pay for the best you can get chargers that indicate battery level and automatically cut themselves off.

The big news on chargers is lithium batteries, a lithium battery that is charged or discharged too fast can burst into flame , people that fly electric model aircraft have taken to putting the battery into a clay flowerpot for its charging cycle. Good chargers for lithium batteries  sense charging rate and do not allow the battery to heat. Boeing had a lot of trouble with this.




Plane

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #5 on: August 30, 2014, 05:44:00 PM »



Under what circumstances do things not equal themselves?

Like 2+2=5 for extremely large values of 2?

 I recommend that you read better explanation than I can give you , I barely get it myself. google this later when you have a minute to kill.

But I will try.

  When you have a set there are rules that define the set.

   When you have a set made up of smaller sets there is an over arching rule for them all and more specific rules for the subsets .


You may have a set that is" all the forks on planet earth', "all the silver forks on planet earth" would be a subset of "all the earths forks" , "all the forks in China" would be a subset of "all the forks on earth" and it might overlap the subset "all silver forks" if some of Chinas forks are silver.
 

So "all the forks on earth" is a set of sets and itself would be a subset of "all the eating utensils on earth".

Each of these sets and subsets would have a number of members , a finite number since all the sets and subsets are of materiel objects.

But what happens when the rule that defines the members of a set is self referencing?... self contradictory?

The set of allowable rules in this comic is a pretty good example, the defining rule is that there shall be NO rules.

So what is the number of rules?

Bertram Russell was a pretty smart guy. Just to notice this.

Xavier_Onassis

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #6 on: August 30, 2014, 10:50:57 PM »
But what happens when the rule that defines the members of a set is self referencing?... self contradictory?


What does this mean? How can a set be self contradictory?
"Time flies like an arrow; fruit flies like a banana."

Plane

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #7 on: August 30, 2014, 11:17:27 PM »
      I knew I couldn't explain that.




    Try this.
http://en.wikipedia.org/wiki/Russell's_paradox
Quote
................. naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell's paradox.

Alternately

Quote
Let us call a set "abnormal" if it is a member of itself, and "normal" otherwise. For example, take the set of all squares in the plane. That set is not itself a square, and therefore is not a member of the set of all squares. So it is "normal". On the other hand, if we take the complementary set that contains all non-squares, that set is itself not a square and so should be one of its own members. It is "abnormal".

Now we consider the set of all normal sets, R. Determining whether R is normal or abnormal is impossible: if R were a normal set, it would be contained in the set of normal sets (itself), and therefore be abnormal; and if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.


    Some people think of paradox as a sort of illusion, but this is not entirely correct there are real things that are paradoxical and this is one of them.

     Now if our brains worked better would it be resolved or is it such a natural paradox that it cannot be resolved into a nonparadox at any level of examination?


     It is fun to think about , but is it useful for anything?

       Not yet , but when imaginary numbers were discovered they remained useless for a generation . Then it was discovered that they describe the phase relationship of AC currents .

     Perhaps something in the world we live in will be better understood in the light of Bertrand Russell's paradox, just nothing yet.

Xavier_Onassis

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #8 on: August 31, 2014, 12:16:28 AM »
I do not doubt that Russell was a mathematical genius. I can do algebra, I have studied trig and calculus, but don't remember much if that as I never use it.

It seems that to say there are "no rules" is a problem, because in nature there always are rules, though we may not have discovered them yet.

Ay NMSU.I wanted to take the "teacher's matth" course, because I was going to be a teacher. But the course was full, and all I could get was a course taught by a guy doing his PhD in set theory. With the help of an EE major named Roger, I got a B in the class, but I never found any use for set theory.
"Time flies like an arrow; fruit flies like a banana."

Plane

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #9 on: August 31, 2014, 09:52:37 AM »
   As a language expert you might do very well in sets.

   A key part of it all is describing the situation , describing the process and describing the members of the set.

    That is something that you probably have examined in the context of spoken language.

     The real world has problems that can be resolved with sets and processes developed to manipulate how sets are understood.

     Math has a lot of things that were discovered in theory years before any practical use for them was ever found.

Xavier_Onassis

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #10 on: August 31, 2014, 11:20:36 AM »
I might do well in sets, but why would I wish to?

I might be an excellent opera singer, but I detest opera music. at least the vocal parts. All that warbling I find annoying..

I find math for math's sake to be tedious and boring. I see math as a useful tool. Anything more complex than Bollinger bands and 50 day running averages is beyond anything I want to do with math.
"Time flies like an arrow; fruit flies like a banana."

Plane

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #11 on: August 31, 2014, 04:58:58 PM »
   I don't know what Bollinger bands are , fill me in .


     The esoteric and abstract in math seems useless , but what happens over and over is that the understanding of the math happens long before any practical use.


   Boolean algebra predates the machines that depend on it , imaginary numbers got that name because their discoverer didn't know that they were good for describing phase relationships .

     I would just bet that the math that the Egyptians needed for building the pyramids was quite old before they ever used it.

     Abstract understanding is an enabler for improvement in practical engineering.

      This brings to mind another paradox.
      Our technology has moved from machines that a minority of us understand , to machines that exactly no one understands entirely.

      The building of a modern car or computer or aircraft requires the use of expertise in so many fields that exactly no one understands the entire process of production. I like how Matt Ridley covers this.http://www.wired.co.uk/news/archive/2010-07/21/ideas-having-sex-matt-ridley-steven-berlin-johnson

     So since new machines require that someone understand at least most of it before the first one gets built , will the production of new types of machines slow down about now, because it is getting harder to have abstract ideas of great complexity relate to one another within one head. Everything new now requires bigger and bigger teams, which is harder and harder to make happen.

   































 

Xavier_Onassis

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Re: Elegant demonstration of Bertrand Russell sets of sets idea.
« Reply #12 on: August 31, 2014, 06:05:13 PM »

The Basics Of Bollinger Bands®
By Investopedia Staff   A A A
Related Searches: Macd, Moving Averages, Macd Indicator, Understanding Macd, Simple Moving Averages Examples
In the 1980s, John Bollinger, a long-time technician of the markets, developed the technique of using a moving average with two trading bands above and below it. Unlike a percentage calculation from a normal moving average, Bollinger Bands® simply add and subtract a standard deviation calculation.

Standard deviation is a mathematical formula that measures volatility, showing how the stock price can vary from its true value. By measuring price volatility, Bollinger Bands® adjust themselves to market conditions. This is what makes them so handy for traders: they can find almost all of the price data needed between the two bands. Read on to find out how this indicator works, and how you can apply it to your trading.(For more on volatility, see Tips For Investors In Volatile Markets.)

What's a Bollinger Band®?
Bollinger Bands® consist of a center line and two price channels (bands) above and below it. The center line is an exponential moving average; the price channels are the standard deviations of the stock being studied. The bands will expand and contract as the price action of an issue becomes volatile (expansion) or becomes bound into a tight trading pattern (contraction). (Learn about the difference between simple and exponential moving averages by checking out Moving Averages: What Are They?)

A stock may trade for long periods in a trend, albeit with some volatility from time to time. To better see the trend, traders use the moving average to filter the price action. This way, traders can gather important information about how the market is trading. For example, after a sharp rise or fall in the trend, the market may consolidate, trading in a narrow fashion and criss-crossing above and below the moving average. To better monitor this behavior, traders use the price channels, which encompass the trading activity around the trend.

We know that markets trade erratically on a daily basis even though they are still trading in an uptrend or downtrend. Technicians use moving averages with support and resistance lines to anticipate the price action of a stock. Upper resistance and lower support lines are first drawn and then extrapolated to form channels within which the trader expects prices to be contained. Some traders draw straight lines connecting either tops or bottoms of prices to identify the upper or lower price extremes, respectively, and then add parallel lines to define the channel within which the prices should move. As long as prices do not move out of this channel, the trader can be reasonably confident that prices are moving as expected.

When stock prices continually touch the upper Bollinger Band®, the prices are thought to be overbought; conversely, when they continually touch the lower band, prices are thought to be oversold, triggering a buy signal.

When using Bollinger Bands®, designate the upper and lower bands as price targets. If the price deflects off the lower band and crosses above the 20-day average (the middle line), the upper band comes to represent the upper price target. In a strong uptrend, prices usually fluctuate between the upper band and the 20-day moving average. When that happens, a crossing below the 20-day moving average warns of a trend reversal to the downside. (For more about gauging an asset's direction and profiting from it, see Track Stock Prices With Trendlines.)

Figure 1
Source: MetaStock
You can see in this chart of American Express (NYSE:AXP) from the start of 2008 that for the most part, the price action was touching the lower band and the stock price fell from the $60 level in the dead of winter to its March position of around $10. In a couple of instances, the price action cut through the center line (March to May and again in July and August), but for many traders, this was certainly not a buy signal as the trend had not been broken.

Figure 2
Source: MetaStock
In the 2001 chart of Microsoft Corporation (Nasdaq:MSFT) (above), you can see the trend reversed to an uptrend in the early part of January, but look how slow it was in showing the trend change. Before the price action crossed over the center line, the stock price had moved from $20 to $24 and then on to between $24 and $25 before some traders would have confirmation of this trend reversal.

This is not to say that Bollinger Bands® aren't a well-regarded indicator of overbought or oversold issues, but charts like the 2001 Microsoft layout are a good reminder that we should start out by recognizing trends and then simple moving averages before moving on to more exotic indicators.

The Bottom Line
While every strategy has its drawbacks, Bollinger Bands® have become one of the most useful and commonly used tools in spotlighting extreme short-term prices in a security. Buying when stock prices cross below the lower Bollinger Band® often helps traders take advantage of oversold conditions and profit when the stock price moves back up toward the center moving-average line.

(For more on gauging trends with this technique, see Using Bollinger Band® "Bands" To Gauge Trends.)

=========================================================
That is the explanation. I find Bollinger Bands fairly good for predicting how much to offer for an Exchange Traded Fund, and when to buy it or sell it using a limit order, and when to buy or sell a mutual fund.

When the price it toward the upper band, it is a better time to sell and I set an ETF limit order within a 5% of the last bid.  When the price is toward the lower band, it is a better time to buy and I will offer a price 7-10% lower than the last bid.

The goal is to buy low and sell high. I never buy or sell  an ETF at market price, because all I normally have to do is name my price and someone willing to sell at the market price will always come along. within between an hour and a week. Mutual funds buy and sell for only one price, which is set at the end of each day.
 
Bollinger bands generally result in me buying at a lower price and selling at a higher one. There may be better ways of doing this, but this works for me.

ETF's always involve paying a small commission ($7.00 to $12.95). I rarely pay any commission to buy or sell mutual funds UNLESS I think I can make iit up within a week.
If I hold a mutual fund for at least 90 days, the broker eats the commission. 

Bollinger Bands are tied to the standard deviation of a stock or mutual fund.

Another important figure is the beta.   If a stock is equal in volatility to its corresponding index, the beta is 1.0.  1.10 means it is 10% more volatile, 90 means 10 less volatile. Investing is all about the risk vs reward

What oft-quoted figure is mostly worthless  to an investor? The Dow Jones Average. It is a weighted average of thirt stocks that change from time totime,

"Time flies like an arrow; fruit flies like a banana."