Gullibility and the Bell-Shaped Curve

I believe that a great many people know about IQ and the bell-shaped curve. That is, if you randomly pick 4000 people in the United States and plot a graph of how many people have an IQ of 50, 51, … , 100, 101, …, 150, you would find that the graph looks like a bell-shaped curve. But why is that so?

Mathematicians have an answer for that. It is called the Central Limit Theorem, and the curve is called the Normal Distribution or the Gaussian Curve. Briefly. what it says is that averages of random samples from large populations will assume the shape of a Normal Curve. This theorem has been proven mathematically. But how does this relate to IQ?

Consider what IQ is. It is the average of a random assortment of genes, nutrition, and environmental factors. Together they fall under the umbrella of the conditions that satisfy a Normal Curve, ranging from lower IQs to higher IQs.

Now take gullibility. Like IQ, gullibility is the result (average) of a random assortment of genes, emotions, experiences, and nutrition. So, if we could measure gullibility and graph a frequency curve of those measurements, we would get a Normal Curve ranging from lower gullibility to higher gullibility. So, what about it?

Well, the Normal Curve has 2 parameters: An average (the Mean) and a spread (measured in terms of a standard deviation). We can increase or decrease the Mean and/or we can increase or decrease the spread. With respect to IQ it would be desirable to increase the average IQ and decrease the spread, if we could. But note that decreasing the spread would result in less diversity.

The same thing would apply to gullibility: the average gullibility could be lowered or raised and the spread from least gullible to most gullible can be decreased or increased. With respect to gullibility it would be desirable to decrease the average and to decrease the spread.

In the meantime, the human population has a spread from extremely gullible persons to extremely skeptical persons. Similarly, the human population has a spread of extremely callous persons to extremely kind and thoughtful persons. And we have a problem when callous persons abuse gullible persons.

This perspective of the Normal Curve goes a long way to understand human interactions.

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On an often, and regular, basis I get a catalogue from the Great Courses. A few weeks ago I got a catalog and casually looked through it. I spotted a course, The great Questions of Philosophy and Physics, by Professor Steven Gimbel. I looked at the table of contents and read some of the descriptions. Then I said to Sharon that this would be interesting but I don’t think I’m up to watching any lectures. Raquel and Mia overheard me and the three of us got into a discussion, but I maintained that I just didn’t think I could concentrate and stay awake. Whatever, the girls decided to get it for me for Christmas. It came with a booklet describing the contents of each lecture and providing historical backgrounds. Oh, man, how could I resist? I watched the first 2 lectures on 2 successive days (these are 50 minute lectures and he speaks fast) and it has gotten me to do some thinking. So I have taken time off to indulge in my thinking. And I’m going to share it with you, and probably bore you or turn you off.

So far, the 2 lectures have re-aroused my thoughts about multivalued logic and the Universe’s destiny. So first let me clarify multivalued logic. Consider a person who reaches the age of 90, what is the likelihood that the person will reach 100? Well, you can get data of persons who lived to 100 and data of 90 year olds who did not. Forming  appropriate ratios from the data, you can estimate the 2 probabilities for they will and they won’t. You can do the same for the survivors who reached 91. And so on. But then how would you estimate the following conditional probabilities: What is the probability that if a 90 year old lives to 91 that he/she will live to 100; what is the probability that if the 90 year old lives to 92 that he/she will live to 100; and so on. It might be possible to take the data and piece it together to arrive at estimates. But note that in every case we have subdivided the question into 2 choices: live or die. And we associated probabilities with those 2 choices. In Mathematics we have true versus false, only 2 choices. Theorems in Mathematics are either 100% true or 100% false within the framework of the axioms and definitions used by these theorems.

Yet, even in Mathematics there are conjectures that have never been proven to be either true or false, yet there seem to be empirical evidences that they could be true. So we would need a “maybe”: a 3 valued logic with probability assignments. That would be the simplest form of a multivalued logic. But Nature is not simple. Keep that in mind.

So let’s go back to the 90 year old person. I tried to set up a situation where we could ask the question: if this step happens then what is the likelihood that this next step will happen, which would suggest “what is the probability that a certain step, B, would take place IF another step, A, has taken place”. So B depends upon A to have taken place so the probability of B is dependent upon the occurrence of A. In other word, the probability of B is contingent on the probability of the occurrence of A, or as mathematicians would say, “the conditional probability of event B given the event A”.

So now the whole idea of multivalued logic running over Time is that you have a plethora of alternatives with infinitely branching conditional probabilities.  

So, going back to the time I gave Trump a probability of 0.90 or 0.95, I treated it as a yes or no. However, the 0.90 or 0.95 could have been subdivided into a series of contingencies, one of which could have been that he would or would not encounter a catastrophe along the way. If I had any notion of the odds of a catastrophe occurring I would have stuck it in and considered his conditional probability of getting elected given that the catastrophe could occur. Of course there are a whole bunch of things that could have happened, and they all would have had to be considered with conditional probabilities that he would then get elected.

You can see, then, that the Evolution of the Universe and the Evolution of Life on Earth and the Evolution of our Societies are branching conditional probabilities with increasing numbers of branches and with at least a “sprinkling” of randomness.

Nevertheless, there appears to be some sort of direction. For example, I sense that the direction of the Evolution of our Societies is towards their becoming more civilized. However, there are contingencies such as how would Societies react to an expansion of our Sun; how would Societies react to a dark sky; how would Societies react if the Universe becomes static; how would Societies react if the Universe begins to contract? And what are the probabilities associated with these phenomena?

I have more to say about Dark Energy and Dark Matter, and growth and decay curves, and the Normal Distribution, but I think I have said enough right now.

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A Nice Day For A Walk



Nelson looked up from his computer, got up, walked across the room, and kissed his wife, Dorotea, and said, “I think I’ll go for a walk to clear my head. It looks like a nice day for a walk.

Nelson was a physicist, a Professor at the local University. Dorotea was much more inclined to the arts. She did artwork on the computer and made jewelry. Her work was well in demand. Nelson was a demanding Professor, and not very much in demand by his students. His colleagues, however, had some respect for him.

Nelson stepped out the door and was greeted by a cool, gentle, caressing breeze. The sun was out, but there were a few clouds in the sky; a nice day for a walk. He walked, listening to the birds, taking in the scent of the lilacs, opening his arms, and watched a beautiful red cardinal land on a branch and start his song. He thought, “There is so much beauty here, does it have to end?

The thoughts he had intended to escape came rushing back at him. The evidence is there. The Universe is expanding exponentially. Will it continue to do so forever? If so, what will happen to all that we are and to all that we see here? Will memories, memorials, history, and any semblance of life be preserved in some form of “Heaven”, or will it all vanish in an infinitely expanding Universe? Can Religions deal with it? What good are morality, abstinence, kindness, fair play, and helping thy neighbor if everything gets dissipated with eternity? Why not just get what you can and as much as you can for yourself in the time allotted to you? Why put off for another day what you desire for today?

But there is another factor to consider: What is the cause, or force, driving this exponential expansion? Could it be Dark Energy? If so, then what does Dark Matter do? Is it possible that Dark Matter possesses a force that would pull at the expansion and cause it to slow down, and maybe even stop it or, perhaps, reverse it? What scenarios would that create?

Slowing it down would mean that it would take longer to achieve the ‘forever’ expansion. Stopping the expansion would mean that at some point in the exponential curve there would be a levelling off of the expansion, and the Universe would occupy a fixed space forever. We have no idea what the Universe would look like at that point in time. And we have no idea what effect a non-changing, stagnant Universe would have on the contents contained in that Universe. How would people respond to that? How should religions respond to that?

Nelson, puzzled with his thoughts, suddenly became aware of the people who were also walking, and enjoying their walks on such a nice day. He thought, “Why can’t we have this forever? Why can’t this last for every generation, forever? Is this what could happen in a non-changing, stagnant Universe”. “You know”, he thought, “Religions could handle this. They would have Eternity on their side and they can preach that Heaven on Earth could become a reality if we all accepted and respected each other. They can preach that we could all share nice days for walking, listening to the birds, taking in the scents of the flowers and the baking and the cooking, and taking in the sights and sounds of the beautiful and the not so beautiful.”

But then he thought, “What would happen if the force of Dark Matter reversed the exponential expansion and turned into an exponential contraction?” This possibility jarred him. The idea of an exponential contraction could, or would, he thought, result in a new Big Bang and the creation of a new Universe with same Mass and Energy and the same Mathematical and Physical Laws. He wondered, “Would that result in a replica of this Universe, but with a different consciousness? Or would the Laws of Probability alter the courses of events to provide a more unique Universe?”

Nelson stopped and looked around, and spied an empty bench. He went to it and sat down. “This”, he thought, “requires a lot more thought and I had better sit down to think about it.”

First, would information from one Universe be carried over to the next Universe? Probably not, but suppose it did. Who, or what, would receive it, and how? How would that affect the succeeding Universe? Would it make it possible for intelligent life in the succeeding Universe to alter the course of events to stop the contraction? How would Religions approach this subject?

Second, if intelligent life in one Universe cannot transfer information to the succeeding Universe, is it possible for the succeeding Universe to never develop an intelligent life form to discover that which has been discovered in the preceding Universe?

Third, would this process of Big Bang-expansion-contraction-Big Bang go on forever? If so, what would religions look like in those iterations?

Fourth, what would be the shape of the expansion/contraction curve? Would it be the shape of a 3-dimensional Normal curve? Would that reveal or imply anything?

Nelson had no answers to these questions, and he could not see how Physics or Cosmology could answer these questions. But, nevertheless, we know that we have a few billion years, of Earth time, to think about and explore these matters.

The beautiful day was turning into an exceptional evening, and Nelson got up off the bench and headed home to share the exceptional evening with Dorotea.

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2020-05-11        PERFECTION

If any object in this Universe, or the Universe itself, is perfect, should it, or would it ever change?

I submit that perfection would be synonymous with never needing to, or resulting in, change. In other words, I submit that if something is perfect it would never change. Conversely, if something changes then it was not perfect.

The evidence shows that this Universe is expanding and changing; this would indicate that it is not perfect. Perhaps somewhere in TIME it will become perfect, and cease to change.

The evidence also suggests that everything contained in this Universe is changing; this would indicate that everything in this Universe is not perfect. Perhaps somewhere in TIME they will all become perfect, and cease to change.

What would happen to this Universe and its contents if, in TIME, all ceased to change and became perfect?

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2020-04-15        GOD

A simplified representation of Evolution is often shown by various stages from fish to humankind. This is a caricature and does not represent the development of such entities as the lungs, the eyes, the spine, the heart, and the brain. Developments were neither helter-skelter nor were they absolutely well-coordinated. But they did work together. For example, as the heart developed from a simple muscular bulge to a single chamber heart, to a double chamber heart, to a triple chamber heart and, finally, to a four chambered heart, the owners of those respective hearts increasingly expanded their domains on this planet. Warm blooded attributes did not occur until the presence of the four chambered heart. Warm blooded attributes contributed to the development of the mammalian brain. We might wonder if this is the pinnacle.

Is it possible to conceive of this as the work of God? The experimentation, the molding of the clay, what if God set these things in motion?

Suppose Theologians and Clergy took an integrated course in Comparative Anatomy and Embryology, such the one that had been taught by Professors Florence Moog and Viktor Hamburger at Washington University in St. Louis in the 1950s. Would they see the wonders of God’s experimentation? Would they embrace Evolution as God’s work? Would they reconcile Evolution with “and God created the Universe”?

And then there are equations and geometries that appear to describe the properties and attributes of the Universe. Did God create the Universe using equations and geometries as scaffolds to build on? Did God create Numbers – Natural numbers, negative numbers, rational numbers, real numbers, complex numbers – and build a Logic around them? Did God create a multiplicity of Geometries based on various combinations of “self-evident” truths? Did God create Infinities? Is God the beginning and end of Infinity?

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What you say or do

You needn’t lament things you said or didn’t say, or things you did or didn’t do. You could think about them and consider them and perhaps become the wiser for them, and perhaps become more compassionate because of them.

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The Universe As I See It

The Universe as I see it. 2020-03-12
Multivalued logic (the two-valued logic of Mathematics is a proper subset)
Growth curves
Failure rate curves
The Central Limit Theorem (the Normal curve, the Bell-shaped curve)

Change:  All objects in the Universe, including the Universe itself, change. This assertion leads to a contradiction in Mathematical logic but probably does not lead to a contradiction in Multivalued logic.

Chance:  Chance (Probability) is everywhere. There are regularities which can be observed in the short term, but there are always elements of probabilities in the long term.

Multivalued logic: There are always two or more possibilities to an outcome, and each possibility has a probability weight to it. In Mathematics we seek statements that can have only two possibilities, true versus false, and we seek truths that must have probability weights of one. But in the overall aspects of the Universe statements generally have more than two possibilities, each with a probability weight of less than one but greater than zero, and whose probability weights add up to one.

In Science we observe phenomena which can have a variety of causes, or origins, and we assign probability weights to the possible causes, or origins, and we generally pursue an investigation of the cause or origin with largest probability weight. Investigations of this type can lead to a reassignment of the probability weights and sometimes introduce new possibilities into the possible causes or origins with a reassessment of the probability weights.

Growth curves: Growth curves are a manifestation of an exponential rate at which objects initially expand and grow.

Failure rate curves: Failure rate curves are a manifestation of an exponential rate at which objects decay.

The Central Limit Theorem: This is a proven Mathematical Theorem. In words, it states that averages of random samples taken from populations which have a finite mean (average) and a finite standard deviation (spread) will tend to have a bell-shaped curve. In many cases ten random samples, each of size ten, will begin to show the pattern when their values are plotted on graph paper. The pattern becomes much more obvious when the number of samples and the sizes of the samples increase.

We have evidence that Life can exist in this Universe where we have a confluence of energy, water, oxygen, carbon, and nitrogen. There is also evidence on Earth that life can exist when oxygen is replaced by sulfur. There also appears to be that Life on Earth can exist at some extreme temperatures and pressures.

It is possible that carbon can be replaced by silicon, resulting in a silicon based life system instead of a carbon based life system. As we explore space we may be surprised to find the existence of many different combinations of elements on which Life is based.

As with everything else in this Universe, living things change. They evolve. Life forms may seem stable in the short run, but in the long run they come and go with varying probabilities and with chance encounters from other parts of the Universe. Survival of life forms depends upon adaptability and to what some refer to as “luck”.

Time is a human construct to measure changes and rates (the passage of Time). There is no beginning and no end to what we call “Time”. Provide any time date, such as the “Big Bang”, and one can ask, “What preceded that?” And does “Time” end if our Universe ends? And is our Universe unique, or are there other Universes? Will our Universe expand “forever”, or will it contract to where there will be another “Big Bang”? Will such “Big Bangs” go on forever? And if there are other Universes, how did they originate and what patterns could they exhibit over “Time”?

In this respect we are dealing with infinities. The good news is that we can explore “forever”. The bad news is that we can never discover THE true origin of matter, energy, and how everything came to be. Or is there a small outside chance?

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They make sense

Why do we study and explore Science and Religion, Mathematics and Philosophy, Music and The Arts, Language and History, Literature and Theater, and all the other subjects we learn in our secular learning institutions? Why? Because they make sense. The more we learn and explore the more we are impressed with their making sense, and the more convincing it becomes to think of an Intelligence behind it all.

You may call that Intelligence God, Divinity, The Father, The Almighty, Supreme Being, Jehovah, Jesus, Allah, Adonai – but in reality this Intelligence may not be a being. It may be whatever it is, in its own order of infinity.

But why create a Universe where things make sense?

This Universe was created with Matter, Energy, and Chance. It was created with Properties and Laws. As we explore the Properties and Laws of Matter, Energy and Chance we find regularities, accidents, and Change. The Universe, and everything in it, is Dynamic and Changing, with Change based on Chance (a probabilistic logic).

With respect to the evidence of an expanding Universe there are at least five possibilities: The expansion may be exponential, the expansion may be linear, the expansion may be an S-shaped curve with either a flat top or followed by a continuing sequence of S-shaped curves to continue the expansion, or the expansion may slow down and then proceed to contract. Why would the Intelligence want the Universe to expand forever, either exponentially, linearly, or with a sequentially repeating S-shaped curve? Why would the Intelligence want the Universe to stop expanding and remain at a fixed size forever as in an S-shaped curve with a flat top? But if the Universe expansion slowed down and contracted that could result in another Big Bang creating a new Universe. Might the Intelligence prefer to see a sequence of Universe renewals where Change and the Laws of Chance could lead to an infinite variety of sequential Universes, all based on the given Properties and Laws of Matter and Energy we have been witnessing in our Universe? The repetitions (iterations) could go on for as long as the Intelligence provides for it to repeat. Perhaps there is an as-yet unrecognized force that will slow the expansion and cause a contraction. This could make sense.

There could be parallel Universes with other sets of Properties and Laws, different from the Properties and Laws of our Universe. These parallel Universes could exist on other Timelines created by this Intelligence, or even created by other Intelligences. We are finite beings embedded in layers of infinities. But thus far our Universe appears to make sense.

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Change 2019-09-23

Scientists say that our Universe is expanding. In other words, it is dynamic and changing. As a matter of fact, everything in this Universe is dynamic and changing: stars are born, age and die; galaxies move through space; planets orbit stars, and planets and their orbits change; and our planet and everything on our planet changes with time. Change is ubiquitous and inherent to our Universe and to its contents.

And so it is that species change and human societies change. And so it is that some humans welcome changes to their societies while other humans do not. And the tendency is to label those who welcome change as “liberals” and to label those who resist change as “conservatives.” It would seem that “conservatives” fight an uphill battle against a fundamental property of the Universe. Some humans might label it “bad” to resist change, and some humans might label it “bad” to change for the sake of change. But the Universe does not recognize “good” and “bad.” Changes take place regardless of human placement of “good” and “bad” on the outcomes.

To illustrate the point that “good” versus “bad” is a human construct that has nothing to do with the nature of the Universe, consider a person who sets off a bomb in a crowded marketplace killing himself and many others. To the bomber’s allies he’s a martyr, a hero –“good”. To the victims and their allies he’s a terrorist, evil – “bad”.

So, for humans, when is it “good” to change and when is it “bad” to change. “Good” or “bad”, change will inevitably take place. But it does not have to come via trauma or violence. It is true that many changes that occur in the Universe are violent changes, but there are many changes in the Universe that take place gradually and with much less trauma. Humans may have the capacity to make changes with much less trauma and much less violence. It may be essential that they do so if they are to survive the changes they cannot control: the ubiquitous and inherent Universe changes.

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Animals have ways to communicate. Mammals and birds, for example, communicate things like “there is food” or “there is no food”; “there is danger” or “there is no danger”. But we humans have added another dimension: “maybe”, which brings with it probability (uncertainty). We could additionally say, “there may be food” or “there may not be any food”; “there might be danger” or “there might not be any danger”. And we attach levels of certainty or uncertainty to the possibilities.

This dimension creates a certain amount of confusion in our communication with each other. The meanings of what we try to communicate generally have multiple possibilities and we filter these possibilities through our experiences and insights, and oftentimes through our emotions. There is much room for misinterpretations and miscommunications in almost everything we say.

As an example:
I was teaching a summer statistics class and students asked me some questions and I wondered, out loud, where the confusions were. After class, one student came up to me and said I shouldn’t take this wrong, but he was a high school teacher and he knew where I was coming from when I wondered out loud. He said he knew that I wondered where the text and I did not express ourselves clearly but, he said, the students interpreted the wondering as a reflection on their intelligence. I never did figure out how to communicate it properly to the students so I quit wondering out loud but made it a point to privately figure out where the confusions might be, and proceed from there.

Communications with multiple possibilities are confusing: Languages have their flaws and our filtering mechanisms are extremely varied. We need patience and understanding.

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