An Ecology of MInd (18 page)

They wanted a spot that was close to a major population centre, but not right in one. They also wanted to contact a higher civilization on the planet. The
patterns of the electromagnetic emissions had large areas with very few. The impression was of differing areas of development, but they could not be sure.
They were using assumptions of how the inhabitants were organized and those assumptions may not be accurate. They had made other contacts with alien
species over the years and had learned that assumptions could easily be wrong and get you into trouble.

After some deliberation, it was decided to land a little way inland from a large system of lakes and rivers on one of the larger land masses. They sent a
messenger drone back to their superiors as to their initial findings and their intentions. This meant all information they had collected so far was safe.
If the landing went badly, their superiors would use a different method than they had used.

In extreme cases, complete sterilization of a planet was carried out. It was unlikely that would be required here. Leader *'s race had spread to over two
hundred star systems so far and had only found it necessary to sterilize a few planets.

"WE'VE TALKED ABOUT LANGUAGE," said Dr. Pearson. “Mathematics is often described as the language of the universe. Through the use of mathematics, we have
discovered much of how the universe actually works. It has described the movement of the planets and the stars. It has been used to harness the energy of
the atom with both fission and fusion. It has been used to predict the presence of sub-atomic particles. It can describe the infinite and the
infinitesimal."

"Mathematics is also present in life. The mathematical formulae encoded in DNA give the spiral shape of shells and give the leopard its spots. Mathematics
can describe the world around us and be used to predict new aspects of the world that we had not previously imagined.”

“Despite its strengths, it is still just another language and has the same inherent shortfalls as all other languages. If the language does not have a
particular concept expressed within it, then the language itself acts as a barrier to communicating, understanding or thinking that concept. This is as
true with mathematics as it is with other languages.

“But how can that be? You might argue. We are talking about mathematics here. It is not English, French or Chinese. Mathematics transcends languages like
that and represents the actual workings of the universe.”

“Actually, the truth is, mathematics does all of that, but, like all languages, it must be created by the mind and have symbols created to represent
different concepts. Let me give you a historical example. Dr. Wales is getting antsy since I haven’t mentioned history in a while.”

Dr. Wales simply smiled from the corner of the room. He was extremely used to Dr. Pearson's small shots in his direction and recognized that they were just
a tool for transitioning the lecture to an historical example.

“The mathematics of Western civilization did not include the number zero until the 14
^th
century. It was introduced to the West by the Arabs.
Roman and Greek civilizations architecturally created the Parthenon, the Coliseum, the arch and the dome. They were civilizations that were at the core of
much of our own, and seen as the ideal to try to achieve by Medieval Western society. These civilizations had a well-developed understanding of
architecture and astronomy and kept detailed financial records, but had no zero in their mathematics.”

“The entire number system we use today in the modern world came from the Arabs. Even the name, “Arabic numerals," tells you that, but you may not have
thought to question it. The Arabic numerals are the familiar 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. They were an incredibly better system of mathematics when
compared to the old Roman method. Roman numerals are the ones written as I, II, III, IV, V, VI, VII, VIII, IX, X. Try carrying out some simple mathematical
calculations using those symbols, and you will quickly see what I mean.”

“Today, in our American society, if you say Arab, many people will automatically think oil or terrorists. How many people realize that they used to lead
the world in the area of mathematics? “

“The Arabic symbols made performing mathematical calculations far easier. Today, the mere concept of any kind of meaningful mathematics without having zero
is extremely difficult to wrap your brain around. What we take totally for granted did not exist in the concepts of mathematics in the West until it was
introduced from an outside civilization. All the things that having zero opened up in mathematical calculations, was not available before then because the
West’s version of the language of mathematics did not have the initial concept and symbol in it.”

“This leads to the conclusion that there may be many other things available to be uncovered by mathematics if improvements or new concepts are added to our
current language of mathematics. We just don’t know what they are. Mathematics as a language has continued to grow since the 14th century with additions to
it and a corresponding greater understanding of the universe around us. I am sure there will be more additions to it in the future.”

"Now, we have already looked at a number of properties of how our brains function. Let's look at another one. Much of our technology and understanding of
the world around us is based on mathematics. How does the human brain handle mathematics?"

"The technology that permeates our modern society requires a lot of mathematics. From this, you could conclude that our brains are quite good at handling
it."

"Let's look at a simple mathematical problem dealing with probabilities. For this example, I will use a variation of a dilemma from an old story. The
scenario is this. You are presented with three identical pistols. Two of the pistols are empty but weighted to feel like they have bullets. One pistol has
a clip of real bullets. You are allowed to choose one and only one pistol. In a few minutes, a hungry man-eating lion will be released into the room and
the pistol you choose will be your only defense. You select one of the pistols. I then take the two remaining pistols and knowing which gun is the one with
the bullets, I discard one, which has no bullets. I give you the option of exchanging your pistol for mine if you want. One of the two remaining guns has
bullets, and one doesn't. Which of the two pistols do you choose, or are your odds the same either way?

"Mathematically it is really a simple problem; you start with only three pistols and reduce them to just two, one of which has bullets and one that
doesn't. It should be something you can easily figure out in your head."

"What do you people think? Yes, you sir in the back."

"There are only two pistols and the bullets are in either one or the other so it would be an equal chance. It's like a coin toss, two choices with a 50/50
chance whichever way you choose."

"Good, any other answers?" No further hands went up.

"Raise your hand if you feel it is the same odds regardless which of the two pistols you choose." Everyone in the audience raised their hand confused that
he seemed to be making a big deal about something so simple and obvious.

"Unfortunately, you are all wrong. If you trade your pistol for mine, you would be twice as likely to have a gun with bullets."

There were rumblings in the audience and comments of "No way."

"You are not alone in your thinking. There have been mathematics teachers and even a Nobel prize winner who agreed with your argument, but I say you are
wrong. We will do an exercise now to see which of us is correct."

"Everybody pick a partner. We are passing out three playing cards to each pair. When you get the cards, between the two of you decide which card you want
to represent the gun with the bullets. One of you mix the cards randomly face down while the other is not looking. The partner who does not mix the cards
will select one card and not look at it. The other partner will look at the other two cards and discard one that is not the card representing the gun with
the bullets. Now turn them both over and record which of you has the card representing the winning choice. Do this several times and then Dr. Wales will
collect the results and tabulate them for the whole class."

The cards were handed out, and the teams completed the exercise several times each. Dr. Wales then collected the results from each team and entered them
into a spreadsheet on a laptop.

People returned to their regular seats if they had moved to partner up for the exercise. Dr. Pearson projected the spreadsheet with the results. The total
result for the class showed on the bottom.

"Well, are you willing to concede that your chance at the prize is really two to one if you trade your pick for the other one? The total is not exactly two
to one in our test, but it is very close. If you continued with a larger sample size you would approach an exact two to one ratio."

"Intuitively the human brain insists it is an equal chance, but it is not. Originally, there is an equal one in three chances of getting the gun you want.
Once you pick one, there are a two in three chances that the loaded gun is in one of the other two choices you did not make. When one of the incorrect
choices is discarded from those two, the entire two in three odds are transferred to the remaining choice."

It is an incredibly simple math problem. Three choices are reduced to two. This is something that should easily be solvable in your head, but the vast
majority of people get it wrong."

"Surprisingly, the human brain is not good in some areas of mathematics. We are incredibly bad at having any kind of intuitive feel for probabilities. We
may be able to go through the process and use the tools of mathematics to get detailed and accurate results, but our intuitive, off the top of our heads
grasp of mathematics is definitely skewed. When you consider human behaviors related to casinos and lotteries, maybe this is not that difficult to
believe."

"It would be good to keep this in mind when a decision you are looking at making involves a quick mental estimate of the odds. We can do the calculations
and get a correct answer if we know the math involved. Our brain's intuitive grasp of probabilities, however, is poor."

"Doing a quick mental assessment of the probability of an outcome happening or not happening is something we do all the time in everyday life. Normally,
the odds we are trying to intuitively estimate are far more complicated than three choices reduced to two. Historically, how many actions were carried out
based on a total misunderstanding of the odds of success or of adverse results? How many military attacks? How many financial decisions?"

"When you think about it a little more closely, you start to realize the potential scope of this seemingly little glitch in our brain function in human
events is very large. How many unlikely successful results were finally achieved because the people involved could not accurately guess the probability of
success and continued on despite probabilities of success that would make someone with a firmer grasp of them not even bother to try? How much of the famed
human spirit to continue in the face of overwhelming odds has been because we didn’t really understand what they were?"

"This also means that we would be unlikely to notice events around us that violate the mathematical odds of happening naturally."

"There are other things the human brain does not handle well. Another example is very large-scale items. Try to visualize or get a firm grasp on an
infinite universe. Perhaps even harder, try to get a mental grasp of total non-existence. Not just empty space but no existence at all, nothing, no space,
no time, no matter. Try as you might, you can't really do it. Yet another area our brains are not good at dealing with, using the mental tools at our
disposal."

"We are going to change the topic slightly now. I want to look briefly at a couple of things that may cause you to question some of your basic assumptions
about the concepts of good and evil."

"In a behavioral study, two groups of people were given two tasks to perform. For the first task, one group was given a task that was considered morally
neutral to carry out. The other group was given a task that was considered morally positive. Both groups were then given the same second task to perform."

"For this second task, it was possible to complete the task in either a way that was morally neutral or morally negative. In the second task, the test
subjects had the option of short-changing someone when they could not be aware of it. The result was the group that completed a morally positive act for
the first task was much more likely to short-change the person than the group that had done a morally neutral first task."

"The results show that people that perform morally positive acts seem to feel more justified in later performing morally negative acts. These are
interesting results in terms of our cultural understanding of right and wrong and of good and evil. Part of the good/evil dichotomy of behavior could be
related to brain function and not strictly to conscious behavior choices like we assume."