Category Archives: Tutoring
In my previous posts, I discussed two critical questions about the rise of science in Europe in the 1400 to 1700 hundreds:
- Why there?
- Why then?
Let me begin with a older message by The Meeting House in the Greater Toronto Area that I watched on March 1, 2022 on YouTube (see Footnote), After describing the message, I will then show how it relates to the rise of science.
The message was part of a series entitled REASONS TO BELIEVE, and in this case was delivered by a guest speaker from Australia, Jerrod McKenna. It has nothing to do with science per se, but dealt with differences between the Greek view (the New Testament was written in Greek) and the Jewish view (most of the Old Testament was written in Hebrew) in understanding and interpreting the holy writings. Here are two figures adapted from the notes I took as I watched.
Figures 1 and 2
In Figure 1, the circle with the cross-hairs in the middle and the X at the center, represents the Greek view. The Greeks, valuing perfection, were always looking for the one perfect principle that unified. This is also the goal of science. Believing that these unifying principles exist is a major impetus for the search leading to their discovery. However, what happens if the “perfect principle” is not only imperfect, but wrong? The impetus that spawned the search for the perfect principle now becomes an impediment to changing it. When the data point arrives that destroys the beautiful law, one can always say, “Let’s put that data point in the filing cabinet until we know more. I’m sure with more data and more thought, it will eventually fit. After all, all my lectures and my reputations are built on the beautiful principle. If I claimed the principle is disproved, what would I teach?”
In Figure 2, the Jewish or Hebrew view is expressed, according to McKenna. The circle has two X’s on the periphery, representing two teachings or data points which are paradoxical, hard to reconcile, and from some perspectives, contradictory. Inside the circle is an area that could he termed “The Mystery of God.” In other words, one may encounter truths which are both true, but hard to reconcile (perhaps only at the moment). One can live with that because we are not God and cannot expect to understand everything. In other words, the Jewish view allows for uncertainty in the explanations. These are theological statements. How do the apply to science?
From Aristotle to Newton
A thorough description of Aristotle’s laws of motion has been presented:
The key one for our discussion is summarized in the figure above. Aristotle believed that natural state of terrestrial objects was no motion. In other words, to keep an object moving, one had to apply a force. This law is supported by observation a thousand times a day, by anyone who cares to look. You throw a stone, shoot an arrow, or kick a soccer ball, it moves for a while, slows down, and eventually stops.
The data that destroys the perfect theory usually comes before the new explanation comes. One has to live with knowing the theory is wrong and broken before one can describe what will replace it.
Aristotle’s laws of motion were seen to be incorrect, before the correcting explanations became apparent. Observing the four large moons of Jupiter clearly showed objects which did not come to rest. Galileo showed that some falling objects fall at the same rate independent of density. Quantitative estimates on how an object should behave were also not explained by Aristotle. But it took until the brilliance of Newton and his laws of motion, before an explanations emerged that overcame the problems.
Speaking as both a student and a tutor, I think one of the great failings in teaching science has to do with the false perception which leaves the student thinking that every question has been answered, and every science problem solved. It is much better to train the student to live with not knowing, or at least knowing that the principles we teach and talk about is likely fatally flawed, and we don’t yet know what the correct answer.
Summary and Final Comments
The philosophical climate in Europe in the 1400-1700 hundreds was precisely the climate necessary for the emergence of modern science:
- The Greek view of the perfect principle gave the impetus for finding a unifying explanation for data.
- When data came along that destroyed a well-established theory, the idea of The Mystery of God enabled scholars intellectually to realize the theory was wrong well before a better theory came along. Belief in The Mystery of God made it intellectually possible for them to say, “I really don’t know the correct explanation at this time. I know what we believed before was wrong. There are some things we may never know.”
- When a scholar is in a position where a much-beloved theory is discredited, yet no explanation has yet arisen to provide the new principle, one needs a bedrock of philosophic thought that allows this uncertainty to exist.
- The ability to say: “I don’t know” or “I no longer believe I know” is the scholar’s only sure defense against Confirmation Bias which makes it nigh impossible to dethrone a beloved, discredited explanation.
- The vivid imagination of pagan culture, which was carried over was an aid for rethinking explanations.
This discussion began with a book review of Peter Kreeft’s BACK TO VIRTUE. I hope this example was useful in understanding Kreeft’s and Meyer’s points in answering the question about the rise of science in Europe:
Footnote added: The messages in the WE BELIEVE series, at the time of writing, were no longer available on YouTube. If they become available again, I will add a hyperlink for the reader’s convenience.
One of my Facebook friends commented on this simple, apparently long-circulating, arithmetic problem and so it prompted many other of my Facebook acquaintances to also weigh in. The statistics of this FB post, as a whole, captured my attention. With 516K votes (“likes” I suppose) and 5.5M comments that is almost too impressive.
I don’t think the interest in this question would have been so high if everyone had arrived at the same answer. Since some did not, from the few answers I’ve seen, it seems many were prompted not only to correct the errors, but to also provide detailed explanations on the order of precedence rules in arithmetic.
Now, I’m naturally skeptical and suspicious (not always a good trait) and so I could not help suspecting that some of the wrong answers presented with conviction were nothing more than “click bait” and perhaps led to the phenomenal response to this simple post.
As a tutor in chemistry and physics this discussion provoked some interesting thoughts …
- In any math problem that involves a mathematical expression, the expression is a language that connects the person who set up and solved a math problem and someone else who uses the solution to find the correct answer to a similar problem. The conventions around the rules of precedence, that is to say: “multiplication and division must be done before addition and subtraction” are established so that the users of the equation understand how they are to perform the various operations correctly to get the right answer. If they are not followed, then using hyperbole, bridges will fall down, planes won’t leave the runway, and patients will received incorrect dosages. The rules involve shorthand (default rules that everyone is supposed to know) that make the expression as compact as possible.
- since multiplication is done first, as most respondents noted, the expression simplifies to:
- 50+50+0+2+2=? and so the answer is 104
- If the person who set up the expression wanted a different outcome, then brackets would be used to change the order of operations … (50+50-25)x0+2+2=? … this answer would be 4
- The conventions communicate from the person who set up the equation to the user. Like all conventions of this sort, they are only effective if we all agree to the same ones.
- The second interesting point has to do with calculators. Depending on the calculator, a person who has not bothered to learn the order of precedence conventions can easily get the wrong answer. Using a calculator is no guarantee of accuracy.
- For an older, simpler calculator that forces you to enter a number and an operation and another number to complete the operation, going from left to right will give the incorrect answer. By beginning at the left the user imposes an incorrect order of operation on the whole equation. You will in effect solve … (50+50-25)x0+2+2=?
- A more sophisticated calculator that lets you enter the whole expression will follow the rules of precedence