Wow! That was a lot of reading! In general, it was all about
the beginnings, criticisms, and applications of calculus, as well as some
information on some early mathematicians. Now what does this all mean? Well,
the way I saw (or read) it, ever since Newton (and Leibniz) brought forth
Calculus, the subject has been under much debate. In fact, one of the first
criticisms that caught my attention from the readings was when Leibniz accused
Newton of “implying an imperfect God” (Gleick, 171), and apparently Newton took
the comment to heart as it was noted to have stung. In today’s society, we (or
at least I) don’t acquaint God to mathematics. This alone shows me the type of
thinking that went on during this time period. For some reason, the people of
that time period believed that God and mathematics were related. What do you
think?
Another thing that got my attention the Feynman article on
the relationship between physics and mathematics. Now if I recall correctly, it
has been said that Newton invented calculus in order to understand physics.
Now, the article has been written many many many years after the lifetime of
Newton, so it stands that Feynman has a different mindset than say, Newton and
the Bernoulli brothers. Reading deeply into the article, it somewhat implied
(at least to me) that in order to understand physics, once must know math. Of
course this makes sense to me because in today’s society, calculus and physics
is intertwined. However, this makes me want to know how physics was taught back
in the Newton time period. What do you think? If what we know now is all thanks
to the creation of calculus, what was the understanding of physics like back in
the day? Clearly that had some concepts of basic physics like the concept of
gravity, but I’m sure the understanding was different.
• I think when looking back and societies, everything came from God. They would do human sacrifices to appeal to these Gods, so it didn't shock me to see that they had this relationship with Mathematics and God. Something that I have been pondering how the discovery of mathematics affected the beliefs of individuals. Whether or not seeing that there are equations and formulas that explain that natural world affected their beliefs. Looking at today though, I think the same type of problems can occur with evolution. We have the mathematics to explain it but does the mathematics explain that there is a God? Did God create humans in a way to ensure that we discover and create mathematics? Did God create Newton to make the principia? I think you can get lost in a lot of theological questions, and predetermination questions, and I do not have any of the answers, and I'm not sure anyone really does.
ReplyDeletePhilip, it’s interesting that you mention Leibniz’s accusation of Newton “implying an imperfect God.” The role of religion in mathematics and/or science reminds me of Galileo’s struggle with the Catholic Church when he presented his heliocentric universe model. I think there was a conscious effort to tie explanations in with religion during the time of Galileo (1564-1642) and Newton (1642-1727). In class, we stressed the word “natural” in Newton’s Principia’s full title. During Newton’s time, people often associated natural phenomena with a God which would account for why people so wanted to incorporate religion into mathematical/scientific findings. Even now, some people struggle with balancing religion and science. It is obviously less prevalent now than it used to be, but do you think the intensity of that struggle is any less now than it was back then?
ReplyDeleteAn argument for an implied God through the mathematics of physical perception.
ReplyDeleteI also enjoyed your mention of Leibniz’s accusation of Newton implying that God is imperfect. By no means do religion and mathematics work together to resolve worldly issues of the physical realm but to those who imply that the universe, just so happened to manifest with the degree of fluidity seen at all scales without having help through the divine seems to me to be preposterous.
I find it not too farfetched that God and mathematics coincide to a certain degree. Upon the creation of the universe, whether that be by God or an anomalous source, the encoded rules for forces have been persistent in carrying out what they were designed or encrypted to do. These rules that forces appear to abide by are known to us as the laws of physics. Mathematically these laws derive themselves in such a way that we find them to be computational. Whether by means of sheer chance or divine intervention it seems to be apparent that physically the applications to which we involve ourselves, so happen to find resolve in mankind’s discovery of mathematics. I believe that mathematics itself eludes towards the existence of a God. Such a systematical approach that uses such finite detail to have simply popped into existence by means of only chance seems impossible to me. I think that God designed the universe with mathematics in mind not only to make it work as a system, but moreover to revile to us his glory, that we might one day find mathematics and in doing so use it to see God in the perfections of the universe. Not only so that we might marvel at its granger but also to help us understand our existence in the physical world as a part of something bigger then ourselves. It is without a doubt that the quantum mechanical forces of the universe preexisted humanity, meaning that mechanically the forces that govern the universe supersede our understanding of them. This preexisting notion bares the question that is; if the universe was created simply by chance then for what reason and how did it create itself with such exactness, so much so that we are able to mathematically interpret its physical characteristics with a great deal of precision.
I also agree historically many societies have related all that exists in the world to God in some way. In spite of this historical pattern I do not see how the development of calculus or other subject matters would lead to the questioning of faith in today’s society and I think it is important to realize the human race does not know everything. I also disagree with the mentioned concept of a "grand plan" by God. If we are to reason God created Newton to forever change the world with mathematics then we are assuming God created everyone for a specific purpose. In what way does this perspective explain, for example, child fatalities and individuals who grow up to be killers? Clearly a person of faith wouldn’t argue this is the work of God.
ReplyDeleteWhat I found most interesting about the various articles was the depiction of the lifestyle led by Newton and the Bernoulli brothers. Newton’s contributions to mathematics and understanding the world are unmatched but at what price? As a result of his character and dedication to his work Newton essentially cut himself off from the social world. In many ways Newton was a celebrity with few friends and no social life. Likewise the Bernoulli brothers dedicated their lives to their studies, which caused them to grow apart. These lifestyles conflict to today’s social standards and are uncharacteristic of mankind. It is this degree of dedication that we rarely hear about in the modern world. Nonetheless I believe it is the uniqueness and variety of the human race that promotes progression and advancement, which may be why some of the greatest minds the world has seen are so different.
"In what way does this perspective explain, for example, child fatalities and individuals who grow up to be killers? Clearly a person of faith wouldn’t argue this is the work of God."
DeleteBe careful here, I think you're taking this from the viewpoint of a christian interpretation of god. That is to say, that god is a loving god and is intrinsically good. This might be 'clear' to you but it may be completely opaque to someone, say, from mesopotamia who thought their gods were wrathful. But is this really the case? Could it be god is absent of moral considerations or apathetic to them? If not, why? This was an issue that my Gods and Persons philosophy class delved into some detail. As I recall, certain theological standpoints to account for the apparent existence of evil require the sacrifice of one of the big three godly properties: omniscience, omnipotence or omnibenevolence. These theological arguments are sometimes called theodicities.
In response to phillip's post, i'd have to wonder if people during this time were more likely to see god, rather than people, in the sciences merely because they lived in a time where religious faith was an integral part of existence. To this end, i'd imagine that prior to calculus physics was largely understood intuitively, with perhaps some simple algebraic or geometric arguments in accompaniment where applicable. (For example it was a muslim scholar by the name of Ibn al Haytham, or sometimes latinized as Alhazen, who first came up with an accurate explanation for how the eye functioned using an early form of geometric optics).
Philip, I like the question you raise in your post about equating God with mathematics. I think the reason people of Newton's time equated the two was because of mathematic’s ability to describe the natural world and because of its apparent accuracy in predicting future events or even in predicting the existence of phenomena which had previously been unobserved. Some scholars today maintain this viewpoint, I think, because mathematics points to a certain intelligibility in the design and workings of the Universe, which is not evident without mathematical tools. These tools reduce seemingly complex, unrelated phenomena to mathematical relationships which are widely, if not universally applicable (i.e., the laws of gravitation). In other words, mathematical relationships (i.e., equations, or inequalities) seem to be the language or “code” that the Universe uses to operate. Some individuals see this idea as pointing to some sort of “creator” or “code-writer” who invented the code or the laws which govern the Universe.
ReplyDeleteI also thought it was interesting that Will touched on the implications of apparent disorder (deaths of young people, natural disasters, etc.), on the “grand scheme” idea. I think from a Christian perspective, as Nate mentioned, you’re right; such events do rule out the presence of a omnipotent, benevolent creator with a grand, predetermined (or premeditated) scheme. But, it’s also important to realize that these events do not break or deviate from the natural laws which would necessarily apply to them. In fact, quite often, such events can be predicted or modeled (on a macro scale) by the closely related field of statistics.
In response to your second question, I think physics without Calculus would be somewhat “watered down” and limited by lack of computational power. Certain quantities whose rate of change cannot be modeled linearly, for instance, would be difficult and time-consuming to compute, and would require some approximation probably relying more on geometry than anything else. Since none of the concepts associated with modern-day calculus were rigorously defined or understood, I would also guess that considering the infinite, as well as infinitesimal quantities (of time, perhaps) was difficult, if not impossible.
I also found it interesting what a huge presence God had in each of these readings. While traditionally, I would never think to mix mathematics with theology, the discussion of many of these articles does just that. I personally see theology and mathematics as being two entirely different spheres, and while they do not necessarily contradict one another, one does not need to have an understanding of mathematics to understand theology, nor does one need to have a theological basis to understand mathematics. These early mathematicians did make a point of having theological debates however. Leibniz, for example, accused Newton of implying an imperfect God in one of his publications. Although I was surprised at first, I suppose it does make sense to include theological discussion in these contexts. These early mathematicians and scientists worked to understand the natural world. Without scientific or mathematical reasoning, people turned to the divine to explain everything. As more discoveries were made and they came to realize how the natural world functions, it became less necessary to turn to God for explanation. Most explanations lie in the laws of the natural world. This is not to say, however, that math and science have taken the place of a divine being. It is important to realize that these two separate studies can be (and should be) considered together. I particularly liked one of the points made in the Berkeley article. He argued that anyone who can conceive of infinitesimals should be able to comprehend the possibility of the existence of a divine being. Mathematicians have developed this universally accepted notion of infinity. Infinity is not a number, and no one will ever find it, however, its existence is not questioned, rather it is accepted. In the same way, we will likely never find any physical being that is God, or any undisputable proof that he exists. However, that does not mean that he does not exist. Like infinity, just because we may never physically reach God, does not mean that we cannot know he exists, and use what we do know to study him.
ReplyDeleteI, as well, thought Berkeley's writing about the idea of infinity was very interesting and applicable to many conversations about God. He mentions that thinking about infinity can be very difficult but can be very similar to understanding divinity. I think that is a very interesting point. It caused me to think of one of the arguments for the existence of God created by Anselm in which he defines God as "that than which nothing greater can be conceived. He then argues that if this being can exist in the mind then it can exist in reality. Berkeley's talk of infinitesimals reminded me of this philosophical argument. Erin, you mention that infinity is not a number and no one will ever find it but they do not question its existence. I think this is a very valid notion in relation to the discussions about the existence of God and having no physical evidence for that belief.
DeleteLike most of the people commenting above, I do not understand how the development of calculus would lead people to question the existence of God. For me, the opposite is actually true. While many biological scientists seem determined to tear God down, what we are learning in physics and math seems instead to validate God's existence. The existence of handful of simple laws that govern everything from the movement of the planets to the movement of cellular organelles seems to me, as George mentioned, improbable without the help of a divine creator. On a side note, I find it really interesting that although the purpose of the readings was not to debate God, everyone seems to have focused on that small part of the reading.
ReplyDeleteAs to your second question, I would imagine their study of physics looked almost nothing like a physics class today looks. As we discussed in class, the study of science was considered philosophy and involved a lot more word pushing than number pushing since they did not have the math to use Newton's laws or the kinematics equations.
Wow! I have to admit first that the rivalry between Newton and Leibniz is astounding to me! I never knew that two people had created Calculus independently, and with Newton portrayed in school is such a magnificent light, I would have never thought such a fight could exist. “Intense and flaming spirit” indeed! It’s incredible how huge of a fight this was with so many people involved with determining who was the true inventor of calculus. I will have to say that I don’t think this mathematics, calculus, was invented, but rather discovered, and if these two had not discovered it (observing its phenomenon), that someone else would have come later to discover it instead.
ReplyDeleteThe conversation about God and math is very interesting too. (Very hot topic, I noticed...) I personally cannot equate God with mathematics, and mathematics as a sign that a God exists. One of these topics can have proofs while the other is philosophical in nature and in my opinion, unprovable; religion is faith. I agree with you Erin, that one does not need one of these subjects to understand the other. I am not saying that God does not exist, just that these two subjects are like comparing a unicorn to a horse.
I think it is so interesting like Joelle said that both Newton and Leibniz created calculus independently. I think it interesting that in class we defined math as our interpretation of the world around us. The idea that two peoples concepts could or would be that similar seems to be quite intriguing to me especially, even after this article, calculus to me seems like such a foreign language.
ReplyDeleteI also believe like Joelle that math and faith are two very different concept areas that are not interrelated. However, math is a key part in science and so is faith. So independently no math and faith are not related. But math as it pertains to our physical world and faith paths cross a little more directly.
Perhaps my favorite part of your post was when you asked me what I think :)
ReplyDeleteBut, as I have already posted two other things this week (and my posts always tend to be mega-long), I will restrict this simply to the former question that most people who commented have touched on - how/to what degree God and mathematics are related.
And while people have touched on this same idea, I feel it hasn't been stressed enough that God and mathematics/science are - wait for it - completely independent of each other. Mind I said independent, not unrelated. As Newton himself pointed out, "I have told you how it moves, not why."
And really I think that's the heart of the topic. Religion was (or, nowadays, is) primarily used to probe the question of why, so from it any attempt to answer to the question of how will be paltry and consist merely of thought processes like "God made the earth." "Well how'd that happen?" "Oh well he's God he just willed it to happen." I mean if we're talking about practicality, that answer means nothing.
So, too, math and science say nothing of the question of why - for anyone who has the very human desire to question the meaning of life and existence, they can only draw their own inferred conclusions from the experimentally determined results.
As such, being independent of each other, one can pretty much be incorporated into the other in any way you like. For my part, being a highly-scientific minded yet heavily spiritual hardcore Catholic, I find it simple enough to say that science describes the universe that God created. And so, though the two are independent, I can intertwine both disciplines into a complementary mix of both.