Calculation without Understanding

[coberst]

Calculation without Understanding

Early in our institutional education system we learn arithmetic. We learn to add, subtract, multiply, and divide. We learn to calculate without understanding.

This mode of education follows us throughout our formal education system. We learn to develop answers devoid of understanding. We do this because, in a society focused upon maximizing production and consumption, most citizens need only sufficient education to perform mechanical type operations; that is perhaps why our electronic gadgets fit so well within our culture.

If we think about this situation we might well say that this form of education best serves our needs. It is efficient and quick. However, beyond the process of maximizing production and consumption we are ill prepared to deal with many of life’s problems because we have learned only how to develop answers that are “algorithmically friendly”.

In grade school we are taught to manipulate numerals (symbols) not numbers (concepts). We are taught in grade school not ideas about numbers but automatic algorithmic processes that give consistent and stable results when dealing with symbols. With such capability we do not learn meaningful content about the nature of numbers but we do get results useful for a culture of production and consumption.

We have a common metaphor Numbers are Things in the World, which has deep consequences. “The first is the wide spread view of mathematical Platonism…[it] leads to the metaphorical conclusion that numbers have an objective existence as real entities out there as a part of the universe…Given this metaphorical inference, other equally metaphorical inferences follow, shaping the intuitive core of the philosophy of mathematical Platonism.”

Quotes from Where Mathematics Comes From by Lakoff and Nunez

[JacobF]

You speak as if arithmetic is the only subject taught in school. Of course, it isn't , and although a lot of my understanding of the world has come from my independent curiosity I can recall many stimulating discussions with my classmates on subjects such as philosophy and literature (I go to public school). And even though I detest the approach to education that the government takes sometimes, I've had some really bright teachers in the past who've taught me a lot.

I don't know what you are trying to get at with the fact that numbers are a concept. Math is permanent, and I'm not sure what there is to understand from it other than the mathematical processes that are taught in school. While the government is interested in producing obedient workers, those who are conditioned to stay "inside of the cave," there are many opportunities for people like me who want to learn about philosophy and literature... and life in general. Maybe not job-wise, but education-wise at least.

Also, mathematical type professions are quite difficult and also enjoyable for some. You seem to imply that they are inferior to liberal arts types of professions (such as working at McDonalds :P) where understanding is key. You need to be intelligent if you want to be a programmer or engineer of some sort.

In short, I don't really see your point. The fact that society runs on production and consumption is nothing new, and it will be that way for as long as we last.

[blp]

Brecht said that we must always beware of mistaking what is common for what is natural, but sometimes I think those who want to critique mathematics and science make a reverse mistake, mistaking what is apodictic for a system of oppression. I can't be sure if that's what you're doing because I'm not sure I understand your point either, but it sort of looks that way.

[coberst]

Our educational system has been designed to prepare its students to maximize production and consumption. It prepares its students to get good jobs after graduation day. This is important but it is only part of the preparation that you will need in your life.

I recently had occasion to hang out in the waiting area of St Joseph Hospital in Asheville for a few hours. I was free to walk many of the corridors and rest in many of the waiting areas along with everyone else. It was early morning but it was obvious that the hospital functioned fully 24/7.

A person can walk the corridors of any big city hospital and observe the effectiveness of human rationality in action. One can also visit the UN building in NYC or read the morning papers and observe just how ineffective, frustrating, and disappointing human rationality can be. Why does human reason perform so well in some matters and so poorly in others?

We live in two very different worlds; a world of technical and technological order and clarity, and a world of personal and social disorder and confusion. We are increasingly able to solve problems in one domain and increasingly endangered by our inability to solve problems in the other.

[weltanschauung]

Calculation without Understanding

Early in our institutional education system we learn arithmetic. We learn to add, subtract, multiply, and divide. We learn to calculate without understanding.

This mode of education follows us throughout our formal education system. We learn to develop answers devoid of understanding. We do this because, in a society focused upon maximizing production and consumption, most citizens need only sufficient education to perform mechanical type operations; that is perhaps why our electronic gadgets fit so well within our culture.

If we think about this situation we might well say that this form of education best serves our needs. It is efficient and quick. However, beyond the process of maximizing production and consumption we are ill prepared to deal with many of life’s problems because we have learned only how to develop answers that are “algorithmically friendly”.

In grade school we are taught to manipulate numerals (symbols) not numbers (concepts). We are taught in grade school not ideas about numbers but automatic algorithmic processes that give consistent and stable results when dealing with symbols. With such capability we do not learn meaningful content about the nature of numbers but we do get results useful for a culture of production and consumption.

We have a common metaphor Numbers are Things in the World, which has deep consequences. “The first is the wide spread view of mathematical Platonism…[it] leads to the metaphorical conclusion that numbers have an objective existence as real entities out there as a part of the universe…Given this metaphorical inference, other equally metaphorical inferences follow, shaping the intuitive core of the philosophy of mathematical Platonism.”

Quotes from Where Mathematics Comes From by Lakoff and Nunez

so true! throughout our lives, we're taught to memorise and never to think. we're taught to learn what others discovered (by endless thinking and analising), and use the same paths they did to achieve the same final destination they did. why you think that happens? i really dont believe teaching people how to think instead of memorising would be much harder work, however, its never done. is that an accidental flaw of our society?

it would be naive to assume so...
i encounter this problem so often, it always leaves me with a feeling of hopelessness. i go to classes and i have a really hard time learning everything that is being spat at me, i feel like i dont have enough time to learn all of that, yet, classmates who are not smarter or more intelligent than me find it not so troublesome to get higher grades... but this never fails, though: if i have a doubt, and i go ask them, the high gpa guys, they cant answer. and i always get "well, thats how the teacher said we should do". theyre just puppets with good memory, but they have no idea what theyre doing..
no one is taught to THINK. no one is taught to analise. from birth to death, we are doomed to repeat and not to create or criticise.

as an overall analisis of this characteristic of our society, i can certainly affirm that this is imposed into us on purpose. im mostly unwilling to write gigantic posts with all my thoughts in detail, because that would be doing the same thing they do to us in school, i prefer to leave the meaning of what i am saying implicit and let the person take his/her own conclusion... so to finish this gigantic post i would say that the answer to this "conundrum" is in the undeniable analogy to brave new world.
it also made me think of bunuel's "el angel exterminador" in a way..

[0=2]

Thank you. I tried explaining this with little result.

Equations commonly perceived as "fact" are situational... ALWAYS. They are abstractions commonly misapplied to life.

[NikolaiI]

"Consciousness is usually identified with mind, but mental consciousness is only the human range which no more exhausts all the possible ranges of consciousness than human sight exhausts all the gradations of colour or human hearing all the gradations of sound — for there is much above or below that is to man invisible and inaudible. So there are ranges of consciousness above and below the human range, with which the normal human has no contact and they seem to it unconscious, — supramental or overmental and submental ranges."
Sri Aurobindo

" The gradations of consciousness are universal states not dependent on the outlook of the subjective personality; rather the outlook of the subjective personality is determined by the grade of consciousness in which it is organised according to its typal nature or its evolutionary stage."

[coberst]

"Consciousness is usually identified with mind, but mental consciousness is only the human range which no more exhausts all the possible ranges of consciousness than human sight exhausts all the gradations of colour or human hearing all the gradations of sound — for there is much above or below that is to man invisible and inaudible. So there are ranges of consciousness above and below the human range, with which the normal human has no contact and they seem to it unconscious, — supramental or overmental and submental ranges."
Sri Aurobindo

" The gradations of consciousness are universal states not dependent on the outlook of the subjective personality; rather the outlook of the subjective personality is determined by the grade of consciousness in which it is organised according to its typal nature or its evolutionary stage."

First, there is emotion, then comes feeling, then comes consciousness of feeling.

What are the emotions? The primary emotions are happiness, sadness, fear, anger, surprise and disgust. The secondary or social emotions are such things as pride, jealousy, embarrassment, and guilt. Damasio considers the background emotions are well-being or malaise, and calm or tension. The label of emotion has also been attached to drives and motivations and to states of pain and pleasure.

Antonio Damasio, Distinguished Professor and Head of the Department of Neurology at the University of Iowa College of Medicine, testifies in his book “The Feelings of What Happens” that the biological process of feelings begins with a ‘state of emotion’, which can be triggered unconsciously and is followed by ‘a state of feeling’, which can be presented nonconsciously; this nonconscious state can then become ‘a state of feeling made conscious’.

”Emotions are about the life of an organism, its body to be precise, and their role is to assist the organism in maintaining life…emotions are biologically determined processes, depending upon innately set brain devices, laid down by long evolutionary history…The devices that produce emotions…are part of a set of structures that both regulate and represent body states…All devices can be engaged automatically, without conscious deliberation…The variety of the emotional responses is responsible for profound changes in both the body landscape and the brain landscape. The collection of these changes constitutes the substrate for the neural patterns which eventually become feelings of emotion.”

The biological function of emotions is to produce an automatic action in certain situations and to regulate the internal processes so that the creature is able to support the action dictated by the situation. The biological purpose of emotions are clear, they are not a luxury but a necessity for survival.

“Emotions are inseparable from the idea of reward and punishment, pleasure or pain, of approach or withdrawal, of personal advantage or disadvantage. Inevitably, emotions are inseparable from the idea of good and evil.”

Emotions result from stimulation of the senses from outside the body sources and also from stimulations from remembered situations. Evolution has provided us with emotional responses from certain types of inducers put these innate responses are often modified by our culture.

“It is through feelings, which are inwardly directed and private, that emotions, which are outwardly directed and public, begin their impact on the mind; but the full and lasting impact of feelings requires consciousness, because only along with the advent of a sense of self do feelings become known to the individual having them.”

First, there is emotion, then comes feeling, then comes consciousness of feeling. There is no evidence that we are conscious of all our feelings, in fact evidence indicates that we are not conscious of all feelings.

Human emotion and feeling pivot on consciousness; this fact has not been generally recognized prior to Damasio’s research. Emotion has probably evolved long before consciousness and surfaces in many of us when caused by inducers we often do not recognize consciously.

The powerful contrast between emotion and feeling is used by the author in his search for a comprehension of consciousness. It is a neurological fact, states the author, that when consciousness is suspended then emotion is likewise usually suspended. This observed human characteristic led Damasio to suspect that even though emotion and consciousness are different phenomenon that there must be an important connection between the two.

Damasio proposes “that the term feeling should be reserve for the private, mental experience of an emotion, while the term emotion should be used to designate the collection of responses, many of which are publicly observable.” This means that while we can observe our own private feelings we cannot observe these same feelings in others.

Empirical evidence indicates that we need not be conscious of emotional inducers nor can we control emotions willfully. We can, however, control the entertainment of an emotional inducer even though we cannot control the emotion induced.

I was raised as a Catholic and taught by the nuns that “impure thoughts” were a sin only if we “entertained” bad thoughts after an inducer caused an emotion that we felt, i.e. God would not punish us for the first impure thought but He would punish us for dwelling upon the impure thought. If that is not sufficient verification of the theory derived from Damasio’s empirical evidence, what is?

In a typical emotion, parts of the brain sends forth messages to other parts of the body, some of these messages travel via the blood stream and some via the body’s nerve system. These neural and chemical messages results in a global change in the organism. The brain itself is just as radically changed. But, before the brain becomes conscious of this matter, before the emotion becomes known, two additional steps must occur. The first is feeling, i.e. an imaging of the bodily changes, followed by a ‘core consciousness’ to the entire set of phenomena. “Knowing an emotion—feeling a feeling—only occurs at this point.”

Quotes from “The Feelings of What Happens” by Antonio Damasio

[sara999]

In response to your post about how we perceive and learn in relation to our emotions. I work in a customer service department at a book store and I've noticed that sometimes customers can be more irate at times than others.
Science is starting to show that human behaviour is following a trend.
Some companies are now plotting this trend and creating a forecastable index. There is one company called Mightyz, you can find them on the web, and by using their service, we just add more customer service people on heavier negative days and bring more emphasis to customer service on these days and on the more positive days, we add less staff to the customer service department, because we know that the day will have fewer irate customers.

So this new science proves that human emotion and behaviour is coming from outside our understanding, but only when it occurs in large groups. In the near future, human emotions and behaviour in groups will be just as predictable as the weather. I know, I've also watched it against the Dow Jones and the Dow closes higher/lower based on the forecated values.