Marion Nestle writes in Food Politics "Although most scientists view scientific methods - testing hypotheses by controlled experiments - as inherently valid and truthful,... many people regard science as just one of a number of belief systems of equal validity and importance. Religious beliefs, concerns about animal rights, and views of the fundamental nature of society, for example, influence the way people think about food. So do vested interests."
The same thing applies to people's religious beliefs. Although to most people with a science background it seems obvious that science is our best way of knowing, this is apparently not true for people in general. They adopt a religion, or stick with it, because it feels right and they believe their feelings reveal truth.
One's feelings do reveal truth about inner realities, and it's crucial to be in touch with one's feelings. Taking one's feelings as evidence about objective realities extends "being in touch with one's feelings" beyond its proper area of authority, but that's what people do.
I like Marion Nestle's writing about food politics so far, because it reveals a lot of corporate and advertising interests that we are often influenced by without realizing it. These influences contribute to people being overweight, and other problems. And it's a good question, in what ways economic interests reinforce religious belief as well.
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The Pythagoreans a long time ago apparently thought that you can arrive at mathematical truth by religious methods. For mystical reasons, they believed that all numbers are rational (the quotient of one integer by another). They were very shocked when someone found an irrational number.
The story is actually slightly different. The Greeks (and the Pythagoreans) did have the concept of whole numbers and ratios of those numbers and used both in geometry. It was natural for them to believe that geometric lengths constructed from a given unit length would be a whole number or a ratio --that it would be measurable.
Hippasus gave a proof of the incommensurability of the diagonal of a square with the side length in the fifth century BCE. He showed that if the side length of the square was a whole number multiple of any given unit length, then there was an easy contradiction to the diagonal being either an odd multiple or an even multiple of the same unit. Hence it could not be measurable. (His proof used the Pythagorean theorem which implies that the square of the diagonal is twice the square of the side length.)
Legend says that Hippasus was exiled for his discovery.
At least according to Wikipedia there are several inconsistent accounts and it's uncertain whether Hippasus was the one who discovered irrational numbers. The mildest version mentioned in Wikipedia was that the person who did was a Pythagorean who was expelled for the discovery. Another version is that the person who discovered irrational numbers was drowned at sea "for impious behavior". Wikipedia gives references for these various stories.
It does sound like the Pythagoreans associated "rational" numbers with morality. It's natural for people to believe various things, including religions they were brought up with.
The Pythagoreans don't seem to have had our modern notion of proof.
The Greek concept of number—arithmos—was always a multitude of units. You can find this definition given over and over again by Thales, Eudoxus, Aristotle, not just the Pythagoreans. The number 1, representing the unit, was not even included, and of course there were no negative numbers or zero. Ratios were not considered numbers but a relationship of numbers. The Greeks including the Pythagoreans had no notion of rational numbers, let alone irrational numbers.
When they compared the diagonal of a square with its side, they thought there must be some very small unit such that each was a multiple of that unit. Hippasus or whoever discovered the proof of incommensurability showed there was a contradiction in that notion, but that did not in itself establish the existence of irrational numbers.
Our modern number concept formed very slowly over thousands of years and was not really complete until the middle of the nineteenth century.
So the Greeks had no notion of one ratio being greater than another ratio? as in 2/3 > 1/2?
With that idea of greater-than, it seems one essentially has rational numbers. It becomes natural to think of rational numbers as sitting on a line, and then to think about the nature of that line ...
Mathematics in ancient Greece developed over time so that what was known varies. Certainly the Pythagoreans compared ratios in dividing a string to produce musical tones, but they did not recognize ratios as numbers or to think of them as represented by points on a line.
Euclid, who came later by a century or two, deals with ratios more rigorously and even defines when two ratios are equal in a rather complex and roundabout way that shows he did not conceive of them as numbers or as points on a line.
What Euclid defines is the statement p is to q as r is to s— so clearly he not defining equality of the rational numbers p/q = r/s. Here is the definition Euclid gives:
Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
The Pythagoreans don't seem to have had our modern notion of proof.
What I mean is, it sounds like the idea of logically right was conflated with morally right and esthetically right.
Luara, I can see what you mean. But I am definitely not a math/science person. I am a wordsy/artsy/feelings kind of person. I just understand that some things are make-believe, and science is real. I think science is wonderful and so interesting, but I don't understand a lot of it. I know it's not pretend like 'god' is though. ~ Melinda
Luara, you said
But I went through the overturning of a (nonreligious) belief system that I had without even realizing it. If you have an explanation for something; even if it explains things well, even if it satisfies your heart and your life is organized around it, that doesn't mean it's THE explanation.
I'd be interested to hear about your experience.
Today I learned a new word from Suzette Haden Elgin's Native Tongue trilogy.
zhaláad – the act of relinquishing a cherished/comforting/familiar illusion or frame of perception
I think we need to embrace this concept, because it's easier to grasp and promote something once it's named. Sharing our zhaláad stories is a start.
Zhaláad … interesting concept word. I'll have to run a memory scan of my gray matter storage ap to find the most significant personal incidence of zhalaad in my life. It could be a useful exercise. I think the emotional component is also important – what was the affective impact on your life?
I have zhaláad when I'm forced to give up the comforting/familiar feeling of safety and of being treated with respect when an iconic authority figure turns out to be racist or misogynist or an iconic cultural symbol turns out to have a nasty meaning or significance previously hidden. Learning that some of our founding fathers profited from piracy, that Richard Dawkins has misogynist tendencies. The biggest zhaláad recently is giving up the frame of perception associated with a stable planet. Coming to grips with the gap between where we are and where we need to be, to avoid catastrophic Climate Destabilization, which Alex Steffen calls planet shock.
I'd be interested to hear about your experience.
That's rather involved, no time to get into it now ...
Zhaláad
paradigm shift.
Don't force them, just let them happen.
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