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02-13-2020, 04:50 PM - 1 Like   #121
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From a discussion on reddit," in physics what we're looking for is what can be described with maths." Indeed our language directs our awareness.
Our language gives shape to a concept but as the article discussed points out, "just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate."
The Unreasonable Effectiveness of Mathematics in the Natural Sciences

02-13-2020, 06:18 PM - 2 Likes   #122
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QuoteOriginally posted by swanlefitte Quote
From a discussion on reddit," in physics what we're looking for is what can be described with maths." Indeed our language directs our awareness.
Our language gives shape to a concept but as the article discussed points out, "just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate."
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
I'm not sure what your point is here, but keeping to the subject of words and what they represent, (remember words are a label for concepts) there are similarities in task between concept-formation and applied mathematics, just as philosophical epistemology and theoretical mathematics have a similar goal: the goal and task of bringing the universe within the range of man’s knowledge—by identifying relationships to perceptual data.
It looks like the process of concept-formation is, in large part, a mathematical process. If you consider the definition of a concept you can see the similarities. A concept is a mental integration of two or more units which are isolated by a process of abstraction and united by a specific definition.

Sorry if this subject is getting too specialized for general interest, but my point was simply - that first come perceptions which are then organized into concepts which are retained by (words in) language. This allows us to hold an enormous amount of information we can process, far more than our perceptual capacity would allow.
02-13-2020, 06:20 PM - 1 Like   #123
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Here are some other ways of seeing how language shapes our views.

How good does water taste? Tap water in different bottles tastes different.

Water is good for us but dihydrogen monoxide is bad.
02-13-2020, 07:34 PM - 2 Likes   #124
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QuoteOriginally posted by c.a.m Quote
Actually, I'm finding this branch of discussion quite interesting. As an engineer/scientist having had a career in research and development, I'll admit that this is the first time that I've heard of the word "epistemology" (had to think for a moment how to spell it there).
Epistemology is useful stuff with a deep interrelationship with science.

QuoteOriginally posted by c.a.m Quote
You give several examples of differing interpretations. I would guess that this variation in concept applies especially to words such as "soft," which can have quite a broad range of meanings to different people. For example, when we refer to the degree of sharpness in an image -- the corners are "soft" -- a lack of a definitive specification for "soft" means that we will interpret the concept in various ways. Some will think "that's actually pretty sharp" while others might conclude the lens is terrible.
Good point! Almost any adjective will come with subjective thresholds - how soft is soft, how sharp is sharp, etc. Perhaps an engineer or scientist can design a objective measurement tool that ranks things on some measured property such as lens sharpness. And yet some people might disagree with the measurement's ranking, have a different ranking system, and build a different "objective" measurement tool. And then we face the ugly truth that we cannot merge these different ranking systems in any reasonable way due to the Arrow's impossibility theorem - Wikipedia. So maybe lens A is sharper than lens B but maybe lens B is sharper than lens A.

But even some simple noun concepts like "life" or "species" or "tree" or "human" end up creating a hairball of edge cases where reasonable people might reasonably disagree on whether something belongs in the set or outside the set. No doubt this is where "authoritative" definitions come in and yet any succinct definition is likely to make "mistakes" even in the eyes of the authorities. (And lets not forget there can be religious or political differences in definitions.)

For the most part, though, we all know what we mean and probably all agree.

QuoteOriginally posted by c.a.m Quote
I would agree. On the other hand, approximations of circles are often satisfactory in the real physical world. Whether one needs to know pi to 5 or 15 decimal places is a matter of its application, I suppose.
"Often satisfactory" is the operative phrase. What's interesting is that the discrepancy between a real world object and its conceptual counterpart is a land sowed with failure that reaps scientific advancement. One might think that planets orbit in circles based on their periodic perambulations across the firmament. That approximation is good enough to estimate the month-by-month visibility of Mars. However, more accurate measurements disproved this and forced some to postulate complex assemblies of epicycles. Then Kepler came along and gave us nice elliptical orbits driven by gravity which worked a lot better but were still only approximations in that they could not explain the precession of Mercury. Then came Einstein and a much more accurate view of how gravity really works and how it influences the celestial motions. But then someone found that the orbits of stars around galaxies was not right given the amounts of visible matter so now we have dark matter. But is dark matter real or is it a kind of epicycle kludge that is awaiting a better theory?

QuoteOriginally posted by c.a.m Quote
I think I'm following the conversation.

- Craig
Me too!

02-14-2020, 01:49 AM   #125
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Now, there's a nice distinction, @Photoptimist, between the "reality" of dark matter and an "epicycle kludge". I was a psychology major for a few semesters (changed majors because I thought all the "theories" I'd been reading about were hogwash and the people who came up with them were all nuts). As such, I was compelled to take courses in statistics. One of the professors went off one day railing against people who referred to theoretical propositions as "true" or "false".

If I can make an analogy to the law of defamation, when A sues B because B said that he was of the opinion that A was a felon with a loathsome disease, B wins because his statement was about his own opinion, which (1) can never be either "true" or "false" because it's not a statement of fact but "mere opinion", and (2) B's statement was true, insofar as he actually holds that opinion ("The state of a man's mind is as much a fact as the state of his digestion." -- Oliver W. Holmes).

This professor made much the same argument about theories. A theory is merely a way of perceiving a body of fact, along with whatever conclusions one might draw from those facts. It is not a statement of fact, itself, nor is it a description of reality.

And, with regard to "epicycle kludges", when Copernicus proposed a heliocentric model of planetary motion, all he was proposing was a different way of seeing the reality that exists. He and The Church had no argument about the fact of planetary motion, or observations thereof. He just thought he had a better and easier way to describe that motion. The Church disagreed not because his theory was in any way untrue as a matter of physics, but because it was more important to them that Man be the center of the Universe; they didn't care how that shaped up mathematically. Just two different ways of seeing the same facts, neither essentially "true" or "false".

The confusion comes when people mistake the model of the universe they've created for themselves, since and before birth, for the real thing. We've all got a sort of mathematical model of the real world in our heads that gives us an interface of sorts to the "real world". The fielder can suddenly run out after a high fly ball (apologies to people in countries that don't have baseball) after having spotted its trajectory for a brief moment; suddenly stop, jump up, and turning in the air, outstretch his glove and snag the ball out of its trajectory. It's a very effective model that allows him to do this. But it's only a model. "Maya", the "wall of illusion", in Hinduism is the error people make of thinking their model of reality IS reality, and thus the only right and true reality. We cannot apprehend reality directly, much less comprehend it. All we can do is try to make our models of reality correspond as closely as we can to the real thing. But people who are blinded by Maya can't do that, because of their axiomatic adherence to the notion that their view of things is truth.

(I ended up with a degree in History, by the way, because I had amassed more credits applicable to that major than any other at the end of my eight years as an undergraduate.)

Last edited by Unregistered User; 02-14-2020 at 01:54 AM.
02-14-2020, 01:57 AM   #126
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QuoteOriginally posted by photoptimist Quote
It may be true that words represent concepts but do we all have the same concept with any given word?

A child might learn the word "tree" but then misapply it. The child might fail to recognize a sprouting acorn as an oak tree -- a false negative. Or the child might falsely say that a banana plant is a tree -- a false positive. Moreover, many of the adults around the child might make the same mistakes which then reinforces the child's erroneous concept of a tree. But if a social group shares the same "erroneous" concept of a given word, then maybe that's not problem because the principle purpose of words is communicate so mutual agreement suffices. It may not be until misconceptions affect actions that problems might arise such as trying to cut down banana plants for timber or firewood or killing all the oak sprouts in the forest on the assumption they are non-tree weeds.

It's worth noting that "there is no universally agreed upon definition of 'tree' even in a strictly botanical sense. While it is initially a question of grouping plants with similar characteristics, it is ultimately a function of subjective criteria that change from context to context." (University of Miami | College of Arts & Sciences | John C. Gifford Arboretum | Smartphone Tour | What is a tree?) The physical world is like that -- it laughs at humanity's quest to create neat little concepts.

The only realms of human thought that can have precise definitions are the artificial realms of math and logic where axioms can define a set of discrete symbols and operations. As soon as one delves into the real world, things become messy, boundaries become fuzzy, and even the simplest math concepts are revealed to be only approximations. (For example true circles only exist in math, not in the physical world because a host of microscopic and macroscopic effects make pi as the ratio between diameter and circumference an approximation.)
I think you've just invented Platonism.
02-14-2020, 05:00 AM - 1 Like   #127
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QuoteOriginally posted by photoptimist Quote
...But then someone found that the orbits of stars around galaxies was not right given the amounts of visible matter so now we have dark matter. But is dark matter real or is it a kind of epicycle kludge that is awaiting a better theory?
Present theorising implies dark matter and dark energy to be the vast majority of the universe and familiar matter in the single figure percentages. Kludge seems the kindest way to describe entities unobserved and to date unobservable invoked to explain hideous shortfalls between theory and observable behaviour. Colour me scornful.


Last edited by StiffLegged; 02-14-2020 at 03:44 PM.
02-14-2020, 10:13 AM - 1 Like   #128
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Is scornful azure or blue (to circle back in time a little)?? <insert smart-ass grin here>
02-14-2020, 10:41 AM   #129
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QuoteOriginally posted by dlh Quote

The confusion comes when people mistake the model of the universe they've created for themselves, since and before birth, for the real thing. We've all got a sort of mathematical model of the real world in our heads that gives us an interface of sorts to the "real world". The fielder can suddenly run out after a high fly ball (apologies to people in countries that don't have baseball) after having spotted its trajectory for a brief moment; suddenly stop, jump up, and turning in the air, outstretch his glove and snag the ball out of its trajectory. It's a very effective model that allows him to do this. But it's only a model. "Maya", the "wall of illusion", in Hinduism is the error people make of thinking their model of reality IS reality, and thus the only right and true reality. We cannot apprehend reality directly, much less comprehend it. All we can do is try to make our models of reality correspond as closely as we can to the real thing. But people who are blinded by Maya can't do that, because of their axiomatic adherence to the notion that their view of things is truth.
I find the underlined sentence at odds with your description of a fielder successfully accomplishing a skilful feat in the real world. A couple of years ago I took a course on the history of philosophy and the world views offered by philosophers through the ages. All were trying to makes sense of how we know things. Other than Aristotle, so many others had to find some way of validating their worldview that did not depend on their perceptions. They simply refused to accept the evidence of their senses as a primary. Descartes for example used a convoluted reasoning that since he could think, he must exist. In short, nearly all tried to DEDUCT through pure reason (Hello Kant) how we knew what we knew. If I remember correctly, Hume realised his rationalizations while flawless, should be ignored if one wanted to live in the real world.

But our senses are our only direct cognitive contact with reality and, therefore, only source of information. Without sensory evidence, there can be no concepts; without concepts, there can be no language; without language, there can be no knowledge and no science. Aristotle looked to the outside world for answers, St Augustin looked for truth in the Bible.
By undercutting the validity of the senses we cut ourselves off from the real world. Try to disprove the evidence of sensory perception without using data obtained from such perception.

As for "certainty", it is possible - in a given context. Water will boil at x* at a given altitude and pressure. Dropped objects will fall to earth but not if accelerated to 17000 mph. There are no absolute (without context) certainties other than perhaps that nature to be commanded needs to be obeyed.
02-14-2020, 10:57 AM - 1 Like   #130
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QuoteOriginally posted by arnold Quote
It looks like the process of concept-formation is, in large part, a mathematical process. If you consider the definition of a concept you can see the similarities.
As the physicist above pointed out we can easily use the languge of math so we use it to find concepts. Math is infinite and most math is not helpful to define concepts. In fact if we do not find the math "pretty" we reject it on faith. Many concepts are understood only through the language of metaphor. Perhaps love, as a concept, can be quantified in some meaningful way, but it can never get to the heart of the meaning. Case in point, the concept, "heart of the matter". There is no nucleus of the matter because in the language of metaphor there is no particular worth attached to the metaphor.
02-14-2020, 03:35 PM   #131
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We need to inquire if there Has to be a theory that is unique in that it can make sense of everything perfectly. If there is more than one of these theories can we say one is correct and the other is wrong? If several theories can describe, predict, and formulate everything that every was and ever will be, it still doesn't mean that is reality, only that they correspond perfectly with reality. Is one correct? Are they all correct? Are none of them correct? Does it even matter?
In the 19th century spontaneous generation was a fact. Rats, maggots, fungus, etc. was just spontaneous. It is now fact since Louis Pasteur that this false, except it isn't. Pasteur did experiments and wrote the books history shows you confirmed once and for all clarified that notion. (clarified is another term metaphorically understood) In fact Pasteur had a contemporary who took hay infused bottles and performed Pasteur's experiments. He was meticulous. He performed his experiments at different altitudes and documented this well. His experiments "proved" Pasteur wrong. He did find spontaneous generation in his bottles that used the prescribed method of Pasteur. He wrote Pasteur and he got a tongue stuck out at him. (again metaphor) Well the Catholic leaning of France at the time overwhelmingly credited Pasteur despite the fact evidence showed he was wrong. Pasteur was correct for the wrong reasons. There are in fact bacteria that can with stand boiling but his "germ theory" has stood the test of time because is gets results. We still use germ theory and it has proven sound. It may be totally correct or just useful in an incomplete understanding, or just works.
Is the concept sparkling wine different from champagne? Ask a grape grower, a chemist, and an economist and you get different answers.
How about the colors bleen or grue? Do they exist or not and why is the criterion you use one someone else should?

Are there an even number of stars in the sky or odd? I submit it is all faith.
02-14-2020, 05:22 PM - 2 Likes   #132
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QuoteOriginally posted by arnold Quote
I find the underlined sentence at odds with your description of a fielder successfully accomplishing a skilful feat in the real world. A couple of years ago I took a course on the history of philosophy and the world views offered by philosophers through the ages. All were trying to makes sense of how we know things. Other than Aristotle, so many others had to find some way of validating their worldview that did not depend on their perceptions. They simply refused to accept the evidence of their senses as a primary. Descartes for example used a convoluted reasoning that since he could think, he must exist. In short, nearly all tried to DEDUCT through pure reason (Hello Kant) how we knew what we knew. If I remember correctly, Hume realised his rationalizations while flawless, should be ignored if one wanted to live in the real world.
The deductive is seductive -- logic is far cleaner and more absolutely true or false than any possible statement about the natural world. If one seeks certainty, math and logic tied to a simple fixed corpus of axioms are the way to go. Of course the real world isn't listening to the incantations of the rationalists and even logic loses its certainty if one starts looking at complex things like arithmetic and must face Godel's scary theorem. It's more than a little ironic that an animalistic subjective desire for stability lead the rationalists' so astray.

QuoteOriginally posted by arnold Quote
But our senses are our only direct cognitive contact with reality and, therefore, only source of information. Without sensory evidence, there can be no concepts; without concepts, there can be no language; without language, there can be no knowledge and no science. Aristotle looked to the outside world for answers, St Augustin looked for truth in the Bible.
By undercutting the validity of the senses we cut ourselves off from the real world. Try to disprove the evidence of sensory perception without using data obtained from such perception.
This is very very true -- the senses are our channel by which our internal thoughts get information about external conditions.

However, information theorists would categorize the human senses as noisy channels with both stochastic and deterministic sources of error. There are several fascinating branches of science spanning cognitive science, neuroscience, and behavioral economics that delve into the deep discrepancies between Homo sapiens and the fairy tale concept of rational man. One really can't trust one's senses to the last iota which is why some much of science involves building measurement instruments that end up having better repeatability than human senses do.

QuoteOriginally posted by arnold Quote
As for "certainty", it is possible - in a given context. Water will boil at x* at a given altitude and pressure. Dropped objects will fall to earth but not if accelerated to 17000 mph. There are no absolute (without context) certainties other than perhaps that nature to be commanded needs to be obeyed.
"Certainty" is elusive! First, one can heat water above its normal boiling temperature under some conditions (e.g., one exception is a clean smooth-walled container and water free of any bubbles which can easily happen when microwaving a cup of water). Second, a dropped helium ballon or butterfly typically does not fall to earth.

These exceptions aside, science has done a pretty good job of sensing, detecting, and characterizing the many natural phenomena that affect thermodynamic states, physical motion, and many other things. And engineers have become quite adept at applying this scientific knowledge to build things that reliably do what people would like them to do. It's a happy marriage between inductive and deductive techniques.

But any certainty offered by science or engineering comes with fuzzy limits defined by the limits of the science (the span and density of experimental conditions) and the limits of the considerations and approximations used by the engineers. For example Ricoh says its cameras can operate between -10°C to 40°C(14°F to 104°F) based on how its engineers designed the camera. However, the basic materials and physics of the camera are likely stable over a broader but unknown temperature range.

Last edited by photoptimist; 02-14-2020 at 05:46 PM. Reason: typos
02-14-2020, 05:35 PM - 1 Like   #133
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QuoteOriginally posted by swanlefitte Quote
As the physicist above pointed out we can easily use the languge of math so we use it to find concepts. Math is infinite and most math is not helpful to define concepts. In fact if we do not find the math "pretty" we reject it on faith. Many concepts are understood only through the language of metaphor. Perhaps love, as a concept, can be quantified in some meaningful way, but it can never get to the heart of the meaning. Case in point, the concept, "heart of the matter". There is no nucleus of the matter because in the language of metaphor there is no particular worth attached to the metaphor.
• An engineer thinks that equations are an approximation to reality.
• A physicist thinks reality is an approximation to equations.
• A mathematician doesn't care.
02-14-2020, 05:53 PM - 1 Like   #134
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QuoteOriginally posted by photoptimist Quote
• An engineer thinks that equations are an approximation to reality.
• A physicist thinks reality is an approximation to equations.
• A mathematician doesn't care.
Great statement but then explain why mathematicians believe in god much more than biologists.
02-14-2020, 06:24 PM - 1 Like   #135
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QuoteOriginally posted by swanlefitte Quote
Great statement but then explain why mathematicians believe in god much more than biologists.
For biologists, the fascinating complexity of life is not only explicable, it's inevitable. Take a nice stew of carbon, nitrogen, oxygen, hydrogen and other trace elements, add various external energy sources, and autocatalytic cycles of chemicals lead to more complex self-reproducing critters. Cook at room temperature for some billions of years in a 500 trillion square meter oven and voila!

In contrast mathematicians are used to intelligent creatures constructing artificial worlds so it's natural they might assume this world is the same (and deeply fear the coming of the cosmic rubber eraser!)
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