Giordano Bruno - spatial concepts of geometry to language

[01101001]

Some people dig being exposed to new information.

Some people dig in their heels.

[Jens]

I see where you're going here, and it's not good, accusing someone of suspension of reasoning, just because they converted from your side. Some people are capable of reasoning, evaluating the evidence, learning, realizing they had a misconception, and move on to other things.

It's not a lack of courage, just the opposite. Some people cling to their beliefs, maybe out of fear of the unknown, maybe out of not wanting to ever be wrong, maybe just because that's the way they're wired whether they want to be or not. It's a lot like cricket.

Thanks. Yeah, I actually disagree that it is even deference to authority, rather deference to the fact that they actually did analysis. But in any. Are, if changing your beliefs based on new information is cowardice, then I'm afraid I'll have to plead guilty.

[Canis Lupus]

... if changing your beliefs based on new information is cowardice, then I'm afraid I'll have to plead guilty.

No need to take the comment too personally. I confess the same lack of fortitude all too often and know myself to be hardly up to the task.

What is the hardest task in the world? To think.

R.W. Emerson

A little authority for you

From the same authority:

In every work of genius we recognize our own rejected thoughts; they come back to us with a certain alienated majesty.

But Emerson wasn't a scientist, nonetheless ... and back to the real topic ...

[Canis Lupus]

Some people dig being exposed to new information.

Some people dig in their heels.

Information is one thing, data, but what do we make of it - that is thought. So, can we add, "some people dig thinking"?

I hope so, otherwise what is the use of all that information?

[Strange]

There's nothing wrong with skepticism - it's a virtue. If I stated "cynical" that would be different.

Forgive the correction, you didn't simply assume, you provided observation and reasons.

Research is one thing, it can reveal a lot, of course - that being its purpose or intention of research. Conducting research per se means little by way of proof or evidence.

The downside with all this authority based thinking, despite its advantages, is it tends to put one's own mental faculties in neutral. The expert said "this" and the expert said "that'. I'm always interested in what the experts state, don't get me wrong, but I don't let them think for me, but rather suggest and guide, provide "food for thought". I suppose there is some intelligence involved in familiarising yourself with what the expert (the authority) states (book learning), but there is a decided lack of intelligence if we suspend our own supreme arbitrator not evaluating for ourselves what the expert states.

You seemed to be on the right track to start with, but someone comes along with "the expert says there's a 'simple rule of thumb'", and then what happens: suspension of reasoning, deference to so called expert, and a backtrack?

I must trot over to the Mozart thread and add courage as a characteristic of genius.

This would appear to be getting off topic, but I think it is much more dangerous to let your "supreme arbiter" decide that your own common sense assumptions are more important than evidence. (You also seem confused about the role of experts vs evidence.)

[Strange]

Potentially there can be very little or none. The test of these signs and how these signs are used will be their connection with geometry.

And how do you do that? How do you test the geometry between the word "apple" (or "ringo" or "miele") and a physical apple? Or the concept of an apple?

If they cannot be reduced to geometry or be shown not to reflect geometry, then they are indeed totally arbitrary and as useful as a fairy tale without a moral or deeper meaning - a bit Harry Potterish.

With the exception of some slight evidence for a small role of sound symbolism, I am not aware of any evidence that words are not arbitrary. Do you or Bruno have any?

[Canis Lupus]

And how do you do that? How do you test the geometry between the word "apple" (or "ringo" or "miele") and a physical apple? Or the concept of an apple?




With the exception of some slight evidence for a small role of sound symbolism, I am not aware of any evidence that words are not arbitrary. Do you or Bruno have any?

The particular symbols are arbitrary. The way we use them can either be geometric or arbitrary.

Your example of an apple is a good one. We can call an apple anything providing we all know what we are dealing with - a common meaning - an accepted definition. But if we want to scrutinize that definition to a degree of exactness, we will apply geometric thought processes to complete the task.

How we construct thoughts through the various symbols used from time to time and place to place, is a different matter. Despite the differences in symbols, the geometric nature of thought will be universal if the thought has validity. If it doesn't, then it is fanciful. There is a place for fancy, no doubt, but it will be largely unintelligible to those from a different place and time - unintelligible for good reason. It's one of the reasons we can never fully understand the Ancient Romans, Greeks or Persians or even people from last century.

It isn't overly complicated. In this post, I have divided something into two parts, reflecting geometry to help explain a thought. I've separated the symbol from a line of thought, or process of thought using the symbols.

We do it regularly, if not all the time in some way. Once you see it and appreciate it, you see it more and more. You also see more clearly when the thought process drifts or becomes ungeometric. In which case, it is almost always inevitably flawed or misconceived.

It is perhaps worth noting that definitions themselves play a pivotal role in geometry.

[Jens]

and back to the real topic ...

Yes, that sounds like a good idea. What about Bruno?

[Canis Lupus]

This would appear to be getting off topic, but I think it is much more dangerous to let your "supreme arbiter" decide that your own common sense assumptions are more important than evidence. (You also seem confused about the role of experts vs evidence.)

Ok. It's a point worth making. We can take it up somewhere else, I'm sure

[Strange]

The particular symbols are arbitrary. The way we use them can either be geometric or arbitrary.

Your example of an apple is a good one. We can call an apple anything providing we all know what we are dealing with - a common meaning - an accepted definition. But if we want to scrutinize that definition to a degree of exactness, we will apply geometric thought processes to complete the task.

How we construct thoughts through the various symbols used from time to time and place to place, is a different matter. Despite the differences in symbols, the geometric nature of thought will be universal if the thought has validity. If it doesn't, then it is fanciful. There is a place for fancy, no doubt, but it will be largely unintelligible to those from a different place and time - unintelligible for good reason. It's one of the reasons we can never fully understand the Ancient Romans, Greeks or Persians or even people from last century.

Can you explain how geometry applies to either the use of language or to thought? This is a bit vague, so far.

It isn't overly complicated. In this post, I have divided something into two parts, reflecting geometry to help explain a thought. I've separated the symbol from a line of thought, or process of thought using the symbols.

So you are saying that splitting things into sentences or paragraphs is "geometry"?

[Canis Lupus]

Can you explain how geometry applies to either the use of language or to thought? This is a bit vague, so far.



So you are saying that splitting things into sentences or paragraphs is "geometry"?

No, but that isn't an invalid way of looking at it either. More ideas, rather than sentences. Separating thoughts into parts, removing or putting aside some part to deal with another part, comparing a part to the whole etc.

And, yes, atm things are bit vague, I will freely admit. I'm learning as we go along. I hope to be more specific after I have more time for some reading and to connect things a bit deeper to understand how it works at a pre-language/symbol level with both humans and animals.

Give me time but fire your points or questions at will. It will help give my reading focus.

[Strange]

No, but that isn't an invalid way of looking at it either. More ideas, rather than sentences. Separating thoughts into parts, removing or putting aside some part to deal with another part, comparing a part to the whole etc.

Hmmm... I can see a vague analogy to geometry. Is it useful?

[Canis Lupus]

Yes, that sounds like a good idea. What about Bruno?

I need to read more of him to understand more deeply his approach. I will get back to him as best I can with the limited time I have.

[Canis Lupus]

Hmmm... I can see a vague analogy to geometry. Is it useful?

I think so. I've stated this before in another thread, but two geniuses which stand out for me are Mozart and Jane Austin in this regard. With Mozart the geometry should be obvious even to those who aren't musically trained. With Austin, likewise, it's a tour de force of rhetorical geometry, she constantly dissects ideas at will, bringing them together again, to convey her meaning in the most minute detail.

Both characters seem to have proven their worth to humanity.

[Canis Lupus]

So you are saying that splitting things into sentences or paragraphs is "geometry"?

Just to return to this question briefly. Geometry as we generally think of it is "geometry" as we learn it at school and is used in formal mathematics. Its power and significance comes from what it reflects - its not an abstract creation divorced from a reality. What we commonly think of as geometry shadows, reflects, a more primeval pre-symbolic type of geometry which the universe itself reflects, as we do, and which is behind the calculations which occurs in nature - in animals and us instinctively without the need for formal education. The formal education we receive, if soundly based, is the transference of that "primeval" instinctive geometry into symbols and language which we can then communicate these fundamentals common to all of us.

A poor education will consist of disconnecting the two.

[grapes]

... if changing your beliefs based on new information is cowardice, then I'm afraid I'll have to plead guilty.

No need to take the comment too personally.

Other than it was obviously directed personally. Avoid doing that again.

I confess the same lack of fortitude all too often and know myself to be hardly up to the task.

There, that. Characterizing "changing your beliefs based on new beliefs" as a lack of fortitude. Avoid personal insults.

[Canis Lupus]

I think I may understand the issues raised in this thread a little better now.

Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometricaltheorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.^[6]

it seems Bruno may be suggesting by his idea of spatial concepts in language/thought that the geometric spatial reasoning of the brain/mind occurs at such speeds we are not conscious of it generally. We are always doing it with our movements and physical attempts to master, cope or survive. We do it from the outset but very simply. As we mature, the process becomes faster and faster, better developed. It can be developed to a quite fine, extraordinary, degree, despite being limited forever by approximation. It's the approximation which allows for indefinite refinement. In a way, the sky is the limit for how fine the "calculation" can be- the sky at the same time never being a limit.

The brain/mind does not need calculus, (except in the form which pre-dates it as used by Archimedes) in order to achieve what is practical. I think it better to regard the achievement and the means of achievement as a workable approximation necessary for the task, rather than a rule of thumb, but the difference may be one of semantics when examining a rudimentary achievement of a young child doing something simple like catch a ball. There is a great margin of error in the task of catching a ball - generally, within certain parameters, the bigger the ball, the bigger the margin of error, and the less exhausting the method of exhaustion needs to be. In that situation you can take your pick whether you regard it as a "rule of thumb" or a "basic stage of the method of exhaustion".

Developing the speed of this spatial reasoning, necessary for all higher thought and very complex physical activity, is a combination of latent intelligence and education - the two feed off each other continually. It will be developed easier and more efficiently by the study of disciplines which incorporate its principles best but in the preliminary stages best by physical activity. Familiarity with specific situations will assist the process because from memory of previous calculations/constructions held by the brain/mind comes the ability to make ever finer calculations/constructions geometrically according to the method which Archimedes used.

Archimedes is the greatest mathematician because he reflects best the natural working of the brain/mind when it is constantly solving the problems set it from moment to moment, naturally, in order to achieve whatever task befalls it. It is little wonder, therefore, he was so practical.

The skill of spatial calculations/constructions is latent but the speed is something which must be developed. The speed becomes so fast as we develop that it occurs beyond our general ability to perceive it. From our normal point of view, "it just happens" in accomplishing almost all tasks, particularly in environments or routines we are familiar with.

[Canis Lupus]

Developing the speed of this spatial reasoning, necessary for all higher thought and very complex physical activity, is a combination of latent intelligence and education - the two feed off each other continually. It will be developed easier and more efficiently by the study of disciplines which incorporate its principles best but in the preliminary stages best by physical activity. Familiarity with specific situations will assist the process because from memory of previous calculations/constructions held by the brain/mind comes the ability to make ever finer calculations/constructions geometrically according to the method which Archimedes used.

A couple of points about this, one of which only occurred yesterday. The other was on my mind when I posted and has been troubling me a little ever since.

Firstly, the equating of "higher thought" with "complex physical activity". That didn't seem absolutely right at the time of posting and left the thought there must be a difference. The very best sportsman I have generally noticed are far from stupid people, although the temptation of loads of money and sexual attraction may often lead them into regretful actions. They may not be particularly articulate or intellectual sounding in their speech but listen closely and it is not hard to detect intelligence. However, putting them on the same plane as academics and other intellectuals is probably a bridge too far. This is where that feedback loop comes into play cited by 01101001 ("Our Binary Member") earlier in this thread.

The visual cues that people use to catch balls on the fly are not that different from the automatic motion detectors built into the tiny brains of critters that catch flies on the wing: frogs. A frog "would have to use the same sort of optical cue to intercept the fly with its tongue," Kaiser said. "And it might make a decent outfielder as well."

http://articles.latimes.com/print/1995-04-28/news/mn-59922_1_wall-ball-catching

*Pity we don't have a link to the source paper for the above media story

It helps to distinguish the intelligent sportsman or those engaged in complex physical activity from the theoretical intellectual. The "physical person" (those engaged in complex physical activity) has the benefit of on the spot updated data constantly being fed into his/her calculations, allowing for greater adjustments. The theoretical intellectual does not have this immediate advantage. His task, therefore, is harder in the calculations he must perform, therefore, making greater demands. In fact, it is so hard we have invented a method, slow and sure, to overcome the difficulty - "science".

Secondly, yesterday, while weighing up the order of my shopping expedition at the local shopping centre awash with holiday makers who invade this Port Stephens paradise at times like this, I noticed myself performing this geometric weighing up of pro and cons of the order of shops I wanted to visit and tasks to be performed. Now, the aim was not to reach any exact figure or number, but rather think it through to determine the best order in light of available information. For this purpose, it was sufficient, it seems, for me to use spatial images, dividing off tasks, comparing their pros and cons in terms of desired order which had to be done relative to a larger concept. I didn't talk myself through these calculations, I used shapes and sizes, I noticed. After noticing this, it appeared to me, that those people who are able to calculate quite large numbers almost instantaneously, probably use the same method but incredibly faster. I have always wondered how they achieved this. It's possible Bruno had accomplished it himself, leading many to regard him as a magician.