Numbers are used to measure volume or force or speed. Plato's tradition did think human aesthetic should be reflected in the world, but you need to defend that with argument

Are we drawn to shapes like the equilateral triangle from more than personal preference. Are such symmetries important to us at some primordial subconscious level? — Paul S

Someone on another thread posted this:
https://en.wikipedia.org/wiki/Significance_of_numbers_in_Judaism

I think when anyone studies numerology however, they will find there is no consensus on any number or relationship between numbers whatsoever. And the same probably applies to shapes. That is my personal opinion. I think it's all relative. There is no guarantee that the outside world should accord with our "primordial subconscious", but I appreciate where you are coming from

Modern mathematicians seem to have forgotten that Aristotle covered up this problem with a sophistry and that Kant presented this problem in one of his antimonies. If I want to know how many parts an oven has or a loaf of bread baked in it, I simply have to ask how many times I can mentally divide it. And it turns out I can do this infinitely, yet the bread and the oven are finite. Mathematicians now longer see this as a problem or as even strange, and I don't know why

If something is spatially finite it's finite, not infinite. — fishfry

Yes, but this is contradicted by infinite divisibility, which all space must have.

Do you mean how can a finite length, like the unit interval [0,1], contain infinitely many points? That's pretty simple, if nothing else 1/2, 1/4, 1/8, 1/16, ... are infinitely many points contained within the interval. — fishfry

Presenting the problem in terms of numbers instead of space obscures the issue

There are a lot of buzzwords in there but the Wiki proof is pretty decent. — fishfry

I am trying to comprehend the first few axoims of all geometry, and i'm not sure the specifics of B/T relate. I only was talking about B/T in terms of taking an infinite of points out of another infinity of points.

But to be honest, earlier you claimed that 1 + 1 might be 4, and you didn't respond when I asked for clarification. May I suggest nailing that down first. — fishfry

Sure. If we have two 12 inch rulers, they are equal 1 to 1. However with numbers half of 1 is also a number, so if we apply to this the ruler we have 2 six inches on one side and 2 six inches on the other, hence instead of 1 and 1 being compared, it's 2 and 2. The reason is that in arithmetic you have to have basic numbers that are understood as not divided. In geometry, all space is divisible and its impossible to find the basic unit.

Do you follow the calculus in Gabriel's horn? The integral of 1/x from 1 to infinity is infinite, and the integral of 1/x^2 is finite. It's just how it is and the proofs are perfectly straightforward. — fishfry

Not precisely. I was good at pre-calculus in high school but in college I only did geometry and that was over ten years ago. I am coming at this from a more basic fundamental level and perhaps I can't avoid highwe mathematical ideas but I had wanted to find the first few axioms of geometry and am confused why it's become to problematic

Aristotle said in his book on the heavens, if I remember corectly, that 3 was a special number. I'm more modern in my thinking. For me all numbers, colors, shapes, and lots of other things are equal because they have no aesthetic objectivity. But if someone believes reality must be naturally beautiful in the sense they believe beauty to be, it's natural for them to present their theories to see who else sees things as they do

After reading that work you might like the Tibetan Book of the Dead. At death, so it goes, you see a light. If you realize the light is you, you are free. If you fail, you then see many Buddhas who express their emotions to you. If you identify all this as yourself, you are free. If not, you see in a vision either two animals or two humans mating and you become their offspring in being born again as either animal or human. The key for this tradition is to disbelieve in the soul yet there is still the feeling of subjectivity which we grapple with in our dealings with the paradox of Ego

I'm not sure there is any best way to read Nietzsche

If something with mass suddenly traveled at the speed of light it would gain infinite mass, but from where? Where does the mass come from? From the perspective of those not traveling that fast the object disappeared but if we were the object we would be infinitely big. But again, how does something in that situation increase its mass? Does it take mass from its environment?

On the purely speculative side, suppose we have a race track that literally goes out forever into the horizon. A hypothetical geometric object goes towards this horizon and miraculously jumps to infinite speed. Since his destination is endless he will never reach it yet his infinity of speed is as infinite as the track. Would this simply tear the fabric of reality of such a situation occurred?

The vsauce video was where I first encountered B\T. His supertask video also showed me that I was not alone in thinking about "Zenonian cubes". I know that mathematicians look at Banach-Tarski with many equations in mind, but I've always looked at it from the angle of Zeno's paradox alone. So my series of questions has been

1) if space is infinitely divisible than it has infinite parts despite the fact that we experience geometric things as finite

2) calculus says that a infinite number can be subsumed by a finite measurement. But in spatial terms how is this possible?

3) how can something be spatially finite and infinite is what appears to be "the same respect"?

4) if an object has infinite parts we can take infinite parts out and have a new object, hence Banach Tarski. But isn't this entirely counter intuitive?

5) this is all paradoxical to because of the way I think of objects as finite. What is the way forward?

I wanted to explore the non-Euclidean stuff with more care because it is also counter intuitive and might give me a clue on how to find the fundamental principle of all geometry and space. I'm not trying to prove anything to other people, but trying to find an understanding that satisfies myself. Some are ok with Gabriel 's horn. I don't have peace with it

Entropy makes people depressed because they feel that disorder is taking over. Howecer, I think entropy is about randomness. Order and disorder are in the eye of the beholder. Randomness and determinism are objective on the other hand. The world started with less randomness and is now becoming less determined. However if consciousness is founded on quantum uncertainty than the more random the universe becomes in the future the more it will be capable of create great consciousnesses.

When we do arithmetic, any number can have a half, so 1 plus 1 can really equal 4 in that case, which I believe means that we have to start with numbers which are discrete (numbers so fundamental that they are the landscape of all number theory). Such a state of innocence doesn t seem possible to me with geometry even though I've wanted to find that pure fundamental for space. Every part has a part in order to remain spatial and an infinite gel of uncountable infinities seems to me to put what is blurry at the start of geometry when I wanted it to be clear. I see your point about the series of halves which I presented as already having the limit of the surface area before actually breaking apart the geometrical object. If I can find what is most fundamental despite all this about geometric space I will finally be able to put the question behind me. I found the most basic book I could find on non-Euclidean geometry on Amazon and since I know there is something missing in my understanding about geometric space I am going to go over the basics so carefully that I can find the false assumptions I've made which have thrown a monkey wrench into my understanding of geometry. I hope to become bolder and use my ambition to solve the paradox of Banach and Tarski

To be fair much of string theory is speculation and based on aesthetic preferences. Platonic solids are dominated by triangles being at the center of its geometry. Saying that triangles are the basic structure of spacetime is a fine idea

I saw a video one time about Christians "lying for Jesus". The Christians whos videos were shown clearly knew all the Bible verses that were relevant, but they told their audience that slavery allowed to the Jews by Jewish law only involved indentured servitude. They didn't mention that the laws said they are to keep the women and children of those they conquer as slaves and those individuals' descendants as slaves for all perpetuity. In fact the descendents of all non-Jewish slaves were to remain slaves to the Jews. This was common in those times but the more I've read the more commonplace the Old Testament becomes. Kant said he believed in the New Testament only and that most of the Old was not true religion. Germans latter argued that the Jews started the idea of "my race is specially chosen" but of course they fell for that themselves and called themselves the master race by nature (instead of election by God).

I don't look to ancient times for authority. That is, others bind themselves to laws they hate because they think they are bound by what ancient history "tells them". Those times are so long ago however that for me they don say much to us with certainty and it certainly won't tell me how to live my life

I am from the Catholic tradition. Catholics usually say that the Jews may follow mosaic ritual laws and all that but only within the Christian theological scheme wherein. Otherwise they are seen as rejecting their Messiah of course. Some more progressive Catholics say that Jewish people are actually bound by God to follow both Mosaic and Catholic law. I remember Art Sippo and Robert Sungenis debating this years ago. I don't see how it's truly progressive to put such a burden on Jewish people and this goes to show how viewpoints look different from different angles. Another example of such phenomena is removal of the clitoris in Africa. Some secular progressive anthropologist support it, although if it had been an exclusively traditional Catholic practice these same people would be raising hell over it. The 3 major monotheistic religions are very related and have their place in history. What place they have in the future is for us to determine. Throwing gays off building, wives being obligated to burn themselves to death with their dead spouse, and many other practices fall to the waste side of modern society evolves and adapts

A smallest unit, if its spatial, has parts, and so on etcetera. This has to do with the building blocks of shapes, but I think this thread is only about shapes so

.

Well what holds a compactified infinity is its limits, hence infinity is limited by the finite. I don't see how the tangible can be so extremely textual without it having infinite parts. A mind blowing idea is that if the world is eternal the only limit of the infinite past is the ever moving present, which goes on and on itself towards infinity. So time's limit is a potential infinite "not yet". That's how I understand time, but perhaps time is a digression from Platonic shapes in 3d space. I'm sorry. I was thinking in terms of Minkoski geometry

All religions make up stories because that along with ritual is the societal function of religions. The stories are more for the young and the rituals are for the adult and meant to be followed blindly. Christianity starts as stories and believin in the book of Revelation takes blind faith as well but not long after Jesus rituals set in

I have lots of questions about this. That arranging of objects and even cities in certain ways has an affect on the universe is a very Eastern concept, to start. Qui. The Western analogue is God being pleased with churches. But whether the order of space itself has symmetry needs to be asked in regard first to time and then to geometry. Time works aligned with space. It is dynamical. Cyclical basically means dynamic, right? I mean you can think of eternal time as a circle or a line. You can even take the circle and turn it into a line. What distinguishes time is movement of event. Is there something unchanging in space that resists flux? Maybe I guess. Patterns are functionally finite things with events at its root. Sections of space can be infinitely divided so they have infinite parts, and we can then ask what is the shape at the bottom (limit). How it "behaves" may be the only way forward at that moment and thus we learn about reality "out there" by its effects on us. That is always tricky affair however.

Our thoughts themselves need to resemble reality to be objective

Good thread

Answer: blind obedience

Remember when God told one of his prophets to use his poop as fire fuel when he cooked his food? It's in the Bible. Christians like to call Muslims primitive (Tucker Carlson called middle easterners backward monkeys) but their Old Testament is just another Quaran

Other questions:

How diverse are the many cultural societies of the world?

Are they all equally bad or good?

Is there just one "Western culture" or many?

What elements of a society are inherently linked to others and where are the "logical atoms" which philosophical analysis sought for a hundred years ago?

I listened to Bertrand Russell's chapter on Rousseau tonight. It was fascinating. The Frenchman associates each achievement of the then modern society with a vice. Social cohesion in the General Will is good politically for him, but the tinsel of socities' cultures bad. Everyone has their own opinion however, and one man's rationality is as different from another's as are their "sentimentalities" (an important Romantic word for the Frenchman). Cooperation in mutual esteem made possible city states, wherein the individual interests cancel each other out until what is left can be elevated as the substantial General Will. The favors of nature allowed humans to advance in technology, but maybe you are asking what advance really is.

Property just means some thing is possessed by an object or subject as its own

That kind of thinking can go all the way back to Plato's Cave — Don Wade

I love that idea. It would be so cool to have asked Plato about brain mechanics and questions brought up by the likes of George Berkeley and others on this issue

I think that if one reads his writings he does have a lot to say that is worthwhile. — Jack Cummins

Ive only read his General Introduction book. It was balanced

I would also say that your view of the essential underlying truth of the principle seems based on the importance of satisfaction. I am just wondering to what extent would this be about satisfying it, or of relinquishing it?I am inclined to believe that we are left with this conundrum because it is not easy to overcome desires, and do we really desire to overcome all of our desires? — Jack Cummins

The school of thought embodied in the writings of Napoleon Hill says that we must make our desires stronger so that we can attain what we desire. This belief is based on the thought that our desires can be satisfied. It does seem very anti-Buddhist, but I don't want to speak for the latter's tradition. Whether a person should start throwing fuel on his desires or cast out the flame would depend on the desire and the person. Freud said that to suppress most of our desires results in rebellion of our unconscious. He wasn't very spiritual I don't think nonetheless, and might have basically been a quack

We can have thoughts of objects we have seen. Are those thoughts emergent properties of the brain? — Don Wade

You might want to better understand the process method of writers like Josiah Royce, Francis Herbert Bradley, Alfred Whitehead, and Gilles Deleuze. Again, I am talking more about method than overt content. A lot of people are used to thinking of your question in terms of analytic philosophy (Russell, Ayer, and even Bergson) and it gets really difficult to think on those terms.
Just a morning thought. Cheers

If someone says "I am lying that I am lying that I am lying that..." ( to infinity) we linguistically have negative infinity. Godel showed there are (1) infinite things in math that can be proven and (2) infinite things in math that cannot be proven. So we have many infinities, and to go from nothing to some thing is an infinite jump, but maybe infinite infinities can bridge it. If particles and anti-particles can annihilate each other, do you think we can, instead of thinking of something coming out of nothing, think of it as two things annihilating each over in reverse? This would be the absolute emergence.

The idea of zero is very interesting because we can play around with ideas of infinite zeros and how many infinite zeros equal a normal number. Just as in math you kinda have to postulate a number that can't be subdivided, so with infinity you can never logically a rule out another higher infinity with an infinity of more members. At what point do the zeros become a proper number? I don't know, nor if you can negate an infinity or zero without it just duplicating. Anyway, the idea of nothing has been a notion that many thinkers throughout time have found meaningful and productive. What is the most fundamental thing that can be a factor in any emergence??

Nietzsche was profoundly influence by Hegel, who's philosophy I can best express simply by the saying "your mind is changing as you read this sentence". I found that phrase and its idea in a book called Evolve your Brain, which I read a long time ago. It's connection to how Hegel works out his ideas came to me much matter.

"Integrative changes in the brain come from integration of consciousness" is another phrase I just came across tonight. The spectrum of our perceptions is very wide and we quite literally desire infinite things. The idea that we live in an eternal cyclic universe sounds good, if only we can find satisfaction. Our mind is like a fountain, and our experiences are like water. "Movement is the language of the brain" (Anat Baniel)

In the latter part of the 20th century when the 19 measurement constants were codified, a lot of people (pastors, priests, and lots of others) wrote books and stuff about how it was very unlikely that life would result from the Big Bang. Some people respond that we don't how many times the "universal" dice (in that the universe was a pair of dice) was rolled. I don't see this is THE appropriate initial response because it directly denies the premise without looking at the evidence for it. However, what actually tipped the balance in the favor of the current universe could have been a marble (we can call it Parmenidian if we like, or not) we can't detect, a random flutuation we can't detect, or anything the imagination can imagine and beyond. The core, basic "principle" behind the universe can be random or deterministic, personal or material. Furthermore, we don't know what forms of life would have arise if the "universal dice" fell differently. We are physically "talking meat" as one writer put it (who's article on the subject I read in college). A metal based life would think we were weird. My perspective is that even beauty is subjective, so we can't say that life is the roll's outcome that "should have happened". Any way the universe fell is equal to any of the others, in those terms. The universe is beautiful because of our "collective dream". We are made of what the universe is made of in a sense. We are not dark matter or dark energy however. I don't know what life made of those things would be like, but their lives might be better than ours if they exist. So my basic point is that we can't prove spiritual things from the necessary (determined) and contingent (random) aspects of science. Nonetheless, General Relativity is a trip, and gaining a better understanding of it from a philosophical perspectives perhaps is something that is understudied these days. Too many people wasting their ink trying to prove their is a God (and just one of them! lol)

If you run the known motion of the matter in the universe backward, you get the big bang. That was the initial oomph. And what caused the big bang, and what came before it, and do we know it's even true? Nobody knows but everyone has an opinion. Lawrence Krauss says that In the Beginning was the quantum soup and the laws of physics. Genesis says that In the Beginning God created the heavens and the earth. Can anyone clearly distinguish science from theology here? Of course the simulationists say that In the Beginning was the great computer in the sky, and we're all programs. I'm Microsoft Word, and you're Tetris. Science? Or theology? The Many Worlds folks insist that while in this universe I wrote this paragraph, in some other universe I thought better of it and didn't. Science? Or theology? And why is it exactly that so much of our science lately is indistinguishable from theology? — fishfry

Very good

"take a sunrise..sprinkle it with dew..a miracle or two.. the world taste good.. take a rainbow and wrap it in a sigh, soak it in the sun"

If you have a motion (try picturing it) and then another, previous to it in time, we have the a series (causality comes into the picture and was a question raised by Hume). The series either goes on (or went on, rather) forever in the past, or it stops at... what? If you've reached a singularity, you have fluctuations still in it, one previous to the other. Otherwise, what do you have in material terms?

Doing away with absolute time is essential to understanding this in modern terms. But force and causality is still a concept we use. It seems to me the series has to be either eternal or it came out of nothing. An intermediate stance between these 2 postulations would be interesting and I've had a lot of glimpses of it but it's hard to put into words and if I can't explain it to others well enough I probably don't understand it well

Maybe all poems

kaleidoscope — Jacob-B

Ye the kaleidoscope and lots of poems can be used for philosophical insights

Here is one of the quotations that has got me thinking about these issues: "The philosopher's claim is based on the intellectual insight that the extremes of an external body do not coincide but actually have a certain distance between them. An extended body has an objective and definite length even if we have no means of measuring this length absolutely. The attribution of objective length to a body does not mean that the size remains the same regardless of the state of motion of the body. A body's length may stretch or shrink whenever the body undergoes a change in its state of motion, or may appear longer or shorter when observed from different rest frames." Henry J. Koren,1965

Newton perfectly well explained the motions of the planets in the solar system using equal and opposite reactions as one of his physical principles. — fishfry

Hmm, well those who propagated his theories to the public said that God had to be the ultimate engine behind everything. Descartes's alternate vortex theory had God behind it as well, but Descartes wrote in his Reply's on the Meditations (1642) that physical motions of extension don't necessarily need a supernatural cause as its absolute explanation (in terms of physics). So yes I'm thinking about how to imagine and conceptualize that. Stephen Hawking thought a lot about this as well

The largest mass in the universe gains weight from all the rest of the mass of the universe. — fishfry

Oh your right. We can't imagine every action causing an equal immediate reaction in the opposite direction though because things wouldn't move in that case.

It's hard to imagine and conceptualize on these things, at least for me

Yes, that "species" is not precisely defined I think is the answer to my questions. If it was a static feature I don't see how evolution could work. With birds and rabbits which can't mate with other birds and rabbits anymore, I would like to see these groups go on and evolve another set of animals that cannot mate with the original evolved groups we have now

Dr. Grande has an episode on Tesla. He is always a little harse but that is his job I guess. He provides some interesting biographical facts within a framework. You can view it on you-tube

Thanks guys. I wrote an initial paragraph in response in Notepad but then accidentally deleted it. The point I am trying to make is that simply because something cannot be measured absolutely or because two motions cannot be distinguished by physics does not mean, to me, that there is no objective shape and size of objects. Natural heaviness as a property would then be a further thought based on this, and motion could be based upon that property. There is a relation because opposite sides of an object that is maintained by the matter they bind and that is why geometry can describe them. There is some confusion in how GR is presented to the public in general. It is often said that Einstein found that his equations meant that the universe expands. He added a "constant" to the equation to make the equations tell us that the world is static, although he didn't have evidence as yet for its existence. So it sounds like this added part of the equation says how the cosmological constant prevents the universe from expanding. However people now call dark energy the cosmological constant even though it appears to do the opposite of what that term meant for Einstein. There seems to be a lot of moving around, among and within, equations and it creates confusion for a lot of us. I am just looking for a basic material format in which to see frame the universe so that it is self consistent. (The details may vary)

The capitalist market moves by selection of the fittest product. To say that this "invisible hand" is really the Illuminati or something behind the scenes is a conspiracy theory. So following Occam's its natural to look, not to supernatural intervention, but to be the universe itself to see if matter, time, space, and causality can work together in the sense of a universal physics. Using the "God of the gaps" argument is giving up on the question and positing, within that context, a supernatural conspiracy theory. If the likelihood of the whole universe being here and having life is very unlikely, whether its more likely that there is a God or many Gods is another question. How they can exist and what is the likelihood of they being able to exist is philosophy. But ye we are talking about science, and there can always be posited a further realm of matter that hypothetically explains how our visible universe could have allowed life within all reasonableness. A material object, it seems to me, can definitely change what would be a random event into something determined. It could answer the fundamental why, although some would say it's still a "how" and not a "why". However, what I think about a lot during the day is how matter can move and cause things within the bounds of matter only and how all of matter (all it's kinds whatsoever) can be and make sense on its own.

I like my original paragraph better :( Darn electronics

"Information" is a quality or "accident" (in the old usage) and needs matter in order to emerge. A lot of stuff spoken of in quantum mechanics could be private interpretation. They have two principles for example: (1) a particle can be two places at once, and (2) a particle can pop out of nowhere (through teleporting into a work hole or whatever). Now, if you are studying a new particle, how can you possibly determine if it came from the wormhole or if it is really a neighbouring particle in superposition? THAT is a matter of perspective, so be cautious when people try to prove their points by the philosophical implications of quantum physics

Sorry for the delay is elaborating.

This is a philosophical question in that it relates to what a human is and the mathematics of biology

Birds and rabbits are often pointed out as an example of speciation since some groups of these can only now only reproduce within their group. It would be an example of evolution of from there they developed totally new skills. If a species is defined as that which cannot reproduce outside ones species, the first of a species must be lucky enough to have a mate that evolved like them. This makes evolution-s mathematics very confusing for me. I'm not seeing how it works in the sense of the game Life for example (The one invented by John Conway)

I don't have a problem with nominalism. Some think that it is necessary t o posit quasi-spiritual natures in living things. I'm ok calling a female a female or a male a male even without reference to so-called "natures". So evolution makes philosophical sense to me. If someone disagrees, please join in. However, what i ve been reading over the past day about when a species is made is not adding up in my head. So sorry again for not getting back to this sooner. This complements questions I've asked about pattern formation in the past