I had thought Newsom would have a good chance, but news out of CA has not been good lately.

How do you finitely and completely describe these mathematical entities (irrational numbers)? — keystone

Pi is the ratio of circumference to diameter of a circle. The Golden Ratio can be defined as the ratio of a particular line segment to another - you can look it up on Wikipedia. Other irrationals, have at it.

I had never heard of the Stern-Brocot tree before you brought it up. But my knowledge of number theory is poor.

2024: Banana Republican Donald Trump vs Senility Candidate Joe Biden. :roll:

I can't say I recall a single revolt in history with a median age of 55, but if you look at armed protests in the US that would be my low end estimate for age. It's weird, especially since half the nation's budget is transfer payments to seniors. I suppose it is more about social control, not economic factors though. — Count Timothy von Icarus

I would like to see some statistics to this effect. That would not be my guess.

Ageism is still considered fair game, while other forms of discrimination may be declining.

Wikipedia says that the decimal representation of the Golden Ratio is 1.618033988749894...
https://en.wikipedia.org/wiki/Golden_ratio

Do you disagree with this? — keystone

This is a numerical approximation to a geometric concept, like 3.14159... approximates another ratio, pi.

Since these expansions are non-ending they do not completely describe the mathematical entities they represent. On the other hand when these entities are used in a numerical sense the tail ends of these expansions are chopped off according to the degree one wishes to approximate an answer.



:up:

The Tree gives rational approximations to the GR. There is no infinite digit RL. How would you use infinite decimal digits to define the GR?

You can call RL anything you like, but that does not mean it is so under foundation theory.

This is just a scheme associated with ratios of Fibonacci numbers and the Euclidean algorithm and continued fractions. You can call the GR the "last" RL if you like. Perhaps there are those who would agree with you. Just not in the mathematical community.

Any alternative to subscribe without going through PayPal? Got hacked in an account years ago.

I get scam claims through their site frequently.

1+1 = 2 is true in all circumstances because it’s a calculation performed on values which are simple by their numerical nature — invicta

No. Better stay away from mathematics for your "true under any circumstances" example.

A poetic and well written OP. :chin:

If 5 machines can make 5 devices in 5 minutes, that means each machine can make one device in 5 minutes. — Pierre-Normand

There is a subtlety here that GPT4 fails to address. But that's better than the other GPT.

Reasoning is a problem, as seen in the question,"If 5 machines produce 5 products in 5 minutes, how long will it take 100 machines to produce 100 products?" I'm not sure what version was asked the question, but even with coaxing and additional info it could not give the correct answer.

but whatever the case may be I don't think that my role in life is one of imitation although I could be mistaken. — Average

My late aunt used to say about my grandfather, "It took him a long time to find his niche".

Certainly, biologically, we are here to reproduce. We are fitted through evolution to survival and procreation. But most of us go beyond that, thinking,There must be a higher level purpose to our lives. I assume you are not an old person. Am I right? Because, when old we look back on our lives, thinking, What have I achieved and is it important to have achieved anything? Have I made may mark, and is that a necessity?

Or, we don't think about these things. Living life as we can. I have been an existentialist for most of my life; when I reflect, I think creating meaning has served me well. Don't ponder too long about this issue. Get movin' and find your niche. :cool:

:up:

Btw, I think Nicko got banned — Metaphysician Undercover

Yes, he did. And that is too bad. You get a scientist on the forum who "have at it" an argument using science in panpsychic realms and he's banned.

↪Largo

I was assigned to read primary texts. I came to appreciate commentary later on. But I am glad I did not start with that. — Paine

I had the opposite advice in my one (senior level) course back in 1958: Read commentaries first, then primary sources. I had tried to understand a particular philosopher in order to write a report, but flamed out there with little understanding of what he was writing about. The professor then told me to go to commentaries at first - which worked.

My name for Christian culturist is "Jesus fans." The don't actually follow his teaching, but they say he's a really great guy. — Art48

George W. Bush when asked who was his favorite philosopher answered, "Jesus Christ". Then, I thought, How ridiculous. Now, not so much.

But philosophical practice and philosophical writing are not the same. The ancient practice of philosophy was not about writing but a way of living. — Fooloso4

Is it possible some philosophers when writing run out of ideas, but continue writing? :chin:

If something cannot be experienced and cannot be exactly defined, then we should not speculate about it. — ClayG

Does that mean that a great many if not most threads on TPF should be removed? It's already been decided that definitions here need not be exact - or, in some cases, comprehensible.

I don't see how there are any issues of incomprehensibility that are not ultimately an issue of length, — Ø implies everything

Quite possibly. I don't know. Sometimes it may seem to take forever to get to a point of understanding a complicated idea or general area of study. Which causes me to wonder if AI may move beyond our comprehension of mathematics it devises - length or not. Here is an interesting introduction to a paper on Scheme theory - a topic beyond me, I fear:

Scheme theory, perhaps more than any other subject, has a reputation for being extremely
difficult and tedious to learn. One gets the impression that the subject involves many highly
technical and difficult constructions, is exceedingly vast and abstract, and that it takes
considerable time and energy before one is able to prove anything of value. Quite famously,
the subject originated from Grothendieck’s attempt to “simplify” an eighty page paper by
Serre into the thousand page document that was to become Les ́El ́ements de g ́eom ́etrie
alg ́ebrique — a fact that is both oddly remarkable and offers little encouragement.
It is perhaps somewhat surprising, then, that there seems to be no shortage of graduate
students and even undergraduates eager to devote time to understand schemes. The usual
procedure is to sit down with a copy of Hartshorne, formally sift through a seemingly endless
series of complex definitions, and then grudgingly admit defeat. Usually absent from these
attempts at understanding schemes are good sources of intuition, motivation, and clear and
identifiable goals. The result is that students learning the subject this way have difficulty
explaining the “point” of a definition or a construction, and so don’t know what it’s related
to, why it’s there, and consequently can’t use it.
The purpose of this article is to give the basic definitions of scheme theory in context.
We will take the view that it is just as important, if not more so, to explain the definitions
themselves as it is to explain the lemmas and the proofs. In doing so, we hope to remedy a
common affliction that befalls those who read Hartshorne’s book: not having any idea what
is going on

David Urbanik

Brilliant OP. I would expect nothing less. :clap:

Could you elaborate? Do you mean their theorems/concepts would have so many steps/components that it would take longer than a lifetime for a human to properly go through it/grasp it? — Ø implies everything

You mention one possibility. Yes. And the sheer breadth and size of the subject is overwhelming, almost impossible to keep up with, having over 25,000 pages on math on Wikipedia. Also, 200-300 research papers a day, every day, on ArXive.org . Then we have things like the Four Color theorem which required a computer to evaluate a huge number of cases to "prove". By themselves, humans can only process a limited amount of interwoven logical steps. Then there are probably limitations on the size, scope and complexity of new math concepts humans can conjure up. So mathematicians with computers may enhance the realm of the subject enormously, but if Tegmark is right the entire universe is somehow mathematical and probably beyond comprehension. Being all-invasive, this math structure would be conscious in some way, sending out trivial ideas to people calling themselves mathematicians. :cool:

Max Tegmark's Mathematical Universe ideas might relate to this. I think it is only a matter of time before AI fabricates concepts, techniques, theorems and proofs in mathematics that lay beyond the grasp of human mathematicians. There is your higher intelligence, embedded in a universe whose Matrix is more akin to Hilbert Spaces than what is seen in the movie.

I want not a life without wants. But I want not to have too many wants. It's a matter of balance.

I will be unhelpful and say it depends . . . . . — Count Timothy von Icarus

Yours is among the very best posts I have read on TPF. :clap:

Sensations are nervous system-dependent — 180 Proof

:up: This sums it up pretty well unless you believe rocks have feelings.

Do you think there is a math brain or a type of person to whom math speaks? — Tom Storm

Genetics are a big part. A little like musical talent. My father grew up in a poor coal mining community in Pennsylvania where almost all the young men went into the mines after high school. He worked after school in his senior year in the mangers for donkeys underground, doing his homework by lantern light. But he escaped his origins and became a professor of business statistics and directed the grad program at the University of Georgia for a while. He had a masters in mathematics, then a PhD in statistics. My degree was in math.

People who get stuck on specific definitions are often irritating pedants and seem to miss the point. — Tom Storm

Guilty. Just my math background showing. :yikes: And the old adage from CS: "garbage in = garbage out".

But, as @fdrake explained, definitions in math sometimes undergo revisions as the process of exploration or problem-solving progresses. Research in math is a very fluid work space if one is not forced to make it advantageous in some applied problem. It can be remarkably loose, going back and forth. I'm looking at something now that will necessitate a revision of hypothesis - the starting points, like definitions, for successful arguments.

Although it irritates me at times to read sloppy, ill- formulated definitions in these philosophical discussions, I am growing to understand it's part of the process that might converge to an interesting conclusion.

It's a little hazardous to form an analogy outside physics with a concept or result in physics that one does not fully understand. Especially when numbers are involved. But bully for you to give it a try. No cigar, however. :roll:

Atoms are particles. Neutrons protons, and electrons are also particles. So are quarks. As far as I know, their respective volumes do not consist of "particle fields". — 180 Proof

Theorist Sean Carroll thinks it’s time you learned the truth: All of the particles you know—including the Higgs—are actually fields.

Fermilab Symmetry Magazine

Don't forget that 99.999% of baryonic "matter" also consists of empty space — 180 Proof

Would you consider it empty if permeated by particle fields? Is it really empty if sustaining a magnetic field?

As Bear Bryant said, "Victory is 10% inspiration and 90% perspiration." Wait, no, he said "When the going gets tough, the tough get going," or was that Picasso — T Clark

Well, he could have said that, but what he did say was (Wiki):

Again, as at Kentucky, Bryant attempted to integrate the Texas A&M squad. "We'll be the last football team in the Southwest Conference to integrate", he was told by a Texas A&M official. "Well", Bryant replied, "then that's where we're going to finish in football."

During the 1960s in visits to my parents in Tuscaloosa I would go exercise climbing on Bear's metal coaching tower, maybe thirty feet high with a covered roof and staunch guardrail fence around the top to keep him from falling off. He had a metal seat/cage attached to a hoist that his players would crank him to the top where he would sit with his feet hanging over the edge and chest against the guardrail fence. Not saying much, letting his assistant coaches do most of the yelling. There was a metal winding stair to the top but I don't think he used it. He was the next thing to a Deity in Alabama. The photo below taken maybe ten years after I last watched him doesn't show the hoist. That would detract from is popular image.



Pop philosophy from Bear:

1) It’s awfully important to win with humility. It’s also important to lose. I hate to lose worse than anyone, but if you never lose you won’t know how to act. If you lose with humility, then you can come back.

2) I think the most important thing of all for any team is a winning attitude. The coaches must have it. The players must have it. The student body must have it. If you have dedicated players who believe in themselves, you don’t need a lot of talent.

3) Losing doesn’t make me want to quit. It makes me want to fight that much harder.

4) I know what it takes to win. If I can sell them on what it takes to win, then we are not going to lose too many football games.

5) If you believe in yourself and have dedication and pride – and never quit – you’ll be a winner. The price of victory is high but so are the rewards.

6) I have tried to teach them to show class, to have pride, and to display character. I think football, winning games, takes care of itself if you do that.

7) I honestly believe that if you are willing to out-condition the opponent, have confidence in your ability, be more aggressive than your opponent and have a genuine desire for team victory, you will become the national champions. If you have all the above, you will acquire confidence and poise, and you will have those intangibles that win the close ones.

8) First there are those who are winners, and know they are winners. Then there are the losers who know they are losers. Then there are those who are not winners, but don’t know it. They’re the ones for me. They never quit trying. They’re the soul of our game.

9) If we’d beaten ‘em, I wouldn’t be going out.

10) If wanting to win is a fault, as some of my critics seem to insist, then I plead guilty. I like to win. I know no other way. It’s in my blood.

From Psychology Today:

The scientific research is clear about the psychological implications of looking at greens generally. Studies have shown that seeing the color green is linked to enhanced creative thinking.

In this regard the forum needs all the help it can get. :cool:

'Quantum mechanics says that classical objects — including brains — don’t exist'.(Hoffman) — green flag

I wonder where? What a waste of time.

This "thesis" is about formulating a paradigm that unifies scientific explanations with panpsychist/spiritual or theistic ones — Benj96

The proof is in the numbers, so explain how that comes about.

I see a comparison between "pop philosophy" and "pop science", although authors of the latter generally have more impressive credentials. Nevertheless, I cringe when I see the image of the Earth resting in a basketball net in space. Or read quantum woo attempting to describe the indescribable. Victor Toth commented on Quora at some point that the subject was virtually all mathematics and attempting to uncover analogies from the macro world, simply a bit of nonsense.

Both pop philosophy and pop science have their places, however, in sparking curiosity and reflection. And you do have to be a real philosophy buff to appreciate the finer differences of thought between two intellectuals who lived centuries, even millennia ago.

I'm ready. What is the known ontology of matter? — Metaphysician Undercover

:up: Bullseye.

How could anyone not appreciate this, a Sach's Puppet? :smile:

Back in the saddle. Great! :cool:

How does matter arise from consciousness? — TheMadMan

We become involved in life's experiences and discover what really matters.

Oh, wait . . . that's another kind of matter. But, you see, the crux of the matter is poorly defined words and concepts in philosophy. As a matter of "fact", take being. Many have tried, but few if any have succeeded in this matter. :cool:

My perspective on it would be to find others that want to harmonize not only different perspectives and insights, but also experiences, moral and everyday life as well. — Caerulea-Lawrence

Welcome aboard . It would be interesting if members would speak more about their life experiences as they argue philosophical points. Sometimes they do.