sorry.just lost the internet for about a week.

I have about 10 different books on Hilbert space only. — Corvus

Really? You must be a mathematician like I was. And one working in functional analysis. I have perhaps four books that speak of Hilbert spaces in certain chapters.

The first idea in the mind of primitive man would have been the first concept. Impossible to narrow down from there.

At 77, it's been a long time since I was in school — BC

Me too. 87 here.

Thanks to an intervention, I attended a state college. It was tremendously valuable in terms of acquiring some social skills and general knowledge (I majored in English). The degree itself was still very useful in 1968 — BC

I taught at a state university for thirty years. These institutions are undervalued in an era in which media focuses on Harvard and other elite schools. Many an undergraduate education is a real bargain in these reasonably priced universities. As a math professor I have seen a number of our graduates (in math and/or physics) go on to obtain doctorates and have successful careers.

I will make one observation on formal education versus autodidact learning: the absence of studied criticism in the latter.

Can you explain why? I'm not seeing it — Janus

As a retired math person I can see the possibility of the mathematics of Quantum theory somehow reifying into a form of reality. However, I suspect not.

What happened?

It captured and reinforced the liberation experienced by many people as WW2 ended. — Ludwig V

Indeed, I came upon it a bit later, in the late 1950s, and it became popular among young, adventurous men - particularly from California - looking for a path forward that was new and exciting. I suspect its popularity dwindled during the Korean and Vietnam wars when one's path to an exciting and adventurous life either threaded for many through dense jungles or for others freezing cold and was not a freely chosen one.

The Golden age of climbing is now seen by many as the mid 1950s and early 1960s, especially regarding Hillary's conquest of Everest and similarly impressive feats in Yosemite Valley. I got caught up in that adventurous period and, like others, discovered existentialism - an approach to life that correlated well with climbing. But, its popularity dwindled, I suspect, during the decades that followed, especially the Vietnam conflict. I really don't know. It worked for me all the rest of my life.

Though it is true that the world that I am part of and which makes me what I am is a not a matter of choice, but of chance, in a sense — Ludwig V

That's the obvious bug in the ointment, of course. I can only reflect on my own upbringing. As an only child of an roaming academic, I felt a sense of individual responsibility that allowed me to expand my thinking beyond traditional bounds. And when I chose to become a climber through a fluke during my junior year in high school in Georgia, my parents were shocked, but composed. However, when I joined a fellow young climber from Atlanta and we drove to Colorado in the summer of 1954, my father later revealed to me he bought burial insurance for his son.

On the other hand, a friend roughly my age grew up in difficult circumstances, with an absentee and violent father, and he also chose the existentialist path. And another, coming from very humble circumstances, also without a father, may have considered himself an existentialist, but I don't recall talking about the subject. The first of these became known as the most revered climber of that era and in later life created a prominent clothing company. The second became a billionaire.

The complete last sentence of Hazel Barnes' quotation is "Existentialists values intensify consciousness, arouse the passions, and commit the individual to a cause of action that will engage their total energies." A promise of relief from the real pains of anxiety in a meaningless world and also a promise of trouble and fear. But perhaps that's just me — Ludwig V

Barnes seems to view existentialism in a extreme form. It provides a focus - or more than one - and a feeling of the power of an individual to control much in his life. Not all of it by any means. How much of this feeling of control exists before the acceptance of this philosophy varies.

Finally, looking back at the first sentence in Hazel Barnes' quotation - "The function of Existentialists values is to liberate humankind from craven fear, petty anxiety and apathy or tedium." - I notice the powerful rhetoric that she chooses to attach to "humankind", "fear" and "anxiety". This is not existentialist cool at all, is it? — Ludwig V

All I can say is that her comments seem bizarre and don't fit those who I knew who considered themselves existentialists.

I meant that a lot of people choose not to use what intelligence they have, because they just don't care about the truth — Brendan Golledge

There are those on the Forum who think of "truth" as a relative concept. As a retired mathematician, I know mathematical truth is dependent upon certain axioms. One changes the axioms and the notion of truth becomes a bit more vague. But you seem to refer to the existence or character of God. Am I correct? Possibly I misinterpret what you have said.

You mention being awakened by your baby crying. Isn't that a form of truth?

I do wonder whether the frequently-aired complaint that 'quantum physics is incomplete' might arise because of the fact that matter does not exhaust the totality of existence — Wayfarer

Good point. :up:

As it is for just sitting, in Soto Zen, the reward is in the doing. — ENOAH

The meditator strives to be aware of the stream of thoughts, allowing them to arise and pass away without interference.

(Wiki)

Without interference, perhaps, but philosophical thoughts are posted here on the Forum before they pass.

I'm not as concerned with Trump winning the election as I am with him losing the vote count. He has been busy keeping his MAGA base stirred up, and if he loses he might incite them to disrupt procedures at the Capital and overturn the presidency by force of arms, not simply wandering the Halls of Congress.

Perhaps not. I wish he would calm his rhetoric.

Sartre's The Gaze and The Look are interesting additions to his fundamental idea of creating meaning in one's life. I suspect every athlete who moves from the playground to the big leagues learns to deal with how others perceive him as he performs. To some the roar of the crowd is stimulating, while others might have a harder time dealing with the interaction between observers and himself. How easy is it for a pro golfer to handle sudden small noises in a crowd? On the other hand how can one reach those levels without mastering control of The Look?

As much psychology as philosophy. Pardon an intrusion into a discussion about past philosophers.

If I see references to God, or when an OP is very lengthy and rambling I usually lose interest very quickly. That's just me. As for thinking and solving problems, I recall Richard Feynman saying something to the effect that one should attack problems that one feels are within one's capabilities to solve.

Alex Honnold ("Greatest athletic feat of all time") and scientists pull their sleds over the Greenland ice cap in a recent Nat'l Geo offering. I wasn't paying a lot of attention as they slogged over the ice, but at some point a scientist remarks that the sheet (glacier) is in good shape, not melting away as suspected. I probably have it wrong. Any others watch this?

Math is not a science, of course, but it is very much a social activity. In general, if one states a proposition one needs to convince others of its validity. For relatively simple results this might be fairly easy - following the logical steps the author has presented. At times, however, even this task is so complicated that verification is illusive. The great mathematician, Poisson, regarded Galois theory as presented by its creator, as unintelligible. And in rare instances computer programs must be brought into play for analyzing huge numbers of examples.

If anything, math is dependent on human involvement to an even greater extent than areas of science. But in a different way. And if the foundations are shifted results may be reinterpreted.

We need more individual rebellion. — Rob J Kennedy

I don't think an existential existence requires rebellion. Maybe sometimes it does.

Just joking about the New Zealand lawyer. He's a bright guy.

Perhaps you are visiting from another planet — Truth Seeker

I've wondered about that. :cool:

If you are saying that compassion and caring doesn't solve any problems for those being shown compassion and caring, that doesn't seem to make sense to me. — Beverley

Of course compassion and caring solve many problems, but not all. Clearly not all. For example, in the event of a plague compassion and caring helps enormously, but many will still die.

I used to be quite an active musician & composer/songwriter, but sadly I’m still not famous & successful — niki wonoto

You chose a profession that is unbelievably competitive. I would suggest you try to find an unexplored niche in that community, one that fits your talents, and work hard at it, but you may have gone that direction already. Half of success is being in the right place at the right time. I have a stepson who, years ago, toured with a rock band as a singer, but found a niche in the industry as an audio engineer. He worked, later, under the stage, recording Taylor Swift's performances.

Maybe you could claim to be an existentialist — Moliere

In the most elemental sense, yes. I had the opportunity to choose and follow paths that gave meaning to my life. Others may not be so lucky.

So when you were in your 20s-30s did you ever wonder about the power of humans to choose who and what they will be? Or did the abysmal events of the 20th Century leave you hopeless? — frank

The answer to this question resonates on this thread. Of what value is a philosophical idea if it does not change lives? Or does philosophy as an approach to life live on mysteriously within endless discussions of Russell's paradox and something arising from nothing? Much of what I have read is inconsequential, like the pure mathematics I have enjoyed.

Many years ago - the late 1950s - as a young man I read Sartre at a time I was looking for a meaningful life. I came away with a very simplistic idea of creating meaning in something that captured my interest, even though few if any others thought it worth pursuing in earnest. I had and have no desire to know more of the erudite philosophy embedding my core understanding. If others say existentialism is far more complex that that, I say, operating along my elementary understanding has worked. If anyone says I didn't understand what I read, I say, so what. What I focused on to give meaning now has meaning for many others. (it's an Olympic sport)

Of course you always have to be careful with AI - it makes stuff up so needs confirmation — Gary Venter

I have adequate knowledge of two areas of thought and/or practice: mathematics and rock climbing. Yesterday I asked ChatGPT about a close friend of mine in the latter, what he is best known for. AI produced a reply that was entirely wrong, stating my friend was famous for a certain climb, while in fact he never did that climb and is known for an entirely different accomplishment. Made up facts.

A farewell to one of the few military veterans on the site, as if that means anything on a philosophy forum. But Wittgenstein was a military hero. Did that influence his writings?

Possibly. But I suspect from observations over time that, for example, women seem to have an ability to categorize and perceive relationships that correlates with algebraic structures.
And there is an ongoing discussion concerning men vs women in regard to spatial perceptions.

From ChatGPT:

some studies have indicated that women tend to be more represented in certain areas of mathematics compared to others. For example, fields such as mathematical biology, mathematical education, statistics, and applied mathematics have seen relatively higher levels of female participation compared to more traditionally male-dominated areas like pure mathematics or theoretical physics.

I might have guessed math education, but not the others.

When we try to understand reality only through external physical things imagined from this outside position, we lose sight of the necessity of experience. This is the Blind Spot, which the authors show lies behind our scientific conundrums about time and the origin of the universe, quantum physics, life, AI and the mind, consciousness, and Earth as a planetary system

I wonder how this might apply to math research?

Another QM interpretation holds that the quantum field is a Hilbert space, not just mathematically but actually, which would make the physical world part of the set-theory universe, reversing the question this thread raises. I personally find this non-appealing for a few reasons. — Gary Venter

From ChatGPT 3.5:

Quantum field theory (QFT) is a theoretical framework that combines quantum mechanics and special relativity to describe the behavior of elementary particles and their interactions. In the context of QFT, the quantum fields themselves are typically described mathematically as operator-valued fields defined on spacetime.

A Hilbert space is a mathematical concept used to describe the state space of a quantum system, where states are represented by vectors and physical observables are represented by operators. In quantum mechanics, the state space of a single particle is often described by a Hilbert space.

In quantum field theory, the state space becomes more complex due to the infinite degrees of freedom associated with fields defined at every point in spacetime. The state space of a quantum field theory is typically described by a Fock space, which is a direct sum of tensor products of Hilbert spaces associated with different numbers of particles. Each mode of the field (corresponding to a particular momentum) can be thought of as a harmonic oscillator, with its own associated Hilbert space.

So, while individual components of a quantum field theory can be described by Hilbert spaces, the full quantum field itself is typically not described by a single Hilbert space, but rather by a more complex structure known as a Fock space.

Maybe this will get the thread back on original tract. Thanks for your comments. I agree that Hilbert spaces are useful for the manipulations of Q Theory, but are more descriptive than fundamental.

:up:

But the point stands nonetheless — Lionino

Sorry, I missed this discussion. How does this bit about group theory relate to postmodernism?

Commenting on this, I don't think it is quite correct to say that multiplication is not defined in <ℝ,+>. It doesn't exist in the scope of <ℝ,+> of course, but whether it is defined or not is not a pertinent question. But the point stands nonetheless — Lionino

Postmodern?

Show me how you will determine the calculation of input values and a binary operator after you die; show me how the universe will determine the calculation of input values and a binary operator after all sentients die. — ucarr

Sorry. No idea what you are talking about.

The effect comes from the cause (by definition), so the effect includes the cause — LFranc

This has been my take on mathematics. Once certain definitions and processes are settled, all that logically flows from them does, in a sense, exist. It's a matter of discovery.

You’re saying it’s not empirical in the way that a novel or poem is not empirical, right? — Joshs

Sounds right.

math philosophers who argued for the construction of mathematics as an empirical endeavor. — L'éléphant

I think of Newton, developing calculus to describe physical phenomena. And perhaps some math is created in this fashion today. But by and large it's not an empirical process. Although math is called the Queen of the Sciences, it is not really a science.

↪jgill

My version — Mark Nyquist

That's OK. We all have our versions.

Absent any physical theory, logic says non-existent and non-physical things don't have any cause and effect relation. — Mark Nyquist

Is mathematics non-existent? Some might say yes. It's certainly non-physical. But cause and effect run thorough it like an intellectual river. In a typical theorem there is an hypothesis which gives rise to a conclusion.

- Brazillian Jiu jitsu;
- Drums, voice, guitar, bass, keys.. few others, including Irish Whistle!;
- Songwriting in light of the above - 23 albums and counting;
- Free Running/Parkour (mostly handstands and other power moves);
- Writing comedy for television and other stand-ups;
- Writing battle raps that will never see the light of day (though, there is footage of me doing several battles out there on the internet... )
- Collecting/enjoying Whisky/ey and fine Wine;
- Currently Learning Spanish and Arabic;
- Trying to solve the origins of the Voynich manuscript;
- Visiting puppy litters; and
- Writing science fiction (two pieces, thus far.. but one is a Trilogy for which i've only begun the first volume). — AmadeusD

Are you real, Amadeus, or are you an AI bot? :gasp:

AI can think like a human: it plagiarizes well.

Yeah those were the days — Sir2u

Look at my icon, from a BASIC program on infinite compositions of complex functions. :cool: