Of course this is nothing new. During WWI already, Malinowski discovered on the Trobriand Islands that the Oedipal Complex varied with the culture and was based more on power than sex.

80 years seems like a long time for knowledge to percolate from one academic specialty to another.

hmm, simile or metaphor... the longer Largo quote:
'Getting folks to try something new is always a task. I sometimes had to beg people to try new routes, when they could just do an established classic and know what they were getting into.'

maybe could be read differently, I read an inferred "like" after the first sentence, so not metaphorical, but more of an example...

"getting people to work on the paper (a new idea)" is like "getting people to climb my new route"

rather than creating the metaphor (which would be much enlarged) that writing a "new" paper and doing a "new" route, with all the difficulties it entails, including getting people to "read/climb" it.

That might be an apt metaphor, but not one I saw Largo writing.

Mike, here's clarification by Harold Bloom from my copy of How to Read and Why.

"I have been chided by reviewers for suggesting that Shakespeare 'invented the human,' as we know it. Dr. Johnson said that the essence of poetry was invention., and it should be no surprise that the world's strongest dramatic poetry should have so revised the human as pragmatically to have reinvented it. Shakespearean detachment, whether Sonnets or in Prince Hamlet, is a rather original mode...

"Hamlet speaks seven soliloquies; they have two audiences, ourselves and Hamlet, and we learn to emulate him by overhearing rather than just hearing. We overhear, whether or not we are Hamlet, contrary to the speaker's awareness, perhaps even against the speaker's intention. Overhearing Yahweh or Jesus or Allah is not impossible, but is rather difficult, since you cannot become God. You overhear Hamlet by becoming Hamlet; that is Shakespeare's art in this most original of his plays. Refusing identity with Hamlet is by now almost unnatural, particularly if you tend to be an intellectual...

"One learns from Shakespeare that self-overhearing is the prime function of soliloquy. Hamlet teaches us that imaginative literature can teach, which is how to talk to oneself... But it [poetry] has a crucial function for the self; Hamlet very nearly heals himself, but then touches a limit beyond which even the most intelligent of literary characters cannot progress."

My sense of Lynds paper was that it was neither a rigorous philosophical nor yet a math presentation, and that as a hybrid - or neither - that perhaps what Lynds is saying, or whatever might be implied there, is not fully or even partially understood. I'm not surprised that Ed would consider the paper in strictly math terms, even though those were not the terms in which the paper was presented. In fact from what I read per commentary, there was no agreement about what he was saying at all. Perhaps he isn't saying anything.

I was simply made curious by this, but not enough to do much about it because I have other stuff - and assumed others do as well - to do. But I met a physicist at the gym the other day and we'll see what comes of it.

One thing about Lunds is the debt he pays to Xeno and his paradoxes. My favorite concerns plurality, and runs like this, according to Dartmouth math proff Lesley Salmom:

A PARADOX OF PLURALITY

Although Zeno is best known for his four paradoxes of motion, he did propound a number of other paradoxes, including one that is even more fundamental. Although it is generally known as a paradox of plurality, it can plausibly be construed as a geometrical paradox which calls into question the very structure of the geometrical line (or any other continuum). Zeno presents the argument in terms of physical things and their parts, but the considerations he brings to bear seem to depend only upon the fact that these things are extended — that is, they occupy some finite, non-zero stretch of space. Although he talks about the possibility of subdividing the parts, he is not talking about the possibility of cutting up a physical object into separate physical parts that can be moved away from one another. He is not dealing with the physical hypothesis of the atomic constitution of matter. Rather, his arguments depend upon the possibility of making conceptual or mathematical divisions; for example, even if there are physical atoms (or subatomic particles) that cannot be split in two, if they occupy an extended region of space — be it ever so small — that space can be divided in the sense that we can distinguish its parts geometrically.

Since physical separation of parts is not at issue, we can just as well discuss the composition of the mathematical line. Zeno's argument runs as follows.27 As we have seen from both the Achilles and Dichotomy paradoxes, any line segment is infinitely divisible. If we stop short with only a finite number of divisions, it is always possible to carry the division further. The process of halving the line, and then halving the half, is one which has no end. Hence, if the line is made up of parts, as it surely appears to be, then there are infinitely many of them. Now, Zeno poses a simple dilemma. What is the size of the parts? If they have zero magnitude, then no matter how many of them you add together, the result will still be zero. The process of adding zeroes never yields any answer but zero. If, however, the parts have a positive non-zero size, then the sum of the infinite collection of them will be infinite. In other words, a line segment must have a length of either zero or infinity; a line segment one inch or one mile long is impossible.

An immediate objection might be raised against the claim that the whole must have an infinite magnitude if the parts have non-zero size, since our discussion of the Achilles and the Dichotomy paradoxes showed how it is entirely possible for an infinite series of positive terms to have a finite sum. But this response is inappropriate here. In order for an infinite series of positive terms to converge, it is necessary that there be no smallest term; the sequence of terms must converge to zero. This condition clearly rules out the possibility of convergence for an infinite series of positive terms all of which are equal to one another. In the Achilles and the Dichotomy paradoxes we could rest content with the division of a line segment into unequal parts, for we were not trying to divide it up into its ultimate parts. It is hard to see, however, how different ultimate parts could have different sizes. If one "ultimate" part were larger than another, it would seem that the larger would be further subdividable, and hence not ultimate after all.
Zeno apparently saw this point quite clearly.28 So, the second horn of the dilemma still stands: if the (ultimate) parts have non-zero size, the whole is infinite in extent.

If you're looking for mathematical paradoxes Largo, Banach-Tarski blows Zeno out of the water. Imagine cutting up an orange into finitely many pieces and then moving the pieces around by rigid motions to make a new orange the size of the sun. Find a knife that cuts oranges into "nonmeasurable sets" and Banach-Tarski says you can do it!

Are you sure that is a paradox, yanqui? Technically, I mean.

I loved hearing about it back when. It was fantasy made real.

I am sensitive after once calling something 'paradoxical' and having a senior researcher tell the audience that it was not a paradox.

But I am also reminded of a roommate at Chicago who told me of listening to Chinese colleagues of his whose conversation might have been bird song for all he could understand, until "Banach space" popped out. I often have a similar experience in the West Van Aquatic Centre sauna, though what I more usually hear is, "West Van-Koo-Vair."

Enough to give one pause. Which machine did ya have in "mind"?

Since the negative answer to the halting problem shows that there are problems that cannot be solved by a Turing machine, the Church–Turing thesis limits what can be accomplished by any machine that implements effective methods. However, not all machines conceivable to human imagination are subject to the Church–Turing thesis (e.g. oracle machines). It is an open question whether there can be actual deterministic physical processes that, in the long run, elude simulation by a Turing machine, and in particular whether any such hypothetical process could usefully be harnessed in the form of a calculating machine (a hypercomputer) that could solve the halting problem for a Turing machine amongst other things. It is also an open question whether any such unknown physical processes are involved in the working of the human brain, and whether humans can solve the halting problem

Edit to add: I found it interesting to see that the "Hahn-Banach Theorem", a standard result in soft analysis that says, in a specific way, that the continuous dual of a Banach space has lots more stuff than 0, implies the existence of nonmeasurable sets (and Banach - Tarski).

Only years later did another teacher give me specific instructions on what to do. I won't bore people with what that was, and is, but the process was basically to observe, as objectively as possible, phenomenon like self, attention, awareness, and so forth. This basically is a matter of using awareness as a kind of clinical instrument to observe - with no bias or interpreting - the "self" that we toss around like we know what that actually is, as it supposedly exists right this second. We assume that we actually know who we are but when I observed my internal landscape I discovered, as many had before me, that the landscape was rife in tangible elements, like the felt sense of being in a body, sensations, feelings, memories, evaluations, and so for - except none of these, individually or collectively, amounted to a "self" as an entity. And whenever I observed the residue of this belief in self as an entity, there was the nagging question of who - if anyone - was observing my self.

I'm pretty sure every dog chasing his own tail at some point or another has a nagging question of exactly who it is they're chasing...

The word paradox has many meanings, but I use it here in a broad sense to include any result so contrary to common sense and intuition that it invokes an immediate emotion of surprise. Such paradoxes are of four main types:

1. An assertion that seems false but is actually true.
2. An assertion that seems true but is actually false.
3. A line of reasoning that seems impeccable but which leads to a logical contradiction. (This is more commonly called a fallacy.)
4. An assertion whose truth or falsity is undecidable.

To nineteenth century mathematicians it was enormously paradoxical that all the members of an infinite set could be put in one-to-one correspondence with the members of one of its subsets, and that two infinite sets could exist whose members could not be put into one-to-one correspondence. These paradoxes led to the development of modern set theory, which in turn had a strong influence on the philosophy of science.

Back to my words:

In brief, paradoxes are surprising but not all that surprises is a paradox. The word paradox is often used loosely or even incorrectly. We can try to avoid criticism from the language usage experts (or nitpickers if you will) but to call it the Banach-Tarski Big Surprise doesn't seem to work.

Paradox is merely the shadow of infinity on a material/finite mind. Just as linear causality is only a single dimension in a multidimensional reality.(3D+time) Causality in practical terms is multidimensional and perhaps layered? I don't know, just a thought.

Learn to see it in thyself and thou wilt understand the infinite essence, hidden in all illusory forms. Understand that the world which thou knowest is only one of the aspects of the infinite world, and things and phenomena are merely hierolgyphics of deeper ideas.

Thanks for the link, Tim. After working with infinite processes for so long none of those paradoxes, like Zeno's Paradox of the Arrow, even register with me. Here is an improved version of the image I posted a few pages back. It was too dark. Think of this as a piece of jewelry designed by weak emergence from an infinite mathematical expansion:

I had to look that up. I am not familiar with the material. I do remember coming across the name at a library or two.

I was merely pondering the possibility of infinite mind or rather a mind that could experience infinity of time or space or both. How might the finite seem to the infinite and visa versa.

Your earlier post reminded me of a sentence I may have once read. What I remember: "Eternity is only a plane crossed by the line of time." I took that, in a sort of multi-verse way, to mean that there could be many different eternities, and that our time-line is only one of many.

I have never found the exact quote I remember, but a similar one occurs here: