Information is that which eats away at entropy.

Eating the tomato does not advance one up some ladder — Nuke

But eating a mushroom might. :cool:

So is there more to patterns than complexity? — Gregory

Some patterns are very simple, others more complex. Complexity, itself, does not imply patterns. Nor does it necessarily imply chaos.

Discussion could instead focus on how to have experience. We can observe how practical information like that is typically missing from discussions. — Nuke

Mystical events, which are only incompletely communicable in words, cannot be fully understood by those untouched by such experiences.
~Max Weber — Pantagruel

I made this point some time back, but the two central protagonists on this thread enjoy discussing philosophical perspectives of mystical experiences that are, themselves, better understood by actual practitioners.

I'm an existentialist, having read Sartre over a half century ago. I spend very little time reminiscing over past experiences. Even at an advanced age I look to the future. My purpose evolves. :cool:

Avoid A Far Country. :wink:

It makes a difference in athletics. Title IX assumes equal but different, and argues against transgender participation.

Otherwise, I don't think it's that important.

Years ago I occasionally taught History of Mathematics and I seem to recall that an ancient variety of the sine function was found on cuneiform tablets from roughly 3000BC.

In all fields, finding common principles that underlie many diverse phenomena is an admirable goal. — Pfhorrest

That is certainly true. Higher levels of generalizations in mathematics has led to understanding how seemingly diverse concepts are alike. But this knowledge may not shed light on many existing puzzles in specific areas beneath these umbrellas. Generalizations avoid the nitty-gritty. Sometimes abstraction is merely abstraction.

Knowledge needs to be combined with wisdom. That's where 'religion' comes in — EnPassant

Religion brings wisdom? Tell that to a young girl being stoned to death for becoming pregnant. :worry:

Science is concerned with primitive knowledge about material things. Consciousness is concerned with knowledge about life and being. — EnPassant

Science vs consciousness? Scientists are not conscious? :roll:

If you include political philosophy - modes of governing - I would say that is clearly an area of intense interest today, and perhaps progress is being made there. But, if you are speaking of topics like ontology, I see very little of substance being produced. A little like highly abstract mathematics IMO.

Did you mean virtuous sex? It may not be ethical, but the irony is pleasing. :smile:

That something other than this 3+1 dimensional reality exists is undeniable — Possibility

Please provide references for this statement. Or, do you mean the subjective "I find it undeniable"?

Aleister Crowley : He founded the religion of Thelema, identifying himself as the prophet entrusted with guiding humanity into the Æon of Horus in the early 20th century. — Gnomon

Just a passing comment about this very interesting gentleman. He was a pioneer British rock climber and mountaineer. He was on an expedition to the Himalaya (K2) in 1902. Also, he wrote the first British bouldering guide in 1898, illustrated by a famous artist.

It would be entertaining to read about other little known aspects of the lives of well-known philosophers - show they were not one-dimensional.

And a tiny factoid about the Schrödinger equation: Under certain (unrealistic?) restrictions, it has the form dQ/dt=CQ(t), which is the familiar expression from elementary calculus stating that the rate of change of a quantity at time=t is proportional to the amount of the quantity existing at time=t. :cool:

people seem reluctant to disagree that, according to chemistry (science), water is H2O? — TheMadFool

And why should they disagree? Is there some alternative that makes more sense?

There's no evidence nature is a specific kind of (mathematical) dynamic system.

Has any philosopher ever written something related to this? — Ada

Who knows? But you have described a rock climber. :cool:

Switch off brain, and there goes consciousness. — jgill


There goes identity, not consciousness — bert1

I pity the poor, innocent chunk of dead flesh lying in the morgue, conscious, but not aware of itself. Wes Craven where are you? :groan:

Considering speculative theories of history, the butterfly effect is one extreme. Another is Stanislaw Lem's ergodic theory of history: There are social "attracting fixed points" so powerful that minor or even major alterations of history have no substantial effect on a particular outcome. For instance, had Hitler been assassinated early on, the outcome - a disastrous WWII - might very well still have happened, more or less in the way it happened.

Ergodic theory of history

The Grandfather Effect is fun to contemplate. An outlandish form of multiple universe theory is that the universe is constantly splitting into uncountable alternative states, so that murdering your grandfather when he is young would simply lead to an alternative world history. :cool:

A property-to-property analysis shows no coherent relation between consciousness and a physical brain. — MonisticIdealist

Switch off brain, and there goes consciousness. You assume that because a coherent relation is not detectable now, it will never be detectable because it does not exist. What kind of reasoning flaw is this, philosophers? :gasp:

Attention just is, or so it can feel. — Nuke

That's exactly how my old friend, a thirty year Zen devotee, described it. Empty awareness. We can all have this sensation from time to time when completely relaxed, unfocused, and awake.

Could be. I'm awaiting an application of the hyperreals that is useful in describing or predicting physical phenomena. Perhaps quantum theory will be couched in those terms at some point. But for now they seem to be pretty darn abstract.

Probability may not be appropriate here. Especially using numbers. :roll:

the mystical practise attempts to show you your soul. — Metaphysician Undercover

It seems more appropriate to describe mysticism as the experience of being — Nuke

Is being = soul? The conversation has turned philosophical. :chin:

There's a decimal-like notation for the hyperreals, called the Lightstone notation — fishfry

I keep learning things on this forum. I wonder if hyperreals will ever supplant the real number system. Infinitesimal calculus, touted as a more intuitive way to teach the subject, shows up here and there around the world, even in some high schools. The following seems to be a kind of advanced calculus course centered on the hyperreals that complements a similar elementary calculus course that apparently was abandoned years ago:

https://www.math.wisc.edu/~keisler/foundations.pdf

The author even has diagrams showing "where" infinitesimals and transfinites are located on the real line! :cool:

↪fishfry
Whatever line the surreal is on, I'm still wondering how you would describe writing down the decimal expansion of it. — tim wood

An infinitesimal is technically a "mathematical quantity", but not a real number. Real numbers have decimal expansions. Infinitesimals have an arithmetic that is not the same as real numbers. r+r=r, e.g. How would that work with a hypothetical decimal expansion? Not all arithmetic is with real numbers.

I tend to look at physics to see what kinds of math are consistent with the physical world. Virtually all I see there is real and complex analysis, functional analysis, group theory, matrix theory, etc. None of which seem related to anything but real or complex numbers. (Well, the Hahn-Banach theorem in FA generates lots of functionals and requires in its proof a single transfinite step, unless this is avoided by requiring a tad more in the hypotheses) . Even string theory - seen as a flop by many - doesn't invoke esoteric number systems.

But I read that surreals are connected to game theory. So what do I know? :roll:

The future of philosophy may be the past of philosophy, when the natural sciences and philosophy were closer and philosophy was able to keep up with the sciences. In a similar vein, a lawyer who is a philosopher has an edge over a legal philosopher who isn't.

Words are like the variables in a computer program. They need to be defined for some function to use them properly. If they aren't defined then the function will produce an error. This is the problem that I see occur most in philosophy - where the terms themselves aren't properly defined to do any work with, or that the function references the wrong part of the array if the variable/word has multiple definitions. A word can have an array of definitions and if you confuse which one you are working with, then you will get an error. — Harry Hindu

Amen to that. :up: "Garbage in = garbage out"

In the 83 years I've been alive, the "perfect candidate" has not appeared...although there have been some good candidates and good winners.

Biden, no matter his many faults, will be a marked improvement over Trump. But even Mickey Mouse would be a marked improvement over Trump. — Frank Apisa

You and I, at 83, can barely remember FDR - who along with Washington and Lincoln top the list IMO.

I'm not so certain Biden will be a huge improvement over Trump. He will certainly be a more traditional president. We will probably have the opportunity to find out. :chin:

Please have a little patience, I think we might be getting somewhere soon. — Punshhh

Of course. :cool:

You are familiar with mathematics. By what principle would you say 10 is "higher", meaning a greater value, than 2? — Metaphysician Undercover

The "Looking at one's hands" principle. :smile:

OK. Forgive the intrusion. I was curious about first-hand knowledge of the topic being discussed. In other philosophical areas, like panpsychism, this is not a consideration. For several years I belonged to a forum in which a lengthy thread dealt with various aspects of mind. One participant had practiced Zen for thirty years, and we had some interesting conversations about his epiphanies and how they might have related to brain activity.

From SEP:In the wide sense, let us say that a ‘mystical experience,’ is: A (purportedly) super sense-perceptual or sub sense-perceptual experience granting acquaintance of realities or states of affairs that are of a kind not accessible by way of sense perception, somatosensory modalities, or standard introspection.

This definition is more inclusive than one positing some aspect of the divine. Have either of you had such a "mystical experience"? If so, please describe them. How did you enter into the mental states that led to revelations beyond normal sensory or introspective means? Did you meditate? Was there an epiphany at some point, an astounding and memorable moment?

Philosophizing about such internal adventures seems so remote from actually having them. Like discussing Citizen Kane without having seen the film.

I don't mean to be rude, but this is an area of which I have had some limited first hand knowledge, and so I see the disparity between participation and external ruminations. If all you wish is to speculate and discuss the analytic parameters of mysticism, then I beg your pardon, please continue.

Surreals by any other name are just an infinitesimals? — tim wood

No. I'm old enough that I knew Leibniz, and am familiar only with his basic ideas about infinitesimals. Surreals by Conway are much more elaborate. One can teach a calculus course using only the basic elements of infinitesimals. IMO the surreals are for set theorists and philosophers. Purer mathematics than anything I've done. The real and complex numbers are challenging enough for me!

The finite number line is a fiction. It may be useful for some things, but to insist that it is somehow 'real' and try to make meaningful inferences from that is meaningless. — A Seagull

I'll pass that on to my colleagues. What a bitter disappointment. :sad:

In mathematics one learns the concept underlying a symbol, then develops a skill for manipulating it. I once read of a prominent mathematician saying that the most valuable competency he had acquired was how to mechanically manipulate elementary calculus as if without thinking.

1:A natural spiritual need. The human propensity to look to a divine agency. — Punshhh

IMO wrong from the outset. The divine is not required.

Forgive me for being blunt, but this conversation is like two guys throwing frisbees in a meadow discussing how to pilot an SR-71 Blackbird. Are either of you serious mystics? If so, I will humbly retreat. :worry:

It's funny how ubiquitous the delta function still is in physical and engineering mathematics, and yet it is completely non-kosher from the point of view of standard analysis — SophistiCat

One way to make it kosher is to consider it a generalized function. I never worked with those either.

https://en.wikipedia.org/wiki/Generalized_function

So just where are, what are, the surreals? — tim wood

On the finite number line, infinitesimals are everywhere and nowhere. If r is an infinitesimal then 2+r lies to the right of 2 but to the left of any real number greater than 2. Your job, Tim, should you accept the assignment, is to find it and neutralize it! If you fail we will disavow any knowledge of it. :worry:

Is it not more accurate to say that some surcomplex numbers are surreals, or that there is a complex extension of the surreals? — Pfhorrest

Picky, picky, picky! :smile:

In over fifty years of complex analysis mathematics I don't think I ever really thought of these critters.

The Dirac Delta function (0 everywhere except at x=0, there infinite) can be thought of in terms of infinitesimals, here in terms of alpha:

$\int F(x)\delta_\alpha(x) = F(0)$

Surreal numbers are on the number line, unlike complex numbers, which are not. That is, surreal numbers are not complex numbers — tim wood

Every real number is a complex number, but not vice-versa. There are certain types of surreal numbers that are complex: s = a+bi , where a and b are infinitesimals:

Wiki: A surcomplex number is a number of the form a+bi, where a and b are surreal numbers and i is the square root of −1.[9][10] The surcomplex numbers form an algebraically closed field (except for being a proper class), isomorphic to the algebraic closure of the field generated by extending the rational numbers by a proper class of algebraically independent transcendental elements. Up to field isomorphism, this fact characterizes the field of surcomplex numbers within any fixed set theory.

You guys are going down a rabbit hole here. :nerd:

The concept of infinitesimals goes back at least to Leibniz and Newton. Modern day non-standard analysis incorporates these ideas in a legitimate mathematical model. One can prove basic theorems in calculus using infinitesimals, and there have been textbooks that have done that. I once considered teaching an experimental calculus course this way but decided against it. I have heard that for some students calculus is more understandable taught in this non-standard way. I view infinitesimals as metaphysical entities that have achieved a kind of actuality.

The set theory aspects are something else, and seem to appeal to philosophers. Have at it! :cool:

Banach-Tarski is merely the result of bad grammar? :roll:

Maybe by "grammar" you mean math here, and the AOC is "bad grammar"