joigus

No. Suppose I completely reject any notion of free will (which I don't). It's possible to say: 1) There is no free will 2) The question of free will has nothing to do with determinism Where is the contradiction? I'll get back to your other points later. Although, I must tell you hastiness when dealing with a complicated problem has nothing to do with how much time you spend later insisting on your hasty proposition. That doesn't prove that Dennett's concept of free will is hasty, but possible it is. I've heard Dennett say that he's deeply concerned about people running away with the idea that we're not free and the consequences on society. What I meant is that he's just a little bit too willing to approve a concept of free will that's a practical compromise that's useful in society. I suppose I will deal with your main points. Although I'd rather have more time to think about them. If there were a graded notion of free will, going from the "bottom" made up of people with serious neurological disorders and the like (let's say a Charles Manson) up to the top, made up of people with high level of responsibility, honesty; both intellectual and behavioural (let's say an Eise, or a Dennett); where exactly would we draw the line? The spectrum would be complicated, more similar to what I think it is the isomophism with reality that good theories should be demanded to have. So criteria would be needed to decide, so to speak, how much free will you lose from suffering PTSD, for example. The other idea, a switch to declare the split of humanity between free agents and non-free, based on whether they can take decisions based on just internal system of ethical checks and balances instead of external conditionings, is, to me, a bit "hasty". By that I suppose I mean: Not as satisfactorily thought out as other concepts by the same philosopher. Humility for those who are free I think is the main point. Something like: Don't think so highly of yourself, your proteins are doing it. That's all. An ultimate frontier of intellectual humility for those who have been fortunate enough to become respectable members of this society. Something like: Hey, don't boast so much that you're a free agent, had you been born as a sickly orphan, son of a poor Peruvian copper miner, with no money, no health, no wealth, no hope of any of it, you would probably be stealing apples in the market. Or worse.

Being wrong requires making sense. Bye.

Not even plastic surgeons can do that. You're 1 non-sensical/non-sequitur comment away from my ignore list. Time is indeed precious.

Fine-grained, or microscopic entropy, never changes. It's a constant. It's the volume of phase space; a measure of how much information is in the system. That's called Liouville's theorem. Dynamical systems conserve the distinctions, the amount of information. It's just that evolution always de-correlates most of your system's dynamical variables with the "macroscopic handles" you may establish to study it (volume, pressure, fields). So most of this dynamical information is lost for your macroscopic "description handles", in my figure of speech. Coarse-grained, or macroscopic entropy, always increases for closed systems. Time? You're trying to take too big a leap here. Time has to do with entropy growth (its direction), but it's not defined by it. Time doesn't stop. What makes you think it does? The grandfather paradox has to do with geometry of space-time, not with entropy. What's that about???

That's not what I said. "Reverse entropy" doesn't make any sense. You must mean "reverse entropy change". How could it define time? Entropy doesn't define time.

Nobody says that. That's not how you formulate irreversibility. No. It's a measure of ignorance or "randomness" if you will. And yours is going through the roof.

My concept of information comes from Shannon, which fits the definition of entropy given by Boltzmann (information deficit). There are other definitions of entropy that are more useful in different contexts and are qualitatively equivalent. None of those do I recognize in what you say. For example, you've got Rényi entropy: https://arxiv.org/pdf/1102.2098.pdf In some respects it's a more solid definition, meaning that in some systems for which Boltzmann entropy is not well defined, Rényi entropy is. And you still haven't answered: What's the connection between time and entropy? Information defines a thermodynamic arrow of time, but not its units. Another thing you haven't answered: Nature goes from more information to less information. It's the opposite of what you suggested.

I'm not aware that you've accepted any guidance here. Please, correct me if I'm wrong. You've just pressed your initial point while ignoring all the counter-arguments. Can you show that? I'm not convinced. "It needs to be consistent" is obviously not good enough. I don't think that's what the Einstein transformation of velocities implies.

Neither am I. It's about consistency. I use irony as a tool. Irony is a universal language and helps you make a point. I'm not convinced by your concept of time as information. I don't think you've thought it through.

I think you just put your finger on it. It's definitely a flaw of information we're talking about.

Devil DNA and enzymes are hard to come by. Also, an expedition to Hell to pick up samples is bound to be costly and dangerous.

Where does this anti-thermodynamics of yours hold? Not in this universe. Sorry. It wasn't @michel123456 who said this. It was @Edgard Neuman. The quote function (or my misuse of it) did that.

OK. Give me a list of books, papers, and authors I'd better read to meet your standards. I really would like to improve my knowledge in the part. Another victim of the peer-review system! No specifics? The referees didn't get past the generalities! May I ask what generalities were those that the experts found so unpalatable? Or is this not relevant to the present discussion, like talking about energy and Noether's theorem?

How do you convert seconds to bits? That is only too obviously not the case. Fixed set of rules do not in general determine behaviour. Nor true in literature in particular. OTOH, literature obeys patterns rather than strict rules. Where does this anti-thermodynamics of yours hold? Not in this universe.

I think you're living the "deductive only" delusion. Either that, or completely missing the essential connection between induction and deduction. Plus, may I say, everything most people are telling you here. There's a common understanding in science and rational thinking that apparently you're not privy to: All thinking starts with induction/observation (that comes first) Then: --> inference of patterns --> proposing definitions and laws --> deduction of both seen and previously unforeseen consequences --> Testing --> Refinement of induction --> confirmation/rejection of theory --> formulation of new theory or refinement of previous one. Something like that. It's long, it's arduous; it takes time, effort, money, and many brains working together. That is the process. You need to get over the axiomatic dream, or the illusion that induction and deduction occur in completely separate levels that don't talk to each other. That's not how it works. And the absolutely essential piece that closes the circle is experiment. As to connecting experiment, religion, and common sense as different motifs for "belief"... I think you've really lost your bearings there. Evidence and belief are not the same thing. It is true that the evidence is always affected by the theory as to its format; the language, if you will, in which the answer is presented. But the process by which we acquire evidence, and the one by which we acquire belief; plus the degree of certainty of both, the objectivity the achieve... It could hardly be more different.

I do remember: It's not possible. It is completely on-topic, as we're talking about symmetries and conservation laws in dynamics, which is relevant here. You haven't answered any of my questions/objections, or anybody else's really, which can only mean one thing: You have no answers but just insist on foisting your idea on everybody by means of a war-of-attrition tactics. Repeating your initial point over and over and not paying heed to anything anybody tells you won't get your idea very far. And I honestly think I'm being very generous by saying "your idea". If you're so sure about it, why don't you send it to a peer-reviewed journal?

They do. I know, and you know. And I know you know. And you know I know you know. Can we stick to the topic, please? It's algebra. Group theory. That's why we are @ Linear Algebra and Group Theory normal subgroup problem Ah, OK. I'm sorry if I misunderstood your question in any sense.

Also, by "normal" (in this context) I understand: \[gHg^{-1}\subseteq H\] Not "perpendicular". Any more questions?

Bingo!! "Is a group" refers to algebraic properties. \[g_{1},g_{2}\in H\Rightarrow g_{1}g_{2}\in H\] We're not talking topological groups. (I'm not aware that anybody mentioned a basis of neighbourhoods). Welcome to page 1. Neither have I read anything about a metric space.

To tell you the truth, this has caught me a bit unawares, because I've noticed that my comments on philosophy go largely unnoticed. And there must be an objective reason for that. I think people here (serious people like yourself, I mean) instinctively perceive that I'm a bit flabby when it comes to philosophy. Not that I'm complaining; I was just kind of assuming that I'm probably not up to the standards of the community in this particular front. I think I can make more significant contributions on the interface of mathematics and natural science, helping with insights in problem-solving, physical concepts, etc. Also learning about them. My attitude towards philosophy is more like that of a tinkerer. I do have a problem with philosophers, I must say. I tend to get enamoured of different tidbits of philosophical thinking. I see them as cute little thinking gadgets. Some examples are Wittgenstein's critique of classical categories, or Kant's "cardinal" partition of categories of judgement into a priori, a posteriori, analytic and synthetic. What I've never been able to feel comfortable with is their systems of thinking as a whole, for lack of a better phrasing. I am very suspicious of the claims for generality and encompassing power of almost every philosopher, or philosophical school. Even the usefulness of big chucks of it. "Their big picture", I think are the right words. I suppose the same happens to me with respect to Dennett. For some reason I find his criterion of free will as a hasty one. I think he's succumbed to the pressure of the need for a practical criterion, rather than facing up front the hairier aspects of it.* It's only natural for every great thinker. They all have their fuzzier areas, I suppose. And I do agree that Dennett is one of the most brilliant philosophical minds of our time. In the particular arena of free will, I would feel more comfortable with a graded concept, rather than a switch to decide when people enjoy free will and when they don't. I think a concept like that would be far more powerful, amenable to the usual hypothesis-prediction-falsifiability sequence of science. The backcloth would be: 1) Nobody is really free, because, in the end, we're all physical systems. But, having said that: 2) There is a working definition of free will which is of great practical, social importance. You'd better have something like that going on in your life or you're going to have a very difficult life and be a problem for others and for yourself. And, 3) This practical definition, you can fall short of achieving for many different reasons: neurological, biochemical, societal, educational, etc. (necessary qualifications and criteria for measurability, predictability, falsifiability would go here). Something like that would make me much, much happier. I don't like conceptual switches. * Edit: Although I agree that his dissociation of determinism and the problem of free will is very enlightening

Take a guess.

Please, be patient. It's been a long time since my last homework assignment.

No mercy, please! +1

Far fewer. I hate to make grammatical mistakes!

Good tip.+1. Is this homework, @Prasant36? Edit: You also need Abelian character for showing closure