Brent696 » July 19th, 2018, 7:59 pm wrote:So am I gingerly pulling the chair back from the table to sit back down, last time I had food thrown in my face and was told I didn't belong. Now are you inviting me back, I just want BIV to take note, this really was a long dead thread ...
Ok I'm back from my errands, usual inexplicable mass of traffic going 20mph on a freeway built for 80. Where are they all going in the middle of the day? You know when they build a freeway, they don't alleviate any traffic. All that happens is that the suburbs move much further out and and endless traffic jam just gets longer and wider.
@Brent696 I like your poems. I wonder why you've chosen this particular site.
Ok my thoughts on the interesting points you raised, some of which I think I can definitively answer.
Brent696 » July 19th, 2018, 7:59 pm wrote:>>>>>>>It's not all that bad. You're raising a good point. I have this question in my own mind. We do have this wonderful theory of the infinite going back to Cantor, and frankly back to Archimedes and Eudoxus.<<<<<
May I ask you why you use a custom quoting style of your own, when the Quote function works perfectly well on this forum?
Brent696 » July 19th, 2018, 7:59 pm wrote:"Theory" is ok with me, I figure if I am truly right, we will one day see it or we will one day will not, I might even be both right and wrong. But I do have my own views and may or may not agree with these guys.
Ah. You are using "theory" the way people sometimes argue against evolution. "It's only a theory." As if "Gravity is only a theory."
This is a misunderstanding of how scientists use the word theory. A scientific theory is an organized body of knowledge in a particular area. So a math major might study "Group theory," or "the theory of polynomial equations." It just means there's a body of theory and practice around a certain professional area of study.
So in fact Cantor's theory of infinite sets would be valid even if physical infinity were falsified totally. You think Cantor's theory of the infinite is something that can be true or false. But it's not. It's a really interesting and brilliant set of ideas that's served as an organizing principle for most of twentieth century math. It couldn't be falsified. It's just a way of thinking about things. It could come into style (as it did a century ago) or it could go out of style. But it could never be
wrong. It's just a self-consistent set of ideas that mathematicians have found to be beautiful and interesting. Those are the only criteria.
Whether physicists use a particular piece of math to get some cool lab results is all well and good, but it's not why mathematicians do math. If some piece of math turns out to have nothing to do with the real world, mathematicians don't care in the least.
You might get some insight by mentally separating math and physics. Mathematicians do all kinds of crazy things. Some of it turns out to be useful in the world, often centuries or even millennia after mathematicians first started caring about it. Some math has no known use in the real world. Infinitary set theory being a prime example.
Brent696 » July 19th, 2018, 7:59 pm wrote:Aren't physicists those guys who are trying to tell us matter is traveling back in time, no, no, don't believe anything they tell you, next they will be telling us a cat can be both dead and alive, In the REAL? world my girl friend is either pregnant or she's not, don't go messing around with my head. (Jokes)
I fear your jokes have too much truth in them. I wonder if you are failing to separate the achievements of science with some of the popularized accounts that people are confused about. I think I read that in quantum electrodynamics (the thing Feynman got his Nobel for) they made a prediction that was verified in the laboratory to 12 decimal places. That's not nothing! It means that the most abstract, advanced mathematical physics that nobody really understands the "meaning" of, matches the real world to an incredible degree of approximation.
You have to give that human achievement some respect. It goes back to people like Archimedes, who used math-thinking to figure out the world.
Of course Schrödinger came out with his cat story to make a point about the collapse of the wave function, and now if there's one thing the person on the street knows about quantum theory, it's Schrödinger's cat. But really, if you want to understand some physics, better to study the Schrödinger equation and not Schrödinger's cat. Because Schrödinger's cat is not a physics argument, it's a popularization of a physics argument, so it loses all subtlety, technical detail, and context.
You can always find some physicist saying some crazy stuff at a Ted talk or in a popularized book. So we do always need to work to separate out the actual achievements of science, and the technical work that goes into those achievements; from all the silly stuff people say about those achievements. You can see this, yes?
Brent696 » July 19th, 2018, 7:59 pm wrote:It SEEMS, once physicists opened the door of "probabilities", not they can do damn well whatever the hell they please with their math.
If I'm understanding your reference, you must be speaking about people like Boltzmann, who showed that the world can be understood through the statistical properties of atoms. Again, this approach has been extremely successful in understanding the world around us. You don't have to personally like the idea. You do have to respect the power of the explanation as a conceptual structure and a predictor of what we see in the world.
I don't see why you think physicists can do what the hell they please. Physicists are constrained by (1) the requirement to put together a logically coherent theory; and (2) their theory must accurately predict the results of experiments designed to probe and challenge their theory.
Physicists are HIGHLY constrained. It's mathematicians who are unconstrained. Beauty and interestingness, that's all that matters. Mathematicians are not constrained by the real world. Physicists are.
Brent696 » July 19th, 2018, 7:59 pm wrote:But once Mathematicians opened the door to statistics and game theory, now they also can do whatever the hell they want with their math.
Now you're complaining that mathematicians can do whatever they want. But that's inherent to the field of math. Mathematicians do math, not physics. It's true that SOME mathematicians do math that has the real world in mind. But many, actually most professional mathematicians do not work in applied fields at all. So you are complaining that the Pope is Catholic. It's a requirement of the job. Mathematicians are ALWAYS free to do whatever makes sense in the context of their work, and applications to the real world are rarely part of it.
Please understand this distinction. If you want to complain that physicists shouldn't use statistical methods, then fine, go ahead and make your argument. But why shouldn't mathematicians study anything they want? That's what they do!
Also I don't get your remark about game theory. It's the economists who jumped onto game theory, not the physicists.
That's fair. I hope that you are taking my point of distinguishing math from physics.
Brent696 » July 19th, 2018, 7:59 pm wrote: I'm the visual thinker, my wife is the accountant and she has the talent for making numbers grew, not me. But Infinities, as I understand how they are used in conjunction with universal realities, exist on paper as it were and potentially.
This sentence is a little murky. First, I have no idea what "universal realities" means. What if I deny there is any such thing? You can't prove otherwise. Nobody knows if there are any universal realities, or what that would even mean.
Exist on paper? What does that mean? It seems to me that a universal reality would be independent of human beings evolving and inventing paper. What exists on paper is historically contingent. What "exists on paper" is the opposite of a "universal reality." Wouldn't you agree?
I hope you can see that this sentence you wrote is hopelessly vague.
And when you say that "infinities are used in conjunction with universal realities," I have to tell you that this phrase does not refer to ANYTHING I can make any sense of no matter how generous I try to be in my interpretation.
So if I formerly called something like this word salad, and that was pejorative, then I apologize. But what I would say instead is that it's totally incoherent. "infinities are used in conjunction with universal realities" Doesn't mean anything. Can you challenge yourself to ground your vague thought in things that are factually true? Give an example of an infinity used in conjunction with a universal reality.
Do you regard my criticisms as fair? Is "incoherent" a more polite word than "word salad?" Can you take my remarks not as a personal attack, but rather as helpful pointers to ways in which you can strive to be more clear in your thinking and exposition. Can you live with that?
Brent696 » July 19th, 2018, 7:59 pm wrote:In math class we learned that multiplying 4 or 8 times infinity left only infinity, but that is never a reality, it simply describes a "relationship" between infinity and finite math.
Is it possible that your vague recollections of someone who told you something in high school or college may not be the way professionals think about the subject? And that if you took the time, you could sit down and learn exactly how these matters are sorted out by mathematicians?
What do you mean it's "never a reality?" Who told you that? Was it a high school teacher making an offhand remark? You know, we all have limits to our knowledge. But we should realize we have these limits. You say you were taught "in class" about something. Well ok. Do you think that's the last word on the subject? Aren't you aware that at every level of teaching, we lie by simplification in order to teach hard concepts. Then when the student goes further, they unlearn the previous lies and learn new ones. Don't you know this??
Your recollection of some class should not be taken by you as the final word on how professionals think about things. And if you studied more you'd develop more sophisticated perspectives yourself. It's just a matter of learning. Not denying everything you haven't learned about yet just because you "learned something in class."
Doesn't most of life involve unlearning everything we learned in class?
Uh-oh.
Ok good, self-awareness. So when I say "word salad" or "incoherent" I'm not saying you're a bad person. I'm asking you to work harder to think and write clearly.
Brent696 » July 19th, 2018, 7:59 pm wrote: it may not be the exact language mathematicians use but I always suppose if you think about it, you can grasp what I mean assuming I'm close enough)
Sometimes I can and sometimes I can't. Using infinities as part of absolute realities or whatever from above, I really have no idea what you mean. In this case, quotients of infinities, do you mean limits in calculus? The mysterious limit of the difference quotient that Newton used to prove his remarkable law of universal gravitation? That then took mathematicians another 200 years to properly explain? Do you mean dy/dx?
Or do you mean something else? Like, the probability that a dart thrown randomly at the unit interval has a 1/2 chance of landing between 0 and 1/2. We have one uncountable infinity inside another, yet we can formalize a mathematical theory to make what's intuitively true, also be logically true? That's a pretty good achievement of math, wouldn't you say?
So no, I don't know what you mean here, but at least I can think of a couple of sensible interpretations. But feel free to clarify.
That's a metaphysical claim. Neither you nor I nor anyone else has any idea whether that's true.
Brent696 » July 19th, 2018, 7:59 pm wrote:For example, a potential infinite number of even numbers. as a potential this is a reality within a potential equation, but it is never a reality in the physical (real) world.
Sure. Totally agreed. But it's simpler than that. Take the counting numbers themselves. A child has an intuition of them. 1, 2, 3, 4, 5, 6, 7, ....
They never end. Even children play the game, "Name the highest number," and they always figure out, "Whatever number you say, plus 1!!!!"
So we have an
intuition of the infinitude of the counting numbers, and that intuition is the start of infinitary math.
But are there infinitely many of anything in the real world? There's no evidence there is and plenty there's not. So on the one hand we have this abstract idea about an infinitude of counting numbers; and I have my observations of the physical world in which there are (as far as we know) no actual infinitudes.
So you know, why is this bothering you so much? After all I have a perfectly clear visualization of a purple flying elephant. Yet there are no such things in the real world. So every person past the age of 4 knows that there is the REAL world, and the world of MAKE BELIEVE.
So there are infinitely many counting numbers, which have some sort of abstract mental existence; and there are manifestly NOT infinitely many of anything in the real world.
I perfectly well stipulate to this.
Brent696 » July 19th, 2018, 7:59 pm wrote: This Universe, the same universe that is manifesting finite attributes from top to bottom, from the life of a fruit fly to the death of our sun to the end of the expansion and final collapse, I see finite attributes reigning. And this might be a bit of logic, but if everything within this universe is finite, then the universe itself, as the parent so to speak, is also finite.
Of course nobody knows for sure. But I believe the world is finite. And
contemporary physics says the world is finite. Again, separating actual physics that's been proved in the lab, as opposed to celebrity physicists selling popularized books.
So now I get that it is the heart of your argument to claim that the world is finite.
But I agree with you entirely. I hope you understand that.
I also happen to enjoy learning about mathematical infinity. I make no ontological claims for it. But then again, I make no ontological claims for 1 + 1 = 2 either. The math is interesting on its own terms, without reference to the real world.
I hope this is clear. I never make any ontological claims for math. I make none for the mathematical theory of infinity. However, insofar as anyone does speak about infinity, they at least have to acknowledge the work that's been done on the subject. Because math, even crazy math -- ESPECIALLY crazy math -- does in fact have a funny way of turning out to be useful, decades or centuries or even millennia down the road. So even if you don't believe in physical infinity, it doesn't hurt to know a little about mathematical infinity.
Brent696 » July 19th, 2018, 7:59 pm wrote:This finitude is not abstract, the very conditions of existence depend upon the time and spatial dimensions. Math would not be superior to time and space but rather as they are constants which define the universe, they provide the underlying structure from which math is derived.
No. Math is not physics. Math is inspired by the real world, just as my vision of a purple flying elephant is inspired by aspects of the real world. But just like my imagination, math is not
constrained by the real world.
Math says NOTHING about time or space.
I think once you get that you will be enlightened. Or at the very least, you'll take your wrath out on the physicists and leave us poor mathematicians alone! We are not responsible for what those crazy physicists do!!
Yeah, I can go along with that.
Brent696 » July 19th, 2018, 7:59 pm wrote: What help in understanding this transcendent reality is when we stop thinking of the universe as an addition, as if creation truly added something, but rather in the infinity of nothing, nothingness was squeezed down by imposed limitations.
Incoherent. Can you see that? Much of your post is coherent so I know you can see the difference. If this sentence is important to you, can you please help me out and give an example or two of what you're talking about?
Brent696 » July 19th, 2018, 7:59 pm wrote:IOWs, the universe would be happening all at once, but when the speed was restricted to the speed of light, that allowed for a separation of time units. The limitation of the speed of light allows and creates time. What I am proposing is upside down from how we normally think of it.
Ok. Frankly I am not qualified to comment on alternate models of physics. I will have been successful if I explained to you that none of this is about math. Maybe others can comment on the physics. I find the finitude of the speed of light very puzzling myself. I've seen all the popularizations and the photons bouncing on the ends of a moving rail car. I have no idea. If all the smart people say time is relative, I believe them. The metaphysical implications haven't really been worked out. Anyway it wasn't Einstein, it was Fitzgerald and Mach and Poincaré and others. These ideas were "in the air." Apparently it's true about the way our world works.
Brent696 » July 19th, 2018, 7:59 pm wrote:Most of the questions you pose can only be answered when the attribute of Infinity and the attribute of the finite are kept strictly apart, this means that ultimately such potential infinities in math do not really exist.
You get no argument from me. Are you disappointed that we're in complete agreement?
According to known physics, mathematical infinities don't exist. On the other hand, physics is based on infinitary math. Some philosophers and physicists are concerned about that. Most physicists I gather never give the issue much thought, or actually believe that the world is the same as the mathematical model. I think they're wrong but in the end it's tedious arguing online with all of them.
But yes, you and I are in agreement on this.
Well it sure did give me something to write about! I do have an interest in the fact that the universe is manifestly finite, and modern physics is based on highly abstract infinitary mathematics that can't possibly be true in any meaningful sense. There's a mystery to be solved.