<p>
</p>
<p>Why? There is still some substantive discussion on the earlier pages.</p>
<p>Good point.</p>
<p>Although the following ~30 pages may very well negate the positive effects of the first few.</p>
<p>I still await a response to my earlier post, however.</p>
<p>
</p>
<p>I won’t pretend to understand the content of all of these theories. I don’t know what a manifold is, and I don’t understand what you mean when you say ‘uncertainty in the geometry’, but these theories kind of sound similar to the non-relativistic QM i learned in class. </p>
<p>space & time are some sort of uncountable set and particles are described by functions on that set. Observable quantities are represented by operators which act on those functions. Those operators have eigenvalues which, according to the theory, are observable physical quantities. A difference between the new theory and the QM I learned is that in the new one, it sounds like you are saying that the observed quantities predicted to be discrete. In the old theory, sometimes the observed quantities are predicted to be discrete and sometimes they form a continuous spectrum.</p>
<p>i still can use my criticism that these things are just abstractions. Space & time are real quantities because they are easier to deal with mathematically. treating them as real quantities gives results that are not so bad.</p>
<p>In fact, if i understood you correctly, if the theory only predicts discretely-spaced observable quantities, then you can’t even hope to point to that theory as ‘evidence’ that in real life physical quantities are like the reals. all of the other stuff in the theory is just formal baggage. </p>
<p>
</p>
<p>Every bit of evidence thus far has not been a measurement of an irrational number. You can’t just handwave this away. The fact that they are used in theories, models of how the world works, doesn’t mean that we can experience them. </p>
<p>You will always be able to maintain your faith that there are irrational physical quantities. The fact that there have been no measurements of such won’t bother you because you will always attribute it to error in the measurement. You aren’t doing science here when you insist that they exist.</p>
<p>
</p>
<p>If this is the way things should be done, then why are you assuming that we can observe the reals when it has never been done before? The fact that they appear in theories isn’t ‘evidence’. I’ll repeat: sometimes objects appear in a theory because they are convenient.</p>
<p>What is your explanation for the 45-45-90 triangle? If discrete numbers exist and I can measure out lengths of 1 and 1 for the legs, then what do you think the hypotenuse is?</p>
<p>We don’t have “faith” about continuity because we have evidence for it. “Faith” is a blind concept, which is NOT what we’re dealing with here. That is a very frequent misuse of the term.</p>
<p>We have proof that things are continuous because we’ve defined, within our language of mathematics, what it means for something to be discrete and continuous. And when we use that language to describe our reality, we find that it all coincides with continuous spacetime. The operator’s eigenvalues may be discrete, but they are discrete within a <em>continuous manifold</em>, which means the values would be <em>different</em> if we had to resort to a sort of discrete manifold.</p>
<p>It is like taking irrational quantities and then extrapolating something discrete such that the discrete nature of the outcome <em>wouldn’t be possible mathematically/in reality</em> if our initial states were rational/discrete.</p>
<p>This, then, lumps the discrete and irrational (both of which are infinitely precise) into the same logical category. The question is when we can apply what to our model of spacetime.</p>
<p>You can always say “Well, even if we get discrete outcomes given a continuous underpinning, we can never prove that the discrete is actually discrete” (which is what I think you were saying earlier) due to the nature of our measurement.</p>
<p>We can always go deeper, but the nature of what it means to go “deeper” is well-defined in mathematics and we can describe things in a very finite and precise way. You may be tempted to say “Well, we can never know <em>for sure</em> because we can <em>always</em> argue <em>anything</em> is a sort of abstraction with inherent error.” And this would be true.</p>
<p>But science is not meant to say anything is true with 100% certainty. A hypothesis, by definition, must be falsifiable. We <em>may</em> find that when we go deep enough, calculus breaks down and continuous manifolds no longer apply. But we have yet to hit such a mark. We may keep going and never find anything requiring a discrete approach.</p>
<p>Either way, we call the continuous/irrational nature of numbers “true” because so far, they are. It’s true in the same sense that it is true we orbit the Sun. We may find God to be “true” in some way. But it is not faith to say something is true when we have evidence in its favor.</p>
<p>If I were to use the God analogy, which I’ve continually said has no evidence in its favor and is not necessary, this is like saying the discrete nature of the universe has no evidence in its favor and is unnecessary. Everything is explainable (so far) without God. Everything is (so far) explainable without needing a discrete universe or the impossibility of irrational numbers. We have evidence in favor of one side of the argument and NOT the other (so far). Therefore we call these things true because they are universally consistent and non-contradictory.</p>
<p>It, again, comes down to “Do I want to believe in the thing that has 99%+ evidence in its favor, or the thing that does not?” The “thing that does not” may actually turn out to be true one day. But until we run into that wall, there’s no good reason for us to assume it. We can be <em>open</em> to it (which is why I always laugh when theists call atheists closeminded), but that does not mean we need to believe in it.</p>
<p>
Okay, all previous arguments about arbitrary numbers aside, this statement is confusing–all scientific theories should have 100% of the evidence in their favor, otherwise they would be falsified and require revision or replacement. I think that this is really a false dichotomy, in any case. I don’t see how “God did it/God exists” is really a testable or falsifiable theory. Really, what you seem to be trying to do is appeal to Occam’s Razor i.e. we need not multiply the complexity of our explanation beyond what is necessary (though Occam’s razor is just a heuristic, not a law). Still, I can research all modern scientific theories with great thoroughness, consider them to be true, and still believe that God exists without any contradiction. I don’t see why it is a “pick one or the other” scenario. Unless you are just arguing that the idea of anything “supernatural” at all necessarily contradicts our scientific theories…but I don’t see how–the theories still work.</p>
<p>I guess I should back off from my claim that science tells there are no real numbers in the real world. I guess what I should be saying is that science doesn’t give a good answer to the question either way. </p>
<p>
</p>
<p>I’d measure the hypotenuse. I’m sure I wouldn’t come up with 1.41421356237310 . . .
(emphasis on the . . .). Now, if I were given the luxury of dealing with abstract math concepts, I could say with 100% certainty that that triangle has a hypotenuse of sqrt(2).</p>
<p>
</p>
<p>We don’t. We invoke the abstract concept when trying to understand the world, but we have never achieved resolution good enough to measure something and go, ‘aha! a subset of the real line’. You are using faith when you say space is like the real numbers, and not ‘well the way we treat space in theories has given us good answers so far’. People who disagree with you aren’t the only ones who have faith.</p>
<p>
</p>
<p>Not necessarily. I don’t really understand this theory you keep invoking (I’ve never taken a math or physics class that has explicitly talked about manifolds), so maybe there’s a point you are making that I’m not getting, but it isn’t like each theory has its own unique answers. I bet you could contrive different theories that give the same answers, even though the inner workings of each theory were different from each other.</p>
<p>
</p>
<p>Right. But this is all guesswork. this question isn’t really a scientific question.</p>
<p>
</p>
<p>Yes, this is why if you are doing science, you shouldn’t try to make a conclusion one way or another about things which have no hope to be observed. When you claim that real numbers are very real things, you need to support that with observations. Well, right now you can’t.</p>
<p>
</p>
<p>This is your opinion.</p>
<p>
</p>
<p>1) The religious person’s belief in god isn’t science. He doesn’t believe in god as a way to explain how physical things work. I’ve said this a lot. You keep on arguing against a god that not many people have. </p>
<p>2) On the other hand, you keep on insisting that physical quantities are real-valued even though there hasn’t been one such measurement supporting that thus far. hmm, i wonder what other sort of belief this is similar to . . .</p>
<p>
</p>
<p>this is rich. i agree that if you want to be scientific about things, you should abandon your belief that space is real-valued. you really shouldn’t have a belief about the topic until evidence (a measurement; not some gay idea inside some dudes mind) actually shows up.</p>
<p>To be honest though, the idea of being able to perform a real-valued measurement is absurd. You haven’t argued against this. You’d need a computer with a reallllllly large memory to be able to record that measurement . . .</p>
<p>if you needed to measure a spectrum, you’d be sitting there a looooooooong time waiting for your instrument to scan that interval . . .</p>
<p>I think I am done with this debate. We’re going in circles, here, and I feel like you’re glazing over the main points that directly refute your position. It’s honestly really tiring. If you’re going to argue a point, you have to <em>stick to that point</em> and not misinterpret what’s being said. Maybe this is because of our differences in our understandings of science or math or something, but it is really frustrating to put forth an argument and have it get completely dodged and refuted with the same sort of logic. I am going to put together one last reply and then back out of this thread.</p>
<p>I find it is best not to argue with cockroaches, but to crush them.</p>
<p>First to Sithis:</p>
<p>
</p>
<p>Yes, all theories have 100% of the evidence in its favor until contradictory evidence pushes that theory down from 100%, in which case the theory is rejected/rendered questionable until a better theory is put in its place.</p>
<p>But while theories (up until contradiction) have 100% support, we can never claim that they are 100% true because they are based on confirmed hypotheses which MUST be falsifiable by definition. There’s a famous quote by Haldane describing that “Rabbit fossils in the pre-Cambrian” would be all you’d need to throw evolution out the window. </p>
<p>“God did it” is, correctly, NOT a testable concept, but many people will believe it anyway. But you are right – Occam’s Razor tells us that if we can explain X fully and thoroughly using A and B, we do not need C if it adds no new information. You miss my point though – it isn’t a “law” but a way to live by reason. You can indeed believe in God and not contradict anything, but my question to you is “Why bother?” Why not believe in Thor, or a theoretical particle nobody has believed in/found, or Sonic the Hedgehog, or unicorns under the pillow, or the FSM, or the Celestial Teapot, or the tooth fairy, etc? Occam’s Razor is a useful heuristic here because it lets us, as humans, not need to deal with the infinitely large set of possible things we could believe in that are without evidence. I say “it is like picking one or the other” because either you’re forming your views off evidence or you’re not. You can either stick to the knowns and say “I don’t know” to the unknowns, or you can acknowledge that the knowns are indeed known but “believe” in a non-contradictory (yet arbitrary) unknown. </p>
<p>While there is nothing (necessarily) fundamentally wrong with either side of that coin (unless you are, morally, impinging on others or holding back overall utility somehow), but more pragmatically, the question is “Why complicate what doesn’t need complication”? That’s all. I personally find it disconcerting when someone believes in God only because it is so arbitrary compared to the countless other possibilities. You don’t see people running around believing in completely disparate, evidence-less concepts on a wider spectrum. “God” has a fairly large emergence, and yet it is just as arbitrary. This is strong evidence for the well-supported notion that the God is really nothing more than an emergence from the ego – AKA there are better explanations for why people believe in God. “It is not contradictory” is, empirically, NOT the reason why we see so many people believe in a God.</p>
<p>Sithis said:</p>
<p>
</p>
<p>You could.</p>
<p>But you’d have to realize that whatever kind of god you chose to believe in would be no better, no more respectable, nor more truthful than any other god, whether that god be of a rival religion, fairy tale, or satirical pseudo-religion.</p>
<p>In other words, believing in an Abrahamic god is just the same as believing in an almighty purple hermaphrodite who has elephants for eyes.</p>
<p>If you’re willing to accept that, then go ahead.</p>
<p>
</p>
<p>So what do you think its “true” value would be? If you do not accept that the hypotenuse, in reality, is sqrt(2) with 100% certainty, then you must also not believe that it is possible to say that the legs are exactly length 1, either. And yet we cannot say “the length isn’t discrete/continuous, real, rational/irrational, etc” because it clearly has a finite length that we can see and interpret in existence. I mean either they’re infinitely precise or they’re not. If you reject infinite precision, you reject the irrational, and if you reject the irrational, you reject the rational, and in general you’d be rejecting real numbers at all just because you can’t prove with 100% certainty that infinite precision is somehow measurable.</p>
<p>Earlier you made some argument (forgive me if I am misquoting – too lazy to look it up) like “I believe in 5 because I can hold 5 apples with certainty,” but then I ask you: What are 5 apples? What is an apple? An apple is just a collection of atoms with uncertainty, and, according to your logic, you shouldn’t be able to say that you’re holding 5 apples. We’ve abstracted what an apple is in terms of human perspective empirically, much like we’ve abstracted all measurements in reality empirically, but at the end of the day, this is how we define our reality.</p>
<p>If you want us to agree that “We may have trouble measuring anything without some degree of uncertainty,” then you got it. We agree on that. But I will still be able to say, “And yet everything we do in physics, chemistry, math, etc – behaves just as if irrational numbers exist in the real world.” From the extremely small to the extremely large, it all holds true, even on the quantum scale. Even if you want to say “I don’t believe irrational numbers exist because, like God, you have yet to prove that they exist or don’t exist,” I would say the examples are not comparable. We have tons of evidence in favor of irrational numbers being “real” due to the way we employ limits and infinity. While they are, in themselves, “ideas,” they behave in a way that allows us to define very definite, quantifiable things with finite boundaries (and on continuous manifolds, no doubt). We can say there’s no good reason to believe in God and yet we have very good reason to believe that irrational numbers exist in real life. We may find ourselves wrong in the future, but until then, “Why assume something that has nothing in its favor?”</p>
<p>
</p>
<p>Mincing semantics. You’re calling evidence “faith,” which is a misuse of the word when comparing "faith’ in a God. If you want me to say that evidence in favor of something (with no other explanation) is a “faith,” then yes, I am using “faith” under that definition. But this is just debating terminology. I define “faith” as something that has no evidence going for it. You might say, “Well, technically continuous/discrete and irrational/rational have no evidence for them either way – we can’t confirm EITHER and therefore you’re just picking one side as faith,” but this ignores the fact that we derive very real, countable, rational things FROM irrational concepts. You can’t just hand-wave things like the 45-45-90 or the ratio of circumference to diameter and say “Well, those don’t exist,” because they do exist if you assume that the rational exist. You can’t pick and choose – they both come hand-in-hand by definition. If you reject irrational you must reject a series of other assumptions that ultimately result in you rejecting the notion that “numbers” exist altogether. This leads one to necessarily define what a number is and what it means for that number to exist.</p>
<p>In the end, it’s akin to asking “Do we exist at all?” We could argue that existence itself is just an interpretation of abstractions. When you go deeper down the rabbit hole, it doesn’t really get us anywhere. The short answer is “We know irrationals exist because they work,” but to say “because they work” implies a lot more than what may be obviously/readily apparent. It’s not a lack of evidence. Evidence is all we have, but math is what we use to describe it.</p>
<p>
</p>
<ol>
<li><p>This ignores the vast count of people who DO invoke God to explain things that we have perfectly good science for. I’ve met MANY – almost more than the count of people who just believe in something nebulous that put the universe into motion and left it alone, if not more.</p></li>
<li><p>See earlier explanation.</p></li>
</ol>
<p>@legend</p>
<p>I think I more fully understand where you’re coming from now. While I don’t necessarily agree with you, I can respect your position.</p>
<p>@nbachris
This does not concern me; my God does not have anything to do with religion. He (I use this gender form arbitrarily) is so poorly defined that I would never venture to compare him to other conceptions of God in the first place.</p>
<p>
Haha, I am sure some people would take offense to this suggestion; but again, it is not relevant to my perspective.</p>
<p>
</p>
<p>Believing in an Abrahamic god allows people to believe that they’ll one day be reunited with dead loved ones who had the same belief. A hermaphrodite or flying spaghetti monster or whatever does not accomplish this.</p>
<p>This thread reminds me why I just don’t like young people in general. I don’t care if they are liberal or conservative!</p>
<p>Sithis said:</p>
<p>
</p>
<p>Are you saying that you believe in some nameless creator? </p>
<p>Otherwise, if you don’t and believe in one of the conventional major gods, then your god has EVERYTHING to do with other religions. Religion (and I’m mainly talking about the Abrahamic religions) is a zero-sum game: if you’re right about your god, then everybody else has to be wrong about theirs (and are therefore going to be denied a lot of good things unless they change their minds), and vice versa. </p>
<p>There are 3 possibilities to the god question: </p>
<p>1) All claims of supernatural activity and explanation can be true</p>
<p>2) None of the claims of supernatural activity and explanation can be true</p>
<p>3) Only MY claim and MY people’s claims of supernatural activity and explanation can be true</p>
<p>The most likely is #2. Less likely, though not utterly impossible, is #1. Most improbable and extremely arrogant is #3.</p>
<p>LogicWarrior said:</p>
<p>
</p>
<p>I was talking about the principle, not the incentive.</p>
<p>
I’m approximately a Deist.</p>
<p>it is Generation Y…generation Y is the generation that is dominating the college culture and they are really like the Baby Boomers, and they seem to be left leaning. The next generation might be more conservative…I seen that all ready. You might be seeing more conservative college students in a few years down the road.</p>