Bignose

The major problem here, simplify3, is that all you have at this moment is a story. You've present absolutely nothing in terms of predictions, and how well those predictions agree with observations. In short, you have nothing too terribly scientific. Just to head off at the pass most of the usual arguments we get: yes, an idea does not necessarily need math. But, in order to make objective, clear cut, quantitative predictions, math is needed. Math is also great in that words are fungible -- for example, what you may describe as 'bending' may not be my idea of bending. That's where the math comes in. If you say 5 degrees of bending, then everyone knows exactly what it is. So. My point being: can you actually present something more scientific in terms of objective quantitative predictions? Or is this just a story?

As John pointed out, it's not roundoff errors. It's in error by many orders of magnitude. This is why I pointed it out. If your calculations are in error, there is zero point in reading about any kind of conclusions about them.

[math]\pi^{12}=924269.181..... [/math]. Your equation is wrong here. Also this is dead wrong. pi^12 = pi^47+1 = 48

None of this is implied in kristalris's system as he's laid out, though. He's explicitly stated that what is 'just' is what the law says. And in his perfect just system, there are no such things as extenuating circumstances, or unclear laws, etc. Just simply 'just' and 'unjust', and that some cadre of the exceptionally smart, wise, brilliant can figure it out. Why I think swansont's question cuts right to the heart of the manner is that kristalris's system needs to account for the fact that defining terms like 'just' requires flexibility and that what was considered just in once circumstances can be easily unjust in another. And that two otherwise conscientious and intelligent individuals can disagree on what exactly is just. If you want a current example, I personally think it is unjust that a corporation can decide not to follow the law if it decides that that law is against its religious values. But, there are plenty of people who think it is just. And that's fine. If kristalaris's super judges just decided that what was in the law was the only thing that was just, then it misses the whole point of actually debating this stuff. Actually, I've got a really good example. Legal ethics is often at odds with most people's moral ethics. If you are a lawyer and your client tells you they committed the crime, I think most people would morally agree that the just thing to do there is to share that knowledge and ensure that the person is punished for their crime. But, it is also just that we have a legal system wherein everyone is provided a defense, so the lawyer has to do their best to defend their client. Your two results here are at odds with one single all-encompassing standard of justice. Grey areas and different points of view must be acknowledged.

Boom! the perfect question. I've got a list historically and currently on the books today. But I want to see how this is replied to.

But again, you are the one who in particular invoked the phrase 'in the statistical sense' -- again on a science forum, in the math subforum, implying using the definitions as in common use by working mathematicians and statisticians. And in this case, chance and probability are used interchangeably. I guess I remain unconvinced that the two words 'embody different concepts'. All the way back to your post #4 talking about the causes... the mathematical descriptions of the randomness don't care about the causes. If there is something more than randomness, or something that skews the distribution, then that can be accounted for, but I have never seen the words chance versus probability to denote that. Your other example of the handedness vs. ambidextrousness doesn't really work either in my opinion. Because that is well covered by the mathematics of hypothesis testing. And the words chance and probability can be interchanged there, too. E.g. what is the probability this batch of pills have the correct does in them? What is the chance the transmission will fail on the MY15 truck line after 30 thousand miles? These two questions mean the same thing to me. Same thing at least to me... Any chance you can provide an example from the literature where this specific word choice is done? A very quick cursory glance at the texts I have don't seem to make any distinction at all.

Speculation is another subforum here. http://www.scienceforums.net/forum/29-speculations/ It is there specifically to post ideas that are not currently mainstream physics. It is a crucible, all ideas posts there get a lot of arrows and slings thrown at them. But, if you take those as constructive criticism instead of personal attacks (which are not allowed and any mod will remove), they only help make your idea stronger. And really, some criticism from an anonymous internet forum is 1/1000th the criticism you would receive if you presenting a paper at conference or submitting it to a journal. In short, it is good practice. As swansont posted, it is not against the rules to have a non-mainstream idea. Heck, all of science at some point was non-mainstream. Just be prepared to support any statements you make with objective clear-cut evidence. If you can do as you claim, then let's see it.

Correct. What is really interesting is that give someone "pick a number between 1 and 10" and there is a much larger than 10% chance they will say 7. But, this is much more a question of psychology and how the human mind works more than a mathematical or statistics problem.

Prometheus, you are correct in your integral math here. But not your interpretation that the definitions are messed up. What happens is that because there are an infinite number of numbers on any interval on the real line, the chances of getting any individual number does indeed go to zero. That is, 1.99999999999 [math]\ne[/math] 2.0 [math]\ne[/math] 2.000000000001. And so on. So, given that the above is the answer to the question as asked, does asking that question make sense? What I am driving at is that basically, usually one doesn't care that the exact value of the variables is 1.98435638726323636752387532276354... One normally only cares if it is in some range. "Is the value within 5% of the mean?", "Is the value more than 3 standard deviations from the mean?". Or, similarly, every measuring device we have has some margin of error. If I put a ruler down, the best I can say with confidence is that the length is between a pair of tick marks. So, the question that needs to be asked is: how likely is the variable to be in some range? Or how likely is it that the fly lands in a certain area? That changes your integral not from a to a, but from a to some b not equal to a. Then, if you use your graph there, you can plainly see that [math]\int^{1}_{-1} f_{Gaussian}(x)dx > \int^{1}_{-1} f_{Uniform}(x)dx [/math] as the chances of the variable taking a value near the mean are much higher in a Gaussian distribution than a uniform one. In short, the definitions work as intended, we just need to take care in asking the right questions.

Yeah. I disagree being called condescending when I correct what I think are mistakes. If you have a problem with me, report it to the mods; there is not need for personal name calling. My quote was NOT identical to yours. You used the OED to say "Governed by or involving equal chances for each of the actual or hypothetical members of a population". But, as I have said several times now, is NOT how it is used in science. I mean, look, let's go back to the example of the variable being the sum of 2 6-sided die. The members of the population this variable can take are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. But it is completely and wholly wrong to assume that just because there are 11 members in this population, that this random variable takes the value of them 1/11th of the time (i.e. equal chances for each member). The definition as you cited in the OED is wrong in this case, and is typically wrong in all but a very few cases. And, I'm sorry, but if we're on a science forum, in the mathematics subforum, and someone has invoked "in the statistical sense", I really think the word ought to be used correctly. I apologize if my pointing this out has offended you in any way, that was not my intention. My sole intention is to make sure the word is used per its most commonly used definition in mathematics and science.

studiot, it starts from here. You invoked the clause "in the statistical sense", implying this was the definition in use in the branch of mathematics known as statistics. But it isn't. Wikipedia's definition is actually pretty good: http://en.wikipedia.org/wiki/Random_variable I don't give a hoot about what the Oxford English Dictionary says, it is not a mathematical text. You invoked the 'statistical sense'; I merely corrected what you said because you misrepresented what is actually done by the mathematicians who work in this area. I thought it was important to get this correct.

Mitch, if this is all leading up to some grand idea of yours, why don't you cut the coyness and just go and post it in the Speculations section already? 'Empty' is a relative term. Especially with the existence of virtual particles that pop and out of space. So, if you have some grand idea about the emptiness or lack thereof in space, why don't you post it and show us what predictions it makes and how closely those agree with what is known today?

It doesn't matter between single events or combinations. The fact is that it is exceptionally rare for uniform probabilities of events to occur. My example, a random variable that describes the sum of 2 fair 6 sided dice is a 'single event', because I have defined it as so. Sure, in this example, it can also be looked at as two random variables with uniform distributions, but that is an exceptional case, not something that can happen every time. A more complex example: What are the chances a pill manufactured by a drug company has the correct amount of medicine in it? Hopefully that isn't a uniform distribution of 50% yes and 50% no. The assumption of a uniform distribution is usually pretty terrible, all in all. I don't understand what you are asking with "Would you say that a probability of 1.0 is not deterministic?" And the above fits perfectly fine with the statistics of random walks and diffusions. In those case, it is usually explicitly stated up front that a particle has a uniform distribution of directions it can walk in. And then when you get a very large number of those particles obeying that rule, you get diffusion which can be exceedingly well described by a deterministic equation. Another equivalent example would be quantum mechanics and everyday mechanics. Sure, a baseball is made up of atoms and quarks and all these things that obey to-the-best-of-our-current-knowledge random quantum mechanical things. But, when I throw it 97 mph with a little spin at the end, I can still make it dart away from the batter's bat and get the strikeout following deterministic drag and lift fluid mechanics equations. The difference between determinisitc and non-determinisitic is many times a question of scale and a question of numbers. But all this is an aside to my original point that the word 'random' does NOT mean all outcomes are equally likely, and that that is typically a fairly terrible assumption. If that is what was meant, you need to use the term 'uniformly random'.

This is not the common use in statistics today. The variable that is the sum of 2 fair 6 sided dice is obviously random, but the probability of rolling a 2 is not the same as rolling a 7. Random variables can be distributed in all manner of ways. And only when a random variable is described as 'uniformly random' can you take that to mean that every outcome has the same probability. The word random in the scientific sense simply means not-determinisitic.

Mitch, did you look at the dark matter map I linked to in my last reply to you? http://www.scientificamerican.com/article/biggest-map-yet-of-universes/

Most of the matter we know of is because we have seen it in one way or another. If not visible light (e.g. stars), via other signals along the light spectrum like IR or X-Rays (e.g. quasars). When you sum up everything that we can see today, and then we use a model to calculate the trajectories and behavior of objects like galaxies, the model makes predictions greatly different from what is observed. But, if you add in more mass to those models, then the predictions match very well. This is what has led us to dark matter -- we think that there is more mass out there, but we haven't been able to see it directly in all the traditional ways. (A very similar story can be told about dark energy. The best models we have don't agree with observations unless we add some more as-of-yet unknown energy to the balance, and hence we call that dark energy.) Now, that doesn't mean we cannot detect dark matter at all. Because we can, indirectly. We can even make maps of where we think it is highly concentrated. See http://www.scientificamerican.com/article/biggest-map-yet-of-universes/ But we still don't really know what it is. Not knowing what it is is different than calling it undetectable, though.

But this ISN'T a fact, and it IS arguable. Because if this bald assertion can be proven, then let's see it. Show me 'completely determined'. If it is so determinable, show us right here what the next largest prime will be. Heck, I'd even accept a prediction of exactly how many digits it has to be at least somewhat meaningful. If you are making this claim, then you need to provide definitive evidence of it. Because it sure doesn't represent what is being published as our current best knowledge today. ... and I think people took this to mean uniformly randomly distributed, which I think we all agree is not right.

If you wish to state that, then it must be said that your claiming that there IS a pattern has got to be more misleading. I guess I stick to science's conservative nature in which I am not going to just assume that a pattern exists without a proof thereof. I didn't have a tone -- this is the danger in reading more into posts than are really there. All I was trying to do was point out that what you claimed the link was saying was in fact NOT what it was saying. I thought the slides were well measured in the word choices it used, as opposed to what has been used in this thread. Random variables can have plenty of structure. A normal (a.k.a. Gaussian) distributed random variable has plenty of structure. But it is still a random variable. I don't think anyone is claiming that the primes are uniformly randomly distributed. But, the fact remains, that even if there is structure, there still isn't a deterministic way to produce primes. The 'structure' may increase the odds on where to bet to find prime -- just like the 'structure' in the sum of two fair 6 sides dice -- I'll bet on the sum being 7 every time -- but you can roll a lot of non-sevens in a row with two dice -- just ask any avid craps player. And that same structure in the randomness is not the same at deterministic. Maybe this has all been a nomenclature issue, but I do think that it is important to get it right.

Sure, sure. But what best describes our current state of knowledge? How do you support this? How is it profoundly misleading? If you know of a definitive pattern, then prove it and publish it! None has come out yet. If there is no pattern, then the word 'random' is applicable. I'll repeat what I wrote above -- that just because we don't know a pattern today doesn't mean one doesn't exist. Nor does it mean it is useless to look for one even if one is never found. But these statements made by your guys need to accept the current state of knowledge. That there is no deterministic function or pattern that is 100% accurate. That the adjective random, in both its colloquial and mathematic sense, is appropriate. Again, if you disagree, just publish something demonstrating otherwise and again, start collecting awards as it will be a major advancement of our knowledge. Otherwise, can you please drop this objection to what is an accurate description of our knowledge today?

Did you even read the slides you cite here? He repeats several times that there are no deterministic methods to generate primes. This is exactly what has been said the last 40 posts or so. If someone thinks there is a deterministic way of generating primes, then present it. And then go and collect your Fields Medal or other similar prizes in mathematics. Because no one has found a deterministic method to date. Then, the next slides in your link there go on to talk about some of the random and pseudomethod random methods that have shown some success. But none of them are anywhere near 100% accurate. Some show some promising leads into the idea, but again, if anyone actually could demonstrate something definitive, it would be a major advancement. I get the appeal of looking for a pattern in the primes. The human mind craves patterns. But we can't claim a pattern unless it is demonstrated. This doesn't mean that we shouldn't keep looking or that even if the looking is never successful, that it wouldn't be worth it. And so, with no definite pattern been proven, and no deterministic method available... what other words describes our current state of knowledge about the distribution of primes other than 'random'?

This might be a new one. If you liked their answer so darn much, why did you bother to ask this forum? Or, put another way, you must not have liked their answer at one time because you still came here to ask us. So, what changed (and maybe changed again)?

Not sure I buy this. Units of entropy are energy per temperature and units of time are time. This equation you've presented here isn't dimensionally sound. Maybe the bigger issue is that what predictions can you make based on your idea? What you've written here is a good story, but isn't very scientific because of the lack of specific testable objective predictions.

You have perform an inverse Laplace transform

Come on. Don't read context into posts that aren't there. What you take as condescension, I might call being straightforward. E.g. see my very first post. More than that, there is no need to be insulting about it. I have not been deliberately insulting to you. Again, as was pointed out, you cannot just look at the sum total of entropy for one part of the process. In your cycle, you are only looking at the fluid that is going through that cycle. If it comes back to the same state, the change in entropy in that fluid -- entropy being a state function -- will be zero. But that is not the change in entropy of the universe. That has increased. Something was done irreversibly. If it wasn't, I could build a perpetual motion machine of the second kind. Proof is given in Tester and Modell.

What do want, then? Is this better? Reversible if [math]\Delta S = 0[/math] and Irreversible if [math]\Delta S > 0[/math]. There, now it is in math. If you want to define entropy, I can do that, too, though I suggest you go and take a peek at a good thermodynamics text, because as I wrote above, it is tricky. I'd suggest Smith, Van Ness, and Abbott's Introduction to Chemical Engineering Thermodynamics simply because that is what I learned from (5th edition) and I thought it was good. If you really want to know thermo, though, no better text than Tester and Modell, though it is extremely advanced (don't start with it). Just so that you don't accuse me of not answering you again, entropy is a particular thermodynamic state function. It's calculation can be based on internal energy, enthalpy, pressure, etc. It has a formal definition for heat added reversibly given by [math]dS = \frac{dQ^{rev}}{T}[/math] but with this definition, the above properties can be shown, so it is not just defined for reversible processes. It can be demonstrated to be a state function, so its value is only based upon the current state of the system, not the path on how it got to that state. I didn't think I needed to answer post #3 because I agreed with the answers you have already been given. I have no idea why you think it is incorrect. Please see the above texts. You asked what made a process reversible or irreversible -- zero or positive change in entropy answers that. So it isn't 'not correct'. Or if you think so, please provide some sources, because the definitions I've given above can be found in any decent thermodynamics text (and many no so good ones, too). The answer I gave is directly from the definitions of reversible and irreversible. Again, just because you don't like it, doesn't mean you get to just declare it 'not correct'. If you you really think so, you have some work to do to overturn the standard definitions of thermodynamics as we know them -- and as they have proven themselves supremely successful -- today.