the reason i know there is no god is because religion, every religion, from paganism to scientology, was created by humans in order to fill a void that those same otherwise brilliant people could be trying to find out instead of taking another group of peoples theories as their own.
The topic of this thread is discussion of the "Burden of Proof".
What is "proof"? How is it defined? And which kind of proof are we talking about?
In the quote above, the proof Druganator is seeking is proof of God's existence. This is a proof that could be said to be a logical/mathematical proof, in that there must be a list of valid statements that can be made about God that result in a "proof" that God does indeed exist.
This is an old problem, and there are many like it. I would like this thread to be a little discussion of proof, especially this - I believe that very little in the universe is completely provable/verifiable, and therefore that IMO, asking for proof of this or that OR it is simply impossible, is a cop-out, as well as a logical fallacy.
I have intentionally left out sentential logic, induction, predication, and epistemological concepts from this initial post, as I do want to include the whole group, even the younguns. If it needs to get technical to shut up the do-do, then that might happen...
My list of things that cannot be proved -
3. The sun will rise tomorrow.
4. I am the biological son of my mother and father.
5. Mathematics is 100% reliable.
Things that can be proved are often axiomatic, as the following sentence proves itself.
1. All bachelors are unmarried men.
Having dealt a little poorly with my first two unprovables in another recent thread, may I suggest we focus on other topics that are less close to home for some, so that the conversation can be educational, interesting, and not just a bunch of "I think this, and if you don't you're a moron" :|
So, just to set the table, take on #3 - it is the easiest, and then maybe we can have some real argument over 4 & 5.
After discussion with the OP and getting a clarification on what he meant with his post, I removed all the off-topic posts about theism/atheism and have re-opened the thread. Please carry on, but know that any theism/atheism posts are going to be deleted as spam and warnings or infractions handed out accordingly. You've been warned....
Other than that, please carry on with what should be an interesting topic. :)
"The sun's going to come up tomorrow too, you know."
Such statements can't be proven. Naturally! Some extraordinary and doubtless pristine reasoning follows this that usually involves treating as a concept something which isn't. IF IT DOESN'T FOLLOW LOGICALLY, YOU CAN'T KNOW IT! It's like the solipsistic inquisition all over again! The question is, who is to be master? Suffice it to say that if someone were to tell me I don't know that the sun will rise a few hours from now I'd be inclined to believe they were not quite clear what it means for someone to know that the sun is going to rise. The wish to conflate these two senses of "knowing" is abominable, I SAY ABOMINABLE.
Carry on.
The wish to conflate these two senses of "knowing" is abominableAgreed, if I understand you correctly - we are focusing on surety, things that are entirely provable by today's mathematical/logical standards, and how limited a universe is provided by "known" "provable" things. Socratic ignorance FTW!
In the case of the sun rising or not, this is the classical 101 case of induction. It is often safe to proceed from inductive basis, but it is not grounds for "knowledge" - it cannot pass our burden of proof.
Thank you Jae Onasi for providing the definition of "Burden of Proof" in the formal sense. It is a good reference for those that are not familiar with the basic concept.
We as a forum have entirely different views on every topic imaginable, and have strong, educated and opinionated minds, some strongly so, more impressively or less. We can certainly agree that very few topics with strong opinions on either side ever settle out with a conversion for either side. Granted, that has a lot to do with culture and environment, but it also has to do with a failure by either party to really satisfy the burden of proof required for a jury panel of our magnitude and diversity. It is an awesome task to behold, in my humble opinion.
Carry on.Thank you, and I hope we will, and I will do my best to provide a topic here or there that will be interesting enough in and of itself to discuss with at least some interest, without being so provocative as to incite the flaming and vitriol that some of our contentions result in. As you can see from Jae's intervention and reopening of the thread ( Thank you Jae! ) that kind of behavior is not only unwelcome and unhelpful to the actual questions to be presented, but will simply not be tolerated. Mostly this means, keep questions 1 & 2 out of the area. As a matter of fact, I will now edit that post and remove them, but leave this here as a sweet reminder.
***
Now, whether "knowledge" exists is an entirely different question, perhaps for this thread if it is related to our focus on things that can pass the "burden" of proof in our case. (Not likely....)
***
More difficult a question is mathematics - we could start there. I will look for some citations to not be just a talking know-it-all (far from it).
Math seems so beautiful, pristine, perfect and flawless in every way, a logical masterpiece beyond the matrix (obviously :facepalm: )... yet it could be just a bunch of hablooey abracapocus. This is agreed upon by many scientists and philosophers, but certainly not all!
More difficult a question is mathematics - we could start there. I will look for some citations to not be just a talking know-it-all (far from it).
Math seems so beautiful, pristine, perfect and flawless in every way, a logical masterpiece beyond the matrix (obviously :facepalm: )... yet it could be just a bunch of hablooey abracapocus. This is agreed upon by many scientists and philosophers, but certainly not all!
This part interests me, I don't quite understand 100% what you mean by math possibly not being real. I understand how it could not be real from a philosophical standpoint, but from a scientific one?
Please expand.
^^^Probably what qui gon glenn is referring to is the theoretical math with 2 or more unknowns. I think that's calculus, but I never made it that far, or even halfway far enough to be a laser engineer.
I'm sure qgg can clarify though.
^^^Probably what qui gon glenn is referring to is the theoretical math with 2 or more unknowns. I think that's calculus, but I never made it that far, or even halfway far enough to be a laser engineer.
I'm sure qgg can clarify though.
I'm not sure what he means, but he definitely isn't referring to calculus or differential equations type stuff (two or more variables). I think he means advanced theory of mathematics, stuff that people rarely use.....calculus is very much accepted to be true.
My list of things that cannot be proved -
3. The sun will rise tomorrow.
4. I am the biological son of my mother and father.
5. Mathematics is 100% reliable.
Things that can be proved are often axiomatic, as the following sentence proves itself.
1. All bachelors are unmarried men.
Having dealt a little poorly with my first two unprovables in another recent thread, may I suggest we focus on other topics that are less close to home for some, so that the conversation can be educational, interesting, and not just a bunch of "I think this, and if you don't you're a moron" :|
So, just to set the table, take on #3 - it is the easiest, and then maybe we can have some real argument over 4 & 5.
@ #4: Well, a paternity test determines the difference (or not) of your genes. So would you please enlighten me as to how such a test is not proof?
Mathematics is 100% reliable as an extrapolation of cause and effect, but it describes only what it describes. The only problem is where someone infers results which are neither correlated by physical observation, nor directly suggested by the math.
Wormholes are an excellent example of this. Theoretically possible because the math is correct, but not a description of a physical object because a) none have been observed or inferred by observation, and b) the math doesn't directly suggest wormholes, it leaves a space for them due to an unsolvable equation (singularity)
But math extrapolating the working of a combustion engine for example is 100% reliable as a description of its theory, in a closed environment, in the form of a working model. You could use it to accurately predict changes in inlet manifolding for example, with extremely detailed results directly proportionate to data input, though it would only describe "ideal operating conditions."
For scientific theorum math must be correlated by physical observation. General Relativity was blatantly unerring for example, but was not accepted until it made accurate predictions of Mercurian perihelion and Solar gravitational lensing, ie. these were physically observed. Even here it remains falsifiable, but is simply the best and most complete theorum which concords with physical observation.
So whilst math is 100% reliable, no theory is ever the final word on anything. ~snip~
Okay... circular arguments.
I keep using this term because ever so often an argument is made that hinges upon a supposition. It makes absolutely no sense why so many pieces of evidence forming a theory are brought together, hinging upon something that can't be proven. If it hinges upon something not yet accepted as proof, then the entire theory falls apart.
You can have 99% of the evidence you need, but if that 1% contradicts it all; then the entire theory is disproved. That is why you must first deal with such evidence before you can progress the hypothesis into theory.
"The sun's going to come up tomorrow too, you know."
Such statements can't be proven. Naturally! Some extraordinary and doubtless pristine reasoning follows this that usually involves treating as a concept something which isn't. IF IT DOESN'T FOLLOW LOGICALLY, YOU CAN'T KNOW IT!
Based on what we've observed over the 100,000 years that humans existed, there has not been once when the sun hasn't risen(assuming you mean the Earth stopped spinning or the Sun went nova). It is safe to say that this will always be true because there has been nothing to suggest it won't happen as it always has since the cycle of day and night had begun. (In the future, there WILL come a point when this changes, but not under the conditions that exist today)
If you want to mean it literally, then one should say 'The sun will rise tomorrow unless a catastrophic event disrupts the Earth's rotation, or the sun's behavior.' Either of these would be very unlikely, but possible. Given that none have happened yet, nor is there any reason to assume they would any day now, it is not logical to say that we don't know that the sun will rise tomorrow.
What you know isn't that the sun WILL rise tomorrow, but as you correctly note, the sun SHOULD rise tomorrow, barring unforseen circumstances. Reasonable projections, however, do not equal certainty.
3. The sun will rise tomorrow.It did not rise even once, ever. Having Earth orbiting around the Sun, both are always on the same 'level'.
4. I am the biological son of my mother and father.If you're not the offspring of those who you call father and mother, that doesn't mean anything, you're still the biological son of your biological parents, always.
5. Mathematics is 100% reliable.By definition, it is.
We can pick at the flawed statements all we want, but the issue is whether something is accidentally stated absolutely, or if it is meant literally. Obviously anyone who knows that the Earth rotates would also know that the sun doesn't orbit and rise in the literal sense of the statement. Same thing with who you call 'mother' and 'father.' You could even pick at the axiomatic sentence by saying that a married man who lost his wife, but doesn't know it, technically is a bachelor again. But without a valid death or divorce certificate, he would still be officially married.
See how ridiculous it is to pick at such statements? Most people interpret these properly and the fact that one would essentially make a statement go from true to false by a mere technicality makes it frustrating. If someone said by mistake 'this is impossible'... it would be more appropriate to say 'it's remotely possible' than for some to simply say 'it's possible.' The absolute statement was wrong, but if the odds were like 1 in a million; remotely possible would be a more accurate way of rephrasing the statement.
Saying something is possible opens an extremely wide range of answers. It's possible that Elvis is still alive, but without proof to confirm that he is; I would rather just assume he is dead unless proof emerges that brings the accepted belief into question. I would rather that assumptions not be considered as possible because of a lack of proof for an alternate theory. Any theory that gets shot down should only be done so when a more complete alternate theory emerges.
You don't like a certain theory in front of you... then come up with a better one, or don't get involved.
Ok, I am a little unprepared for this post atm, but I will do my best to answer the questions put to me, and will have to do a later follow-up post with some citations, because my memory fails me....
@ Darth Yuthura - good observations all. One of the annoying things in philosophical arguments are people going to the "one exception" and saying that holds the burden of proof for sinking the opposite argument. Sometimes it does, sometimes not, but when semantics get involved it seems no one is happy.
@ Ray - of course, you have made DY's point :) You know what I mean by "sun rising", yet have also been completely correct in your assertion. In that claim of #3, what I am really trying to say is, tomorrow we might wake up cold and in the dark, as the sun is no longer there. This is and always will be a possibility, until it finally comes true.
@ Ray pt.2, RE #4 - Well, I am getting into a little bit of probability theory here. and a little bit of my own "evil genius" thinking... It is a possibility that at the exact moment I was born, there was another being born with identical DNA to my own, born of other parents, and we got switched in that moment, neither of us any the wiser. This is absurd, but logic and science exclude neither. I will find a better example of this point, with a little citation, because I feel the heat already....
@ Ray pt.3.... by definition? Heard of the special theory of relativity? There are many things in physics that, based on mathematics should exist, yet we cannot find. This does not mean that math or physics is wrong, but it leaves a little grey area. I do have the goods on this one somewhere, but I have to look it up and share it or else you will all rightly dismiss this. Bimmerman was following where I was going in his post.
@Totenkopf - a fairly excellent summary of the problem of induction... thank you!
@vanir - you are close to what I am getting at with math, but I have some stronger examples, I simply have to find them. Your post reminded me of a conundrum though.... where are all the "white" holes, since the law of opposites demands one, if we are to take singularities as "real"?
The most simple way that math could be a joke is the obvious and stupid one.... the one from "The Matrix", the concept of the Evil Genius/Deceiver ala Descartes. We generally ignore this as it seems to be evading any real discussion, but it does remain a possible alternative - I know I often feel like a rat in a cage.
Agreed, if I understand you correctly - we are focusing on surety, things that are entirely provable by today's mathematical/logical standards, and how limited a universe is provided by "known" "provable" things. Socratic ignorance FTW!
In the case of the sun rising or not, this is the classical 101 case of induction. It is often safe to proceed from inductive basis, but it is not grounds for "knowledge" - it cannot pass our burden of proof.I don't think that knowledge is gained only from the conclusion of a logical argument. E.g., the premises of a logical argument. Godel's incompleteness theorems have shown that no formal system (i.e., deductive logic) can prove itself. That leaves you with definitions, concepts and actions previous to logical analysis, and it certainly is possible to know (or be ignorant of) those things.
That is why I asked (sarcastically) if it was the solipsistic inquisition; anyone who believes it's impossible to prove something without a logical argument is essentially practicing philosophical skepticism, which is based on an impoverished idea of what knowledge is. Descartes, in his analysis in the Meditations, believes he can escape from his method of "doubt" (I'm none too sure it's appropriate to call it that) by asserting "I think, therefore thinking exists." But he has no logical reason to believe that he knows what "thinking" is, if anything, and he was incorrect to think he had discovered the foundations of certainty with the Cogito.
Doubt can be satisfied by an explanation. If there's doubt as to whether the sun will rise in the morning, one can always show the laws of gravity, etc, and provide that sort of reasoning. Philosophical doubt is is essentially meaningless in this sense: since there is no possible answer, no answer is required. Philosophical skepticism isn't refutable; it's just nonsense.
Now, whether "knowledge" exists is an entirely different question, perhaps for this thread if it is related to our focus on things that can pass the "burden" of proof in our case. (Not likely....)This is an example of my point from above. If you're unaware of how to use the word "knowledge", dictionaries are always useful.
More difficult a question is mathematics - we could start there. I will look for some citations to not be just a talking know-it-all (far from it).
Math seems so beautiful, pristine, perfect and flawless in every way, a logical masterpiece beyond the matrix (obviously :facepalm: )... yet it could be just a bunch of hablooey abracapocus. This is agreed upon by many scientists and philosophers, but certainly not all!I don't know what you mean by "it could be a bunch of hablooey abracapocus." Math is a set (or sets) of rules governing the use of concepts which have formed due to our living in the world. Its relationship to reality is no more mysterious than that of language. If you want to say that 1+1=2 could be a bunch of hablooey abracapocus, you'll have to explain what you mean. To me, that's similar to saying that a stop sign at a busy intersection could be a bunch of hablooey abracapocus. I don't know what it's supposed to mean, if anything.
I don't think that knowledge is gained only from the conclusion of a logical argument. E.g., the premises of a logical argument. Godel's incompleteness theorems have shown that no formal system (i.e., deductive logic) can prove itself. That leaves you with definitions, concepts and actions previous to logical analysis, and it certainly is possible to know (or be ignorant of) those things.
If not by logic, then how would you suggest we expand upon our base of knowledge? It really is the only way we do. It doesn't mean that all our answers are right, but we certainly have come to many more RIGHT answers than before we started doing analytical thinking.
Doubt can be satisfied by an explanation. If there's doubt as to whether the sun will rise in the morning, one can always show the laws of gravity, etc, and provide that sort of reasoning. Philosophical doubt is is essentially meaningless in this sense: since there is no possible answer, no answer is required. Philosophical skepticism isn't refutable; it's just nonsense.
I couldn't agree more. If one logical argument is pushed out the window, I would like for something more plausible to take its place. The point of presenting the big bang theory, despite not having proved it, is to demonstrate the most likely scenario we have based on the evidence we've collected so far. The more we learn, the more likely we will know what actually happened. If it's not true, then they will have to change the theory in order to work within the confines of the evidence. When evidence is found that contradicts a theory, you must either change the theory or disprove the validity of that evidence. Otherwise you go nowhere with an argument that you know can't work.
I don't know what you mean by "it could be a bunch of hablooey abracapocus." Math is a set (or sets) of rules governing the use of concepts which have formed due to our living in the world. Its relationship to reality is no more mysterious than that of language. If you want to say that 1+1=2 could be a bunch of hablooey abracapocus, you'll have to explain what you mean. To me, that's similar to saying that a stop sign at a busy intersection could be a bunch of hablooey abracapocus. I don't know what it's supposed to mean, if anything.
The rules of mathematics always remains consistent. You will ALWAYS get the same answer no matter which state you are in, or what language you speak. The errors in mathematics comes when humans attempt to apply it. You will always get the same answer from a calculator, no matter how many times you punch the equation in. The only times math falls apart is if you use a method or if the tool you work with malfunctions. A programing error would fall within the category of malfunction.
If not by logic, then how would you suggest we expand upon our base of knowledge? It really is the only way we do. It doesn't mean that all our answers are right, but we certainly have come to many more RIGHT answers than before we started doing analytical thinking.You misunderstand. I'm not interested in saying logic isn't an extremely useful and productive way to go about learning things. It is. It's just I don't think that all knowledge is necessarily reducible to the results of deductive logic.
The rules of mathematics always remains consistent. You will ALWAYS get the same answer no matter which state you are in, or what language you speak. The errors in mathematics comes when humans attempt to apply it. You will always get the same answer from a calculator, no matter how many times you punch the equation in. The only times math falls apart is if you use a method or if the tool you work with malfunctions. A programing error would fall within the category of malfunction."The rules of stop signs always remain consistent. You will ALWAYS stop no matter what state you are in or language you speak. The errors in following the rules of the stop sign [only] come [in] when humans attempt to stop at them...the only times stop signs don't work is if you don't understand the sign or if your car malfunctions..."
I'm not saying you're wrong about the whole mathematics thing, but you can see why I'm wary of speaking of the transcendental nature of mathematics - or of stop signs. They're both things we have a use for and neither one requires any sort of metaphysical justification.
@vanir - you are close to what I am getting at with math, but I have some stronger examples, I simply have to find them. Your post reminded me of a conundrum though.... where are all the "white" holes, since the law of opposites demands one, if we are to take singularities as "real"?
It's actually the subject of some discussion from me at a number of science forums and I've managed to achieve an amount of concordance among at least one PhD theoretician and a highly qualified mathematician, not something I say in pride but simply appreciative since I'm really fairly unqualified to dispute or confirm working theorum.
Singularities are a mathematical paradox, purely mathematical in nature. The Black Hole models for example (say the classical Kerr metric) is a working basis for extrapolating other theorum under exotic circumstances. In this case it is an accurate depiction of say, quantum mechanics in this environment and their relation to the macrouniverse. However the very nature of a singularity is a one-sided equation, which is essentially how they're formed, they are by definition incomplete theorum, but a working model based upon what we know so far, only what we know so far. Lines of infinity do not exist in the real world, but serve the purpose of workable mathematical models for the mid section of a graph let's say.
Where you get a problem is when someone, typical scientific journalists decide to take this conundrum and turn it into a physical description, for example singularities might lead to other universes, or a wormhole between geometric localities. It doesn't really work that way, even though the math is good. It's based on the fact the math is incomplete to start with.
What appears most likely at this stage, for an accurate physical description of a Black Hole is the string theorists "fuzzy star" which is an essentially black body object with exotic properties and a diameter equal to the event horizon. But string theory is still in the hypothesis stages of development and requires a lot of improbable correlation to become a working theory. So what we have is a physical description which is highly likely but doesn't have the math to back it up at this stage, the math which works is the Black Hole models using QP and GR (but no UFT).
What I'm saying is that singularities describe objects which do not exist in the real world, but accurately describe the properties of objects which do, but are something else entirely and no less exotic.
So no white holes, but a black body with exotic properties and in some cases even inert and latent (the Reisner-Nordstr'm solution with a fuzzy star bend, the elusive naked singularity is really a death-moon of ultimate inertia but no tidal forces).
No white holes, no M-brane, just classical physics and incomplete theorum.
----> to minmartin, my apolegies for reference in previous post. I shall be more vigilant in future, and had honestly thought it kochure (hence I should be more vigilant). Sorry mate, never wish to cause probs at LF, which I quite like. I'll be more careful.
To all, I'm a little confused about where math itself breaks down in 100% reliability as a working model for the physical universe. If it works, there's math for it, if there's a process and what isn't, there's math for it. We may not know it or its full scope of constituents (complex evolutionary diversity can compound mathematical model into chaos theory), but there is math and it is 100% reliable assuming no limitation of processing power or data input. Math is after all the language of science, it is the one language beyond language and in a sense is transcendant. You could communicate with an advanced technological civilisation with it, even where your normal modes of communication were rendered unusable.
Palaeoanthropologists use it to understand the cultural scope of ancient civilisations such as the Mayans, have totally changed existing preconceptions about human development concordant with technology (current theory is a constant intellectual potential, just a changing technological industry). It is even transcendant in a closed environment from this perspective.
I fail to see at this point where it breaks down in philosophy, the womb of science.
I think I can see what it is you're getting at, Qui-Gon Glenn. Metaphysics, what it would be like to understand things beyond our current comprehension... Well, Math is pretty solid, as far as I know. The thing you're getting at here is that Mathematics was invented by humans, humans are flawed and limited in their comprehension of the universe, and thus, since humans are flawed, is it possible that mathematics is flawed as well?
Well, since I am a human, my method of calculatory reasoning is based on mathematics. 0,1,2,3,4,5,6,7,8,9; these are the ten numbers by which we understand the universe. But the point you're trying to get at, I'm guessing, is, what if the universe's mathematics are different than human mathematics? What if the universe works by five digits, or twelve? What if the universe is so complex and mysterious that it only appears to function consistently through the 10-digit system, but in fact, doesn't? What if the universe is mysteriously outside of human understanding?
Well, it's possible, but my cognition of the processes of ~everything~ only work through human reasoning, and so it is really a waste of time for me to attempt to comprehend it in any other way but the ways that I can already comprehend it.
Well mathematics is essentially always perfect, assuming you follow the rules established by our own laws of 1-10, the methods by which you do calculations, and so forth. It should be noted that the symbols of 0-9 are just units of measurement and there could very well be many more symbols made to represent 10,12, 15... it doesn't matter, so long as you are able to properly translate the theoretical numbers back into what they would represent in the 1-10 system.
The units may change, but whatever you use them for don't change if you were to switch to metric time, making a right angle be 100 instead of 90 degrees. All you have to do is remember to translate the integers from any alternate system back into what we use. A metric clock would have to make each hour represent 72 minutes, but it would work.
There is no universal system, but each one can work just as properly as the one we are accustomed to. We use systems of 3 quite a lot actually, so it does work in our everyday lives alongside the metric system.
The units may change, but whatever you use them for don't change if you were to switch to metric time, making a right angle be 100 instead of 90 degrees. All you have to do is remember to translate the integers from any alternate system back into what we use. A metric clock would have to make each hour represent 72 minutes, but it would work.
There is no such thing as "metric time" with a day split into two halves of 10 hours of 72 minutes. Metric time is based on the second and also based on a proportion of the solar day. Just cause the simpsons and futurama used it as a joke does not make it true....because most Americans are clueless when it comes to the metric and SI system.
True metric time is based on the second and uses standard SI prefixes (megasecond, kilosecond, etc). Since a megasecond is the next higher recognized order of magnitude above a kilosecond (3.6 kiloseconds are in a standard hour btw), one megasecond is 1000 kilosecond is 11.574 days. That's not usable for humans. True "metric time" is used for occurrences on a galactic scale, or for incredibly fast acting occurrences (nuclear fission, picoseconds, etc). For normal use, our current system of twenty four hours of sixty minutes each is in accordance with "metric time." Myth conclusively debunked.
What you refer to is so-called "decimal time," or "French Revolutionary time." Both of these use non standard units of measure, and do NOT use the metric second as a basis. The standard measure of time, our 24 hours of 60 minutes of 60 seconds DOES use the standard metric second. Thus....noone seriously uses the "decimal/French Revolutionary" timescales.
As for degrees, the metric unit is radians which is based on the definition of a circle. It is defined as the angle where the radius of the circle is equal to the arc length described by the angle. This is the metric measurement.
Degrees aren't arbitrary either. You can place at most six equilateral triangles inside a circle, with one side of each equilateral triangle being an equilateral chord of the circle that is also equal to the radius of the circle. Six such chords make up the circle, and each chord desribes one sixtieth of it. Hence, six times sixty, 360 degrees. This has been known and described since Babylonian times. Again, degrees aren't arbitrary, so you cannot try to rename 90degrees as 100 degrees.
An attempt was made to do exactly as you suggest, and convert a circle to 400 "grads" or "gon." This has gained little traction outside of fields like surveying. Degrees and radians are the correct accepted units of angular measure.
Well mathematics is essentially always perfect, assuming you follow the rules established by our own laws of 1-10, the methods by which you do calculations, and so forth. It should be noted that the symbols of 0-9 are just units of measurement and there could very well be many more symbols made to represent 10,12, 15... it doesn't matter, so long as you are able to properly translate the theoretical numbers back into what they would represent in the 1-10 system.
The units may change, but whatever you use them for don't change if you were to switch to metric time, making a right angle be 100 instead of 90 degrees. All you have to do is remember to translate the integers from any alternate system back into what we use. A metric clock would have to make each hour represent 72 minutes, but it would work.
There is no universal system, but each one can work just as properly as the one we are accustomed to. We use systems of 3 quite a lot actually, so it does work in our everyday lives alongside the metric system.
Agreeing with what Bimmerman said in debunking the metric clock idea, Doesn't this break also down when it comes to numbers like Pi? If another sentient life form were to exist, it would seem logical that they would end up using Pi too, except that their numbers might just be in another language. But still, the 10 digit system seems pretty universal to me. Otherwise they'd calculate Pi incorrectly.
I'm wasn't actually suggesting that you would actually use metric time. Obviously it makes no sense to have 60 sec, 72 min, 20 hours; but it can work just as well. The beauty of metrics is that every increase in units is done by factors of ten, which is simply moving the decimal place around to make 1.3 x 10^7 instead of writing 13,000,000. When you get into standard units, this ability is lost.
It doesn't mean that ten is some magical number that makes this function everywhere in the universe. As stated by Arcesious, you could do the same thing using 12 as a basis, so long as you create additional symbols that represent the numbers for 10 and 11. These symbols (10,11) are based on the powers of ten, which is why you would have to scrap them and create something like 'T' and 'E' so that you would have a numbering system that treats these as integers.
1,2,3,4,5,6,7,8,9,T,E,10 Then 11,12,13,14,15,16,17,18,19,1T,1E,20
Towards the end: E0,E1,E2,E3,E4,E5,E6,E7,E8,E9,ET,EE
The last number in this sequence would be 100, but it would represent 144 (12*12) under this system. This is odd to conceive, but if you had 12 groups of 12, how is that different from metric?
In my example, '10' now represents all of the following integers: (1,2,3,4,5,6,7,8,9,T,E,10) The symbol is the same as metric, but it actually represents 12 integers now.
My point is that if you theoretically came across another race of sentient beings who devised their own system of mathematics, they could very well have used a different system that works just as well as ours. Which one is right? Both work just as well, but are simply different. I'm not proclaiming that we switch or anything, but I'm saying that our systems are not the only ones that work in the universe.
Pi would universally be 3.12159 no matter what language you use; but that doesn't mean it must abide by the 1-10 system of integers. These are pretty universal, but the 1-10 integer system is not.
I'm wasn't actually suggesting that you would actually use metric time.
I know, I just wanted to explain the fallacy before someone who doesn't know better runs with it.
Obviously it makes no sense to have 60 sec, 72 min, 20 hours; but it can work just as well. The beauty of metrics is that every increase in units is done by factors of ten, which is simply moving the decimal place around to make 1.3 x 10^7 instead of writing 13,000,000. When you get into standard units, this ability is lost.
Yes, but metric time itself, when adapted to our time scale, does not fit the nice exponential powers-of-ten graduations nearly as well. That was my point. I'm not sure what you mean by the bolded statement however.
It doesn't mean that ten is some magical number that makes this function everywhere in the universe. As stated by Arcesious, you could do the same thing using 12 as a basis, so long as you create additional symbols that represent the numbers for 10 and 11. These symbols (10,11) are based on the powers of ten, which is why you would have to scrap them and create something like 'T' and 'E' so that you would have a numbering system that treats these as integers.
1,2,3,4,5,6,7,8,9,T,E,10 Then 11,12,13,14,15,16,17,18,19,1T,1E,20
Towards the end: E0,E1,E2,E3,E4,E5,E6,E7,E8,E9,ET,EE
The last number in this sequence would be 100, but it would represent 144 (12*12) under this system. This is odd to conceive, but if you had 12 groups of 12, how is that different from metric?
In my example, '10' now represents all of the following integers: (1,2,3,4,5,6,7,8,9,T,E,10) The symbol is the same as metric, but it actually represents 12 integers now.
Yup, you just described base 12. The "T" in yours is often an A or X, but the symbols themselves hardly matter.
My point is that if you theoretically came across another race of sentient beings who devised their own system of mathematics, they could very well have used a different system that works just as well as ours. Which one is right? Both work just as well, but are simply different. I'm not proclaiming that we switch or anything, but I'm saying that our systems are not the only ones that work in the universe. Same goes for computers. We use hexadecimal which is like base 12 but is base 16.
Pi would universally be 3.12159 no matter what language you use; but that doesn't mean it must abide by the 1-10 system of integers. These are pretty universal, but the 1-10 integer system is not.
Exactly. Pi is a ratio, nothing more or less. Depending on what base system you use, the exact number will change, but the ratio itself and meaning of the ratio is universal.
'When you get into standard units, this ability is lost.'
Bad wording. I meant that inches, feet, yards, and miles are not as easy to work with as meter/centimeters/kilometers. These units of measurement work on factors of ten where standard American lengths are 5280, 1760 (yard), 63360 (inch) Liters and ML as opposed to cups and gallons. These American units are not as easy to convert as metric and although they tend to follow factors of 3 (length) and 4 (Volume), they are not neatly arranged like hexadecimal.
I would assume that when working with computers, you have a system of increase that works exponentially. You add a new 50/50 function to a system, you double the possible outcomes that you originally had. If you go 2,4,8,16,32,64,128... this universally makes sense to me.
'When you get into standard units, this ability is lost.'
Bad wording. I meant that inches, feet, yards, and miles are not as easy to work with as meter/centimeters/kilometers. These units of measurement work on factors of ten where standard American lengths are 5280, 1760 (yard), 63360 (inch) Liters and ML as opposed to cups and gallons. These American units are not as easy to convert as metric and although they tend to follow factors of 3 (length) and 4 (Volume), they are not neatly arranged like hexadecimal.
I would assume that when working with computers, you have a system of increase that works exponentially. You add a new 50/50 function to a system, you double the possible outcomes that you originally had. If you go 2,4,8,16,32,64,128... this universally makes sense to me.
Ahh, gotcha. The "Imperial" system....sucks. I hate working in it. However, because all old American engineers don't speak metric, and all the new engineers in school are taught metric primarily (but are expected to understand Imperial nontheless), there is a bit of a disconnect. Every engineer I know under 25 or so, when confronted by a problem in English units, immediately converts everything to metric, does the problem, then converts the final values back to English. It sucks, but that's how we do it.
Cliffs: Metric is win, Imperial sucks, Americans need to quit being stupid.
Back on thread: The exponential system you described is base two, and is binary converted to digits.
0 = 0
1 = 2^0 = 1
2 = 2^1 = 10
4 = 2^2 = 100
8 = 2^3 = 1000
15 = 2^3 + 2^2 + 2^1 + 2^0 = 1111
...and so on. Every number can be described as combinations of powers of two, which is the basis for binary.
Ahh, gotcha. The "Imperial" system....sucks.
Back on thread: The exponential system you described is base two, and is binary converted to digits.
Yeah, I really need to get my terminology down. I'm good at mathematics, but certainly would be hopeless at teaching it.
But in regards to the thread...
It can properly be assumed that mathematics is perfect, but any errors that come with it are primarily a result of human error. When a Mars spacecraft was lost as a result of the Imperial units not being converted to metric, the math was perfect; but not properly applied to the situation. The only times when it does fail is when the logic is flawed. Other than that, you will always get the same answer for a given equation and never anything different.
I recently spoke with someone about my arguing on this forum and how I go about the subjects. He suggested that before I ever make an argument or counter argument that I go back and brush up on what I know. Then when introduced to something new by other people, go back and read about subjects that I haven't already studied. The whole purpose of this kind of thread isn't so much presenting all the facts you already know, but to allow others to introduce you to new concepts. At that point would you step away and read up on the subject to a broader extent than what you would see on a forum post.
'The burden of proof' is what this subject is about. Is there really any argument where one does not ask for another person to present evidence to prove their point? Most who've already made up their minds don't need evidence while others would seek out what evidence leads them to their own conclusion. Therefore I would assume that the art of proving a point isn't so much in the evidence itself, but the manner in which you present it to other people. If you downright disregard or insult the other person, they will not be bloody likely to take all the proof in the world that you can throw at them. Instead it requires more understanding their side of the argument and deciding whether to try and get them to think what you believe, or maybe to consider what they have to say instead. There is no shame in withdrawing from an accusation if you see good reason to do so, but don't make an assumption based on your personal feelings on the matter. All too often people will let their pride get in the way and they make the most absurd justifications in order to keep you from saying 'I told you so.'
It can properly be assumed that mathematics is perfect, I would not put that much faith in something created by man. I would not make the mistake of saying it's 'proper' to assume that it's 'perfect'.
Other than that, you will always get the same answer for a given equation and never anything different.
'You can get different answers when working with Non-Euclidean geometry and string theory.
Have to agree with Jae's sentiment although possibly for different reasons. Given a series of assumptions, math is reliable. It would be better to say the actual workings of the physical universe are perfect although I'd suggest placing even that statement within a strict context.
Math works fine in non-Euclidean geometry but true enough the math for string theory is largely absent and that for QP is incomplete, lending itself to singularities. These are the reasons for some interest in a unified field theory, Einstein's philosopher stone.
Some like myself believe however, like Einstein that it lay in plain view among Relativity and classical physics. This may be supported by recent JPL observations indicating a variant c. based upon gravitational energy distribution. The implications are not yet clear to me, but my academic instincts are way up on this.
In non-Euclidean geometry and string theory, those are incomplete. This doesn't mean mathematics doesn't function in these fields; it simply means that these subjects remain incomplete. If you don't know how to properly apply the mathematics into what you are working with, it goes to human error. In such fields are an assortment of unknowns. It doesn't result in math being imperfect; just incomplete.
Logic shows that every cause has an effect and as long as all the causes are the same, the effects will also be the same. If even the slightest distortion is present, you should get the same outcomes within mathematics as you did before. If you are including something such as cloning a person, you will NEVER get the same fingerprints because such traits are completely random. If in the case you calculate something random, then you cannot create a definite effect. That is because something random can't be predicted or projected.
In non-Euclidean geometry and string theory, those are incomplete. This doesn't mean mathematics doesn't function in these fields; it simply means that these subjects remain incomplete.
If they're incomplete, then how can they be perfect?
You'll have to excuse me, I generally don't like pulling apart posts as often this is simply done in an argumentative way at forums, but there are a couple of specific sentences I'd like to examine.
Logic shows that every cause has an effect and as long as all the causes are the same, the effects will also be the same.
This is actually where math makes the departure from mechanics to modelling. Logic also shows that any evolutionary system is so complex that no amount of processing power can replicate predictive results. It's chaos theory and integral to modern views of modelling natural mechanics.
Here's what happens, you put the same data in, exactly the same data, and you use exactly the same equations, you get different results every time with no prediction. Been tried. Evolutionary processes, even such generalised and simplified ones as a proto-solar evolution simply happen anthropically maybe once in a thousand tries, using the same math and same data trying to model the early formation of the solar system. One time you get four planets, another none, the next two planets out near Pluto's position, it seems completely random but is in fact complex evolutionary diversity. It was actually a revolution among mathematicians which created Chaos Theory, because they were expecting at least some degree of rational predictability with a model for the formation of our solar system, since we've pretty comprehensive data for it. It was a completely unexpected result.
If you are including something such as cloning a person, you will NEVER get the same fingerprints because such traits are completely random.
Not so much random as complex diversity. There is a formulaic process, but even where concentrating solely on the macro scale the data input and calculations are so complex that results are unpredictable. This is also shown in animal evolution, some species traits have nothing to do with natural selection, however certainly some process is at work.
If they're incomplete, then how can they be perfect?
I should think even if they were complete, perfect wouldn't be an accurate description. More like, interesting.
If they're incomplete, then how can they be perfect?
Obviously before Newton, there was a means by which to calculate every aspect of calculous he was responsible for; we simply did not know it yet. Newton showed it to us. Evidence shows that Orcemedies may have figured out calculous centuries before, but the knowledge was lost until another person figured out the same things.
Don't forget that math is not corporeal. It is not a physical identity, but exists entirely as idea. You can reasonably assume that once you know the right methods, you will always get the right answer. If you don't, you can't.
It is like coming across a crime and not knowing what happened and who was responsible, but perfecting a theory in order to determine what happened. Just because you don't know what happened at first doesn't mean you can't eventually figure it out.
In regards to the 'evolutionary theory,' that does not work in regards to mathematics. And even if it were; just because something is too complex to figure it out doesn't mean it can't be calculated... just not by us.
You can use mathematics to calculate the trajectory you need to position a spacecraft into Mars' orbit, but they can't possibly account for ALL forces that would act on the spacecraft. If their math was wrong, they COULD be able to diagnose the problem and adjust the course of the spacecraft in order to account for those unforeseen forces. If the spacecraft was lost, they could go back and generate an alternate solution that WOULD have worked, had they plugged in an alternate trajectory and velocity. If math weren't perfect, then they might as well just assume it doesn't matter and throw the spacecraft wherever it wants to go and assume the outcome will be different each time.
Obviously before Newton, there was a means by which to calculate every aspect of calculous he was responsible for; we simply did not know it yet. Newton showed it to us. Evidence shows that Orcemedies may have figured out calculous centuries before, but the knowledge was lost until another person figured out the same things.
Don't forget that math is not corporeal. It is not a physical identity, but exists entirely as idea. You can reasonably assume that once you know the right methods, you will always get the right answer. If you don't, you can't.
It is like coming across a crime and not knowing what happened and who was responsible, but perfecting a theory in order to determine what happened. Just because you don't know what happened at first doesn't mean you can't eventually figure it out.
In regards to the 'evolutionary theory,' that does not work in regards to mathematics. And even if it were; just because something is too complex to figure it out doesn't mean it can't be calculated... just not by us.
You can use mathematics to calculate the trajectory you need to position a spacecraft into Mars' orbit, but they can't possibly account for ALL forces that would act on the spacecraft. If their math was wrong, they COULD be able to diagnose the problem and adjust the course of the spacecraft in order to account for those unforeseen forces. If the spacecraft was lost, they could go back and generate an alternate solution that WOULD have worked, had they plugged in an alternate trajectory and velocity. If math weren't perfect, then they might as well just assume it doesn't matter and throw the spacecraft wherever it wants to go and assume the outcome will be different each time.
Now we're in fascinating territory. Here's where some PhD physicists believe in God. Incredible isn't it? Not really.
We don't have any lack of data for the formative solar system for example. You point a telescope, use some field equations, the data is right there. We're not talking about unknown values, we're talking about inherent variables and probability functions. A lightwave, is a probability function. No less real, but you can't describe it in math any other way. Toss in probability, you get a lightwave, get definitive and it disappears, the math no longer works. You have to describe a wavefunction duality or the description just breaks down, probability is an integral part of physical reality, an atom cannot exist without the probability wavefunction, it is an entirely inaccurate description otherwise and simply does not work when applied to engineering.
So first you never get the right answer. You get one of many right answers based upon a series of premise or presumption.
Secondly algebra was invented by the Tibetans ca.10th century, the name is from the Middle East which is where it came to our hands via the Silk Road. Calculus is not usable for theorum because there is no zero value to it, so it can't postulate. Calculus might be said to be retrospective, algebra predictive.
Physical evidence shows clearly calculus was used by the ancient Egyptians, who aligned megalithic structures geometrically and astronomically.
The criminal forensic analogy is a very questionable one as forensics is wholly circumstantial evidentiary procedure, it is designed mostly to manipulate juries but otherwise can only suggest avenues of further research as according to the anthropologist ethic "correlation does not infer causation."
Just because you weren't there means precisely you cannot possibly have the slightest idea what actually happened. And all you can attempt to do is suggest reasonable possibilities based upon purely circumstantial and necessarily biased evidentiary procedure. This is how the court systems work, hence it is a matter of reasonable doubt and presumption of innocence among the more democratically benevolent ones. One of the most important steps in criminal procedings is the establishment of criminal intent, because all other evidence is circumstantial and largely open to interpretation. The smoking gun is just a smoking gun, not a slam dunk except for soap opera junkies who hate life and are looking for a Jesus to crucify.
For the space probe analogy, geometric probabilities are a lot easier to figure than complex evolutionary diversity since it is not such an evolutionary system until great distances become involved. But certainly a recent problem has been identified by JPL in 2004 termed "a weak anomalous acceleration" which has thrown the entire current cosmological model into doubt.
Little things affect big things, complex evolutionary diversity.
In other words the probes aren't where they should be right now, none of them. Nobody knows why.
But certainly Newtonian caluculations were in far greater error. If Relativistic math had not been used by NASA since the very first space launches not a single probe would've ever reached anywhere near its destination, and again, nobody would've known why.
I have some homework for you DY. Look up Brownian motion and tell me what you think.
So first you never get the right answer. You get one of many right answers based upon a series of premise or presumption.
Secondly algebra was invented by the Tibetans ca.10th century, the name is from the Middle East which is where it came to our hands via the Silk Road. Calculus is not usable for theorum because there is no zero value to it, so it can't postulate. Calculus might be said to be retrospective, algebra predictive.
For the space probe analogy, geometric probabilities are a lot easier to figure than complex evolutionary diversity since it is not such an evolutionary system until great distances become involved. But certainly a recent problem has been identified by JPL in 2004 termed "a weak anomalous acceleration" which has thrown the entire current cosmological model into doubt.
I have some homework for you DY. Look up Brownian motion and tell me what you think.
We're straying off the subject. I want to remind people that I have only breached the surface of calculous. Beyond that, I'm climbing onto a limb.
I did examine the Brownian motion theories and I understood not so much the calculations themselves, but why they apply to certain situations. 'Random' doesn't exactly mean you'll get any answer just as easily as another, but it could be like a bell-shaped curve, where a some numbers are simply more likely to come up than others. If you used Brownian motion theory, you could predict a pattern after a few random outcomes with a degree of certainty. But this can only be done for a short-term model and breaks down the further in time you try to predict the pattern.
I would think that my opinion isn't worth much if I don't know how the Brownian theory actually functions, but... I would say that I am fascinated by the idea that you could see something seemingly random and be able to discern a pattern to it that you could apply to a problem with a degree of certainty. It would be extremely difficult, if impossible, for me to actually apply this to a real use.
You are right that it's easier to launch a spacecraft to a specific destination with the gravity of the sun, moon, earth, jupiter, saturn, and many other bodies light-years away exerting their astronomically-small pull on the craft. That tied with the presence of solar wind, the not-quite-so empty vacuum of space, and margin of safety for human error... you can never account for every force of nature, but because the major forces are the gravitational pull of planets and solar wind, you really just have to account for those.
I would continue to say mathematics is perfect, but it's only as perfect as it was created to be. You will ALWAYS determine that the cube route of 329 is 6.903. Of course that is not literally correct if you had to be precise to the 1:10,000 scale, but few people care whether you estimated 328.937 up for a nice, solid number.
I think it would be best to assume that you will always get the same results on paper, but that what's on paper won't always be what you took from the real world. The more complex the function, the less reliable your equations will become. Any malfunctions in math are due to either human error, or that something in the real world hadn't been taken into account on paper.
When an equation doesn't work to describe a physical phenomenon the way it's ought to describe it, it doesn't mean the least maths or its laws have failed. The equation is wrong or insufficient, which is a huge difference, actually.
My point with the Brownian motion was simply an interesting observation. There is no such thing as an inert field. For all intents and purposes it is like watching a pool of water in a closed laboratory environment for long enough and getting waves for no reason. Probability function. What's more recent observation dictates these seemingly random probabilities are intensely dramatic, not even the bell curve Einstein supposed.
The dramatic way to put this, and what I'm talking here is strict science, get some nothing and somethings spontaneously create themselves. We'll call it virtual particles or information potential for the string theorists. Any field, even a zero point field (ie. classical "nothingness") has motion. We use fluids to study this phenomenon and call it Brownian motion.
The point is that according to professional mathematicians and theoretical physicists no matter how complete the data is or comprehensive the math, the best possible result is a likelihood. Math can model natural process, but it cannot ever hope to adequately describe it.
When mathematical models for the formation of the solar system were being calculated the seemingly random results were not due to any lack of data or innacurate calculations, they were not due to human error, the math wasn't wrong, incomplete or insufficient.
They were due to an inordinate number of equal likelihoods in the actual formation of the solar system. Given precisely the same circumstances any number of things might've happened.
When we say what did happen was a right answer and try to use process of elimination as a scientific process to determine wrong answers we're making a mistake known as anthropic principle.
If you recreated the actual formation of the solar system, done precisely the same way, without changing a thing, something completely different is just as likely to happen as what did happen.
The M-theorists describe this with alternate timelines. We exist simply upon one particular timeline where several were/are possible for every circumstance and situation, all coexisting as alternate realities in separate dimensions. Reality is surprisingly like that.
In one alternate dimension our solar system has two planets, another it is just a large gas cloud, another again it is a twin system and all of them resulting from an identical initial formative process. Just all equal likelihoods, nothing to do with the math.
In the past what's been done is to try to describe higher likelihoods of probability with bell curves, but recent observations suggest this in error, with extreme variation in equal likelihood to subtle ones at any given instance.
Here's an interesting thought-experiment. Get a zero point field, a nothingness and watch it for a while, virtual particles pop into and out of existence and at some point a real particle creates itself. Spacetime immediately folds around the presence of mass-energy, it's a snowball effect, which is a description of spacetime crunch, big bang, inflation...
Okay; way too much effort exerted on that subject. I do comprehend that aspect that you are speaking about, but that doesn't make the statement about math's credibility being in question. Three squared will ALWAYS be nine unless the symbols for three or nine should change before the problem is solved.
The thread is meant to emphasize the burden of proof, I believe. The issue is where that burden lays when proof is demanded. Those who make a bold statement should be expected to provide the evidence or proof needed, or their statement doesn't mean all that much. You should not be expected to have your statement taken for granted unless someone disproves you. Because quite frankly, there are an infinite number of statements that you can make which are BS, but can't be disproved. Only when something has been presented and acknowledged as the truth, it holds no water.
When a subject hinges upon a vital piece of evidence, then that is when you cannot rely upon a supposition. When you contribute a small element to a larger issue, then it is not so critical to emphasize whether it could be wrong or not.
When you shoot down a theory, then I think it should be expected that you provide a better alternate theory. Of course there are some dilemmas that don't have any favorable solutions, so that brings this into question. I have no idea how the US should pull out of Iraq, because I don't see any effective means by which you can do so without the country going to hell.
I could go more into detail about this, but that would violate the rules of this thread.
First let me just say DY that I really respect the deep thought you place in things. You're a cool chick. Oh awesome, arctic monkeys just came on the radio, ya gotta listen to them, very cool band, right up your alley.
Three squared will ALWAYS be nine unless the symbols for three or nine should change before the problem is solved.
Yes but the point I was trying to make is that when you use 3-squared to describe a physical/natural process you are talking about a mathematical model and not the process itself. The study of the natural universe should not be confused with the natural universe itself.
The thread is meant to emphasize the burden of proof, I believe.
Precisely, which is why math cannot be accepted by theoretical physicists to conclude any natural process alone. It must be correlated by reproducible experimentation/observation in nature and then it is forever subject to falsification. Math is great, 100% reliable and does not describe physical reality in all its complexity. It is just a language, with precepts involved.
As physical evidence it is only circumstantial, but can offer one of several reasonable likelihoods for any given problem.
The alternative theory I would propose for strict calculus is probability function.