»
Discussion
»
Philosophy 101
»
Of the sciences...
| Philosophy 101 |
|
Of the sciences... |
|
|
JnR4eva Member
since 2000-08-07
Posts 377Bronx, NY |
This is really a continuation of Christopher's "perspective reality" discussion held here in philo 101. Towards the end, the discussion kind of diverged with the topic [perspective reality] at hand and dealt with more of the sciences. So I'll ask the questions what they are? How valid are they? Which ones are considered 'soft' 'hard' and 'gooey'? Should there be more subdivisions? Which ones hold more weight against another field of science? Should we respect physics more than psychology? Hopefully such a discussion will lead to many new questions concerning the fields of sciences such as psychology, chemistry, mathematics, biology, physics, ect. One can discuss how some overlap with one another. The discoveries that men and women make within these fields is remarkable, but at the same time most of those discoveries are not forever. Theories are changing every second. Is it due to our 'Primitiveness' concerning the tools we use and knowledge we have? Is this universe too intricate, yet elegant, to understand? Would love to hear some points of views concerning all fields. |
||
| © Copyright 2000 JnR4eva - All Rights Reserved | |||
|
JnR4eva Member
since 2000-08-07
Posts 377Bronx, NY |
..continued from perspective reality i have read the positions of Trevor and Ron and i will say for the most part i totally agree. our world is this great big ball of mystery on to which we try and fiddle with its truths. the truths will forever remain constant...they will, but how we draw our conclusions is the difference. for instance...the most basic element of life was considered the atom...then it became the protons, neutron and electrons and so forth that made up the atom...then scientists said no, there exist even smaller entities called quarks....BUT now there is something called strings which make up quarks!!! called superstring theory...therefore our knowledge is constantly changing ... such as for Trevor's argument with the medicine...micro organisms have might have always been the cause, or rather they have played an integral part of the main cause...but it is our 'advances' that hinder us b/c we simply do not have the best tools and know how to realizes these universal truths to our maximal potential. in a nut shell our knowledge can only grow and grow, but is never ending.. i am a math major...and i will state that math is thee most rigid science there is b/c the mathematical proof need only to work once in order for u to say you have a universal truth!....if you can mathematically prove a property or characteristic of numbers by justifying it with sound logical mathematical reasons (assuming that what we believe about numbers is true)...then my friends u have a mathematical theorem....there is no, experimentation with numbers....you do not need to run the first 600 integers in an equation to determine whether something is correct, for instance... Fermat's last theorem simply that there are no whole number solutions for n>2 that satisfy the equation X^n + Y^n = Z^n. this proposition was stated by Fermat in the 16th century but it was only proven in 1994 by Professor Wiles. since he proved that there are no solutions greater than 2, there is no use or reason for any man or woman to check numbers that stretch as far as infinity trying to find a counterexample! its been proven that there exist no such thing!! b/c of this discipline i believe that math is the most stern and rigid science, u must be precise with what u say and claim... Ron...i was wondering about your categories i liked the way u divided them even more... i am very used to separating them as hard versus soft...hard being anything that is well...chemistry and physics and biology are all hard sciences while things such as psychology and sociology are of a soft nature..though i must tip my hat to the soft sciences for they remain true to the scientific method as much as possible.... and you said... Let's call science that is based on pure mathematics Hard Science. If 2 + 2 does indeed always equal 4, we can say that the predictability of Hard Science is 100 percent. Much of the so-called physical sciences fall into this category. If you accelerate a particle to 97 percent the speed of light, Einstein's equations predict exactly how much energy you'll need to apply to get it up to 98 percent. The Soft Sciences are based on experimentation, rather than on mathematics but physics is very relying on experimentation...if it wasn't for experimentation there would be no understanding of physics for us. we wouldn't know things such as the speed of light, for scientist had to run many test to finally deduce how fast it traveled (though the mathematics was extracted AFTER the experimentation...physics is still very dependent on experimentation)(and yes i read how u said certain aspects are gooey and soft...but this im just saying that physics does rely heavily on experimentation as well  as for brad...2+2 =5.... interesting, its all a matter of language like u said...anybody brought up to the mathematics that has been proven by many mathematicians will say that 2+2=5 is all wrong....and they will be justified b/c they used their rules....now if we met a boy from the jungle who will argue that 2 and 2 spears used for hunt will result in 5 dead bores .then he is justified for his belief. or that 2+2 =10 b/c (two hands = 10 fingers), ... however when we do our math .. our understanding of numbers aren't dependent on any other factors....24=24=24!! or u can think 24 = 2 x 2 x 2 x 3 but the point is that 24 = 24... so going back to thing of the boy... u have to question then if this is the same mathematics we are talking about? is this the universal math that the world holds true? will this boy's math lead us to light's speed? Unless the person who claims that 2+2 =5 or that 2+ 2= 10 by legitimate proof where the number means themselves and nothing else, then they are in the wrong... actually brad i am left to think about a discussion my class had one day..that math is based upon certain axioms...axioms being mathematical statements we MUST take as truth without any proof...there are exactly 9 axioms which math is built upon...b/c of those 9 axioms we can prove then 1 + 1 = 2 yet..a famous mathematician whose name i forget said that even though our axioms are great and all....there still exist proofs which the mathematician can never solve for b/c those axioms which we have based our mathematics on are not in their entirety...( that's why some believed that fermat's last theorem might have been victim to this theory since fermat's last theorem had gone unsolved for soooo long) ... in a nutshell he is suggesting that we may have overlooked something..but what we do not know... i think i have said enough and deviated from the topic at hand..hope i was insightful lol [This message has been edited by JnR4eva (edited 09-04-2000).] |
||
|
Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
While I don't think we disagree on much, I do think there's some misunderstanding over "my" definitions. That's my fault for using "Hard" and "Soft," which pretty much already have meaning to those in the field. My definition of Hard, however, is much harder than most would ascribe to. Hard means we know we're right and there is no possibility of new research contradicting our conclusions. Your example using Fermat's last theorem is such a case. Hard, to me, means it is based on incontrovertible mathematics. It is 100 percent predictable, because 2 + 2 always equals 4. My definition of "Soft," however, contains most of what you might consider Hard. For example, you list Biology as a Hard science, but most of it is based on experimentation and is beyond mathematical representation (with the obvious exceptions of genetics and chemistry). Mitosis is observable and well understood, and it's unlikely a new discovery could contradict what we already know. Unlikely, but nonetheless possible. To use JP's words from the other thread, just because something has happened several million times in the past is no guarantee it will happen tomorrow. In contrast, we know no number greater than three will solve Fermat's equation, and we know there will be no new number discovered tomorrow to prove us wrong. The predictability of Soft science can be very, very high, but we can never guarantee it to be 100 percent - as we can guarantee with Hard science. My Gooey science classification probably coincides more closely to your Soft definition. Predictability is not high, for a large variety of reasons. Essentially, we are making educated guesses. In the earlier thread, Trevor was willing to concede that 2 + 2 equals 4, opening the door to my contention that "some" realities are not a matter of perception. I knew I should have waited for Brad.  Still, I think it's clear that Brad's argument is semantical, rather than mathematical. You can debate the meaning of the words all day long, but 2 + 2 is still going to equal 4 when you crawl into bed tonight. Except - maybe not. Our mathematical system hasn't changed in a very long time, but it is nonetheless an evolutionary attempt to model reality. In the beginning, were positive integers. Next came negative numbers, then fractions. Interestingly, the concept of zero didn't come until much later. The ancient Egyptians never used a zero symbol in writing their numerals. Nor, more surprisingly, did the Greeks until about 1500 BC. The concept of nothing being a number was apparently not an easy leap to make. The inclusion of zero into our system, however, produced a conundrum. If 2 times 0 equals zero, then what does 2 divided by 0 equal? Many still insist the answer must be infinity. The opposite of zero, after all, is infinity. And consider the series: 10/10=1 10/5=2 10/1=10 10/.5=20 10/.05=200 10/.005=2000. It seems evident that the smaller the divisor, the larger the result. To this day, many competent scientists make the mistake of assuming that X/0 equals infinity. Most of Einstein's Special Relativity equations (from which the ultimate result was the famous e=mC^2), include the divisor quantity C^2 - V^2, where C is the speed of light in a vacuum and V is the velocity of matter. (Note the ^ symbol represents exponents, typically pronounced e=mc squared). Einstein's equations proved that as velocity increases, so too does the length and mass of matter, something that may be counter-intuitive but has been amply demonstrated in particle accelerators. But notice that when V exactly reaches the speed of light, C^2 - V^2 will then equal zero. Many laymen will tell you that when a particle reaches the speed of light its mass will become infinite, a blatant impossibility (even the mass of the Universe is finite). Ergo, one can never travel faster than the speed of light. But division by zero does NOT equal infinity. Consider the following very simple equations. (a).(a) - a.a = a2 - a2 In other words, the result of division by zero is anything you want it to be! Which is exactly why it is not allowed in mathematics. If we allow people to divide by zero, everything else in our mathematical system gets thrown out with the dirty water. So, very simply, it is forbidden. A bit over 3,500 years ago, Mankind discovered zero because there existed real-world phenomenon that made it necessary. Indeed, every single addition to our system has been the result of the need to reflect reality, which is precisely why mathematics can be used to define reality - beyond our perceptions. Interestingly, Einstein's equations may yet lead us to accepting the bitter necessity of dividing by zero. It was his equations (from the General Theory, this time) that predicted the Black Hole, a singularity with such dense mass that light cannot escape its gravity well. Mmmm. Einstein also showed us that gravity and acceleration are indistinguishable, so anything that can suck in light would also accelerate mass beyond the speed of light. It would, in effect, divide by zero. That's why Stephen Hawking says you "could" find a dragon flying out of a black hole. Because, when you divide by zero, anything is possible. So, yea, Brad - 2 + 2 could equal 5. But only within the confines of a singularity.  |
||
|
JnR4eva Member
since 2000-08-07
Posts 377Bronx, NY |
Ron I must confess that I knew you were headed in that direction when you said that physics is harder than biology b/c of the fact that physics deals very much with mathematics...you brought up some cool stuff..let me review.. For the most part I do agree on some things while I wanted to include this little tidbit about perception.... In the earlier thread, Trevor was willing to concede that 2 + 2 equals 4, opening the door to my contention that "some" realities are not a matter of perception. I knew I should have waited for Brad. Still, I think it's clear that Brad's argument is semantical, rather than mathematical. You can debate the meaning of the words all day long, but 2 + 2 is still going to equal 4 when you crawl into bed tonight. Except - maybe not. Rene Descartes in his book Meditations took into account our belief in numbers and stated that we may be very wrong with out belief for we can never be sure that their is some deceiving demon or a deceiving god who has made us believe that 2+2 =4... the example that come to mind for me is total recall..ever seen it?...where Arnold is strapped in a chair and he is taken to another reality..i believe it was a vacation spot that he was in...well that is what Descartes was talking about how we may be under the influence under an ill-willed entity which is causing us to misinterpret numbers....personally though i do not believe such things...it was a bit on the solipsism side of things and i personally favor the existence of a real world ... but I just wanted to include that just to show how someone like Descartes would argue with that statement.... Our mathematical system hasn't changed in a very long time, but it is nonetheless an evolutionary attempt to model reality. In the beginning, were positive integers. Next came negative numbers, then fractions. Interestingly, the concept of zero didn't come until much later. The ancient Egyptians never used a zero symbol in writing their numerals. Nor, more surprisingly, did the Greeks until about 1500 BC. The concept of nothing being a number was apparently not an easy leap to make. total agreement...the math that was used by Professor wiles to solve for Fermat's equation dealt with the convergence of two areas of math that NEVER were thought to be meshable...(hope that's a word) To this day, many competent scientists make the mistake of assuming that X/0 equals infinity. Most of Einstein's Special Relativity equations (from which the ultimate result was the famous e=mC^2), include the divisor quantity C^2 - V^2, where C is the speed of light in a vacuum and V is the velocity of matter. (Note the ^ symbol represents exponents, typically pronounced e=mc squared.) Einstein's equations proved that as velocity increases, so too does the length and mass of matter, something that may be counter-intuitive but has been amply demonstrated in particle accelerators. But notice that when V exactly reaches the speed of light, C^2 - V^2 will then equal zero. Many laymen will tell you that when a particle reaches the speed of light its mass will become infinite, a blatant impossibility (even the mass of the Universe is finite). Ergo, one can never travel faster than the speed of light wow i didn't know this..yes it would assume that if v ever was equaled to the speed of light then we have ourselves a problem..yet it does strengthen the fact then that one can never travel quicker than the speed of light "The inclusion of zero into our system, however, produced a conundrum. If 2 times 0 equals zero, then what does 2 divided by 0 equal? Many still insist the answer must be infinity. The opposite of zero, after all, is infinity. And consider the series: 10/10=1 10/5=2 10/1=10 10/.5=20 10/.05=200 10/.005=2000. It seems evident that the smaller the divisor, the larger the result." "In other words, the result of division by zero is anything you want it to be! Which is exactly why it is not allowed in mathematics. If we allow people to divide by zero, everything else in our mathematical system gets thrown out with the dirty water. So, very simply, it is forbidden." Interesting point indeed...reminds me of the series 10/x lol....check this out...why cant we divide by zero (it explains all numbers except 0 itself)....not that its forbidden but its proven why u cannot.... -assume A and B are elements of the number system -A does not equal 0 (for the sake of not using the *indeterminant form 0/0*) -assume A/0 proof: A/0 = some element by which a number (B) multiplied to zero shall produce A.... HUH?... A/0 = B -----> A= (B)(0) ---> A=0 Since we claimed already that A cannot equal zero..then there is no way that this equation is satisfied b/c A (which is a number other than zero) has been set equal to zero(proof by contradiction)!!!...for those who may not be too keen on math...lets take.. 1/0 ...then that means there is a product of 0 and a NUMBER(N) such that...N times (0) = 1...however if u multiply 0 to N u get zero back...and u get... 0=1 !!!!! that is why u cant divide by 0...so what i believe hope u liked the proof i tried to accommodate for all readers Like I said before...we may be missing axioms on to which we are restricting ourselves..like when you said.... Interestingly, Einstein's equations may yet lead us to accepting the bitter necessity of dividing by zero. It was his equations (from the General Theory, this time) that predicted the Black Hole, a singularity with such dense mass that light cannot escape its gravity well. Mmmm. Einstein also showed us that gravity and acceleration are indistinguishable, so anything that can suck in light would also accelerate mass beyond the speed of light. It would, in effect, divide by zero. That's why Stephen Hawking says you "could" find a dragon flying out of a black hole. Because, when you divide by zero, anything is possible. Such concepts may now question what part of mathematics we are missing...the proof I provided support that division by zero is not valid..however perhaps there is something about math we don't know that in certain cases it is permissible to divide by 0 and thus explain Einstein's theory.... Can't wait to hear back....and oh... *indeterminat form 0/0: u have to think of this... its intuitive.... u have 0/0 whenever 0 is divided by any number (other than 0) u get back 0....whenver u divide by zero(or rather if u divide by an extremely small number that approaches 0)...u get a number that stretches to infinity (sorry Ron) thus u have a conflicting idea with 0/0 b/c its either u get nothing..or u an extremely large number!!! that's why such a form is called indeterminate* [This message has been edited by JnR4eva (edited 09-04-2000).] |
||
|
Trevor Senior Member
since 1999-08-12
Posts 700Canada |
Hello good folks, First off let me say how interesting you guys have made this subject. Secondly, I only have a few minutes before I have to run but wanted to add an idea I had and apoligizing for not fully getting into the discussion but I just wanted to get this out before I forgot what I was going to say. "But division by zero does NOT equal infinity. Consider the following very simple equations. (a).(a) - a.a = a2 - a2 for any finite a. This can be written as a(a-a) = (a-a)(a+a) dividing both sides by (a-a) gives a = 2a now, dividing by a gives 1 = 2, Voila! In other words, the result of division by zero is anything you want it to be!" I think by your own words Ron you just pointed out that it does equal infinity...as in infinite possibilities. Now for me, and I could be wrong, numbers are nothing more than the renaming of pre-existing things, they are a representation of our reality. 1 does not actually equal 1 nor 10=10. These are just generalized things we have created to help gauge our world. Each number in 10=10 represents something physical, something more than a number, something more than the idea of a number. That's the very reason why math does help us define our reality. Our numeric system is a man-made thing, however the patterns we apply it to are not. One of the earliest techniques teachers use to demostrate mathematics is, if Billy has one apple and Suzie has 3 apples, how many apples in total are there. The equation would go 1+3=4. 1 isn't really a one but instead an apple and 3 isn't just a three but instead 3 apples...same for 4, but we lose individuality in an equation and because a number is as general as one can be, each of those numbers could actually represent anything within our existence. I use the same 1 to describe an apple as I do to describe a universe yet they are completely different things. Now through your equation you pointed out that dividing something by zero can equal anything therefore it means it can equal all or nothing and anything in between the two as well or even those three at the same time, if in fact numbers are actually a representation of existing things. Technically speaking, because numbers only represent something and never themselves, every number can be infinite, if in fact infinite does exist ie. 1+1=1 when 1 is representing infinite, a singular yet all engulfing idea, one idea, yes its a matter of semantics but that is only because math only represents the physical world and not actually itself. If numbers only represented themselves the equation could only read 1+1=1+1, but because every number describes something that is a non-number, a number does not represent itself. I think I'm repeating myself . Sorry to be rude and not finish all my thoughts on this or address all the great points being made....you guys blow my mind and open up such interesting subjects and ideas. Thank-you,take care everyone, Trevor |
||
|
JP Senior Member
since 1999-05-25
Posts 1343Loomis, CA |
OUCH! Y'all are making my brain hurt! I must confess, mathmatics and hard sciences are not my forte... I've spent my life in the soft science arena, and actually most of those are better classified as gooey. A phsychology major who changed to Organizational Communications, I spend my time dealing with Performance Management, Employee Development and the like. Most of what I do and study is prediction of behaviors based on what experience tells us we should expect... most definitely NOT a reliable science. What the hell was I talking about? Oh yeah, my brain hurts....  Yesterday is ash, tomorrow is smoke; only today does the fire burn. JP "Everything is your own damn fault, if you are any good." E. Hemmingway |
||
|
JnR4eva Member
since 2000-08-07
Posts 377Bronx, NY |
"Now for me, and I could be wrong, numbers are nothing more than the renaming of pre-existing things, they are a representation of our reality. 1 does not actually equal 1 nor 10=10. These are just generalized things we have created to help gauge our world. Each number in 10=10 represents something physical, something more than a number, something more than the idea of a number. " hey Trevor...at first i had a hard time swallowing this concept that perhaps 1 does not equal 1, but i reconsidered and thought about it more...( u went on to say 10 didn't equal 10...but I'm going to stick to 1 b/c 10 is only the succession of the number 1 therefore if we can justify 1 then we can justify 10.) .. i think this brings up the whole concept and understanding of 1.... mathematicians have had a hard time saying what exactly 1 is...for instance our numbers are based on the pattern {n+1}....and from this we can derive our whole numbers...but the very fact of what 1 is, or what 1 represents still baffles mathematicians to this day..and to me...like for instance I'm sitting in 1 chair..yet this is composed of 6 million atoms let say..does this 1 still have the same meaning as 1 before? but look at me talking of 6 million atoms...six million is, to our understanding, is a number that succeeds1..therefore this line of thinking goes on infinitely b/c if u try to describe 1, you wind up speaking of numbers that succeed 1 when from the start we were trying to isolate 1 alone...did that make any sense whatsoever? sorry if it didn't "One of the earliest techniques teachers use to demonstrate mathematics is, if Billy has one apple and Suzie has 3 apples, how many apples in total are there. The equation would go 1+3=4. 1 isn't really a one but instead an apple and 3 isn't just a three but instead 3 apples...same for 4, but we lose individuality in an equation and because a number is as general as one can be, each of those numbers could actually represent anything within our existence" Wanna hear a good one that I read as an e-mail?....there are 3 birds on a wooden gate and a farmer goes to shoot one of them....so he goes aims and fires and kills one bird..how many are left on the gate? mathematically 3-1 = 2 philosophically 3-1 = 0.....the birds that were left alive would have fled in horror to hear the gunshot (assuming they could hear) "1+1=1 when 1 is representing infinite, a singular yet all engulfing idea, one idea, yes its a matter of semantics but that is only because math only represents the physical world and not actually itself. If numbers only represented themselves the equation could only read 1+1=1+1 " a damn good point that 1+1 = 1+1... it does not equal two unless we go into the physical world and saw for ourselves that 1 and 1 of the same thing makes for 2 of the same thing ... if we taught a child that numbers were only themselves and asked what is 2+3...then that child would be forced to say 2+3 = 2+3..it is what it is., it equals what it equals, he/she wouldn't be able to make the connection that 2+3 may equal 5 b/c they were working independent of the physical realm and its truths ... yet the physical realm does claim that 2 and 3 of the same thing does equal, a new number, {5} of the same thing, mathematically though, perhaps not philosophically..depends on how u read into it this only speaks well of our reality as it helps define the real valid world that exist independent of our perception. is this what u were trying to get at or did i truly botch it up? "Sorry to be rude and not finish all my thoughts on this or address all the great points being made....you guys blow my mind and open up such interesting subjects and ideas. Thank-you," are u kidding? u have already given enough insight with this one paragraph, thanx for stopping by. [This message has been edited by JnR4eva (edited 09-04-2000).] |
||
|
Trevor Senior Member
since 1999-08-12
Posts 700Canada |
Hello I'm back, Jen: "hey Trevor...at first i had a hard time swallowing this concept that perhaps 1 does not equal 1, but i reconsidered and thought about it more...( u went on to say 10 didn't equal 10...but I'm going to stick to 1 b/c 10 is only the succession of the number 1 therefore if we can justify 1 then we can justify 10.)" I've been thinking about it more too. I think numbers have a dual nature, they are both equal to themselves and equal to what they are representing. When speaking strict mathematics, not applying math to anything but math, a number represents itself, the idea of a number, one number, etc. "...( u went on to say 10 didn't equal 10" Yeah but I'm going to retract that statement and say 10 can equal 10 if 10 is representing itself as the math concept of the number 10. Same as the 1+1 can only equal itself sometimes. "but look at me talking of 6 million atoms...six million is, to our understanding, is a number that succeeds1..therefore this line of thinking goes on infinitely b/c if u try to describe 1, you wind up speaking of numbers that succeed 1 when from the start we were trying to isolate 1 alone...did that make any sense whatsoever? sorry if it didn't." No you made perfect sense and I agree with you. Very good point. If you take that train of thought even further you might be able to argue that there is only one number and that it is 1 and that 10 is nothing more than a division of 1. This is because there is only one existence and all that we percieve as an individual thing is nothing more than a part of a larger whole except when 1 is representing the whole of existence. Now the only way to stop such thought is to limit what math may be applied to or what a number is allowed to represent. "Wanna hear a good one that I read as an e-mail?....there are 3 birds on a wooden gate and a farmer goes to shoot one of them....so he goes aims and fires and kills one bird..how many are left on the gate? mathematically 3-1 = 2 philosophically 3-1 = 0.....the birds that were left alive would have fled in horror to hear the gunshot (assuming they could hear)." I like that one "yet the physical realm does claim that 2 and 3 of the same thing does equal, a new number, {5}" Yes but it also can equal 1 as well. One group of identical things, this I believe is also represented in math equations. Blame Ron for getting me on the duality of things and you for inspiring this long-winded response of mine. Lets say atoms are all identical in nature and you were to take five and add them together. We are now dealing with a identical physical things. You'd have five seperate atoms all represented by the number one, 1+1+1+1+1=5 which is equal to atom+atom+atom+atom+atom=5 atoms in succession or 1 grouping of 5 atoms or there are five atoms. Math still shows the singular while the many by stating there is 1 group of 5 indenticals because five is a single number that is representing the many. A singular thing representing the many???...Looks like we just found the theory behind what created politicians Therefore an equation such as 2+3=5, even when pertaining to the physical world and identical things, still might not always be true nor false but will create a new number. Now I must ask, am I making any sense? Cause I don't feel like I am. Tell you the truth, I don't even know if this pertains to the statement you just made...felling a little dizzy cause I'm "overthinking" right now "this only speaks well of our reality as it helps define the real valid world that exist independent of our perception. is this what u were trying to get at or did i truly botch it up?" No you didn't botch it up, that's what I was trying to get at with my 1+1=1+1 comment. Now you've said a couple times that there is a chance that math is missing its own equation to be completely workable for us....perhaps its the humanization of it that's missing, perhaps it lacks a liberal attitude . Instead of just numbers maybe there should be a mesh of numbers and words and a multitude of valid answers for each question..... 1 apple + 4 oranges + 1 bunch of grapes + 1 wooden bowl = one nice kitchen table center or a healthy lunch or 1a+4b+1c+1d=1e, maybe they're all right at the same time. I guess that's all I can say for now, thanks for the interesting conversation, take care, Trevor |
||
|
Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
Trevor said: "I think by your own words Ron you just pointed out that it does equal infinity...as in infinite possibilities." Infinity is actually a fairly well defined concept, thanks to Cantor, but I don't think it should be confused with infinite possibilities. Especially when the two concepts logically arrive at different conclusions. To return to my earlier example, if accelerating a particle to the speed of light resulted in infinite mass, then it would require infinite energy (work, including acceleration, doesn't happen without energy input). Clearly impossible. But if light speed results in indeterminate mass - it could be anything! - then the energy required is also indeterminate. But possible. JnR4eva said: "…for instance our numbers are based on the pattern {n+1}" While I'll agree that's the simplest pattern, Jen, it's certainly not the only one. And it's clearly not the most useful. We could just as easily define our whole numbers as an {n+2}{n-1} sequence (which would be equally lacking in usefulness). Many have tried to define whole numbers in terms of the Primes, which would add a magnitude of usefulness. But, of course, the point of your statement is nonetheless true and important - we cannot define the base quantity of one in any meaningful and significant way. Unity simply exists. Trevor said: "…numbers are nothing more than the renaming of pre-existing things, they are a representation of our reality." While that's certainly the genesis of math, its strength is that it has evolved beyond its own beginning. Indeed, if we hobble numbers to pre-existing things we are crippling our steed. In such a case, proving that two oranges plus two oranges always equaled four oranges would tell us absolutely nothing about apples. It is math's generality that makes it so useful for prediction. Insisting that a number must represent an object eliminates the purity from which math gains its strength. Case in point: One of the reasons zero as a number came so late to mathematics was because it does not exist in our physical world. |
||
|
Trevor Senior Member
since 1999-08-12
Posts 700Canada |
Hello everyone, Ron: "Infinity is actually a fairly well defined concept, thanks to Cantor, but I don't think it should be confused with infinite possibilities. Especially when the two concepts logically arrive at different conclusions." I'm having a little trouble discerning one from another. I did a little reading on Cantor and Set theory but it might have been written in ancient greek....well it wasn't that bad but I just can't grasp them as truly different nor can I seem to understand how they arrive at a different conclusion. To me, in my opinion, they both arrive at a conclusion of uncertainty or perhaps you could describe it as a non-conclusion for it never ends therefore it can not conclude itself. If the same formula to describe an infinite sequence of numbers can describe an infinite amount of change and if there is an infinite amount of change, then there is an infinite amount of possibilities. To me that says infinite and infinite possibilities are the same...though I guess a distinct difference might be that one is measuring the idea of numbers and the other the idea of possibilities. "To return to my earlier example, if accelerating a particle to the speed of light resulted in infinite mass, then it would require infinite energy (work, including acceleration, doesn't happen without energy input). Clearly impossible." Now I'm probably way off the mark here, I'm not claiming to be a scientific mind but if a particle is accelerated to the speed of light then theoretically doesn't it become energy. Does energy have a mass? Not a rhetorical question...I really don't know. I guess we catergorize energy in different ways, but what if the base of all energy is the same..and lets say energy exists in all things that exist and also physically holds existence together or in order. Now lets say that existence is infinite in mass, that would also mean the base of all energy sources would have to be infinite as well or vice versa. Now if there is an infinite energy source then there could be infinte amount of power to accelerate a particle, perhaps a speed faster than light is this base of energy that I'm theorizing on....okay I better stop this thought cause I can't remember what I was trying to say. It's amazing how hard I'm working to present a point I don't even understand "While that's certainly the genesis of math, its strength is that it has evolved beyond its own beginning. Indeed, if we hobble numbers to pre-existing things we are crippling our steed." Well here's where I'll budge a bit. It can represent things that do not exist as is the case perhaps in chemical engineering or any other science where we muck about with new combinations...and I guess they also represent wrongs sometimes too, theories that are proven incorrect....something that does not really exist. However when I made that statement I was thinking more of when math is applied to defining our reality. When Einstien developed his theory of relativity he was not inventing the effects of light-speed travel but rather defining it with numbers. It already existed before his equation (though we don't know for certain if it is 100 percent accurate but for the sake of this discussion I'll say it is), he was describing something that he believed existed. He was describing his idea in numbers. Math often describes the unknown but still a pre-existing thing. I guess a better example might be an equation that predicts the existence of a specific planet. We may not know for certain if that planet exists, because to see is to believe, but through numbers a mathmetician could describe how and why they think a planet exists there through numbers with a large degree of accuracy.....defining the unknown yet pre-existing. And that's where my train of thought was when I made that incorrect statement about math and pre-existing things. "In such a case, proving that two oranges plus two oranges always equaled four oranges would tell us absolutely nothing about apples." I don't quite understand this statement Ron....it was the apple thing that threw me off. I guess I don't see why you'd be trying to learn about apples through adding oranges. "It is math's generality that makes it so useful for prediction. Insisting that a number must represent an object eliminates the purity from which math gains its strength." Yes I agree after reading your points, math has strength because it can represent existing things, it helps us organize our reality and define our reality but at the same time it is invaluable at showing us a possibility, such as creating something that does not exist. It was that part of math that allowed mankind to build a rocket ship so we could put a pinky toe into the ocean of space and a nuclear bomb.....notice how the invention of a nuke was first, maybe unintentionally it sparked the need to get off this planet One last thought on this. It is the idea that comes before the equation, the idea pre-exists and the equation of what could be and the equation describes the pre-existing idea. "One of the reasons zero as a number came so late to mathematics was because it does not exist in our physical world." This is where I will still disagree. I believe zero can accurately represent something that does exist in the physical world. Perhaps the creation of zero was not to not only represent a nothingness but also a none...no I did not say anon or a nun but a none . If I gave you 2 apples then took away two apples you would have zero apples, none. It is showing the lack of a specific.Well I guess that's all I'll say for now and I look forward your next corrective response. It's always a pleasure having you in a discussion, you are indeed an interesting and knowledgable person. Thanks and take care, Trevor [This message has been edited by Trevor (edited 09-05-2000).] |
||
|
Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
"To me that says infinite and infinite possibilities are the same." For the sake of our discussion, Trevor, the biggest difference is again in the conclusion to which each leads. Let's use a different example. If an action leads to infinite mass, then I can't possibly hold it in my hand. If, on the other hand, it leads to indeterminate mass - say two kilograms in once instance - then maybe I can. Or, think of it this way. Infinite possibilities still lead to a finite decision. The mass can be anything, but this time it is something very specific. And finite. "…if a particle is accelerated to the speed of light then theoretically doesn't it become energy." Theoretically, no, at least not any theory with which I'm aware. But possibly? We just don't know and, according to Einstein, we never will know. "Now lets say that existence is infinite in mass…" Current theory indicates it not only isn't infinite in mass, but there's a whole lot of mass we can't find (those darn neutrinos again). The Universe is an expanding ball, like a balloon being inflated, we think as the result of the Big Bang. Now there are two things that can happen to an expanding Universe. It can expand forever, in which case there is eventual heat death (energy and mass become so diluted as to be vaporous). Or, as the force of the Big Bang dissipates with time, the mass/gravity of the Universe will cause it to begin contracting - into what will eventually become another Big Bang. Scientists have very carefully calculated the mass of the Universe, trying to determine which of these two eventualities your children's children's children (ad nauseum) will face. Those calculations indicate there should be enough mass to contract - but we can't find it. (BTW, if there was infinite mass there would never have been a Big Bang; the gravity would have been infinite and no force could have separated it into our Universe.) "I don't quite understand this statement Ron....it was the apple thing that threw me off. I guess I don't see why you'd be trying to learn about apples through adding oranges." My point, Trevor, was that proving two oranges plus two oranges equals four oranges automatically provides the result of adding two apples to two apples. This is ONLY true because mathematics is general, rather than specific. "If I gave you 2 apples then took away two apples you would have zero apples, none." Ah, but the apples would still exist, Trevor. At no time do we have zero apples (even if you eat them). Man can, indeed, conceive of zero, as you just did. And there are many, many such mental justifications. But we cannot yet point to anything in reality that represents zero. We've been trying to reach absolute zero (the complete cessation of movement) for what seems forever. To no avail. We can look at any given object and say it lacks a characteristic - such as a particle with zero charge - but in no case can we point at something and say, "This is zero." There appears to always be no such thing as nothing. |
||
|
JnR4eva Member
since 2000-08-07
Posts 377Bronx, NY |
hey guys i would love to reply to most of the info that you all have supplied, some thoughts that i would love to add on and discuss...but i'm pressed for time since i have about 600 pages of textbooks to read for just one class lol...the only thing i would say for the momemt, that both Ron and Trevor have gotten incorrect,...is my name lol...its not jen. lol you can call me j for short if u wish [This message has been edited by JnR4eva (edited 09-05-2000).] |
||
|
Trevor Senior Member
since 1999-08-12
Posts 700Canada |
Hey Ron, "If an action leads to infinite mass, then I can't possibly hold it in my hand. If, on the other hand, it leads to indeterminate mass - say two kilograms in once instance - then maybe I can. Or, think of it this way. Infinite possibilities still lead to a finite decision. The mass can be anything, but this time it is something very specific. And finite." I understand now what you were saying and must agree. Thanks for clearing this up for me. "Theoretically, no, at least not any theory with which I'm aware. But possibly? We just don't know and, according to Einstein, we never will know." I must've confused it with something from Star Wars...."..laugh it up fuzzball." "Current theory indicates it not only isn't infinite in mass, but there's a whole lot of mass we can't find (those darn neutrinos again). The Universe is an expanding ball, like a balloon being inflated, we think as the result of the Big Bang." But the possibility that something does exist outside our universe is there so I believe that though the mass may not be from our Universe, there is still a chance that there is mass outside our Universe and therefore still a chance of infinite mass. I don't know how likely this is or if science has "proven" this wrong but even the slimest of theories are sometimes correct. "(BTW, if there was infinite mass there would never have been a Big Bang; the gravity would have been infinite and no force could have separated it into our Universe.)" No force we know of could seperate it into our universe...we don't even know the exact nature of the force that created the Universe nor if there is anything outside our Universe. Perhaps our Universe is just surounded by other Universes and we're just pushing into them? Yes, far fetched but you never know. "My point, Trevor, was that proving two oranges plus two oranges equals four oranges automatically provides the result of adding two apples to two apples. This is ONLY true because mathematics is general, rather than specific." I understand now, thanks for clarifing that. "But we cannot yet point to anything in reality that represents zero. We've been trying to reach absolute zero (the complete cessation of movement) for what seems forever. To no avail. We can look at any given object and say it lacks a characteristic - such as a particle with zero charge - but in no case can we point at something and say, "This is zero." There appears to always be no such thing as nothing." I guess the problem with gauging or measuring nothing is that there is nothing to measure. Lets say that outside our Universe there is infinite nothing, well I guess it couldn't really be infinite nothing because our Universe exists but lets say its infinite nothing - our Universe. If you were to leave our Universe into this almost endless void of nothing you'd probably immediately end up on the exact opposite side of the Universe. Nothing to pass through, nothing to slow you down, nothing to see. It's a long shot but I'd thought I'd throw it out there for discussion. Anyways, I gotta run, thanks for responding Ron and taking the time to re-explain your thoughts....I know I can be a bit of pain cause I ask all these questions but hey too bad JnR4eva: J, what's with the name then? Are Ron and I even correct about the gender? Girlfriend's name? I give, I cry uncle, let us know so I don't feel like a clown. |
||
|
Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
Trevor suggested: "Perhaps our Universe is just surrounded by other Universes and we're just pushing into them? Yes, far fetched but you never know." Maybe not as far fetched as one might think. Remember my description of a Universe with enough mass to again begin contracting, one that will eventually repeat the Big Bang? Doesn't that sound a bit like something else mentioned in this thread? Some have theorized (or perhaps speculated is a better word) that our Universe is one gigantic black hole. If so, it would certainly be logical to stretch that speculation into the possibility that our Black Hole Universe is just one of many inside a much greater Multiverse (which may, itself, be a black hole). But, sadly, it doesn't much matter, because we'd never be able to investigate what's outside our Universe. Getting out of a black hole ain't an easy thing. |
||
|
Steve B Member
since 2000-08-07
Posts 140Southern PA |
Well J, you definitely opened a large can of worms here...and siences mixed with philosophy is a great thing to ideate about. I get along with most all math except Algebra which I find little use for, other than programming loops...I compare it to english grammer, full of unknowns, ifs, ands, buts, with ridiculous factoring and logarithms, longer and diverse as the universe..... when straight forward trig and calc will do the job in an orderly fashion...lol enough fun with algebra :P.... Back to somewhere....but where do I start... how about a new simple math of the universal question why? 1+1=1 1-1=-1 -1+1=-1 -1-(-1)=-1 you see, any way you add or subtract the only true numbers of the universe, (ie 1 and -1) you will always get either 1 or -1....ZERO of course is a falicy, an untruth, non-exsistent....and plays no role in the universe....to make it simpler there is -1 and +1....or just - and +.... Most will say that this is just too simple, but then maybe it is just this simple...at least to the question why?... Next I will quote myself... " Man is by far the vainest of all beings in the universe, as he likes to think he is the only one." Not to mention that when man does attempt to concieve of other beings, the bizzare and wild conceptions as to their appearance and possible inhuman attributes.. which gives to the second quote of my own... "Money is not the root of all evil, ignorance is!" And I would ask you mathematicians for the odds of how many and how similar, would other beings in the universe be... given that the universe is made up of pretty much all the same materials and or elements known to us, and that the re-occurence of planets being re-generated may fall within the wide spectrum of even our known possible conditions, that would promote and sustain life.... hmmm I am not so much a mathematician, but common sense would tell me we are talking a substancial number of similar conditions with similar materials at an unlimmited, or I should say, non-exsistent time period, and I use the word time (which is also an untruth, a false thing) for lack of a better term. As to the validity of different sciences and their breakdowns and divisions....they can be treated as they have in their own little worlds, as those so minded or those so closed minded, in each specific field of their choice have become.... I have watched and seen, and followed the progress of many brilliant minds in many fields, and am amazed to see so many wearing blinders. They become so intense on just one thing, that they lose sight of perspective and common sense, and it only slows their work down to a crawl.. when if they would step back and look around them and explore other not so obvious possibilities that may at first not seem valid to their work but may indeed hold the key they are searching for...that and the overlooking of the most obvious and simple solutions ...We I believe, all tend to look at things much to hard, our minds tend to want to make things much more complicated than they ever are.....So if up to me, Science should be science and not broken down as strictly as most accept, still to have divisions in general areas but not to give to the thought of sinularity without connection to all else.... I would point out the time it took for scientific minds to make the break through in the operating temperature of super conductor materials... some 70+ years, and why? they restricted their line of thought and experimetation to the narrow limits of electrical properties and theory, and only after exhausting all those possibilities and after much frustration did they discover the key to their quest,,, and what was that? a non related , (so they thought), simple, basic element....ceramic.....So I say simplify, broaden your scope of thought, and see all as a whole, and science will take bigger steps ahead.... well this is my general take on what many would say would be very vast and complicated,,, I say is all so very simple.....Steve B Also I am wondering why I have found nothing on the application of super conductor fields being applied to the containment of anti-matter....does any one know if there is any one working on this possibility? I see they have a working super conductor generator and have done test models for anti-grav tubes... transportaion of course, but not for the other obvious thing that I see... force fields of great intensity.. Would love to know any thing more about this field... thanks SB “The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal” |
||
|
Not A Poet Member Elite
since 1999-11-03
Posts 3885Oklahoma, USA |
Hey guys, I just discovered this thread so haven't had time to read in depth. But I have briefly scanned through most of it. I just have 2 quick comments before I have to get back to work. As for mass accelerating beyond the speed of light becoming energy: If we are to believe Einstein's theory at all then mass, at any speed, is just energy. E=mc^2 proclaims that mass and energy are entirely equivalent. That is, they are nothing but different manifestations of the same thing. But then the theory is one regarding physics, not mathematics. Of course, it makes use of many mathematical concepts in its description, but it is still a theory dealing exclusively with physics. On the nature of mathematics as a hard science: Mathematics has been called the only true science (not necessarily by me) and it probably is the only fully hard science. There is one overriding reason why this is true. Mathematics as a science is not dependent upon any real phenomenon, physical or otherwise. It is not something God created for us to study. It is, instead, a human invention. One created by man as a tool to try to explain or at least quantify his environment. So yes, once a mathematical theory is proven, it becomes fact. The reason is because it was designed that way, it didn't just happen or develop on its own. Finally, the reason dividing by zero causes us such problems is that, as Ron has hinted, it was an added on feature. x/0 is not infinity and actually it is not whatever you want it to be (although I understand your line of thinking and find it to have a lot of merit). It is simply not defined. Remember this is a defined or designed science and that particular function was simply not given a meaning. Now I don't mean to claim that it necessarily could have been given a meaning either. But, for all the situations we can conceive of and comprehend, we have no valid definition for such a function. Thanks to the calculus, however, we do have an understandable concept of the limit of x/w as w becomes smaller and smaller and finally approaches zero. Well, thanks for letting me jump in and have a word or two. Very interesting discussion here. Pete Never express yourself more clearly than you can think - Niels Bohr |
||
|
JnR4eva Member
since 2000-08-07
Posts 377Bronx, NY |
Hey everyone..i see we have soon new faces and i have some old things to discuss..i hope this one isn't too long.... JP my apologies but i just wanted to say thank u for stopping by and replying We could just as easily define our whole numbers as an {n+2}{n-1} sequence (which would be equally lacking in usefulness). Many have tried to define whole numbers in terms of the Primes, which would add a magnitude of usefulness. I am assuming you wrote{n+2} and {n-1} as separate correct? I am taking number theory as we speak so I don't know the exact name of it (unique factorization I believe)...but thus far it is show-able(no such word) that most numbers are the multiplication of many primes..however it isnt proved that all numbers are the make up of primes. "Current theory indicates it not only isn't infinite in mass, but there's a whole lot of mass we can't find (those darn neutrinos again). The Universe is an expanding ball, like a balloon being inflated, we think as the result of the Big Bang." Ron I was wondering if this deals with the space between an atom's electron and its nucleus..being that there is a vast space (in a micro-perspective) then how can we account for the many concrete and solid objects we touch (like this keyboard) if in fact it is composed of atoms which have voids in their make-up? Let me know Some have theorized (or perhaps speculated is a better word) that our Universe is one gigantic black hole. If so, it would certainly be logical to stretch that speculation into the possibility that our Black Hole Universe is just one of many inside a much greater Multiverse (which may, itself, be a black hole). But, sadly, it doesn't much matter, because we'd never be able to investigate what's outside our Universe. im about to switch majors LOL (actually i wanted to major in astronomy!! oh man is this stuff good).....i have never heard of such a thing and this one is REALLY making me think...ok....im just gonna have to wallow in this one...our universe a blackhole?...theorectaically containing blackholes itself since our universe is to be believed that it, too, has black holes in it... well then just one or two questions...assuming we are a black hole..then why do things seem 'under control' (even though i hesitate to use such a phrase)..but in comparison to what is believed to happen when one enters a blackhole?...we seem to be rather on the normal side of things..but then again is such a perception just that?....perhaps im reading too into it?...and if we were...why can we see light?..but then again we wouldn't even being living, b/c such strong gravitational forces would rip our bodies to shreads...i don't know ...let me know..this one is truly something that i shall think on for days. I get along with most all math except Algebra which I find little use for, other than programming loops...I compare it to english grammer, full of unknowns, ifs, ands, buts, with ridiculous factoring and logarithms, longer and diverse as the universe..... when straight forward trig and calc will do the job in an orderly fashion...lol enough fun with algebra :P.... hey steve well i think im gonna have to support algebra on this one b/c though lets say a scientist has found an equation to the lets say to a black hole...the very workings and manipulation of algebra is VERY much needed...he/she will take a derivatives and its summations (integrals i really wanna say) in order to find properties of such a function ... but u can't take the derivative without respect to algbra how about a new simple math of the universal question why? 1+1=1 1-1=-1 -1+1=-1 -1-(-1)=-1 you see, any way you add or subtract the only true numbers of the universe, (ie 1 and -1) you will always get either 1 or -1....ZERO of course is a falicy, an untruth, non-exsistent....and plays no role in the universe....to make it simpler there is -1 and +1....or just - and +.... Most will say that this is just too simple, but then maybe it is just this simple...at least to the question why?... i was about to question if that was Boolean algbra..but i see that it isn't....well u might have a case with 1 and possibly -1..i still like to think that if u have 1 and u can explain it, then u can have any other number as well...but going back to your point ...the zero i am going to have to disagree with....zero is very much an existing, unexistable thing..hope that made sense ...to paraphrase what Ron had stated early, it wasn't easier to conceive of such a notion of 0 b/c u can not point it out in the real and existent world. that is to say that yes we shall call it a number b/c we can generalize it in the real world and say ...1 apple eaten leaves me with no apples how to represent no apples?..we shall say 0 apples are left remaining.,.but i shall correct myself and say, "that apple u just ate does not exist anymore" therefore we shall represent it as 0 apples are left...but it certainly doesnt follow that an apple has never existed or ever shall it just means that specific apple is no longer in existence...thus 0 did that make any sense what-so ever??? And I would ask you mathematicians for the odds of how many and how similar, would other beings in the universe be...given that the universe is made up of pretty much all the same materials and or elements known to us, i think one would need a team composed of a biologist as well and chemist and physicist and mathematician maybe...if there was water on a plant..then these scientist would be able to deduce some sort of a conclusion....indeed math couldn't possibly tell all about appearance alone without the aid of the other subjects As to the validity of different sciences and their breakdowns and divisions....they can be treated as they have in their own little worlds, as those so minded or those so closed minded, in each specific field of their choice have become.... I have watched and seen, and followed the progress of many brilliant minds in many fields, and am amazed to see so many wearing blinders. They become so intense on just one thing, that they lose sight of perspective and common sense, and it only slows their work down to a crawl.. when if they would step back and look around them and explore other not so obvious possibilities that may at first not seem valid to their work but may indeed hold the key they are searching for...that and the overlooking of the most obvious and simple solutions ... VERY TRUE...i believe imagination is much more important that having a 100% sure fire technique and style for trying to answer the turths of the universe...for when a student, let's say of biology, has been through sooo many years of rigorous training that he/she knows the work as is..and therefore becomes a robot to some extent b/c all they can spit back out are just facts that the erring human has related in such a case they will have a hard time facing the unknown for the unknown has not been studied..there fore no texts to which we can get cold ahard facts..therefore imagination is VERY essential..like Einstein lol an imagination he had indeed.Also I am wondering why I have found nothing on the application of super conductor fields being applied to the containment of anti-matter. Couldn't help u with this one..sorry. As for mass accelerating beyond the speed of light becoming energy: If we are to believe Einstein's theory at all then mass, at any speed, is just energy. E=mc^2 proclaims that mass and energy are entirely equivalent. That is, they are nothing but different manifestations of the same thing. But then the theory is one regarding physics, not mathematics. Of course, it makes use of many mathematical concepts in its description, but it is still a theory dealing exclusively with physics. im a bit unsure of what i will say, but i surely dont believe anybody here is denying the such. we are showing the relationship between the two....though the topic at hand seems to deal with math and physics a lot...the topic is of the sciences, all of them,...just at the moment we are dealing with these two since it was a continuation from perspective reality... oh and thank you for stopping by Mathematics as a science is not dependent upon any real phenomenon, physical or otherwise. It is not something God created for us to study. It is, instead, a human invention. no no no ..it is a human discovery. math has always existed...it is possible that our math may be the "wrong" kind of math...but the math we are using helps us to understand the physically universe that has existed for long...if anything..math has been the foundation and heart of such a subject(physics)..i am kinda of tired from replying..but i think this example works okay lol...to say u are cold..does that mean it is b/c u are generated from an ice cube or b/c u touched one? or u were near a glacier??...no it is b/c u are a certain number X in temperature which has given u Y qualities..i hope that was a good example cause im getting really tired now  The other thing u wrote about the function x/0...i wrote proof as to why it doesn't work out mathematically when u divide..but i don't think its too much of the proof but the idea of what it must be that intrigues u..i am unsure, but if u haven't seen the proof, do check it out Trevor: J, what's with the name then? Are Ron and I even correct about the gender? Girlfriend's name? I give, I cry uncle, let us know so I don't feel like a clown. actually i am a male and my name isn't the j component, its the R...its rick the reason i said call me j..meaning short for jnr4eva..but the j is the first letter of my love's name [This message has been edited by JnR4eva (edited 09-06-2000).] |
||
|
Trew Member
since 2000-06-10
Posts 365Ottawa, Canada |
Wow! Quite a discussion going on in here! Just to add my two cents worth (not a 'hard science' guy myself) I have to comment on the math/hard sciences quandry. Is it not true that hard sciences are just as soft as the soft sciences? At one time it was accepted that the sun revolved around the earth, that the earth was flat and that we were the only universe in existence. The newest theory (law) in physics that is currently being dispelled is the speed of light. Researches in the US have accelerated light up to 300x its believed set speed of 186, 000 miles per second. This is acheived by directing the light through specially treated Caesium gas. In following this new set standard, it appears that Einstein's theory of relativity is in jeopardy, due to it's assumption of light speed as a set standard. My view is that hard sciences are simply soft sciences with a better ruler. It takes longer to advance the 'hard sciences' only because we understand them better. This was just some food for thought! Enjoyed reading everything on this topic... Even the math that went about a mile over my head. Trev. |
||
|
Not A Poet Member Elite
since 1999-11-03
Posts 3885Oklahoma, USA |
Well, it seems that most of the discussion here is of topics which are subject to later revision when the scientists actually "discover" more about their respective underlying natures. Therefore, all we can really establish is current thinking or broad speculation. One place where you are quite wrong though jnR is in the "discovery of mathematics". I still maintain that it was not discovered but invented instead. Where have you ever heard of Newton being the discoverer of calculus? I think nowhere. Instead, he is referred to as the "inventor of calculus." The sams is true of all branches and forms of mathematics. Early man found it useful to be able to enumerate things. He most likely started by using his fingers, holding up one finger for each apple he wanted. When quantities got to be more than the available number of fingers, he then discovered he could also use other digits, his toes. (It seems that men have a small advantage over women here.) Eventually, this led to the idea that he could use just the concept rather than the actual digits. At some point, he then discovered that but conceptualizing, he could enumerate many more items than he had digits. Man, being the thinking animal he is, soon began to extrapolate on the concept of enumeration and some sage discovered that he could define lengths and widths as so many conceptualized units. He also found that it was useful to do simple arithmetic so he defined rules as to how these functions would be performed. This eventually led to the ability to quantify. This is not some natural phenomenon but just a tool by which we describe nature and our environment. As an example, I would refer you to Euclidian geometry, surely one of the purest and most logical forms of mathematics. But if you review its basis in fact, you will find that there are several axioms upon which the entire science is based. Now there is little doubt that these axioms accurately represent the real world, at least as it was perceived at that time. One of the most basic of these paraphrased is "there is one and only one straight line which passes between two points." The more we study and question this axiom (using, of course, really logical and valid means) the more we become convinced that it is true, a fact of nature. Armed with this information, we are inclined to accept it as fact. Hence, we accept it as an axiom, something which neither requires nor is capable of proof. We then build the entire "science" of geometry upon this and a few other axioms, all of which share that same proof trait. Then I would refer you to Einstein's book "Relativity: The Special And General Theory." In it he very clearly explains why this cannot be true in the general sense. I feel certain that his discussion, as well as that of many others, will convince you that mathematics is an invented tool rather than a discovered science. Just as Newton invented calculus because he needed a tool to explain the actions of a moving body, all of mathematics was invented because some scientist needed a tool to explain some natural phenomenon or some accountant (tongue-in-cheek) needed a tool to quantify or enumerate his assets. If you do change your major to astronomy, you will eventually believe all this (well, most of it). Mathematics has long been called the "queen of sciences" but mostly by mathematicians. I know, my undergrad degree was mathematics and it is still my first love. I also taught math for a few years at a medium sized university. But I have another degree in physics. So I do have a respect for all those other scientists who must discover and try to explain their chosen fields. Well, I begin to ramble too much here so better get back to work for a while. Pete BTW Steve, another interesting and appropriate quote, I believe it was Mark Twain: "Man is the only animal that blushes -- or needs to" |
||
|
Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
Pete, I'm going to both agree and disagree. I will concur that mathematics is, in its entirely, purely an invention of mankind. But so, too, are the laws of gravity. And it still hurts like hell when you fall down. The difference between "discovered" and "invented" is a semantical one, I think. Would the telephone exist had not Bell (or someone) invented it? No, of course not. Would I still avoid ice skating even if Newton and Einstein hadn't quantified gravity. You bet. And the truth of 2 + 2 equals 4 would still exist even had mankind not "invented" mathematics. Now, I'll flip over to the other side of that fence by granting that our "discovery" of mathematics has too often been muddied by our "invention" of mathematics. Case in point, another one of Euclid's axioms essentially states that parallel lines never join no matter how far they are extended - and most agree it is the only axiom that is not self-evident (though in today's world of relativity and quantum mechanics, one must question whether "self-evident" has much meaning any longer). Euclid's first four axioms could each be stated in less than a dozen words, but this fifth nonintuitive axiom required nearly as many as the other four combined. It just didn't seem right, and mathematicians spent a few hundred years trying to show it could be derived from the first four. It couldn't. And, of course, modern science gives us a lot of good reasons to think it's likely not true. Did Euclid "discover" four Truths and "invent" a falsehood? Personally, I think it was a little bit of both. Mathematics exists separate from humanity's discovery of its usefulness, but - as in every other science - our understanding is often less than perfect. And it is our understanding we have invented. |
||
|
Not A Poet Member Elite
since 1999-11-03
Posts 3885Oklahoma, USA |
Hello Ron, Well I think we are pretty much saying the same things here. But again, there is a small semantic difference. You said the laws of gravity were invented. That, of course, is untrue. The laws of gravity are there and always have been. It is our perception of those laws, the quantification thereof, which was invented. This was done through the use of invented mathematics. As such they are subject to revision as we learn more about them but the laws themselves are natural. As you say, it hurts like hell when you fall down, regardless of whether you are able to quantify the actual impact or not. Again, you are right when you question the realities of parallel lines not crossing and in fact, that is exactly the line of reasoning Einstein used in his book I referred to above. Pete BTW, I slightly misstated the book title above. It properly is: "Relativity: The Special and the General Theory" ISBN: 0517029618. This is a revealing and interesting book, translated to English by a British professor (I don't have his name right now). For the most part, it is readable and useful to most people, whether educated in math and physics or not. I highly recommend it to anyone who has an interest in the subject. |
||
|
Local Rebel Member Ascendant
since 1999-12-21
Posts 5767Southern Abstentia |
Heisenberg Uncertainty Principle An odd aspect of Quantum Mechanics is contained in the Heisenberg Uncertainty Principle (HUP). The HUP can be stated in different ways, let me first talk in terms of momentum and position. If there is a particle, such as an electron, moving through space, I can characterize its motion by telling you where it is (its position) and what its velocity is (more precisely, its momentum). Now, let me say something strange about what happens when I try to measure its position and momentum. Classically, i.e., in our macroscopic world, I can measure these two quantities to infinite precision (more or less). There is really no question where something is and what its momentum is. In the Quantum Mechanical world, the idea that we can measure things exactly breaks down. Let me state this notion more precisely. Suppose a particle has momemtum p and a position x. In a Quantum Mechanical world, I would not be able to measure p and x precisely. There is an uncertainty associated with each measurement, e.g., there is some dp and dx, which I can never get rid of even in a perfect experiment!!!. This is due to the fact that whenever I make a measurement, I must disturb the system. (In order for me to know something is there, I must bump into it.) The size of the uncertainties are not independent, they are related by dp x dx > h / (2 x pi) = Planck's constant / ( 2 x pi ) The preceding is a statement of The Heisenberg Uncertainty Principle. So, for example, if I measure x exactly, the uncertainty in p, dp, must be infinite in order to keep the product constant. This uncertainty leads to many strange things. For example, in a Quantum Mechanical world, I cannot predict where a particle will be with 100 % certainty. I can only speak in terms of probabilities. For example, I can say that an atom will be at some location with a 99 % probability, but there will be a 1 % probability it will be somewhere else (in fact, there will be a small but finite probabilty that it will be found across the Universe). This is strange. We do not know if this indeterminism is actually the way the Universe works because the theory of Quantum Mechanics is probably incomplete. That is, we do not know if the Universe actually behaves in a probabilistic manner (there are many possible paths a particle can follow and the observed path is chosen probabilistically) or if the Universe is deterministic in the sense that I can predict the path a particle will follow with 100 % certainty. A consequence of the Qunatum Mechanical nature of the world, is that particles can appear in places where they have no right to be (from an ordinary, common sense [classical] point of view)! |
||
|
Local Rebel Member Ascendant
since 1999-12-21
Posts 5767Southern Abstentia |
So if you give me a penny for my thoughts: In a universe of uncertainties... therefore... I would postulate that the only 'hard' science is one that measures probabilities -- and that is Statistics -- an application of Math -- not Math itself... and there's my two cents... a bargain since you only gave me a penny.. |
||
|
Not A Poet Member Elite
since 1999-11-03
Posts 3885Oklahoma, USA |
Rebel, That was very well stated and explained. I particularly liked your "bump into it" description. That makes more sense to the layman than the traditional "cannot observe without interference." Your bringing up the uncertainty principle reminds me of a slightly eccentric physics prof I once had. Like most, he wrote a lot of stuff on the chalkboards. Also like most, he broke a lot of chalk in the process. Well, he had this unique and quirky habit of always looking up instead of down when one broke (and always fell to the floor). When asked by inquisitive students why he did this, his response was, quote: I probably don't need to say that he was an outstanding teacher. Pete [This message has been edited by Not A Poet (edited 09-07-2000).] |
||
|
Local Rebel Member Ascendant
since 1999-12-21
Posts 5767Southern Abstentia |
Sounds like a teacher I would've liked to have had.. thanks Pete |
||
|
JnR4eva Member
since 2000-08-07
Posts 377Bronx, NY |
"Is it not true that hard sciences are just as soft as the soft sciences?At one time it was accepted that the sun revolved around the earth, that the earth was flat and that we were the only universe in existence." trew thank you for stopping by and putting in ur two cents.. now about this comment, u might be able to debate and argue for ur positon..but then again its all a matter of language...when we say 'soft' we mean in respect to the fact that it deals with interpretation and subjectivity...certainly u could not provide a universal truth as to why children start crying in the bank with their mothers...but it has been justified how those tears do come out of those child's eyes i understand very much that ur saying sciences undergo interpretations just as psychology...but scientific findings are based on what the world has provided for us...i may say that back in the day sciences weren't as rigid as they are today and that's why ur statement now holds true..but to say now that the derivative of velocity = acceleration is just one man's interpretation..well u better provide some strong evidence stating how so! "The newest theory (law) in physics that is currently being dispelled is the speed of light. Researches in the US have accelerated light up to 300x its believed set speed of 186, 000 miles per second. This is achieved by directing the light through specially treated Caesium gas. In following this new set standard, it appears that Einstein's theory of relativity is in jeopardy, due to it's assumption of light speed as a set standard." thank you for this bit...certainly is something to look into. "One place where you are quite wrong though jnR is in the "discovery of mathematics"" not a poet...ur absolutely right...it wasn't discovered, though i wish not to excuse myself...i think i should be given a pardon b/c when i wrote up that reply i was VERY tired...it was invented...but it doesn't mean that it hasn't always existed with out or knowing..i believe you and Ron have discussed it and came to a conclusion which is pretty sound so no need for me to add on to what was already said "Then I would refer you to Einstein's book "Relativity: The Special And General Theory."" At the time I am reading, or trying to finish, a book called the elegant universe by brain greene..it is about the superstring theory and it covers, in an undergraduate way lol, some of the basic principles of Quantum physics and theory of relativity and a whole slew of topics that the strong theory is trying to enmesh into one "one theory of a unified everything" but thank you for the recommendation. "Mathematics has long been called the "queen of sciences" but mostly by mathematicians." would physics be the king?? let me know lol hello local rebel.. thank you for stopping by and giving us that explanation to HUP.. i can not say much about it b/c i am not learned in that field...but from my understanding physics is built on two pillars...one being Quantum mechanics (the study of our world in its smallest of size) and the theory of relativity (the study of our world in the biggest of all sizes such as galaxies and such)...and though I know the two beliefs are incompatible however does the theory of relativity take into account this particle that has the possibility of being somewhere it isn't supposed to be? Can it better explain why, or rather show how, this particle is where it is supposed to be as opposed to the HUP? "In a universe of uncertainties ... therefore... I would postulate that the only 'hard' science is one that measures probabilities -- and that is Statistics -- an application of Math -- not Math itself..." sorry im gonna have to go against this one..statistics is certainly beautiful and great but it does not do what physics does. it doesn't do what math does..i mean lets just say this...u put ur trust into an apple, but not its core? u put more trust into statistics but not the math that makes statistics what it is? statistics will never fathom what physics has proven....i certainly understand where u were probably going with ur statement..but u seem to neglect the fact that math and physics have approximations and likelihood's within their laws as well like (when calucating bounds of error, and probality theory)...not everything is an absolute number..the hypotenuse, of an isosceles triangle with legs 1, has the length of an infinite number..so what to do? well round off the number and u have urself the length...just like in physics when one tries to find tensions in pulling block A (lol sorry i had to incorporate my homework into this lol ) it is ideal to find a whole number..but approximations are just as good not a poet... cool teacher. [This message has been edited by JnR4eva (edited 09-08-2000).] |
||
|
Ron
Administrator
Member Rara Avis
since 1999-05-19
Posts 8669Michigan, US |
quote: For those interested, here's the original article in Nature, a very prestigious science journal. The findings are, indeed, very important. But, sadly, the results were entirely blown out of proportion by the media. Hey, we all know the newspapers love snappy headlines. The experiment involves sending a pulse of light through a chamber filled with a caesium vapor. Think about it. A pulse of light is not a simple object. It is not infinitely short in time, nor in space. The shape of the pulse is the critical part of the experiment. Any light pulse can be thought of as starting with an intensity smoothly rising from zero up to a maximum value and then dropping away again. When you tell me the "burst" of light exited before it had fully entered, you have to also tell me which part of the burst you were measuring. The leading edge? The peak? It makes a difference. What essentially happens (some think) is that the leading edge is "rebuilt" into a burst of lesser light (dimmer) of exactly the same "shape." If you are measuring the peak of the burst entering, you seem to see the peak leaving more quickly than can be accounted for in relativistic terms. But, in reality, you are seeing the leading edge leave. The really critical factor, however, is that no information can be transmitted in this manner. If you wish to actually transmit information, you need to measure more of the pulse. When you work out the details, it turns out that you need to measure enough of the pulse to bring the total transmission speed back down below the speed of light in a vacuum. For a more balanced view of the experiment (something you won't find in many places), here's an article by Chris Colin at Salon.com quote: Einstein did not like quantum theory. One of his more famous quotations was, "I refuse to believe that God plays dice with the Universe." During the 1930's Einstein and Niels Bohr fought tooth and nail over the particulars. And of course, Einstein spent most of the next 25 years, until his death in 1955, trying to unseat quantum mechanics. I mention this because the "cannot observe without interference" interpretation of HUP was Einstein's. He wanted very much to believe the consequences of HUP were simply a reflection of our own clumsiness. The standard interpretation of quantum physics, known as the Copenhagen Interpretation, was established largely through the efforts of Bohr, who argued that the fuzziness was an intrinsic feature of the quantum world, and that within the limits set by Heisenberg's uncertainty principle an electron itself does not "know" both where it is and where it is going. (Incidentally, momentum and position are not the only complimentary properties that cannot be measured simultaneously. Spin, for example - or more correctly, angular momentum - can never be measured accurately in more than one axis.) If you accept Einstein's interpretation, then HUP is simply a consequence of our own limitations. But if you accept the Copenhagen Interpretation, it goes a long way towards explaining some of the paradoxes of modern science. For example, in other threads, we've occasionally mentioned the fact that light (and we're discovering just about everything else, right up to molecules) seems to exist as both a wave and as particles. Some of its characteristics can only be explained as a wave function, others by assuming it is composed of particles. Einstein's own Nobel Prize, by the way, wasn't for Relativity, but rather for showing the particle nature of light (the photon). In one of the most ironic examples of wave-particle duality, the physicist J. J. Thomson received a Nobel Prize for discovering that the electron is a particle, while his son George received a Nobel Prize for proving that the electron is a wave. This wave-particle duality is linked with the uncertainty principle. "Waviness" is a property associated with momentum - a typical wave is spread out, so it has no definite location in space, but it does have a direction in which it is going. By contrast, a particle can have a precisely defined position. Heisenberg found that the quantum equations imply a strict tradeoff between the two complementary properties. If the position of a quantum entity is precisely defined (for example, when it hits a detector screen), its waviness is suppressed; but if it is allowed to give full expression to its wave nature, the particle aspect vanishes. Sound confusing? Think of it this way, then. Photons and electrons travel through space as particles. Given their direction, we cannot then tell exactly where they are. But we can predict approximately where they will be through probabilities. And if you graph those probabilities? By golly, it looks just like a wave! |
||
|
Not A Poet Member Elite
since 1999-11-03
Posts 3885Oklahoma, USA |
Ron, Excellent explanation. You mentioned a few things in there which I either hadn't heard or had forgotten, or both. I particularly appreciated your debunking of the media's hyping of the recent "faster than a speeding photon" experiment. In fact, I had just captured the same quote you did to write my own answer. But I find that I like yours better. but there is one thing which hasn't been mentioned yet, and it is VERY IMPORTANT. Einstein's theory of relativity states that the fixed speed of light IN A VACUUM is 3x10^8 meter/sec. There is nothing in that statement which would preclude light from traveling faster in some specially prepared medium. However, your further discussion IMO explains why the experiment may not mean anything at all. I say that because it exactly matches my thinking on the subject. Also, you are quite right in stating that Einstein didn't like the concept of quantum theory and spent much of his life trying to disprove it. Personally, I'm not sure that he didn't believe it so much as he wanted a more logical explanation or theory. It is interesting though that one of the important tools of quantum mechanics is Bose-Einstein statistics, although I cannot remember what is its purpose (attribute that to brain atrophy and a long time since used I'm afraid). So, it looks like you saved me not only a bunch of writing but also a bunch of thinking which would have gone into that writing. Pete Never express yourself more clearly than you can think - Niels Bohr |
||
|
Local Rebel Member Ascendant
since 1999-12-21
Posts 5767Southern Abstentia |
and having said all that Ron... I'm a subscriber to String Theory myself... best I've yet seen for GUT...thanks for your post man.. no time to write more right now... sorry... |
||
|
|
⇧ top of page ⇧ |
|
| All times are ET (US). All dates are in Year-Month-Day format. | ||
