Christer said:
Understanding is a matter of degree; it's not an all or nothing thing. The "just get used to them" people just understand the concepts enough to use them in practice, rather than understanding their raison d'etre.
You just about equated understanding with intuition. Yet a person can understand unintuitive things, as long as they can be broken down into the appropriate level(s) of abstraction, where the necessary concepts are already integrated into the person's semantic memory. An understood concept can be explained by describing at a lower level of abstraction; a person, however, cannot introspect and likewise describe his/her intuition.
Prune said:
Sure, and I am sure Hardy, or whoever it was, didn't meant
that too literally, but I think there is still a lot of truth to it.
Some things you just have to try to accept at first, and then
hopefully they sink in over time and you gain an increased
understanding of them.
Not sure if this is quite what you mean, but if you know some
logic, you can usually break down an argument into smaller
manageable pieces you understand and then use logic deduction
to derive the original concept from these. That may be a
convincing proof, but it is not necessarily easy to grasp the
whole, despite being able to understand the pieces and put
them together. I have proved many theorems in my research
where the proofs run up to ten or twenty pages. Although I
carefully evaluate it and convince myself that the logical
reasaoning is correct, I sometimes have a hard time convincing
myself that the proof as a whole is correct since it becomes too
complex to grasp and the intuition is lost in the myriad of details.
Hi,
Suffered from that disease since my childhood...It kept me awake all night and convinced the other kids I was errr..: "different"
After twenty years of heavy sedation, desperately trying to kill off as many braincells as I possibly could, I finally succeeded to blend in with the average crowd...
I'm much happier now....
Finally, after much hesitation, I took an apple in both hands and joined both hands...Suddenly it hit me!
When I join one to the other I have two?
Mathematically yes, in reality, no.
At the end of the day I decided to stop worrying about it and try to make a living for myself and have a life...
I knew it would be hard as there would be little communication between me and all the ordinary people...
Tell me, how can you relate to the ordinary? These people are so down to earth it shatters all your absurd and mind twisting theories that there's just no way they could possibly understand your musings....
You won't let it drive you bonkers either so what do you do?
Kill the excess hyperactive braincells...Hold on...Seems I still carry an excess of those...
Intelligence is a curse, let me tell you........It's driving me nuts, messes up my social life...Bah.
Is this feeling familiar to any of you?
Enjoy the little parody,😉
Suffered from that disease since my childhood...It kept me awake all night and convinced the other kids I was errr..: "different"
After twenty years of heavy sedation, desperately trying to kill off as many braincells as I possibly could, I finally succeeded to blend in with the average crowd...
I'm much happier now....
Finally, after much hesitation, I took an apple in both hands and joined both hands...Suddenly it hit me!
When I join one to the other I have two?
Mathematically yes, in reality, no.
At the end of the day I decided to stop worrying about it and try to make a living for myself and have a life...
I knew it would be hard as there would be little communication between me and all the ordinary people...
Tell me, how can you relate to the ordinary? These people are so down to earth it shatters all your absurd and mind twisting theories that there's just no way they could possibly understand your musings....
You won't let it drive you bonkers either so what do you do?
Kill the excess hyperactive braincells...Hold on...Seems I still carry an excess of those...
Intelligence is a curse, let me tell you........It's driving me nuts, messes up my social life...Bah.
Is this feeling familiar to any of you?
Enjoy the little parody,😉
SY said:
I guess my assumption is at that physicists deep into QM etc. are so permeated by the relevant formalisms that their intuitions are substantially mathematical, though I understand this was not the case with Einstein for either special or general relativity. And perhaps of some relevance is that despite his marvelous paper on photon stimulated electron emission, QM was not for him.
From my layman's understanding of string theory it seems that those little vibrating strands have as much to do with our intuitions regarding a violin string as our intuitions of spin on a billiard ball have to do with electron spin. By which I mean it seems that it is formal abstractions that justify, if not first suggest, these physical models, not the other way around. And the more closely one looks at these things the more necessarily formal the ideas become while "physical" models become not only less relevant but more implausible.
SY said:
Am I mistaken or isn't that as much a problem of explaining to someone that their intuitions and first hand experiences of reality are inadequate for an understanding of its form and substance at anything deeper than its surface features as it is a problem of explaining that much of the salience of physical reality is only assessable with some degree of mathematical sophistication?
eStatic (who hasn't got much--sophistication--but boy can he digress 🙁 )
Disabusing people of their notions of what is "logical" can be a real challenge. People conflate "logical" for "the way I think the Universe works."
Re: Re: Re: 1+1=?
Yep. That's the way my 5.5 years old daughter "computes"...
Sum it up : 1+1=11 for largely large values of 1 ... 😉
But remember : "The answer is 42"
Stopping thread hijacking now...
HiggityHank said:
Yep. That's the way my 5.5 years old daughter "computes"...
Sum it up : 1+1=11 for largely large values of 1 ... 😉
But remember : "The answer is 42"
Stopping thread hijacking now...
Re: Re: Re: Re: 1+1=?
Exactly. Taking this further: The whole confusion laymen have about wave particle duality (so is it a particle or a wave?...) is that waves and particles are stupid analogies -- quanta are neither waves nor particles. It just so happens that some of the equations look like those for waves, and some like those for particles. Indeed, it is waves and particles (and other things we can perceive through our senses) that are unreal, illusions built up on a quantum reality that has no correspondence to anything in we can directly sense. Of course that 'reality' may itself be illusory, but is the most fundamental we have with current science and can practically work with.
Ouch. I think my head just exploded
eStatic said:
Exactly. Taking this further: The whole confusion laymen have about wave particle duality (so is it a particle or a wave?...) is that waves and particles are stupid analogies -- quanta are neither waves nor particles. It just so happens that some of the equations look like those for waves, and some like those for particles. Indeed, it is waves and particles (and other things we can perceive through our senses) that are unreal, illusions built up on a quantum reality that has no correspondence to anything in we can directly sense. Of course that 'reality' may itself be illusory, but is the most fundamental we have with current science and can practically work with.
CheffDeGaar said:
Ouch. I think my head just exploded
fdegrove said:
I don't worry so much about it in everyday life, since I don't
usually try to prove everything. Professionally, on the other
hand, I have to worry about such things since part of my
work is to prove things mathematically and to analyze other
peoples proofs.
It can pop up, though, in electronics for instance, when trying
to understand something in an app note, or my own calculations.
Every single step and formula seems OK, but it is still difficult
to get the intuition of the result. Just found an app note the
other day that finally made me understand a thing of that
type by adding a brief comment that gave the intuition. Actually
the problem was just as much with other app notes claiming
a simplified and wrong interpretation of the results.
Re: Re: Re: Re: 1+1=?
Don't worry Cheff. Your daughter is probably still counting
in unary notation, then 1+1=11 is correct. Next year she
may have advanced to the computer level of binary notation,
then she will get it to 10 instead. Then she will get past the
computer level and realize she has ten fingers and get the
usual result of 2. Just make sure she stops there and doesn't
start to count her toes also. She may get difficulties in life if
she insists on counting with base 20. 🙂
CheffDeGaar said:
Don't worry Cheff. Your daughter is probably still counting
in unary notation, then 1+1=11 is correct. Next year she
may have advanced to the computer level of binary notation,
then she will get it to 10 instead. Then she will get past the
computer level and realize she has ten fingers and get the
usual result of 2. Just make sure she stops there and doesn't
start to count her toes also. She may get difficulties in life if
she insists on counting with base 20. 🙂
Re: Re: Re: Re: Re: 1+1=?
Hi,
Some guys only count to eleven:
http://www.diyaudio.com/forums/showthread.php?postid=281474#post281474
Sorry couldn't not resist. It all fits in place now......
Christer said:
Hi,
Some guys only count to eleven:
http://www.diyaudio.com/forums/showthread.php?postid=281474#post281474
Sorry couldn't not resist. It all fits in place now......
fdegrove said:
Naaa. No problem. I just spend my "social" time with cattle, horses and dogs. BTW cattle are quite amicable creatures for the most part. And generally better company than most (but not all) simians I know. When I get to the feed store I just put a stupid grin on my face (comes quite naturally) and say "Howdy!" Works every time.
eStatic
eStatic said:
Oh, so that's why cows have started going mad also over
there? You talk to much philosophy and math with them.
They can't take too much of that, you know. 🙂
Re: Re: Re: Re: Re: 1+1=?
I am only a layperson who loves physics and has studied it within the limits of a relatively short mathematical reach. But Prune, I will have to take some exception to the statement
Part of the problem seems to me that there is no wave/particle duality, rather a wave/particle paradox. If an object walks like a wave and quacks like a wave I think we are well justified in using that term to describe those properties. It is good and helpful. Further is seems unlikely that a physicist uses the term wave without an implicit formal definition in mind. The problem is that most laypeople do not grasp the magnitude of the error made when one assumes our physical intuitions about waves, or what ever, derived from macroscopic experience will serve in other contexts.
And I am certainly no philosopher but I feel this is not correct. " Things we can perceive through our senses" are (for the most part) surely as real as our abstract scientific models. The problem is that the surface features of reality are not a reliable guide to its deeper structures and significance. Again and as SY has pointed out we are want to err in that direction.
eStatic
I am only a layperson who loves physics and has studied it within the limits of a relatively short mathematical reach. But Prune, I will have to take some exception to the statement
Prune said:
Part of the problem seems to me that there is no wave/particle duality, rather a wave/particle paradox. If an object walks like a wave and quacks like a wave I think we are well justified in using that term to describe those properties. It is good and helpful. Further is seems unlikely that a physicist uses the term wave without an implicit formal definition in mind. The problem is that most laypeople do not grasp the magnitude of the error made when one assumes our physical intuitions about waves, or what ever, derived from macroscopic experience will serve in other contexts.
Prune said:
And I am certainly no philosopher but I feel this is not correct. " Things we can perceive through our senses" are (for the most part) surely as real as our abstract scientific models. The problem is that the surface features of reality are not a reliable guide to its deeper structures and significance. Again and as SY has pointed out we are want to err in that direction.
eStatic
Re: Re: Re: Re: Re: Re: 1+1=?
Good point, and there are cases where models different from
physically correct ones have been developed based on human
perception instead. Incidentally I recently referred to one
such case in another thread, regarding models of colours
http://www.diyaudio.com/forums/showthread.php?postid=300021#post300021
eStatic said:
Good point, and there are cases where models different from
physically correct ones have been developed based on human
perception instead. Incidentally I recently referred to one
such case in another thread, regarding models of colours
http://www.diyaudio.com/forums/showthread.php?postid=300021#post300021
Re: Re: Re: Re: Re: 1+1=?
Sorry, to revisit this but it's bothering me even while I try to do chores, as I can see no justification for the analysis. The results of QM (as well as relativity) converge smoothly to those of Newtonian mechanics as one moves from their relevant scales to the scale of every day experience. You could construct a fluid dynamics out of QM and get results perfectly consistent with classical derived fluid dynamics in its description of the motion of waves at sea. We don't do this simply because QM is a big pain in the butt when used this way, and its results are, practically speaking, no better; not because it "has no correspondence to anything in we can directly sense."
Or did I miss something?
eStatic
Prune said:
Sorry, to revisit this but it's bothering me even while I try to do chores, as I can see no justification for the analysis. The results of QM (as well as relativity) converge smoothly to those of Newtonian mechanics as one moves from their relevant scales to the scale of every day experience. You could construct a fluid dynamics out of QM and get results perfectly consistent with classical derived fluid dynamics in its description of the motion of waves at sea. We don't do this simply because QM is a big pain in the butt when used this way, and its results are, practically speaking, no better; not because it "has no correspondence to anything in we can directly sense."
Or did I miss something?
eStatic
A deer, a female deer
"Whi-ich brings us back to Do!"
A not unimportant point about scale you bring up. Let's say you solved (at least to a high degree of approximation) all the QM equations to understand the change in electronic density with time and space in the innards of a simple calculator- the positions of every copper nucleus, the states of all the core, valence, and conduction band electrons, the electron density changes in the circuit board, the crystalline structure of the silicon, etc, etc, etc. What insight would that enormous/overwhelming amount of information give you toward understanding the calculator's actual function, i.e., 1 + 1 = 2?
Sometimes it really IS best to not pay attention to the details.
"Whi-ich brings us back to Do!"
A not unimportant point about scale you bring up. Let's say you solved (at least to a high degree of approximation) all the QM equations to understand the change in electronic density with time and space in the innards of a simple calculator- the positions of every copper nucleus, the states of all the core, valence, and conduction band electrons, the electron density changes in the circuit board, the crystalline structure of the silicon, etc, etc, etc. What insight would that enormous/overwhelming amount of information give you toward understanding the calculator's actual function, i.e., 1 + 1 = 2?
Sometimes it really IS best to not pay attention to the details.
Re: Re: Re: Re: Re: Re: 1+1=?
There's only a paradox when trying to reconcile one's concept of a wave with one's concept of a particle: obviously they are incompatible. But obviously such mathematical descriptions both apply to quanta, and the paradox is nothing but our necessary failure to imagine what a quantum is 'really' like -- we can't, it's not directly perceived through our senses (well we perceive photons for example, but that doesn't give you a feel for what a photon is like).
Sure. In the appropriate circumstances, and in the mathematical sense of a wave. The problem is when you use the analogy to 'help' explain the concept to a nonscientist, whose concept of a wave is not mathematical but what they've seen in the macro world.
Well that's part of what I'm saying.
Yes, when you look at the ocean you don't see a bunch of molecules. But that doesn't mean they are not there. We can even see them on an electron microscope.
Sorry for my loose use of the word 'real'. Of course there are various appropriate levels of abstraction depending on context. I was refering to the lowest level that we can achieve in physics, and as I've claimed before as a reductionist, all is built up from this level. But of course like everybody else, I do not deal with the world at this level in everyday life.
So what? Colour models involving perception do not need to be physically based exactly because they involve perception.
I think now that I've clarified that I was refering to the lowest level of description as the closest to reality because it is a foundation upon which the rest is built, there should be no problem (other than of course reductionism, which was already discussed previously in this thread).
eStatic said:
There's only a paradox when trying to reconcile one's concept of a wave with one's concept of a particle: obviously they are incompatible. But obviously such mathematical descriptions both apply to quanta, and the paradox is nothing but our necessary failure to imagine what a quantum is 'really' like -- we can't, it's not directly perceived through our senses (well we perceive photons for example, but that doesn't give you a feel for what a photon is like).
Sure. In the appropriate circumstances, and in the mathematical sense of a wave. The problem is when you use the analogy to 'help' explain the concept to a nonscientist, whose concept of a wave is not mathematical but what they've seen in the macro world.
Well that's part of what I'm saying.
Yes, when you look at the ocean you don't see a bunch of molecules. But that doesn't mean they are not there. We can even see them on an electron microscope.
Sorry for my loose use of the word 'real'. Of course there are various appropriate levels of abstraction depending on context. I was refering to the lowest level that we can achieve in physics, and as I've claimed before as a reductionist, all is built up from this level. But of course like everybody else, I do not deal with the world at this level in everyday life.
Christer said:
So what? Colour models involving perception do not need to be physically based exactly because they involve perception.
eStatic said:
I think now that I've clarified that I was refering to the lowest level of description as the closest to reality because it is a foundation upon which the rest is built, there should be no problem (other than of course reductionism, which was already discussed previously in this thread).
Re: Re: Re: Re: Re: Re: Re: 1+1=?
Actually, if I understand you, I think you may be wrong. As I understand them, both the elementary equation of the frequency of a deBroglie wave and the Schrodinger Wave Equation are equations where mass is a dependent variable that acts as a scale behavior control. That is, as the mass increases the wavelength decreases--eventually to the infinitesimally small and wave phenomena fade away to the imperceptible. At the mass of an electron the wavelength is long enough to be easily detected. A baseball has a wavelength and theoretically exhibits wave phenomena. It's just that when you plug in the values for a baseball the resulting wavelength is so small it leaves the baseball acting like a particle.
The basis for my objection to notion of duality is that it can leave the impression that this is a state of affairs that one is to get used to, but not to understand. And that is consistent with the standard QM interpretation. But there are others. I am a fan of the Many Worlds Interpretation of QM and it provides a resolution to that paradox.
eStatic
Prune said:
Actually, if I understand you, I think you may be wrong. As I understand them, both the elementary equation of the frequency of a deBroglie wave and the Schrodinger Wave Equation are equations where mass is a dependent variable that acts as a scale behavior control. That is, as the mass increases the wavelength decreases--eventually to the infinitesimally small and wave phenomena fade away to the imperceptible. At the mass of an electron the wavelength is long enough to be easily detected. A baseball has a wavelength and theoretically exhibits wave phenomena. It's just that when you plug in the values for a baseball the resulting wavelength is so small it leaves the baseball acting like a particle.
The basis for my objection to notion of duality is that it can leave the impression that this is a state of affairs that one is to get used to, but not to understand. And that is consistent with the standard QM interpretation. But there are others. I am a fan of the Many Worlds Interpretation of QM and it provides a resolution to that paradox.
eStatic
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