about maths: strictly speaking, off topic, but justified.
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From: J. Clarke on 14 Mar 2010 22:13 On 3/14/2010 7:43 PM, rabid_fan wrote: > On Sun, 14 Mar 2010 15:24:02 -0700, tonyb wrote: > >> My question is really about evidence and >> inductive reasoning. For example, we would probably agree that there is >> a large amount of consistent phenomena/data indicating the existence of >> the electron, less for a gluon, or a Higgs Boson. > > The evidence is incomplete. More will come in the future if > our "elected" politicians have the wisdom to divert the resources > of our civilization toward continued and expanding research. > > >> In machine learning, questions like this would be stated in terms of >> Hypothesis X havibg a probability P, based on the likelihood of the data >> and our model. >> Yet when we talk about fundamental particles (and processes) it sounds >> almost as if they are handled (roughly speaking) as either concrete or >> conjectured (P=1 or P=small) but there doesn't seem to be an attempt to >> use probability and likelihood (aka Bayesian networks) to quantify this. >> >> So my question is really about how we/do we deal with this system of >> apparent probabilities into our reasoning (personally, as Scientists.) > > I do not understand what is being asked. > > But, we cannot know what a particle *is*, we can only know > how it behaves. A particle is a solution (function) to an > equation. > > Probability is the new determinism and certainty. > > The sooner we stop trying to grasp the nature of a particle > with our inborn tools of comprehension, the better off we will > be. In other words don't try because the problem is hard?
From: rabid_fan on 14 Mar 2010 23:02 On Sun, 14 Mar 2010 22:13:45 -0400, J. Clarke wrote: >> >> The sooner we stop trying to grasp the nature of a particle with our >> inborn tools of comprehension, the better off we will be. > > In other words don't try because the problem is hard? No. In other words the human organism is not equipped to comprehend quantum phenomena. Inborn tools of comprehension. Get it? They are what has been endowed to us by the evolutionary development of life on this planet. That hunk of jelly within our skulls can only do so much. Our concept of a particle, i.e. a localized bit of matter that can follow a well defined trajectory, cannot be extended downward into sub-atomic realms. Whatever happens in that minute world cannot be envisioned by the human brain. Only mathematics can allow us to get a handle on the reality of the quantum events.
From: tonyb on 15 Mar 2010 05:58 On 14 Mar, 23:43, rabid_fan <r...(a)righthere.net> wrote: > On Sun, 14 Mar 2010 15:24:02 -0700, tonyb wrote: > >large amount of consistent phenomena/data indicating the existence of > > the electron, less for a gluon, or a Higgs Boson. > > The evidence is incomplete. > > > In machine learning, questions like this would be stated in terms of > > Hypothesis X havibg a probability P, based on the likelihood of the data > > and our model. okay, just to be clear, I'm not talking about probability in relation to wave equations. I'm talking about the probability that a descriptive mathematical statement about the behaviour of a phenomena is correct. > > > So my question is really about how we/do we deal with this system of > > apparent probabilities into our reasoning (personally, as Scientists.) > > I do not understand what is being asked. > > But, we cannot know what a particle *is*, we can only know > how it behaves. A particle is a solution (function) to an > equation. > > The sooner we stop trying to grasp the nature of a particle > with our inborn tools of comprehension, the better off we will > be. okay, I'm with you here. We can't perceive these quantum phenomena directly. In fact, I'd also argue that we can't perceive *any* phenomena directly, as 'the thing in itself' - for example, our eyes use light as a probe particle; our ears infer vibration energy from external objects and our mind uses all the data from our senses in unison, cross-referencing to infer secondary information. (this is the cause of a 'p'/'b' illusion) So I guess what your saying is that we have no intellectual intuition about the behaviour of these particles, because they are new phenomena presented to our minds via the enhanced senses of our apparatus e.g. the LHC detectors. Our minds haven't evolved a pre-existing apparatus for these phenomena (e.g. in contrast to the pre-existing apparatus that children have to acquire language or recognize faces) So we have to rely on the variations produced by the game-of-pure-mathematics to supply the necessary intellectual intuitions. Okay, now I'll try to give an account of Science to explain my point, because this requires a deeper explanation to avoid ambiguity. Having put all theory into the same category - namely description - we then create models about the 'appearance of things' in terms of mathematics, based in observation but also, and very importantly, guided by the consistency of our theory with other more supported theories. (e.g. a theory that breaks some relativistic principle is possible, but less likely; as an aside, its this prior probability assigned to a theory in terms of pre-existing theories that made us reluctant to modify Newton's ideas in the first place) So then we use experiment to test the theory - but we'll always get systematic and random noise over our data - there is never a perfect fit; often we must also invoke secondary theories to remove unwanted artefacts from our data. So, in fact when we demonstrate the data is consistent with a theory, we should (I would argue) assign a probability to that theory and also take into account the current probability of any invoked secondary theories. The second part of this problem, for me is that pure mathematics lives in a realm of pure reasoning, uncorrupted by doubt (although often abstracted from reality.) In order to apply it to Physics, we have to assign meaning to all our variables. c becomes the velocity of light etc... In order to do this, we must take into account *how* we are measuring that variable. If we use different methods, we might actually be measuring different phenomena. Without any understanding of the probability of our hypothesis or phenomena, this could be assumption which is *probably* unreasonable. So my question is, how do we as Scientists, reason within an uncertain (essentially probabilistic) framework in a rigorous manner; but primarliy how do we do this issue into account on a daily basis, as we go about our business? (I hope I've nailed my question this time.)
From: tonyb on 15 Mar 2010 06:08 On 15 Mar, 09:58, tonyb <tony.band...(a)googlemail.com> wrote: > On 14 Mar, 23:43, rabid_fan <r...(a)righthere.net> wrote: > > > On Sun, 14 Mar 2010 15:24:02 -0700, tonyb wrote: > > >large amount of consistent phenomena/data indicating the existence of > > > the electron, less for a gluon, or a Higgs Boson. > > > The evidence is incomplete. > > > > In machine learning, questions like this would be stated in terms of > > > Hypothesis X havibg a probability P, based on the likelihood of the data > > > and our model. > > okay, just to be clear, I'm not talking about probability in relation > to wave equations. > I'm talking about the probability that a descriptive mathematical > statement about the > behaviour of a phenomena is correct. > > > > > > So my question is really about how we/do we deal with this system of > > > apparent probabilities into our reasoning (personally, as Scientists.) > > > I do not understand what is being asked. > > > But, we cannot know what a particle *is*, we can only know > > how it behaves. A particle is a solution (function) to an > > equation. > > > The sooner we stop trying to grasp the nature of a particle > > with our inborn tools of comprehension, the better off we will > > be. > > okay, I'm with you here. We can't perceive these quantum phenomena > directly. > In fact, I'd also argue that we can't perceive *any* phenomena > directly, as 'the thing in itself' - for example, our eyes use light > as a probe particle; our ears infer vibration energy from external > objects and our mind uses all the data from our senses in unison, > cross-referencing to infer secondary information. (this is the cause > of a 'p'/'b' illusion) > > So I guess what your saying is that we have no intellectual intuition > about the behaviour of these particles, because they are new phenomena > presented to our minds via the enhanced senses of our apparatus e.g. > the LHC detectors. Our minds haven't evolved a pre-existing apparatus > for these phenomena (e.g. in contrast to the pre-existing apparatus > that children have to acquire language or recognize faces) So we have > to rely on the variations produced by the game-of-pure-mathematics to > supply the necessary intellectual intuitions. > > Okay, now I'll try to give an account of Science to explain my point, > because this requires a deeper explanation to avoid ambiguity. > > Having put all theory into the same category - namely description - we > then create models about the 'appearance of things' in terms of > mathematics, based in observation but also, and very importantly, > guided by the consistency of our theory with other more supported > theories. (e.g. a theory that breaks some relativistic principle is > possible, but less likely; as an aside, its this prior probability > assigned to a theory in terms of pre-existing theories that made us > reluctant to modify Newton's ideas in the first place) > > So then we use experiment to test the theory - but we'll always get > systematic and random noise over our data - there is never a perfect > fit; often we must also invoke secondary theories to remove unwanted > artefacts from our data. So, in fact when we demonstrate the data is > consistent with a theory, we should (I would argue) assign a > probability to that theory and also take into account the current > probability of any invoked secondary theories. > > The second part of this problem, for me is that pure mathematics lives > in a realm of pure reasoning, uncorrupted by doubt (although often > abstracted from reality.) In order to apply it to Physics, we have to > assign meaning to all our variables. c becomes the velocity of light > etc... In order to do this, we must take into account *how* we are > measuring that variable. If we use different methods, we might > actually be measuring different phenomena. Without any understanding > of the probability of our hypothesis or phenomena, this could be > assumption which is *probably* unreasonable. > > So my question is, how do we as Scientists, reason within an uncertain > (essentially probabilistic) framework in a rigorous manner; but > primarliy how do we do this issue into account on a daily basis, as we > go about our business? > (I hope I've nailed my question this time.) actually, now I've removed the rather misleading emphasis on mathematics, perhaps I might move this to a new thread.
From: jmfbahciv on 15 Mar 2010 08:00
Ste wrote: > On 14 Mar, 13:39, tonyb <tony.band...(a)googlemail.com> wrote: >> Apologies in advance for posting somewhat off topic, but I would like >> to address this questions to scientists only as I'm not interested in >> the view of Phil-Sci students in this particular instance. >> >> Its a fairly simple one. >> >> I'm studying physics and am okay with the scientific process - using >> maths to describe reality, supported by experiment. But then I start >> running into trouble and wanted to hear some other opinions. Which of >> this statements would you (as scientists) agree with the most?: >> >> 1. Mathematics is a language, with some really handy adjectives, which >> we use to describe reality. If experiment doesn't contradict the >> predictions of this description, then it is a useful description of >> reality. Things like electrons are only models and may/may not exist. >> Who knows? >> >> 2. Mathematics is used to describe real external entities. They really >> exist, and experimental physics helps us refine our understanding of >> these entities, allowing us to build a clearer picture of reality. >> >> 3. Something else, because I disagree with premise X implied within >> the above statements >> >> Cheers, >> TonyB > > Mathematics is undoubtedly a language. If so, what are the verbs? /BAH |