studiot Posted April 1, 2015 Share Posted April 1, 2015 The answer to your question is: yes, they are called analogies and they are crude approximations of limited use to explain the idea to those who don't understand the science or the maths. But, really, it is the wrong question. It should be: Is it possible to make a scientific model of an idea without maths? And the answer to that is: no. If the underlined proposition were so then all of science is based on one or more acts of faith. Godels Theorem tells us that about Mathematics, and applies to anything founded on it. This is of no consequence if the mathematics is an abstract construct, since we can change the founding parameter at will, and arrive at many systems of maths. But Science is meant to enquire into of which physical reality which we would like to think unique. Link to comment Share on other sites More sharing options...
Strange Posted April 1, 2015 Share Posted April 1, 2015 None of that appears to be relevant to what I said. (And I think you are exaggerating the significance of Godel's theorem.) Just to be clear, what I said was: You can't create a scientific model without maths. (I'm surprised that is controversial. If it isn't a mathematical model, then it isn't rigorously and objectively testable.) Link to comment Share on other sites More sharing options...
studiot Posted April 1, 2015 Share Posted April 1, 2015 None of that appears to be relevant to what I said. (And I think you are exaggerating the significance of Godel's theorem.) Just to be clear, what I said was: You can't create a scientific model without maths. (I'm surprised that is controversial. If it isn't a mathematical model, then it isn't rigorously and objectively testable.) Appears? You made the assertion so it is up to you to support it with a logical train of thought, not wishy washy flannel. Link to comment Share on other sites More sharing options...
Strange Posted April 1, 2015 Share Posted April 1, 2015 Appears? Yes. What you said does not appear to have any connection to anything I said. It appears to be a non sequitur. Please feel free to explain the relevance, if you wish. You made the assertion so it is up to you to support it with a logical train of thought, not wishy washy flannel. If it isn't a mathematical model, then it isn't rigorously and objectively testable, and therefore isn't scientific. (Is that wishy-washy flannel?) Link to comment Share on other sites More sharing options...
studiot Posted April 1, 2015 Share Posted April 1, 2015 (edited) strange to have any connection to anything I said Of course it does or I wouldn't have said it. Though, equally of course, I am happy to explain further. Every system of mathematics has two characteristics, both of which have to be taken on faith. Taken on faith means accepted without question. These characteristics are (1) the axioms and (2) the unprovable deduction(s) required by Godel. (2) is the 'incompleteness' if you like. Edited April 1, 2015 by studiot Link to comment Share on other sites More sharing options...
Strange Posted April 1, 2015 Share Posted April 1, 2015 Of course it does or I wouldn't have said it. Though, equally of course, I am happy to explain further. Every system of mathematics has two characteristics, both of which have to be taken on faith. Taken on faith means accepted without question. These characteristics are (1) the axioms and (2) the unprovable deduction(s) required by Godel. (2) is the 'incompleteness' if you like. And how is that relevant to the fact that science uses (must use) mathematical models? Link to comment Share on other sites More sharing options...
studiot Posted April 1, 2015 Share Posted April 1, 2015 So how do you model the axioms or the unprovable deduction(s)? Link to comment Share on other sites More sharing options...
Strange Posted April 1, 2015 Share Posted April 1, 2015 So how do you model the axioms or the unprovable deduction(s)? What unprovable deductions are there in physics, for example? Link to comment Share on other sites More sharing options...
swansont Posted April 1, 2015 Share Posted April 1, 2015 So how do you model the axioms or the unprovable deduction(s)? You don't. Science models nature, not math. Link to comment Share on other sites More sharing options...
Strange Posted April 1, 2015 Share Posted April 1, 2015 And if there were unprovable deductions that had to be modeled then, arguably, it wouldn't be science as you couldn't have a model and therefore it couldn't be tested and falsified. Which brings us right back to my original point. Link to comment Share on other sites More sharing options...
Mike Smith Cosmos Posted April 2, 2015 Author Share Posted April 2, 2015 (edited) The answer to your question is: yes, they are called analogies and they are crude approximations of limited use to explain the idea to those who don't understand the science or the maths. But, really, it is the wrong question. It should be: Is it possible to make a scientific model of an idea without maths? And the answer to that is: no. .This juncture is the ' fork in the road' or ' the division in the river tributary ,up stream ' . Going up the Nile , looking for its source , was going to lead Livingstone to Lake Victoria Or a dead end. If figuratively the one leading to the dead end was solely maths ( in its present state of understanding ) , and the one leading to Lake Victoria was figuratively the tributary like some modest amount of maths conjoined with a high percentage of Analogy taken from a direct view of nature with ALL her mysterious, yet undiscovered features . Then success , we would have gained access to waters ,unimaginable , analogous to Lake Victoria in all her depth ,opportunity and glory. Wa hey ! Mike Analogies + Maths . . Maths ONLY Q.E.D. .....WA hey ! Edited April 2, 2015 by Mike Smith Cosmos Link to comment Share on other sites More sharing options...
Strange Posted April 2, 2015 Share Posted April 2, 2015 You gave that the wrong way round. Link to comment Share on other sites More sharing options...
ajb Posted April 2, 2015 Share Posted April 2, 2015 Is it possible to make a model of a scientific idea , without maths in it .? Almost by definition no. A model is a mathematical model. Link to comment Share on other sites More sharing options...
Mike Smith Cosmos Posted April 2, 2015 Author Share Posted April 2, 2015 (edited) Almost by definition no. A model is a mathematical model... What is the matter with a physical object as a model, a visual picture as a model, a lingual description as a model ? I appreciate none of these is as ridged and precise as maths, but maybe a characteristic that is sought out of the model is not precision but paradigm change ,to move forward ? I am not sure there is a mathematical expression for " Paradigm change. " , is there ? Mike Edited April 2, 2015 by Mike Smith Cosmos Link to comment Share on other sites More sharing options...
ajb Posted April 2, 2015 Share Posted April 2, 2015 Analogies + Maths Analogies have their place, both in science and mathematics. They can help you think and understand your observations or calculations. But they have to come from somewhere and will be in hindsight, or at best developed along the way. Link to comment Share on other sites More sharing options...
Mike Smith Cosmos Posted April 2, 2015 Author Share Posted April 2, 2015 (edited) Analogies have their place, both in science and mathematics. They can help you think and understand your observations or calculations. But they have to come from somewhere and will be in hindsight, or at best developed along the way... Why can they ( the Analogies , observations and Hypothesis ) not " lead in front " as the name of the thread infers ? . In other words " indicate " to blind maths , the way to go and calculate ,or contort , or whatever it is you guys do. , ( tongue in cheek ) Go on, say it " Yes they can " . Cough splutter ! Mike Edited April 2, 2015 by Mike Smith Cosmos Link to comment Share on other sites More sharing options...
ajb Posted April 2, 2015 Share Posted April 2, 2015 (edited) What is the matter with a physical object as a model, Like a 'mechanical model' build on your desk? These can be useful for trying to understand macroscopic phenomena, maybe fluid flow or similar. I would put these under the heading of an experiment rather than a model. You gain information and insight into the real world, which should then be used to help build or test mathematical models. a visual picture as a model, Graphics and graphical notation can be useful, but again these need to come from some mathematical model. Otherwise how were they obtained? I may do some experiments say on fluid flow around some object. I can draw the flow lines. I could possibly make an educated guess as to what would happen if I put some other object in my experiment. But if I have a working mathematical model then I can really calculate what will happen in the experiment when I change object. Maybe my model is good, maybe it is bad, by I can calculate and make real predictions. Of course, in practice one will have to make some simplifying assumptions and them maybe put all this into a computer, but in principle I calculate things to be measured. a lingual description as a model ? This would be closer to an analogy or really an interpretation. It would be some description of a calculation useful for explaining it to others or gaining insight as in what to do next. The other problem is that a lot of physics language does not 'translate' well into English and has specific meanings. My lingual description of something to say Swanson may have to be different to my lingual description to Witten, which for sure would have to be different to my lingual description to the man of the street, unless the street is in Cambridge maybe ;-) Why can they ( the Analogies , observations and Hypothesis ) not " lead in front " as the name of the thread infers ? Where would these analogies come from? Observations okay, we have examples of observations giving us surprises; dark matter, dark energy, neutrino masses, the fractional quantum hall effect etc. Nobody will disagree with this. Hypothesis would be based on what? Well, it seems either observations or calculations. Edited April 2, 2015 by ajb Link to comment Share on other sites More sharing options...
Mike Smith Cosmos Posted April 2, 2015 Author Share Posted April 2, 2015 (edited) Like a 'mechanical model' build on your desk? These can be useful for trying to understand macroscopic phenomena, .......You gain information and insight into the real world, which should then be used to help build or test mathematical ..."........Where would these analogies come from?Observations okay, we have examples of observations giving us surprises; dark matter, dark energy, neutrino masses, the fractional quantum hall effect etc. Nobody will disagree with this.Hypothesis would be based on what? Well, it seems either observations or calculations... .Yes . how about Observations . Then the observations can give rise to a hypothesis , ( leading ,in front ) . Then you guys go away and calculate, and model even greater things, having been lead by the " Observation and Hypothesis " from the Gold mine to the ' Trough ' . Then you produce the precise model on which to build a new technology / product ,whatever? I am sure ' bridges are built this way ' ? Mike Edited April 2, 2015 by Mike Smith Cosmos Link to comment Share on other sites More sharing options...
studiot Posted April 2, 2015 Share Posted April 2, 2015 swansont studiot, on 02 Apr 2015 - 12:16 AM, said: So how do you model the axioms or the unprovable deduction(s)? You don't. Science models nature, not math. Yes you are strictly correct my wording was bad. Maths has axioms and deduced statements. Physical reality has observations. However that does not cover up the fact that a mathematical model must contain mathematical axioms and at least one unprovable mathematical deduction. All these are taken on faith as I said if you are to believe that they also apply to the physical reality. There may be statements in the model that are not reflected in reality. Equally statements in the model may lead us to statements in reality that we have not previously discovered. My position is still the same as set out in my posts 251 and 283 and also by ajb in his post 267. ajb I thought we more or less sorted the opening question with the answer "both are needed". Link to comment Share on other sites More sharing options...
ajb Posted April 2, 2015 Share Posted April 2, 2015 how about Observations Observations can and so lead to surprises. Thus they are fundamental in driving science as well as confirming what we do know. Then the observations can give rise to a hypothesis , ( leading ,in front ) . Then you guys go away and calculate, and model even greater things, having been lead by the " Observation and Hypothesis " from the Gold mine to the ' Trough ' . In physics by a hypothesis one would mean some calculation of something that can be measured. I don't see how one could make a testable prediction otherwise. General statements like 'increases' or 'decreases' is not really enough. Then you produce the precise model on which to build a new technology / product ,whatever? Building technology is not the role of science or scientists. Generally, science uncovers basic knowledge of the world that can then be used by engineers and technologists to build things. Applications of the science needs to be quite separate from the evaluation of the science. Link to comment Share on other sites More sharing options...
studiot Posted April 2, 2015 Share Posted April 2, 2015 ajb In physics by a hypothesis one would mean some calculation of something that can be measured. I don't see how one could make a testable prediction otherwise. General statements like 'increases' or 'decreases' is not really enough. I suggest physical reality is more complicated than that. That is why I asked about the output of a 74C126 integrated logic chip in my post 264 and received a rude raspberry for it (not from yourself) I chose that chip because there is no calculation or observation that can be performed which can unambigouusly answer the question What is the output state of the chip? The chip is part of a family of chips designed to reflect a sort of Godel's Theorem in electronics where the output can be definitely 1 or definitely 0 or indeterminate. Link to comment Share on other sites More sharing options...
Mike Smith Cosmos Posted April 2, 2015 Author Share Posted April 2, 2015 Observations can and so lead ......In physics by a hypothesis one would mean some calculation ......... I don't see how one could make a testable prediction otherwise. ......General statements like 'increases' or 'decreases' is not really enough.... I think it is just right here is where we are getting potentially. .Derailed . Yes the hypothesis might well be vague in its description of " increase " or "decrease" . But this could be a major hypothesis in its own right. Previously we may have adamantly thought something was a fixed constant . Now a hypothesis comes along and proposes 'NO ' . This characteristic is a variable , things are changing all the time , things are adapting to changing circumstances. Now all we are saying ' hypothesising ' is that things are not fixed , but increasing and decreasing over time ! Now , you guys , go and do your sums and tell us the detail! Surely that is hypothesis leading . .? Mike Link to comment Share on other sites More sharing options...
ajb Posted April 2, 2015 Share Posted April 2, 2015 (edited) I suggest physical reality is more complicated than that. That is why I asked about the output of a 74C126 integrated logic chip in my post 264 and received a rude raspberry for it (not from yourself) I chose that chip because there is no calculation or observation that can be performed which can unambigouusly answer the question What is the output state of the chip? The chip is part of a family of chips designed to reflect a sort of Godel's Theorem in electronics where the output can be definitely 1 or definitely 0 or indeterminate. I do not know enough about electronics to really comment. I know that digital logic gates can fail to give the right answer when the voltage is in a certain region, known as the 'Indeterminate Region'. However, I think you are talking about something else? Yes the hypothesis might well be vague in its description of " increase " or "decrease" . But this could be a major hypothesis in its own right. It would not usually be enough. Physics is about making models and testing them. Just saying 'increase' or 'decrease' is not really a prediction. It maybe what one is looking for in an experiment and this could then be used to rule out certain classes of theories. Edited April 2, 2015 by ajb Link to comment Share on other sites More sharing options...
studiot Posted April 2, 2015 Share Posted April 2, 2015 (edited) ajb However, I think you are talking about something else? Yes indeed, I am not talking about circuit failure or incorrect circuit action. There is a family of logic chips that can be deliberately put into an indeterminate state. This is known as Tri state logic. http://en.wikipedia.org/wiki/Three-state_logic Edited April 2, 2015 by studiot Link to comment Share on other sites More sharing options...
Strange Posted April 2, 2015 Share Posted April 2, 2015 What is the matter with a physical object as a model, a visual picture as a model, a lingual description as a model ? I appreciate none of these is as ridged and precise as maths You have answered the question. The purpose of a model in science is to derive precise results. Either to test the theory or to produce useful results. That means it must be mathematical. A physical object, a visual representation or a verbal description may tell you something qualitative but it is not scientifically useful. Link to comment Share on other sites More sharing options...
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