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Thread: The Mathematical Universe

  1. #76
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    Re: The Mathematical Universe

    Nonlinear does not mean unpredictable. There are many non-linear equations for which we have closed solutions, which means that we can predict the behaviour of any object exhibiting that solution.

    The problem you are dancing around is that natural science (whether you call it physics or something else) consists of non-quantified theories. These are verbal descriptions of processes that explain what happens and how, but do not provide quantified predictions. An great example is the theory of evolution. However, the effects of some theories can be quantified using mathematical models. The important thing to understand about mathematical models is that they are based on assumptions. The assumptions are simplifications of what happens in the real world. The reason we use simplifications is that it makes the mathematics tractable, allowing us to find solutions that in turn give us quantifiable predictions. But there is a significant trade-off: the simplifications make the models inaccurate because they stop the model expressing what really happens. The equations that we use in science are thus approximations. They work for particular conditions, but not for all. Refinements of theories often allow us to improve the mathematical model by making fewer simplifications, or less drastic simplifications, but they are simplifications nonetheless.

    The only case where this might not be true is in particle physics where we are describing the interactions of elementary particles. But the simplification we have to make in order for the mathematics to be tractable is that we limit the number of particles we consider to an unrealistic number for any large-scale description of the universe. In principal, if we can get a powerful enough computer we should be able to model the behaviour of more particles, not using solutions of equations, but by modelling the possible interactions. This gives us a number of possible outcomes, some of which are more likely than others. This is what we do for weather reports. There is a lot of mathematics that can help in producing these models, but again, the mathematics is a model of how large-scale effects emerge from small-scale interactions. And, being a model, it is not precise (in fact, it is probabilistic). Thus, sometimes the weather forecast turns out to be wrong. That doesn't mean that there was not a model that predicted the weather that actually happened. Rather, it means that there were more models that predicted something else.

    And this is what you do with aeroplanes and turbulence. You use models (i.e. approximations) to predict what will happen. Usually, the models are not equations that predict the path of air molecules for all time, but rather they are algorithms that calculate the position of the air molecules at a number of instants and use each instant as the starting point for estimating the next one. Varying initial conditions or various parameters leads to different results (sometimes very different), but we pick as our prediction the result that occurs most frequently (or rather, we pick the large-scale effects that occur most frequently).

    And then, in the aeroplane business, you go and test it in a wind tunnel (or perhaps on a real plane flown by a test pilot). Usually the prediction is correct (just as the weather forecast is usually correct), but sometimes it isn't.

    Presumably, in the aeroplane business you have to consider the fact that whatever situation you are modelling is likely to occur huge numbers of times over the life of plane. So in some circumstances, results that do not occur in the wind tunnel must also be accounted for.

    But none of this means that physics isn't informing us as to what happens. Physics is informing us how to make the transition from one instant to the next in our model.

    The scary thing is that you appear not to understand this.
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  2. #77
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    Re: The Mathematical Universe

    Archie, are you offering a closed form solution to the surface profile at a hydraulic jump?
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  3. #78
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    Re: The Mathematical Universe

    I don't think so. Even if I knew what a hydraulic jump was.
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  4. #79
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    Re: The Mathematical Universe

    I agree that we can solve non linear equations such as the KDV equations to obtain soliton solutions such as happens in the river Severn Bore.
    (I understand there is also one on the Amazon).
    These are travelling solitary waves that travel up a shoaling and narrowing estuary under suitable tidal influx conditions.

    A hydraulic jump is a standing wave of step form that has two profile solutions (ie in theory the water surface is vertical at a certain section) that occurs at an abrupt change of bed slope to lower gradient, when the change is of sufficient magnitude.
    This levelling off is used to dissipate energy in the water outflow from reservoirs.
    Upstream and downstream of this section the water flow obeys the normal laws of flow.
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  5. #80
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    Re: The Mathematical Universe

    I am sorry Mr Westwood, I cannot engage you. You inference that the loss of airbus aircraft was due to incompetence on the part of the company has been taken very seriously. A formal complaint from Airbus and Volvo is being prepared and will be presented to the Website on September 16th. While the companies accept that the website is not responsible for the language people use, it is responsible for not removing statements by 'experts', which bring the companies into disrepute.
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  6. #81
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    Re: The Mathematical Universe

    Actually, Peter, the statement was a conditional one taking as a premise that the company shares your flawed understanding of mathematical modelling.

    Your response is pretty pathetic. Much as I dislike Matt's general tone, he does have a valid point concerning your apparent lack of understanding and the possible implications for the safety of aircraft.

    Invoking legal proceedings in a scientific discussion is not science.
    Last edited by Archie; Aug 14th 2015 at 05:15 PM.
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  7. #82
    MHF Contributor Matt Westwood's Avatar
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    Re: The Mathematical Universe

    Quote Originally Posted by petercookintaiwan View Post
    I am sorry Mr Westwood, I cannot engage you. You inference that the loss of airbus aircraft was due to incompetence on the part of the company has been taken very seriously. A formal complaint from Airbus and Volvo is being prepared and will be presented to the Website on September 16th. While the companies accept that the website is not responsible for the language people use, it is responsible for not removing statements by 'experts', which bring the companies into disrepute.
    Yeah, that's a laugh. See how far that gets. You really are ridiculous.
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  8. #83
    MHF Contributor Matt Westwood's Avatar
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    Re: The Mathematical Universe

    Okay then, let's take a step back and analyse this.

    Man walks into a room he's never been before and engages the occupants in conversation.

    "I say, you fellows! The entire philosophical underpinning of the belief structure upon which you have rooted your existence is fatally flawed!"

    He then goes on to explain why, but his arguments are badly structured and ill-conceived.

    The occupants of the room respond in various ways, from "Balderdash!" to "An interesting idea, if only you could explain it properly, but if I understand you correctly, you appear to misunderstand the basic tenets of what our philosophy actually is."

    The new arrival replies with a common variant of the classic argumentum ad verecundiam:
    "But I'm right! I know I'm right! What nasty people you are for not taking me seriously! I'll have you know I'm the very kingpin upon which depends the design of some very complicated machinery that is responsible for the safety of millions of people!"

    One of the more blunt-speaking, practical and forthright occupants of the room then replies:
    "Aargh! Good grief! If what you say is true, then that would explain some of the highly publicised disasters we've heard about on the news! And, if that is the case, you'll never get me up in one of those things!"

    "Now you're being unfair!" wails our new arrival, fighting back with what is nothing more than an argumentum ad baculum:
    "You'd better agree with me or the company for which I work, of which I am can now reveal I am an officially sanctioned spokesman, will kick your bottom! Everybody in this room will be punished severely by the mighty weight of the legal team of which I command the attention like a conductor at a podium! Bwahahahahaaa!"


    Incidentally, Peter Cook in Taiwan: I would be interested to learn the reaction of the companies whose names you cite to your associating their names with your philosophy. I would be more inclined to suspect that it would be you to whom they will turn their attentions. I suggest you lawyer up soon. As for me, you don't know who I am.
    Last edited by Matt Westwood; Aug 14th 2015 at 11:06 PM.
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  9. #84
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    Thanks from romsek
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  10. #85
    MHF Contributor Matt Westwood's Avatar
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    Re: The Mathematical Universe

    I'd love to go and rough-music him out of there as well, but I have a DIY job to do which is going to take up most of the day.
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  11. #86
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    Re: The Mathematical Universe

    Here in Canuck Land, it's a DIM job!
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  12. #87
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    Re: The Mathematical Universe

    Quote Originally Posted by petercookintaiwan View Post
    I am sorry Mr Westwood, I cannot engage you. You inference that the loss of airbus aircraft was due to incompetence on the part of the company has been taken very seriously. A formal complaint from Airbus and Volvo is being prepared and will be presented to the Website on September 16th. While the companies accept that the website is not responsible for the language people use, it is responsible for not removing statements by 'experts', which bring the companies into disrepute.
    I am relatively sure that this site is housed in the US, and, under US law, there is no responsibility for site publishers to correct or delete comments, which are solely the responsibility of the commenter. Moreover, under US law, opinions and hyperbole are not defamatory so Volvo and Airbus had best hire lawyers who know more about US law than you apparently do. Moreover, your comment that Matt Westwood has represented himself as an expert in airplane design appears to be manufactured completely out of thin air. I am wondering, however, whether you in fact are an expert in designing aircraft. If not, you are trying to argue from authority, a weak form of argument when the authority is legitimate, and no argument at all if the authority is spurious.

    EDIT: Inferences are NEVER actionable in the US. "The mind is its own place."
    Last edited by JeffM; Aug 15th 2015 at 12:33 PM.
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