How can I tell if F is a string or if it is a number?
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From: Pioneer1 on 5 Apr 2008 09:31 Hi, I've been trying to understand data types in physics. http://www.densytics.com/wiki/index.php?title=Data_types_in_Physics I see that there are similarities with data types used in computer science. I am confused about what is number and what is string in physics. When I look at F=ma I see F as a string. F is a label for ma. But physicists, like this one, http://globalpioneering.com/wp02/science-is-legal-physics/#comment-16779 see it differently and say it is a number or a quantity. And indeed F stands for a number, ma, but to me F is just a placeholder, not a quantity. I know I'm not using the correct terminology. Can anyone help me understand this? At least, help me state the problem clearly? Many thanks.
From: Richard Harter on 5 Apr 2008 11:00 On Sat, 5 Apr 2008 06:31:19 -0700 (PDT), Pioneer1 <1pioneer1(a)gmail.com> wrote: >Hi, > >I've been trying to understand data types in physics. > >http://www.densytics.com/wiki/index.php?title=Data_types_in_Physics > >I see that there are similarities with data types used in computer >science. I am confused about what is number and what is string in >physics. When I look at F=ma I see F as a string. F is a label for ma. >But physicists, like this one, http://globalpioneering.com/wp02/science-is-legal-physics/#comment-16779 >see it differently and say it is a number or a quantity. > >And indeed F stands for a number, ma, but to me F is just a >placeholder, not a quantity. > >I know I'm not using the correct terminology. Can anyone help me >understand this? At least, help me state the problem clearly? > >Many thanks. Oh dear, oh dear. You appear to be confusing the idiosyncratic notation of imperative programming languages without ever having passing through mathematics and physics. The = sign in many languages, e.g. C and Fortran, means assignment. In physics and mathematics generally it means identity. Secondly, F=ma is not a statement in the sense of a statement in a programming language; rather it is a formula, i.e., a governing relationship between the three quantities, F, m, and a. Thirdly m and a are separate quantities. Fourthly, it is normal in maths and physics to use single letter variables (using a variety of alphabets, subscripting, and superscripting as needed) and to indicate multiplication by concatenation. Fifthly, more subtly, variables stand for something specific; the association is intrinsic (albeit by definition) rather than happenstance (as is so often the case in computer programs). To recapitulate: F = ma is a formula that expresses the relationship between force, F, mass, m, and acceleration, a. It says force is equal to the product of mass times acceleration. I hope this helps. Richard Harter, cri(a)tiac.net http://home.tiac.net/~cri, http://www.varinoma.com Save the Earth now!! It's the only planet with chocolate.
From: Pioneer1 on 5 Apr 2008 16:59 On Apr 5, 11:00 am, c...(a)tiac.net (Richard Harter) wrote: Thanks for the help. > > The = sign in many languages, e.g. C and Fortran, means > assignment. In physics and mathematics generally it means > identity. I think in physics the = sign is context sensitive and has many meanings. I think this is part of my problem. http://www.densytics.com/wiki/index.php?title=Equality_sign >Secondly, F=ma is not a statement in the sense of a > statement in a programming language; rather it is a formula, Ok. I understand this. I was hoping to use concepts of computer language and math to decipher physicists' F=ma > i.e., a governing relationship between the three quantities, F, > m, and a. I think here the assumption is that F is a quantity like m and a. But I am questioning this assumption. How do I test mathematically that F is not just a label or a placeholder or a pointer to ma? Let's say I want to write a program to compute F, it should be something like this: (def force (m a) (* m a)) I assume in this case force is merely the name of the function (* m a). There is not something distinct from (* m a) called force. Is this correct? > Fifthly, more subtly, variables stand for something specific; the > association is intrinsic (albeit by definition) rather than > happenstance (as is so often the case in computer programs). So in this case, does F stand for anything other than ma? Thanks again.
From: Chris Smith on 5 Apr 2008 17:52 Pioneer1 wrote: >> i.e., a governing relationship between the three quantities, F, m, and >> a. > > I think here the assumption is that F is a quantity like m and a. But I > am questioning this assumption. How do I test mathematically that F is > not just a label or a placeholder or a pointer to ma? This isn't making any sense. Can you express more clearly what you are looking for? I am not sure of this, as I don't understand what you're saying yet; but I strongly suspect you are asking meaningless questions. In general, when you've got several related concepts, it's a rather arbitrary choice what you choose to call a definition, and what you choose to call a fact. > (def force (m a) (* m a)) > > I assume in this case force is merely the name of the function (* m a). > There is not something distinct from (* m a) called force. Is this > correct? What do you mean? As a matter of programming language semantics, you want to know whether 'force' (by the quotes I mean I'm talking about your function, not the concept from physics) has some identity that would let you distinguish it from a different function that returns the same value for the same inputs? That depends on your programming language: usually no, but occasionally yes. If you intend to infer something about physical quantities from such accidents of language semantics, though, I'll join in warning you against it. -- Chris Smith
From: Barb Knox on 5 Apr 2008 22:29
In article <871757b5-ab88-4134-ba4e-2c991456cba6(a)1g2000prg.googlegroups.com>, Pioneer1 <1pioneer1(a)gmail.com> wrote: > On Apr 5, 11:00�am, c...(a)tiac.net (Richard Harter) wrote: > > Thanks for the help. > > > > The = sign in many languages, e.g. C and Fortran, means > > assignment. In physics and mathematics generally it means > > identity. > > I think in physics the = sign is context sensitive and has many > meanings. I think this is part of my problem. > > <http://www.densytics.com/wiki/index.php?title=Equality sign> Your problem here is treating that page is authoritative. Pretend you never saw it. For your purposes, equality is unambiguous: if alpha and beta are mathematical expressions, then alpha=beta means that any alpha(s) may be replaced by beta in any expression, and vice versa, without changing the value of the expression. Basically, alpha and beta are expressions that represent the same value. E.g.: 2 + 2 = 3 + 1 F = m*a Note that unlike programming, alpha=beta means *exactly* the same thing as beta=alpha. 3 + 1 = 2 + 2 m*a = F > >Secondly, F=ma is not a statement in the sense of a > > statement in a programming language; rather it is a formula, > > Ok. I understand this. I was hoping to use concepts of computer > language and math to decipher physicists' F=ma Do NOT attempt to use programming conventions to understand physics. As Richard wrote: [unsnip] > > Oh dear, oh dear. You appear to be confusing the idiosyncratic > > notation of imperative programming languages without ever having > > passing through mathematics and physics. [/unsnip] > > i.e., a governing relationship between the three quantities, F, > > m, and a. > > I think here the assumption is that F is a quantity like m and a. But > I am questioning this assumption. How do I test mathematically that F > is not just a label or a placeholder or a pointer to ma? The letter 'F' is a variable that denotes some value. (This is a *mathematical* variable, NOT a programming one. For example, you can not change its value.) Similarly, 'm' and 'a' denote values. F=m*a constrains those 3 values to have the relationship that F's value is the same as m's value times a's value. NOTHING in physics is analogous to a C pointer. > Let's say I want to write a program to compute F, it should be > something like this: > > (def force (m a) (* m a)) > > I assume in this case force is merely the name of the function (* m > a). There is not something distinct from (* m a) called force. Is this > correct? > > > Fifthly, more subtly, variables stand for something specific; the > > association is intrinsic (albeit by definition) rather than > > happenstance (as is so often the case in computer programs). > > So in this case, does F stand for anything other than ma? None of 'F', 'm', or 'a' *stand for* any combination of the others. They do however *relate* in a particular way in F=m*a. Note that when m is non-zero, F=m*a is EXACTLY equivalent to F/m = a Say to yourself several times: "Programming is worse than useless for understanding first-year physics". Repeat this until you believe it. > Thanks again. -- --------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- |