Is History a Science?

 

On the other hand, to a certain degree, we are abit more liberal to other views, because this is the scientific method! Simply coming up with one theory and dismissing anyone who things differently is not!

Science is making a theory and putting it to the test to see if it holds. In history, this means making an interpretation and seeing if others are possible. If all other views are considered 'anti-history', all progress is stopped, and history is dead.

It's not until SR and the dependency of mass on speed that the (mv) can't be split up, and you need to substitute dp/dt.

As I've shown motus for Newton means p, then Newton's own formula gives dp/dt, so no substitution is needed

 

You're ignoring the dimensionality of k. More importantly it is what Newton actually wrote. He said the 'change in the motion' was proportional to the force applied. Temporarily ignoring the question of what 'motion' means here - call it x - you therefore have directly dx/dt = k F - the change in something is a constant times the force. It is not necessarily a dimensionless constant, any more than g is a dimensionless constant.

If you bring original entities, please bring their definitions too. Usually, k is a numeric a-dimensional constant if not specified otherwise.
And you cannot claim your formula is implied by Newton's text because it's not. It was en euphemism to call it just wrong, but your insistence bring the revelation. F = m*dv/dt = m*d2s/dt2 - to write the force as function of space/position (s) and time (t) you have to invoke the double derivative!! (in plain English that would be the variation of the variation). Therefore, to use your original notation k = 1/m, the equations would look like d2s/dt2 = kF, not ds/dt = kF - a formula which has absolutely no connection to Newton's laws.

 

Originally posted by Chilbudios Quantitas motus est mensura ejusdem orta ex velocitate et quantitate materiae conjunctim. This is how Newton understood motion (basically motion is a compound/conjugation/product of mass and speed - it's not a variation of position in time, that is the speed, the velocity - to use a closer word to Newton's) . You're playing with m*a = m*dv/dt = dp/dt with no respect to Newton's formulations.

Fine. But the point is that Newton considered the 'quantitate materiae' - 'mass' as we might say - to be independent of the speed. 'Motus' is therefore a constant times the velocity, and since it is constant, then d(mv)/dt = mdv/dt - the constant can be taken out of the brackets.

 

It's not until SR and the dependency of mass on speed that the (mv) can't be split up, and you need to substitute dp/dt.

 

And actually the formula ds/dt = kF is simply wrong because it doesn't fit the physical units in left (m/s) and right (N) terms.

You're ignoring the dimensionality of k. More importantly it is what Newton actually wrote. He said the 'change in the motion' was proportional to the force applied. Temporarily ignoring the question of what 'motion' means here - call it x - you therefore have directly dx/dt = k F - the change in something is a constant times the force. It is not necessarily a dimensionless constant, any more than g is a dimensionless constant.

 

If x is taken to be velocity (not speed) then the dimensions of k are 1/m in standard terminology, which balances the dimensional equation. 

Let's cut off this ridiculous quarrel and let people talk about history if there's anything left to say.

Edited by gcle2003 - 16-Sep-2006 at 08:39

This is how Newton understood motion (basically motion is a compound/conjugation/product of mass and speed - it's not a variation of position in time, that is the speed, the velocity - to use a closer word to Newton's) . You're playing with m*a = m*dv/dt = dp/dt with no respect to Newton's formulations.

And actually the formula ds/dt = kF is simply wrong because it doesn't fit the physical units in left (m/s) and right (N) terms. 

 

Let's cut off this ridiculous quarrel and let people talk about history if there's anything left to say.

 

Originally posted by Chilbudios Originally posted by gcle2003 Hume and Popper certainly deny absolute truth is knowable. In that school, a statement is only scientific if it can be falsified. If it is absolutely true - cannot be falsified - then it is not scientific.  Some observations: - who's talking of absolute truth?

Anybody who says something is not an approximation. If it's true, but not approximately true, it must be absolutely true.

 

- you can't state anything without an axiomatic foundation. Axioms are unfalsifiable by definition.

Unfalsifiable by deduction, yes. However, an axiom can be false if it not empirically true. I can accept as an axiom that the earth is flat and certain conclusions follow from that (like Pythagoras' Theorem applies on its surface). However, empirically, the axiom is false.

 

If you put all axioms down you'll see yourself unable to state anything. Anything at all.

I don't put down axioms. Any old axioms can be the basis of a deductive system, and they cannot be proven wrong within that system. However, that is absolutely no guarantee at all that the axioms apply to the real world. They may do so of course. They may do within the limits of our measurements. Whether they do so absolutely can never be proven.

 

Moreover Popper's understanding of falsifiable as scientific was challenged by Kuhn and Lakatos.

So? It's still the most commonly accepted scientific paradigm. You conceive a hypothesis, and you experiment in order to disprove it. If you fail to disprove it it remains an acceptable hypothesis, until that day in the future when it like all scientific hypotheses is disproven.

 

- what is truth anyway? You're presupposing logical truth (as in prepositional logic, for instance), but I was specifying clearly enough truth as understood in the scientific paradigm.

No I wasn't, I was talking about empirical truth. And no you aren't. See above.

If you want to understand the scientific truth, you may want to read other modern logicians (Tarski, for instance) and get aquainted with a modern concept of truth as correspondence between two certain realities (reality here means a populated space, a mathematical space modelling something, not physical reality).

I've read Tarski. If you redefine 'truth' to mean something different from what it has traditionally meant then of course you can go anywhere you like.

 

What there has basically been over the centuries since Hume is a rearguard action being fought by metaphysicians who cannot stand the thought that truth - empirical truth - about the real world is forever unknowable. If in that rearguard action a few definitions have to be changed - well, they don't mind that as long as they can end up saying "We know that what we know is true".

 

The religious mindset is difficult to defeat.

By the very authorities you quote, scientific assertions, whether you call them laws or not, cannot be proven true. They can only (Popper) be proven false. If you think what you are saying is proven true, then you're into metaphysics and religion, not science. The only scientific assertions are the hypotheses. The other statemnts are "proven true" as the scientific method requires it, by incomplete induction i.e. 1) P(1) <- hypothesis 2) P(2) ... P(k, where k is finite) <- confirming the hypothesis === P(n) <- conclusion They are true until proven otherwise, i.e. until !P(m) where m is finite > k.

 

There you go making 'truth' relative. If they're proven untrue then they were untrue all along (assuming we are talking about universal propositions: the statement I am 55 years old is no longer true, though it was once, because reality itself has changed).

 

Unless they are such time-dependent statements, you cannot say something is false in 2006 but was true in 1200. It can't have been true that the planets revolved around th earth in 1200 if it is true in 2006 that they revolve around the sun.

 

That way madness lies.

Concluding they are not true ("proven true"), results to self-annilihation. Who cares what Popper said if he can't value his own statements.   'Valid' is another concept - an engineering one if you will. It is frequently perfectly valid to make an assumption that you know is untrue. Thus it was perfectly valid in calculating the trajectory of an 18th century naval gun on the assumption that the earth was flat. That won't work for ICBMs, but it is perfectly valid to calculate their trajectory on the assumption the earth is spherical, which it is known not to be.   So validity has nothing to do with it. Valid is an english word.

I'm aware of that.

I'm not talking about valid/invalid/sound/unsound. But valid as well-grounded, justifiable (check a dictionary). Your impetus to deny what others write overcomes the undestanding. Chill down!   Yes, but then p was assumed proportional to velocity which makes a huge difference. 'p' in the 19th century was a different concept to that post-Einstein.   The distinction between Newton's original formulation and the revised version is that mass was assumed by him (and anyone else around at the time) to be independent of velocity. So you could take it to the left of the derivative: F=mdv/dt with m constant. If mass varies with speed as we would now hold then m has to be part of the derivative F=dp/dt.   But that is a major change in the law. It isn't Newton's Law any more.   Incidentally Newton didn't even write F=mdv/dt since that notation for the derivative hadn't been invented yet.  The law is still working in its original formulation: Mutationem motus proportionalem esse vi motrici impressae, & fieri secundum lineam rectam qua vis illa imprimitur. The only change is in what mutationem motus means (and not fully, conceptually they are almost the same in classical physics and SR, is just that in SR the mass is dependent on velocity). But I already said that.

I know it's the only change. But for Newton 'motus' meant 'speed', not what we would call momentum. Granted he didn't actually use the concept of 'mass' but he was saying that change in speed was proportional to the force applied - in modern terminology dv/dt = kF. He was quite obviously NOT saying d(mv)/dt = kF, because he had no 'm' and therefore no 'p'.

 

In any case you write 'the only change is in what mutationem motus means and i would agree with that. But a change is a change is a change, and this is a fundamental change, only emphasised in a latterday attempt to square the law with SR, something which it is quite nonsensical to attribute to Newton.

 

Actually what we have again here is that same reluctance that I described above to admit science was and always is essentially untrue. Abandon that belief and essentially you abandon science for metaphysics.

 

As for derivative, you seem to have no idea of concepts like variation which were well-known and understood at Netwon's time.

Don't be silly.

 

There wasn't a mathematical operator, but I clearly stated "suggested" not "wrote".   Nope. It's still only an approximation as long as it is expressed as mdv/dt, which is how Newton expressed it. To say "F = m*a for v small enough and for m large enough" is not an approximation, is a precise statement.

Oh, come on! Yes if i say 'X is approximately true' that is a precise statement that X is approximately true. But that goes nowhere.

�

It's X that is approximate, not the statement about X.

To say "F = m*a" is an approximation. Newton's own formula (as you can read it above) is not an approximation even if we read it in SR. Only when we write "p = m*v" with no further details, then it becomes an approximation.   Well if you change them then you've changed them. They're not his concepts any more, are they? Duh! I am saying Newton's laws as enounces written in our modern textbooks, you're talking about his concepts as he owns them or something.

 

Of course I am. The phrase 'Newton's Law' means the law that Newton proposed. It doesn't mean some latterday variation of it. (Note what I said about the Mona Lisa above.) 'Newton's law' doesn't mean Newton owns it, but then 'Shakespeare's Hamlet' doesn't mean Shakespeare owns Hamlet.

 

But when Charles lamb bowdlerised Hamlet the way he did, the result was no longer Shakespeare's Hamlet, but  Lamb's Hamlet.

 

When Riemann generalised Euclid's geometry by dropping the fifth axiom, no-one went on calling it 'modern Euclidean geometry' as opposed to 'ancient Euclidean geometry'. We call it 'Riemannian geometry'.

I'm not sure what you mean by discourse.     http://www.m-w.com/dictionary/discourse Check definitions 3 and 5.

Edited by gcle2003 - 14-Sep-2006 at 07:37