On 4/9/2012 7:28 AM, Evgenii Rudnyi wrote:
On 08.04.2012 19:55 meekerdb said the following:
On 4/8/2012 5:20 AM, Evgenii Rudnyi wrote:
I believe that we should consider Newton in his historical context. As
far as I have understood, because of not quite right empirical values
(masses, etc.) and/or because of low level of mathematics that was
available at his time, his use of his laws did not agree with
Right. There was no "clash between the facts and Newton's law of
gravitation used without additional assumptions." There was a clash
between Newton's calculations of the consequences of his laws and the
It depends on how you define fact. Imagine that at Newton's time the ideal scientific
standards would have been accepted.
I don't know what you mean by 'ideal scientific standards'.
Then his idea and his paper have been just rejected. "Okay, your idea is nice but you
have to work on it some more to make it scientific." Don't you agree?
No. The scientists then were not fools. They were well aware that observational data has
errors in it. They could recognize that accounting for the gravitational influence of one
planet on another was mathematically intractable, so even if the theory were exactly right
the approximations necessary to get solutions would not be exact (the same problem with
This is Feyerabend's point, that the Newton laws have been just ad hoc hypotheses,
That's a silly remark. Newton's insight was that things fell down on the surface of the
Earth and if the same for extended out indefinitely it would pull down on the Moon too.
But if the Moon was moving fast enough it wouldn't fall to the Earth it would fall around
the Earth in an orbit.
You cannot say that they come from observations, as they have contradicted to the
observations at that time.
Newton was influenced by the observation that orbits were ellipses (approximately) and his
1/r^2 law produced ellipses.
The most interesting that "Who cares?". The Newton laws have been accepted by the
scientific community long time before they have been brought in agreement with
But they were never 'brought into agreement' by your 'ideal' standards. The advance of
the perihelion of Mercury was never explained until Einstein, although people tried
postulating an unobserved planet to account for it.
"But this meant that Newton's theory gave correct results only when used in an ad hoc
way. It did not reveal a feature of universe. Did scientists give up? No. The theory was
plausible, it had astonishing successes so it retained despite the fact that, taken
literally, it led to absurdities. Besides, many scientists were interested in
predictions only and did not care about a metaphysical notion like 'reality'."
So, to state that a theory is driven by the facts is actually wrong.
No one has stated that. Theory is tested by the facts.
In the historical context, the facts are actually driven by a theory.
All observations depend on some theory, but not necessarily on the theory being
It happens the same way nowadays. Take for a example the superstring theory. It is has
not been driven by facts in any way. Or this notion that information is equivalent to
the thermodynamic entropy. It has nothing to do with facts at all.
Still trying to ride that horse? It's your loss if you can't see the
Hence his use of God.
This also raises a question about mathematics that bothers me. If we
assume that mathematics (for example Newton's laws written as
equations) is the result of neuron spikes, then to me this whole story
seems like a wonder. For example, try to think about the history of
Newton's laws according to the quote from
(the references are in pdf)
"Materialists believe that mathematical objects exist only materially,
in our brains. Mathematical objects are believed to correspond to
physical states of our brain and, as such, should ultimately be
explicable by neuroscience in terms of biochemical laws. Stanislas
Dehaene suggests that human brains come equipped at birth with an
innate, wired-in ability for mathematics. He postulates that,
through evolution, the smallest integers (1, 2, 3 . . .) became
hard-wired into the human nervous system, along with a crude ability
to add and subtract. A similar position is defended by George Lakoff
and Rafael Nunez, who seek to explain mathematics as a system of
metaphors that ultimately derive from neural processes. Penelope
Maddy conjectures that our nervous system contains higher order
assemblies that correspond to thoughts of particular sets. She
posits that our beliefs about sets and other mathematical entities
come, not from Platonic ideal forms, but, rather, from certain
physical events, such as the development of pathways in neural
systems. Such evolutionary explanations seek to derive all our
mathematical thoughts from purely physical connections between neurons."
The same view expounded by W. S. Cooper's book "The Origin of Reason"
which I have recommended.
I see some problems along this way.
Let us consider the story with Newton laws in this context. Laplace was able to create a
new mathematical theory that did not exist at Newton's time. What does it mean?
He stood on the shoulders of Newton.
That there was a gene mutation for time being between Newton and Laplace? Or that Nature
has made natural neural networks in abundance already at ancient times and Newton just
failed to employ full capabilities of his brain?
Also let us take my experiment with two mathematicians, I have made now a nice picture
to this end, see slide 26
The theory above means that Pi exist only when mathematicians' brains are running. Yet,
it seems that a mathematical theory due to inexorable laws describes the experiment
correctly even at the state when mathematicians are dead.
You mean you have a mathematical model which agrees with your observations of an
experiment, even though the guy that thought of the model is now dead. Why is that a
problem. My grandfather was named "Isaac Newton" and that's a true description even
though he's dead.
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