By 'ideal scientific standards' I have meant for example this statement from Wikipedia

'The Oxford English Dictionary says that scientific method is: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses."'

Yet, if we consider how science has been done according to historical facts (not how it could have been done), then there are discrepancies. After all Newton has called in God who from time to time corrects the planets to preserve stability of the Solar system. It is written in his book and this is a historical fact. According to statement above one can even say that this was a result of systematic observation, measurement and experiment.

As for entropy and information, I may missed some your arguments. Yet, in all papers you gave me there was written that the equivalence of the thermodynamic entropy and information follows from similarity of the two equations. There were no experiments, observations and measurement to this end. Even more, people who have made this statement have not applied it to typical thermodynamics problems and have not shown how conventional thermodynamic problems (heat engines and computing phase equilibria) benefit from such a statement. My examples to this end are here

Finally, you are right that when living brains still exist, one have right to say that a mathematical model survives a death of a couple of mathematicians. The question is how the inexorable laws have functioned when there were no human beings. How the Universe computed itself when the mathematics has not been yet developed?


On 09.04.2012 18:21 meekerdb said the following:
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
actual consequences.

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 string theory).

This is Feyerabend's point, that the Newton laws have been just ad hoc
hypotheses, nothing more.

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 observations.

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

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 tested.

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.[3] 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.[4] 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.[5] Penelope
Maddy conjectures that our nervous system contains higher order
assemblies that correspond to thoughts of particular sets.[6] 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

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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