Re: model for thought


"Aaron" <anodide@xxxxxxxxxxx> wrote in message news:1170500991.860927.219790@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Feb 2, 11:03 am, "Dumbledore_" <Headmas...@xxxxxxxxxxxxxxxxxx>
wrote:
"Aaron" <anod...@xxxxxxxxxxx> wrote in messagenews:1170410960.321168.191890@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hello,

I have taken basic physics and calculus.

Math seems like endless abstraction all boiling down to the act of
counting. It is not natural to me.

But, I am good at programming computers.

Ah, computing...an endless abstraction all boiling down to the act of
counting. It is very natural to me.

Hey, I meant to respond to this in my last po
I am not so good at interpreting implied meaning from a statement, but
I'm going to do my best here.

I said I was good at computing and, "Math seems like endless
abstraction all boiling down to the act of counting. It is not
natural to me."

You responded with, "Ah, computing...an endless abstraction all
boiling down to the act of counting. It is very natural to me."

My best guess is you used rules of logic and implication to make a
statement which I should be able to make, but at the same time points
out that I am not really saying anything at all because mathematics
and computing are equivalent (?)

Mathematicians (and computers) do not guess. Not even best guess,
unless programmed to do so, in which case a random number generator
would be employed to "roll the dice".
The closest to guessing that I know of is a statistician's estimate.
He applies a probability to his estimate.
Guesses are subjective opinions and of no scientific value.
Any implication that you perceive I may have made is a matter of
your opinion only. The statement above refers solely to me, I said
nothing about you.
What is your worst guess and your average (mean) guess?




Math seems to use the notion of quantity and function. So we figure
out functions that describe what we percieve in our surroundings.
Functions, as far as I know, transform values in their range to values
in their domain.

Functions transform values from the domain to the codomain (or image).
Values outside the range are not in the domain upon which the function
operates. Now you should know a little further.


For example, you pull on a spring and measure the force it exerts on
the aparatus which is pulling it to various lengths. You then look at
data and derive a function to describe that resistance at any
arbitrary length. You note that the function accurately predicts the
force at points you did not previously test.

Are you discussing linear interpolation for your benefit or mine?

You not that the
function is continuous.

Is f(x) =1/x a function?
Is f(x) = 1/x continuous at x = 0?
A mathematician says 0 (zero) is not in the domain of f(x) = 1/x.
There is no value of x such that 0 |--> f(x)
f(x) is a function for all x belonging to R except x = zero.
Most computers and calculators will inform you of this fact.

To further understand relativity (your stated objective), no mathematician
would say "the velocity of light in our theory plays the part, physically,
of an infinitely great velocity" and still be a mathematician.
Einstein was not a mathematician. Whether he was a ranting lunatic
or a con artist is not provable. Thos that make money from relativity
are con artists and criminals, those that preach it for free are lunatics.


You become satisfied that the function is a
statement of "truth" about reality.

A mathematician is quite happy with the valid statement:
"All bright green flying elephants lay their eggs in black holes."
and will willingly discuss the breeding habits of bright green
flying elephants.
He is far less happy with "There are bright green flying elephants"
or "There are black holes".
He is not crazy enough to go looking for either entity, but should
you find broken eggshell in a black hole he may be persuaded as
to some truth about reality.


Programs are more than functions, I think. My reason is that programs
do not just transform input to output. They do start with input, but
they do can do more with the input than mathematics allows because
they "run", as opposed to "describe".

Computers execute an ordered sequence of mathematical statements,
the order being conditional on the data.



I don't feel like I am being precise enough.

FWIW, I agree with your feelings.



Let's say I the input is X.

A continuous function describes an process to attain the output, which
is always Y. so f(X) = Y.

Now take a program and give it X.

A program can run in a loop, and the result is a series of outputs.

x = 4
do while ( x >= -1)
{
print 1/x
x = x-1
}
Run
0.25
0.33333333333333333333333333333333
0.5
1.0
Division by zero in line 4.

Now change the data.
x = 1.5

Run
0.66666666666666666666666666666667
2.0
-2.0
Done.

The data changed the expected program behaviour. Caution
is needed in programming. If you do not handle exceptions
yourself a good operating system handles them for you,
usually halting.

x = 4
do while ( x>= -1)
{
if x print 1/x else print "Cannot divide by zero, dumbo"
x = x-1
}
Run
0.25
0.33333333333333333333333333333333
0.5
1.0
Cannot divide by zero, dumbo
-1.0
Done.

The computer does exactly what you tell to do, if it can.
There are only two reasons people will not do what you ask
of them. They can't or they won't.
Do not ask a surgeon to repair your car or a mechanic to amputate
your leg. They either cannot or will not, but as a team they'll do
their best to extracate you alive from a car wreck.
Do not ask a physicist about mathematics, it could cost you
your life.




You may argue that all I describe above is a function taking two
variables, such as f(X,s) where f is the step.


I may.


However, there is no way to arrive at F(X,s) without running the
program from X to s. It takes time and energy. The greater s is, the
longer it takes to arrive at the output.

Ok <shrug>
What would you like me to do about it?



I have been thinking for many, many years.... I am not generally
egotistical, so I'm interested if I am missing something here. I
"think" programs are fundamentally different from functions.

A telephone directory is not a phone number, it is a list of phone numbers.
A computer program is a list of functions.

YES, I am aware of the book by Steven Wolfram. I have been thinking
about this for many years. I am NOT, in any way, trying to open the
can of worms that his book does - I just don't even want to go there,
pretty please :)

Then don't, nobody is forcing you to. Go and play soccer instead. :-)


Anyway, sorry this got a bit long winded, but if programs and
functions are truly equivalent, I really want to understand it.

I'll do the best I can for you. Functions are often lists of more
primitive functions. No computer will ever generate sqrt(2) = 1.414...
or pi = 3.14159265... for example, because there is no solution that
doesn't have an unlimited number of decimal (or binary) places.
So we stop when a desired accuracy is achieved (a random choice)
and guess, but the guess is an educated guess.
In physics the guesses are less well educated, physicists are
playing with mathematics which they do not understand.








I want to understand special relativity better and leverage my
aptitude for writing simulation programs to do so.

Start here:
http://www.androcles01.pwp.blueyonder.co.uk/PoR/PoR.htm



My hypothesis is that a minimal set of relevant artifacts derived from
human perception can be represented as simple elements in a simulated
universe.

I am hoping to simulate "cube universe" with the following parameters:

- a particle is a three dimensional cube
- a particle is currounded by 6 adjacent particles called siblings
- a particle has a state of empty, massive, or lit
- an empty particle can become massive only if a sibling is massive
- a massive particle can become empty only if a sibling is empty
- an empty particle can become lit only if a sibling is lit
- a lit particle can become empty only if a a sibling is empty

I am still thinking about exactly how to define velocity in this
model, but it will correspond with newton for massive particles and
einstein for lit particles.

From that, I hope to laws of physics from newton up to special
relativity.

I think this is the way I will learn it most effectively.

College was such a waste. Sitting in giant rooms with a nutty guy
ranting and scribbling on a black board. I just didn't get it. Now
I'm 31 years old and I'm trying to finally get it :)- Hide quoted text -

- Show quoted text -


.

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