I agree that we are both on the same side of an argument against some entrenched, but poorly founded, ideas in physics.Ben Saint-Clair wrote:I have to say, Treatid, that i feel we are on the same page but both reading in a different language.
That is, we both agree with each other, but it feels like we disagree because we are talking to each other in different terms and from different viewpoints. I'm not exactly frustrated with physics and mathematics like you seem to be (no doubt because you are deeply passionate about your subject area), but i feel that my argument does act in a very strong way to highlight this century old issue by making the case for the inexistence of time in the framework of McTaggart's old argument - seeing as McTaggart was met with universal disagreement in the Philosophical community.
It is my intention to shake things up a bit. Perhaps if enough people like us make a ruckus then we can start to make real change towards resolving this problem.
However, merely pointing out unfounded assumptions in mathematics and physics is too little.
Having fully grasped the non-existence of axiomatic knowledge - the path is now opened to properly understanding physics.
"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."
Axioms are impossible. Without axioms, we are left with very little. Which is quite handy - because with virtually nothing to choose between, working out what to do next isn't nearly as complicated as one might expect.
Since we cannot define anything at a fundamental level, we must describe the universe in terms that do not rely on definitions.
Describing the universe as specific changes in a network of relationships is not "/a/ way of looking at things". It is the only possible way of looking at things.
[One may feel that this requires "change" and "a network of relationships" to be defined - which seems to go against the non-existence of definitions. In practice we have a "by our bootstraps" situation. The meaning/significance of concepts only becomes (sort-of) clear once we have built the context (which consists of these concepts). The distinction between this construction and axiomatic constructions is not entirely dis-similar to the distinction between Newtonian Physics and General Relativity. While both systems appear to contain similar concepts - the thinking for one system simply does not apply (let alone work) for the other system).]
Many of the individual words you use sound good. I'm inclined to agree with the sentiment of some of your sentences.TimBandTech wrote:Time is unidirectional, and so long as the real value is used as its representative then an early conflict in representation is bound to have consequences, and hence much of the nonsense arguments on time, including respected physicists who are obsessed with the laws of physics working backwards in time. The real line is bidirectional and so cannot be an accurate representation of time; particularly not its geometrical quality.
But... You cannot define anything.
You cannot define "continuous". It can't be done. No one can do it.
The Real number line is an impossible fantasy. As fundamental postulates, dimensions don't mean or describe anything.
Mathematics and mathematicians are mistaken in thinking that they have ever defined a dimensions, or numbers or anything else.
You are right to challenge the real number line as fundamental. It isn't anything except a set of ad-hoc rules that we find to be conveniently similar to real world experience (in certain places).
Tell me what you mean by "continuous".
I'm sure you have a solid intuition about what 'continuous' means. But any attempt you make to explain that intuition to me will mean explaining the word by reference to other words. And then I'll ask you to define those words... and the ones after that... and after that... until you run out of words or try to re-use a word that we are in the middle of defining.
This is the difference between a relative understanding and an absolute definition.
We have direct experience of what distance is. Of velocity. Of Time. But that experience isn't the same as defining distance, velocity and time.
We can define time as being what clocks measure. This is technically correct - but not all that helpful in understanding time. Since clocks were made to measure time, defining time with reference to clocks is a tad tautological.
Every possible definition is tautological in a similar way. A 'continuous' thing is a thing that has the property of being 'continuous'. No matter how much indirection and obfuscation we manage to pull over our own eyes - this is the only thing you can say about the concept of 'continuous'.
Distance is velocity times time. Velocity is distance divided by time. Time is distance divided by time.
Does this tell us what Distance, Time or Velocity are?
It specifies a set of relationships. This isn't worthless (although it is tautological still). Our relationships with distance coupled with our relationships with time informs our sense of what velocity is. This is meaningful and significant to us humans. What it profoundly isn't, is a definition of any of distance, time or velocity.
Which is to say, there are things that we can know. Life is not without meaning and significance for us.
However, that meaning and significance does not come from axioms. There cannot be a fixed starting point from which we build... anything.
"There are continuous wires in my computer that form circuits that carry electrons."
We understand what this sentence means. "Continuous" has a significance that we can use to communicate concepts with.
Yet we know that matter is not continuous. We know that what appears to be an unbroken smoothness at large scales breaks up into molecules, atoms, quarks and other fictitious ideas.
Our concept of 'continuous' only works for certain scales.
You might argue that we can extrapolate the concept from what we do know. This is what mathematics and physics currently do whether consciously of unconsciously.
When extrapolating a curve or trend one is assuming that the curve or trend will continue in a predictable way.
There are infinitely many curves. As much as we might prefer consistently self-similar curves - that is our bias - in an absolute sense one curve is as significant as any other curve.
And trends can be tricky to fit a curve to. The same trend in different contexts may well warrant a quite different curve.
...
It may seem odd to have a clear concept of what you think 'continuous' means and yet be unable to define the term in an absolute sense. Most mathematicians and physicists are right there with you in thinking that their intuitive understanding of terms must be backed up by some definable meaning.
Indeed the terms are meaningful and significant to us as humans.
I don't need to know the difference between an inline and a rotary internal combustion engine in order to drive a car. You don't need to know how to build semi-conductor junctions in order to type on a computer.
Mathematicians don't need to understand why mathematics works in order to design a bridge or calculate taxes.
A river doesn't need to be conscious to flow, nor a bacteria to multiply.
However, if we wish to claim to be conscious; if we desire to have genuine understanding of our place in the universe; then we cannot be satisfied with pretending to know.
Physics cannot be described axiomatically. No-one can define anything as a fundamental property.
Starting with a continuous space, or one-signed numbers has no meaning. There is nothing you can construct from this basis - because there is no basis.