What I will ask in return is that, in posting, can some effort be made in incorporating some of the science in TUB or at least mention some reference to the book?
Well, here is the Urantia Book quote which explains why I am still discussing this before any consideration of “digging deeper” as you’d like:
“Do not make the mistake of the foolish carpenter who wastes valuable time squaring, measuring, and smoothing his worm-eaten and inwardly rotting timber and then, when he has thus bestowed all of his labor upon the unsound beam, must reject it as unfit to enter into the foundations of the building which he would construct to withstand the assaults of time and storm.” (156:5.3)
It’s foolishness to attempt a deep and complicated exploration of concepts when at the first most elementary step there’s already a sideways shooting off into wrongness. When there’s an unsound timber at the very beginning of the building project, then there isn’t any hope of being able to make anything useful from it.
You have a tendency to make various big grandiose claims — and as I’ve seen, very unsound claims — and in this thread it has been that there’s a very specific rotten timber at the basis of mathematics and physics that you’ve been eagle-eyed enough to spot though nobody else has.
Therefore, the derivative of nl(x) was to equal 1/x. WHAT A COLOSSAL BLUNDER!
When you consider that all motion is logarithmic, this is a major problem that has gone unrecognized.
The current derivative of nlog(x) is said to be 1/x but if you just look at the table, that isn’t true.The truth is that the curve y=e^x is its own derivative. The curve y=nlog(x) is its own derivative. Why? Because e^x = 1/nlog(x). LOGARITHMIC FUNCTIONS CANNOT BE RECTIFIED, THEY ARE NOT SUBJECT TO THE CALCULUS!
The inversion or mirror image of y = e^x is y = nl(x). Therefore, Y = nl(x) must also be its own derivative.
This is not trivial but a big, big deal.
As usual you’ve then wanted to go ahead with all sorts of intellectual building projects based on logic and math that is based on stuff like this taken as gospel truth in your mind, which no one else you can point to even agrees with. To me, it seems clear you’re perfectly comfortable doing this because, rightly or wrongly, you have supreme confidence in your own intellectual conclusions even if it means they’re contrary to every mathematician in the world and for centuries in the past. You have no problem with declaring loudly and publicly that they are wrong and you are right.
I don’t have a problem with that either really, and it’s been of a bit of interest to see what all your noise is about. In looking ever so slightly closer however, it becomes very very evident to see that this isn’t a situation of someone giving remarkable insights, despite the delivery with the rhetorical flourishes of someone thinking they are giving out huge and important and world-changing information.
I won’t belabor the topic much longer, for this post however I’d just like us to step back a moment, and let’s just re-visit a very basic mathematical truth and definition about this topic. Your beef is with differential calculus as applied to the natural log. We’ve been arguing about the “derivative” of ln(x): I know it to be y’=1/x and you claim that all the world is wrong and it’s very different. Well, what is it that differential calculus does for us? What meaning do we get from the “derivative” of an equation?
It’s actually very simple. Here is a definition from wikipedia:
“The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point.”
I agree with this. The meaning of the derivative is that it provides us with an equation that tells us what is the slope of the original equation at any given point on its curve. That is all we are talking about.
What is the slope. If we take an equation like y = 2x, which is just a line, the derivative is just y’=2. The slope is just a constant of “2” and for all infinity it’s the same. If the equation is y = x^2, which is a curve, the slope is always changing and depends on where we are on the curve. The derivative of this function is y’=2*x. We are now able to calculate the slope of the curve for any value of x using this simple formula, 2*x.
A slope has two components of information. It has a magnitude, which tells us how steep or shallow the slope is, and beyond that, it is also either positive or negative. A slope which is proceeding upwards is a positive slope and one that is proceeding downwards is a negative slope.
As I proved in an earlier post, for the natural log function y=ln(x), the equation that tells us the slope of this curve at each point is in fact 1/x.
You do not believe this result. Instead this is what you believe:
“The inversion or mirror image of y = e^x is y = nl(x). Therefore, Y = nl(x) must also be its own derivative.”
You believe that the slope of the curve ln(x) is itself also described by the very same function, ln(x). I do understand your logic for believing this. Since the slope of the function e^x is itself e^x, therefore you think that the same must be true of ln(x). You think this is “not trivial but a big, big deal” that mathematicians have gotten such a basic thing wrong.
While I understand your intuition on this point, it is of course extremely simple to test your intuition against reality, just like it was easy to test my earlier points by punching numbers into a calculator. No matter how attractive and inherently persuasive the intuition is in your mind, if in comparison to reality it in fact doesn’t match reality, then your intuition has not been correct. You can take either of two paths from there however you’d like: either not accept the reality or not accept that you had a good intuition. You won’t find that many people will want to follow along on your journey away from reality for too long and deeper into your own system of personal intuitions, so that’s one reason not to go that way, but on the other hand you seem to see these intuitions of yours as very deep and profound insights and so you also seem extremely attached to them. That’s my impression from your posts on this message board and the other one where you often participate, take it or leave it as you’d like.
So, now let’s compare your conjecture against reality. Let’s not worry about mathematical expressions and equations again, let’s just simply examine the curve of the function ln(x), we really can learn all we need just from that.
Again, here is a graph of it using WolframAlpha. The way the site works at the moment, it’s showing me two versions of the function’s plot, one on the scale of -1 < x < 1 and the second is on the scale of -6 < x 6. I’d ask that we focus on the second one since it gives us more to look at.
Starting at x=0, the curve is down off the charts in the depths of infinity at -y. As we move forward along x, the curve rapidly springs upwards from this negative infinity. You can see easily for each little bit of movement up x, huge strides upwards for the y value are made. The curve is ascending at this point and therefore the slope is positive. Not only is the slope positive but it has immense magnitude, it is very steep. In fact in just going from x=0 to x=1, the curve ascends all the way from -infinity up to intersect with the y=0 axis. That is an immense journey to make for traversing just one value of x!
But you can already see that by that point, x=1, its slope seems to have slowed and rounded a bend of sorts. What happens for the next value of x, x=2? Do we go shoot up to infinity? No — and for this I’ll use my calculator — but instead we just ascend from
ln(1) = 0
to
ln(2) = 0.693
We certainly are not going up at such a steep rate anymore… Let’s see some more values:
ln(3) = 1.099
ln(4) = 1.386
ln(5) = 1.609
ln(6) = 1.792
ln(7) = 1.946
ln(8) = 2.079
ln(9) = 2.197
.
.
ln(100) = 4.605
What is happening is that the curve is continuing to ascend. Its slope is still positive. We can see already that that is never going to change now. For each next value of x, the result of y is always going to be a little bigger than the earlier y value: The slope of the curve for ln(x) is always positive for all values of x>0.
What you can also see from the curve however and from the numbers is that the amount of change gets to be less and less as we go higher with x: The magnitude of the curve’s slope is always getting smaller as x gets bigger.
So, let’s see how that compares to your beliefs. Your conjecture is: “Y = nl(x) must also be its own derivative.”
First test: We know that the slope of the curve is always positive. If we find any result of ln(x) for x>0 where we get a negative value, then that definitively disproves your conjecture that ln(x) describes its own slope.
Result: For all values of x between 0 and 1, the result is negative. Therefore your conjecture is definitively disproven.
Second test: We need to see magnitude of slope decreasing as x gets bigger in order to accurately describe the curve.
Result: For every increase in x the result of ln(x) actually increases, not decreases. Therefore your conjecture is disproven for this characteristic also.
There is a function however that does capture these characteristics perfectly and mathematicians have known it and proven this to be the case for centuries. They will be able to continue to rely and trust on this fact indefinitely, because it’s true.
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