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Hi all,
I decided to attempt to explain why the Large Hadron Collider at CERN will find the Higg’s particle under BigFoot’s paw. In other words, why they will never find it.
The standard model describes the Higg’s as a “scalar” boson. We must first be sure that everyone understands the meaning of scalar. This is simply a quantity without direction. As an example a scalar is 10 apples on a scale. It has no direction as opposed to ten apples being shot from a canon towards the east. That is a “vector” quantity.
So, the Higg’s is a particle that has no spin. The next question you should ask is: How can it be a particle if it does not spin? It must move in order to be a particle.
Riddle me this: How can a particle move but move in no specific direction? The answer is that it can move in infinite directions, simultaneously. Say what!!!???
Think now of the primary motion of space. This is space respirations. Imagine a sphere that expands and contracts. From its center reference, it is moving in infinite directions, its radii, following it in and out as it breaths. This is not spinning. Spinning is the secondary motion of space.
The scientists are trying to find the particles that breaths ‘apart’ from bosons that ‘spin’.
The problem is that these motions, along with relative motions of counter spin, are all included in the spiral motion of one single particle. These motions cannot be teased apart. Yet they all constitute what a particle can do.
The infinite genius of the Creator has provided a pattern that has essentially infinite degrees of freedom of motion.
A spiral motion is moving in infinite directions at all times! Tell me if you can see that.
This is a model I’ve been pushing for some time now. It is taken from TUB directly. The physics blogs just don’t take me seriously. There is no math for them to model this motion. It is infinity everywhere and you cannot calculate infinity. This they will not stand for. If there is no math, just a simple explanation, there is no curtain to hide behind.
Manny
Not to diverge from your thread but before I try to respond to it I have a standard model question, sorry to go back there but:
Is the top quark still missing? detected the tau neutrino yet? found rest mass of neutrinos yet? is CP symmetry violation really the origin of matter? I mean – really – the Higgs idea with its field and boson is really relevant to all of the above and would at least preserve the consistency of the standard model if it were found, no?
I mean, what about the standard model to date is not accurate?
Hi nelsong,
“Nature never deceives us; it is always we who deceive ourselves.’ ROUSSEAU
QM has been astonishingly successful in many ways. It has given us a good first look into the mechanics of the very small. But it is time to get past the self-congradulations and the backslapping and to realize that both mathematically and theoretically the explanation is very partial. Physicists never tire of pointing out how accurate QM has been, but this due in large part to the amount of fudging that has been allowed. If you are allowed to correct your math after every experiment, without ever being required to explain exactly how the math corrections tie into the theory, then of course your math is going to be very accurate.
The theory of QED and the standard model does not subscribe to the concept of “time quantization”. TUB tells us that time is circular simultaneity and a succession of instants, which means that time is chopped up into segments that occupy intervals between these non events. Therefore, it stands to reason that time must be quantized. In QED time is asymmetric in order to preserve CPT symmetry. We must seriously question standard model explanations of space expansion and antimatter influences. TUB clearly tells us that time is symmetric and the means the CPT must be completely false.
We know that the origin of matter is Paradise. Like I said, if anyone finds the Higg’s boson it is not what they were looking for.
Remember that TUB tell us that the wave-like energies emitted by a particle have wavelengths equal to 860 time the diameter of the particle thus performing. The particle’s diameter is in constant and rapid spin AND breathing motion. The diameter is in constant change. The waves are superimposed and this causes unending confusion the the scientists.
I mean, what about the standard model to date is not accurate?
I would be much easier to ask; what about the standard model is accurate? It’s not the math and not the theory. We may be able to make some sense of the data but with the wrong theory we cannot interpret the volumes of data accumulated.
Is the top quark still missing? detected the tau neutrino yet? found rest mass of neutrinos yet?
What are these? Nobody can tell you. We can no more explain the mechanics of gravity than could Archimedes. We give cute names to sub-sub-subparticles and propose to measure their wobbles to the trillion-trillionth part of an eyelash but we cannot explain the orbit of the moon.
Physics is long overdue for a re-focus.
Manny
emanny3003 wrote:
“The next question you should ask is: How can it be a particle if it does not spin? It must move in order to be a particle. Riddle me this: How can a particle move but move in no specific direction?”
Hi emanny3003,
Just checking some assumptions here: As you know, the Higgs boson is different from the Higgs mechanism. The “mechanism” was a prediction about how one type of “mass” is induced by the rate of chiral oscillation (flipping from left to right) of the quantized spinors in Dirac’s 1928 equation.
This mechanism was proposed by at least 4 separate teams in 1964.
The boson was an extra prediction made by Peter Higgs. As he explained, for the “mechanism” to work, there would have to be a field of weak hypercharge within which these Dirac spinors would be flipping. His prediction was that given enough energy, it should be possible to cause some sort of compression wave in this field of weak hypercharge. It was a signature of this sort of Higgs-like compression wave that was measured at the LHC.
But here the story gets interesting. The rate of decay of this compression does not line up well with predictions. When the LHC gets switched back on next year, there are lots of tests ready to be applied — exploiting the enhanced luminosity of the upgraded LHC.
Thanks for being interested in all this!
PS: if you want to be taken seriously on physics forums, one first step may be to adjust your style, or rather, allow your style to be adjusted? Just a thought.
Nigel
PS: if you want to be taken seriously on physics forums, one first step may be to adjust your style, or rather, allow your style to be adjusted? Just a thought.
Hi Nigel,
I am really not interested in being taken seriously by folks on the physics forums. My “style” is one of asking pesky questions. This is part of seeking truth in science. Perhaps some resist being questioned. That is not my problem nor does it require an adjustment on my part.
Just checking some assumptions here: As you know, the Higgs boson is different from the Higgs mechanism. The “mechanism” was a prediction about how one type of “mass” is induced by the rate of chiral oscillation (flipping from left to right) of the quantized spinors in Dirac’s 1928 equation.
I am glad you brought up the Higgs mechanism. The Higgs field is supposed to induce a spontaneous symmetry breaking. What part of motion can become asymmetric and remain in existence or produce a boson? Pesky question number 1. Symmetry breaking would produce nothing, annihilation.
Symmetry can never be broken since motion would cease. TUB tell us the space motions are logarithmic spirals. The logarithmic spiral and hyperbolic space and circular time are all “unbroken symmetry”.
Graph out y=e^x, y=nlogx, y=1/x and x=y. The first two are inverses (mirror images) across identity (y=x) as is the hyperbola y=1/x. A circle is perfect symmetry as is an ellipse.
Other pesky questions:
In an expanding space how does the speed of light remain constant? What is the frame of reference in gauge math?
If time is linear, is it asymmetrical or is time reversible? TUB says time is circular.
How are ‘quanta’ possible if time is not quantized? If time is quantized, then is CPT symmetric?
If time is quantized then is space quantized? Time and space are inseparable (TUB).
How can light speed be a frame of reference for motion? How can motion frame another motion? TUB tells us that Paradise is our only still reference frame.
Is the ellipse a logarithmic construct? Why are orbits elliptical? Where is the force from the second focus in the ellipse? Why can’t current gravity theory explain the forces of an elliptical orbit?
The boson was an extra prediction made by Peter Higgs. As he explained, for the “mechanism” to work, there would have to be a field of weak hypercharge within which these Dirac spinors would be flipping.
The Dirac spinor ψ = ωp e^-ipx is a logarithmic function because it has the base of the natural log, e. If The Dirac spinor were to flip, its mirror image would be a function of the natural logarithm. Neither of these functions are calculable. All functions of the form y = e^ax are their own derivative. The function will never rectify, it forever diverges. Just look at the graph.
e^iπ + 1 = 0 This identity tell us that space is bound by time. Only time as circular and space, as hyperbolic, can sit orthogonally to one another. That is the significance of (i) (imaginary) as a power actually means.
Manny
P.S. I rarely ask questions in a forum that I do not know the answers to.
Just checking some assumptions here: As you know, the Higgs boson is different from the Higgs mechanism. The “mechanism” was a prediction about how one type of “mass” is induced by the rate of chiral oscillation (flipping from left to right) of the quantized spinors in Dirac’s 1928 equation.
Hi Nigel,
I think this deserves more attention. I have not written more on the eternal ellipse thread because I got side tract.I am prepared to show that the ellipse is indeed a logarithmic construct despite Newton’s rejection of this notion. All motion is logarithmic and that is why we have such a mess. I will elaborate on this presently.
Leibniz got stuck on the integral of the function of 1/x because the rules were that the solution was 1/0, or undefined. Since it was one of the most common operations in physics, a more reasonable solution had to be found.
This is what was presented and never questioned: ∫1/x = Natural logarithm (x)
Therefore, the derivative of nl(x) was to equal 1/x. WHAT A COLOSSAL BLUNDER!
Considering that the function y = e^x is its own derivative, what would you expect the derivative of its inverse (mirror image) to be?
When you consider that all motion is logarithmic, this is a major problem that has gone unrecognized. Let me illustrate the major cheat that has been perpetrated for over 300 years.
The following is the current method of finding the derivative of the natural logarithm function.
dln(x)/dx = lim d→0 [ln(x+d) – ln(x)]/d =
lim ln[(x+d)/x]/ = lim(1/d) ln(1 + b/x) =
lim [ln(1 + d/x)^1/d]
Set u=d/x and substitute⎯
Lim u→0 [ ln (1 + u)^1/u ]
= 1/x ln [ lim u→0 (1 + u)^1/u ]
= 1/x ln(e) = 1/x
That derivative is false.
The step⎯ lim as u→0 [ ln (1 + u)^1/ux. ] = 1/x ln [ lim u→0 ( 1 + u)^1/u
Pulling the 1/x down from the exponent and putting it in front of the ln is permissible, but there was also a shifting of the lim u→forward, so that it is now in front of the ln, and this most certainly is not permissible. One cannot separate the ln from its number. The reason this is important is that because, as confirmation of the last step, we are sent to the definition of e⎯
e = lim n→0 (1 + n)^1/n
Take note that this does not read⎯
e = lim n→0 ln (1 + n)^1/n
These two equation are not the same and this invalidates not only the derivative of the natural logx , but invalidates the integral of 1/x as the nlx as Lebniz asserted.
The integral of 1/x according to the integrating method of Leibniz results in a contradiction; the undefined expression ‘1 divided by 0’.
∫1⁄x dx = x^-1+1 / -1 + 1 = X^0 / 0 = 1/0
This is naturally unacceptable for mathematics to have this embarrassingly undefined expression. A so called ‘reasonable solution’ was accepted as the natural log x. The false derivation shown above was offered up as the solution. Because of the mathematical step of integrating the inverse function (1/x) is the most frequently used mathematical operation in physics (reflection), one can only shake one’s head at the sloppiness with which this science has ignored the natural logarithms. Had they been more rigorous they would have arrived at the same conclusion I have come to and realized that motion is not calculable.
Manny
P.S. What ever happened to the work you were doing on the Apollonian gasket of a Kleinian group?
Hi Manny,
Before trying to understand your mathematical insights, let’s check a few more of those assumptions you appear to be making regarding all things Higgs. You wrote:[e3] “I am glad you brought up the Higgs mechanism. The Higgs field is supposed to induce a spontaneous symmetry breaking. What part of motion can become asymmetric and remain in existence or produce a boson? Pesky question number 1. Symmetry breaking would produce nothing, annihilation.”
The symmetry thought to be broken is not geometric or topological. It’s a group symmetry that allows the four electroweak force carriers to be rotated into each other. As you know, the four bosons concerned are the W+, W-, Z, and photon. The theory goes that when the energy available to the associated fields dropped below about 100 GeV, these four bosons took on their currently measurable attributes.
The “symmetry” that was broken was that the photon could no longer be rotated into a superposition of {W+,W-,Z}.
Regarding your assertion that your insights into ellipses and logarithms can help correct a certain sloppiness committed by all mathematicians for centuries, I will make an effort to try to understand your point.
Nigel
Therefore, the derivative of nl(x) was to equal 1/x. WHAT A COLOSSAL BLUNDER!
Good lord. Proof that the derivative of ln(x) is 1/x in four steps that are a lot simpler than the math you tried to go through….
y = ln(x)
therefore e^y = x
taking the derivative of y as a function of x gives:
dy/dx e^y = 1
by substitution that e^y = x then very obviously gives:
dy/dx x = 1
divide each side by x to give you the dy/dx solution and that’s all there is to it:
dy/dx = 1/x
Here’s a great and well presented 3 minute video that similarly explains this basic proof that anyone can follow easily.
Hi Nigel
The symmetry thought to be broken is not geometric or topological. It’s a group symmetry that allows the four electroweak force carriers to be rotated into each other. As you know, the four bosons concerned are the W+, W-, Z, and photon. The theory goes that when the energy available to the associated fields dropped below about 100 GeV, these four bosons took on their currently measurable attributes.
The “symmetry” that was broken was that the photon could no longer be rotated into a superposition of {W+,W-,Z}.
Let us discuss the electroweak force. The weak interaction is supposed to be mediated by W and Z bosons. Bosons are supposed to be mediating particles with huge masses, “heavier than entire atoms of iron”. The W boson is the mediator in beta decay, and its entire job is in facilitating the reversal of a quark. This reversal is called a flavor change, because the quark goes from being a down quark to being an up quark.
d→ u + W-
But why would we need a boson the size of an iron atom to flip a quark over? Has anyone ever asked? (pesky question) The mass of a quark is said to be about 4MeV; and of a W boson, about 80GeV. So the mediating particle outweighs the mediated particle by 20,000 to 1. That is like using an atomic bomb to flip your mattress. A tad more force than the job calls for. Lets call this a red flag.
The W then decays into an electron and an antineutrino.
W- → e + v
Since the neutrino is said to weigh nothing and electron weighs .5MeV, we have a slight imbalance here. That decay is not intended to be an equation, but still. We have a huge amount of energy coming from nowhere and then disappearing into nothing. Is this another red flag or is Paradise the “nowhere” and the “nothing”? In predicting the W and Z physicists used an SU(2) gauge theory, but the bosons in a gauge theory must be massless. We must assume that the masses of the W and Z were “predicted” in some other way, then, since the gauge theory predicted zero masses. We are then told that the symmetry of the gauge theory must be broken, to give the bosons, mass, and that the Higgs mechanism does this job.
What we find is that the Higgs mechanism is a form of spontaneous symmetry breaking. What is spontaneous symmetry breaking? It is symmetry that is broken spontaneously. Something that happens spontaneously requires no mechanism, so the Higgs mechanism is a mechanism with no mechanism. And what evidence can you give for something that happens spontaneously? In other words, the SU(2) problem is solved by calling that breaking a Higgs mechanism. What gives?
We are told that the evidence for the Higgs mechanism is overwhelming, but this evidence turns out to be evidence that particles near the predicted W and Z masses exist. So, we are to understand that because big particles exist for very short times, this means the SU(2) gauge theory can’t be correct in predicting zero masses. And this means that the gauge symmetry must be broken, which means that the theory must be correct. This is unbelievably circular.
All that the fake Higgs mechanism does is allow you to break something you wanted to break, without having to give a mechanical reason for the breaking. It allows you to fudge your math while giving a fancy name to the fudging. But if your gauge theory requires you to bypass it with symmetry breaking, it could and probably does mean that your gauge theory isn’t any good to start with.
Manny
Hi tas,
y = ln(x)
therefore e^y = x
No, No, No. You have rotated your background 90 degrees. You cannot separate the nl and the base e from their axis.
The derivative of y=e^x is y=e^x, the same curve ad infinitum. Its inverse is y=nl(x)
You must look at their graphs to see this clearly. They are mirror image functions across identity.
Your conclusion would give dy/dx = 1/y. This function does not even intersect with y=e^x or y=nl(x) even to infinity.
The derivative is defined as the rate of change of the given curve, and it is defined as the slope of the tangent at x.
You must look at the actual table of differentials of nlog(x)
In this way you can see that we aren’t straightening out our curve as with power functions. There is no derivative of nlog(x) will ever give a straight line. Every derivative of nlog(x) is a greater curve than nlog(x) itself.
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!
Manny
Hi tas,
tas wrote: y = ln(x) therefore e^y = x
No, No, No. You have rotated your background 90 degrees. You cannot separate the nl and the base e from their axis.
Yes, yes, yes, yes. It’s not a “rotation of 90 degrees” or a separation from any axis but the same expression.
y = ln(x)
is the exact same relationship between y and x that is given by
e^y = x
You’ve confused this expression with e^x = y. Yes the curve of y = e^x is the mirror image of y = ln(x). They are different equations, so they have different curves when graphed. The relationship of y = ln(x) is the exact same relationship as e^y = x on the other hand and they are the exact same curve on a graph, it doesn’t make a difference to axes in the least. You can even simply plug any sample numbers you’d like into a calculator to show for yourself that the two forms of the relationship are identical and the axes aren’t changed a bit.
Take x to be 100.
y = ln(100) = 4.60517018….
So, we have y = 4.60517018….
Plug it back into the other form of the equation:
e^4.60517018
It equals 100.
Differentiating each with respect to x is no different either way since they are the exact same. I didn’t expect that you’d care for the proof though, I know the preference is SHOCKING HIDDEN FLAWS OF 300 YEARS OF MATHEMATICS – REVEALED!
Hi tas,
Take x to be 100.
y = ln(100) = 4.60517018….
So, we have y = 4.60517018….
Plug it back into the other form of the equation:
e^4.60517018
It equals 100.
Lets do another number, tas, and see how it works.
Take x to be 0.5
Y = ln(0.5) = -0.693
So, we have y = -0.693
Plug it into the other form of the equation:
e^-0.695
It equals 2.7182 Wow! What the heck happened taz?
Furthermore, IF indeed you and Wiki and everybody else were correct and the differential of y=nl(x) was y’=1/x, then,
If x is 0.5 then y = -.693 and y’= 2. The differential of a function must be the same positive or negative slope but not opposite.
Again, if y=nl(x) and y’=1/x, solve for x = -1.
y = nl(-1)
y = error (undefined); whereas,
y’ = 1/x
y’ = 1/-1
y’ = -1
Wow! What the heck happened tas?
So nl(x) is undefined at x= -1 and the derivative of nl(x) is equal to -1 at x = -1. Wow! What the heck happened tas?
I’ll explain why. You must see that the function y=1/x is two curves not just one. It is the ‘pair’ of hyperbolas commonly known as a rectangular hyperbola.
They are defined in only two of the four cartesian quadrants, (+,+) and (-,-).
So, NO, NO, NO, you cannot rotate your background 90 degrees and get away with it. I hope you understand this.
Differentiating each with respect to x is no different either way since they are the exact same. I didn’t expect that you’d care for the proof though, I know the preference is SHOCKING HIDDEN FLAWS OF 300 YEARS OF MATHEMATICS – REVEALED!
What you did was gloriously illegal! No charges will be brought against you nor any of the mathematical geniuses that have missed this for over 300 years. You are pardoned and released to you own recognizance. Just kidding.
I would not have stressed the importance of this major mistake in mathematics if it did not have consequences beyond this apparently trivial derivative. It also implies that the integral of 1/x is nl(x). Also untrue. The inverse function is the most common operative in physics. And my contention that all motion is logarithmic due to revelation from TUB of the space motions which are logarithmic spirals. This is not trivial but a big, big deal.
SHOCKING HIDDEN FLAWS OF 300 YEARS OF MATHEMATICS – REVEALED!!!
MANNY
Hi tas, Lets do another number, tas, and see how it works. Take x to be 0.5 Y = ln(0.5) = -0.693 So, we have y = -0.693 Plug it into the other form of the equation: e^-0.695 It equals 2.7182 Wow! What the heck happened taz?
Well, it should have been immediately obvious to you what happened. If so you would have immediately recalculated and never even mentioned it. That you think you know so much math and science and didn’t instantly realize the meaning of that number says everything about how much credence to give all your grandiose crazy claims about math and science.
What happened is that you simply didn’t do any calculation at all. The value of 2.7182 should be as recognizable to you as the value of pi, it’s just e itself. You goofed in the use of your calculator and did nothing more than bring up the value of e. Try again, take e to the power of -0.693
Or here, to make it simpler, here is the result using google.com as a calculator. Anyone can just click and see it for themselves.
Of course, ln(0.5) isn’t exactly -0.693 and so the result above isn’t exactly 0.5 but I’ll make the tiny assumption that you do understand ln(0.5) is an irrational number like pi, and with precision out to infinity the answer really is 0.5.
But it’s crazy, do you actually think that the result of ln(0.5) taken to the power of e would be anything else other than 0.5? By definition of what a natural log is that is going to be the case!
Why in the world are you even questioning this?
So, NO, NO, NO, you cannot rotate your background 90 degrees and get away with it. I hope you understand this. What you did was gloriously illegal!
I did really think earlier that you must have just read my post too fast, but here you are, sticking to your guns, railing against high school algebra. What you call “gloriously illegal” is algebra.
Take any simple two-variable equation and it’s not a surprise you can express it in terms of either of the variables and it’s still the same thing.
a=2*b
the exact same thing but instead as an expression in terms of finding b:
b=a/2
Here are likewise a couple other similar pairs:
a=1/b
b=1/aa=b^2
b=squareroot(a)Within these pairs each expression plots exactly the same as its counterpart on a graph no matter which form you want to pick, because each is precisely the same thing as the other. Now you tell me this, given this equation:
a=ln(b)
What is this:
b=????
You tell me.
Because that’s the step you’ve unbelievably tripped on in my posts above. You can’t even do high school algebra and you’ve flubbed simply punching numbers into a calculator without realizing it, what in the world are you doing pretending to declare all the rest of the world wrong on differential equations. All I see here so far is the Dunning-Kruger effect pushed forward by towering self regard, nothing more. Seriously. Like in the other thread where since Newton doesn’t make sense to Manny Logic, ergo Newton must be wrong (and not on any minor point, but the very proofs that nearly all the rest of the world recognizes as placing him as the #1 scientific mind of the modern era, others placing him second to Einstein by a hair). Simple high school math doesn’t sit right according Manny Math, therefore all the mathematicians of the world have been wrong. QED. Well, I do know the rest of the world is right and you’re not on these particular topics, but since your view is that in a showdown between Manny Logic and Newton, that Newton is wrong, I also know I’m in plenty of good company.
Hi Tas,
emanny3003 wrote:
Hi tas, Lets do another number, tas, and see how it works. Take x to be 0.5 Y = ln(0.5) = -0.693 So, we have y = -0.693 Plug it into the other form of the equation: e^-0.695 It equals 2.7182 Wow! What the heck happened taz?Well, it should have been immediately obvious to you what happened. If so you would have immediately recalculated and never even mentioned it. That you think you know so much math and science and didn’t instantly realize the meaning of that number says everything about how much credence to give all your grandiose crazy claims about math and science.
You were correct. In my haste before going to work I made this mistake.
Allow me to do this again.
Take x to be -0.5
y = nl(-.5) is undefined, correct?
If y’ = 1/x, then y’ = 1/-.5, then y’ = -2
Tell me if you think that a function that is UNDEFINDED at x would produce a “derivative” that IS DEFINED at x?
This effectively disproves the assertion that the derivative of y=nl(x) is Y’ = 1/x and visa versa, that the integral of 1/x is nl(x).
QED.
Please just look at the graph of y=nl(x) and that of the hyperbolas y=1/x. The natural log is only defined at x and y greater than 0.
y = 1/x is only defined at if BOTH x,y are greater then 0 AND when x and y are BOTH less than 0.
All that I will tell you about Newton’s work, for I do not know him personally, is that in all of his equations of motion and the calculus he never imagined that his cartesian graph was expanding.
I don’t need to remind you that you are on a Urantia Book website and you must surely know that there is space respiration. It is the primary motion of space. How is it possible for any of Newton’s work to be valid in an expanding universe? This goes for Einstein as well. The cartesian graph is the background by which all calculations are made. Now think of the ramifications of this fact if your chalk board is moving as you write your equations.
BTW, I apologize for not making my case this simple sooner. I, in no way, take your insults personally. I don’t know you.
Manny
To make it simpler let’s instead use the example you first used above, x = -1, and how you said that for y=ln(x) this is undefined. It’s undefined as far as your calculator is concerned but that doesn’t mean it is for mathematics.
You are aware of course of Euler’s identity, you even quoted it up above:
e^iπ + 1 = 0
It uses the term “i” which also isn’t real as far as your calculator is concerned (square root of -1).
Don’t you see that this identity in fact directly leads to the answer of what is ln(-1)? I’ll show it to you:
e^iπ + 1 = 0
therefore
e^iπ = -1
therefore
ln(e^iπ) = ln(-1)
by definition since ln(e^x) = x then
ln(-1) = iπ
Of course from the definition of the natural log (like the definition of square root), there isn’t meaning in the realm of real numbers for ln(-x), instead you’ve simply crossed into dealing with imaginary numbers.
With that in mind now click on this link to WolframAlpha for a graph of the function ln(x) (aka log(x)).
For ln(x) its property as a real function includes that its domain is all positive integers (x > 0) and that would apply to its differential as well. For this function the slope is positive across its entirety of this domain. That’s obvious just from looking at the graph. The slope (the derivative) of ln(x) across its domain as a real function is in fact yes, for real, a fact of reality, described by the function 1/x. Where x = 400 the slope is 1/400. Where x = 0.5 yes the slope is +2 (even though the value of y at this point is -0.693 — what you seemingly described in your post about the slope needing to be positive or negative to match the y value is entirely wrong — you can see this is incorrect in as simple a function as cos(x). The x, y, and y’ values can all be positive or negative independent of each other, it simply depends on the shape of the curve).
You readily can see in the graph at the link above, where there is the imaginary part of log(x) that it is the mirror image of the real domain (with the x=0 axis as the mirror) and the slope of it is *negative* across its entirety. That is where the (-,-) hyperbola is at to complement the (+,+) one.
As for “insults” I’m just calling it like I see it, I’m always going to be very pointed and direct in response to rhetorical grandiose hyperbole that I see is unwarranted and I’ll explain exactly why. I do look forward to plenty of other conversations where there isn’t any of that.
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