Congratulations! Your video, The Riemann hypothesis explained, has reached the #1 spot in the current Top 15 New Videos listing. This is a very difficult thing to accomplish but you managed to pull it off. For your contribution you have been awarded 2 Power Points.

This achievement has earned you your "Golden One" Level 20 Badge!

Thanks for this, haven’t seen riemann hypothesis explained this well.

Your video, The Riemann hypothesis explained, has made it into the Top 15 New Videos listing. Congratulations on your achievement. For your contribution you have been awarded 1 Power Point.

*quality

I'm currently reading "Superintelligence" by Nick Bostrom and it's pretty *fear inducing.

If we ever do hit the singularity... it doesn't really matter what we do.

First up, if it's an AGI is to be any use, it needs to be at least as smart as us. Which means, by definition, it will be capable of writing its own AGI.

There are any number of nightmare scenarios where even a seemly benevolent goal might be disastrous for humanity.

"Multivac, fix the environment!"
"Ok, what's the major issue with the environment?"
/wipes out humanity

"Multivac, solve the Riemann hypothesis!"
"Ok, but I'll need a lot of processing power"
/converts entire planet to a giant cpu

Even if, by some miracle, we end up developing a benevolent AI that understands our needs and is aligned with them, (e.g. the Culture Minds), we are no longer in control.

We might be along for the ride, but we're certainly not driving.

The other thing that's interesting is a question of scale. We tend to think of intelligence in human terms, like this.

infants..... children.....mentally impaired..Sarah Palin.....normal people.....Neil deGrasse Tyson.....Feynman, Einstein, Newton, etc.

But that ignores all the lower intelligences:

bacteria...Trump......insects.....sheep.....dogs...chimps, dolphins, etc............................... dumb human..smart human.

But from a superintelligence's point of view, the scale looks more like this
bacteria.. humanity ... Tesla ................................................... ..................................................................................................
..................................................................................................
............................................................................................. AI

You are correct, the way it is written in the title is wrong. One possible notation as I was taught many years ago would be to add an "R" for Ramanujan above the equals sign to point out that we're talking about the sum of a diverging infinite series.

No idea if it's the correct notation, especially since I've seen different versions of it.

That said, there are multiple proofs that the Riemann zeta function of -1, which is the infinite series mentioned above, does in fact equal -1/12.

As a reminder, the Riemann zeta function is this:

zeta(s) = sum(n=1,inf) 1/n^s

If you restrict it to real numbers, it converges for all s>1, so by evaluating it at s=-1, you are messing around with a diverging series, which is why it looks so funky. It's a holomorphic continuation outside its defined area and it seems to work for theoretical physics. And it gives me a headache.

^ You can make all of that make sense by simply shifting your epistemological position to the only ones which truly make sense i.e. phenomenology &/or perspectivism.

To rephrase that in less impenetrable terms:
"Materialism" (or in your case I assume "Scientific Materialism") that is to say 'matter is primary', from a philosophers POV is a deeply flawed assumption. Flawed because there appears to be not one experience in human history that did not occur entirely within the mind.
When one see's say a Dog, one only ever experiences the images and sensations occurring within ones mind. You don't see the photons hitting your retina, only the way your mind as interpreted the data.

However the opposite position "Idealism" (mind is primary) is also fundamentally flawed in the exact opposite way. If our minds are the only "real" things then where exactly are they? And how do we even derive logic and reason if there is not something outside of ourselves which it describes? etc. etc.

Philosophers like Husserl, Heidegger and Sartre' got around this by defining a new category, "phenomena". We know for certain that "phenomena" exist in some sense because we experience them, the categories of mind and matter then become secondary properties, both only existing as definitions we apply retrospectively to experiences. i.e. stuff happens and then our brains kick in and say "that happened because of X because in the past X has preceded similar experiences" or "that thing looks like other examples of Y so is probably Y".

The problem then is that this appears to come no closer to telling us what is objectively happening in the universe, it's more like linguistic/logical housekeeping. The phenomenologists and existentialists did a superb job of clearing away all of the old invalid baggage about how we try to describe things, but they did little or nothing to solve the problem of Kants "nouminal world" (i.e. the "real" stuff that we are experiencing by simulation in our minds).

Its stumped philosophers for centuries as we don't appear to have any way to ever get at this "nouminal" or "real" world we naturally assume must exist in some way. But....

I reckon ultimately one of the first western philosophers in history nailed the way out 3000 or so years ago. Pythagoras said "all is number" and due to the work of Euler, Riemann and Fourier in particular I think we can now make it stick. (yeh its turning into an essay sorry )

Without wishing to go deep into a subject you could spend half your life on; Fourier transforms are involved in signal processing. It is a mathematical means by which spatio-temporal signals (e.g. the vibration of a string or the movement of a record needle) can be converted with no meaningful loss of information into frequency (analog) or binary (digital) forms and back again.

Mathematically speaking there is no reason to regard the "signal" as any less "real" whether it is in frequency form or spatio-temporal form. It is the same "signal", it can be converted 100% either direction.

So then here's the biggie: Is there any reason why we could not regard instrumental mathematical numbers and operations (i.e. the stuff we write down and practice as "mathematics") and the phenomena in the universe they appear to describe. I.e. when we use man made mathematical equations to describe and model the behavior of "phenomena" we experience like say Physicists do, could we suggest that we are using a form of Fourier transform? And moreover that this indicates an Ontological (existing objectively outside of yourself) aspect to the mathematical "signals".

Or to put it another way, is mathematics itself really real?

The Reimann sphere and Eulers formula provide a mathematical basis to describe the entirety of known existence in purely mathematical terms, but they indicate that pure ontological mathematics itself is more primary than anything we ever experience. It suggests infact that we ourselves are ultimately reducible to Ontological mathematical phenomena (what Leibniz called "Monads").

What we think of as "reality" could then perhaps be regarded as non dimensional (enfolded) mathematics interacting in such a way as to create the experience of a dimensional (unfolded) universe of extension (such as ours).

(R = distance between two points)
Enfolded universe: R=0
Unfolded universe: R>0

Neither is more "real", they are simply different perspectives from which Ontological mathematics can observe itself.

"Reality": R>=0

I've explained parts of that poorly sorry. Its an immense subject and can be tackedled from many different (often completely incompatible) paradigms. I hope at the very lest I have perhaps demonstrated that the Holographic universe theory could have legs if we combine the advances of scientific exploration (i.e. study of matter) with those of Philosophy and neuroscience (i.e. study of mind & reason itself). The latest big theory doing the rounds with neuroscience is that the mind/consciousness is a fractal phenomenon, which plays into what I've been discussing here more than you might think.

Then again maybe you just wrote me off as a crackpot within the first few lines "lawl" etc..

Well, space-time coordinate of one of those space-time manifold charts (covering the space-time manifold) is one object that you certainly can "travel" back and forth(remember Godel formal PDE's solution for Einstein equation ). However , what realy counts and play the role of the Newtonian time in general Einstein relativity is the unique proper-time of a given event !(this can not be back!). Note that still remains a problem to "adjust" colectivelly the proper time of several geodesics associated to the motion of several particles moving in the back ground of a given relativistic gravitational field (The twin paradox has not been fully understood !).Let me explain better : In the Einstein framework , one gives a certain energy-momentum configuration (the "Sun") (mathematically a tensor of rank two in relation to the Local dipheomorffism space-time manifold group) in the (tensorial bundle) of space-time manifold :a object from the beginning possesing solely a differentiable topological structure and after that (and if compatible with the manifold topology-Chern /Gauss theorem constraint, Riemann completeness ,etc..), one determines the topologically compatible local metric structure of the smooth space-time by means of the famous Einstein Equations.If everything is smooth from a geometrical point of view , one starts the prediction of the "falling" bodies trajectories in this gravitational field throught the solution of the Boundary-Value Sturm liouville like problem associated to the geodesics non linear equations (you should know the beginning and the final point of the falling body trajectory into the space-time ,not the initial point and its "initial velocity" as in Newton Equation).Now one can make further steps on the Einstein program by exchanging the mater-energy Einstein's source by boundary ad-hoc conditions simulating point sources -delta sources-(not dipheomorffism covariant) ,like the Schwartz-Schild solution for Einsteinian particle motions around the Sun), and thus leading to a rich mathematical universe ( astronomical and astrophysical/cosmological observable ?)

>> ^Quboid:
G2) I don't believe in evolution. OK, I agree in general, but does it explain what it aims to accurately and completely? I very much doubt it. In fact I'd be amazed if the original work wasn't mostly discredited by now, just like much of Newton's work, Einstein's work and so on. Darwin's work was certainly a big step in the evolution of knowledge

The reason Evolution isn't discredited yet is the same reason Gravity wasn't discredited by Einstein: both are facts of life, however you choose to explain them. Why Darwin's work isn't discredited yet is the same reason Euclides' work isn't either: they're basic algorithms for solving precise problems. Unless the problems themselves change (more precisely our understanding of the problems), the solutions don't either.

Both Euclides and Newton ignored a pretty important variable: the three dimensional nature of space (four for space-time). That is why their algorithms were updated later by, among others, Riemann and Einstein. Darwin gave an algorithm for the Evolution of Life. It has been updated since, but there hasn't been a "three-dimensional" revolution yet (it's still a young theory by any standard, and note that the Theory of relativity hasn't been discredited yet either on macroscopic levels) . Even with that kind of revolution though, we would still talk about Evolution, just as we still talk about Gravity.