Universal Hyperbolic Geometry 0: Introduction

[TheFlightguru]

@FluffyBunniesOnFire In my personal opinion, there is a great difference between theism and atheism. God is an intelligent entity, no amount of maths will bring a being other than what god has created. Now, without going off on a tangent (if you'll pardon the pun), I assume you understand conservation of mass. Therefore, how can our universe be created from nothing? I'm no finitist, but something infinitely small in nature (and not some imaginary domain) is nothing.

[TheFlightguru]

I noticed how you said 'it's the way god wants to express the beauty of natural world'. I'm intrigued as if you are christian or any religion ( as I am christian). My maths teacher is an atheist and always tries to use maths to deny the existence of god when in fact I think such beauty and complexity could only be created by god. If you're an atheist, I have no problems with that, I am just intrigued. 

[njwildberger]

@TheFlightguru I wouldn't say I am particularly religious in a standard way, but I certainly share your feeling that the beauty and complexity in the mathematical world suggests some kind of organizing principle/entity beyond what we can see directly---possible evidence of a god(s). See my paper Evolution versus Intelligent Design: A mathematician's view at my unsw webpages, under views.

[Npowell01]

@njwildberger

Why must organization principles in nature necessarily point to a conscious originator of said principles? Is it not conceivable that the principles simply occur? Why must there be something comparable to a human mind behind it all? It is certainly comforting, but I see no evidence. Just human desire for cosmic companionship, which is completely understandable.

Ultimately there is little way of knowing either way, but why entertain the unfalsifiable/unprovable hypothesis?

[FluffyBunniesOnFire]

@TheFlightguru When you get to a certain point of understanding the first difference between theism and atheism is merely the different terminology they use to describe the same thing. "God" is the unifying source concept, and it communicates to us through math.

[alexzarhin]

I have a question about the model that you build in this course. Is it you, who invented this "projective model" which you build in this course? I mean not the Klein model, but the "improved" model, which holds on the whole plane?

[njwildberger]

@alexzarhin Yes this is my model, building on the classical Beltrami Klein projective model, incorporating features of Rational Trigonometry to provide the metrical foundation.

[TupperWallace]

Professor Wildberger, congratulations on passing the 10^5 mark in the number of channel views! I'm one of the retired people interested in math you surmised might be in your audience. I still bitterly remember my disappointment in high school trig in October, 1963, when I asked Mr. Kennedy when we were going to get to the good stuff instead of memorizing formulas. He just shrugged. There is good fun stuff in trig but I had to wait all these years to see it in your videos. Best Regards.

[njwildberger]

@TupperWallace Hi, I think you are not alone in these sentiments. Up to now there hasn't been much of an alternative to the usual horrible trig. Now there is! Hope you enjoy the videos.

[atypicalguy]

I'm way behind you in terms of math prowess but regarding the problem you mentioned. The first part:

(q + q + r)^2

isn't this the same as:

(2q + r)^2

or am I missing a subtle difference?

[njwildberger]

@atypicalguy Yes the two expression are the same, but there is a reason I choose the first form---this is a special case of the (hyperbolic) Triple quad formula.

[yoursuchagoodguy]

Thank you.

Your discussion about the proper formulation of elementary concepts is much appreciated.

But perhaps someone should speak up for the proper formulation of that elementary concept grammatical number. I speak of course about the distinction between singular and plural.

At 10:39 "There's no absolute values, there's no square roots, there's no transcendental functions."

Perhaps you mean

"There ARE no absolute values, there ARE no square roots, there ARE no transcendental functions."

[njwildberger]

@yoursuchagoodguy

In fact I have a lot of sympathy with your last statement.

[mysticdolphin17]

Totallly intriguing! I'm in.

[joshuabowman]

I've taught many different levels of college math, and I've always been able to throw in some hyperbolic geometry. At Cornell, where I did my graduate studies, and other places (e.g., wherever Vi Hart is hanging out) several ways have been invented to experience hyperbolic geometry hands-on, without any formulas. I'm glad you're making this material available, but IMO you're being a bit harsh on the system. I don't know anyone who's told anyone they wouldn't understand hyperbolic geometry.

[njwildberger]

Hi joshuabowman I am being harsh on the current system, but only because it deserves it! Most of the weaknesses of modern mathematics are hushed up, and slid under the carpet, the idea being that if you don't mention the problems, I won't either and all will look fine. This is not a proper environment for a science. Criticism needs to be acknowledged, debate is healthy, and young people ought to know there are difficulties. So mathematics needs more alternative theories and points of view.

[crittinger]

I love you.

[peterhi503]

Another magnificent contribution, Wildberger. Well done.

[Babyspam]

Thank you for making interesting video's dealing with mathematics. I enjoy each one.

[QuantumMaths]

I would like to thank you for your very interesting and expansive work in the topic of pure mathematics. I have had a wonderful time watching your lectures and trying to wrap my mind around the concepts in them.

[Waranle]

I love your Linear algebra approach, please continue, and thank you for this new series :)

[simonsillitoe]

hmmm this sounds familiar...

[njwildberger]

Hi Simon, Yes you are one of the few that know already about (some of) this.

[LeavingCertMaths]

Looking forward to this

[AdamLore]

Wow! I'm really excited about this series!