wtf

Can't hold a job? Just a joke. But your self-aggrandizing paragraph fairly cries out for mockery. Serious job hunting advice: Cut the resume down to two pages, max. One page if your name's not Max. A 15 page resume will be instantly roundfiled by any hiring manager.

A Google search on "transfinite geometry" turned up this interesting paper. https://www.washingtonpost.com/local/public-safety/commanding-general-of-dc-national-guard-to-be-removed-from-post/2017/01/13/725a0438-d99e-11e6-b8b2-cb5164beba6b_story.html I love your drawings.

<CheapPoliticalJoke> I was fooled by more fake news from the Washington Post :=) <CheapPoliticalJoke>

https://www.google.com/search?q=long+hdmi+cable&oq=long+hdmi&aqs=chrome.0.0j69i57j0l4.2084j0j7&sourceid=chrome&ie=UTF-8

No diff at all. Different words used in different contexts that mean the same thing. Function. Like the Eskimos who have 50 different words for snow. Mathematicians have many words for function. Interestingly the Eskimo story has been called a myth but it's actually true. https://www.washingtonpost.com/national/health-science/there-really-are-50-eskimo-words-for-snow/2013/01/14/e0e3f4e0-59a0-11e2-beee-6e38f5215402_story.html

Quantum computers are computationally equivalent to classical Turing machines. Just faster. But only for highly specialized problems. http://cs.stackexchange.com/questions/23162/quantum-computing-and-turing-machines-are-turing-machines-still-an-accurate-mea

How do you define hypercomputation? Do you mean performing infinitely many computations in finite time? Or models of computation that go beyond the Church-Turing thesis? It would be helpful to know what you mean by that word. https://en.wikipedia.org/wiki/Hypercomputation

Conservation of belief? Does that imply that if I change my mind about God, someone else with the opposite opinion must change their mind at the same time?

In fact that's what I was trying to get at. Without having read everything studiot wrote, I can't say whether I agree with it or not. I speak only for myself. That was my only point.

So the universe proceeds from one discrete state to another like the frames of a movie or video game? I wonder how it is that you know that for certain. How do you know the universe isn't continuous, with the "states" being analogous to real numbers? Then there is always a state between any other two states and there is no such thing as the next state. This seems like a rather important point, don't you agree? For that matter, you don't even need the real numbers. What if the states are ordered like rational numbers? Then there's still a distinct state between any two states, but you don't even need uncountably many states to model that.

Sorry, which two? I speak only for myself here. And sometimes not even that

Counterintuitively, you CAN pair the natural numbers with the rationals. But you can't pair the naturals to the reals. http://www.homeschoolmath.net/teaching/rational-numbers-countable.php https://en.wikipedia.org/wiki/Cantor's_diagonal_argument

No. Each of the sets of even numbers and odd numbers are bijectable to the natural numbers. Right?

If you start with the counting numbers 1, 2, 3, 4, ... and you remove all the even numbers, how many numbers are left?

To the best of my knowledge, hypercomputation refers to carrying out infinitely many steps of a computation in finite time. Hypercomputation is an abstract concept. It's inconsistent with the laws of physics as they are currently known. We know from history that tomorrow's physics will refine and even overthrow today's. So it's always possible that some future genius will find a way to do hypercomputations in a physical device. Until that day, hypercomputation is a purely theoretical or abstract idea. Of course it's still a very interesting and useful idea. But unless the OP has some different meaning of hypercomputation in mind, it's not possible that our brain carries out hypercomputation, since our brain is subject to the laws of physics. I would only add that "The pharmacological regulation of dopamine and serotonin via cannabinoids (THC) administration may enhance synaptic hypercomputation" sounds like a fine bit of late night stoner philosophy from back in the day.

On the contrary, there are many different "sizes" of infinite sets and your question is a good one. Any two intervals of real numbers are in bijection (synonym for 1-1 correspondence). However the interval [math][3,5][/math] is indeed twice the length as the interval [math][4,5][/math]. The branch of math concerned with making that statement precise is called measure theory. https://en.wikipedia.org/wiki/Measure_(mathematics) No, for example the set [math]\{1, 2, 3\}[/math] is clearly not the same size as the set of all real numbers. Of course what you mean is, are all infinite sets of reals of the same cardinality? And the surprising answer is no! In the 1870's a brillian mathematician named Georg Cantor showed that some infinities are bigger than others; and that in particular, the infinity of all the counting numbers is strictly smaller than the infinite of all the real numbers. https://en.wikipedia.org/wiki/Cantor's_diagonal_argument So now we have another question: Are all infinite sets of real numbers bijectable to either the set of all real numbers, or the set of counting numbers? This question is called the Continuum Hypothesis and it's one of the deepest questions in set theory. Nobody knows the answer, or even whether the question is meaningful; and if so, in what way. https://en.wikipedia.org/wiki/Continuum_hypothesis I've given you a lot more info than you asked for. The tl;dr is that * There are in fact many different sizes of infinity in modern math. * Any two intervals of real numbers have the same cardinality. * Even though they have the same number of points, two intervals can have different lengths. In effect, we can take the points in an interal of real numbers; rearrange or relabel them; and end up with an interval twice as large. Poor Cantor was attacked for his ideas, and the stress drove him to be institutionalized for depression. Today his ideas are accepted as basic math. But yes, these are very odd ideas. We can be mathematically precise about infinity, and we can logically prove that there are infinitely many different levels of infinity. https://en.wikipedia.org/wiki/Georg_Cantor

Ok, no prob. Now if we have the two intervals [math](3,4)[/math] and [math](3,5)[/math] from your original example, we can match up their points with a 1-1 correspondence via the function [math]y = 2x - 3[/math]. Each point of the first interval corresponds to exactly one point of the second, and vice versa. So in this case we say that the two intervals have the same cardinality. Informally we can say they have the "same number of points," but that just means there is a 1-1 correspondence. Of course the two intervals do in fact have different lengths. That shows that length and cardinality are different ways of assigning a notion of "size" to a set of points.

This is incoherent. I say that not to be condescending or rude; but to emphasize that when you're trying to understand the real numbers, incoherent thinking is very unhelpful. "... any real number which there is an infinity of between any given range of numbers because they can get exceedingly small the more you count them" simply does not express any thought or idea at all. If you desire to understand the nature of the real number system, it's essential to think and speak clearly. These are not language issues, but rather conceptual misunderstandings you have about the real numbers. I hope you can see that "... any real number which there is an infinity of between any given range of numbers because they can get exceedingly small the more you count them" does not express a coherent thought. What is the subject of the sentance? "Any real number?" That's only one number, there's nothing "between" it. Can you explain more clearly what you are trying to say? I am not trying to give you a hard time. I'm trying to help you to understand the nature of the real numbers.

There are no infinitesimals in the real numbers. This is not a language issue, it's a fundamental math issue. An infinitesimal by definition is a nonzero quantity [math]x[/math] such that [math]x < \frac{1}{n}[/math] for each [math]n = 1, 2, 3, \dots[/math] Clearly there is no such [math]x[/math] in the real number system. There are mathematical systems of numbers that do contain infinitesimals, but they are not the real numbers. This is an important thing to understand about the reals. The answer to your question is that there is a 1-1 correspondence between any two intervals of the real numbers, so we say they have the same number of points. But it's important to note that "same" is only a figure of speech. The mathematically significant fact is that there is a 1-1 correspondence.

Bacon and dates? Is this a thing?

All I saw was pretty pictures in Euclidean 3-space. I think Euclidean 3-space is a solved problem, as they say. I am not understanding what you think is wrong with it. The other thing is that you are talking about applying this to physics. But physics is all about infinite-dimensional function spaces in which the "length" of a vector is some norm given by an integral; and "angles" are replaced by the inner product. If you are doing anything at all in Euclidean 3-space this is at best an exercise in second-year calculus. Physicists use manifolds and advanced abstract differential geometry. I think in your exposition you are failing to put your ideas in proper context. Are you proposing a new way of looking at Euclidean 3-space? In terms of physics, are you trying to reform classical mechanics perhaps? Because certainly your work does not appear to be challenging the established orthodoxy in differential geometry. I'm just tossing out ideas. I think what happens is that when people have pet theories, they have everything very clear in their own mind and they don't realize that they are failing to communicate a lot of context to their readers.

For the sake of those of us with limited attention spans, can you explain in simple words what is the purpose of all this? Are you inventing a new coordinate system for three-space? Or what, exactly. I skimmed your paper and the diagrams are beautiful but I have no idea what you're trying to do. The metaphor is the "elevator pitch." In the field of tech startups, your elevator pitch is what you say to a venture capitalist if you happen to run into them in an elevator and hope that they will fund your company. You haven't got five hours or even five minutes. You have abut 15 seconds. Uber: "Airbnb for taxicabs." Boom. Three words, everyone gets the concept. If you saw the movie The Player, Hollywood does the same thing. You have a pitch meeting in which you have a couple of minutes to get the favorable attention of some studio executive who hears a dozen stories a day. Can you just explain to me what you're doing? New coordinate system? Better in some way? Like stereographic projection perhaps? Or the roll/pitch/yaw system used by airplane pilots, in which the origin of the coordinate system moves with the airplane. Clever idea, right? "Coordinate system that moves with the observer." Boom. I got that in less than a second. I need your elevator pitch please. I'm fairly sure I'm not the only one. To know if you've succeeded, it should be at most a sentence or two but ideally just a few words. "Improved coordinate system," or "Pretty pictures." By the way, "reverse vectors" isn't helpful. Not to me anyway. I have no idea what a reverse vector is. Can't help mentioning that we have recently seen a striking example in public life. "Make American great again" defeated "I'm with her." You can never overestimate the importance of your elevator pitch.

Yes, just like 2 is a very odd prime.

Your ribbon analogy is causing you to have the wrong mental picture of the continuum. You are thinking of points jammed up against each other one after another, like a string of bowling balls. But between any two points on the line there is a third. There is no notion of "next to" on the line. Between any two real numbers [math]x[/math] and [math]y[/math], there's a third real number [math]z[/math] strictly between them; that is, [math]x < z < y[/math]. For example we can take [math]z = \frac{x + y}{2}[/math]. The linear continuum is modeled by the real numbers. There is a third point strictly between any two given distinct points. The idea of "little squares" side by side simply fails. It's the wrong mental picture. Suppose we take a line segment and zoom in on it. It still looks the same. Zoom in more. It looks exactly the same. The continuum is self-similar at every zoom level. It's not a string of bowling balls. It's more like a bowling ball travelling through a big vat of molasses or maple syrup. It's a continuous line. It is made up of points. But it is not a "row" of points. There's not a first a and a next. You are confused on this I think. As far as how zero-dimensional points make up a one-dimensional line, that's a philosophical mystery. In math we just ignore it. We allow countable additivity but not uncountable additivity. In other words if you have a countably infinite collection of sets, you can add their lengths. But with uncountability, all bets are off. You are correct to notice that the question of how points make up a line is a mystery. But you are wrong to let yourself get stuck on that question.

Studiot, We agree that pengkuan is confused about the nature of the continuum. The philosophical issues have not been solved. But the mathematical issues are fully solved by modern real analysis based on modern set theory. In my opinion, it is not helpful to penkuan to encourage his misunderstandings; when in fact there is a modern mathematical theory that resolves them. Mathematically at least. Not, I agree, philosophically. It is my understanding that pengkuan is asking about the mathematical and not the philosophical nature of the continuum. So there is no need to pretend that non-parallel straight lines in the Euclidean plane intersect in a point. We can use analytic geometry to solve the system of two linear equations. What Euclid might or might not have thought or said two thousand years ago is quite beside the point. In my opinion of course. Secondly, I simply cannot imagine that Euclid had in mind anything other than a point as the intersection of two lines that are not parallel. For you to imply otherwise is either sophistry or ignorance OR I'm simply missing your point completely! So I'm not being pejorative, simply baffled at your claim that Euclid does not think the intersection of lines is a point.