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I watched it, I liked it.
If you want to listen to someone who doesn't say 1x1 = 2, then much of what he was talking about reminded me of Eric P Dollard. If you can stomach a two hour podcast, maybe consider this three-and-a-half hour lecture, History and Theory of Electricity.
The real meat and potatoes of his views are not new. He's deep into the waves/frequencies/spin is everything method of analysis, which makes sense. This is also part of his criticism of 1x1=1, in that it assumes axiomatically a rectilinear universe, which is not the way the actual universe exists. The most interesting parts were when he was talking about the periodic table and the solar system.
For the periodic table, he claims that elements are essentially harmonics of one another, the same frequencies (spin) doubled can turn one element into another.
As for the 1x1=2, I'm very sympathetic. I distinctly remember my complex algebra course, where we rederived addition, subtraction, multiplication, and division such that they are consistent with what we see in a number line. It reminds me that these operators are axioms themselves, and that axioms are taken as true, not proved. Ultimately, I think he gets lost in the weeds of units. For example, he asks what is $1 x $1, and reports that people say $2, and don't want to accept $1. But of course, $1 x $1 is $^2 1 (one dollar-squared, or one square dollar). What the hell is a square dollar? The same thing as a square second, but with currency.
The other reason I dislike it is because you can derive multiplication from your fingers, in a similar manner to addition. Put one finger up on each hand, and count them, and you get to 2 (addition). Two fingers on each hand gets you 6, and three fingers gets you 9. Now, instead of counting them, cross the fingers of one hand against the other and count the overlaps. One finger and one finger, overlapped, gets one intersection. Two fingers on each hand, 4 intersections, and three fingers gets 9 intersections.
His problem is root 2. For our finger example, what combination of fingers gets you two intersections? You have to use different numbers on each hand.
But notice, we have changed units! We are counting intersections, not fingers! So again, I'm sympathetic in general, but in particular it breaks down.
It is possible to build up a thorough and comprehensive axiomatic theory starting from a geometry without the parallel postulate. But what's described here seems like an extremely painful, sloppy, and intentionally confusing usage of notation. Possibly just wrong, probably not even wrong.
In terms of foundational mathematics, building up from geometric definitions like crossing lines is an extremely cumbersome method of defining your axioms. Even if you do not insist on using intentionally confusing notation like 1x1=2. As you said, you immediacy run into annoyances in terms of defining basic things like the irrationals in sqrt(2).
If you wanted to make a serious attempt at analyzing alternatives to the conventional axiomatic assumptions, it would be much more clear to begin with variations on Zermelo–Fraenkel set theory, with or without the axiom of choice and the continuum hypothesis. This would be a much more rigorous and clear way of showing how your systems produces a non-Peano arithmetic. If someone is unwilling to go through that work, it seems extraordinarily unlikely that they are producing anything interesting, correct, and non-trivial.
Though the foundational crisis may non be resolvable, the generally accepted formalism provides the necessary mathematical tools to do an extraordinarily good job of describing reality. If someone wants to propose a different formalism, it better provide a better or more useful description of reality. Saying that the current formalism does not perfectly describe reality so we should adopt a formalism that is less useful and more confusing, is pure nonsense.
To quote Hilbert (1927 The Foundations of Mathematics):
Laying out a formalism with overlapping but ill-defined versions of "spin" and "product," is not cleverness or some deep philosophical insight, it's an expression of sloppy thinking.
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Perhaps I’m missing something, but what you’re describing with the units and the axioms sounds like sophistry. As in—sure, he can define whatever domain-specific operators or fields or rings or whatever the math term is. (Wow, it’s been a while). That doesn’t privilege his definition over the boring version that works on Peano numbers. Does he have a reason to go there other than scoring points in arguments?
Also, I don’t think that’s what “spin” means. But what do I know.
Yes, reality does not conform to our models, and therefore we should look to reality instead of retreating into theory. Although I suspect he leads with it out of contrarian impulse.
He also gets into this on the idea of the identity property. The identity property, when it comes to multiplication and division, states that you can perform an action on something and get the same thing back. That in itself doesn't really make sense in the world, does it? If you act on something in any way, it will change, and if it didn't change, you didn't really act on it, did you? For 0, our conception is one of nothingness, emptiness, or lack, but that's not what exists in reality. There is no such thing as emptiness, or lack, or 'zero' in that way. We we do observe in nature and the universe is that 0 does not represent nothingness, it represents equilibrium. It represents inflection points, it represents the middle of the sine wave, the repeat of periodicity, and spin.
So his argument is essentially that our conception of numbers, especially 1 and 0, are inconsistent with observed reality, and therefore we should keep reality and reject our conception. At least, that's how I understood it.
Thank you.
I don’t like how he makes claims about “our conception.” Or I really disagree with them. There’s something very perverse about a guy complaining about misleading terms and then throwing out his own underdefined versions.
I will freely admit this is my interpretation of what he's saying, which is as inconsistent and incoherent as you expect. That particular phrase is mine alone. The sentiment absolutely applies. He describes everything and explains nothing.
As I mentioned elsewhere, this is basically warmed over electrical universe, free energy, Tesla stuff. He's got some cool geometry that I find fascinating, which are his props and visualizations. I prefer Eric Dollard, who has at least spent his life building and using electrical equipment.
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Okay, so let's say I get on my bike and I ride for one hour at one mile per hour in a straight line. When I'm done, I will have traveled:
A. One mile
B. Two miles
Which of these answers most closely resembles reality?
I know how to do math, thank you.
Do you know how to do complex math?
I'll answer your question with my own. If I go a mile in either direction, what does the shape of the earth look like? Does it look curved, or does it look flat? Which one of these is a better model of reality?
All of the sensors and equipment on an airplane assumes a flat, stationary earth. They do that because the approximations are good enough, not because the earth is actually flat.
Yes, I do know how to do complex math.
Of course it is curved, and furthermore a geoid.
Now that I've answered, please explain if 1 mile or 2 miles traveled at 1 mph after 1 hour is a better reflection of reality, and how that connects to why 1 x 1 = 2 is a reasonable statement.
You can't tell that from walking around a mere mile. You can barely tell that at all. You certainly can't derive that from first principles without significantly more information.
That's the point. The flat earth model is a good one, for many things. Imagine, if you will, your house. It has walls, and those walls are vertical. For simplicity, let's say that a plumb bob was used, and that therefore the walls are plumb, and the ceiling which joins the walls at right angles is level. Except, it's not. The two plumb bobs are not parallel, and in fact converge. That doesn't matter for your house, because there's no difference at that scale. It's wrong to assume a flat earth, yet we do it anyway in many circumstances because the differences don't add up and aren't apparent.
In your example, if you travel for 1 hour, and at the end are 1 mile away, then you could say you averaged one mile per hour. However, in reality you were above and below that speed at many points throughout the hour. I say your hypothetical does not reflect reality, it merely approximates it locally.
Very interesting. However, I still am curious if 1 mile or 2 miles is a better reflection of the reality of my travel distance, since you said that 1x1=2 is looking at reality rather than avoiding it and retreating into theory.
So by all means, let's look at reality.
You sure can if you're walking uphill.
The problem you’ve presented is not comparable to 1x1, but rather to (1x/y) x (1y), which would equal one in either system.
A better comparison is: you have a property that is 1 mile in length, and 1 mile in width. How large is it? Certainly not 1 mile. Is a response of 1 mile or 2 miles closer to reality?
I think the system we have for math is very useful, but it’s not necessarily cleaving reality perfectly at the joints, and maybe there’s a way it could be.
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It's one mile, but you have very helpfully included units and a divisor.
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