\forall t2\ \forall t1\Bigg(\bigg(Pays(C,5000,t1) \wedge (t2 \ge t1)\bigg)\to GetsDiamond(C,t1+1)\Bigg) where C is the customer. Substituting 1002 (10...
Here is the sign: "“If, at any particular time, you have given $5000 to the sales-clerk (under no circumstances will it be returned), then, within 60 ...
That is a claim, not a definition. Observe how it does not say 'we define X to mean' or any of the equivalent forms of words that flag a definition. T...
The parallel postulate does not define parallel lines. They are defined in Book I Definition 23, as being two lines that never meet. What the parallel...
The problem is that by asking what 'caused' something you are moving from physics to philosophy - metaphysics, and there's quite a bit of sensitivity ...
They always look parallel, and that's what matters to our intuitions. There is no part of the triangle we can look at in which the bit we can visualis...
Yes, it's a bit like if we snap-froze the ocean while it was wavy. Then we'd have a physical wave shape, but one that was constant across time. I thin...
Indeed. I approach this by regarding 'laws of nature' as descriptive rather than prescriptive. That way they do not need ontological classification. T...
The average direction across all galaxies is away from one another. However that does not mean that every single pair has to be moving apart. Each gal...
I agree with you. I don't find the phrase 'interferes with itself' meaningful or helpful. My current way of looking at it (it has changed in the past,...
I have also been thinking about what it would mean to have an intuition of the parallel postulate, if that means being able to visualise constructions...
I've had another response to my question on measuring curvature of space. It makes the excellent point - which I had completely missed - that the path...
I believe the statement was not true when the person first inquired, because the words 'at any particular time' are not constrained to cover only the ...
I can only repeat what I said above, that we don't need to imagine it. Cognising space as a Riemannian Manifold is not non-Euclidean, but aEuclidean (...
Say there are three poles, coloured red, yellow, blue, at distances of 3 1/3 steps away from one another, in a straight line in the direction I'm look...
If the rail line were stationary relative to Earth, the lines could not be both straight and parallel, because in that reference frame the spatial sli...
I'll describe below how I imagine it, but that's beside my point, which is that I think we don't need to imagine it. I think all we need to cognise th...
This got me thinking. How would we build a rail line to circumnavigate the equator, if there were a 5m wide land bridge all the way that followed the ...
My intention is to defend not Kant, with whom I disagree on many important things (although I do have enormous admiration for him), but what I see as ...
Yes, I mean what ordinary people mean by intuition, not what Kant means . He uses words too weirdly for me. Yes. It may be, as you say, cos I'm a math...
I think that's exactly the correct response in that case. I hope it lasts. Do you think May will give in and invite him over at some stage, despite th...
I don't agree that it does, but I was wondering who might be an example that strong view that Wayfarer mentioned some people holding. So now I know. I...
For a start, there are plenty of people saying that Trump got elected from people reacting against what they saw as an excess of authoritarian politic...
Fair enough. I had assumed - wrongly, it now seems - that you were aligning with the group that @"Wayfarer" identified in this post ( ) that assume th...
Unlike spacetime curvature, which is coordinate-independent, the curvature of space (strictly, of constant-time hypersurfaces) varies according to the...
Looking up Euclid's axioms on wiki, I noticed something interesting. Here's wiki's translation of them: Unless I'm missing something, the 5th postulat...
What exactly is the criticism? That he didn't discover the existence of elliptic and hyperbolic geometries in 1781? That's a pretty harsh standard, si...
What I'm pointing out is that the words 'Euclidean Geometry' have a different meaning now from what they had in the 18th century. In the 18th century ...
Two examples you might find interesting to contemplate: 1. I believe Antarctica is not 'owned' by any country. I think there's an international treaty...
Thank you for contributing an actual quote from Kant to the discussion. As is usual with me and Kant, I'm not very sure about what he means by it, but...
There were no admissions. You're making stuff up again. My position has not changed one iota. The only thing that has changed is that maybe you are fi...
The curvature that gives us our fairly modest Earth gravity is a curvature of spacetime, not a curvature of space. The difference between the two conc...
The implication cannot be seen because it is not there. You are imagining it. You are never going to be able to conduct a sensible discussion if you k...
More made-up irrelevant nonsense. Nowhere did I say that police who shoot blacks are all white, or even predominantly white. I suppose it's futile to ...
Now you're just making things up: Nobody but you said anything about epidemic levels. Nobody but you said that racism was a factor, let alone the most...
Really? You think we should be glad that racial abuse of Asians, and police harassment and shooting of blacks occurs regularly? OK. To be clear, do yo...
One counter-example is me. I used the phrase a few posts ago. I know that white privilege exists but, sadly, I have no prescriptions to offer to eradi...
For me they seem to. When I visualise many-dimensional branes colliding in even higher dimensional space, I visualise hanging, wobbly two-dimensional ...
No I didn't (Well spotted!). I was going to heap special praise on him for that valiant attempt, but decided not to because I didn't want to embarrass...
Non-Euclidean geometry does follow Euclid's assumptions at the scales that are meaningful to humans. So there is no conflict. A geometry that is not l...
Since Kant was tremendously intelligent, and not only understood physics but even published important papers in it, I have no doubt he would have very...
All they need have is a dislike of bullying, which is a very common dislike. Regardless of whether such protests actually are bullying, they look like...
Could you please elaborate on what that means? Does it just mean that the amendment protects a person from prosecution, or administrative sanction, fo...
I apologise unreservedly, wholeheartedly and ashamedly for mentioning the placard on the lectern of Jordan Peterson (remember him?). It seems to have ...
Sorry, I couldn't get through it. I love Canadians and Canadian accents, and I like that Peterson talks thoughtfully and intellectually rather than ha...
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