I like this: Hawking talks about no clear Big Bang and no boundary to space-time | NextBigFuture.com . . . In physical cosmology, imaginary time may be incorporated into certain models of the universe which are solutions to the equations of general relativity. In particular, imaginary time can help to smooth out gravitational singularities, where known physical laws break down, to remove the singularity and avoid such breakdowns (see Hartle–Hawking state). The Big Bang, for example, appears as a singularity in ordinary time but, when modelled with imaginary time, the singularity can be removed and the Big Bang functions like any other point in four-dimensional spacetime. This might lead to a new understanding of dark matter and dark energy. In engineering there are problems that can only be addressed by "i", the square root of -1. A math trick, yes, but very useful. Bob Wilson
It is not calculus. It is an abstract math concept that has real application to hard problems. Matrix math helps but I'll give it a try: AC analysis intro 1 (video) |Khan Academy If you get electricity from your house outlets, this explains how transmission lines work. Bob Wilson
I get the sense that there's something we're not quite getting. The Hawking quote reflects this: there is much vagueness and uncertainty, "laws" are invoked, terms bandied about, all of which reflects a lack of complete understanding. I haven't a clue, but suspect reality will be absurdly simple.
part of my problem is that try as i might, i don't understand electricity either. oh sure, i can size the wires and circuit breakers, and install things, but electricity itself makes absolutely no sense to me. and to most electricians, i suspect. it's like 12v batteries here. i haven't seen one poster who really understands them.
I'm still not certain which direction the electrons travel, in a battery. If electrons are "negative", do they start at the "negative" terminal. I don't think I want to know. Guess it was kinda ballsy, saying Hawking doesn't have a clue. One of the perks of the blissfully ignorant I guess.
An analogy: with only partial understanding, you start to build up a "bow wave" of obtuse verbiage, to compensate. I'd postulate that bow wave can bring you to a standstill, create a mountain between you and understanding. Like a wrinke in the carpet, that goes from bad to impenetrable. Younger son came up with one yesterday, while we were battling with modem/router issue: when you have insurmountable issue, just step away for a bit, it may be easier when you come back.
Does anyone else believe $$ Oil has been subsidizing anti global warming theory? Just one of my big 3 indicators 1 - population growth acceleration - UN global pop count ( currently estimated at almost 8 billion ) stats say it is decelerating slowly using % math 2 - global temps 3 - First tenet of the current Business Model - Bottom Line - at the top of the plan. 10 years later
absolutely, check out koch industries, purveyors of anti everything except truth. they are very good at it too. i mean, if i were in the oil business, i would have a dilemma.
and doing business in china is not as attractive as it was when big everything moved there in a windfall of reduced expenses.
@Mendel would it help if I use the simplest constructs to describe all I perceptions around me including all the waves around us. traveling through us [add 2 edit here] that our human sensors can't pick up and the sensors developed currently can't detect yet either. edit 1: replace all I perceptions around me what I perceive around me edit 2 : 24 7 365 dog this post is gettin uglier by the second
This has a "tree falling in the wilderness" feel to it, describing the sensations that we don't sense? Not sure.
Electricity are electrons that in an ordinary conductor act as if a they are a set of tiny, incredibly hard balls in a row, touching. Push one electron in and nearly instantly the one at the far end jumps out: Semiconductors have other tricks. We'll save that for another day. But back to Hartle-Hawking. Math does not have to be coupled with physics but we can't really understand physics without it. What is proposed is to transform time into an complex entity, a combination of real and imaginary numbers, which can be used to model what would be impossible with ordinary algebra. Quoting from Wiki: Complex numbers have essential concrete applications in a variety of scientific and related areas such as signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis. The novel thing is transforming time into a complex number. This lets us play 'Thought Experiments' that can give insights on how things work. Then we can run experiments to see if we can observe the predicted effects. An early example, E = m * c**2 Bob Wilson
I got this "revelation", many many years ago, that time was the main thing, the elephant in the room that's so hard to notice, omnipresent. Anyhoo.
Yes. But then somebody like Hawking comes along and says that it isn't the electrons that move.......but positive "holes".