DannyTR

But none of that could exist without a start to the universe; there has to be a start in that great chain else nothing in the chain exists. Anything without a start is undefined. If I ask you to build a universe with a start in space and time what might you say? Maybe with God-like powers I could do it. If I ask you to build a universe without a start in space and time what do you say? Remember base reality is timeless so it does not need a temporal start. It has spacial starts though... Well I'm thinking about the universe in the 4D space time way. You have to imagine a static brick, spacial dimensions along the short edge, time dimension along the long edge. This is analogous to a higher dimensional view of our universe. So it is permanent, finite and encapsulates time. This is the way Einstein thought of the universe.

I don't actually believe in quantum foam as the cause of the big bang. I think instead there was/is a timeless reality which our space-time is contained. Something in the timeless realm created time. The full argument is as follows: Something can’t come from nothing So base reality must have always existed If base reality is permanent it must be timeless (to avoid an actual infinity of time) Also something without a start cannot exist so time must have a start Time was created and exists within this permanent, timeless, base reality So time must be real, permanent and finite When discussing 'cant get something from nothing' I have a specific definition of nothing: no energy/matter and no dimensions. So it really is nothing; not even quantum foam and truly nothing can come from it...

OK, how about a collection of related parts that recognisably function as a whole and exist within a fixed spacial and temporal windows. Sounds like a thing? We could drill right down though; a quark counts as a thing. Without spacial and temporal starts a quark cannot logically exist. Well that quantum foam qualifies as a thing IMO. Empty space has vacuum/dark energy associated with it so its a thing. Being a thing, it should have a spacial and temporal start. So the quantum foam/pre-BB-universe cannot have existed forever; it must of had a start. Besides, if the universe really did not have a start, we should be in thermodynamic equilibrium by now, but we are not.

Well I guess we have to define 'thing' somehow first. How about a collection of related parts that recognisably function as a whole? Then a car (and a universe) would then qualify as a thing. Whats your definition of a thing?

Yes, the temporal 'start' of objects is typically a time window (assembly using the car example) rather than a specific moment of time, but that time window still qualifies as a temporal start...

It is defined in the OP: Sorry, a car has a spacial start; the front fender for example. It has a temporal start in the factory when assembly is complete...

No there is no problem with this integers, reals, complex numbers; they all behave consistently under the basic mathematical operators (+ - * /) and they all have mirrors in nature. How can the cardinality of an infinite set be anything other than magical? Well because Actual Infinity was included in set theory because of religious rather than logical reasons. Cantor and Co believed God was actually infinite and mathematics was made to reflect this; much to its detriment IMO.

I'm not a theist BTW. Potential Infinity, as in the limit concept, is not magical/spiritual. Actual Infinity, as in transfinite numbers is magical/spiritual: "Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from mathematical contemporaries... Cantor, a devout Lutheran, believed the theory had been communicated to him by God" https://en.wikipedia.org/wiki/Georg_Cantor

Please show the premises and logical steps that lead to that conclusion. I'm not sure I can; I think its axiomatic; a self-evident truth... there is nothing in reality without a start. It does not make sense logically for something to exist without a start. Something without a start is necessary not fully defined; IE it is undefined, IE it can't exist. Well that is a mathematical function not a real world object. And it has a start for any real range of the function we plot; IE as soon as we try to make the function real, it has a start (IE where we choose to plot it from). I know its possible to imagine things without starts in your head using the concept of infinity; but I'm asking for examples of things without a start from reality.

The logical error of discounting the possibility of something because no evidence has yet been observed for it... So you would not discount magic from a role in the creation of the universe then? Cosmology is an extension of the Natural Sciences and it should favour natural solutions rather than magical/spiritual concepts like infinity... finite solutions are much more compatible with a materialist world view. Yep, off topic, but I think if God exists, he is timeless, that is he exists as a 4D object of finite spacial extents but with no temporal aspect. So God would exist permanently outside of time. Not permanently inside of time because then he would not have a start.

Its not a problem with my brain; Its just plain logically impossible for something without a start to exist. Everything has a start I think; unless you can you give a counter example? The only counter examples I can think of are concepts like infinity and that does not exist (there is no number oo such that oo > all other numbers because oo + 1 > oo). I can't think of anything real without a start and the universe is real so it follows in had a start; both logically and empirically. The Big Bang is certainly a strong candidate for a start of the universe.

So it can't exist. Reductio ad absurdum. The universe has a start. Everything has a start.

No I can't but I'm not a Ornithologist. On the other hand I have much experience of objects and stuff which leads me to believe that everything has a start. I've spent a while thinking about it; but I can think of nothing without a start. Can you? And just logically; something without a start is a contradiction...

Things without a start can't exist... its a simple proposition but if it were true, it would clear up some big questions about the universe. First, what do I mean by start? To be specific, for things to exist they must have: - Spacial start point(s). For example, a circle you can choose any point as a spacial start point. Yourself you could choose your feet as start points, etc... - A temporal start point. For example, your date of birth was when you started (roughly speaking) There are no examples of things without starts in the material world I can think of; so we could take that as empirical evidence supporting the proposition. If the proposition is true, we can we apply it to a number of things: - The universe must of had a start in time and space. - Matter/Energy must of had a start in time and space. - Time itself must have a start in order to exist - Infinity in general can't exist physically because it has no start/end. Purely a mental concept. So this proposition would generally be reinforcing of the 4D Space-Time view of the universe... Any thoughts? Any counter examples of 'things without starts'?

What I mean is the information in a region of space is the sum of the information of the particles within that region. But the particle has a position independent of any measurement we do, IE the centre of its wave? So the positional information exists, its just not measurable by us. So a region of space has information in it whether we measure or not. If space is truly continuous then a 1 meter cubed region of space is graduated as finely as a 1 light-year region (implicit from the definition of continuous). That seems contradictory by itself: suggests the small region contains as many distinct (infinite) states (therefore information) as the large region.

But would a specific region of space count as a 'system' in information terms? IE A system with N states depending on all the possible positions of the particles (and other factors) and then the information content of the system is then log(N)? The coordinates would be chosen separately for each specific region of space for which we are calculating information content. When not measured, the wave form must have a centre. Could this could be used in place of the particles position, when calculating information content?

I believe particles have a definite position when measured. When in wave form, the wave must have a centre (not sure thats the right term) at a specific position? Presumably where the probability of the particle being is highest? QM does also suggest that matter is discrete...

Please note this is rather speculative… I was wondering about information. Is it reasonable to regard the position of particles as information about the volume of space containing the particles? If yes, then there seems to be a simple argument for space being discrete: - Assume space is continuous - Implies particles have infinite positional precision. We might not be able to measure with infinite precision; but the underlying system is continuous so possesses infinite precision - So there is an infinite amount of information in a spacial volume of 1 cubic unit - And there is also an infinite amount of information in a spacial volume of 10000 cubic units - Both infinities are the same kind and have the same cardinality - But this is a logical contradiction, there must be more information in the larger volume. - So there must be a false assumption in the argument; space must be discrete - (or maths treatment of infinity is not rich enough) I was reading about the Bekenstein bound, which also seems to suggest discreteness: https://en.wikipedia.org/wiki/Bekenstein_bound

I only have a problem with the ‘axiom of infinity’; the rest of ZFC I’m not questioning. Calculus worked just fine for 300 years before the invention of infinite sets. I think the limit concept is fine as that can be defined with just potential infinity.

Hilbert’s Hotel illustrates the illogical nature of set theory: https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel A completely full hotel with room for an infinite number of new guests. Sound! I don’t call that a ‘firm mathematical basis’. I believe that past, present and future are ‘real’ and all exist. If time is real it must be finate, hence an end of time. Eternalism is defined here: https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time)

Actual Infinity does not behave like a quantity or even an object. What other thing can you add to without changing? I’m Eternalist and a Finitist so I have to believe time has a end.

Well it’s old but not really outdated. Aristotle came up with potential/actual infinity 2000 years ago and no one has come up with a better explanation of infinity since then. Set theory merely defines Actual Infinity to exist in the form of a complete infinite set, by way of axiom and without proving anything. Calculus uses the limit concept; approaching but not reaching Actual Infinity. So maths sort of ducks the issue of defining Actual Infinity. Not surprising really; it’s a mad concept, hard to define.

I’m not sure I can define Actual Infinity directly. I can define potential infinity as the results of repeated interations of the same process. Then actual infinity is the result of carrying on these iterations for a unlimited period of time. But I think that is a circular definition: ‘unlimited’=‘infinity’. Actual Infinity is difficult to define because it does not exist exist mathematically or in nature; just exists in our heads as a (flawed) concept. Something that we cannot cleanly define and is not a rational concept, does not have a place in scientific theories IMO.

Yes you can picture Actual Infinity in your mind by imagining things as above, but that does not mean it exists mathematically or in the real world. Actual Infinity is a self contradictory concept: that’s why it makes our heads hurt to think of it. And when you try to visualise Actual Infinity, it is always in the form of a potential infinity anyway (such as imagining zooming in on a line and seeing more and more points). The cardinality of the set of natural numbers is not a number by any reasonable definition. For example what other number can you add to and not change! A point has size 0, so there are (line length) / 0 = UNDEFINED points on a line.

An axiom is meant to be a self evident truth. The axiom of infinity is a self evident falsehood. That falsehood has made its way from the abstract study of sets into the non-abstract study of the universe and IMO is causing much confusion and time wasting.