Those are a lot of questions, Bhup, and I can only answer them in as far as I understand the questions.
The one I must address is infinity. We did not work with infinity until Newton (and contemporaries if I am not mistaken). This must be addressed head-on.
Infinity is not a scientific word, just like the word God has no place in science.
Let's take the person who said he is going to drive forever, and two scientists checking that out.
One scientist gets in the car, and off they go. After months of driving, the scientist says, “Yes, we are still driving toward infinity.” Long story short, they never reach it, so infinity cannot be declared a scientific subject to work with. The actual data remains missing.
The other scientist remained in place, seeing the car drive away. After ten minutes, she is going home because there is no more data coming in.
Why do we accept infinity as a concept?
Two reasons:
1. Space is infinite. Then again, space is not a something. It is real, but it is a phenomenon, which means that space does not have any attributes of its own.
We must describe space therefore in negative terms.
* Space does not move
* Space does not interact
* Space does not have any borders
2. Infinity is quite real in any virtual reality. When we set up a banking system, then people can indeed have negative money (loans/mortgages). Yet money itself is not negative because the negative money is actually the positive money provided by someone else.
Same in computer land, where it is easy to work with infinity. The Golden Ratio a prime example. It is found in nature quite a bit.
Yet cut an apple in half and continue to cut the parts in half ad infinitum, and we end up with apple sauce rather quickly. Continue to cut all pieces in half and at some point even the apple flavor will be gone. Infinity is a concept, like God is a concept. It exists in our brain, and we have a real and easy time understanding it. A child gets it. Yet the concept is not a workable concept except in our virtual realities, such as money.
That brings us to the point you asked about early on in your reply. Matter such as the Milky Way being on the move in a straight line provides us two views.
1. The Milky Way is involved in that straight line direction, collective in essence, but all that matter is also circling and dancing around itself. So, we have the singular motion (straight line behavior) and we have the specific and more complex behaviors (Milky Way circling, Solar System revolving, planets spinning with moons in tow).
2. The Milky Way is moving through space. That is only possible if space is infinite. So, we have an infinite context in combination with a finite contents.
It is very important not to make the mistake many physicists love to make of combining all into one thing that explains it all. Scientists should not be looking for God (religion is a top-down exercise), but be looking for what science can show to be true or assumed to be true (science is a bottom-up exercise).
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Is mathematics real?
Absolutely. But in mathematics itself, we already work with many different systems, some self-based, some mixtures of systems, and the term mathematics itself is therefore a concept only. It is a name tag that points to all that fits the category.
The quick point to make is that the binary system and the decimal system can both do the exact same things, mathematically. Yet these systems are not identical.
We are trained to think in the decimal system, but the ‘decimal 1' does actually not exist in the binary system. There are many 1s in the binary system (and many 0s), and not a single one of them is thé 1.
For example, the word Unity is not automatically present in the binary system. We have to create it, establish it. For instance, we can agree that 11100100 represents Unity every time we use that combination of 1s and 0s.
Now look at the decimal system. We can say that 1 represents Unity (and unit as well). Done. Handy.
We use shortcuts in the decimal system, so we benefit from these shortcuts. Yet when we declare the shortcuts the real thing, then we are fooling ourselves. The decimal system is a virtual mathematical system with lots of real mathematical importance, whereas the binary system is the most basic natural mathematical system, kind of unhandy, but natural in essence nevertheless.
We have ten fingers, so we ended up embracing the decimal system and worked out things much faster. Understanding the big picture, we must recognize our own virtual realities. We have to move back to the less intelligent level, back to basics.
Nevertheless, the mathematical structure is real.
1 + 1 = 2 indeed, but we did not say anything yet. 1 apple + 1 apple = 2 apples is the real thing, and 1 + 1 = 2 is part and parcel of the real thing.
Translation example: Many people believe that everything is Love. They thrive on understanding that ultimately everything is based on love.
But that is not true. Nature also requires us to eat and we may love to eat certain things, we are not loving these things enough to let them live (plants or animals). That means that the minute we walk to the highest level and are trying to find a single answer, then we will automatically not find that desired single answer.
Gödel already showed us this with his Incompleteness Theorems. In translation, the completenesses are found at minimum one level below the overall level. So, if we overstep ourselves and try to place anything as fully comprehensive at the highest level, then we made fools of ourselves.
The example I often use is about human beings capable of growing a mustache. In reality, the completed box with people with a mustache will not contain children nor will there be many women in that box. The ability to grow a mustache, therefore, is correct by itself but cannot be placed at the highest level of all people. At that level, it will show up as an incompleteness.
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I am not really qualified to dig in at the specific mathematical level. Yet taking the Cauchy sequence presents me the same idea as entropy: there is a limit, whereas many folks think there isn’t one.
It is important to distinguish between the Cauchy concept and the realization of the Cauchy concept. One is a virtual truth, and the other is putting the virtual truth to the test.
Again, when we walk this in the direction of infinity, then we may be able to go a real long way. Yet the option to proceed will peter out.
Spinoza mentioned this already. When words are not available, then we cannot move further. When data is missing, then we cannot move further.
The Big Bang event is about matter first appearing. It is not about time, space, or energy first appearing, because we do not have any data about the beginning of time, space or energy. We should not meld things together when we only have one ingredient and not the others. We should focus on what we know, and accept that there are things we can never know because there is no data at all.
The Big Bang event was a one-time event, so we can 'read' that event. Like seeing an omelet, we automatically know that the egg was broken, without the need to see the egg shells nor investigating the contents of the egg. That what is obvious is obvious. One-time events can be ‘read’. Contrast this with repeatable answers, which can be seen as facts. So, science is itself not based on a single foundation. There are distinctions inside science that must be recognized.
Bhup, I hope this answers some of your questions.
You probably notices that I provided answers while trying to stand with my feet on reality and not on concepts. I distinguish that words are not the actual items, even though I'll do my best to present them as such.
If you have specific questions, it would be my honor to work them out together with you. If so, please formulate them in ordinary manners (I can look up things on the internet so it need not be simplistic).
