[David]

I think you should read the books on infinity by Peter Erickson. He addresses this same concept quite nicely. https://www.amazon.com/Nature-Infinitesimals-Peter-F-Erickson/dp/1479701823

[Mark]

Hi David,

Thanks for taking the time to watch my video, I hope you enjoyed it. I had a quick look at that book and it appears to try to defend the concept of an ‘infinitesimal’ along with the so-called number line and other infinity-related concepts that, as you’ll have gathered from my video, I am strongly against due to them supposedly not relating to anything in physical reality.

I find it bewildering that people can be fully aware that there are massive foundational problems in mathematics, and yet they are happy for it to continue. We have the bizarre situation where proofs depend on a consensus of opinion to determine if they are valid or not. If mathematics is a science then why don’t we insist that it is dependent on empirical evidence?

Surely we invented mathematics to describe quantities and lengths in the real world. For example, we might describe two steps forward as +2 and three steps backwards as -3, and we can apply these plus and minus symbols to different scenarios, but they don’t take on their own mysterious meanings or their own existence. The expression ‘-3’ doesn’t have a valid meaning if we try to relate it to taking apples out of a bowl that initially has 2 apples in it. There should never be the need to use expressions like “the mystery of mathematics”. It should be a very straight forward set of ideas all of which can be drilled down to real world actions and objects.

I find it staggering why I appear to be alone in my dismay. Our science and technology is propped up by this discipline that has a foundation of subjective make-believe opinions that sound like nonsense. The whole world should be up in arms about this and yet nobody appears to care. And if I try to tell anyone about it my comments get removed and I get banned from ever darkening their doors again.

I can only assume that people find it comforting to believe that they can imagine infinite things and they enjoy the fact that there appears to be a lot of mystery at the heart of mathematics. And almost everyone wants to believe that they can conceive of non-physical concepts. Basically, humans appear to be pre-programmed to readily accept the supernatural in one form or another. So I guess I am the freak because I don’t see things the same way as everyone else. It seems so obvious to me what’s gone wrong. It’s not rocket science. You don’t have to be a genius to see the problems. It is everywhere in lots of simple arguments like what is 1 divided by 3. Why would anyone accept that ‘infinitely many non-zero terms’ makes any sense at all? And why would anyone believe that they can somehow ‘sum to a constant’. We indoctrinate people at a very young age with this rubbish and this is the only reason that I can think of why the situation prevails.

Sorry about the rant, and thank you again for your interest.

[Andy]

“Can unending decimals like 0.333… and 0.999… be static unchanging things containing an actual infinity of digits?”

I think the simple answer is no. Mankind made up numbers, a fact that gets lost on human beings most of the time. There cannot be an infinity of any quantity in reality.

For example, could we claim there was an infinite number of apples in the universe? No, not really. But I think the real conundrum lies in the question, can there be a finite number of apples in the universe? The answer to that question is also no, believe it or not.

Think about it for a moment.

Even if we knew for a fact that apples only grow on Earth, the quantity of apples could never be defined as finite in the universe. They could however, be described as finite in time.

You can only describe the rate of change in the quantity of apples on earth, which is either rising, or falling. Freeze time and the number of apples becomes finite. Start time and the answer is no longer definable if finite terms. New apples are being created every day, and existing apples are being destroyed everyday.

The quantity of apples in the universe is always in a state of flux. There is not a finite number of apples in the universe, nor is there an infinite number of apples in the universe, because the real answer is time dependent.

I suppose you could have a condition where the number of apples being destroyed is equal to the number of apples being created, but that’s still a dynamic state of change and not really finite as far as individual apples are concerned.

The only way to have a finite number of apples in the universe is to stop time. And that, obviously, is impossible.

Digits suffer the same fate, because they don’t exist until we make them exist. After all, we invented numbers. They only exist in our imagination, and they don’t physically exist until we perform a calculation and can physically see them. We can obviously deduce an endless potential to generate numbers, but like an apple, we also know it is somewhat impossible to yield an infinite number of either. That answer is always time dependent.

We could say on Tuesday, March 8th, at precisely 3pm, there were exactly 183,723,232,102 apples, but that would be about it. Only if we had some means of instantaneously counting every single apple on Earth all at once. Not possible though, is it?

Same holds true for everything in the universe.

There is no such thing as an infinite quantity of anything in the universe, nor is there such thing as a finite quantity of anything in the universe.

Change is the constant.

What is infinity?

What is finite?

I don’t think anyone has a clue. We hold to colloquial meanings, and that’s not very scientific.

We cannot prove endlessness for the universe, nor can we prove a limit.

But, we do know 1 and 0 is a finite value. And mathematically speaking, our existence is the difference between something and nothing.

The question in my mind isn’t whether the universe is infinite or finite, it’s what does either mean? In my view, neither state is defined. Infinity certainly has nothing to do with quantities, anymore than finite. They describe the state of numbers. Static, versus dynamic values. Our universe is clearly observed as dynamic, not static.