Some excellent conversation going on here, I'm glad this topic is now thriving in the way I'd originally hoped.
Do you think numbers exist? Or to put it under another way which of the "three schools of thought" do you prefer?
I'm almost certainly a Mathematical Fictionalist, in that I do tend to question the existence of numbers, or at least what we understand about "numbers existing", and I do tend to regard them as being products of thought rather than original truths. However, they are incredibly useful, and number systems are responsible for many of world's great advancements.
What Numberphile says about the Fictionalist reconciling this dichotomy as "numbers are successful, but this doesn't make them true" resonates with me more than anything else that was mentioned in this video, so that would probably be where I stand. Of course, it's a very tentative standpoint based on relatively limited understanding, hence my fascination with the subject and desire to discuss and learn more.
I'm torn between nominalism and factionalism. I'm not sure as it may depend on the definition which could get a bit squirrelly.
Since squirrels are cute, fast, intelligent and resourceful, I wouldn't worry too much about things getting squirrelly.
The first two fall short especially when pushed to limits... If numbers are real; that is some kind of objects that exist in the world; where are they, what are they?... If numbers are merely a language to describe reality what is the reality that is being described with a number like pi? It's just an approximation
Agreed. This is the root of my fascination with the subject. In the video, the example was used of describing numbers to a child using objects: "here's a pencil, add another pencil and you have
two pencils!"
I can't help but then think: yes, but a pencil is made up of 1 piece of wood and 1 piece of lead, so 1 pencil is equal to 2 parts. This would seem, on the surface of things, to prove that 1 = 2, but of course it doesn't prove that at all. The object of "1 pencil" is here being treated as a whole object, despite being made up of multiple elements.
However, it leaves the question behind: the fact that the pencil is being treated as 1 object
has been decided - i.e. it is a product of human decision and system-making. It it not, therefore, a
truth.
This thinking is not necessarily useful, of course, as it somewhat arbitrarily challenges a system that's proven to be successful, valid, and progressive. It merely asks the question: yes, but is it true? However, I keep coming back to that, and always have done. Maths is amazing, no doubt, but it has its limits.
Math is an aspect of our mind; a language, a code that describes the world or makes up the world. Perhaps it is universal. Or it might turn out that other intelligent life operates with a totally different set of mental tools instead....
That would be incredible: if we were to meet beings from other planets who also use Mathematics, or - better still - have some other way of understanding things that seems completely bizarre to us at first, but works for them!
I thought this was why the Pangaea theory was formed? And I thought Pangaea is/was proven by plant/animal fossils being similar in certain places like Africa and South America etc.
The evidence all points to the continents being joined at some point in history, and Pangea theory was developed in support of Plate Tectonics theory. However, ask yourself which is more
plausible:
1. All of Earth's continents were once joined together one one side of the planet, whilst all of its water made up the other half. Because... reasons.
2. The Earth was once smaller, and as it grew the crust broke apart, new crust was formed, and the gaps filled with water (likely from comets).
OK, I've biased the second option slightly, but it's really hard not to when you describe each theory in these terms!
Are you familiar with project Kepler space telescope?... What's interesting to me is they've discovered many "super earths"... In hubris we always say "Earth is perfect for life" But it may turn out we our unlucky and there are in fact BETTER places for life elsewhere.
This is fascinating: I'll look into this, for sure! I have no doubt that there are other places in the Universe which humans may find more temperate and better suited to us than Earth. It's just an issue that we can't seem to stop squabbling with each other long enough to make significant progress in finding these places, but... it's only a matter of time.
What are you're thoughts on alien life?
Aliens exist. There simply
must be other planets out there which support life. It simply wouldn't make sense that, in a seemingly infinite Universe, there is only
1 inhabitable planet with life on it. As far as I'm concerned, the very idea is proof enough of life elsewhere. It would be good to find some, though.
"Existence" is a pretty slippery concept anyway... Numbers seem more aligned to the programming of a simulation while "real" objects seem more aligned to the data.
So, God is a coder! Who'd have thought a programmer would take such a viewpoint?
Seriously though, this is a very interesting idea and would indeed account for the difference between the existence of manufactured systems (languages, numbers, programming code, etc) and the existence of "real" objects (lemmings, humans, ice cream, etc).
My main objection to this theory would be that it's based on our recent understandings of science and technology, and isn't compatible with more historical thinking. The average human living a few centuries ago wouldn't have had any concept of what a "simulation" was. We only understand it now because we've brought about the possibility through our various technological and linguistic advancements. So, naturally, this leads us to question whether such advancements may explain our own reality. An interesting idea, but isn't independent enough to stand up against more constant, abstract ideas about truth and the nature of existence/reality.
I was never a huge fan of simulation theory. For one; it has the same problem the God problem has: you just ask who created/maintains the simulation of the simulator?
Yeah, exactly - that, too.
Pi is not an approximation. "3.14" or "3.14159" are approximations of pi. It so happens that Pi does not have a finite representation as a decimal number, but its definition is simply based on the ratio of circumference to diameter. In a way, the circle is the embodiment of Pi.
But then - which came first, Pi or the Circle?
It is true that it can be very difficult if not impossible, to ascertain how much of our perceived reality is just a product of our mind versus having an independent existence outside of the mind, though I feel like this goes for anything not just numbers though.
Absolutely agreed. Numbers are a good place to start the discussion though, because they are a man-made system which holds up to extensive scrutiny, meaning that they could represent a
doorway to truth.
To expand on this: if I say "flying unicorns exist", the response is either likely to be amusement, pity or ridicule. However, if I say "the number 7 exists", it stands up to further discussion. So, better to pursue this particular line of enquiry - even if we may not agree that numbers exist, we can agree that the
concept of numbers may be a key to better understanding of reality. Rather than focus on the key though, I'm more interested in finding the door and seeing where it leads.