"2 + 2" = "two plus two"

I read back those last few posts on my way home from work yesterday (Was it yesterday or the night before? All the days are blurring into one this Christmas). Either way, whenever I read them, they read a bit stilted. I think this is the problem when you want to do something, but don't have the time to catch the moment. You end up trying to fake it by retracing your steps, but the essential salience goes missing somewhere. So I hope I at least conveyed the general idea, especially on the topic of Number Worship. In fact, this is another problem: when you read something back that's fresh in your mind it can be hard to tell if you expressed what was on your mind on the actual page, as it's all tied up as one blob. Really you need to come back with fresh eyes in a few months' time, when you've forgotten all the mental rehearsals. Then it's easy to spot the mistakes, or the bits that don't make sense because you failed to include something important that the reader would've needed to know.

Anyway, today I'm gonna return briefly to Number Worship as something popped up that spurred me further.

The following exchange appeared on Twitter.

Firstly, neither of these tweets were in response to the particular point I was making, so it would be unfair to reply to them as if they were. It's more the case that they're convenient for me to make a point off the back of.

The initial tweet shows a meme that, slightly tongue-in-cheek, states that "Math isn't real." The reply then asks, "Why does 2 + 2 = 4?"

I like both these people, so I don't want to unfairly accuse anyone of stating something they were not. However, the reply tweet so neatly encapsulates the Number Worship mindset that I was trying to explain in my last, rather meandering, post.

Instead of just acknowledging, "Yes, mathematics is a language," the response is a defensive one. Making an argument implying that number is a fundamental aspect of reality. In fact, another tweet popped up in response to the debate that highlighted the worldview even more plainly.

It sums up the view in a nutshell, and if you remember the point from the last post - that literature gave rise to a belief in written bibles, which has since been supplanted by a belief in bibles written in mathematics  - you'll notice the common themes. (Though to be fair, looking up the quote online, it appears that the sentence only paraphrases Galileo, and in his original passage God is not mentioned. It is, nevertheless, the classic refrain.)

Anyway, the claim that maths is real because "2 + 2 = 4" misses the point. As just because a language can be used to make a true statement doesn't mean the language itself is fundamentally real and not conceptual. For instance, I can make a true statement in English. Let's say, "If you heat a solid it will turn to liquid." This is true, but no one would argue that therefore English, or some other spoken language, is the true essential root of all physical reality. (Though again, in the age of the written bibles we had, "In the beginning was the Word, and the Word was with God, and the Word was God" [My emphasis, not God's :p .)

Likewise I can write "2 + 2 = 4" in English, .."Two plus two equals four."

There's this vague notion, as per the Galileo quote, that the universe is constructed entirely from number. Like numbers are somehow the essential building blocks. However, even if the numbers themselves were not conceptual, which they are, the language of mathematics is held together by symbols that are not numbers. Even the simple "2 + 2 = 4" is not simply numbers. The + sign is a symbol that symbolises the concept of adding. The = sign the concept of things being the same. So we're dealing with concepts here, abstractions from the real world.

Plato's Forms

The Number Worship worldview is a little bit similar to Plato's theory of Forms. This notion that conceptual ideas are somehow more real than the physical examples. That the concept of an Orange, or a Tree, is truer and more perfect in form than its real world imitations. This is an interesting idea from a philosophical, or even religious point of view, but it's not science. Science is about observing the real world - so it would be a topsy-turvy science that deemed concepts more fundamental than physical reality.

Nevertheless, it serves as a good illustration of how language is indeed conceptual. There are, of course, real actual oranges. However, when we use the word orange we're conveying a concept. Even if I have an actual orange, the minute I express to another person, in writing or in speech, "I have an orange," the words are conceptual. And I'm relying on the fact that the other person shares the same concept, and understands that the symbols on the page symbolise that concept. I'm not giving them an actual orange by writing the word orange.

This belief that the numbers themselves are somehow truer than the real world objects they're counting, is, like Plato's Forms, actually quite a mystical idea. Though those who believe it are generally quite oblivious, so much do they confound the notions of maths and science. It's also more restrictive, as the Plato theory can appeal to all concepts, whereas the more modern form is exclusive to just numbers (and also geometric shapes).

(In fact, geometric shapes - the circle, the triangle, the perfect sphere and so forth - also very much fall into this category of concepts that are taken as more real than reality itself. It's likewise interesting to note that at the macro and micro level we have worldviews that mirror this. Be it the spherical suns and planets orbiting in space, or electrons whizzing around protons and neutrons. In contrast to what we witness in our everyday lives - where flowers, humans, clouds, birds, etc, are complex shapes. Though here the round orange does indeed seem perfect in its radiance.)

..Back To Christmas

Anyhow, I better get back to Christmas. I'm back at work tomorrow, so I'm gonna have to get presents wrapped tonight. Sadly the perfectly wrapped presents that exist in my mind's eye won't be viewed quite like the real thing by the people receiving them. So I'm a slave to reality, and my poor wrapping skills will have to suffice.