Earlier quoted context omitted.
Physics creates us, universe creates physics, … creates universe
Math creates universe? The answer normally lies in the open. (I don't know though)
... creates math.
How inevitable is the concept of numbers?
131–140 of 211 posts
Re: How inevitable is the concept of numbers?
#132Earlier quoted context omitted.
A tree adapts to its environment and I would bet money that trees in their phenomenology can’t count.
Lots of animals have been verified to understand and use abstract count which is what numbers are at their basics. Plants are much less adaptive than animals by definition. The problem isn’t whether they know numbers but how do you even test what plants “know”.
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Re: How inevitable is the concept of numbers?
#133Earlier quoted context omitted.
Could you prove for every real value between 0 and 1 that it's greater than or equal to 0? That's an uncountable amount of proofs
No, because proofs have to consist of a finite number of words. Thus there are only countably many proofs of anything. In particular, there are only countably many reals between 0 and 1 which can be expressed in a finite number of words.
Are there a finite number of words? Language seems to grow and adapt to new concepts as needed, perhaps there is an infinity of linguistic descriptions available to us.
Re: How inevitable is the concept of numbers?
#134Earlier quoted context omitted.
Yep. Q: "How many times has it rained this week?" A: "It has rained zero times " Zero is a perfectly natural state.
I think humans could predict solar eclipses and solve quite a few differential equations before they managed to give that answer. The normal answer to that question was “It hasn’t rained this week” or even “What do you mean? It hasn’t rained this week”. https://en.wikipedia.org/wiki/Brahmagupta#Zero : ”The Brāhmasphuṭasiddhānta is the earliest known text to treat zero as a number in its own right, rather than as simp…
These are semantics, the concept of zero is still obviously everywhere in nature.
"How many fish have you caught?" "None."
Just because you reply none doesn't make it some wildly different concept than if you had replied with the word zero. In fact it's exactly the same thing.
Re: How inevitable is the concept of numbers?
#135When I used to teach a class called “Mathematics for Liberal Arts Majors,” the first class began with having students “draw six.¹” I refused to give more explicit instructions. It was fascinating to see the results that came out of this, along with the ideas about numbers that it sparked.
1. I have to confess that the choice of six was not arbitrary.
Re: How inevitable is the concept of numbers?
#136Numbers are not fundamental. What is fundamental is laws of arithmetic. 1 + 2 == 2 + 1. Laws like that can only be expressed in some language, which we call "numbers". But only by knowing and using such laws "numbers" become useful.
So in some weird sense numbers allow us to define the laws and the laws define numbers. No?
Re: How inevitable is the concept of numbers?
#137I think numbers are wonderful and cool abstract thingies. We grow up being taught them (in my case Arabic numerals in base 10) and they become such part of our being that we start to think that we know what “5” is. Then I was introduced to Roman Numerals. Didn’t like those much. That one taught me that 4 is more related to 5 than it is 3. Then some of us learn a base 2 number system or base 16 number system and for a…
Does the base really have anything to do with 5? I can represent 5 in base 10 as 5, or I can represent it in base 2 as 101, but both encode the same information.
Using different bases, to me, is just about storing information. How many symbols do you want to create before you increase the length of your number and start re-using them.
Re: How inevitable is the concept of numbers?
#138I can understand how natural numbers can be “constructed” (for lack of a better word) as a byproduct of counting, what I could never understood on a deeper level are negative numbers, I can’t see how a number i.e. a count can be lower than zero. Maybe related, while I can also partially understand multiplication (syntactic sugar for adding) I could never understand multiplication by zero, meaning how come when you mu…
On multiplication, it's better to not think of multiplication as being repeated additions, but instead to think of it in terms of areas. Taking that approach, it becomes easier to consider, e.g., (x² + 2x - 1)×(3x² -4x + c) since we can write the terms along the sides of a rectangle and divide the rectangle into the products of the terms.
One of the things I did in my math for liberal arts majors class I used to teach was also to do a fictionalized version of the expansion of the concept of numbers from *N* to the whole numbers to integers to rationals to algebraic numbers to reals to complex numbers. I say fictionalized because whole numbers and negative integers historically come after (positive) rationals, algebraic numbers and transcendental reals, but for pedagogical purposes, its easier to go in order of increasing supersets.
Re: How inevitable is the concept of numbers?
#139When I used to teach a class called “Mathematics for Liberal Arts Majors,” the first class began with having students “draw six.¹” I refused to give more explicit instructions. It was fascinating to see the results that came out of this, along with the ideas about numbers that it sparked. 1. I have to confess that the choice of six was not arbitrary.
This is really intriguing. Do you have any examples of what people came up with?
Re: How inevitable is the concept of numbers?
#140When I used to teach a class called “Mathematics for Liberal Arts Majors,” the first class began with having students “draw six.¹” I refused to give more explicit instructions. It was fascinating to see the results that came out of this, along with the ideas about numbers that it sparked. 1. I have to confess that the choice of six was not arbitrary.
Why six?