Is Maths Truly the Universal Language?
Discussion
Peter3442 said:
Numbers are only part of mathematics. Maths isn't and can't do everything, but it's as 'universal' as universal can be. We can’t do much without it or, at least, it allows us to do many things much better.
I don't understand people boasting of their ignorance of maths. No one boasts of illiteracy. Worse still is the total lack of mathematics unashamedly demonstrated by almost all of our politicians - and don't just mean their failure to recall numbers.
But if you didn't have numbers you couldn't have maths.I don't understand people boasting of their ignorance of maths. No one boasts of illiteracy. Worse still is the total lack of mathematics unashamedly demonstrated by almost all of our politicians - and don't just mean their failure to recall numbers.
Mr Pointy said:
Peter3442 said:
Numbers are only part of mathematics. Maths isn't and can't do everything, but it's as 'universal' as universal can be. We can’t do much without it or, at least, it allows us to do many things much better.
I don't understand people boasting of their ignorance of maths. No one boasts of illiteracy. Worse still is the total lack of mathematics unashamedly demonstrated by almost all of our politicians - and don't just mean their failure to recall numbers.
But if you didn't have numbers you couldn't have maths.I don't understand people boasting of their ignorance of maths. No one boasts of illiteracy. Worse still is the total lack of mathematics unashamedly demonstrated by almost all of our politicians - and don't just mean their failure to recall numbers.
Esceptico said:
Mr Pointy said:
Peter3442 said:
Numbers are only part of mathematics. Maths isn't and can't do everything, but it's as 'universal' as universal can be. We can’t do much without it or, at least, it allows us to do many things much better.
I don't understand people boasting of their ignorance of maths. No one boasts of illiteracy. Worse still is the total lack of mathematics unashamedly demonstrated by almost all of our politicians - and don't just mean their failure to recall numbers.
But if you didn't have numbers you couldn't have maths.I don't understand people boasting of their ignorance of maths. No one boasts of illiteracy. Worse still is the total lack of mathematics unashamedly demonstrated by almost all of our politicians - and don't just mean their failure to recall numbers.
Mr Pointy said:
But if you didn't have numbers you couldn't have maths.
There are large areas of maths dedicated to the subject of numbers. However, there's a great deal that exists without them. Very often, we need a number to make use of the maths, but by no means always. School geometry provides a lot of examples. Ask an old gardener to make an oval flower bed in the centre of your lawn. If he knows his work, he'll male a nice ellipse, centred, oriented and sized as required with a long piece of string and two sticks. It's a nice piece of applied maths all done without numbers.
Peter3442 said:
Mr Pointy said:
But if you didn't have numbers you couldn't have maths.
There are large areas of maths dedicated to the subject of numbers. However, there's a great deal that exists without them. Very often, we need a number to make use of the maths, but by no means always. School geometry provides a lot of examples. Ask an old gardener to make an oval flower bed in the centre of your lawn. If he knows his work, he'll male a nice ellipse, centred, oriented and sized as required with a long piece of string and two sticks. It's a nice piece of applied maths all done without numbers.I'm genuinely asking, I'm fascinated by the responses so far, so thank you all who have contributed.
I understand what Esceptico said about studying maths without numbers, however, do we have that ability because the numbers came first allowing us to prove the calculations of such things?
Almost "chicken and egg", what came first, the numbers and understanding of them, or the calculations?
AshVX220 said:
However, in order to do that he'd need to know how the numbers fit in to the design wouldn't he? Even to understand that one length is twice the length of the other.....
Not really. There has to be a concept of 'size,' but that's you saying bigger or smaller; it doesn't need to be a number. Similarly, there have to concepts of 'centre' and 'shape,' but numbers only come in if you want them too.TellYaWhatItIs said:
I believe maths is indeed intrinsic to the design of all nature.
Research the Golden Ratio, 1.618.
But it's only that value in a Western base 10 framework. What would it be to the Mesopotamians or the Incas? Could the Romans have evaluated it? Is there a number framework in which it's a non-irrational number?Research the Golden Ratio, 1.618.
Mr Pointy said:
But it's only that value in a Western base 10 framework. What would it be to the Mesopotamians or the Incas? Could the Romans have evaluated it? Is there a number framework in which it's a non-irrational number?
That's an interesting question (equals I never thought about it before). If a number is irrational in one base, is it irrational in all? To be rational it has to be a ratio of two whole numbers (integers). Since integers are always integers, independent of base, I think the answer is no, it's can't be made rational by a change of base.What's interesting about the golden ration (and pi) is that they are features of geometry. They only become numbers because we want to put a numerical value to them. (No need to tell that last sentence sounds thin, but it might be worth thinking about).
Another interesting fact about the Golden ratio is that it is the most irrational irrational number. As a continued fraction phi is the slowest to converge, since phi = 1+1/(1+1/(1+1/ ... )) (Hurwitz's Theorem gives a proof of this).
Mr Pointy said:
Is there a number framework in which it's a non-irrational number?
I think/assume the base would have to be irrational for an irrational number to become non-irrational.Edited by V8LM on Wednesday 27th November 20:49
The set of irrational numbers ie ones like Pi that cannot actually be represented using our numbering system is actually much larger than the set of rational numbers so most of maths must be about “numbers” that are not numbers, if you see what I mean.
One of the proofs that screwed with my mind at Uni was the proof that one infinitely large set (rational numbers) was smaller than another infinite set (irrational numbers) despite infinite meaning infinitely big.
One of the proofs that screwed with my mind at Uni was the proof that one infinitely large set (rational numbers) was smaller than another infinite set (irrational numbers) despite infinite meaning infinitely big.
Mr Pointy said:
There is a tribe who have no concept of numbers so no, maths is not universal.
https://www.spiegel.de/international/spiegel/brazi...
I was performing an automatic task where evidential requirements meant that I had to be there all the time. https://www.spiegel.de/international/spiegel/brazi...
I'd taken a book to read but a pair of pigeons nesting on a ledge outside the window took my interest.
The hen bird, on the next, was approached by her partner and offered a bit of stick for the nest. She refused two and accepted the third. This went on through more than a dozen repetitions. I think it was clear that she, at least, could count up to three. Further, there's a universal trait in females. (Non-scientific for the last bit, but right.)
AshVX220 said:
I have always been led to believe and understand that Maths is a universal language that should be understood by any intelligent civilisation in the Universe.
For me it comes down to very simply that 1 is indicative of a single object, 2 of 2 etc, etc, etc.
Now, my mate (who is quite smarter, certainly smarter than me) suggested at the weekend that it's not, because our entire numbering system is based off of 10 (and multiples there-of, 10, 100, 1000 etc, etc.) And that this is primarily because we have 10 fingers and this is where the depiction of 10 and multiples of it come from.
An alien civilisation, that possess 12 digits would, or could, have a different way of counting and representing numbers.
But, in my mind that's just the way the numbers are represented or counted. But at the very base level 1 is still 1 and 10 is still 10 and calculations using any number work (when done correctly of course).
Does the view that other alien civilisations that represent numbers in a different or totally alien way carry any weight? I'm un-convinced.
This argument doesn't make sense because you claim maths is universal but your mate claims it is not universal by claiming that aliens also use maths.For me it comes down to very simply that 1 is indicative of a single object, 2 of 2 etc, etc, etc.
Now, my mate (who is quite smarter, certainly smarter than me) suggested at the weekend that it's not, because our entire numbering system is based off of 10 (and multiples there-of, 10, 100, 1000 etc, etc.) And that this is primarily because we have 10 fingers and this is where the depiction of 10 and multiples of it come from.
An alien civilisation, that possess 12 digits would, or could, have a different way of counting and representing numbers.
But, in my mind that's just the way the numbers are represented or counted. But at the very base level 1 is still 1 and 10 is still 10 and calculations using any number work (when done correctly of course).
Does the view that other alien civilisations that represent numbers in a different or totally alien way carry any weight? I'm un-convinced.
That is a contradiction.
You and your mate are both agreeing maths is universal for this hypothetical alien.
How does you friend and his alien represent the number zero on his 12 digit hand compared to you on your 10?
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