Comparison codes for DSP module

[Tronic]

It never stops to amaze me...

[RJHollins]

wow I've gone quite philosophical today...

Yes You have

But THANKS for sharing the insights.

I honestly did NOT know of the 'insects reproductive cycle' tied to PRIME numbers.

I DO blame our schooling system.

[Spogg]

Interesting stuff here!
I believe that mathematics isn't "out there" but is a construct of human consciousness. In reality there is only a single item: reality, the universe.
We divide and conquer this reality in order to grasp concepts, like apples. No two apples are exactly the same but there is sufficient similarity between these fruits, in our opinion only, to enumerate them in quantities.
Because consciousness then tries to work with this idea called mathematics we get absurdities like -2 apples. In this way if I steal both apples from my neighbour he could be said to have -2 apples. In actual fact he has NO apples since it's not possible to hold a negative quantity of anything at all. Those amongst us who have no apples could equally be said to have -74 apples, or even a negative infinity of apples.
I believe the lie which is mathematics can lead ultimately to so many daft ideas like multiple unverses and dimensions. We take formulae that relate to nothing real and we manipulate them to make "discoveries" which also relate to nothing real.
So, maybe we should rename the abs function to getreal...

OK, that said, I'm off to carry on with my Vocoder project.

Cheers

Spogg

[KG_is_back]

I honestly did NOT know of the 'insects reproductive cycle' tied to PRIME numbers.

It's crazy, isn't it ... You can actually calculate primes using evolution (although it is fairly inefficient).

I believe that mathematics isn't "out there" but is a construct of human consciousness. In reality there is only a single item: reality, the universe.
We divide and conquer this reality in order to grasp concepts, like apples. No two apples are exactly the same but there is sufficient similarity between these fruits, in our opinion only, to enumerate them in quantities. Because consciousness then tries to work with this idea called mathematics we get absurdities like -2 apples.

That's exactly what I'm talking about. Using wrong model to solve a problem may lead to such absurdities. The amount of apples is a natural number. In case of natural numbers 0 - 2 = complete nonsense. If however you change the property you are quantifying (for example instead of amount of apples that you physically have you count the amount of apples you own) the system suddenly makes complete sense. 0 - 2 = you promised to give 2 apples to somebody (you are 2 apples in debt).
It's exactly what I'm talking about. Math education is heavily oriented towards arithmetic and algebra (being able to operate with numbers and unknowns swiftly and efficiently) to a point that it seems "That's what Math is all about!"
But then most people fail to "mathematize" problems properly.
For example: "solve 0-2=x in N (natural numbers)" natural child question is "why the answer can't be -2?" and the best answer you can get from average math teacher is "because -2 is not in N". And it is a correct and satisfying answer, but what does it REALLY mean? It simply means "You can't take 2 apples from someone who has none. Equation 0 - 2 = x in N simply describes impossible scenario." I don't blame teachers at all. At some point the problems that are being solved become so complex, it is hard to connect them to reality. For example "sqrt(-1)=i" what does the "i" really means? That's insanely hard question for a math teacher.
The answer to the question: In some problems, having two directions of change (positive/negative) is insufficient (for example adding harmonic oscillators). "i" is a "third" direction perpendicular to +/- (and -i is the opposite). This way we can associate a length (amplitude) and an 2D angle (phase) using single number. We could've simply used vectors, but "complex number" is simply much more convenient.

I believe the lie which is mathematics can lead ultimately to so many daft ideas like multiple unverses and dimensions. We take formulae that relate to nothing real and we manipulate them to make "discoveries" which also relate to nothing real.

I disagree! Some in some sciences (namely mathematics and theoretical physics) our knowledge far exceeds our practical capabilities at the time, but that may not be true forever. Example: special and general relativity had no practical use at a time when Einstein formulated it. That was true until GPS satellites were launched. The satellites transmit their precise position and time. Your GPS device calculates the position by comparing the time lag between receiving signals from different satellites. However, because of general relativity, the clocks of the satellites run faster on orbit and compensation was needed. Many people use GPS daily now, and it wouldn't work at all without Einstein's theoretical discoveries.

[tulamide]

What KG says.

We can even go the "natural" route: If some one says math is just a construct invented by humans, I disagree. Most creatures use math. One key feature of all life is the ability to recognize patterns. Wether you see, hear, feel, smell or taste patterns, it's math that enables life to recognize them.

Even nature itself follows the rules. Ever heard of Fibunacci? Maybe not. It was a mathematician and is famous for a series of numbers, that follow a simple rule: Start with two times 1, then sum 2 numbers to get the next number of the sequence. 1, 1, 2, 3, 5, 8, 13 etc.

Not very exciting, ist it? Well, this number series is used by the nature throughout all of its fauna and flora. For example, snail shells are build after exactly that rule. Also almost everything that is in some way spiral (for example a sunflower)

Humans did not invent mathematics, they discovered it.

[KG_is_back]

Even nature itself follows the rules. Ever heard of Fibunacci? Maybe not. It was a mathematician and is famous for a series of numbers, that follow a simple rule: Start with two times 1, then sum 2 numbers to get the next number of the sequence. 1, 1, 2, 3, 5, 8, 13 etc.

Not very exciting, ist it? Well, this number series is used by the nature throughout all of its fauna and flora. For example, snail shells are build after exactly that rule. Also almost everything that is in some way spiral (for example a sunflower)

Yes, the famous logarithmic spiral... The explanation is a bit harder, but I'l try:
A snail grows roughly exponentially (after n days it grows by factor of k. After 2n days by factor of k*k). That means it needs bigger and bigger shell opening as time progresses. The shell has a shape of a logarithmic spiral to save building materials (each new segment of shell shares the maximum amount of contact area with the older parts of shell). It turns out, logarithmic spiral is the sweet spot for that:

the new segment (when aproximated as a square) shares 1 full side with the old shell. If the shell grew straight it would waste more and more materials over time.
Again an excellent example of how optimization via evolution leads to mathematically ideal solution.

Humans did not invent mathematics, they discovered it.

Like with every science... The rules of mathematics were always there. Humans just give them names and explore the properties and possibilities. The opinion depends on the definition of word mathematics:
1. it is the mathematical relations that drive the reality
or 2. it's our knowledge of those relations and the way we describe and name them?
In case 1. the math was always there and we just discover it. However, in case 2. the math is just an invention (the discovery of mathematics in meaning 1. )

[Spogg]

Of course I would agree that maths is a hugely powerful tool. No maths, no Flowstone for example.

I maintain however that it is a human construct, a method of codifying what we find around us. The universe basically has one tool available which is not mathematical; namely the trial and error that blindly determines the evolution of both snails and galaxies. No snail ever decided to use an exponential series to make its shell. It just turned out that this method delivered a survival advantage for its construction recipe. It is us that see the patterns and use them to understand and create new patterns. If an alien race evolved intelligence it would probably see the same patterns as we do and may well fall upon what we call mathematics in the same way. This is because, we assume, the universe is homogenous. However, does this mean that mathematics exists "out there" without advanced consciousness? Even birds can't count their eggs, they just seem to rely on "eggness". Hence Cuckoos.

Anyway, I'm having fun with my vocoder but I can't yet see how to set it up in Reaper.

Live long and prosper

Spogg

[KG_is_back]

I maintain however that it is a human construct, a method of codifying what we find around us.

yes, that's what I meant by the meaning of Mathematics no.2

The universe basically has one tool available which is not mathematical; namely the trial and error that blindly determines the evolution of both snails and galaxies.

wrong... Darvinistic evolution is one of the simplest form of artificial (or natural? ) intelligence! Using randomness to generate system and then test it if it's better or worse than previous iteration is a valid and purely mathematical implementation. Slightly improved version of evolution is even used in computers. Just google Newton's method...
There is nothing "non-mathematical" about making a guess.In fact, with a little trick you can win a 2-option guessing game more than 50% times.

[tulamide]

I'm such a huge fan of numberphile for years now! Nice to see others have discovered it also