Discussion in 'Physics & Math' started by Doctor Dread, Oct 6, 2017.

1. ### QuarkHeadRemedial Math StudentValued Senior Member

Messages:
1,556
Yes, it would be remarkable if true. But it is not.

3. ### Write4UValued Senior Member

Messages:
7,905
Yes, it can be found ar 51:38

I have confirmation of this elsewhere but don't remember the paper.

The number one is not a plurality. The number two (2) was specifically the first number that indicated more than 1.
It seems a logical intuitive cognitive ability.
A scratch on a piece of wood has not intrinsic meaning, but two scratches is arithmetic and a series of scratches show a chronology.
There is always one of something, but it cannot be divided without the number 2.

Two (written in many ways in early civilizations) is the first symbolic representation of performing calculus (post # 39). There cannot be less than one of something, Then it does not exist. But there is obviously more than one. The first more than one is two.. I am speaking of very old times in human history.
I think Livio was talking about an intuitive recognition of attributing the human form and other constantly recurring phenomena existing as "pairs" or "opposites" very early in the evolution of the hominid brain. If you lost an arm, you were no longer "whole"[/quote]

Last edited: Dec 4, 2017

5. ### NotEinsteinValued Senior Member

Messages:
1,533
The linked video doesn't state at that time index that the number 2 was first; it just gives a possibility how the concept of the number 2 came to be.

So your statement in post #37 that mathematics "started with the number 2" was wrong. OK.

How is "the mirror image of something" a "logical intuitive cognitive ability"?

One scratch is meaningless, but two scratches isn't? Two scratches is arithmetic? What? Can you please rephrase, because this read a bit like word-salad.

So what? Why does something not has intrinsic meaning if it cannot be divided by two? Do three scratches have no intrinsic meaning then?

Doesn't mean it was the first number to be invented/discovered.

Right, so the number one is quite important, and obvious.

"The first more than one is two." Your wording suggests that two was discovered after one.

Sure, but he didn't say that the number 2 was invented/discovered before the number 1, which was your claim.

7. ### Write4UValued Senior Member

Messages:
7,905
Yes, a natural probability.
Not necessarily.
[
Because they are the most naturally occurring simple patterns. Even Lemurs can learn to recognize simple patterns .
Two or more scratches is counting.
of course they do, but you have get past two in order to get to three.
the symbol 2 as a single cypher to identify a plurailty instead of two scratches, would seem to be the first attempt at arithmatic;
1 (scratch) + 1 (scratch) = 2
In context of history it may well be.
A scratch is not a deliberate cypher, although it still represented as 1 (a scratch).
True and I am not a mathematical historian. He merely explained that "pairs" was probably the first cognition of a symmetrical plurality. And the NOVA clip starts with the identification of regularly recurring pair patterns such as shown in the list above associated with the number 2.

I am not proposing this as a formal scientific paper. It is my perspective when trying to find a logical progression from symbolizing simplest form of identifying quantities or values to complex numbers mathematics which came after the symbolization of larger numbers.
From Lemurs to landing a Rover on Mars.....

Last edited: Dec 4, 2017
8. ### Write4UValued Senior Member

Messages:
7,905
I'm not sure if I understand that posit. In what way is this not true and therefore not remarkable?

p.s. Relativity would not exist without 2 frames of reference.

Last edited: Dec 4, 2017
9. ### NotEinsteinValued Senior Member

Messages:
1,533
What is that supposed to mean?

It was wrong in the sense that you represented it as fact, but it was merely a baseless assertion.

How does this make the "mirror image of something" a "logical intuitive cognitive ability"?

I can count to one. In fact, when I start counting from zero, I encounter one before two!

And you have to get past one to get to two.

You are trying to prove 2 was the first number to be discovered by showing how you can use 1 to get to 2. So you need 1 first, thereby proving 1 was there before 2 was.

You've just said the number 1 is so important, if you have less than it, that thing doesn't exist at all. Sounds way more important than 2 to me.

You misunderstand. In order to prove the number 2 was there first, you keep referencing the number 1. So your arguments presuppose the number 1. In other words, in your argument, you have assumed the number 1 was there first. From such arguments you cannot conclude that number 2 was there first; that's logically inconsistent.

Right, so your original statement is not supported by your own source, and thus was merely a baseless assertion.

I propose that the concept of "one" is simpler than the concept of "two", and that thus is seems natural that the number 1 was discovered/invented before the number 2. As you yourself pointed out: "one" has to do with the very existence of things, while "two" is merely a nice symmetry of several existing things.

10. ### Confused2Registered Senior Member

Messages:
501
I'm not sure the proposition is worth either attacking or defending... however...
If your counting stops at one then for several sheep you might have
1 sheep+1 sheep+1 sheep+1 sheep+1 sheep+1 sheep
= (we can do no better then)
1 sheep+1 sheep+1 sheep+1 sheep+1 sheep+1 sheep
With less sheep
1 sheep+1 sheep=1 sheep+1 sheep
Still simply a statement
BUT
1 sheep+1 sheep=2 sheep is of a different order of sophistication.
Arguably
1 sheep + 1 feast = 0 sheep
is equally sophisticated where
1 feast = -1 sheep.
1 sheep
1 sheep
1 sheep
1 sheep
1 sheep
zzzzzzz.

11. ### Write4UValued Senior Member

Messages:
7,905
Observation of patterns and symmetries.
Not baseless, but the the quoted words of a scientist.
When I face another person. his left side is on my rght side and vice versa. Looking in still water and seeing your mirrored reflection, everything is reversed.
That's true now, but Lemurs don't count zero, one, two, three, yet they can tell more from less and can be taught that, presented with 2 sets of quantities, they know that pressing the set with the lesser quantity of the objects displayed will produce a reward, which is actually counter intuitive but proves they can learn to make an learned calculation. In fact they can do this as well or better that some humans (if the human is prevented from counting 1, 2, 3........)
That is true in arithmetic. But in intuitively, there is either nothing or there is something. Not 1 or 2 or 3 of something , but something and more or less of that something.
No I am trying to suggest that 2 is the first significant mathematical invention where quantities are specifically symbolized by different cyphered symbols as specific quantitative values, rather than more or less.
IMO, at that level of unsophisticated thinking there is only something or more than something. One can argue that "something" represents 1 , but not to a primitive mind.
Not necessarily, the something you are looking at, has attributes which determine it's shape, size, and symmetry, IOW the pattern of the object. In the case of Lemurs these attributes always come in pairs.
Livio did say that when we observe another person, we notice that their attributes always come in pairs. 2 eyes, two breasts, two arm, two legs. If something is missing, they are no longer symmetrical or physically attractive.
But it is the symmetry (the pattern) of the object which tells you what you are looking at.
To a Lemur one tree is an object with many branches which may support your weight, an observation of the utilitarian attributes of the object. A natural probabilistic functional calculation for moving through the trees, or for reaching fruit. A Lemur will not pay attention to the tree trunk which consists of one , but will select a tree healthy tree with strong branches and carries more fruit than a tree with smaller branches and carries less fruit as was shown by the experiments on Lemurs ability to make intuitive opportunistic calculations , Lemurs don't count 1, 2, 3... they reconize differences in quantity and quality on which they base their selections.
One of something has no meaning other than what are its several specific attributes.

As Hazen noted, in a redwood forest the bulk of the biomass is in the trees, but it is the rare species that sets them apart from the greater biomass and their special attributes define the objects.
IOW, something with more or less differently desirable or undesirable attributes is the the natural calculation.

A Lemur doesn't think ; "oh there is one tree" it dwells in the trees, it is its environment. But it does look if the tree has more or less fruits.
When a human walks a beach, we don't count the grains of sand, we call it "sand", it is the rare pebbles with different attributes from the sand that draws our attention.

But all that is prior to actual counting, i.e. recording certain patterns which always come in pairs.
Thus in reality 1 pair = 2 objects. I believe this is what Livio was getting at. His example of the Fibonacci sequence where he conveniently skipped the 0..1..1..2..3..5..8..etc.... is doing advanced mathematics.

But by your representation of counting, zero should then be the very first number, but we start counting as
a single scratch, which represent one cyclical pair or opposite (mirror) states, i.e two of something.[/quote]

12. ### Write4UValued Senior Member

Messages:
7,905
That is exactly what I am trying to say. The evolution from intuitive calculation of quantity, to representing these quantities with single cyphers.
Which introduces the sophisticated concept of subtraction.
Took a quick wink....

...?

13. ### NotEinsteinValued Senior Member

Messages:
1,533
You are making no sense:
Me: The linked video doesn't state at that time index that the number 2 was first; it just gives a possibility how the concept of the number 2 came to be.
You: Yes, a natural probability.
Me: What is that supposed to mean?
You: Observation of patterns and symmetries.

How is the observation of patterns and symmetries a "natural probability", and how is that related to how the concept of the number 2 came to be? Your answers appear to be word salad.

How is this a "logical intuitive cognitive ability"? (And what is that in the first place?)

So lemurs can't count at all; they just understand the concepts of "less" and "more".
Additionally, I'm not a lemur. I can count zero, one, two, three, ... And in order to do so, I need to get to one before I can get to two.

Zero and one.

If that's your argument, you've just destroyed your own position. Let me throw that argument back at you, modified: "Not 2 or a pair, but mirror images." In other words, if you are claiming the existence of a single object doesn't not lead to the number 1, then a mirror image or a pair of somethings doesn't lead to number 2 in exactly the same way.

That is not what you wrote in post #37. Are you withdrawing your statement from that post?

And how exactly can you be sure that mirror images and pairs of somethings do lead to number 2, instead of remaining at the level of unsophisticated thinking?

You mean the single something I'm looking at? That thing of which there is one? See? You've already referenced the number one!

You just suggested that lemurs don't understand the concept of the number 2, just less and more. If that's true, then how is this a response to my statement?

Irrelevant. He didn't say that the number 2 was discovered/invented before the number 1, which was your statement.

So? That patterns doesn't necessarily have to do with the number 2. For example: a tree. Of course you can find symmetries in trees related to the number 2, but those aren't very natural. However, the mere existence of the tree is something that's very in-your-face.
Or the moon. Good luck finding an obvious pattern using the number 2, but there is obviously is a (one) moon.

What is a "natural probabilistic functional calculation"? Also, that's not a full sentence.

Are you suggesting a lemur will try to climb a non-existent tree? I think you'll find that lemurs are pretty good at distinguishing between no tree (zero) and a tree (one).

So nothing to do with the number 2 specifically, and because lemurs don't count, they can't have discovered/invented the number 2.

It'd say existence is a pretty big deal. You can describe the attributes of a something all you want, but without it existing, there's no way to discover/invent the number 2 from it, because on unsophisticated thinking.

Are you suggesting lemurs think they can climb multiple trees simultaneously?

How is this related to anything?

But before you have "2 objects", don't you need to have "1 object"? Let's say I start collecting fruits. I start with no fruits, then one fruit, and then I have a pair of fruits. Typically, I need to get to one before I can get to two. Our human ancestors were pretty good at spotting one lion, and they didn't put specific meaning into a pair of lions. Because, you know, one lion is scary enough to make you run away.

Historically, it indeed took a while before the number zero was discovered/invented. So I'm not making that argument; I'm specifically focusing on the number one.

So one, not two.

What is a "cyclical pair"? How does a single scratch represent "one cyclical pair or opposite (mirror) states, i.e two of something"? You do know that, for example, the ancient Egyptians used counting for their grain administration? How is their number one related to "one cyclical pair or opposite (mirror) states, i.e two of something" instead of one sack of grain?

14. ### Write4UValued Senior Member

Messages:
7,905
The probability that a sentient being with a relatively advanced brain and stereo vision and hearing will recognize symmetries and patterns of various kinds. Where did the gods come from? Where did astrology come from? What was the purpose of Stonehenge? How do migrating birds navigate? How do insects become active when atmospheric pressure drops rapidly?
Are these not results of probabilistic evolution and natural selection of cognition of patterns?
Is that better?

Last edited: Dec 5, 2017
15. ### NotEinsteinValued Senior Member

Messages:
1,533
Ah, I see. May I suggest that next time you start with an explanation like this, instead of just naming terms, points, and concepts that haven't been introduced before?

Yes.

16. ### Write4UValued Senior Member

Messages:
7,905
Regularly occurring natural patterns and using them for predictive purposes. Both/either intuitive or reasoned.

Last edited: Dec 5, 2017
17. ### NotEinsteinValued Senior Member

Messages:
1,533
Ah, OK, I see. And how is this related to whether the number 2 came first?

18. ### Write4UValued Senior Member

Messages:
7,905
Patterns or comparisons require at least pairs (2 of something).

19. ### NotEinsteinValued Senior Member

Messages:
1,533
Sure, but how is this related to whether the number 2 came first? Are you saying that pattern recognition came before basic existence determination? To me that seems weird: "I can't determine whether I see any trees or not, but those trees stand in a pattern!"

20. ### phytiRegistered Senior Member

Messages:
301
From Wiki:

1. The fundamental theorem of arithmetic establishes the central role of primes in numbertheory: anyinteger greater than 1 can be expressed as a product of primes that is unique up to ordering??????

2. The uniqueness in this theorem 1 as a prime because one can include arbitrarily many instances of 1 in any factorization,...

Statement 2 seems to contradict statement 1.

The integer '2' is the product of 2*1, but by (2.), 1 is not a prime.

The arbitrary fudging to make things work could be eliminated.

Generalization is the enemy here.

A cup can contain, water, coffee, tea, juice, etc., but a cup is not a member of fluids/drinks.

Let zero '0' represent the container, (the empty set {} for those inclined), i.e. not a number. (A place holder represents "there are no elements here".)

Let one '1' represent the unit, by definition.

Let M be the set of multiples of the unit, formed using a Peano type algorithm.

Now a prime is defined as "a multiple of 1 only'. Since 1 is excluded from M, it is not a prime, by definition.

Now redefine the fundamental theorem as "all composite integers can be expressed as a product of primes'.

As to which was recognized first, 1, 2, or other, the human hand has 5 digits. Maybe it is a multiple choice.

The prisoner starts marking his days with a '/'.

21. ### NotEinsteinValued Senior Member

Messages:
1,533
I'm getting this: "In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1[3] either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors." https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic
That resolves the issue. The statement 1 you quoted is incomplete.

It's very iffy to have a number (zero) represent something that's not a number.

"Or is a prime itself."

Quite possibly; it's not unthinkable that the transition from "quantities" to numbers was so gradual, that no single numbers "came first". But at the very least you appear to agree with me that it's incorrect to state as fact that the number 2 came first.

A single scratch per day, and not a pair? So you agree with me that even a single scratch can have meaning?

22. ### Write4UValued Senior Member

Messages:
7,905
I agree that a tree dwelling animal would now its environment intimately and would know paths of escape or to abundant fruit trees. Chimps actually go to war over territories wih abundant food sources.

But forests grow in fractal (one of the most complicated) patterns and that kind pattern was not really even recognized until Manderbrot . To a Lemur there would many trees, but it would know how to use the fewest trees or the shortest way to get to where it needed to go.
But it would not know this by counting 1 ,2, 3. More than likely it would be intuitively measuring the approximate distance between 2 trees, so it would not miss and fall to the ground.

The gist of my argument is the invention of creating cyphers to reprent large quanties with single symbolic
numbers. I am confident that the first attempts to indicated a numerical value was by hand, where a closed fist would indicate 0 and one an outstretched hand would indicate some and two hand would indicate many. We still use these expressions as "a handfull" (an approximation), or "a hand" or a "foot" as approximate measuring tools. Only later did a "handfull" come to mean 5 and "two handfulls" 10 and "a foot" became 12" and "a bushel" (I have no clue what quantity is).

Thus hand signals would probably be one of the first methods of long range communication. Especially when quietness was required for stalking, a practice we still use today in law enforcement and war when silence is a prime requirent but still affords long range communication. So this would be a predatory advantage. Hunting packs of early humans often formed funnel formations to drive a vulnerable individual away from the herd.

But I still believe that other than knowledge of self (1), the personal attributes of symmetry contained in the pattern of pairs is so abundant that the compound number 2 had to become the first natural cyphered symbol of a plurality.
Consider the use of a scratch to indicate 1 period of say, 1 day, how would you count a night? Another scratch would just be another day. Thus 1 scratch indicates a pair, a day and a night. A full cycle.
But if you stick with scratches 1 + 1 +1 +1, you would fill up a log in a hurry and then it would become a meaningless exercise.
I think Confused2 stated it very succinctly. The combining of 1 + 1 with a special cypher meaning 2 was at a more sophisticated level of very early counting.

IMO, that would be the point where a compound numbering system allowed for development of mathematical calculations.

But I admit this just my intuitive perspective and I am not a historian in the origin of numbers. I just know that intuitive counting seems to be a hardwired ability of the brain. An evolutionary advantage.

23. ### Write4UValued Senior Member

Messages:
7,905
Not as a single symbol to indicate a plurality except perhaps for a prisoner making 1 scratch to indicate a day/night cycle (24 hr) because for a prisoner that's all there is when serving his time.

Even then 5 days would be written as 4 vertical and 1 diagonal scratch, i.e a "set ". If the prisoner has to serve a hundred days in jail, he would end up with 20 sets of five.

p.s. I just looked at my hand and I see 4 vertical digits (fingers) and 1 diagonal digit (thumb) = a full hand.

Last edited: Dec 5, 2017