Dimensions

[Write4U]

Yeah it is. Zero is a useful element of a matrix. 0-1 matrices are useful.
Hell, so is the general linear group.

I want to come back to this binary 0-1 matrice in artificial data processing. It seems fundamental but is it a natural function?

Where and how would nature make use of a binary function?

 

[sideshowbob]

I said that to show that the term zero, while it is defined as having no value...

No, zero is NOT defined as having no value. It is defined as having a very specific value, depending on the context. Zero degrees (Celsius or Fahrenheit) IS a value. It is halfway between the value of 1 and the value of -1.

 

[Write4U]

No, zero is NOT defined as having no value. It is defined as having a very specific value, depending on the context. Zero degrees (Celsius or Fahrenheit) IS a value. It is halfway between the value of 1 and the value of -1.

You mean that one definition of zero is: the number between the set of all negative numbers and the set of all positive numbers.

The number itself has no value. It can act as a placemat for a countdown; 3, 2, 1, go!

I cite the main definition that zero is: the arithmetical symbol 0 or 0̸ denoting the absence of all magnitude or quantity.

Adding 0 to a number leaves its same. 0 is called the additive identity and the property is called the additive identity property.

4 + 0 = 4

0 + 3 = 3

Multiplication property of zero

Zero times any number is equal to zero. Which means, multiplying any number by 0 gives 0.

0 × 7 = 0

2 × 0 = 0

Multiplication property of one

Multiplying any number by 1 leaves it unchanged. 1 is called the multiplicative identity hence the property is called multiplicative identity.

1 × 36 = 36

23 × 1 = 23

Exponents of one

The number one raised to any power is always one.

1100 =1

1-34 =1

Exponent one

Any number raised to power one remains unchanged.

31 = 3

-51 = -5

Exponents of zero

The number zero raised to any power is remains zero.

024 = 0

0-9 = 0


Zero as numerator

Zero divided by any non-zero number is zero.

0 ÷ 3 = 0

0 ÷ 6 = 0

Zero as denominator

Any division by zero is not defined

9 ÷ 0 = not defined Because 0 has no definitive value

3 ÷ 0 = not defined Because 0 has no definitive value

0 ÷ 0 = 0

 

[DaveC426913]

Oh look. A giant copy-paste splooge of generic dictionary definitions of buzzwords vomited up by the Write4Ubot. How unexpected.

In fact, it's so unexpected, my template for it - which I made more than three years ago - is still just as relevant

 

[arfa brane]

Does a blank DVD have nothing on it? Is it a string of zeros?

Is blank, with a DVD a useful kind of nothing, in that having nothing on it means you can put something on it, and yet, it's still a DVD?
The symbol for zero, 0, isn't nothing; nothing would be no symbol.

If you say 0 means nothing, that's ok as long as you mean mathematically, and really, strictly in a counting sense. Or maybe that's just me.

 

[DaveC426913]

Does a blank DVD have nothing on it? Is it a string of zeros?

It has a string of flat spans and depressions in it that we humans have - purely as an arbitrary convention - assigned the labels "zero" and "one".

That application of the concept of zero (and one) to a physical state is quite a sophisticated mechanism of abstraction; one that only humans - and only modern humans at that - can conceive.

 

[Write4U]

Does a blank DVD have nothing on it? Is it a string of zeros?

No, it has nothing (zero information) on it. It is a blank disk.

[/quote]Is blank, with a DVD a useful kind of nothing, in that having nothing on it means you can put something on it, and yet, it's still a DVD?
The symbol for zero, 0, isn't nothing; nothing would be no symbol.[/quote] Other than its formatting data, it has no informational data.

If you say 0 means nothing, that's ok as long as you mean mathematically, and really, strictly in a counting sense. Or maybe that's just me.

Yes, it is the mathematical definition. However it used as a placemat for other calculations.
IOW in double entry bookkeeping zero in both debit and credit column indicates the book is in balance.

 

[sideshowbob]

You mean that one definition of zero is: the number between the set of all negative numbers and the set of all positive numbers.

No, I meant what I said. I gave you an example and you quoted it.

The number itself has no value.

Of course it does. It has a value as much as 1 degree or -10 degrees has a value

I cite the main definition that zero is: the arithmetical symbol 0 or 0̸ denoting the absence of all magnitude or quantity.

I'd call that a poor definition. Zero is a specific quantity, not the absence of quantity.
.

 

[sideshowbob]

Does a blank DVD have nothing on it?

In the olden days, when computer data was stored on cassette tapes, a one was an audible tone and a zer0 was a different audible tone. The read head would detect one (completely arbitrary) tone and arbitrarily call it a zero - and it would detect the other (completely arbitrary) tone and arbitrarily call it a one. As far as I know, floppy disks did it the same way. CDs and DVDs use pits that reflect a laser in a different way than the spans between the pits. Bar codes use bars which reflect a laser differently from the spaces between the bars.

Those "physical" zeroes are clearly not "nothing".

 

[DaveC426913]

I cite the main definition that zero is: the arithmetical symbol 0 or 0̸ denoting the absence of all magnitude or quantity.

This is why I wonder if W4U is a bot that doesn't really understand what it's saying.

Citing one meaning is a red herring; it doesn't negate all the other meanings.

In an example that has been pointed out several times, zero Celsius certainly has a magnitude and quantity.

 

[Write4U]

No, I meant what I said. I gave you an example and you quoted it.

And it was correct . I quoted the formal definition of that algorithm.
To wit:

You mean that one definition of zero is: the number between the set of all negative numbers and the set of all positive numbers

Of course it does. It has a value as much as 1 degree or -10 degrees has a value

No, that is stretching it.

The absolute value of a number is the magnitude of that number without considering its sign. Since 0 is zero units away from itself, the absolute value of 0 is just 0. The absolute value of 0 is written as |0| and is equal to 0

I'd call that a poor definition. Zero is a specific quantity, not the absence of quantity.

But zero has no magnitude.

Strictly speaking, order of magnitude of zero is not defined, however it's sometimes said to have a magnitude of −∞. This infinitely negative order of magnitude indicates that zero is smaller than any other positive number, and so is its order of magnitude. May 1, 2020

https://physics.stackexchange.com/questions/548172/order-of-magnitude-of-zero#

But all this is theoretical mathematics for human convenience. In nature zero is the absence of a property or (countable) value. Besides for purposes of this discussion, zero dimension means absence of dimension.

 

[DaveC426913]

But zero has no magnitude.
https://physics.stackexchange.com/questions/548172/order-of-magnitude-of-zero#

False. You have confused two things: magnitude and order of magnitude.

The value 1 has a magnitude of one, but an order of magnitude of zero.
The value 10 has a magnitude of ten, but an order of magnitude of one.
The value 0 has a magnitude of zero, but an order of magnitude that is not defined.

 

[sideshowbob]

And it was correct .

But I didn't mean what you said I meant.

But zero has no magnitude.

Zero does have a magnitude on a temperature scale. It's magnitude is one (arbitrary) degree lower than 1 degree and one (arbitrary) degree higher than -1 degrees.

But all this is theoretical mathematics for human convenience.

All mathematics is for human convenience.

In nature zero is the absence of a property or (countable) value.

There is no zero in nature. Zero is an entirely made-up human construct. You're still confusing zero with nothing.

 

[sideshowbob]

False. You have confused two things: magnitude and order of magnitude.

The value 1 has a magnitude of one, but an order of magnitude of zero.
The value 10 has a magnitude of ten, but an order of magnitude of one.
The value 0 has a magnitude of zero, but an order of magnitude that is not defined.

I was going to mention the same thing myself.

 

[Write4U]

All mathematics is for human convenience

All symbolic mathematics is for human convenience. Generic universal mathematics are an inherent function of spacetime geometry.

Is spacetime real, or is it a mathematical construct?

Short answer: Yes to both.
Spacetime is, from a mathematical viewpoint, a manifold, which is a set of points equipped with a certain structure (being locally flat). Physically, each point corresponds to an event (a place for something to happen, a time when it happens), and local flatness simply means that small enough observers can find a reference frame in which they would locally feel like they are in flat spacetime (this is Einstein’s equivalence principle).

Mathematically, spacetime has a little more structure. It has a metric tensor, which is the fundamental geometric variable in relativity, and physically corresponds to being able to measure distances between nearby “events” and angles between nearby “lines.” These both certainly seem physical.

.....

And this is the sense in which spacetime is just a mathematical tool. We never interact with “spacetime.” What we interact with are the functions whose domains are the abstract manifold we call spacetime when describing them (gravitational fields, electromagnetic fields, etc.), and to make any measurement about spacetime occurs only indirectly through the measurements of these fields. Even something as simple as measuring distance requires a ruler, which can only be read through electromagnetic interaction (light).

https://physics.stackexchange.com/q...a-mathematical-construct-and-not-a-real-thing

 

[exchemist]

All symbolic mathematics is for human convenience. Generic universal mathematics are an inherent function of spacetime geometry.

Is spacetime real, or is it a mathematical construct?
.....
https://physics.stackexchange.com/q...a-mathematical-construct-and-not-a-real-thing

And here we are, finally, back at Write4U's religion, which is where he has been trying to drag this thread for the last several pages.

 

[Write4U]

And here we are, finally, back at Write4U's religion, which is where he has been trying to drag this thread for the last several pages.

Here comes the spoilsport!

This thread has been off topic for the last several pages about the meaning of zero, a mathematical symbol, which is only tangentially related to "dimensions" such as vectors and scalars.
I have drawn attention to that fact, so don't try to hang this on me, please.

In mathematics, the dimension of a vector space V is the cardinality of a basis of V over its base field. It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension. https://en.wikipedia.org/wiki/Dimension_(vector_space)#

Is dimension a vector or scalar?

No. As a physicist, if you have a one dimensional object you have the choice to use a scalar (number) or a one dimensional vector to describe this object, as long as the entire space you are dealing with is one dimensional.
A one dimensional vector in a multidimensional vector-space is very different than a scalar.

https://www.quora.com/Is-a-one-dimensional-vector-a-scalar

Moreover, mathematics is part of science, not religion. As a scientist I am sure you have used mathematics religiously yourself, no? Do you pray to it? I don't.

p.s. '"zero" (0) was introduced by the originator of this thread in post #4

The problem stems from the number 0 and as QM now tells us (nothing doesn't exist)
0 does not exist, we must deny 0 -Frege
imo 0 is infinity not "nothing"

 

[DaveC426913]

And here we are, finally, back at Write4U's religion, which is where he has been trying to drag this thread for the last several pages.

Indeed. He has once again mistaken the map for the territory.

Pulling from an amateur's post on stackexchange, he has interpreted the phrase "Spacetime is, from a mathematical viewpoint, a manifold, which is a set of points" literally.
He thinks is means the map (a manifold) is the same thing as the territory (spacetime).

And, since I'm pretty sure he's got me on Iggy, he's going to continue to look foolish indefinitely.

Reported.

 

[Write4U]

Zero does have a magnitude on a temperature scale. It's magnitude is one (arbitrary) degree lower than 1 degree and one (arbitrary) degree higher than -1 degrees.

Well, seems to me the following analysis seems to disagree with your perspective.

• Question: Can magnitude be negative? Can it be zero?
• Answer: Magnitude cannot be negative. It is the length of the vector which does not have a direction (positive or negative). In the formula, the values inside the summation are squared, which makes them positive.
• The zero vector (vector where all values are 0) has a magnitude of 0, but all other vectors have a positive magnitude.

• Question: Can dot product be negative? Can it be zero?
• Answer: The dot product can be any real value, including negative and zero.
• The dot product is 0 only if the vectors are orthogonal (form a right angle). If the dot product is 0, the cosine similarity will also be 0.

https://cmci.colorado.edu/classes/INFO-2301/files/practice_2-1-19.pdf

 

[sideshowbob]

Generic universal mathematics are an inherent function of spacetime geometry.

That's just your unsupported belief, isn't it?

Is spacetime real, or is it a mathematical construct

Spacetime is real and a sugar cube is real. The mathematics that describes them is a human construct, just like the English words that describe them are a human construct.