# The Naked Scientists Forum

### Author Topic: What is number 1 equal to?  (Read 2167 times)

#### Thebox

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##### What is number 1 equal to?
« on: 22/03/2016 16:04:40 »
What is number 1 equal to?

#### chiralSPO

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##### Re: What is number 1 equal to?
« Reply #1 on: 22/03/2016 16:56:34 »
sigh... ok, I'll bite...

The number 1 has a few different meanings depending on context.

In the simplest sense, it is the first whole number greater than zero.

1 also signifies "unity," which can mean the unit of distance (or length or magnitude or whatever), or can also be the entirety of a distribution of probabilities--a probability of 1 means something is guaranteed to happen, and the summation (or integral) of all possible outcomes in a probability distribution must be equal to 1 (unity).

Given a more physical context, 1 refers to a single something. This is simplest in the case of counting indivisible objects, like electrons. Here, the unit is objects. It can also be applied to other types of units, like 1 kilogram of x, where x can be anything that has mass, and kilogram needs to be defined...

(I warn you, this thread will be transferred to New Theories or That CAN'T be True if we start seeing equations like 1 = 0 or 2 = 00... The serious topics are reserved for discussions using (mostly) conventional language and maths.)

#### jeffreyH

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##### Re: What is number 1 equal to?
« Reply #2 on: 22/03/2016 17:31:17 »
Number 1 is a placeholder for the numeric value of 1. It is the 49th character in the ascii table.

#### evan_au

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##### Re: What is number 1 equal to?
« Reply #3 on: 23/03/2016 09:18:46 »
What is number 1 equal to?
The number 1 is equal to itself. 1=1.
It is also equal to an infinite number of expressions of the form 1 = 3-2 = 4-3 = (n+1)-n

It is also equal to the infinite sum of 1 = 1/2 + 1/4 + 1/8 + ......

What is number 1 useful for?
It can be used to generate the natural numbers: Starting from n=0, repeatedly calculate n=n+1

It is the "multiplicative identity": for any number n, n*1=n

#### Thebox

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##### Re: What is number 1 equal to?
« Reply #4 on: 23/03/2016 09:46:00 »
Thank you for the answers, so number 1 is really multi-dimensional?

e.g    x*y*z= 1 thing

#### chiralSPO

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##### Re: What is number 1 equal to?
« Reply #5 on: 23/03/2016 10:07:36 »
as written, 1 is one-dimensional.

There are ways to generate multi-dimensional versions of 1, but the number 1 is one-dimensional.

#### Thebox

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##### Re: What is number 1 equal to?
« Reply #6 on: 23/03/2016 10:13:53 »
as written, 1 is one-dimensional.

There are ways to generate multi-dimensional versions of 1, but the number 1 is one-dimensional.

Interesting Chiral but we know one can dilate if used in a certain context so one can't be one dimensional can it?

Numerology is a science?

« Last Edit: 23/03/2016 10:20:22 by Thebox »

#### chiralSPO

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##### Re: What is number 1 equal to?
« Reply #7 on: 23/03/2016 10:24:27 »
"Dimension" has a very specific meaning in mathematics.

Perhaps one could say figuratively that 1 is multidimensional because there are multiple "types" of 1. But it would be a mistake to treat this as mathematically valid.

1 is one-dimensional because it is a single number.

(0, 1) is a two-dimensional representation of 1; as are (1, 0), (1/, 1/), and any pair of numbers generated by (cos(θ), sin(θ)) for a given θ...

Two-dimensional representations of 1, can also come in the form of complex numbers (like 1 + 0i) or two dimensional matrices/vectors (like [0 1])...

#### Thebox

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##### Re: What is number 1 equal to?
« Reply #8 on: 23/03/2016 10:27:43 »
"Dimension" has a very specific meaning in mathematics.

Perhaps one could say figuratively that 1 is multidimensional because there are multiple "types" of 1. But it would be a mistake to treat this as mathematically valid.

1 is one-dimensional because it is a single number.

(0, 1) is a two-dimensional representation of 1; as are (1, 0), (1/, 1/), and any pair of numbers generated by (cos(θ), sin(θ)) for a given θ...

Two-dimensional representations of 1, can also come in the form of complex numbers (like 1 + 0i) or two dimensional matrices/vectors (like [0 1])...

Ok, so to get a value of one when related to  anything there has to be two points, [0,1]  , is that what you are saying?

or does there have to be 3 points to create one, where 1 point , z, can be an hidden i, meaning that paper looks flat but it is not.

Added - On what you have explained I drew you this

Is this a representation of one?

And thinking about Jeff's matrices I drew this to represent one

1=observer?

Quote
1 is one-dimensional because it is a single number.

That can't be a valid statement if statement, (to get a value of one when related to  anything there has to be two points, [0,1])  is true.

Only i and 1 exist?

i=i only if one agrees with one

we have to see i to i on this

Before the big bang there was nothing, 0 can be n-dimensional i

after the big bang there was 1

1=n-dimensional   i

Relativity = the agreement of  i ?

1=σi??????????

i=n  if 1=1

added -  If I was a moon being and born on the Moon, I would have to disagree on i when concerning mass and time.

so if I was a moon being and you an earthling , what are we agreeing that 1=1 on ?

added- If I had a slower rate of time, and I was measuring d/t, then I am measuring a different speed than you are.

added - because on the moon , my second i would be much shorter than your second, so I would not measure the speed of light in a vacuum to be the same speed.

« Last Edit: 23/03/2016 12:23:18 by Thebox »

#### evan_au

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##### Re: What is number 1 equal to?
« Reply #9 on: 23/03/2016 20:24:57 »
Quote
1 is one-dimensional because it is a single number.
You can use this to generate all numbers on the number line (1 dimensional), by multiplying it by a factor x: x*1.
The single dimension is given by x, not the 1.

Quote
any pair of numbers generated by (cos(θ), sin(θ)) for a given θ...
This describes a "unit circle", ie a circle of radius 1.

You can use this to generate all numbers on a sheet of graph paper (2 dimensional) by adding a radius r: (x,y) = (r*cos(θ), r*sin(θ)).
The two dimensions are then given by x and y or by r and θ.
This can also be described as the set of points for which x2 + y2 = 1

You can also have a unit sphere, of radius 1, described by the set of points for which x2 + y2 + z2 = 1
The three dimensions are described by x, y and z.

You can extend this to any number of dimensions that you wish - but it soon ceases to have any physical significance, and becomes more of a mathematical abstraction.

Quote from: TheBox
In the end, it is not the number 1 itself which is multidimensional (it is a scalar), but it becomes multidimensional by the application to multiple axes by means of x, y and z, or by its inclusion in the rows and columns of a matrix.

#### Thebox

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##### Re: What is number 1 equal to?
« Reply #10 on: 23/03/2016 20:54:34 »
Thank you Evan for the interesting reply, I am going fishing in the morning for 24 hrs so will not be about so  will leave you with this to consider

Moont ≠  Eartht

Moonc ≠  Earthc

Moond/t ≠  Earthd/t

If two observers disagree on time, they have to disagree about speed or/and 1?

« Last Edit: 23/03/2016 21:10:18 by Thebox »

#### Thebox

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##### Re: What is number 1 equal to?
« Reply #11 on: 25/03/2016 11:43:43 »
So in numerology , is it safe to say that number one is a natural variant?

#### PmbNEP

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##### Re: What is number 1 equal to?
« Reply #12 on: 25/03/2016 13:05:05 »
Quote from: Thebox
What is number 1 equal to?
I've got to say that this question really wasn't necessary. The answer is obvious as I'm sure you know. You could have simply looked it up in Wikipedia. I can't post links yet so you'll have to find it yourself. Simple Google it. I starts off by saying the following
Quote
1 (one; /ˈwʌn/ or UK /ˈwɒn/, also called unit, unity, and (multiplicative) identity), is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1.

#### Thebox

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##### Re: What is number 1 equal to?
« Reply #13 on: 25/03/2016 14:58:34 »
Quote from: Thebox
What is number 1 equal to?
I've got to say that this question really wasn't necessary. The answer is obvious as I'm sure you know. You could have simply looked it up in Wikipedia. I can't post links yet so you'll have to find it yourself. Simple Google it. I starts off by saying the following
Quote
1 (one; /ˈwʌn/ or UK /ˈwɒn/, also called unit, unity, and (multiplicative) identity), is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1.

Nice to see you comment Pete, your words and answers are welcome.   I am looking for an invariant agreement of 1, a constant that any observer anywhere in the universe could agree on.

I have considered the speed of light , but time dilation prevents this being an equal agreement.

The only thing I can consider is a length of space?

1mm=1mm and invariant.

I thought 0 represent a single entity?   1 represents xyzt

And added (probably not for Petes attention)

[0i,1] + [1,0i] =?

« Last Edit: 25/03/2016 15:06:36 by Thebox »

#### evan_au

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##### Re: What is number 1 equal to?
« Reply #14 on: 26/03/2016 09:58:52 »
Quote from: TheBox
I am looking for an invariant agreement of 1, a constant that any observer anywhere in the universe could agree on.

Physicists also wonder whether anything is really constant across the universe. Without evidence, all you can do is guess that things are basically similar to what we measure in the Solar system.

If there are other universes, we can't even assume that they are like our universe.

There have been suggestions that the fine structure constant may differ slightly across the universe, which would lead to differences in chemical compounds and stable nuclei.

Quote
The only thing I can consider is a length of space?
You can rule out anything that relativity and the Lorentz factor affect:
• Time
• Frequency (which depends on time)
• Length
• Wavelength (which depends on length)
• Speed/Velocity (which depends on both time and length)
• Mass
• Electric & Magnetic fields

While those "single" items vary depending on the observer's frame of reference, it is possible to combine several measurements which allow you to estimate the frame of reference of the source, and hence to deduce the measurement that would be made by someone in that frame of reference.

For example, while you can't deduce the original frequency or wavelength of a single frequency, it is possible to take a series of wavelength observations (eg the spectrum of Hydrogen), analyze the set of frequencies, and make deductions about the relative velocity, or the gravitational field at the source.

By comparing a group of numbers, several fundamental constants have been measured in distant parts of the universe.

Perhaps the invariant you are looking for is the use of 1 in counting discrete objects? Two people in different frames of reference can agree that there is 1 star, 2 stars or 3 stars in a particular stellar system.

#### Thebox

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##### Re: What is number 1 equal to?
« Reply #15 on: 26/03/2016 10:20:58 »
Quote from: TheBox
I am looking for an invariant agreement of 1, a constant that any observer anywhere in the universe could agree on.

Physicists also wonder whether anything is really constant across the universe. Without evidence, all you can do is guess that things are basically similar to what we measure in the Solar system.

If there are other universes, we can't even assume that they are like our universe.

There have been suggestions that the fine structure constant may differ slightly across the universe, which would lead to differences in chemical compounds and stable nuclei.

Quote
The only thing I can consider is a length of space?
You can rule out anything that relativity and the Lorentz factor affect:
• Time
• Frequency (which depends on time)
• Length
• Wavelength (which depends on length)
• Speed/Velocity (which depends on both time and length)
• Mass
• Electric & Magnetic fields

While those "single" items vary depending on the observer's frame of reference, it is possible to combine several measurements which allow you to estimate the frame of reference of the source, and hence to deduce the measurement that would be made by someone in that frame of reference.

For example, while you can't deduce the original frequency or wavelength of a single frequency, it is possible to take a series of wavelength observations (eg the spectrum of Hydrogen), analyze the set of frequencies, and make deductions about the relative velocity, or the gravitational field at the source.

By comparing a group of numbers, several fundamental constants have been measured in distant parts of the universe.

Perhaps the invariant you are looking for is the use of 1 in counting discrete objects? Two people in different frames of reference can agree that there is 1 star, 2 stars or 3 stars in a particular stellar system.

In your list you say I can rule out length, by length are you talking the length of a physical object, the length of light, or do you mean a length of space between two point sources?

Space itself is ''nothing'' and things occupy space, are you saying that nothing is not an invariant in length?

Is not 1*0=1 nothing?

Quote
Perhaps the invariant you are looking for is the use of 1 in counting discrete objects? Two people in different frames of reference can agree that there is 1 star, 2 stars or 3 stars in a particular stellar system.

You missed out one universe, one space, a whole of light propagating through space, but no I am after a measurement quantity such as MM.

« Last Edit: 26/03/2016 10:23:43 by Thebox »

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##### Re: What is number 1 equal to?
« Reply #15 on: 26/03/2016 10:20:58 »