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Capiert
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19 hours ago, exchemist said:

Yes, in a way I suppose they are, though  I had never thought about it like that.  

How (then) did you think about it (=their connection, relation to each other) 
(if NOT (as) multiplication of number & unit)?

Edited by Capiert
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16 minutes ago, Capiert said:

How

How (then) did you think about it (=their connection, relation to each other) 
(if NOT (as) multiplication of number & unit)?

As an addendum, in the form of a piece of explanatory text, rather than as part of the algebraic expression. This I think is how most people see them.

But logically you must be right, I think. 

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2 minutes ago, exchemist said:

But logically you must be right, I think. 

Yes of course he's right.

The best way to think about it to to understand the word 'units'.

A unit is 1 whole of anything.

Even easier to think in terms of something that only comes in whole numbers for example eggs.

So the unit is a single egg or 1egg.

5 eggs

The 5 and the eggs are separate.

So we have 5 x 1_egg.

21 hours ago, Capiert said:

Are number(_value)s multiplied by the unit?

(Surely NOT added.)

1 * meter=1 [m].

Similarly 5 metres is really 5 x 1_metre

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Shall we see how many posts we can generate on this fascinating topic? 😃

17 minutes ago, studiot said:

Yes of course he's right.

The best way to think about it to to understand the word 'units'.

A unit is 1 whole of anything.

Even easier to think in terms of something that only comes in whole numbers for example eggs.

So the unit is a single egg or 1egg.

5 eggs

The 5 and the eggs are separate.

So we have 5 x 1_egg.

Similarly 5 metres is really 5 x 1_metre

Exactly. But it's just not how I have generally thought about it, given that we tend to use algebraic expressions without units until we have a specific application for them.   

Edited by exchemist
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8 minutes ago, MigL said:

So ...
As a count, you might have 5 eggs.
But as an algebraic expression, you have 5*egg ( where egg is the unit ).

I guess it's important to know what you are talking about.

Unless, like me, you have 3 feet.

You need the 1 to go with the egg since there are 3 feet in a yard.

Or is it 2.4 pints ?

Trust the Scots

 

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12 minutes ago, studiot said:

Unless, like me, you have 3 feet.

3?!
I've only got 2 [feet]
& no (way, back)[yard].
 (in the back :-).
:-)

12 minutes ago, studiot said:

You need the 1 to go with the egg since there are 3 feet in a yard.

Or is it 2.4 pints ?

Trust the Scots

(Again, & again. :-)

So I guess
 there is a (small?) language problem (obstacle, of incompatibility)
 with the grammar('s singular versus plural "s", etc);
 versus
 the math('s algebra);
 &
 I suppose, the units'
 acronyms(' short_forms)
 help us (out) there, (at least) a bit,
 by ignoring the plural(s).

E.g.
5 * meters = 5 [m].

Or unit
meter(s)=[m].

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In adding (or subtracting) a physical quantity to another physical quantity, the scalars are added together and the units must match.

e.g. 1 m + 10 m = 11 m

If they do not match, even if they both represent e.g. length, they cannot be added or subtracted.

e.g. 1m + 1 inch

Inches must be first converted to meters, or meters must be converted to inches, so the two units match to add them together.

 

In multiplying (or dividing) physical quantities, the units need not match. A scalar is multiplied by a scalar, a unit is multiplied by a unit.

e.g. 3m * 10m = 30m^2

e.g. 10 m / 5 s = ( 10/5 ) [m/s] = 2 m/s

e.g. 10 N * 5 m = 50 J

 

Dividing a physical quantity by physical quantity with the same units yields a dimensionless/unitless scalar.

e.g. 100 s / 50 s = 2

100 m/s * 10s = 1000 m

(Unit cancellation)

 

Edited by Sensei
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23 hours ago, Capiert said:

(Surely NOT added.)

Did anyone suggest that they might be?

 

 

2 hours ago, studiot said:

A unit is 1 whole of anything.

It's "one whole anything" or "one of anything" but it's not "one whole of anything".

One whole what?

I guess it's "one whole instance of anything".

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25 minutes ago, Sensei said:

In adding (or subtracting) a physical quantity to another physical quantity, the scalars are added together and the units must match.

e.g. 1 m + 10 m = 11 m

If they do not match, even if they both represent e.g. length, they cannot be added or subtracted.

e.g. 1m + 1 inch

Inches must be first converted to meters, or meters must be converted to inches, so the two units match to add them together.

Have you never come a cross aman whose height is 6' 3"  ?

Edited by studiot
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31 minutes ago, studiot said:

So what is 100 + 1 ?

It's the same placeholder idea, as is £, s, p

Yes, I know but £ S and d are different units for the same thing.

I can add a kilo of potatoes to a pound of minced beef adn an ounce of flour.
But I don't get 3 anythings of stew.

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5 hours ago, John Cuthber said:
On 12/5/2021 at 8:07 PM, Capiert said:

(Surely NOT added.)

Did anyone suggest that they might be?

Yes, John.

Added (verb)
 & addendum (noun)
 are (probably) NOT exactly the same;
 but it (=the added_onto method)
 suggests (to me),
 (that its meaning
 is) going
 in that (similar) direction.

E.g.
A hang_on, (that can be) added
 on(to almost anything).

7 hours ago, exchemist said:

As an addendum, in the form of a piece of explanatory text, rather than as part of the algebraic expression. This I think is how most people see them.

But logically you must be right, I think. 

 

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6 hours ago, studiot said:

Have you never come across a man whose height is 6' 3"  ?

Pronounced: "six foot, 3 (inches)".

(Also, please notice the singular (1st) unit (foot, NOT feet)
 although the number (6), is >1;
 until we (might) get stuck in details
 by stating the 2nd (number's) unit(s (as more than 1, e.g. 3)).)

That looks like 2 answers, stuck (=connected) together.
E.g.
6'+3".
Where the (empty) space
(between them (both))
 represents a virtual "plus", + (symbol).

But why is there NO (empty) space
 between the (number) 6 & (unit) '=[feet] or [foot] (symbol);
 &
 between the (number) 3 & (unit) "=[inch] (symbol).

The SI convention
 seems to use the empty space
 between number & units (Notice the s (on units) for both: singular; or plural or more)
 as a virtual multiply=multiplication.

E.g.
6 [m]+3 [m]=9 [m], represents
6*[m]+3*[m]=9*[m].

There is also a subtle difference
 between infinitive, e.g. stone (in a quarry, to build a castle)
 versus more_than_1 e.g. plural or more=many, e.g. (made of) stones.

E.g.
Should we say,
 the building
 is 5 [meter] high? (infinitive).
E.g. NOT 5 [meters]. (Plural or more).

We often say 20°C (twenty degrees Centigrade, please notice: NO (empty) space at the °).
But 300 K (three_hundred Kelvin (infinitive); NOT Kelvins (many).)

Btw
When I look at this (= all that (grammar) needed for the math)
 I am considering artificial_intelligence (e.g. program(ming)) too. (=NOT two, nor plur(e)al (~for crying out load, at reality).)
 & (I am) considering
 what sort of math (algebra)
 would be needed
 to incorporate
 such mixed units (singular or more).

Algebra is perfect equality (e.g. balance);
 but NOT so with grammar
 that is brought in
 to distinguish
 finer differences.

Our brains recognize those discontinuities (=differences).

Edited by Capiert
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7 hours ago, John Cuthber said:

I can add a kilo of potatoes to a pound of minced beef and an ounce of flour.
But I don't get 3 anythings of stew.

But (if you want) you could create a(ny) new "thing" unit,
 (depending on how you wanted it
 to be(come)).

I suppose
 if you divided your stew
 into 3 equal portions,
 then it would be 3*[portions]
 (of that stew).
I.e. That'( i)s wrt (only) that stew itself
 (with only 3 ingredients
 & their own proportions,
 on the spot,
 so to speak)
 NOT anything else.
E.g.
NOT necessarily
 3*[bowls or cups etc].

The new unit [(equally_divided)_portion]
 can be found
 by converting
 all 3 units
 to any same desired_unit
 & then dividing by 3.

That would be your (new) "anything" (unit).
E.g. Some other (irrational?) factored unit
 of your (common) desired_unit.

It'( i)s only a conversion (method).

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9 hours ago, Capiert said:

Yes, John.

Added (verb)
 & addendum (noun)
 are (probably) NOT exactly the same;
 but it (=the added_onto method)
 suggests (to me),
 (that its meaning
 is) going
 in that (similar) direction.

E.g.
A hang_on, (that can be) added
 on(to almost anything).

 

My use of the term "addendum", in the 4th post of this thread, was qualified to make clear it was not intended to signify something added algebraically. 

Let's not descend to word games.  

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9 hours ago, Capiert said:

But (if you want) you could create a(ny) new "thing" unit,
 (depending on how you wanted it
 to be(come)).

Mthematically that is more or less true.

I would be grateful if folks would allow me to know just a little bit of basic Mathematics.
It is, after all, my subject.

Whatever is proposed has to be in accordance with the mathematical rules of 'addition' and 'multiplication'. Both are 'binary operations' that follow specific rules of set and group theory. There is nothing that requires either of the operands to be numbers, or that restricts either from being a number.

In Mathematics the unit of the quantity is regarded as a multiplier for the number. Equally we could regard the number as a multiplier for the unit as Capiert has proposed.

Regarding either as an operand in an 'addition' between the two does not make sense.

However regarding their multiplicative combination as an operand in an addition with another similar (but not necessarily identical)  multiplicative combination can make sense in appropriate circumstance.
It does not always make sense.

 

I quickly dashed off a couple of examples yesterday to try to help.

I am sorry they were so derided as they are correct within the rules of arithmetic I have just described.
 

I can now improve on those examples.

Firstly the decimal system itself.

Consider the 'number' :-  1234.

Children used to be taught that this comprised

1 off of thousands + 2 off of hundreds + 3 off of tens + 4 off of units

or

1x(1000) + 2x(100) + 3x(10) + 4x(1)

Which is arithmetically correct and conforms to Capiert's original proposition.

1234 could be written in a different way using the Roman (Latin) scheme with different bases.



 

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  • 2 weeks later...
On 12/5/2021 at 2:07 PM, Capiert said:

Are number(_value)s multiplied by the unit?

(Surely NOT added.)

1 * meter=1 [m].

A unit is an intellectual construct. Take two squares. Each side is measured to the nearest meter, and found to be exactly one meter. Measure the same squares to the nearest nanometer. What are the odds that each square will remain a perfect square with dimensions of exactly 1.0000000 meters on all sides? Extrapolate to infinity. What are the odds that the side of any square is 1 meter when measured at a level of infinite precision? It is impossible. There is no such thing as a meter, there is no such thing as symmetry, and there is no such thing as a square. There is only one truth: the Universe is infinite. A meter does not define the distance between two points. It contextualizes the observational parameters of infinity in the context of a mathematical social construct.

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3 hours ago, Ragingmoron said:

Take two squares. Each side is measured to the nearest meter, and found to be exactly one meter.

If your resolution was one meter, you could not have a result that’s exactly one meter.

That’s an issue of significant digits and precision, though, not units.

Quote

There is no such thing as a meter

There used to be. Made of platinum and iridium. It was, by definition, one meter.

One problem is that copies are not perfect.

 

Quote

There is no such thing as a meter, there is no such thing as symmetry, and there is no such thing as a square. There is only one truth: the Universe is infinite. A meter does not define the distance between two points. It contextualizes the observational parameters of infinity in the context of a mathematical social construct

 

!

Moderator Note

This is off-topic and would need to be argued (and supported) in its own thread.

 
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38 minutes ago, swansont said:

If your resolution was one meter, you could not have a result that’s exactly one meter.

That’s an issue of significant digits and precision, though, not units.

There used to be. Made of platinum and iridium. It was, by definition, one meter.

One problem is that copies are not perfect.

 

 

!

Moderator Note

This is off-topic and would need to be argued (and supported) in its own thread.

 

In terms of resolution, my point could have been better served by describing squares drawn using a meter stick so that each side is approximately 1 meter.

My point was that all units lack precision by their nature, therefore a number value multiplied by a unit doesn't reveal anything true. I don't want to say it's meaningless because it has relative meaning, even though a meter is ultimately a figment of the imagination. Meaning is ascribed, but nature is absolute. No relative unit can ever tell you anything true about reality, it can only set you on the right track. Measuring the distance between the stars, nanometers are less useful than lightyears, but neither unit can (or any conceivable unit for that matter) yield a truly accurate result, because standardization in reality is impossible. To measure the distance between two stars accurately, you would have to measure to the infinith decimal place, because all information exists relative to the Singularity. I thought this was relevant to this thread but I can see how you would consider it off-topic. So I'll respect what you said and post nothing else here, perhaps I'll start another thread on the topic. Thanks for your feedback.

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