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Old 24-02-2018, 17:56   #61
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Re: Northwest Passage - 2018

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Originally Posted by Reefmagnet View Post
Too be pedantic; 5/9 has an infinitely recurring decimal value of 5, therefore it's not possible to perform an "exact" conversion. Just as it is not possible to get an exact value of PI.
There is a vast difference between an irrational number such as PI and a rational number which happens to be represented as a recurring number when expressed as a decimal. A fraction such as 5/9 is a rational number by definition.

Are you saying that a temperature change of 50C is NOT the same as a change of 90F ? Why would "50 / 5 x 9 = 90" not be an exact convertion.

It may not be possible to perform an "exact conversion" for a single degree when going from Fahrenheit to Celsius if you want to express the result in decimal notation. But the same is true of many things. That doesn't mean the conversion is not exact. There are many fractions which can't be represents as decimal expressions.

(1/3" is 1/3", even if it can't be represented exactly as a decimal. And 3 x 1/3 is exactly 1. 5/9F is no different in concept to 1/3" )

It is is trivial to CONVERT EXACTLY 1 from Fahrenheit to Celsius and express the result as a decimal: 1F = 1.8C
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Old 24-02-2018, 18:37   #62
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Re: Northwest Passage - 2018

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Originally Posted by jimbunyard View Post
An interesting study describing some of the real reasons for the declining icecaps worldwide:

World ocean heat content and thermosteric sea level change (0–2000*m), 1955–2010 - Levitus - 2012 - Geophysical Research Letters - Wiley Online Library

Some exerpts:

[18] Using model simulations based on AOGCM simulations, Dommenget [2009] concluded that continental warming due to anthropogenic forcing (e.g., the warming at the end of the last century or future climate change scenarios) is mostly (80%90%) [is] indirectly forced by the contemporaneous ocean warming, not directly by local radiative forcing. Thus even if greenhouse gas emissions were halted today than regardless of the residence time of the carbon dioxide in today's atmosphere, the ocean would continue to heat the atmosphere (my emphasis) [Wetherald et al., 2001] .

[21] We have estimated an increase of 24 1022 J representing a volume mean warming of 0.09C of the 02000 m layer of the World Ocean. If this heat were instantly transferred to the lower 10 km of the global atmosphere it would result in a volume mean warming of this atmospheric layer by approximately 36C (65F). This transfer of course will not happen; earth's climate system simply does not work like this. But this computation does provide a perspective on the amount of heating that the earth system has undergone since 1955.


In other words, for point [21], without the oceans, the average global temp would be 121F rather that 56F...


Conclusions shouldn't be jumped to as a result of the above exerpts; the study should be read in its entirety to (possibly) begin to grasp the complexity of the subject...
ok the biggest issue I see is that they adjusted the Argo temperature datum to fit their computer models. Not the other way around.
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Old 24-02-2018, 18:44   #63
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Re: Northwest Passage - 2018

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Originally Posted by StuM View Post
It is is trivial to CONVERT EXACTLY 1 from Fahrenheit to Celsius and express the result as a decimal: 1F = 1.8C
Doh! That should obviously be the other way round:

It is is trivial to CONVERT EXACTLY 1 from Celsius to Fahrenheit and express the result as a decimal: 1C = 1.8F

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Old 24-02-2018, 18:52   #64
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Re: Northwest Passage - 2018

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Originally Posted by StuM View Post
Doh! That should obviously be the other way round:

It is is trivial to CONVERT EXACTLY 1 from Celsius to Fahrenheit and express the result as a decimal: 1C = 1.8F

was waiting to see how long it took you
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Old 24-02-2018, 19:14   #65
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Re: Northwest Passage - 2018

Learn something new everyday--the icebreaker operating astern with azipods. One of the things I like about this forum.
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Old 24-02-2018, 22:27   #66
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Re: Northwest Passage - 2018

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Originally Posted by StuM View Post
There is a vast difference between an irrational number such as PI and a rational number which happens to be represented as a recurring number when expressed as a decimal. A fraction such as 5/9 is a rational number by definition.

Are you saying that a temperature change of 50C is NOT the same as a change of 90F ? Why would "50 / 5 x 9 = 90" not be an exact convertion.

It may not be possible to perform an "exact conversion" for a single degree when going from Fahrenheit to Celsius if you want to express the result in decimal notation. But the same is true of many things. That doesn't mean the conversion is not exact. There are many fractions which can't be represents as decimal expressions.

(1/3" is 1/3", even if it can't be represented exactly as a decimal. And 3 x 1/3 is exactly 1. 5/9F is no different in concept to 1/3" )

It is is trivial to CONVERT EXACTLY 1 from Fahrenheit to Celsius and express the result as a decimal: 1F = 1.8C
Ok, so you concede that the conversion is, on further examination, conditionally exact. I can live with that even if it is an oxymoron of sorts. Be that as it may, the inverse of 1.8 is, and always will be, an irrational number.
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Old 24-02-2018, 23:21   #67
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Re: Northwest Passage - 2018

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Originally Posted by Reefmagnet View Post
Ok, so you concede that the conversion is, on further examination, conditionally exact. I can live with that even if it is an oxymoron of sorts. Be that as it may, the inverse of 1.8 is, and always will be, an irrational number.
No I do not so conceed. It is always exact if you divide by 5 and multiply by 9 (or vice versa). It only becomes "conditional" if you try to represent the result in decimal notation. (to however many decimal places you chose) instead of doing it the correct way. 1C is EXACTLY 5/9F

You make the mistake of confusing a number with a specific representation of it. That's like saying that because there is no Tok Pisin word for transistor then transistors don't exist.

It should be noted that a simple number like 1/5 (exactly 0.2 in Base 10/ Decimal notation) is a recurring number in Binary /Base 2 notation. By your logic, 1/5 is an irrational number because expressed in binary it is 0.001100110011 with the "0011" repeating infinitely.

The inverse of a rational number cannot, by definition, be irrational. The inverse of 9/5 (which can be expressed precisely in decimal notation as 1.8) is 5/9, which can be expressed to any desired level of precision as a Decimal expansion.

You may like to learn the difference between an irrational number and a rational number.
Irrational Number -- from Wolfram MathWorld

An irrational number is a number that cannot be expressed as a fraction for any integers and . Irrational numbers have decimal expansions that neither terminate nor become periodic.

(0.555... is periodic!)
Rational Number -- from Wolfram MathWorld
"A rational number is a number that can be expressed as a fraction where and are integers and . "

Clearly 5/9 is a rational number.


Just for fun. Let's do it in Base 3 representation.

Decimal(Base 10) 5 = 12 in Base 3 (1 x 3 + 2 x 1)
Decimal(Base 10) 9 = 100 in Base 3 (1 x 3 x 3)

So 5/9 in Base 10 = 12/100 in Base 3

12/100 in Base 3 is exactly 0.12 - not a recurring number,

Try it yourself in any number base you want here:
https://planetcalc.com/2095/
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Old 25-02-2018, 00:04   #68
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Re: Northwest Passage - 2018

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Originally Posted by StuM View Post
No I do not so conceed. It is always exact if you divide by 5 and multiply by 9 (or vice versa). It only becomes "conditional" if you try to represent the result in decimal notation. (to however many decimal places you chose) instead of doing it the correct way. 1C is EXACTLY 5/9F

You make the mistake of confusing a number with a specific representation of it. That's like saying that because there is no Tok Pisin word for transistor then transistors don't exist.

It should be noted that a simple number like 1/5 (exactly 0.2 in Base 10/ Decimal notation) is a recurring number in Binary /Base 2 notation. By your logic, 1/5 is an irrational number because expressed in binary it is 0.001100110011 with the "0011" repeating infinitely.

The inverse of a rational number cannot, by definition, be irrational. The inverse of 9/5 (which can be expressed precisely in decimal notation as 1.8) is 5/9, which can be expressed to any desired level of precision as a Decimal expansion.

You may like to learn the difference between an irrational number and a rational number.
Irrational Number -- from Wolfram MathWorld

An irrational number is a number that cannot be expressed as a fraction for any integers and . Irrational numbers have decimal expansions that neither terminate nor become periodic.

(0.555... is periodic!)
Rational Number -- from Wolfram MathWorld
"A rational number is a number that can be expressed as a fraction where and are integers and . "

Clearly 5/9 is a rational number.


Just for fun. Let's do it in Base 3 representation.

Decimal(Base 10) 5 = 12 in Base 3 (1 x 3 + 2 x 1)
Decimal(Base 10) 9 = 100 in Base 3 (1 x 3 x 3)

So 5/9 in Base 10 = 12/100 in Base 3

12/100 in Base 3 is exactly 0.12 - not a recurring number,

Try it yourself in any number base you want here:
https://planetcalc.com/2095/
What's 0.56 x 9? Adding more decimal places simply reduces the error, it never removes it so the result can never be exact. Yes, you can use different number bases, but computers and other calculation devices will always use BCD for floating point calculations which have limits somewhat less than infinity. Hence you can never do an exact conversion.

P.s, I did mention the word "pedantic" somewhere, didn't I?
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Old 25-02-2018, 01:47   #69
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Re: Northwest Passage - 2018

Quote:
Originally Posted by Reefmagnet View Post
What's 0.56 x 9?
5.04 Your point is?


Quote:
Adding more decimal places simply reduces the error, it never removes it so the result can never be exact. Yes, you can use different number bases, but computers and other calculation devices will always use BCD for floating point calculations
Huh? Totally wrong again! You may like to look up IEEE-754 Standard For Floating Point Numbers.

Quote:
which have limits somewhat less than infinity. Hence you can never do an exact conversion.
Rubbish. You can do an exact conversion every time unless it involves an intermediate recurring binary value.

9F = 5C is an exact conversion beteen the two temperature units.

Quote:
P.s, I did mention the word "pedantic" somewhere, didn't I?
There's nothing pedantic about correcting a total misunderstanding of fundamental mathematical principles such as the meaning of rational and irrational numbers, to say nothing of a lack of knowledge of the way computers store and manipulate non-integers.

The only pedantry I see here is an insistence that there is some real world benefit in expressing a temperature to an accuracy of 0.000000000000000001
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Old 25-02-2018, 02:19   #70
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Re: Northwest Passage - 2018

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Originally Posted by Reefmagnet View Post
I'm guessing Skeptical science's "Hiroshima bomb-ometer" must really rock your socks.
Other than it's 'awkwardness' I have no problem with it...mental crutches have a valuable place in illustrating difficult concepts.

Here's one I just made up, describing the difference between relative distances; it would take 10.6 years for an average human to walk to the moon. How long to the sun? 3500.7 years. The nearest star? 961,215,120 (using a light year as 5,874 billion or so miles)...
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Old 25-02-2018, 03:50   #71
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Re: Northwest Passage - 2018

Great guys. How about some real practical information, such as, is it too early to invest in companies that intend to take advantage of these shorter transportation routes?
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Old 25-02-2018, 04:11   #72
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Re: Northwest Passage - 2018

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Originally Posted by StuM View Post
5.04 Your point is?


Huh? Totally wrong again! You may like to look up IEEE-754 Standard For Floating Point Numbers.
You are correct on this point. Last bit of machine code I wrote was sometime in the early 90's so I guess I'm out of touch here. Though as a DB developer, BCD remains the goto for accuracy.

Quote:
Rubbish. You can do an exact conversion every time unless it involves an intermediate recurring binary value.

9F = 5C is an exact conversion beteen the two temperature units.
Nope. Imagine a system with precision of two decimal places.

5/9 = 0.56

Converting 5.00 C to F = 8.93F

Converting 9.00F = 5.04C
Quote:

There's nothing pedantic about correcting a total misunderstanding of fundamental mathematical principles such as the meaning of rational and irrational numbers, to say nothing of a lack of knowledge of the way computers store and manipulate non-integers.

The only pedantry I see here is an insistence that there is some real world benefit in expressing a temperature to an accuracy of 0.000000000000000001
Maybe when discussing how much the temperature of the ocean has increased globally in a day or whatever???

We are arguing your declaration that temp conversions are exact. Not mathematical principles. The word "exact" has a very specific meaning. In your last paragraph you are essentially admitting that, despite your considerable efforts to prove otherwise, they in fact aren't exact.
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Old 25-02-2018, 04:14   #73
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Re: Northwest Passage - 2018

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Originally Posted by jimbunyard View Post
Other than it's 'awkwardness' I have no problem with it...mental crutches have a valuable place in illustrating difficult concepts.

Here's one I just made up, describing the difference between relative distances; it would take 10.6 years for an average human to walk to the moon. How long to the sun? 3500.7 years. The nearest star? 961,215,120 (using a light year as 5,874 billion or so miles)...
The fact you forget to factor in the differential speed and directions of the celestial bodies you wish to walk from and to, makes your example as nonsensical as the subject of the post that's resulted in all this off topic diatribe.
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Old 25-02-2018, 06:09   #74
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Re: Northwest Passage - 2018

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Originally Posted by Reefmagnet View Post
We are arguing your declaration that temp conversions are exact. Not mathematical principles. The word "exact" has a very specific meaning. In your last paragraph you are essentially admitting that, despite your considerable efforts to prove otherwise, they in fact aren't exact.
OK, one last attempt and then I give up.

The exact conversion factor is:
One degree Fahrenheit is exactly 5/9ths of a degree Celsuis.

Consequently it is a fact that 9F is exactly 5C (and that 5C is exactly 9F) and that 0.18F is exactly 0.1C.

The fact that some rational numbers when multiplied by 5/9ths using decimal notation result in a recurring fractional part is neither here nor there. Just because some rational numbers can't be exactly specified in units of 10 doesn't mean that they are not exact values. (As I clearly demonstrated using Base 3).
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Old 25-02-2018, 06:17   #75
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Re: Northwest Passage - 2018

Meanwhile the arctic sea ice is getting thicker by the day.
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