Fundies Math

[Charlie99]

Sparticle wins!

Only if he can answer the question of how to tell whether the number 6,000 has 1,2, or 3 significant figures.

A slightly related observation ---- how many significant figures in the standard body temp of 98.6F.

Hint -- convert to Celsius first.

Spoiler

A nice round 37 C. A careful reading of news articles will reveal other unit conversions, such as where a crude ballpark number of 100kg becomes a more precise sounding 220pounds.

 

[ekewaka]

Only if he can answer the question of how to tell whether the number 6,000 has 1,2, or 3 significant figures.

A slightly related observation ---- how many significant figures in the standard body temp of 98.6F.

Hint -- convert to Celsius first.

Spoiler

A nice round 37 C. A careful reading of news articles will reveal other unit conversions, such as where a crude ballpark number of 100kg becomes a more precise sounding 220pounds.

6,000 has 1 significant figure. If you want to write with 2 or three significant figures, then you have to use scientific notation: 6.0 * 10^3 or 6.00 * 10^3.
98.6 has 3 significant figures. Convert to Celsius, and you get 37.0, still with three significant figures.

 

[Charlie99]

98.6 has 3 significant figures. Convert to Celsius, and you get 37.0, still with three significant figures.

With the wide range of "normal" temperature, the more reasonable (and more historically accurate) explanation is that it was rounded off to 37C, and the apparent precision of 98.6F is just an artifact of the units conversion.

In the United States, 98.6 degrees Fahrenheit is widely believed to be the healthy core body temperature for an adult human.

This belief is based upon one German study by Carl Reinhold August Wunderlich which found the mean body temperature of the study subjects, when rounded to two significant digits, to be 37 degrees Celsius. This is 98.6 degrees on the Fahrenheit scale.<emphasis added>

Actual average oral temp is closer to 98.2F / 36.8C. See Wikipedia "Thermoregulation".

My "duh" moment on this was about 15 years ago while living in Japan. I went out and got a little digital thermometer, reading in Celsius of course, to check the fever on my daughter and converted 98.6F to C. Only then did I realize that 98.6F is a nice round 37C.

 

[lamont]

6,000 has 1 significant figure. If you want to write with 2 or three significant figures, then you have to use scientific notation: 6.0 * 10^3 or 6.00 * 10^3.
98.6 has 3 significant figures. Convert to Celsius, and you get 37.0, still with three significant figures.

Is there a nomenclature where you write out 6,000 with a bar over the 6 and first 0 in order to indicate 2 significant digits? For some reason I think I ran into that before...

 

[amascuba]

Whata' bunch of nerds this thread has attracted.:1book:

 

[Charlie99]

What do you expect, the thread title has MATH in it.

If you think that's bad, how about this quote lifted from the trip report TS&M posted today on cavern diving in Yucatan

On this dive, I had a feeling I recognized from years ago, when I did a lot of higher mathematics. I felt as though I'd been transported out of myself, literally exalted and utterly joyful, aware of my skin all the way to my fingertips and totally in the moment.

See what math can do to someone.

 

[Gilldiver]

With the wide range of "normal" temperature, the more reasonable (and more historically accurate) explanation is that it was rounded off to 37C, and the apparent precision of 98.6F is just an artifact of the units conversion.

Actual average oral temp is closer to 98.2F / 36.8C. See Wikipedia "Thermoregulation".

My "duh" moment on this was about 15 years ago while living in Japan. I went out and got a little digital thermometer, reading in Celsius of course, to check the fever on my daughter and converted 98.6F to C. Only then did I realize that 98.6F is a nice round 37C.

How it really started:

History
The Fahrenheit temperature scale became popular through its use on the first reliable, commercially-available, mercury-in-glass thermometers. Daniel Gabriel Fahrenheit manufactured such thermometers in Amsterdam from about 1717 until his death in 1736. The scale we know as the Fahrenheit scale was the last of three scales he used.

As the zero point on his scale Fahrenheit chose the temperature of a bath of ice melting in a solution of common salt, a standard 18th century way of getting a low temperature in the laboratory (and in the kitchen, as in an old-fashioned ice cream churn). He set 32 degrees as the temperature of ice melting in water. For a consistent, reproducible high point he chose the temperature of the blood of a healthy person (his wife), which he measured in the armpit and called 96 degrees. (The number arises from beginning with a scale of 12 intervals, like a one-foot ruler, and then doubling the number of steps as instruments become more precise, making 24 intervals, then 48, and finally 96.)1

Fahrenheit’s successors used the boiling point of water to calibrate their thermometers, which they set at 212 degrees in order to retain the size of Fahrenheit's degree. Fahrenheit himself did make thermometers that could read as high as 600°F, but the largest market was for thermometers for weather observations, and on these the part of the thermometer from 130°F to 212°F would be wasted.

So, the 37C = 98.6 is more of an accident then planed.

Also, Wikipedia cannot used as a cited source in most upper level papers as the data is not confirmed and anyone can change it. However, Wikipedia can be used as a pointer to "good" sources which can be cited

 

[Phil K.]

Putting a decimal at the end of a number, even if nothing follows it, makes everything to the left of the decimal significant. For this example, 60 has 1 and 140 has 2 due to the lack of decimal places after the numbers.
If it were 60. and 140. they they'd have 2 and 3, respectively</hijack>

No arguments, but your conclusion is faulty in the diving application that I was discussing in this thread. When we look at a depth guage or a bottom timer and read 60 fsw or 60 minutes, the number we are reading is actually the number 60 followed by a decimal point. The manufacturers of these devices don't bother to program them to put a decimal point at the end of the last digit, but that last zero is not just a place holder to determine the number of decimal places. Regarding a depth guage, the decimal place is known because our instruments actually measure to the nearest foot, making that zero in 60, while estimated, nonetheless significant whether the instrument, in utter disregard for the law of significant digits, places a decimal point there or not.

How am I doin' dstedling?

 

[Gilldiver]

I think too many are getting obsessed with the accuracy of their timers and depth gages.

The fact is that all decompression theory and tables are inaccurate to a much greater degree that any gages will ever be. Even variance between gages is way over what any decimal point reading will ever be. I have seen three computers of the same make and model be as much as 5 or 6 feet in variance. The quality control of the pressures sensors is just not that accurate and it would need a full gauge reputability and reliability study (R&R) of each gauge to calculate the correction factors.

Do not get so tied up that you start doing what I saw one time – An instructor kept his 4 students floating around for an extra 40 seconds just so that they would have exactly 90 minute surface interval. Does anyone think that 40 seconds is significant in relation to the built in assumptions that all deco models have?

 

[SparticleBrane]

No arguments, but your conclusion is faulty in the diving application that I was discussing in this thread. When we look at a depth guage or a bottom timer and read 60 fsw or 60 minutes, the number we are reading is actually the number 60 followed by a decimal point. The manufacturers of these devices don't bother to program them to put a decimal point at the end of the last digit, but that last zero is not just a place holder to determine the number of decimal places. Regarding a depth guage, the decimal place is known because our instruments actually measure to the nearest foot, making that zero in 60, while estimated, nonetheless significant whether the instrument, in utter disregard for the law of significant digits, places a decimal point there or not.

How am I doin' dstedling?

You bring up a good point, although in my defense I was just talking about pure numbers and nothing in diving applications. I do understand what you're saying though.