Danny Horowitz ]]>

Your February 8 at 5:53 am post makes the identical claim — the denominator unit appears in the numerator and cancels, but in the context of speed.

Nowhere did you limit the generality of that method. Nowhere in your original assertions about this method did you make any mention of weights. I really regret this observation, but every indication is that you argued yourself into a mistake and then equivocated a way out.

In any case, your own most recent example defeats your argument. In your “*((1 mile/5 minutes)*(5 minutes) + (1 mile/6 minutes)*(6 minutes) + (1 mile/7 minutes)*(7 minutes))/(5 minutes + 6 minutes + 7 minutes)*,” you’ve entered superfluous time measures in order to facsimilize your original argument.

All your extra time entries equate to unity and factor out: [(1 mile)*(5 minutes/5 minutes) + (1 mile)*(6 minutes/6 minutes) + (1 mile)*(7 minutes/7 minutes)]/(5 minutes + 6 minutes + 7 minutes) = (1 mile+1 mile+1 mile)/(18 minutes) = 0.167 mile/minute. That’s QED my position, and by way of your argument.

Also, doing a little dimensional analysis: your units of [(mile-minute/minute)/minute] is **identical** to the extended [(Wm⁻²-year_i/year_i)/year] formulation of your denominator-in-numerator method suggested in my February 13, 2017 at 8:40 pm post.

GMST is Celsius/globe. Any other interpretation is meaningless. “Celsius” floating alone without a referent? Please. Twenty years of W/m² divided by the number of seconds in 20 years is Wm⁻²second⁻¹.

This conversation has run its course, and my next several weekends are going to be very busy. So, Dr. Brown, I’ll thank you very much for your interest, offer my admiration for the effort you’ve expended, and wish you all success in your career.

]]>Of course, I am not claiming that there is a special case made for rates. The global mean surface air temperature (averaged over space and time), for example, is expressed in degrees Celcius (C). Not C/s/km^2 or C/year/m^2.

In your “john runs” example from above, if you want to calculate the mean speed over the time period you can add the total distance and divide by the time it took to travel that distance (3 miles/18 minutes =0.167 miles/minute). That’s not using the weighted average formula. That’s just division. If you want to use the weighted average formula to get an average speed you should be averaging *speeds* weighted by the time spent at each speed:

((1 mile/5 minutes)*(5 minutes) + (1 mile/6 minutes)*(6 minutes) + (1 mile/7 minutes)*(7 minutes))/(5 minutes + 6 minutes + 7 minutes)

=0.167 miles/minute

Analogously, if you want to calculate the average LW CRF over a 20 year period you could count all of the net joules associated with the LW CRF term over the entire 20-year time period and over the entire area of the planet and divide that joule total by the number of seconds in 20 years and the total area to get an average LW CRF flux density in W/m^2. Notice that this unit is in W/m^2 not W/m^2/year.

You could also get this number a 2nd way by first calculating the flux densities for each of the 20 years individually. Then you could convert these 20 individual flux densities to a single 20-year mean flux density by averaging these 20 numbers together (using the weighted average formula with 1 year as the weights). You would then get the SAME 20-year mean flux density value with the SAME units (W/m^2) as you got from doing the calculation the first way (i.e., doing the calculation on the entire 20-year time period). Doing the calculation the 2nd way would not give you a different unit of W/m^2/year.

]]>The use of mph in your February 8, 2017 at 5:53 am post discussing speed therefore just indicates a self-contradictory element in your argument. According to your general rule the “ph” should be absent from the units of speed.

]]>The idea that you could think that Patrick Brown was suggesting that speed only has units of distance is bizarre.

With you unfairly deleting my posts at ATTP, by the way, I’m unlikely to post there anymore.

Actually that was the person who helps me moderate my blog, so I’m not quite sure what was deleted. However, he’s often pretty even handed – even I get my things deleted now and again.

]]>