Mind over Math: Throwing Out the Numbers

Opinion by Kip Hansen

Over the years there has been a lot of discussion about the power of numbers both to inform us and misinform us regarding the world around us.

In fact, some versions of the definition of science include the idea that all science is based on measurement – on numbers.  This idea is wrong from the start and extremely unfortunate.  Science – the effort to understand the physical world around us – must start with ideas – not numbers.  Ideas are strung together into hypotheses and those hypotheses are tested first against existing knowledge through the application of logic and critical thinking. 

Of course, many ideas can be confirmed or rejected based on measurements.  However, measurements (and here I specifically mean measurements turned into numbers) in today’s world are often misrepresented, misconstrued and miscommunicated.  With the advent of digital computers and their associated software, calculation and statistical analysis are far too easy and seem to have replaced both logic and critical thinking, even basic reasoning.  Those data sets of numbers are an almost irresistible temptation to many of our colleagues in the various fields of science – they just can’t restrain themselves – they must dive in with Mathematica and other tools of digital analysis, making new sets of numbers and new visual representations of those numbers.  They seldom stop there – they must add their opinions into the data set visualizations as various trend lines and others ideas that are not part of the data set at all. 

In science today, data sets (or here) are often confused with the real world.  We must acknowledge that data sets are nothing but a collections of numbers, hopefully carefully collected, labelled, accurate, precise and they hopefully represent information about some real attribute/s of some object or phenomenon of interest. 

This is not always the case. For instance the data set(s) known as Global Mean Sea Level do not refer to the actual surface height of the global seas or its mean value but rather to a concept of what that height would be under non-existing conditions, such as “if the ocean basins had not expanded” and “if water storage on land had not increased”, as this quote illustrates:  “Eustatic (global) sea level refers to the sea level change of the volume of Earth’s oceans. This is not a physical level but instead represents the sea level if all of the water in the oceans were contained in a single basin.” [ my emphasis – kh  source ]

Regular readers of this blog or any other source of science news and science discussion, including the leading journals of science, are well aware of the problem.  Because some data set exists –> some scientist/s dig in with statistical analysis of some portion of the data set in an attempt to find a publishable result –> they always find such a result.  The fact that the result found is not significant in the real world (for instance, not a Minimal Clinically Important Difference), that the result is trivial, that the result is vanishing small with error-bars that all include zero, that the result is ephemeral, that the result adds nothing to our accumulated knowledge base, that the result depends on the pre-existing bias of the researcher or his field of research, that the result has no applicable reality or that the result is true only in a very limited academic-sort of way – all these are ignored and under-emphasized in the resulting journal paper.  The journal paper is then churned into click-bait by the Science Mass Media and presented as newly discovered truth.

Again, I know that there is a lot of good science being done, and some of it does result from careful considered analyses of good data sets about a topic of interest.  But there is far too much of the other as in the previous paragraph.

So, all that said, let’s look at a recent example and see what one might gain by looking at a data set from a new perspective which allows us to throw out the numbers and by doing so, arrive at a more pragmatic understanding of it all.

Some clever people in the UK have realized that lots of old archival records exist about the tides in UK harbours and that these records might lengthen the data sets of Mean Sea Level (MSL) in those places for those time periods.  It is an interesting topic – made all the rage by the alarming warnings about Sea Level Rise being issued by all sorts of advocacy groups and misguided scientists for the last 30 years.  I wrote a brief report here on historic EU tide gauge data back in 2019. [ I also found an  older UK record, albeit on temperature at Greenwich Observatory and thought it important enough to post here a few years ago. ]

The resulting paper, an interim report of an ongoing project, appeared recently as “Changes in mean sea level around Great Britain over the past 200 years” by P. Hogarth, D.T. Pugh, C.W. Hughes, S.D.P. Williams in the journal Progress in Oceanography.  The paper self-describes in the abstract as:

“We systematically assimilate a wide range of historical sea level data from around the coast of Great Britain, much of it previously unpublished, into a single comprehensive framework. We show that this greatly increased dataset allows the construction of a robust and extended Mean Sea Level curve for Great Britain covering a period of more than two centuries, and confirms that the 19th century trend was much weaker than that in the 20th century and beyond.”

In plain language, what they have done is transcribe old tide journals – recordings of high and low tides, their magnitudes and timings – from various places around Great Britain mostly from the early 1800s, applied a bunch of analyses and averaging and such, then patched that data onto the modern averages of MSL for Great Britain from the Permanent Service for Mean Sea Level (PSMSL). All-in-all a good and valuable effort.

Here’s an example of the type of old records from which data has been extracted.

Their main result is this chart:

Our own Willis Eschenbach re-graphs and throws stats at the data set from this study in an interesting piece here at WUWT.  Note that  the full data set is available only by viewing the original journal article here and scrolling down to the heading for Appendix A.  Just under that heading is a Download All supplemental files link (which somehow cannot be copied, you have to go to the page and click on it.  It downloads a .zip file). 

In this essay I will evaluate this data set using only the mind – meaning  critical thinking, prior knowledge, and logic – and not math, leading up to throwing out the numbers – the individual measurements (in this case these are averaged averages of averages…). 

Things to know about this data set before looking at anything about this paper – especially the numbers:

  •  While the data set is claimed to be an “extended Mean Sea Level curve”.  It is not that, but rather a graph of the annual average of annual average Relative Mean Sea Levels from 174 different sites on Great Britain (GB) and Ireland – some of the data points are modern (20th and 21st century) data and some are historic (19th century).
  • The recorded numbers have been taken from and by instruments of various types that have been used over the last 200 years.  Older data recorded by hand from tide staffs:

More modern records, mostly from the Permanent Service for Mean Sea Level (PSMSL), result from increasingly more accurate float devices in stilling wells.  The most recent are probably “Air Acoustic sensors in protective wells”.

While the chart from the paper shows “error bars” they are error bars for the averages – and not anything like original measurement error/uncertainty.   Tide staff readings, marked in half-meter increments, probably have an original measurement error of at least 2/10th of a meter (20 cm as in +/- 10 cm), even +/- 20 cm.  The most modern, up-to-date, precise acoustic tide gauge has a per-the-technical- specs error range of +/- 2 cm

  • A brief survey of tidal ranges for harbours in GB reveals that a rough average of tidal range (high tide to low tide) is around 5 meters or 16 feet. Some can be 7 meters and more.

In the real world, this looks like this:

One of the historic record sites used in the paper under discussion is a few miles from Port Isaac.  Port Isaac is the filming location for the famous Doc Martin TV series.

  • Most of the data (there are a few exceptions) before 1920 depend on an average of less than 5 data points – compared to data from 1960 onward which is based on of 30 to 40 data points.  Thus, uncertainty increases from two sources as we move back in time:  original measurement error alone increases by at least factor of ten and sample number reduces by a factor of ten, again multiplying uncertainty.
  • None of the tide data has been corrected in any way for Vertical Land Movement of the tide gauges themselves.  This means we can only use the data for judging Local Relative Sea Level as we can not separate vertical movement (up and down) of the Land from the rise or fall of the Sea. Results are thus not applicable to Global Sea Level or its mean.

I am going to show the process by which one might use a philosophical or strictly mental approach — rather than mathematics or statistics — and applying prior knowledge, critical thinking and logic in the place of math or statistics — to evaluate the data set using the points above to gain perspective and reducing the provided chart to ONLY the things that it can really tell us reliably.

I do this in the following slide show of eleven simple images:

I hope the slide show came off as self-explanatory – but I’ve misjudged readers before.  So, I’ll give my justifications slide by slide here below:

Slide 1:  As given in the original paper.

Slide 2:  I add (and later remove) a reminder of scale, for U.S. readers.  The 300 mm of rise is about 12 inches.

Slide 3:  I remove the unnecessary and misleading Red Line Trend.  The paper’s authors ignore the factors of sparse data before 1920 and ignore their own data, by not including the data points before 1830 – instead drawing a trend line that seems to depend on a single outlying data point around 1817 (the first open blue circle on the graph) and seems to disregard the other early data points that are in line with the 20th century data.   The Red Line is – to me and maybe you – viewpoint biased – trend lines drawn on graphs are always opinions – not part of the data.  All of us are capable of looking at the graph without it.

Slide 4:  I have added – as a grey underlay – something closer to the real minimum uncertainty in the tide measurements themselves.  I keep it as small as possible – only +/- 10 cm on the left and the NOAA-spec’d +/- 2 cm for the most modern data.  It is my opinion that the uncertainty is far greater, especially before  the 1950s.  ALL of the data points fall within the band of uncertainty thus we can ignore all those little squiggles – the little ups and downs – only the overall slope of the more reliable gray band, inside which we are pretty sure the real values lay, can be depended upon.

Slide 5 & 6: Trigger Warning #1 and #2.

Slide 7 & 8:  I remove the numerical data points leaving only the more reliable data range seen as the grey area.  The data range fades on the left side (earlier in time) as the data becomes more and more sparse and less and less dependable.  I say in Slide 8, “almost correct view” because, like almost all programmatically created graphs, the scale is automatically set – without rhyme or reason –  to about 120% of the graphed data range.

Slide 9 & 10:  Here the vertical scale of the graph is corrected to be approximately the average Tidal Range — the average range of Relative Sea Level – for GB harbours.  This is about 5 meters or 16 feet.  This allows us to see the relative importance of the change in RMSL against our daily experience in the real world where this change takes place. (See the photos of Port Isaac in the body of the essay above.)

Slide 11:  The final result of using Knowledge, Critical Thinking and Logic to derive the reliable pragmatic finding of the paper: “Changes in mean sea level around Great Britain over the past 200 years”.  The original findings are not nothing . . . but they are not what was claimed, which was “…that the 19th century trend was much weaker than that in the 20th century and beyond.”

By Throwing Out the Numbers, and evaluating the data first as information, comparing it to existing knowledge, critically considering each aspect, applying simple logic and proper perspective, we can arrive at a more pragmatic understanding of the whole. 

Bottom Line:

Hogarth et al., using the addition of historical tide records to modern records, have extended the understanding of long-term (two-century scale) Relative Sea Levels for GB’s harbours showing that average RMSL in those harbours has been rising steadily and more-or-less evenly since the early 1800s resulting in an overall 200-year rise of about 12-16 inches.  In many locations in the UK this is a trivial amount when compared to their normal daily tidal range.

This result is far easier to see when we Throw Out the Numbers.

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Author’s Comment:

Many readers here may disagree with my approach above.  Truthfully, I have just written out the sequential mental steps that I commonly use, when sitting in my easy chair,  to gain a pragmatic perspective on the many data sets and graphs of those data sets that come my way in my daily walk through the ongoing outpouring of scientific results that I see in the journals and the popular science press.

I think it is a grand idea to capture all those tide readings from the old records and that the recovered data will be very valuable.  In this case, when looked at with a pragmatic eye, it confirms that — contrary to the published finding — nothing unusual has happened with relative sea levels in the UK over the last two hundred years and nothing unusual is happening now.  A good scientific confirmation. 

It is a mistake to reify the data – to pretend that all those over-precise numbers and their little wiggles and squiggles are the thing itself: in this case, actual changes in mean relative height of the sea surface at the millimetric scale.   In the reification, they have fooled themselves into calculating accelerations (speeding ups and slowing downs) and “trends” that just don’t exist in the real world. 

The combined overall result, once we have thrown out the numbers, is perfectly sound and probably reliable. 

Address your comments to “Kip…” if speaking to me.  In general, when replying to or addressing a specific person, prefacing your comment with the name of that person makes the Comments Section more readable.

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via Watts Up With That?


March 8, 2021 at 12:11AM

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