English: S&P 500 Index Logarithmic Chart's Interesting Features

While S&P 500 data to linear plot scale is good for analysis of a span of 2 or 3 years, beyond that a logarithmic S&P 500 chart is best. This is because it gives the same Y or vertical displacement for a certain percentage move up or down regardless of date. Moreover, a fixed compound interest percentage gain plots as a straight line on a logarithmic chart, which is very useful as the human eye is very good at judging and comparing data positions above and below a straight line (versus the linear plot's exponential curve for same).
The given chart with Y axis logarithmic $ values was generated using Excel. There is an upper cluster of lines in $ as published WITH INFLATION, and a lower cluster of lines INFLATION SUBTRACTED in 1950 $, (inflation data from: https://inflationdata.com/Inflation/Inflation_Rate/CurrentInflation.asp?reloaded=true )
The upper cluster has two roughly parallel curvy plots using S&P 500 monthly $ MAXIMUM values for the upper line and $ MINIMUM values for the lower line (from Finance Yahoo history: https://finance.yahoo.com/quote/%5EGSPC/history?p=%5EGSPC ) and the X axis shows dates 1945 to 2030, with analysis of 853 months from 1/1950 to 1/2021. The upper cluster has two STRAIGHT parallel lines (upper line named BFU, lower BFL) plotted using a trial-and-error BEST FIT to the S&P 500 plot they are with. The two straight lines represent one line with 'thickness' 6.42% from a calculated average of the monthly S&P 500 Max-Min span; effectively the S&P500 average monthly fluctuation.
BEST FIT was by accumulating excess, i.e. positive for the upper plot above the upper straight line and negative for the lower plot below the lower straight line, giving an accumulated value starting 1950 to January 2021. Where the S&P 500 plot and straight line have ZERO difference is a place where the straight line fits correctly (for example 1/90 and 10/96); these places displayed in a dotted text box.
The lower cluster also has two roughly parallel S&P 500 curvy plots taken from the upper cluster S&P 500 plots but LESS inflation so look different and have less slope. The lower cluster has two additional parallel lines derived from the straight lines BFU and BFL but without inflation so are now no longer straight. These plot lines also start in 1/1950.
The upper cluster straight line BEST FIT slope, based on numerous attempts, has a compound interest of 7.5% per annum and is believed to be accurate to 0.1%.
The lower cluster includes a straight line, added for guide and information, of compound interest 4.0% per annum based in 1990. In addition, a further confirmation is that average inflation over the period 1950 to 1/2021 is 3.5% per annum compound i.e. the rough difference between the two slopes.
Government Debt plot and GDP plots WITH and WITHOUT inflation are added as percentage to show slope relative to S&P 500, both based in 1980 but the Y scale is arbitrary so NOT valid $. Gold is also added as an interesting aside and $ per ounce Y scale IS valid.

Logarithmic Chart's Interesting Interpretations

Firstly the upper cluster S&P 500 plots including inflation follow a straight line percentage gain much better than those without; therefore inflation somehow evens out the ups (over-performance) and downs (under-performance) of the S&P 500 without inflation.
It is interesting to note that the 1955-69 post-war overshoot versus the 7.5% straight line, is eventually negated by a 1974-86 undershoot period below the straight line, returning to the 7.5% line in the 1987/97 region. Also, the Internet Bubble from 1995, peaking way-above the 7.5% line at 2000, is followed by drops, 2002 and especially 2009 below the straight line, returning to the 7.5% line in 2015/6.
Interestingly, the WITHOUT inflation S&P 500 plot best shows index cycles. 1951 to 1994 was 43 years of boom-overshoot, then fallback, and then recovery back to the overshoot peak. Another index cycle of 22 years 1994 to 2016 is shown: 1994 to 2000 boom overshoot-peak, fall back to 2009, then recovery back to the overshoot peak in 2015/6. A new cycle may have started in 2015/6.
The Best Fit straight line is thought to be a very approximate indication of an S&P 500 par slope, shown to indicate whether an index value is above or below the derived slope norm. Owing to the only 70 years of financial data, and the unique technology advances and inflation profile contributing to it, it is not certain whether a 7.5% Straight Line, or for that matter any Straight Line will be maintained in the future.
Interestingly, the US National Debt % slope somewhat matches the overall S&P 500 % slope. Slope increases in Debt seem to precede S&P 500 slope increases by a few years; data from: http://www.treasurydirect.gov/govt/reports/pd/histdebt/histdebt_histo5.htm
The GDP graph % slope underperforms the S&P 500 % slope; data from: http://www.bea.gov/national/index.htm#gdp
Gold in $ per ounce is added so its unusual % slope can also be compared; data from: https://www.usagold.com/reference/prices/goldhistory.php