<div dir="ltr"><div>I am in agreement with Guy Hoelzer in his assessment of the use of log-transformed data.</div>Since I regularly deal with biological growth processes, using log-transformed data is the clearest way to anaylyze proportional relationships in nonlinear sysrtems.<div>By virtue of the way it compresses multiplicative relations log transformation makes scale-free comparison much more tractable and correlations much more obvious.</div><div>And compression is one of the most important benefits of mathematical analysis.</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Jun 3, 2018 at 2:04 PM, Guy A Hoelzer <span dir="ltr"><<a href="mailto:hoelzer@unr.edu" target="_blank">hoelzer@unr.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div>Dear Sung et al.,</div>
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</div>
<div>I appreciate human bias in terms of numerical scale, but I don’t think that is what we actually achieve by using logarithms. If the universe of possibility is fractal, using a logarithm does not eliminate the problem of large numbers. I think
the primary outcome achieved by using logarithms is that units come to represent proportions rather than absolute (fixed scale) amounts. It reveals an aspect of scale-free form.</div>
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<div>On Jun 3, 2018, at 10:42 AM, Sungchul Ji <<a href="mailto:sji@pharmacy.rutgers.edu" target="_blank">sji@pharmacy.rutgers.edu</a>> wrote:</div>
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Hi Krassimir,</div>
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I think the main reason that we express 'information' as a logarithmic function of the number of choices available, n, may be because the human brain finds it easier to remember (and communicate and reason with) 10 than 10000000000, or 100 than 1000000000.
. . . 00000, etc. </div>
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All the best.</div>
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Sung</div>
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<div id="m_4554984804782621599divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt"><b>From:</b><span class="m_4554984804782621599Apple-converted-space"> </span>Krassimir Markov <<a href="mailto:markov@foibg.com" target="_blank">markov@foibg.com</a>><br>
<b>Sent:</b><span class="m_4554984804782621599Apple-converted-space"> </span>Sunday, June 3, 2018 12:06 PM<br>
<b>To:</b><span class="m_4554984804782621599Apple-converted-space"> </span>Foundation of Information Science<br>
<b>Cc:</b><span class="m_4554984804782621599Apple-converted-space"> </span>Sungchul Ji<br>
<b>Subject:</b><span class="m_4554984804782621599Apple-converted-space"> </span>If always n>0 why we need log</font>
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<div class="m_4554984804782621599PlainText">Dear Sung,<br>
<br>
A simple question:<br>
<br>
If always n>0 why we need log in<br>
<br>
I = -log_2(m/n) = - log_2 (m) + log_2(n) (1)<br>
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Friendly greetings<br>
<br>
Krassimir<br>
<br>
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