<h2 id="content"><a href="#content" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>Content</h2>
<ul>
<li><a href="#introduction">Introduction</a></li>
<li><a href="#bernoullis-theories">Bernoulli’s theories</a>
<ul>
<li><a href="#1-expected-utility">1. Expected Utility</a></li>
<li><a href="#2-marginal-utility">2. Marginal Utility</a></li>
</ul>
</li>
<li><a href="#weber-fechner-law">Weber-Fechner Law</a>
<ul>
<li><a href="#webers-law">Weber’s Law</a></li>
<li><a href="#fechners-law">Fechner’s Law</a></li>
</ul>
</li>
<li><a href="#conclusion">Conclusion</a></li>
</ul>
<h2 id="introduction"><a href="#introduction" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>Introduction</h2>
<p>In the book “Thinking Fast and Slow” by Daniel Kahneman, he presents a few ideas that helps to better understand the relationship between human perception and the physical world.</p>
<p>All of these forces influence the way we make decisions in many situations.</p>
<p>In addition, he draws a clear distinction between the “economics model” and the “psychology model”.</p>
<p>The main distinction is that economics assumes rationality and the “best choice” is selected in decision making.</p>
<p>While, psychology is based on observation of actual decisions without making any assumption on rationality of the person.</p>
<p><strong>The Ideas:</strong></p>
<ul>
<li>
<p><strong>Bernoulli’s Theories</strong> - The relationship between psychology value (utility) and dollar value</p>
</li>
<li>
<p><strong>Web-Fechner’s Law</strong> - The relationship between subjective experience and external stimulus (senses - vision, touch, smell, taste and hearing)</p>
</li>
</ul>
<p>These ideas are quite interesting and I believe they can have wide application in many fields.</p>
<p>Let’s start off with Bernuoll’s theories.</p>
<h2 id="bernoullis-theories"><a href="#bernoullis-theories" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>Bernoulli’s theories</h2>
<p>Daniel Bernoulli was a mathematician and physicist who through some experimentation was able to formulate an ingenious theory to explain
the relationship between psychological value (Utility) and Money.</p>
<p><strong>There are two ideas:</strong></p>
<ol>
<li>
<p>Expected Utility</p>
</li>
<li>
<p>Diminishing Marginal Utility</p>
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</ol>
<h3 id="1-expected-utility"><a href="#1-expected-utility" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>1. Expected Utility</h3>
<p>in the 1700s, Bernoulli made an interesting observation that deviated away from original expectation of decision making as it pertains to money.</p>
<p>The original thinking is the assumption that most people make decisions to maximize the dollar value in a situations where there is an element of risk or uncertainty.</p>
<p>Bernoulli argued that in actuality, people make decisions based on the psychological value and the “utility” (perceived value) rather than the dollar value.</p>
<p>So, in the context of money, the idea of utility is that this is a subjective measure based on satisfaction that person derives from the outcome rather than the monetary value itself.</p>
<p>The expected utility of a gamble or uncertain decision then is the sum of the probability multipled by the utility.</p>
<div style="margin: 2em auto;">
  <div style="display:flex;justify-content:center;">
    <img src="/images/expected-utility-formula.png" alt="Expected Utility Formula" />
  </div>
  <div style="display:flex;justify-content:center;">
    <blockquote>Expected Utility Formula</blockquote>
  </div>
</div>
<p><strong>The question becomes:</strong> What is the relationship between this subjective measure and the dollar value?</p>
<p>This was another one of Bernoulli’s observation, that relationship is called “Marginal Utility”.</p>
<h3 id="2-marginal-utility"><a href="#2-marginal-utility" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>2. Marginal Utility</h3>
<p>Another related and important observation that Bernoulli made was that the relationship between utility and money has a diminishing effect.</p>
<p>Meaning the more wealth a person has, the changes in utility levels off.</p>
<p>This effect also explains the risk aversion in decision making with increasing wealth.</p>
<p>At a certain level of wealth, further bets to increase wealth will not change their overall utility by that much.</p>
<p>Dr. Daniel Kahneman mentioned that it explains why “there is a common preference for the sure thing” when presented with a gamble or uncertain choice.</p>
<div style="margin: 2em auto;">
  <div style="display:flex;justify-content:center;">
    <img src="/images/marginal-utility.png" alt="Marginal Utility" />
  </div>
  <div style="display:flex;justify-content:center;">
    <blockquote>Marginal Utility: Utility Versus Wealth</blockquote>
  </div>
</div>
<p>In fact, Bernoulli used the knowledge of expected and marginal utility to calculate the premiums that merchants at the time would pay for insuring their boats.</p>
<p>The “sweet spot” explains how the poorer merchants were more willing to pay the permiums to have the defense against loss of utility in the event of a catastrophe (ie Boating sinking and/or lost trade goods).</p>
<p>These two theories presented by Bernoulli are still used today to understand how decisions are made with applications to economics, risks and gambling.</p>
<p>However, there is a gotcha, Dr. Daniel Kahneman argues that there are some flaws with this theory (which we’ll discuss this in another article).</p>
<p>One of the main argument from Dr. Daniel Kahneman is that there isn’t a consideration for “reference points”.</p>
<p>This is the person’s perception at the time the decision is being made. This can have a strong influence over the decision making process.</p>
<p>Bernoulli’s was not the only one that studied on the observation of this relationship that bridges the human perception and the physical world.</p>
<p>There were many psychologists that studied this relationship as well, namely, Weber and Fechner.</p>
<p><strong>The difference ?</strong> These studies were based on the subjective experiences in our mind and how it relates to the way we experience the world in the physical.</p>
<h2 id="weber-fechner-law"><a href="#weber-fechner-law" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>Weber-Fechner Law</h2>
<p>Ernst Weber and Gustav Fechner both studied the relationships between the perception and physical stimuli (senses).</p>
<p>These senses include vision, touch, smell, taste and hearing.</p>
<h3 id="webers-law"><a href="#webers-law" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>Weber’s Law</h3>
<p>The law was formed based on Ernest Weber’s observation in studying the relationship between external stimulus and human perception.</p>
<p>The law is quite simple, it states that the minimum amount of change of the external stimulus to produce a proportional change is based on the initial external stimulus.</p>
<p>In simple terms, this means our perception of change in the physical characteristics of the object (size, tone, weight etc) is highly dependent on the starting point of the external stimulus (bright light, dim light etc).</p>
<p><strong>Example:</strong> Demonstration of Weber’s Law</p>
<div style="margin: 2em auto;">
  <div style="display:flex;justify-content:center;">
    <img src="/images/human-perception-webers-law.png" alt="Example demonstrating Weber’s Law" />
  </div>
  <div style="display:flex;justify-content:center;">
    <blockquote>Example demonstrating Weber’s Law</blockquote>
  </div>
</div>
<p><strong>Breakdown:</strong></p>
<ul>
<li>
<p><strong>Visual (A1) to Visual (A2):</strong> There is a noticeable (perceived) visual change in spots</p>
</li>
<li>
<p><strong>Visual (B1) to Visual (B2):</strong> There is a less noticeable (perceived) visual change in spots</p>
</li>
</ul>
<h3 id="fechners-law"><a href="#fechners-law" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>Fechner’s Law</h3>
<p>Gustav Fechner’s was another psychologist studying under Weber, his law builds on the Weber’s Law.</p>
<p>He formulated the relationship between the perceived intensity and measured intensity of a stimuli.</p>
<p>Perceived intensity has a logarithmic relationship with measured intensity.</p>
<p>This means that as you increase the measured intensity, the perceived intensity increases at a slower rate.</p>
<p>In addition, the perceived effect levels off as you increase the intensity.</p>
<p>One example of this would be lighting in a room, as you make the room brigher and brighter, the perceived brightness will start to feel less intense.</p>
<p>Beyond just intensity, other subjective experiences and their relationship with senses can be explained by Fechner’s Law.</p>
<p>It follows the same relationship.</p>
<div style="margin: 2em auto;">
  <div style="display:flex;justify-content:center;">
    <img src="/images/fechners-law.png" alt="Fechner’s Law: Perceived Intensity V.S. Intensity" />
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  <div style="display:flex;justify-content:center;">
    <blockquote>Fechner’s Law: Perceived Intensity V.S. Intensity</blockquote>
  </div>
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<h2 id="conclusion"><a href="#conclusion" aria-hidden="true" tabindex="-1"><span class="icon icon-link"></span></a>Conclusion</h2>
<p>And there you have it, 3 ideas that help you to understanding the relationship between perception and the physical world.</p>
<p><strong>Here are a few takeaways:</strong></p>
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  <div style="display:flex;justify-content:center;">
    <img src="/images/perception-physical-bridge-takeways.png" alt="Main ideas bridging the human perception and physical world" style="width:80%;" />
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  <div style="display:flex;justify-content:center;">
    <blockquote>Main ideas bridging the human perception and physical world</blockquote>
  </div>
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<p>And... that’s it.</p>
<p>If you learned something new or enjoyed this article then be sure to share it with someone who you think would like it!</p>


Jerry Chang

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