Recenberg 1/5th success rule applied to life..

For those who are not familiar, Rechenberg's 1/5 rule refers to adaptive mutation in evolutionary strategies (ES). It says that the ratio of successful mutations to all mutation should be 1/5. Deriving from this idea, if you get too successful (i.e., more than 1 out of 5 tries) then you're converging too fast to a local optima (aka safe options) and will result in stagnation later on. So, don't run after too many successes. Ideally, at-least according to Rechenberg, one should try 1 safe thing for every 4 risky things in life to optimally balance stagnation vs. growth.

Flaw with patent law?

Math functions cannot be patented. Imagine sin, cos being patented, that'd be crazy right. Ironically computer programs can be patented. It has long been proved that computer programs are equivalent to mathematical functions. Does anyone realize its the same as patenting math functions?

Kleiber's Law

Last week, I happened to read about Kleiber's law while browsing through literature on natural evolution. Its implications are really fascinating. It establishes a relationship between mass and metabolism as:

Metabolism is ultimately linked to the number of heartbeats (heart pumps oxygenated blood, which is responsible for metabolism). Therefore, #heartbeats is proportional to the mass. Also, smaller creatures have high metabolism (heat generated per unit volume) and therefore have faster heart rate.

Curiously, the number of heartbeats per lifetime tends to be constant. Thus, bigger animals live longer as their heart beats slower. Flies on the other hand have shorter lifespan because of high metabolism (smaller mass).

Come to think of it, if we have fixed number of heartbeats, wouldn't running/exercising make us die faster? We are spending more heartbeats per second and it makes perfect sense. Then why is it that people who exercise live longer? The answer is simple...I'll let you think about it.

The paradox...

Newton made calculus to simplify mathematics...a true paradox!

Are some people more intelligent than others? - A Mathematical Perspective

People consider some to be more intelligent than others. For example, most of us would agree if I consider newton or Einstein to be more intelligent than you. But is this really true? First off, what is intelligence? At birth everyone is (more or less) at the same level. Then why is it that some people are good at studies, while some just aren't?

In my opinion, intelligence is all about making rational decisions given the information/knowledge you possess. People are different because the definition of being rational is different for each of us. For some of us, the act of crossing the road carefully might be rational. For others, most rational thing is to cross the road as quickly as possible. These beliefs are based on prior experiences. Someone who has witnessed a road cross accident might prefer to cross it carefully. Those who got fired because of being late might consider a hush hush approach towards crossing.

Bottom line: People are different because of different experiences they possess. This can actually be explained mathematically by a principle most of us are familiar with. Its called 'Bayes Rule'. Bayes rule seeks to find a hypothesis h with high probability given an observation D. Imagine this: You go to your kitchen, find a chair that was used to reach a cookie jar which is now empty. This is observed data D. Probability of this happening is P(D). Now, you can have a set of hypothesis h belonging to set H (representing all possible hypothesis). For instance h1 can be "My daughter must have stolen the cookie". h2 = "A thief stole a cookie as he was hungry". We don't know which of these are true, all may be equally likely. However if we did observe our house to be messed up (typical indicator of stealing), it increases chances of h2 to be true. This rule may be summarized mathematically as:

Our definition of rationality is based on how our knowledge is updated by this rule. By our experiences, we form various P(D)'s and P(H)'s that direct our thinking.

Back to the original question: "Are some people smarter than others by birth?". According to bayes rule "NO". It is our experiences that lets us update probability distributions of likelihood of events/hypothesis. These probabilities guide our actions. If someone makes an intelligent choice despite this, then he/she just got lucky.

Einstein and Newton are intelligent because of their experiences. Some take their experiences for granted. For instance, most of us would just pick up and eat the apple if it fell on our head. Instead, newton reasoned as to why it happened. Is this an indicator of superior intellect? He decided to do a different action (reasoning instead of eating) which is a manifestation of past experience. He must have observed/experienced that its rewarding when you reason every small aspect.

Why do some people learn faster than others? Is it because of genetics? If so, it is again a propagation of ancestral experiences. It might be the case that they worked hard in their childhood (more experience), thereby improving their intellect. Hence, they don't have to work as hard as you to pick things up.

So, in conclusion: "All people are born with the same intellect. It is their experiences that define them. To some extent you decide your experiences, so you control how intelligent you want to be."

Measuring the Observer Expectancy Effect

If you are performing an experiment in which you tell the participant what you are expecting, then this biases the result due to placebo effect. This is the observer expectancy effect. How can you measure this? Intuitively, the solution seems simple. Do the experiment twice, in the first, tell the participant about the expected outcomes and in the second don't tell him anything about the experiment. Then, you measure the difference in outcomes to calculate the variance introduced due to observer expectancy effect. But, is that accurate?

Lets consider a simple example. Suppose you are to create stress relief program. How would you measure if stress is relived or not? If you tell your subjects that they were participating in stress relief program, placebo effect will come into account and you cannot truly determine if the reduction in stress is actually due to the program you created. If you don't tell anyone about anything, including researchers and participants, you can get rid of the observer expectancy effect. This is the Double Blind trial strategy.

Coming back to the original question, if you do the experiment twice, one with the expectancy effect and another using double blind strategy and consider the difference in performance, do we then have the measure of observer expectancy?

The answer is NO because in both the experiments the state of the participant is different. To be accurate, you'll have to conduct both the experiments in which the researchers, participants and in fact the entire universe is in the same state, i.e., do both the experiments simultaneously, which obviously doesn't work out.

How else can we go about this problem? First we start by formalizing the problem, making it concise. For simplicity, let us consider a single participant. In a given experiment, let the state of the participant be Sp (could involve factors such as personality etc..) and the state of everything else be Se (state of the environment, ideally the entire universe, but a local region would suffice). Therefore, the state of an experiment can be defined by the Tuple (Sp, Se).

Now, perform N experiments with blind trial strategy, each represented by different tuples (S1p, S1e) ... (Snp, Sne) You can now build a regression model to determine the the outcome of the experiment as a function of Se and Sp, after collecting data from sufficiently large number of experiments.

Now we can apply the strategy discussed before. We perform experiment with double blind trial with parameters (S1e, S1p). The second experiment (with expectancy effect) with parameters (S2e, S2p). We can now extrapolate the outcomes of first experiment if parameters S2e and S2p were used instead of S1e and S1p. Since, both the experiments are now virtually conducted simultaneously, we can now determine the observer expectancy effect by computing the difference in outcome.

More accurate the regression model, better is the accuracy of the observer expectancy. With few obvious modifications, one can also build a model to estimate observer expectancy as a function of experiment, Se and Sp.

On a second thought, who gives a damn? If the stress relief program works, be it due to expectancy, that's all we really care about.