TOK Presentation

Implications for SKQ2

>> Human sciences may involve experimental methods, employed to investigate human behavior and reactions through questionnaires, observations, anthropology, activities, statistical methods. >> In the study of the human sciences, many assumptions are made and people are often stereotyped. >> In human sciences, a lot of reasoning and imagination is applied in the acquisition of knowledge and investigation of human behavior to generate theories. The methodology in human sciences requires testing a large number of people and looking at what the majority has shown, from which generalizations can be made. >> Natural scientists regard the human sciences as pejorative. The methodology for which conclusions are drawn form natural sciences is usually logical, and obeys natural laws. >> How should we know what to trust in this world? As long as evidence is appropriated correctly.

1. Explanation

>> In the RLS, the formula that the mathematician deduces uses a set of data acquired through surveys and data obtained from dating websites to find patterns on things such as how individuals choose their partner. >> Through the analysis and interpretation of the evidence, her team were able to identify mathematical patterns and apply them to human behavior patterns. >> In this equation here that comes from the Main RLS, we see that human emotions are each assigned a certain numerical value. The process of applying quantitative values (through Maths) to human emotions and behaviour helps enhance their observations and leads to better critical analysis of the evidence. >> Using Maths in social phenomena makes the process of acquisition of knowledge more effective, and thus we can make better predictions.

Implications for SKQ1 (M)

>> Leads us to questioning the validity of mathematics. Even though we may have rigorous proofs. Mathematics can often lead us to false conclusions. Which is a problem because we place so much trust in Mathematics.

Implications for SKQ1 (S)

>> Mathematics is universal branch of science considered with numbers, quantity and space. Mathematics is free of any cultural context which makes the knowledge associated with it to have a high status compared with other AoKs. >> Mathematics has a high degree of certainty. Its epistemology stands very close to justified belief than opinion, due to the nature and origin of the knowledge and methods which involve rigour and proof. >> However, the reality is that there are numerous mathematical statements which are widely accepted as correct by the vast majority of mathematicians as seen in the area of mathematics in spite of there not actually being a rigorous proof of the statement. >> The fact is that a mathematician cannot possibly examine every proof, and that means that he often relies on what he perceives to be the commonly accepted belief.

2. Example

>> Polygraphy is an interrogation method which measures and records several physiological indices such as blood pressure, pulse, respiration, and skin conductivity while the subject is asked and answers a series of questions. >> In 1991, two thirds of the scientific community who have the requisite background to evaluate polygraph procedures considered polygraphy to be pseudoscience. >> People have tried to use the polygraph for measuring human emotions, but there is simply no royal road to measuring human emotions. >> Therefore, since one cannot reliably measure human emotions, especially when one has an interest in hiding his/her emotions, the idea of valid detection of truth or falsehood through measuring respiratory rate, blood volume, pulse rate and galvanic skin response is a mere pretense. >> Polygraphs measure arousal, which can be affected by anxiety, anxiety disorders, confusion, fear, etc. An examinee might trick the system (they might be able to take countermeasures to produce deceptive results). On the other hand, false positives do occur, and these people suffer the consequences of "failing" the polygraph. >> Thus, due to randomness of human behavior and anomalies in this case, leads to false or inaccurate predictions of human behavior. >> Correlation and coincidence are not causation. So certain physiological indices may not necessarily imply that a person is lying. A person might sweat during the interrogation coincidentally and cause the polygraph machine to detect a lie.

1. Example

>> Scientists predict that an asteroid will approach Earth in 2029. They concluded that due to the law of gravitation, the proximity of the asteroid would lead it to collide with the Earth in the future. >> They estimated an impact that the asteroid would leave a crater 518 metres deep if it hits the Earth. These scientists used intuition and imagination. >> They used imagination by putting pieces of the known together and coming up with something new. They obviously did not come up with these numbers by experimenting with an actual asteroid. They used small scale experiments, and applied them in the real world scenario of the asteroid approaching the earth. >> They also must have used intuition, which is the mind's ability to work on an unconscious level. Since they are experts in this field with a long history of experience in the science, they have enough expertise for their unconscious processing to be trustworthy and accurate. >> For instance, when they found the asteroid would approach the Earth, their intuition was that the force of gravity could attract the asteroid to the Earth and divert its trajectory closer to the Earth, possibly impacting it. >> Scientific evidence comes from observations and measurements made in experiments using the scientific method. >> For example, the evidence for Newton's Law of Gravitation comes from data taken from many experiments. >> The prediction of the asteroid has a high degree of validity as it follows laws from physics that have been supported by evidence over and over. >> The prediction also has some degree of falsifiability. It could be shown to be false if someone were to discover no asteroid is approaching the Earth through a telescope.

2. Example

The Law of demand states that the quantity demanded of a good increases with a decrease in price of the good and vice versa. The law of demand was first brought up by the economist Alfred Marshall. Due to the law's general agreement with observation, economists have come to accept the validity of the law under most situations. The law of demand takes into account certain assumptions, and with those assumptions, it can be justified to be valid. Economists have used evidence and observations to corroborate the validity of this law. For example, by collecting data on the influence of price on the quantity demanded for a certain market, economists used reasoning to justify that when prices decreased, quantity demanded increased.

1. Counterclaim

There are limitations as to the extent to which mathematics can be used to predict the future.

Main RLS (S)

This is our main RLS. It is a TEDx talk by Hannah Fry, who is a mathematician and complexity scientist, where in this TED talk, she applies the principles of mathematics into the problem of love.

2. Counterclaim and Explanation

>> The problem with social sciences is that studies in social sciences can easily lead to false results. >> The first problem is that many assumptions are made. Scientists in human sciences often get carried out and make so many assumptions that it becomes almost inapplicable to the real world. Which in turn destroys the whole point of the study in the first place. >> The other problem is the stereotypical nature in human science studies. When analysing data from experiments such as questionnaires, surveys, observations, and other statistical methods, what tends to happen is generalization. The entire sample of humans is generalized to a single outcome. >> Researchers in social sciences often feel pressured to find statistical significance in their results. To draw conclusions from data, researchers usually rely on significance testing. In simple terms, this means calculating the "p value", which is the probability of results like ours if there really is no effect. If the p value is sufficiently small, the result is declared to be statistically significant. What they end up doing is P-hacking. This leads to false results and conclusions. >> In the RLS, we see a range of data being modelled. We can clearly see the anomalies present. The wide range of data eliminates it from being a coincidence. There is some correlation visually present. But NOT causation. Yet, in the RLS, the mathematician identifies it as a causal relationship.

1. Example

An example of the limitations in mathematics can be seen in Pseudo-mathematics. Pseudo mathematics is a form of mathematics that does not work within the mathematical framework, definitions and rules which we commonly see in the area of mathematics. Essentially, Pseudomathematics is any work, study or activity which claims to be mathematical, but refuses to work within the standards of proof and rigour which mathematics is subject to. Much like other pseudoscience, it often relies on ignoring proven facts and methods, making unsubstantiated claims of fact and ignorance and rejection of the work of experts. This can be represented by the idea of a mathematical fallacy. In mathematics we often see mistakes in proofs and these are known as mathematical fallacies. There is a difference between a simple mistake and a mathematical fallacy though they both lead to invalid proofs. A mathematical fallacy is "an assumption or series of steps which is seemingly correct but contains a flawed argument" and hence it leads to a false conclusion. For example the division by zero. We will now attempt to mathematically prove that 2=1 even though we know that this is not correct. This can be be changed to prove that any number equal any other number. The fallacy can be seen in line five where we dive out (a-b) as (a-b)=0 and dividing 0 by 0 is undefined. This is an example of fallacious reasoning as it does not work within standard mathematical conventions of proof and rigour. Hence the argument is invalid even though the proof is technically mathematically correct.

CKQ (M)

And this poses the question... To what extent can evidence be appropriated to reach false conclusions?

1. Explanation

In the real life situation, the mathematician Hannah Fry refers to the optimal stopping theory as a method for choosing the perfect love partner. The optimal stopping theory in mathematics, is a theory concerned with the problem of choosing a time to take a particular action to maximize the expected reward. Based on the optimal stopping theory, she claims that a person looking for a partner should reject the first 37% of the total number of prospective partners that one would meet in their life, and then choose the marginally best partner. Even though this theory is supported by rigorous proof from the odds algorithm. Through reasoning, the mathematician argues that this theory holds true because the first 37% of people you meet serve as a chassis/background, and gives you a good idea of the love partner marketplace. However what if the perfect partner was one of those first 37%? The problem arises when we apply mathematical theories to the nature of reality.

SKQ1

Let us start with exploring this question through Mathematics and Natural Sciences. How far can Mathematical formulae be used to predict the future?

Link to RLS and CKQ

Mathematical formula in the real life situation is a form of Pseudo mathematics as it refuses to work within the framework of Mathematics; rigorous proof. >> Hence applying Mathematics in a human phenomena such as love can degrade the degree of reliability and lead to false conclusions. >> Quote by Einstein - "Insofar as the statements of mathematics are certain, they do not refer to reality; and insofar as they refer to reality, they are not certain. To make the universe comprehensible we have to employ theories that are not strictly true."

Conlusion (M)

Mathematics by itself has a high degree of certainty. However, when we begin to integrate it into reality and human behaviour, it does help us make predictions, but it is very easy to go astray and make false conclusions when the evidence is not appropriated precisely. Most of the knowledge produced in the world today comes from research conducted by scientists. Scientists should consider the ethical factors prior to publishing their findings to the public. Scientists must ensure their methodology of appropriating evidence to reach conclusions does not have loopholes or fallacies.

1. Claim

Mathematics can accurately be used to predict the future.

Introduction (M)

Say no more Shilen. The video I am about to show you might help you! MIGHT.

Main RLS (M)

She claims that she has observed a pattern and developed a mathematical equation for finding the perfect partner. She presents an equation that predicts whether a given couple is going to get divorced.

Introduction (M)

So. We all must agree that we all experience an intense feeling of deep affection at one point in our lives. Love. And it is essentially one of the most complicated phenomenons and is hard to understand. We can all agree, right? We may have a hard time choosing the perfect partner, a hard time managing a long term relationship, or some of us, including Shilen and I, may even have a hard time getting a partner in the first place!

2. Explanation

Social sciences are concerned with society and the relationships among individuals within a society. In terms of ToK they are known as the Human Sciences. The human sciences corresponds to humanities and social sciences, but also includes aspects of psychology and even mathematics, as one of the key things we are concerned with is how we gather information in our study most importantly the concept of human behaviour.

Conclusion (S)

We have looked at maths/natural sciences as well as the human sciences as so we can assess their relative validities. Although mathematics is widely used and applied to practically everything, there are significant limitations when applying mathematics to human phenomena such as love. Since Mathematics is considered as the most perfect system of knowledge due to its logical steps and rigorous proof, we as humans have the tendency to apply maths where it often don't belong and constantly find formulas and patterns in aspects such as love and human behavior. Doing so is what gives rise to mathematical fallacies and pseudo mathematics which personally completely violates mathematical principles and contribute towards false conclusions. Mathematics goes hand in hand with the area of natural sciences but it is questionable to relate to concepts that edge more towards the human sciences.

Introduction (S)

Well, say no more. Ladies and gentlemen, respective teachers today we will be investigating the mathematics of love. Well, Mohamadali, life would be much easier if only mathematics was the answer.

CKQ (S)

What makes her so confident that she can make predictions with such accuracy.