“When the only tool you have is a hammer, all problems begin to resemble nails” (Abraham Maslow). Applying the ways of knowing as an alternative of the subject matter of “tools”, this quote suggests that if one looks at the ways of knowing as one group rather than individually, the knowledge that will be gained will not be to the best of the ability of oneself. The four ways of knowing are: reason, language, sense perception, and emotion. We will be determining to what extent is reason more reliable as a way of knowing than the other ways of knowing, in math, natural science, and ethics? While analyzing math, natural science, and ethics, we will see that reason is neither more reliable or unreliable, but plays both as a strength and weakness in different areas of knowing.
In this paper I will focus in one particular insight problem called the nine-dot-problem and review some of the experiments and theories that have been proposed to describe a path to its solution. But first I think it is important to become aware of what exactly distinguishes well-defined problems and ill-defined problems from one another. Well-defined Problems vs. Ill-defined Problems Well-defined problems are those that have clear, defined goals and can be met in a formal and set number of steps. An example of a well-defined problem would be a math equation such as 2(x) + 4 = 10. In order to understand how to solve said problem first we ought to know the meaning of the mathematical symbols and numbers, and define the goal, which in this case is to figure out the value of “x”.
Investigating The Answer When The Products Of Opposite Corners on Number Grids Are Subtracted Introduction The purpose of this investigation is to explore the answer when the products of opposite corners on number grids are subtracted and to discover a formula, which will give the answer in all cases. I hope to learn some aspects of mathematics that I previously did not know. The product is when two numbers are multiplied together. There is one main rule: the product of the top left number and the bottom right number must be subtracted from the product of the top right and bottom left numbers. It cannot be done the other way around.
Matrices were always known just as arrays back then. Matrices can be added, subtracted, and multiplied but with different rules. When adding and subtracting, matrices must be the same size in order to be solved. With multiplication, you must first find the dimensions and make sure that the inside numbers match. If they do, you then multiply each row by column.
(b) [1 point] Traverse the BST using DFS and label the vertices by their values as they are encountered, as you did for Homework #5. (c) [1 point] Repeat Question 1b), but for BFS instead of DFS. (d) [1 point] Tell which method - DFS or BFS - would be better for outputting the BST values in sorted order. You do not have to start at the root of the tree. To get credit, you must explain your answer in 1-2 sentences.
Function SelectPaths(U, NSPC) 1:Find the correlations between the paths 2: Prune the paths 3: Generate correlation Matrix 4: Sort the items in the Matrix 5: Prune the Matrix 6: Write ILP formulation 7:Solve ILP Figure 1- The pseudo-code of the proposed selection method In the first step, the correlation between each two paths of the U, is calculated. The correlation between two paths of i and j, Cij, is equal to the percent of the gates of ith path which are shared by the path j. If Cij is equal to 1, it means that path i is completely inside path j. In this case, if jth path violates the TC, ith path violates too. Hence, in this case ith path is removed from the U.
I found the turning point at 3.33cm, it was 592.592cm^3. Now I have found out the maximum size for the cut out square I will experiment by changing the size of the square. I already know that a 20cm square with 3.33cm cut out squares has a volume of 592.
Descartes, the skeptic, said that we could use reason to find certain truth if we used it correctly, while Pascal said that we can't know certain truth, but reason is the best source of knowledge that we have. Descartes: Reason is the tool by which we know everything that we know. But most people make the mistake of basing their reasoning on assumptions which are not known with 100% certainty. As I've said, “I am greatly astonished when I consider [the great feebleness of mind] and its proneness to fall [insensibly] into error” (K&B, p. 409). But it is possible to avoid falling into error if we use the valuable tool of reason correctly.
In relation to Mathematics, I will address that knowledge can be supported by concepts that cannot be perceived or are not necessarily a fact, and that the organization of facts can happen after the knowledge is generated. In contrast, I will look at how knowledge in History is difficult to be justified and therefore can be biased depending on who is organizing the facts. Looking at my IB subjects, I suppose Mathematics is the best example demonstrating that knowledge is a “systematic organization of facts”. The development of mathematical knowledge must follow through logically, establishing according to other knowledge; when knowledge is justified then mathematicians use it as a fact to prove other knowledge that coheres within a logical system. For example, the Pythagorean theorem is justified supported by the fact that length of sides of a right-angled triangle follows the rule.