From 4496f3c0b3f60c1fe6253f948c150dcdba1ed15f Mon Sep 17 00:00:00 2001 From: Viacheslav Ustymenko Date: Sat, 31 Jan 2026 21:11:57 +0200 Subject: [PATCH] fix found typos in introduction --- tex/Introduction.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/tex/Introduction.tex b/tex/Introduction.tex index 0e9e34b..e563a1e 100644 --- a/tex/Introduction.tex +++ b/tex/Introduction.tex @@ -84,7 +84,7 @@ \section{Science and the Scientific Method} \section{Theories, hypotheses and models} For the purpose of this textbook (and science in general), we introduce a distinction in what we mean by ``theory'', ``hypothesis'', and by ``model''. We will consider a ``theory'' to be a set of statements (or an equation) that gives us a broad description, applicable to several phenomena and that allows us to make verifiable predictions. For example, Chlo\"e's Theory ($t \propto \sqrt{h}$) can be considered a theory. Specifically, we do not use the word theory in the context of ``I have a theory about this...'' -A ``hypothesis'' is a consequence of the theory that one can test. From Chlo\"e's Theory, we have the hypothesis that an object will take $\sqrt{2}$ times longer to fall from $\SI{1}{m}$ than from $\SI{2}{m}$. We can formulate the hypothesis based on the theory and then test that hypothesis. If the hypothesis is found to be invalidated by experiment, then either the theory is incorrect, or the hypothesis is not consistent with the theory. +A ``hypothesis'' is a consequence of the theory that one can test. From Chlo\"e's Theory, we have the hypothesis that an object will take $\sqrt{2}$ times longer to fall from $\SI{2}{m}$ than from $\SI{1}{m}$. We can formulate the hypothesis based on the theory and then test that hypothesis. If the hypothesis is found to be invalidated by experiment, then either the theory is incorrect, or the hypothesis is not consistent with the theory. A ``model'' is a situation-specific description of a phenomenon \textit{based on a theory}, that allows us to make a specific prediction. Using the example from the previous section, our theory would be that the fall time of an object is proportional to the square root of the drop height, and a model would be applying that theory to describe a tennis ball falling by \SI{4.2}{\meter}. From the model, we can form a testable hypothesis of how long it will take the tennis ball to fall that distance. It is important to note that a model will almost always be an approximation of the theory applied to describe a particular phenomenon. For example, if Chlo\"e's Theory is only valid in vacuum, and we use it to model the time that it takes for an object to fall at the surface of the Earth, we may find that our model disagrees with experiment. We would not necessarily conclude that the theory is invalidated, if our model did not adequately apply the theory to describe the phenomenon (e.g. by forgetting to include the effect of air drag). @@ -219,7 +219,7 @@ \subsection{Solutions} \begin{solution}{prob:introduction:chemtrails}\label{soln:introduction:chemtrails} -a) You could do an investigation to see if the government is spreading chemicals and try to find out why. You could make measurements of the contents in the atmosphere before and after an airline passes to see if any unexpected chemicals show up. +a) You could do an investigation to see if the government is spreading chemicals and try to find out why. You could make measurements of the contents in the atmosphere before and after an airliner passes to see if any unexpected chemicals show up. b) No he is not, as you just proposed two experiments that could invalidate his theory. \end{solution}