\n",
"Our main hypothesis is that the strength of the illusion has a linear relationship to the amplitude of vestibular noise.\n",
"\n",
"Mathematically, this would write as\n",
"\n",
"\n",
"S = k ⋅ N\n",
"
\n",
"\n",
"where *S* is the illusion strength and *N* is the noise level, and *k* is a free parameter.\n",
">we could simply use the frequency of occurance across repetitions as the \"strength of the illusion\"\n",
"\n",
"We would get the noise as the standard deviation of *v(t)*, i.e.\n",
"\n",
"\n",
"N = E[v(t)2],\n",
"
\n",
"\n",
" where **E** stands for the expected value.\n",
"\n",
"Do we need to take the average across time points?\n",
"> doesn't really matter because we have the generative process, so we can just use the σ that we define\n",
"\n",
"'''\n",
"\n",
"markdown2 = '''\n",
"## Step 4\n",
"