This is literally how I passed 4 different courses (Linear Algebra, Differential Equations, Thermodynamics and Statistics). I was in the research focused engineering stream at UofT, so our courses were heavy on proofs. Whenever I had to do one I'd work towards the middle from the top and bottom simultaneously. Often I couldn't quite complete the proof, but the missing step was in the middle somewhere so it looked like I just made a poorly explained leap of logic.
When I was an undergrad, my advisor was a population geneticist. At a lab meeting, I asked him about two different standard takes that didn't seem to go together. He just did some handwaving and said 'that's a miracle, isn't it!' Later, one of the grad students came to me and told me he had recognized what had happened. It felt good that I wasn't the only one disappointed by the answer. Don't tell me it's a miracle - explain it to me!
ABSTRACT Taiwan is known as the homeland of the Austronesian-speaking groups, yet other populations already had lived here since the Pleistocene. Conventional notions have postulated that the Palaeolithic hunter-gatherers were replaced or absorbed into the Neolithic Austronesian farming communities. Yet, some evidence has indicated that sparse numbers of non-Austronesian individuals continued to live in the remote mountains as late as the 1800s. The cranial morphometric study of human skeletal remains unearthed from the Xiaoma Caves in eastern Taiwan, for the first time, validates the prior existence of small stature hunter-gatherers 6000 years ago in the preceramic phase. This female individual shared remarkable cranial affinities and small stature characteristics with the Indigenous Southeast Asians, particularly the Negritos in northern Luzon. This study solves the several-hundred-years-old mysteries of ‘little black people’ legends in Formosan Austronesian tribes and brings insights into the broader prehistory of Southeast Asia.https://www.tandfonline.com/doi/full/10.1080/00438243.2022.21213156
@Ryan I always did it the hard way, even if it took me forever to do it. But since I was self-instructed in most of the topics, I wasn't under pressure to do it at a particular pace.
5 comments:
This is literally how I passed 4 different courses (Linear Algebra, Differential Equations, Thermodynamics and Statistics). I was in the research focused engineering stream at UofT, so our courses were heavy on proofs. Whenever I had to do one I'd work towards the middle from the top and bottom simultaneously. Often I couldn't quite complete the proof, but the missing step was in the middle somewhere so it looked like I just made a poorly explained leap of logic.
When I was an undergrad, my advisor was a population geneticist. At a lab meeting, I asked him about two different standard takes that didn't seem to go together. He just did some handwaving and said 'that's a miracle, isn't it!' Later, one of the grad students came to me and told me he had recognized what had happened. It felt good that I wasn't the only one disappointed by the answer. Don't tell me it's a miracle - explain it to me!
OT: Negritos in Taiwan
ABSTRACT
Taiwan is known as the homeland of the Austronesian-speaking groups, yet other populations already had lived here since the Pleistocene. Conventional notions have postulated that the Palaeolithic hunter-gatherers were replaced or absorbed into the Neolithic Austronesian farming communities. Yet, some evidence has indicated that sparse numbers of non-Austronesian individuals continued to live in the remote mountains as late as the 1800s. The cranial morphometric study of human skeletal remains unearthed from the Xiaoma Caves in eastern Taiwan, for the first time, validates the prior existence of small stature hunter-gatherers 6000 years ago in the preceramic phase. This female individual shared remarkable cranial affinities and small stature characteristics with the Indigenous Southeast Asians, particularly the Negritos in northern Luzon. This study solves the several-hundred-years-old mysteries of ‘little black people’ legends in Formosan Austronesian tribes and brings insights into the broader prehistory of Southeast Asia.https://www.tandfonline.com/doi/full/10.1080/00438243.2022.21213156
@DDeden Good catch. Interesting paper.
@Ryan I always did it the hard way, even if it took me forever to do it. But since I was self-instructed in most of the topics, I wasn't under pressure to do it at a particular pace.
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