tag:blogger.com,1999:blog-6789188.post7033917786944634467..comments2024-03-27T17:15:37.606-04:00Comments on Triablogue: Apollo 11 mission patchRyanhttp://www.blogger.com/profile/17809283662428917799noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-6789188.post-68766357436836510782019-07-22T11:20:22.087-04:002019-07-22T11:20:22.087-04:00"However, if he had said "There are more..."However, if he had said "There are more transcendental numbers than rational numbers" he would have been correct--rational numbers are countably infinite, but transcendental numbers are uncountably infinite.""<br /><br />Exactly! NdGT failed to grasp the distinction between transcendental numbers and non-transcendental (algebraic) numbers. The former are uncountably infinite, while the latter are countably infinite.Hawkhttps://www.blogger.com/profile/01142879704651632453noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-76372987591176323472019-07-22T11:15:26.134-04:002019-07-22T11:15:26.134-04:00NdGT's sole defense: black science man. :)NdGT's sole defense: <a href="https://i.imgur.com/KtSt8JV.jpg" rel="nofollow">black science man</a>. :)Hawkhttps://www.blogger.com/profile/01142879704651632453noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-15496787945949746652019-07-22T10:46:07.420-04:002019-07-22T10:46:07.420-04:00Hawk said:
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To be fair, NdGT stated that there ...Hawk said:<br />---<br />To be fair, NdGT stated that there are more transcendental numbers than irrational numbers to Joe Rogan. That's false. Both are uncountably infinite.<br />---<br /><br />His quote from Dazed and Confused Magazine is even worse. Here's what he said:<br /><br />---<br />You know how numbers, you can count them forever? Well how about fractions? The infinity of fractions is bigger than the infinity of numbers; and then there are transcendental numbers, like Pi. There are more transcendental numbers than pure irrational numbers, and there are more irrational numbers than counting numbers. And more fractions than all of them. <br />---<br /><br />1. "The infinity of fractions is bigger than the infinity of numbers" <-- assuming "numbers" means "counting numbers" here, and "fractions" means rational numbers, that's clearly false. Both fractions and counting numbers are countably infinite so are equivalent infinities. If instead he is taking "fractions" to include non-integer ratios, like dividing pi by the square root of 2, then what he says is *ALSO* wrong because then a "fraction" isn't defining a number but a mathematical operation.<br /><br />2. "There are more transcendental numbers than pure irrational numbers". "Pure" irrational numbers aren't a thing, so I have no clue what he means by that. Also, *all* transcendental numbers are irrational because they cannot be expressed as a ratio of two integers, but not all irrational numbers are transcendental. (E.g., the square root of two can be expressed as the root of a non-zero polynomial, which makes it an algebraic number, and therefore not transcendental, yet it is clearly irrational.) It's literally impossible for there to be more transcendental numbers than irrational numbers given that transcendental numbers are a sub-set of the irrational numbers. However, if he had said "There are more transcendental numbers than rational numbers" he would have been correct--rational numbers are countably infinite, but transcendental numbers are uncountably infinite.<br /><br />3. "and there are more irrational numbers than counting numbers" <-- finally something correct!<br /><br />4. "And more fractions than all of them." <-- only to be destroyed by this. Again, it's either wrong because the fractions as rational numbers is a countable infinity, or he's wrong because fractions as mathematical operations are not numbers.Peter Pikehttps://www.blogger.com/profile/11792036365040378473noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-56130468773777577882019-07-21T22:33:09.547-04:002019-07-21T22:33:09.547-04:00I think you can watch it on Amazon Prime here. How...I think you can watch it on Amazon Prime <a href="https://www.amazon.com/Apollo-11-Todd-Douglas-Miller/dp/B07RDY2QF1" rel="nofollow">here</a>. However, it's definitely worth watching on blu-ray in a nice home theater if possible. It's such a beautiful film. I don't think I've ever seen a documentary with such well restored footage. I've heard Peter Jackson's documentary on WW1 <i>They Shall Not Grow Old</i> is excellent in that regard too, but I haven't seen it.Hawkhttps://www.blogger.com/profile/01142879704651632453noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-87817901761500629892019-07-21T22:26:36.343-04:002019-07-21T22:26:36.343-04:00By the way, I don't think NdGT is even all tha...By the way, I don't think NdGT is even all that great when it comes to physics. He gets things wrong that he shouldn't as someone with a PhD in physics or astrophysics. For example, here's <a href="http://hopsblog-hop.blogspot.com/2016/01/fact-checking-neil-degrasse-tyson.html" rel="nofollow">a list of his flubs</a>.<br /><br />To be fair, NdGT stated that there are more transcendental numbers than irrational numbers to Joe Rogan. That's false. Both are uncountably infinite. However, I guess NdGT could say he's not a mathematician, but at the very least shouldn't he have said "I don't know because math isn't my expertise"? This illustrates another problem with NdGT: he is rarely modest about what he knows and what he doesn't know. He often acts like he knows everything. Even though in other contexts he will say people should be humble about what they don't know. Hawkhttps://www.blogger.com/profile/01142879704651632453noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-43581820440306269112019-07-21T22:18:20.596-04:002019-07-21T22:18:20.596-04:00NdGT reminds me of this cartoon:
http://www.smbc-...NdGT reminds me of this cartoon:<br /><br />http://www.smbc-comics.com/comic/2012-03-21<br />Hawkhttps://www.blogger.com/profile/01142879704651632453noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-36971789690147694862019-07-21T19:15:44.702-04:002019-07-21T19:15:44.702-04:00I think NDT should stick to astronomy. The stupidi...I think NDT should stick to astronomy. The stupidity of this tweet incapsulates a powerful argument against free-speech.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6789188.post-26835469343437674432019-07-21T16:05:48.913-04:002019-07-21T16:05:48.913-04:00Hawk, I missed that one. I wish I had seen it. May...Hawk, I missed that one. I wish I had seen it. Maybe it’ll come out on DVD or something. John Bugayhttps://www.blogger.com/profile/17728044301053738095noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-84364209396118542412019-07-21T14:39:49.812-04:002019-07-21T14:39:49.812-04:00Thanks, John. I’ll take a look!
Have you seen th...Thanks, John. I’ll take a look! <br /><br />Have you seen the recent documentary Apollo 11:<br /><br />https://en.wikipedia.org/wiki/Apollo_11_(2019_film)<br /><br />It has sharp, clear, gorgeous footage. Beautiful cinematography. It was the best documentary I’ve ever seen of Apollo 11. Whoever restored the footage deserves an Oscar. It looks and feels as if you’re right beside the astronauts. Hawkhttps://www.blogger.com/profile/01142879704651632453noreply@blogger.comtag:blogger.com,1999:blog-6789188.post-27252114159436897792019-07-21T14:03:18.643-04:002019-07-21T14:03:18.643-04:00This is probably the best video that I’ve seen of ...This is probably the best video that I’ve seen of the Apollo 11 moon walk. Start at about 18:00: https://youtu.be/iR3oXFFISI0 John Bugayhttps://www.blogger.com/profile/17728044301053738095noreply@blogger.com