tag:blogger.com,1999:blog-3748625510348961342.post227290203417290703..comments2019-06-19T22:14:58.550-07:00Comments on solidangl.es: A Radical New Look for LogarithmsBill Shillitohttp://www.blogger.com/profile/17774101901445053590noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-3748625510348961342.post-71229539446451021142019-06-13T15:04:35.784-07:002019-06-13T15:04:35.784-07:00Lampung
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I came up with some really nice LaTeX code for it:<br />\raisebox{\depth}{\scalebox{1}[-1]{$\sqrt[\raisebox{\depth}{\scalebox{1}[-1]{\tiny{2}}}]{\raisebox{\depth}{\scalebox{1}[-1]{16}}}$}}Iyan Siwikhttps://www.blogger.com/profile/06005006477287388259noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-1012266931130571012017-12-21T13:23:08.447-08:002017-12-21T13:23:08.447-08:00I love your symbol, and will start using it next s...I love your symbol, and will start using it next semester. I made a bit of Latex code for "log base 2 of 8": \raisebox{.7mm}{\reflectbox{\rotatebox[origin=c]{180}{\Large{$\sqrt{~~}$}}}}$\hspace{-.6cm}{\mbox{\tiny 2}}\hspace{.2cm} 8$<br /><br />To see the compiled image: https://drive.google.com/file/d/1zYqnIFDfsrO-MMQCjI09m_rwmQhqIUfj/view?usp=sharingLynne Ipiñahttps://www.blogger.com/profile/02298838629222120903noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-29002947766656199212017-11-29T19:13:05.351-08:002017-11-29T19:13:05.351-08:00I'm not sure any computer scientist would cons...I'm not sure any computer scientist would consider it more natural than e, it's just useful for many purposes.J Carrhttps://www.blogger.com/profile/03209130188845063324noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-48773914876427939792016-06-29T21:41:36.795-07:002016-06-29T21:41:36.795-07:00Why stopping at the + x exp relation, why not keep...Why stopping at the + x exp relation, why not keep going the pattern with the relations due the Conway chained arrow notation? With these simple relations, computation of the V of parallel wires was obtained, it was something nice! Maybe something deeper may happen if the system is generalized.Daniel de França MTd2https://www.blogger.com/profile/01281817409696805377noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-18584089043896129122015-05-20T14:16:29.116-07:002015-05-20T14:16:29.116-07:00A computer scientist might argue "2" is ...A computer scientist might argue "2" is the "natural" logarithm base (anything binary). <br /><br />PS: damn this commenting system is weird.Victor Hernandeshttps://www.blogger.com/profile/00064218464586434649noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-66242648144597530652015-04-29T18:21:13.317-07:002015-04-29T18:21:13.317-07:00Interesting idea, but I'm not at all a fan of ...Interesting idea, but I'm not at all a fan of that "visual cancellation rule" as phrased. There's no real mathematical reason behind it - it's all smoke and mirrors, which is pedagogically dangerous. You're relying on the "b^\b^" resembling a fraction that "cancels" to be 1, after which a multiplication sign magically appears next to the exponent. Math should be logical, not magical. Cancelling things is ubiquitous, sure, but you have to know *why* it works.<br /><br />That being said, I would be interested in seeing a linear form of the radical symbol and my reflected version of it.Bill Shillitohttps://www.blogger.com/profile/17774101901445053590noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-25252635717616844032015-04-29T17:42:35.800-07:002015-04-29T17:42:35.800-07:00Great idea. I had been searching for a notation t...Great idea. I had been searching for a notation that could be "typed" in linear text form. To that end, I had played around with combinations of the caret ^ and forward and reverse diagonals / \<br /><br />Given the linear notation for power:<br /><br />Power: b ^ e = p<br /><br />For root, I suggest the symbol ^/ (caret, slash):<br /><br /> p ^/ e = (b^e) ^/ e = b<br /><br />My root notation represents an "abbreviation" of the identity: e-th root of p equals p to the power 1/e,<br />that is: (b^e) ^/e represents (b^e) ^ (1/e) = b ^ (e * 1/e) = b ^ 1 = b<br /><br />But to get this advantage, I must reverse the order of base and power in the traditional notation.<br /><br />So, in similar vein, your log symbol could be represented by the symbol: ^\ (caret, back-slash):<br /><br />log: logb(p) = b ^\ p = b^\ (b^e) = e<br /><br />This is suggestive of a "visual cancellation rule" <br />b^\ (b^ e) "equals" ( b^ \ b^) e "equals" 1 * e = e.Joseph Austinhttps://www.blogger.com/profile/11397759210330425019noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-40938453703237601762015-04-28T16:50:42.594-07:002015-04-28T16:50:42.594-07:00My only problem with the new notation stems from t...My only problem with the new notation stems from the laziness of the writer. Since 2 is the most natural root and e is the most natural base for logarithms, we don't bother writing the 2 when we take the square root or writing the e when we take logarithm base e (whether you denote this as log or ln is a matter of preference). It wouldn't make sense to compromise on which should be considered natural for both notations since the e^th root doesn't naturally come up and log base 2 doesn't come up much (except maybe in computer applications). I could see how there would be confusion as to why leaving the number off when the sign is in one direction implies something different than leaving the number off when the sign is in the other direction.<br /><br />That said, I like this idea and think the advantages that you explained outweigh this disadvantage.Robert Williamshttps://www.blogger.com/profile/08525366375056584669noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-78115844630824381482015-04-27T18:59:55.327-07:002015-04-27T18:59:55.327-07:00"literally pointing to the part we're loo..."literally pointing to the part we're looking for in the corresponding exponential expression"<br /><br />Yes, yes, and again yes! This is exactly what I meant. Glad to see that others are understanding why I chose this notation.<br /><br />If you feel this should be a thing, please share it with whoever you think may be interested!Bill Shillitohttps://www.blogger.com/profile/17774101901445053590noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-17144656494600205202015-04-27T13:43:00.100-07:002015-04-27T13:43:00.100-07:00am completely on board with this proposal. I never... am completely on board with this proposal. I never liked log or ln. I always have to remind myself what they mean when I see them.<br /><br />In light of Shillito's proposal, I think I understand why: <br /><br />We have this intuitive difference between procedures that are operations and procedures that are functions. Or maybe not even a merely intuitive difference? PEMDAS, after all, is a thing even if the E should really be expanded to include roots and logs.<br /><br />Yes, we could denote everything with functions. add(3,mul(6,9)) = 57. But we don't, do we? We all know how inefficient that would be, and how much it would obscure the algebraic manipulations we do all the time.<br /><br />No. We recognize EMDAS, specifically, as operations and assign them unique notational forms which help us to perform the manipulations we need to do.<br /><br />And note that these operations come in pairs. Plus has minus. Both operations, denoted with symbols that catenate their arguments. Multiplication has division, which likewise have nicely symbolic forms. Exponentiation uses an intuitive placement of arguments to convey its sense, but still, a semantically meaningful way of writing the arguments.<br /><br />Exponentiation is a little odd, though, in that its two arguments do not have equal relationships to one another. Their roles are fundamentally different. Thus, exponentiation has two inverses: taking roots, and finding logarithms.<br /><br />Why, then, do roots get an operator representation, while logs are written with what amounts to functional notation? There's not a lot of representational daylight between log_2(x) and sin(x).<br /><br />So yeah. I'm all for an operator representation for logs, especially one that so nicely mirrors the one for roots and at the same time helps people remember what each one does by literally pointing to the part we're looking for in the corresponding exponential expression.<br />Jason Blackhttps://www.blogger.com/profile/08181267035103592296noreply@blogger.com