1162: Log Scale - Revision history

2A05:6E02:1113:D510:266E:EAC1:CF84:CC60: /* Explanation */ updated broken wikia.org links to fandom.com

2026-02-18T08:52:57Z

‎Explanation: updated broken wikia.org links to fandom.com

DollarStoreBa'al at 12:59, 12 May 2025

2025-05-12T12:59:02Z

FaviFake: added Category:Comics featuring real people using HotCat

2025-05-11T10:11:03Z

added Category:Comics featuring real people using HotCat

FaviFake at 09:50, 11 May 2025

2025-05-11T09:50:14Z

FaviFake: /* Explanation */

2025-05-11T09:48:12Z

‎Explanation

FaviFake: /* Explanation */

2025-05-11T09:47:46Z

‎Explanation

FaviFake: added Category:Comics featuring Donald Knuth using HotCat

2025-05-11T09:47:04Z

added Category:Comics featuring Donald Knuth using HotCat

FaviFake: Fixed broken link (was a redirect)

2023-05-22T10:20:34Z

Fixed broken link (was a redirect)

172.70.127.53: Q>1 Nuclear Fusion now possible !!!

2022-12-15T20:54:21Z

Q>1 Nuclear Fusion now possible !!!

Theusaf: Reverted edits by Donald Trump (talk) to last revision by CRLF

2022-05-26T20:00:39Z

Reverted edits by Donald Trump (talk) to last revision by CRLF

Show changes

@@ Line 17: / Line 17: @@
 The log scale can also be abused to make data look more uniform than it really is. On a log scale the energy density of uranium looks larger than that of the other materials, but not dramatically so. The joke is that if one wanted to make their point "properly," they would go ahead and use ridiculous amounts of paper to show the difference between bars using a linear scale; this method would focus more on the shock factor of the differences in question, and less on actual communication/representation of data. Cueball seems to be passionate about the MJ/kg of uranium, so he would rather demonstrate the grandeur of the data than use a more efficient scale. See {{w|Logarithmic scale#Common uses|these examples}} for well known day-to-day measurements which are measured on a log-scale.
-The title text mentions computer scientist [[Donald Knuth]]; the fictional notation is a parody of {{w|Knuth's up-arrow notation}}. Using paper thickness as the basis for a log scale would probably give the exponential function a very large base. However, it can be noted that Knuth's up-arrow notation can handle numbers far, far larger than this paper stack notation; for example the number 3↑↑↑3, also known as [https://googology.wikia.org/wiki/Tritri Tritri], very compact in up-arrow notation, would require a number of iterations pinned to the stack on the order of several trillion. 3↑↑↑↑3 , also known as [https://googology.wikia.org/wiki/Grahal Grahal], would require a number of iterations that is not only too large to write down, but attempting to write that number using the same paper stack notation would require printing off a ''second'' stack of several trillion iterations just to hold the ''number'' pinned to the first stack. By repeating this multi-stack repetition, you reach the limit of up-arrow notation.
+The title text mentions computer scientist [[Donald Knuth]]; the fictional notation is a parody of {{w|Knuth's up-arrow notation}}. Using paper thickness as the basis for a log scale would probably give the exponential function a very large base. However, it can be noted that Knuth's up-arrow notation can handle numbers far, far larger than this paper stack notation; for example the number 3↑↑↑3, also known as [https://googology.fandom.com/wiki/Tritri Tritri], very compact in up-arrow notation, would require a number of iterations pinned to the stack on the order of several trillion. 3↑↑↑↑3 , also known as [https://googology.fandom.com/wiki/Grahal Grahal], would require a number of iterations that is not only too large to write down, but attempting to write that number using the same paper stack notation would require printing off a ''second'' stack of several trillion iterations just to hold the ''number'' pinned to the first stack. By repeating this multi-stack repetition, you reach the limit of up-arrow notation.
 ==Transcript==

@@ Line 17: / Line 17: @@
 The log scale can also be abused to make data look more uniform than it really is. On a log scale the energy density of uranium looks larger than that of the other materials, but not dramatically so. The joke is that if one wanted to make their point "properly," they would go ahead and use ridiculous amounts of paper to show the difference between bars using a linear scale; this method would focus more on the shock factor of the differences in question, and less on actual communication/representation of data. Cueball seems to be passionate about the MJ/kg of uranium, so he would rather demonstrate the grandeur of the data than use a more efficient scale. See {{w|Logarithmic scale#Common uses|these examples}} for well known day-to-day measurements which are measured on a log-scale.
-The title text mentions computer scientist [[Donald Knuth]]; the fictional notation is a parody of {{w|Knuth's up-arrow notation}}. Using paper thickness as the basis for a log scale would probably give the exponential function a very large base. However, it can be noted that Knuth's up-arrow notation can handle numbers far, far larger than this paper stack notation; for example the number 3↑↑↑3, also known as Tritri<ref>https://googology.wikia.org/wiki/Tritri</ref>, very compact in up-arrow notation, would require a number of iterations pinned to the stack on the order of several trillion. 3↑↑↑↑3 , also known as Grahal<ref> https://googology.wikia.org/wiki/Grahal </ref>, would require a number of iterations that is not only too large to write down, but attempting to write that number using the same paper stack notation would require printing off a ''second'' stack of several trillion iterations just to hold the ''number'' pinned to the first stack. By repeating this multi-stack repetition, you reach the limit of up-arrow notation.
+The title text mentions computer scientist [[Donald Knuth]]; the fictional notation is a parody of {{w|Knuth's up-arrow notation}}. Using paper thickness as the basis for a log scale would probably give the exponential function a very large base. However, it can be noted that Knuth's up-arrow notation can handle numbers far, far larger than this paper stack notation; for example the number 3↑↑↑3, also known as [https://googology.wikia.org/wiki/Tritri Tritri], very compact in up-arrow notation, would require a number of iterations pinned to the stack on the order of several trillion. 3↑↑↑↑3 , also known as [https://googology.wikia.org/wiki/Grahal Grahal], would require a number of iterations that is not only too large to write down, but attempting to write that number using the same paper stack notation would require printing off a ''second'' stack of several trillion iterations just to hold the ''number'' pinned to the first stack. By repeating this multi-stack repetition, you reach the limit of up-arrow notation.
 ==Transcript==
@@ Line 32: / Line 32: @@
 ==Trivia==
 This comic was seen in the ''[[What If? (book)|What If?]]'' book, taken from "a certain webcomic".
 {{comic discussion}}

← Older revision		Revision as of 10:11, 11 May 2025
Line 44:		Line 44:
	[[Category:Science tip]]		[[Category:Science tip]]
	[[Category:Comics featuring Donald Knuth]]		[[Category:Comics featuring Donald Knuth]]
		+	[[Category:Comics featuring real people]]

@@ Line 32: / Line 32: @@
 ==Trivia==
 This comic was seen in the ''[[What If? (book)|What If?]]'' book, taken from "a certain webcomic".
 {{comic discussion}}
 [[Category:Comics featuring Cueball]]
 [[Category:Bar charts]]
@@ Line 40: / Line 44: @@
 [[Category:Science tip]]
 [[Category:Comics featuring Donald Knuth]]

@@ Line 13: / Line 13: @@
 A {{w|Logarithmic scale|log scale}} is a way of showing largely unequal data sizes in a comprehensible way, using an exponential function between each notch on the y axis of a graph. So for example the first on a Y axis of a graph using a log-10-scale would be 1, then 10, then 100 and 1000 for the fourth. A {{w|logarithm|log/logarithmic function}} is the {{w|inverse function|inverse}} of a corresponding {{w|Exponential growth|exponential function}}.
-[[File:Log_Chart_1162.png|500px|thumb|right|A log-scale version of the chart in the comic.]]
+[[File:Log_Chart_1162.png|400px|thumb|right|A log-scale version of the chart in the comic.]]
-The log scale can also be abused to make data look more uniform than it really is. On a log scale the energy density of uranium looks larger than that of the other materials, but not dramatically so. The joke is that if one wanted to make their point "properly," they would go ahead and use ridiculous amounts of paper to show the difference between bars using a linear scale; this method would focus more on the shock factor of the differences in question, and less on actual communication/representation of data. Cueball seems to be passionate about the MJ/kg of uranium, so he would rather demonstrate the grandeur of the data than use a more efficient scale.
+The log scale can also be abused to make data look more uniform than it really is. On a log scale the energy density of uranium looks larger than that of the other materials, but not dramatically so. The joke is that if one wanted to make their point "properly," they would go ahead and use ridiculous amounts of paper to show the difference between bars using a linear scale; this method would focus more on the shock factor of the differences in question, and less on actual communication/representation of data. Cueball seems to be passionate about the MJ/kg of uranium, so he would rather demonstrate the grandeur of the data than use a more efficient scale. See {{w|Logarithmic scale#Common uses|these examples}} for well known day-to-day measurements which are measured on a log-scale.
 The title text mentions computer scientist [[Donald Knuth]]; the fictional notation is a parody of {{w|Knuth's up-arrow notation}}. Using paper thickness as the basis for a log scale would probably give the exponential function a very large base. However, it can be noted that Knuth's up-arrow notation can handle numbers far, far larger than this paper stack notation; for example the number 3↑↑↑3, also known as Tritri<ref>https://googology.wikia.org/wiki/Tritri</ref>, very compact in up-arrow notation, would require a number of iterations pinned to the stack on the order of several trillion. 3↑↑↑↑3 , also known as Grahal<ref> https://googology.wikia.org/wiki/Grahal </ref>, would require a number of iterations that is not only too large to write down, but attempting to write that number using the same paper stack notation would require printing off a ''second'' stack of several trillion iterations just to hold the ''number'' pinned to the first stack. By repeating this multi-stack repetition, you reach the limit of up-arrow notation.
 ==Transcript==

@@ Line 8: / Line 8: @@
 ==Explanation==
 This comic is a [[:Category:Tips|tip]], specifically the first [[:Category:Science tip|''science'' tip]]. As with most of Randall's tips, it is technically interesting for some applications but not very practical. Uranium is stated to have 76 million MJ/kg, while the next highest material shown on the graph (gasoline) has 46 MJ/kg. Thus the uranium graph should be taller by a factor of 76,000,000/46 = 1.652 million. So, if the gasoline graph were 9mm in height, the uranium graph should be a bit more than 14.868 million mm tall, or nearly 15&nbsp;km (9.2 miles) tall. Thus the need to fold the paper.
 It should be noted that the method of extracting energy from the first 4 materials ({{w|combustion}}) is completely different from the method used with uranium ({{w|nuclear fission}}). If the technology existed to use {{w|nuclear fusion}} at the time of the comic, then the first 4 materials would yield a higher energy density than uranium.
-A {{w|Logarithmic scale|log scale}} is a way of showing largely unequal data sizes in a comprehensible way, using an exponential function between each notch on the y axis of a graph. So for example the first on a Y axis of a graph using a log-10-scale would be 1, then 10, then 100 and 1000 for the fourth. A {{w|logarithm|log/logarithmic function}} is the {{w|inverse function|inverse}} of a corresponding {{w|Exponential growth|exponential function}}. A log-scale version of the chart in the comic would look like this:
+A {{w|Logarithmic scale|log scale}} is a way of showing largely unequal data sizes in a comprehensible way, using an exponential function between each notch on the y axis of a graph. So for example the first on a Y axis of a graph using a log-10-scale would be 1, then 10, then 100 and 1000 for the fourth. A {{w|logarithm|log/logarithmic function}} is the {{w|inverse function|inverse}} of a corresponding {{w|Exponential growth|exponential function}}. A log-scale version of the chart in the comic would look like the image on the left.
-[[File:Log_Chart_1162.png | 600px]]
+[[File:Log_Chart_1162.png|500px|thumb|right]]
 The log scale can also be abused to make data look more uniform than it really is. On a log scale the energy density of uranium looks larger than that of the other materials, but not dramatically so. The joke is that if one wanted to make their point "properly," they would go ahead and use ridiculous amounts of paper to show the difference between bars using a linear scale; this method would focus more on the shock factor of the differences in question, and less on actual communication/representation of data. Cueball seems to be passionate about the MJ/kg of uranium, so he would rather demonstrate the grandeur of the data than use a more efficient scale.
@@ Line 23: / Line 20: @@
 See {{w|Logarithmic scale#Common uses|these examples}} for well known day-to-day measurements which are measured on a log-scale.
-The title text mentions computer scientist {{w|Donald Knuth}}; the fictional notation is a parody of {{w|Knuth's up-arrow notation}}. Using paper thickness as the basis for a log scale would probably give the exponential function a very large base. However, it can be noted that Knuth's up-arrow notation can handle numbers far, far larger than this paper stack notation; for example the number 3↑↑↑3, also known as Tritri<ref>https://googology.wikia.org/wiki/Tritri</ref>, very compact in up-arrow notation, would require a number of iterations pinned to the stack on the order of several trillion. 3↑↑↑↑3 , also known as Grahal<ref> https://googology.wikia.org/wiki/Grahal </ref>, would require a number of iterations that is not only too large to write down, but attempting to write that number using the same paper stack notation would require printing off a ''second'' stack of several trillion iterations just to hold the ''number'' pinned to the first stack. By repeating this multi-stack repetition, you reach the limit of up-arrow notation.
+The title text mentions computer scientist [[Donald Knuth]]; the fictional notation is a parody of {{w|Knuth's up-arrow notation}}. Using paper thickness as the basis for a log scale would probably give the exponential function a very large base. However, it can be noted that Knuth's up-arrow notation can handle numbers far, far larger than this paper stack notation; for example the number 3↑↑↑3, also known as Tritri<ref>https://googology.wikia.org/wiki/Tritri</ref>, very compact in up-arrow notation, would require a number of iterations pinned to the stack on the order of several trillion. 3↑↑↑↑3 , also known as Grahal<ref> https://googology.wikia.org/wiki/Grahal </ref>, would require a number of iterations that is not only too large to write down, but attempting to write that number using the same paper stack notation would require printing off a ''second'' stack of several trillion iterations just to hold the ''number'' pinned to the first stack. By repeating this multi-stack repetition, you reach the limit of up-arrow notation.
 It should be noted that Randall has used log scales in past comics.
@@ Line 47: / Line 44: @@
 [[Category:Statistics]]
 [[Category:Science tip]]
 <references />