I recently made the mistake of commenting on a post over at NewsBusters. I asked for someone to provide evidence for a statement they made and provided links to PolitiFact.com and FactCheck.org articles indicating that their statement was false. It turned out that they were making a more general comment than I was refuting with my links, but the initial reaction of the individual was to call me a jerk and question my intelligence. Other responders accused PolitiFact and FactCheck of being liberally biased or accused me of being someone who I assume was kicked off the forums in the past.
I spent a good two hours researching my responses to everything, which probably doesn't surprise anyone who has read some of my past entries, especially this one. No one else did much in the way of research that I could see. They spent most of their time calling each other names, insulting various people's intelligences, and/or making vague statements and insisting that they are obviously true. It was quite maddening. However, this got me thinking about how to improve the system.
It seems to me that the entire situation, or at least my involvement in it, could have been avoided if the original statement in question had been backed up with evidence to begin with. And wouldn't it be nice if every forum post was thoroughly evidenced? When it takes half an hour to research a response, it is very unlikely that you'll make said response include a personal attack. Why is that? Because it wouldn't fit in with the tone of a research paper. The other forum members would have also spent half an hour researching each of their comments, so there would be a shared experience and the understanding and empathy that goes along with that. Finally, it's very difficult to sustain anger for thirty minutes of reading about policy. Thus, I think the discourse would start, and remain, civil.
Then, with all these informative links being included, perhaps something could get resolved. First, the validity of various links and/or the arguments therein could be established. One pattern that would emerge pretty quickly is that people bring up the same articles as evidence over and over again. Some would be agreed to be accurate, and others would be shown to be flawed. The forum could be tied to a database of links and their truthiness rating. The comments would then have the links color coded using some well-established and meaningful color code. The only problem remaining is how to decide on the truthfulness of the links. Which, of course, is a huge problem, as evidenced by people dismissing PolitiFact and FactCheck as biased. (I am not saying for certain that they aren't, but no one has yet shown me solid evidence that they are.)
So, anyone have any other ideas on how to keep online political (or other) discussion civil and informative? Perhaps more importantly, does anyone have any idea on how we can at least agree on the facts?
Showing posts with label facts. Show all posts
Showing posts with label facts. Show all posts
Friday, December 17, 2010
Political Forum Civility
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Monday, October 25, 2010
Biblical Analysis: Samson's Death
25 While they were in high spirits, they shouted, "Bring out Samson to entertain us." So they called Samson out of the prison, and he performed for them.
When they stood him among the pillars, 26 Samson said to the servant who held his hand, "Put me where I can feel the pillars that support the temple, so that I may lean against them." 27 Now the temple was crowded with men and women; all the rulers of the Philistines were there, and on the roof were about three thousand men and women watching Samson perform. 28 Then Samson prayed to the LORD, "O Sovereign LORD, remember me. O God, please strengthen me just once more, and let me with one blow get revenge on the Philistines for my two eyes." 29 Then Samson reached toward the two central pillars on which the temple stood. Bracing himself against them, his right hand on the one and his left hand on the other, 30 Samson said, "Let me die with the Philistines!" Then he pushed with all his might, and down came the temple on the rulers and all the people in it. Thus he killed many more when he died than while he lived. Judges 16: 25-30
I don't think I've ever seen two structural pillars close enough for a single person to put a hand on both at the same time. Consequently, the preceding passage has always made me wonder about the temple Samson died in. Especially after reading it as an adult: What kind of temple can hold three thousand people on the roof and still have two critical supports that close together? I figured someone out there had already done the research, what with it being in the Bible, and the Bible being the most popular book ever.
I wasn't disappointed. John Roskoski, PhD, seems to have written quite a bit on the subject. I first found his paper that describes the size of the temple, among other things. It was "26 feet wide by 47 feet long," according to Dr. B.G. Wood, as quoted by Roskoski. "The pillars would be within the reach of Samson, a huge man according to most scholars, as they were situated approximately six feet apart." This is based on the excavation of Tell Qasile, which is believed to be very similar to the temple in Gaza. With that question somewhat answered, I moved on to the three thousand people on the roof. A roof that is definitely too small for three thousand people.
John Roskoski's article on Samson's death addressed the number of people in the section appropriately titled "How Many People?"
The Hebrew term ‘elep represents the numeral 1,000. However, there are several specialized meanings attached to this term. One meaning is that the term represents the “largest basic division of leadership in political oversight or military leadership.” Also, “it is occasionally alleged that since ‘elep means a company of a thousand men it could mean any military unit, even of reduced strength” (Scott 1980: 48). Therefore, it seems as though the text is referring to three distinct contingencies that were in attendance, in addition to the followers of Dagon who filled the temple.I have no way of really evaluating the information in that section. For now, I will accept it as it is. I will say that it doesn't strike me as a particularly strong argument, though. It seems odd to have to use some specialized meaning of a word in order for it to make sense. We go from "three thousand men and women" to "three distinct contingencies." It seems rather vague.
For the record, my favorite fact comes from a footnote in the first paper by Roskoski: "The columns were wider at the top and tapered at the bottom, a result of inverting the cypress trunk so to prevent sprouting once in place." I had no idea that was a problem, and I love the mental image that comes to mind when imagining some engineer encountering that problem for the first time.
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Friday, October 8, 2010
Health Care Reform: Federal Funding of Abortions
I realize I'm a bit late to this party, but while researching for another blog post, I read this article accusing Maddow of lying about abortion funding over at NewsBusters.
So, Rachel Maddow was much more correct in her analysis than NewsBusters was. For those curious, current Federal abortion funding is based mostly on the Hyde Amendment. This allowed federal funding for abortions only in the case of rape, incest, or life endangerment. Others, more credible than I, have also verified that the health reform legislation did not increase federal funding of abortion.
Count me as a fan of the cite-the-page-numbers trick as well. I'm especially enamored of what's in the section of the Senate health bill immediately preceding the one cited by Maddow (follow this link for the bill; see page 2,071) The section is titled as follows, with capitalized letters in the original -- "ABORTIONS FOR WHICH PUBLIC FUNDING IS ALLOWED".I went ahead and visited the pdf link and went to page 2070-2071:
As in, public funding for abortions. Once again, a la Maddow -- public funding for abortions. A third time, in case she still misses it -- P-U-B-L-I-C F-U-N-D-I-N-G F-O-R A-B-O-R-T-I-O-N-S.
Gee, where would Congressman Stupak get that impression?
Who knows, maybe the section cited by Maddow trumps the one I'm referring to. The bill is written in such dense legalese that only high clergy of the courts would be able to decipher it and they wouldn't agree on the language either. [emphasis removed because copy/and paste doesn't keep boldness and I didn't want to add "[emphasis in original]" editor's notes]
(A) IN GENERAL. — Notwithstanding any other provision of this title (or any amendment made by this title) —I'm not a "high clergy of the court" but I think I deciphered it without much trouble. Paragraph (A)(i) states that abortion coverage is not required by any health plan. Paragraph (A)(ii) says that the plan issuer has the responsibility of determining what abortion coverage is included in the plan. This has consequences in the next section which describes how payment for such coverage must be separately accounted for such that no Federal funds are used for abortion coverage - unless specifically allowed. What does it mean for abortions to be allowed/prohibited from using Federal funds? That is described in the next two paragraphs. Rather, it is referenced in those paragraphs. This legislation does not alter the existing abortion funding laws. It just states that when determining how abortions are classified for funding purposes, the law as stated six months prior to the plan year shall be used. This gives time for lawyers to go over existing law, brochures to be printed and distributed, etc. It makes perfect sense to me.
(i) nothing in this title (or any amendment made by this title), shall be construed to require a qualified health plan to provide coverage of services described in subparagraph (B)(i) or (B)(ii) as part of its essential health benefits for any plan year; and
(ii) subject to subsection (a), the issuer of a qualified health plan shall determine whether or not the plan provides coverage of services described in subparagraph (B)(i) or (B)(ii) as part of such benefits for the plan year.
(B) ABORTION SERVICES.—
(i) ABORTIONS FOR WHICH PUBLIC FUNDING IS PROHIBITED.—
The services described in this clause are abortions for which the expenditure of Federal funds appropriated for the Department of Health and Human Services is not permitted, based on the law as in effect as of the date that is 6 months before the beginning of the plan year involved.
(ii) ABORTIONS FOR WHICH PUBLIC FUNDING IS ALLOWED.—
The services described in this clause are abortions for which the expenditure of Federal funds appropriated for the Department of Health and Human Services is permitted, based on the law as in effect as of the date that is 6 months before the beginning of the plan year involved.
So, Rachel Maddow was much more correct in her analysis than NewsBusters was. For those curious, current Federal abortion funding is based mostly on the Hyde Amendment. This allowed federal funding for abortions only in the case of rape, incest, or life endangerment. Others, more credible than I, have also verified that the health reform legislation did not increase federal funding of abortion.
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Wednesday, September 22, 2010
Looking For Conservative Facts
I like reading most of the articles on Media Matters for America. They have a nice format where they will outline the claim(s) of some conservative, then detail some facts in rebuttal. In addition to factual errors, they'll discuss biased reporting, misleading on-screen graphics, or anything else they take issue with. There is apparently enough misinformation out there for them to write several research articles and several blog posts a day.
The blog posts, incidentally, are less fun to read. They often use name calling in their arguments and are lighter on the facts. It's where the quicker and smaller updates happen, though, so I still give them a read most of the time.
Media Matters is definitely a liberal website. For example, almost all of their articles are debunking claims made on Fox News. I don't think this is a complete picture of the world. I'd really like to hear conservatives countering liberal reporting with supporting facts.
Unfortunately, I haven't been able to find those facts. The closest thing I've been able to find is the Media Research Center. Mostly, their articles are just reporting that some reporting was done, and we are supposed to recognize the liberal bias - somehow. They rarely counter with facts, which is a bit disappointing. There's also NewsBusters.org (a project of the Media Research Center), but that has the same problem of being light on facts.
Maybe that's just the way things are, currently. Perhaps liberals have facts to back up their positions - or at least tear down the opposition, and conservatives just complain that reporting they don't like is liberal. But there have to be some facts somewhere, right?
Amazingly enough, the best source I've found for "liberal-media" bashing is The Daily Show. However, most of their media bashing is showing the ridiculousness of the reporting and not usually an issue with the facts or arguments. Except when they cover Fox News.
FactCheck.org is useful in fact checking politicians, but they rarely cover the media directly, so they are usually only active around election time. They do an excellent job of remaining impartial, though. FiveThirtyEight does an excellent job of discussing political bias in polls, among other things, but this only helps indirectly. I know that Rasmussen tends to favor conservatives, so Fox News uses it a lot, but there aren't always matching polls from other institutions readily available to compare to.
Which is another problem entirely - facts themselves are often biased. People choose the poll with the results they want to report. Conservative think tanks will make certain assumptions in their studies to yield facts that support the conservative point of view. I imagine there are probably some liberal think tanks that are similarly biased in their studies, but there doesn't appear to be anyone calling them out on it. So, I humbly ask for help. Where do you go when you want to be informed (with facts) on the conservative side of things, and how can you trust those facts?
The blog posts, incidentally, are less fun to read. They often use name calling in their arguments and are lighter on the facts. It's where the quicker and smaller updates happen, though, so I still give them a read most of the time.
Media Matters is definitely a liberal website. For example, almost all of their articles are debunking claims made on Fox News. I don't think this is a complete picture of the world. I'd really like to hear conservatives countering liberal reporting with supporting facts.
Unfortunately, I haven't been able to find those facts. The closest thing I've been able to find is the Media Research Center. Mostly, their articles are just reporting that some reporting was done, and we are supposed to recognize the liberal bias - somehow. They rarely counter with facts, which is a bit disappointing. There's also NewsBusters.org (a project of the Media Research Center), but that has the same problem of being light on facts.
Maybe that's just the way things are, currently. Perhaps liberals have facts to back up their positions - or at least tear down the opposition, and conservatives just complain that reporting they don't like is liberal. But there have to be some facts somewhere, right?
Amazingly enough, the best source I've found for "liberal-media" bashing is The Daily Show. However, most of their media bashing is showing the ridiculousness of the reporting and not usually an issue with the facts or arguments. Except when they cover Fox News.
FactCheck.org is useful in fact checking politicians, but they rarely cover the media directly, so they are usually only active around election time. They do an excellent job of remaining impartial, though. FiveThirtyEight does an excellent job of discussing political bias in polls, among other things, but this only helps indirectly. I know that Rasmussen tends to favor conservatives, so Fox News uses it a lot, but there aren't always matching polls from other institutions readily available to compare to.
Which is another problem entirely - facts themselves are often biased. People choose the poll with the results they want to report. Conservative think tanks will make certain assumptions in their studies to yield facts that support the conservative point of view. I imagine there are probably some liberal think tanks that are similarly biased in their studies, but there doesn't appear to be anyone calling them out on it. So, I humbly ask for help. Where do you go when you want to be informed (with facts) on the conservative side of things, and how can you trust those facts?
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Friday, August 27, 2010
Thinking a Million Miles an Hour
The other day, someone said that they were thinking a million miles an hour. Naturally, this got me thinking about how fast they were really thinking, given all the various pulses traveling between all the various neurons. First, Google tells us that a million miles per hour is 670.616629 times slower than the speed of light. That's still pretty speedy. It's fast enough to take you around the world in 89.6447392 seconds, or get you to the sun in 3.87316198 days.
That's all well and good, but I really wanted to know: How fast do we think?
Unfortunately, I couldn't find the answer, or even enough solid information to compute an answer I was truly satisfied with. I will provide you with the best answer I can come up with, though. First, the relevant facts!
(Actually, facts [9] through [11] aren't particularly relevant, but I spent a lot of time reading about them so I forced you to spend a tiny bit of time reading about them, too. The speed of the pulses doesn't matter for our calculations - it's more than fast enough to cover the length between any two neurons in much less than a second.)
One problem with brain studies is that they tend to focus on specific parts of the brain. This makes it rather difficult to piece together whole-brain statistics. For example, [1] refers to the number of neurons in the entire brain, while [2] and [3] are talking about the length of axons in just the white matter - I think. [4] is at minimum related to the surrounding gray matter, but it's unclear if it includes any of the inner gray matter structures. Perhaps more importantly, the numbers vary considerably and are ambiguous as to exactly what they are measuring! [2] and [3] mention myelinated nerve fibers, which tends to be synonymous with axons, but the axon terminals aren't myelinated, so it's not 100% clear that they aren't included in this length measurement, or how long they would be otherwise. [5], [6], and [7] put the total length of dendrites per neuron at several centimeters, 0.9-1.9 cm, and 1.5-3.5 mm, respectively. Fact [8] gives an indication of where this difference comes from. Presumably, the length isn't tallied past a certain branching level, or below a minimum branch size, or something similar. [4] and [8] also indicate that the total length of all dendrites for a pyramidal neuron would be the sum of the two averages mentioned in [8], or ~11000 micrometers - again, not including the spines. In fact, the wording of [8] makes it unclear if that's total dendritic length for the cell, or for the single dendrite counting all its branches (up to a point). This uncertainty is frustrating, to say the least.
Neuron speeds vary, too, depending on the source. [9], [10], [11], and [12] give values between 10 and 120 m/s for myelinated axons, and between <1 and 30 m/s for unmyelinated fibers - dendrites and axon terminals? That's quite a range, but it isn't the only speed that varies. The frequency of the action potentials is reported as anywhere from 1Hz to 400Hz in [12] through [16], with a theoretical maximum of 1000Hz. So, what can we come up with using these ranges of numbers?
It turns out that we can be fairly pessimistic in our assumptions and still arrive at some staggering results. Let's take 150,000km of myelinated nerve fibers - the axons - and assume 10 impulses per second. 10 pulses seems to be a good compromise, given that we are thinking at a million miles an hour, not resting at a million miles an hour, but not all thinking would necessarily involve all portions of our brain. (That is not to say the myth about using only 3-10% of our brain is anything but a myth!) This alone gives us 150,000km * 10/s = 1,500,000,000 m/s ≈ 5 times the speed of light ≈ just shy of a million miles a second! And we've only included one half of the synapse structure!
Let's be fairly conservative about the total length of the dendrites and axon terminals and any other unaccounted for lengths, and use 19.3 billion as the number of cells with dendrites, discounting everything but the neocortex (fact [17]). We'll go with 7.75 mm of dendrites per cell, since I really don't know what the source behind fact [7] was talking about, and source [14], which didn't have a fact to quote because the length had to be calculated out of other data, indicates total dendrite length of around 1.1 cm, so we're nearing a consensus of 1 cm or more. Anyway, I chose 7.75mm because 7.75 mm * 19.3 billion = 149,575 km, which means we can just double our previous results! Over 10 times the speed of light! 1,864,113 miles per second! And these are conservative estimates (I hope)!
Just for fun, let's see how fast I think. My neurons easily fire 100 times per second. I thought really hard about it, and sure enough all 100 billion neurons in my brain often fire at that rate. It turns out that my brain isn't very conservative when it measures itself, which makes my total dendritic length per neuron around the proposed average of 1.1 cm instead of 0.775 cm. So, when I'm thinking really hard, my mind is racing at (150,000 km + 100 billion * 1.1 cm) * 100/s = 125,000,000,000 m/s ≈ 417 times the speed of light ≈ 77,671,399 miles per second. I actually wouldn't be terribly surprised if this is closer to the true average speed of thinking really hard. (Are there any neuroscience folks out there that want to provide some different numbers?)
It's not a relevant fact, but it's pretty awesome: "% brain utilization of total resting oxygen = 20%[1]." I've always said that I remain thin because I think so much. Now I have evidence! Apparently, your brain running a million miles an hour is a pretty good workout. So, grab a puzzle book and lose some weight!
OK, so maybe this is the teensiest bit nerdy. And maybe it didn't warrant spending a total of about 72 hours of research spread out over three weeks.... But I lost 4 pounds!
That's all well and good, but I really wanted to know: How fast do we think?
Unfortunately, I couldn't find the answer, or even enough solid information to compute an answer I was truly satisfied with. I will provide you with the best answer I can come up with, though. First, the relevant facts!
- Average number of neurons in the brain = 100 billion[1]
- Length of myelinated nerve fibers in brain = 150,000-180,000 km (Pakkenberg et al., 1997; 2003)[1,2]
- At the age of 20, the total length of myelinated fibers in males is 176,000 km while that of a female is 149,000 km[5]
- Number of synapses in cortex = 0.15 quadrillion (Pakkenberg et al., 1997; 2003)[1,2]
- The length of a single dendrite is usually several hundred micrometers. Due to branching, the total dendritic length of a pyramidal cell may reach several centimeters. The pyramidal cell’s axon is often even longer and extensively branched, reaching many centimeters in total length.[4]
- The number of dendrites varied between 4 and 13 (mean 9.1; ± 4.0) and the total dendritic length of adult cat VB neurons varied between 9,421 and 19,646 µm mean 13,120 µm; ± 2,605.[6]
- Dendritic length (µm) 1639 ± 341a 2140 ± 561 3397 ± 524[7]
- Apical dendrites possess a larger average total dendritic length (6332 vs 5062 micrometres) and surface area (12629 vs 9404 square micrometres) [this does not include spines].[11]
- Speed of impulses: 100 m/s (passive) ---- 20–30 m/s (thinking)8
- ...so while nerve impulses in unmyelinated neurones have a maximum speed of around 1 m/s, in myelinated neurones they travel at 100 m/s.[12]
- The speed of propagation for mammalian motor neurons is 10 - 120 m / s, while for nonmyelinated sensory neurons it's about 5 - 25 m/s.[13]
- Human neurons fire approximately 200 times per second, using signals that travel at a maximum of 100 meters per second.[9]
- Frequency of impulses: Thus, a maximum of 1,000 nerve impulses per second is possible. However, firing rates of 1 per second to 300-400 per second are more typical.[9]
- Resting firing rates are generally a few times per second; a stimulated neuron might fire 20 or 30 times a second.[9]
- Simple spikes occur at rates of 17 – 150 Hz (Raman and Bean, 1999) either spontaneously, or when Purkinje cells are activated synaptically by the parallel fibers, the axons of the granule cells. Complex spikes are rapid (>300 Hz) bursts of spikes caused by climbing fiber activation, and can involve the generation of calcium-mediated action potentials in the dendrites. Following complex spike activity simple spikes can be suppressed by the powerful complex spike input.[10]
- Average = about 100 action potentials per second.[12]
- Number of neocortical neurons (females) = 19.3 billion. ---- Number of neocortical neurons (males) = 22.8 billion[1]
(Actually, facts [9] through [11] aren't particularly relevant, but I spent a lot of time reading about them so I forced you to spend a tiny bit of time reading about them, too. The speed of the pulses doesn't matter for our calculations - it's more than fast enough to cover the length between any two neurons in much less than a second.)
One problem with brain studies is that they tend to focus on specific parts of the brain. This makes it rather difficult to piece together whole-brain statistics. For example, [1] refers to the number of neurons in the entire brain, while [2] and [3] are talking about the length of axons in just the white matter - I think. [4] is at minimum related to the surrounding gray matter, but it's unclear if it includes any of the inner gray matter structures. Perhaps more importantly, the numbers vary considerably and are ambiguous as to exactly what they are measuring! [2] and [3] mention myelinated nerve fibers, which tends to be synonymous with axons, but the axon terminals aren't myelinated, so it's not 100% clear that they aren't included in this length measurement, or how long they would be otherwise. [5], [6], and [7] put the total length of dendrites per neuron at several centimeters, 0.9-1.9 cm, and 1.5-3.5 mm, respectively. Fact [8] gives an indication of where this difference comes from. Presumably, the length isn't tallied past a certain branching level, or below a minimum branch size, or something similar. [4] and [8] also indicate that the total length of all dendrites for a pyramidal neuron would be the sum of the two averages mentioned in [8], or ~11000 micrometers - again, not including the spines. In fact, the wording of [8] makes it unclear if that's total dendritic length for the cell, or for the single dendrite counting all its branches (up to a point). This uncertainty is frustrating, to say the least.
Neuron speeds vary, too, depending on the source. [9], [10], [11], and [12] give values between 10 and 120 m/s for myelinated axons, and between <1 and 30 m/s for unmyelinated fibers - dendrites and axon terminals? That's quite a range, but it isn't the only speed that varies. The frequency of the action potentials is reported as anywhere from 1Hz to 400Hz in [12] through [16], with a theoretical maximum of 1000Hz. So, what can we come up with using these ranges of numbers?
It turns out that we can be fairly pessimistic in our assumptions and still arrive at some staggering results. Let's take 150,000km of myelinated nerve fibers - the axons - and assume 10 impulses per second. 10 pulses seems to be a good compromise, given that we are thinking at a million miles an hour, not resting at a million miles an hour, but not all thinking would necessarily involve all portions of our brain. (That is not to say the myth about using only 3-10% of our brain is anything but a myth!) This alone gives us 150,000km * 10/s = 1,500,000,000 m/s ≈ 5 times the speed of light ≈ just shy of a million miles a second! And we've only included one half of the synapse structure!
Let's be fairly conservative about the total length of the dendrites and axon terminals and any other unaccounted for lengths, and use 19.3 billion as the number of cells with dendrites, discounting everything but the neocortex (fact [17]). We'll go with 7.75 mm of dendrites per cell, since I really don't know what the source behind fact [7] was talking about, and source [14], which didn't have a fact to quote because the length had to be calculated out of other data, indicates total dendrite length of around 1.1 cm, so we're nearing a consensus of 1 cm or more. Anyway, I chose 7.75mm because 7.75 mm * 19.3 billion = 149,575 km, which means we can just double our previous results! Over 10 times the speed of light! 1,864,113 miles per second! And these are conservative estimates (I hope)!
Just for fun, let's see how fast I think. My neurons easily fire 100 times per second. I thought really hard about it, and sure enough all 100 billion neurons in my brain often fire at that rate. It turns out that my brain isn't very conservative when it measures itself, which makes my total dendritic length per neuron around the proposed average of 1.1 cm instead of 0.775 cm. So, when I'm thinking really hard, my mind is racing at (150,000 km + 100 billion * 1.1 cm) * 100/s = 125,000,000,000 m/s ≈ 417 times the speed of light ≈ 77,671,399 miles per second. I actually wouldn't be terribly surprised if this is closer to the true average speed of thinking really hard. (Are there any neuroscience folks out there that want to provide some different numbers?)
It's not a relevant fact, but it's pretty awesome: "% brain utilization of total resting oxygen = 20%[1]." I've always said that I remain thin because I think so much. Now I have evidence! Apparently, your brain running a million miles an hour is a pretty good workout. So, grab a puzzle book and lose some weight!
OK, so maybe this is the teensiest bit nerdy. And maybe it didn't warrant spending a total of about 72 hours of research spread out over three weeks.... But I lost 4 pounds!
- http://faculty.washington.edu/chudler/facts.html
- Awesomely, the most relevant paper cited in the first link is available in full: http://postcog.ucd.ie/files/Pakkenberg%202003.pdf!
- http://en.wikipedia.org/wiki/Neuron
- http://en.wikipedia.org/wiki/Pyramidal_cell
- http://en.wikipedia.org/wiki/White_matter
- http://dx.doi.org/10.1016/0006-8993(94)90681-5
- http://cercor.oxfordjournals.org/cgi/content-nw/full/16/7/990/TBL2 which is part of http://cercor.oxfordjournals.org/cgi/content/full/16/7/990
- http://hypertextbook.com/facts/2002/DavidParizh.shtml
- http://askville.amazon.com/average-neuron-firing-rate-humans-include-journal-article-reference/AnswerViewer.do?requestId=1368796
- http://en.wikipedia.org/wiki/Purkinje_cell
- http://en.wikipedia.org/wiki/Apical_dendrite
- http://www.biologymad.com/NervousSystem/nerveimpulses.htm
- http://www.rwc.uc.edu/koehler/biophys/4d.html
- http://www.jneurosci.org/cgi/reprint/14/8/4613.pdf
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