Latest Comments for Numbers on http://www.wnyc.org/http://www.radiolab.org/story/91697-numbers/Latest Comments for Numbers on http://www.wnyc.org/en-usMon, 12 Jan 2015 22:33:49 -0500600cleanComment #562876 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment562876I have heard this broadcast twice. Before, I considered myself too poor in 'math sense'to latch on to its meaning.
Currently, I am amazed with the power and possibilities that the #2 represents both symbolically and mathematically. Symbolically, it represents duality as a function of what we perceive as polarity, ie Black vs White, positive versus negative, left vs right.
This has lead me to what maybe some rather naive assumptions which perhaps I would enjoy going into further here, in this forum.
So just to throw this out there; if all humans enter the world with math skills, there is a 'oneness' that argues against the polarity that we experience in societies throughout the world.
If a 2 can be successfully entered in to the binary code, not as a way to calculate faster, but slower, it will slow things down and thereby speed thing up simultaneously. Less heat, more light.
I believe what all humans experience as polarity is as artificial as our conception of 'time'. One Love, One Heart, And Justice For All.
Jakzen
Mon, 12 Jan 2015 22:33:49 -0500http://www.radiolab.org/story/91697-numbers/#comment562876Comment #562616 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment562616So, can I use Bedford to predict lottery numbers? I have read conflicting accounts about whether or not such numbers conform to Bedford. This source (lotterypostdotcomslashthreadslash148025)concludes that they do, but fails to provide a prediction strategy.
Sun, 11 Jan 2015 18:27:56 -0500http://www.radiolab.org/story/91697-numbers/#comment562616Comment #562559 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment562559EXCELLENT PROGRAM!!
Sat, 10 Jan 2015 23:04:43 -0500http://www.radiolab.org/story/91697-numbers/#comment562559Comment #562520 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment562520I just heard this. Excellent program.
It is not surprising that our "unlearned" concept of numbers is logarithmic based. All of our senses are based on logarithmic values. Linear values are useful for measuring and creating physical items but that seems to be about the limit. Most recently it has become obvious that our monetary systems and national finances would more easily grasped if we used a logarithmic representation.
Sat, 10 Jan 2015 14:18:58 -0500http://www.radiolab.org/story/91697-numbers/#comment562520Comment #468608 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment468608wonderful program
Thu, 03 Oct 2013 22:02:27 -0400http://www.radiolab.org/story/91697-numbers/#comment468608Comment #404224 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment404224So this show is 3 years old but I still want to post...
Logarithmic counting:
We don't lose this ability entirely. Ask a 5 year old person "What is an old age?" and they will answer perhaps 10 or 15 years old. Ask a 20 year old and they will answer perhaps 40. A 40 year old will answer 70 or 80.
At the same time as we age each year that passes will appear to be shorter and shorter. "Where did the year go? Seems like a month ago I was writing 2011 on my checks..."
This is simply because the number of years we have lived increases in a linear fashion, but how long a year represents compared to our lifetime is exponentially reduced each interval. For a two year old a year is 50% of their lifetime. A 10 year old a year is 10% their lifetime. A 50 year old a year is 2% of their lifetime. As we age this will continue to get smaller and smaller (feel shorter and shorter) until death.
Tue, 25 Dec 2012 09:07:50 -0500http://www.radiolab.org/story/91697-numbers/#comment404224Comment #404150 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment404150Could it be that baby"Emiel" is the original analog to digital converter? Does he exchange powers of ten additions for for multiple increments? This show was absolutely fabulous.I'm 70 and I was thrilled.... had to blab it to everybody I know. Thanks
Mon, 24 Dec 2012 11:14:00 -0500http://www.radiolab.org/story/91697-numbers/#comment404150Comment #404115 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment404115I get it now. On the question of concentric ellipses, the foot-wide concrete walkway around the perimeter of a swimming pool, is an ellipse in only one case, when the ellipse is a circle.
If an ellipse is defined as PF1+PF2=2a, then (PF1+1)+(PF2+1)=2(a+1) is also an ellipse. However, a concrete walkway around the perimeter of a swimming pool, which has a a constant width, is an ellipse only in the case of a circle, where F1 and F2 lie on the same point. The width between the inner and outer circumference defined by the concrete walkway will vary from one to one half the cosine of the angle between PF1 and PF2 times the distance between the concentric ellipses (which is the width of the walkway).
So, it is not impossible for the concrete walkway around the perimeter of a swimming pool to be an ellipse, but it is possible in only one case, a circle. In all other cases, it is impossible.
Sun, 23 Dec 2012 23:28:12 -0500http://www.radiolab.org/story/91697-numbers/#comment404115Comment #404114 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment404114The song at 19:40, bjorn in orlando, is the Pi Song by Hard 'n' Phirm.
Sun, 23 Dec 2012 23:10:23 -0500http://www.radiolab.org/story/91697-numbers/#comment404114Comment #404112 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment404112Regarding the comment that Benford's law applies to Fibonacci numbers, factorials, powers of 2 and the powers of almost any other number. But, Benford's law does not apply to square roots?
If Benford's law applies to Fibonacci numbers, and to the squares of Fibonacci numbers, wouldn't Benford's law apply to the square root of Fibonacci numbers squared?
Just curious.
Sun, 23 Dec 2012 22:51:58 -0500http://www.radiolab.org/story/91697-numbers/#comment404112Comment #404110 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment404110The question of concentric ellipses, the foot-wide concrete walkway around the perimeter of a swimming pool, is an ellipse.
If an ellipse is defined as PF1+PF2=2a, then (PF1+1)+(PF2+1)=2(a+1) is also an ellipse. The foot-wide concrete walkway around the perimeter of a swimming pool can't be anything but an ellipse.
Where, PF is the distance from a point on the circumference to a focal point, F1 is focal point one and F2 is focal point two, and a is the distance from the center point between F1 and F2 and a point on the circumference that lies on a line through F1 and F2 bisecting the ellipse.
Sun, 23 Dec 2012 22:32:47 -0500http://www.radiolab.org/story/91697-numbers/#comment404110Comment #403998 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment403998Mystified by the question of concentric ellipses? (The foot-wide concrete walkway around the perimeter of a swimming pool.) Why impossible?
Sat, 22 Dec 2012 11:50:59 -0500http://www.radiolab.org/story/91697-numbers/#comment403998Comment #403952 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment403952How would Benford's Law be observed in base-6? I'd enjoy seeing a comparison of the same measurements recorded in base-6 and base-10.
Fri, 21 Dec 2012 21:19:08 -0500http://www.radiolab.org/story/91697-numbers/#comment403952Comment #376915 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment376915Nearly three years after it was first broadcast, I was delighted to listen to your "Numbers" episode today. The section on Benford's law was great, but I have a small quibble with the assertion that using it for forensic purposes is a recent phenomenon. Fritz Scheuren <scheuren@aol.com>, past President of the American Statistical Association, told me that the Office of Naval Research used Benford's Law for many years to check data from research contracts. You could check with him about how long ago that was, and what other earlier uses he might be aware of. It has also been used to check on election outcome data.
Mon, 20 Aug 2012 21:17:39 -0400http://www.radiolab.org/story/91697-numbers/#comment376915Comment #371920 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment371920What is that song with the woman singing a series of random numbers at 19:40? it's amazing
Sun, 29 Jul 2012 15:14:19 -0400http://www.radiolab.org/story/91697-numbers/#comment371920Comment #364152 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment364152Xavier, it's definitely a version of Ebb Tide (that's the organ at least). The Ken Griffin version was also featured in the season 5 premiere of Mad Men.
Wed, 27 Jun 2012 11:57:20 -0400http://www.radiolab.org/story/91697-numbers/#comment364152Comment #362964 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment362964Does anyone know what the music is at 19:51 with the cymbals and organ? Thanks for any info!
Fri, 22 Jun 2012 00:46:54 -0400http://www.radiolab.org/story/91697-numbers/#comment362964Comment #353893 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment353893The section near the beginning of this show where they studied how babies have the ability to view changes in quantity of the ratio of the change is large enough was very fascinating. Question: what happened in civilized society if we teach math so differently from how our brains are equipped to learn it. I struggled with alogarythims,but it appears that our brains are not meant to struggle against them.
Thanks for the show!
Fri, 11 May 2012 00:54:02 -0400http://www.radiolab.org/story/91697-numbers/#comment353893Comment #339010 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment339010I'm willing to suppose there may be a valid connection between our inability to grasp and adequately problem solve with large numbers (7 billion people, 16 trillion debt, and so on) and the natural logarithmic understanding we have lost, to which our minds may naturally tend towards. (Presumptions, I know. But it is an undeniably curious thought) We may have developed an integer based system that really doesn't illustrate these critical mathematical patterns in ways we can truly digest.
Might logarithmic or, perhaps more so, equational expressions of the values we observe be a more tangible and impressionable idea? That is, however, if these numeric taboos had been nurtured early in life as valid skills. Doubling, exponential growth and other remarkable and simple mathematical facts are all but lost in the public problem solving skill set.
Thoughts. So many good thoughts on Radiolab. Thank you forever.
Mon, 19 Mar 2012 19:44:09 -0400http://www.radiolab.org/story/91697-numbers/#comment339010Comment #297000 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment297000There seems to be a lot of confusion on Benford's Law. People start counting, reach 19, see that a lot of the numbers start with 1, and say "Benford's makes sense."
This is not Benford's Law.
Benford's Law applies to things that have a uniform logarithmic distribution (for example, things that grow exponentially). Compound interest is one of the best illustrations.
Say you have $100 in an account that gets 5% interest. If you left it there for 94 years, you would have balances that began with 1 29 times!
"But wait!" you say, "You started with $100. Of course a lot will start with 1."
Fair enough. Start with $200. Now you won't see a number starting with 1 until you have a balance in the $1000's. However, 94 years later, you still have had 29 balances that begin with 1. (Benford's actually says you should get 1 about 30% of the time.)
The reason for this is that the interest is compounding by this function:
New balance = last year's balance * 1.05.
If your last year's balance starts with a 1, it won't grow as fast as if it started with a 2 (and much slower than if it started with a 9).
Mon, 03 Oct 2011 21:43:29 -0400http://www.radiolab.org/story/91697-numbers/#comment297000Comment #296344 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment296344In response to Connor, I remember using logarithmic tables in college...that was around 2004. So they are still in use and still pretty handy, I think.
Fri, 30 Sep 2011 17:58:34 -0400http://www.radiolab.org/story/91697-numbers/#comment296344Comment #294039 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment294039*Benford's.
Thu, 22 Sep 2011 00:56:08 -0400http://www.radiolab.org/story/91697-numbers/#comment294039Comment #294037 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment294037Bemford's Law makes sense because every power of ten has ten times more numbers that begin with one than the last power... as in, like, within the millions, there are 9 million fewer ones than there are within the ten millions. So as you count up, you're always going to be getting more that begin with 1.
Thu, 22 Sep 2011 00:55:13 -0400http://www.radiolab.org/story/91697-numbers/#comment294037Comment #290871 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment290871 I gotta be honest,this episode was damn boring to me
Fri, 09 Sep 2011 15:33:35 -0400http://www.radiolab.org/story/91697-numbers/#comment290871Comment #287051 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment287051Seriously, how can make a show about numbers without mentioning prime numbers? You could easily make ten shows about prime numbers.
Wed, 24 Aug 2011 06:47:45 -0400http://www.radiolab.org/story/91697-numbers/#comment287051Comment #236721 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment236721I wonder if the intuitive reason why Benford's law is true simply boils down to the fact that the universe prefers lower energy levels, and higher energy levels are less frequent because energy/resource are limited- for anything. So, numbers are just counting quantities, that in the end, are measuring an energy level; hence, why low numbers are more frequent. Bank accounts are a perfect example of what I mean. To make the count of money in the account go up requires that you expend more energy to acquire more money. However, there is finite amount of money and with high competition and limited available resources, it requires one to expend a lot of energy and intelligence to get more money than others. So, it is much more likely that the lowest energy (money) level will be populated the most, and each subsequent energy (money count) level will be progessively less populated. This principle could be applied to anything being counted because everything requires some energy/Intelligence be applied to it for it to achieve the unique state of being that we attribute a name to.
Anyone ever heard of a theory like this? Please email me if so at ari_groups@comcast.net
Wed, 09 Mar 2011 03:44:26 -0500http://www.radiolab.org/story/91697-numbers/#comment236721Comment #225531 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment225531Anyone know any books for laymen explaining Benford's Law?
Sun, 23 Jan 2011 19:58:40 -0500http://www.radiolab.org/story/91697-numbers/#comment225531Comment #210453 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment210453I'm an engineer and I can't understand music at all, but I'm interested that our natural view of numbers is related to harmonics, our view of sound is related to sound frequency, our nerves are sensitive to pulse frequency, our eyes are sensitive to light frequency and our taste/smell is sensitive to the frequency response of molecules. Crazy stuff. I wonder how we quantify smell? Linear or log?
Sun, 05 Dec 2010 18:21:01 -0500http://www.radiolab.org/story/91697-numbers/#comment210453Comment #210450 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment210450The idea of people thinking logarithmically about numbers by nature doesn't seem to be a stretch if you consider sound. If you look at an equilizer each fader represents a particular frequency. The faders on either side of the first will be the first frequency doubled or halved depending on the direction from the first fader. Or consider a piano...Middle C may be near the center of the keyboard, but nowhere near the middle of the frequencies represented on that same keyboard.
I beleive that most people would feel that they have a better understanding of music than they do math, but I think this show has implied a link to the way our brains percieve music and the way we naturally think about math.(?)
Sun, 05 Dec 2010 17:50:02 -0500http://www.radiolab.org/story/91697-numbers/#comment210450Comment #204018 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment204018Regarding Benford's law. The way that I have made sense of it (it seemed counter-intuitive to me for a long time) and the way that I explain it now to people is to ask them to think about a quantity. Whatever quantity you pick to discuss. Then think about it being 10% larger. With a little more explaining, it becomes clear that 10% more than 80 is 90. And 10% more than 90 is 100. And 10% more than 100 is still 110, 120, 130 ...etc. etc. The portion of answers to 10% starting with 1 as a leading number are self-evidently more common.
Sun, 07 Nov 2010 18:00:20 -0500http://www.radiolab.org/story/91697-numbers/#comment204018Comment #194391 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment194391can someone tell me wether im on the right track here...
in my opinion benfords law is just pure logic and im not seeing why so many people doubt it
ofcourse most numbers will start with 1's or 2's cause we start counting from 1
I mean if I open up a saving acoun I will not start with 99,99 I will start with 100 it's just common sense...
*wanted to place something here but lost my train of toughts*
only thing that didn't make sense is that they where talking about benfords law and random numbers
I mean if I did a random 1-100 each one got a equal chance.. but according to benfords law 1,2,10,12 etc. would all have higher chance...
Mon, 27 Sep 2010 10:07:58 -0400http://www.radiolab.org/story/91697-numbers/#comment194391Comment #192338 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment192338This was a neat episode, but I can't believe you totally glossed over the connection between logarithms and Benford's law.
The first piece (natural counting is logarithmic) and the second (Benford's law) were saying the exact same thing: logarithms are natural. If you can wrap your brain around half of 9 being 3, then Benford's law is an easy step. If you asked the Amazonians from the first part to make up random numbers, they would probably follow Benford's law.
Fri, 17 Sep 2010 00:10:26 -0400http://www.radiolab.org/story/91697-numbers/#comment192338Comment #184931 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184931Just started listening to RadioLab after hearing you guys on This American Life. Fantastic. Really really fantastic. This has literally turned my work commute to one of the best parts of my day.
This episode especially is almost life changing for me. I'm so in love with numbers in general.
This episode makes me want to go back to school and study math.
Thanks so much.
Sat, 27 Feb 2010 01:55:00 -0500http://www.radiolab.org/story/91697-numbers/#comment184931Comment #184930 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184930It must be a slow night for me , because I just read most of the posts for this episode...
It must be fantastic to have a brain that thinks math is interesting. I don't. I'm not stupid, I just don't find math that intriguing. I could sit down and try to dissect a math concept I don't fully understand, but I'd rather cook a big plate of cheese enchiladas and have my friends over to devour them. Just a matter of what makes each of us happy.
I listen to RadioLab because it makes the things I might not find interesting just that - INTERESTING.
So, this very excellent radio show is not meant to be an upper level college class that is unequivocally proving something. It is meant to make us think (I think.)
You science dudes need to take a deep breath. Bless you, but the rest of us simply like to be smartly entertained.
I made my husband sit down and listen to this program, I've sent the link to my kids. A few weeks from now we will talk about it at the dinner table. This is not the first time this has happened. Robert and Jad have created moments in non-scientific lives where science (and math) were discussed and enjoyed.
Thank you!
Fri, 26 Feb 2010 01:18:19 -0500http://www.radiolab.org/story/91697-numbers/#comment184930Comment #184928 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184928A new NYTimes series: Steve Strogatz "writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject..."
http://opinionator.blogs.nytimes.com/2010/01/31/from-fish-to-infinity/
Mon, 01 Feb 2010 15:49:22 -0500http://www.radiolab.org/story/91697-numbers/#comment184928Comment #184871 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184871Benford's Law is very intuitive when you consider that even if numbers are random, they are random according to a distribution, and that distribution has a RANGE that is NOT random. If the range is all within the same number of digits, then the starting number will be random, but once the range ticks up an order of magnitude, you get as many again numbers that all begin with a "1," then as many again as begin with a "2," etc. Take a random sample of bowling league scores: lots of 1s, some 2s. Or MLB batting averages: lots of 2s, some 3s, a few 1s (at least for part of a season). Physicians' salaries, hotel maids' salaries: lots of 1s, some 2s. Very intuitive.
Thu, 21 Jan 2010 10:47:25 -0500http://www.radiolab.org/story/91697-numbers/#comment184871Comment #184873 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184873I agree with DU, this started off great but I was disappointed overall. "Numbers" were covered for the first quarter of the podcast, then the episode spiraled into story time with barely any mention of numbers or math. I felt the same way about the "Randomness" episode. Let's get back on track guys!
Mon, 21 Dec 2009 16:53:21 -0500http://www.radiolab.org/story/91697-numbers/#comment184873Comment #184872 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184872I can't help but think the logarithmic understanding of quantity is built into our visual filters as well. Consider this optical illusion, where the weight of the white squares is increased by small, nearby elements, causing the squares to have more "weight" in the field of vision and distorting the perception of space.
http://www.youtube.com/watch?v=QKCSBkdEUXQ
Fri, 18 Dec 2009 13:46:35 -0500http://www.radiolab.org/story/91697-numbers/#comment184872Comment #184880 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184880Numbers are indispensable in a material world that sustains conscious and creative beings since you need to be able to quantify accurately in order to also create something accurately. Ask any architect if they would be able to design anything sensible without using numbers, or, for that matter, software that uses no numbers. The obvious benefits creep up in virtually any preoccupation of humanity.
The case about babies having a logarithmic intuition of numbers defines, on a prima facie level, an interesting conundrum but is very well explainable if one is willing to accept the idea that babies think visually about numbers. With that I mean that babies have a visual conception of quantities of things. The show brings up 8 ducks in the babies' visual field. Now doubling that number obviously leaves a very salient change in the perceived image by the baby. We are then at 16 ducks. Doubling it again, same story, same registration of change. We are now at 32 ducks. Now add one duck. The change from 32 to 33 leaves only a minor change on the babies perceived visual field. So consequently, the baby's mind also notices a small change. With logarithmic perception of numbers is meant that factors (2,4,8,16,...) matter, not so much increments (2,3,4,5...).
Logarithmic counting is quite primitive because it needs the number of quantities in the visual field to increase by a factor in order to properly register in the baby's mind. You know, going from 2 ducks to 4 ducks, to 8 etc... The baby is only able to count because the numbers increase very crudely and visually obviously, namely in factors.
When the baby gets older, the perception of quantities (numbers) gets more sophisticated. Now the baby learns to be able to detect small one-by-one increments in numbers.
The more primitive logarithmic intuition of numbers should be retrievable again by picturing numbers and so think in terms of factor increases (or decreases) again.
Hope this helps.... :)
Wed, 16 Dec 2009 19:06:40 -0500http://www.radiolab.org/story/91697-numbers/#comment184880Comment #184894 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184894I see Damon already beat me to it! But here's a pic of the Paul Erdos icon: http://is.gd/5oYG3
I was particularly moved by the story of Paul Erdos - as I was one of the folks asking "Why is he up there?"
Tue, 15 Dec 2009 17:11:33 -0500http://www.radiolab.org/story/91697-numbers/#comment184894Comment #184879 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184879I just love your weblog! Very nice post! Still you can do many things to improve it.
Sun, 13 Dec 2009 14:13:28 -0500http://www.radiolab.org/story/91697-numbers/#comment184879Comment #184877 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184877Then not only custom, but also nature affirms that to do is more disgraceful than to suffer injustice, and that justice is equality.
Quotation of Plato
Fri, 11 Dec 2009 23:24:35 -0500http://www.radiolab.org/story/91697-numbers/#comment184877Comment #184876 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184876There was some interesting stuff in this episode, but overall I found it pretty disappointing. You have a pro-intellectual, science-y program and yet you found the need to perpetuate several anti-math stereotypes. Several times during the program Jad and Robert both said things like "I could never understand this stuff" or "who needs numbers". Then the long story at the end reinforced the "math is the opposite of humanity" stereotype.
Also, there are so many topics you could cover in math and yet you lumped them all into a single "Numbers" episode. First, numbers are only a small part of math. What of topology, for instance? Second, throwing all of mathematics together in a single episode is like throwing biology, physics and geology under a single episode labeled "Natural Science".
I think you guys can do better and I look forward to hearing the result.
Thu, 10 Dec 2009 22:40:14 -0500http://www.radiolab.org/story/91697-numbers/#comment184876Comment #184875 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184875Poetry is nearer to vital truth than history.
Quotation of Plato
Wed, 09 Dec 2009 03:50:57 -0500http://www.radiolab.org/story/91697-numbers/#comment184875Comment #184893 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184893I am definitely bookmarking this page and sharing it with my friends.
:)
Tue, 08 Dec 2009 11:56:15 -0500http://www.radiolab.org/story/91697-numbers/#comment184893Comment #184892 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184892I've just listened back to this episode, and was reminded how funny I found it when you explained what Logarithmic Tables are – as often used in the first half of the 20th century I think. We had then when I was in primary school in Ireland… and that was in the 80s!
Usually we used the old ones belonging to our older siblings and even our parents – those ones had all the text in Irish to boot.
The were indeed worn more at the front that the back, so the new ones you'd buy in the village store looked sparklingly different.
And then we'd go home from school and watch Ferris Bewler on TV :-)
Tue, 08 Dec 2009 11:15:56 -0500http://www.radiolab.org/story/91697-numbers/#comment184892Comment #184890 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184890There are alot of examples to show that people never lose their logrithmic reasoning. One great one is to think about value comparisons; a person will cut a coupon and carry it for a week to save 40 cents on a can of fruit, but may not be willing to do the same for a car, under the idea that 1 dolar is "farther" from 60 cents than 10000 dolars from 9999.60 dolars, even though they share and equal absolute difference.
Tue, 08 Dec 2009 06:14:45 -0500http://www.radiolab.org/story/91697-numbers/#comment184890Comment #184889 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184889Also, just because I can't resist the urge to join the meta-discussion of Radiolab itself, does anyone else think Robert sounds a little like Shake from Aquateen Hunger Force? Sorry Robert :-)
I really do love this show and think it's one of the best things out there. It's so refreshing to hear people exploring the universality of the natural world instead of just trying to keep up with the machine of human information culture. Especially when you put so much creativity and style into your production value.
Tue, 08 Dec 2009 02:08:41 -0500http://www.radiolab.org/story/91697-numbers/#comment184889Comment #184888 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184888I don't think that there is anything spooky about Benford's law. When we count things, we always start with 1, then go to 2, and so on. That's what counting is. If your chance to stop on any number is completely random, but you can't get to 9 without going through 1, 2, 3... first, then of course your chances to stop on 9 are going to be the smallest, because you had 8 chances to stop before you got there. The reason why sets of counted numbers fall into logarithmic patterns is just because our numeral system is base 10, meaning that every time you get to a quantity of ten in the place you are currently counting at, you move up one place. That place always starts with a 1.
If, however, you counted in hexadecimal, you would create a similarly shaped Benford's curve, but it would be distributed between 1-16 (or 1-F) rather than 1-9. This might be a hard concept to grasp, simply because unlike babies and aborigines, we've been programmed to think in the base ten counting system because that's what our language has evolved as. Unless you know other numeral systems like hexadecimal, or understand why time is base 60, it might seem like magic. Really though, it's all in built into the number systems that we all agree to commonly use. This is where numbers are really amazing, because they show the human preference to standardization in communication, because every language (that I know of) uses a base 10 system.
If you've ever compared metric, which is all base 10, to the English system of measurement, which is all random and crazy and based on the sizes of various body parts, you know how convenient base 10 is. If you can grasp how other base number systems work though, it opens your mind to a lot of possibilities. Thinking like this is what allowed us to understand things like binary and hex, that are more friendly to electrons and computers. These are examples of newer number systems with the computer age, but time, and the minutes and seconds of latitude and longitude remind us that even base 10 was invented to simplify things down from base 60 counting language. I would love to hear Radiolab do a show on how language evolves.
Tue, 08 Dec 2009 02:02:01 -0500http://www.radiolab.org/story/91697-numbers/#comment184888Comment #184887 on Numbers
http://www.radiolab.org/story/91697-numbers/#comment184887The thing that cleared up Benford's for me was understanding that it only occurs in number sets that have logarithmic distribution, and not in every data set. These types of sets do exist all over nature, but we encounter data sets with non logarithmic distribution all the time. For instance social security numbers, zip codes, and phone numbers because they are assigned artificially and often contain digit distributions that signify other things (eg: the area code and exchange in phone numbers).
The thing that's really puzzling is, why does our natural world favor logarithmic distribution so heavily?
Mon, 07 Dec 2009 23:27:25 -0500http://www.radiolab.org/story/91697-numbers/#comment184887