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Innate Numbers?
In "25 Minutes to Go," Johnny Cash counts down the minutes to his hanging. This precipitates an argument between Robert and Jad about whether you could live without numbers. Jad introduces his newborn son, Amil, and insists that he has no concept of numbers whatsoever. Like father, like son? Producer Lulu Miller talks to Stanislas Dehaene, whose work in neuroimaging suggests that Amil probably does have a number sense. You and I might not even know what logarithmic counting is, but apparently we used it as babies. Susan Carey explains why counting pennies is no small feat. Using an experiment designed by Karen Wynn, Susan breaks down the trick that separates us from the animal world: the counting song. Producer Amanda Aronczyk's daughter Mina demonstrates how complicated this whole penny business really is.
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"Innate Numbers?" shows that perception of quantity, like perception of sound pitch, light intensity, or most other things, is a matter of ratios. The ancient Pythagoreans would have loved it: "All is ratio!"
We perceive equal ratios as equal linear steps, the effects being proportional to the logarithm of the cause. ("Logarithm" comes from "Logos," Greek for "word," "idea," and "ratio."
Benfords's Law suggest that logarithms apply to things much more fundamental than just human perception.
As someone who has never really internalized the concept of 'e' I feel cheated to think I once understood logarithms and lost it. Intergers do have their value but it is shame we have to destroy ratios to gain it.
The "pennies" segment went out on a song that had to be digits of Pi -- I can't find a credit for it anywhere. Anybody know it?
I have a commonsensical question regarding the conversation between Lulu Miller with Stanislas Dehaene.
At 09:29, the conversation goes "...we just naturally switch from logarithmic thinking to the numbers we all know now, but this is not true... According to Stan, you'd never switch...stay in this logarithmic world forever."
We, the so-called civilized people, use non-logarithmic thinking. It means either "we'd never switch" is not true, or "we" are different from the indigenous people in the Amazon. These are the ONLY logical explanations. Since the second is highly unlikely to be true, Stan's assertion must be false.(If the second were to be true, then the conclusion drawn from the Amazon people may not apply to all humans.Either way, Stan's assertion is false.)
The fact is, all civilizations had, at some point, switched from log to non-log thinking, which means non-log thinking may be an inevitable stage of a human society.
Also, the switch happened because someone had switched his/her thinking from log to non-log, SPONTANEOUSLY. (Divine interventions, either from God or from the black monoliths in "2001 a space odyssey", are not considered.) This implies the switch can happen to SOME individuals instinctively, even if not everyone.
Are there any logical holes in my deduction so far?
To be continued .....
Continue...
Even under the assumption that non-log switch is inevitable, Stan's observations can be explained. An action exhibited by an infant does not imply the action will stuck with him for his whole life, case in point: drooling. The Amazon tribe's lack of non-log thinking can be explained by many alternatives, like the small size of the tribe (so the first "enlightened non-logic" person has not been born yet), that their civilization is not advanced enough for non-logic thinking to take place (like man-made tools, from stone bronze to iron), or their environment does not provide the necessary stimulus for the switch (an area without iron ore will not breed a civilization with iron tools). Until all the feasible alternatives can be explained away, claiming that "the switch will NEVER happen" is not scientifically acceptable.
We can not take a "pinhole perspective" and generalizing the incomplete observation to untested territory. The tale of "Blind men and an elephant" should have illustrated this point clearly.
I'm not a neuroscientist. But I know logic. Stan's conclusion can not emerge from his observations, even if the conclusion were to be right. Jumping to the conclusion with the premises mentioned in the conversation, is like looking at a 4-week old human fetus and say "Gee, it looks at a fish, so a human will look like fish forever".
BTW, I have been a fan of your show for years. Keep up the good work.
"logharism" of the numbers!!! And again radiolab ceases to fail to entertain me
Alan, I think what Dehaene was saying is that if an infant were raised in a society in which discrete number relations were not a necessity, then that infant wouldn't grow to know non-log number relations. You said that all civilizations have switched from log to non-log, but that clearly isn't true as you've cited the example of the Amazon people who think logarithmically. Those folks are part of a civilization that has no use for non-log number relations.
Also, you're making the assumption that the jump from log to non-log thinking occurred a.) in one individual and b.) that this switch occurred spontaneously. Rather than one person fiddling with numbers in their head until non-log thinking just happened to occur to them and then catch on like wild fire, wouldn't it be a more reasonable to assume that non-log number relations arose when a whole society was faced with the need to deal with discrete number increments? Perhaps when trading with another civilization?
Also also, I too would like to know the name of the song which appears briefly at the end of this segment.
Like "Curt from Minneapolis" I was intrigued by the fragment of song whose lyric is a string of integers. I also felt it likely the song was about pi. I also have looked fruitlessly for some indication of the title or credit, but it seems totally forgotten by the producers. Any info would be appreciated!
PS @ Alan W - I believe you are misinterpreting the statement you've quoted. Basically, I inferred from it that humans are born with a natural "ratio-nal" way of interpreting amounts, and it takes training to allow us to see things integral-ly. He's speaking here of the bulk of humanity, not the outliers like Newton, Einstein, or the middle eastern genius that came up with "arabic numerals". Think about it! Numbers as we use them are recent enough an invention that we can attribute them, at least to a culture. Much more recent than fire, for example, or agriculture, or even the wheel! That boggles me - I had never really considered numerals as a created concept, since because they seem to describe how the universe works they seem as basic as, well, light or gravity, not an invented way of describing them and such...
"Radiolab dedicates this hour to an exploration of numbers..." great topic, mildly interesting stories. However, you missed some much more interesting stories.
Numbers are far more bizarre and interesting than you would imagine. Check out the "Road to Reality" by Roger Penrose.
Some ideas for your next numbers show:
1) the history of zero - historically, people found zero to be pretty disturbing
2) the concept of "real numbers": the pythagaereans thought everything was a ratio of integers. Until someone proved that the length of the diagonal of a 1x1 square could not be the ratio of two integers!
3) this brings in the concept of infinity. Did u know that there are different infinities of different sizes? The person who developed these ideas (Cantor) went insane.
4) which brings us to the unfortunately named "imaginary" numbers. The richness of complex numbers is mind boggling and somewhat disturbing. The Mandelbrot set is an example of this richness.
Also the equation:
e^(2*pi*i) -1 =0
is amazing. It relates the 5 most important number in math (e,i,pi,0,1)
5) There is a debate among mathematicians about whether or not they are discoveres or inventors.
6) why does pi show up on so many equations that seem to have nothing to do with circles?
Keep up the good work,
Chuck
Curt from Minneapolis and other friends,
The music you heard was excerpted from "Pi" by Hard N Phirm, which forms part of the sound track to a WHNP Boston production for children, "Zap." Here is a link to the video on You Tube: http://www.youtube.com/watch?v=Mfr7xG6smhU
If you want a shorter version (with "lyrics"!), see: http://www.youtube.com/watch?v=KgeKx6O2cLQ&feature=related
Your segment on numbers called to mind a section of Carl Jung's Memories, Dreams and Reflections in which he describes how as a child he simply couldn't get it about numbers; that in essence he had to fake it to get by. I thought of this when the program spoke of both the innate sense of number by children and some primitive cultures that sees numbers in an altogether way than we are raised up to see them. Does the indoctrination of numbers that we undergo also have something with blocking the perceptions that came to Jung and seem so odd to most of the rest of us.
I came here to ask the same question about the "Pi digits" song and am glad to see it's already been answered.
Looks like the mp3 can be found at http://zorin.org/share/Hard-n-Phirm-Pi.mp3
I don't think we lose log numbers altogether. How about spending money? Spending $10 on something that costs $1 would seem ridiculous; spending $1,000,010 on something that costs $1,000,001 isn't as big a deal. You're spending $9 more than you should be in both cases, but $9 seems like a lot more in the first case. Or think of obtaining possessions: getting a second tv when you only have one vs. getting your 21st tv when you already own 20. One more tv in both cases; but one more tv seems like a lot more when you only have one.
Hey Chuck,
I think you meant
e ^ (j * pi) + 1 = 0
Euler's identity also contains one instance of each simple mathematical operation -- exponentiation, multiplication, addition, and assignment.
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