# Lack of Freewill doesn't mean lack of choice **URL:** \ **Category:** Great Debates\ **Created:** [November 10, 2021, 3:31pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128 "2021-11-10T15:31:47Z")\ **Posts on this page:** 13\ **Page:** 17
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [February 14, 2022, 6:39am UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/324 "2022-02-14T06:39:12Z")
> [@Crane](#): > > The digits of Pi have highly predictable normalcy. They are therefore random. That’s not how I understand randomness. Pi wouldn’t be considered random in the [algorithmic](https://en.wikipedia.org/wiki/Algorithmically_random_sequence) sense, which essentially says that a number is random if it’s not compressible—i. e. if for any _n_-bit prefix (finite initial sequence of digits), the shortest program needed to compute that sequence isn’t systematically shorter than _n_ bits. For pi, there exists a very short program computing eventually every digit, so it’s very much non-random. This notion of randomness turns out to be equivalent to more widely used definitions, such as 1- or Martin-Löf randomness. It’s true, though, that pi is (conjectured to be) a normal number, and hence, that each sequence of digits occurs with its normal frequency. So for any given coding of letters in terms of numbers, the text of King Lear will appear, and we can precisely predict when we’d expect it to. > [@Crane](#): > > Not as long as it just hops and bops in the ‘normal’ way. Well, the point that was made, which I was responding to, was that it’s enough for a system to be unpredictable by anything other than direct simulation for it to display ‘choice’. That’s true of such a tumbling stone, and of virtually any other complex system, so I was just intending to say that this trivializes the idea of choice. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [February 15, 2022, 2:35am UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/325 "2022-02-15T02:35:25Z")
I offered Pi as a tangible example for discussion. It is a model of randomness. The point I was trying to make is that normalcy is predictable. Normal distribution is the basis of much engineering analysis. Does the normalcy of ‘random’ events have a cause? . ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [February 16, 2022, 8:40am UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/326 "2022-02-16T08:40:44Z")
I neglected to direct the above response. Is the normalcy of random events ‘caused’? ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [February 16, 2022, 2:57pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/327 "2022-02-16T14:57:41Z")
> [@Crane](#): > > I offered Pi as a tangible example for discussion. It is a model of randomness. You can’t interpret the digits of \pi as randomly distributed because they follow a known algorithm. The distribution would be more accurately described as pseudo-random: it _looks_ random, but actually isn’t. You can call it random in everyday discourse but in the precise language of metaphysics, that is not technically random because it is a known pattern. The digits of \pi do make for a good random “seed” for pseudo-random algorithms. Again, you can call pseudo-random algorithms “random” in vernacular, but metaphysically speaking, no computer algorithms seeded by a constant value such as \pi are random. ~Max ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [February 16, 2022, 6:50pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/328 "2022-02-16T18:50:53Z")
> [@Max\_S](#): > > You can’t interpret the digits of \pi π\pi as randomly distributed ‘Random’ is just a label that is applied to some definition of randomness. The term pseudorandom is generally applied to binary shift counters that are useful because they are completely predictable but not linear. They are frequently used as computer/controller instruction counters. PI is not a suitable seed. More commonly you grab a value from the real time clock or an independent timer or both. The point is that observation of PI yields a normal distribution. King Lear cannot appear in PI because the encoding of the text must follow the distribution of vowels and consonants within the language encoded. That distribution is not normal. The point relevant to the OP and some of Mijin’s posts is that the only thing that is predictable is the normalcy of ‘randomness’. It’s a standard of analysis for everything from semiconductor manufacture to political campaigns. It is a property of the state of the universe. So, is normalcy ‘caused’? ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [February 16, 2022, 7:36pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/329 "2022-02-16T19:36:13Z")
> [@Crane](#): > > The point is that observation of PI yields a normal distribution. To my knowledge it is a famously open question in mathematics whether \pi is a normal number. ~Max ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [February 16, 2022, 8:23pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/330 "2022-02-16T20:23:29Z")
> [@Max\_S](#): > > famously open Perhaps, but with 10 trillion decimal places calculated, the matter is settled for all practical purposes. ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [February 16, 2022, 9:24pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/331 "2022-02-16T21:24:45Z")
If it is a normal number then it contains all sequences of digits, including the sequence you would obtain by encoding “King Lear”. ~Max ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [February 17, 2022, 6:21am UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/332 "2022-02-17T06:21:18Z")
> [@Max\_S](#): > > If it is a normal number then it contains all sequences of digits Where is this part of the definition of a normal number? It’s possible to derive a normal number that is 0.[0123456789]recur which is normal, but will _never_ encode Lear. Oh, wait, that’s _simply_ normal, never mind. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [February 17, 2022, 2:02pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/333 "2022-02-17T14:02:21Z")
Thanks for the comment. It lead me to some interesting **[reading](https://docs.nersc.gov/iris/iris-for-pis/)**. I tried a couple of searches on the PI Search **[Page](http://www.angio.net/pi/piquery)** and the ASCII code for King does not appear in the first 200,000,000 digits of PI. Also, MAGA doesn’t either. If act one of Lear were a single 3000 character string it would not have the same probability as any other string of equal length because it is not locally normal. So, it would seem that free will is the ability to defy normality. King Lear is an act of free will because it cannot be generated by randomness. King Lear is not encoded in snow flakes because the patterns of snow flakes are normal. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [February 17, 2022, 3:50pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/334 "2022-02-17T15:50:55Z")
> [@Crane](#): > > I offered Pi as a tangible example for discussion. It is a model of randomness. > > The point I was trying to make is that normalcy is predictable. Normal distribution is the basis of much engineering analysis. > > Does the normalcy of ‘random’ events have a cause? I’m not completely sure, but I think you’re conflating two different meanings of the word ‘normal’ here. A normal distribution is one characterized by a fixed mean and standard deviation, and describes cases where events cluster around a given value. Normality for a sequence of digits means that every string of _n_ digits occurs (assuming base 10) with probability 1/10n (i. e. they are _uniformly_ distributed), including that specific string coding for ‘King Lear’. Any random number is normal, but not every normal number is random. [Champernowne’s number](https://en.wikipedia.org/wiki/Champernowne_constant) 0.1234567891011… is normal by construction, but obviously nonrandom. That said, the point you’re making (if I understand correctly) is a valid one. Random systems without fundamental causality can display lawlike behavior—that’s what I was trying to get at with the example of thermodynamics. But I’m not sure appealing to mathematical concepts is useful in this case. I wouldn’t say, for example, that the fact that the decimal expansion of \sqrt{2} is infinite and non-repeating has a _cause_ in the impossibility of it being writable in the form of a ratio of whole numbers, but that fact is certainly the _reason_ for it. Causes are reasons, but not all reasons are causes. ---
**Author:** ![Max\_S](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@Max\_S](https://boards.straightdope.com/u/Max_S)\ **Post date:** [February 17, 2022, 5:01pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/335 "2022-02-17T17:01:48Z")
> [@Crane](#): > > the ASCII code for King does not appear in the first 200,000,000 digits of PI. Also, MAGA doesn’t either. ASCII operates on 7-bit bytes, not decimal digits. You would want a base 128 expansion of \pi if you are looking for ASCII codes. Or if you’re using 8-bit ASCII bytes, you would want a base 256 expansion. I don’t know whether you think \pi is normal in bases other than 10. If I was looking to find words I would probably go for a base 26 expansion of \pi. And we can make finding arbitrary words much easier by using ciphers. Even the decimal expansion 3.14159 can be interpreted as containing KING if 4=K, 1=I, 5=N, 9=G. > [@Crane](#): > > If act one of Lear were a single 3000 character string it would not have the same probability as any other string of equal length because it is not locally normal. I’m struggling to understand how you’re assigning probability in this situation, and what you mean by “locally normal”. A number is either normal or not normal. _If_ \pi is a normal number, then it is necessarily true that the probability of the digits of \pi containing _any_ particular sequence is 1. ~Max ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [February 18, 2022, 1:15pm UTC](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128/336 "2022-02-18T13:15:21Z")
> [@Half\_Man\_Half\_Wit](#): > > Random systems without fundamental causality can display lawlike behavior I observe that normality is a property of the universe. I cannot know enough about A to predict all of B, but I do know that the same normality will be a property of both. In my example, semiconductor process engineers label normality as ‘natural’. Anything that deviates from normality has a cause and can be removed. So, this raises the question of whether normality is caused. [Previous page](https://boards.straightdope.com/t/lack-of-freewill-doesnt-mean-lack-of-choice/954128.md?page=16)