Path: csiph.com!fu-berlin.de!uni-berlin.de!not-for-mail From: Joonas Liik Newsgroups: comp.lang.python Subject: Re: Compression of random binary data Date: Mon, 11 Jul 2016 21:09:18 +0300 Lines: 30 Message-ID: References: Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: news.uni-berlin.de xBeBfEekBTQot8agQNTkxwxwJo6ZbLns4zcIz49Ui6Vw== Return-Path: X-Original-To: python-list@python.org Delivered-To: python-list@mail.python.org X-Spam-Status: OK 0.003 X-Spam-Evidence: '*H*': 0.99; '*S*': 0.00; 'root': 0.04; 'binary': 0.05; 'cc:addr:python-list': 0.09; 'compression': 0.09; 'encoding.': 0.09; 'rounding': 0.09; 'worse': 0.09; '2016': 0.16; 'cc:name:python': 0.16; 'compress': 0.16; 'numerically': 0.16; 'received:io': 0.16; 'received:psf.io': 0.16; 'restricting': 0.16; 'subject:random': 0.16; 'violated': 0.16; 'wrote:': 0.16; 'memory': 0.17; 'basically': 0.18; 'case.': 0.18; 'cc:2**0': 0.20; 'cc:addr:python.org': 0.20; 'symbolic': 0.22; 'header:In-Reply- To:1': 0.24; 'message-id:@mail.gmail.com': 0.27; 'mathematical': 0.27; 'values': 0.28; 'actual': 0.28; 'relies': 0.29; 'random': 0.29; 'probably': 0.31; 'done,': 0.33; 'lets': 0.33; 'shorter': 0.33; 'similar': 0.33; 'received:google.com': 0.35; 'could': 0.35; 'instance': 0.35; "isn't": 0.35; 'but': 0.36; 'there': 0.36; 'possible': 0.36; 'smaller': 0.36; 'subject:: ': 0.37; 'being': 0.37; 'say': 0.37; 'itself': 0.38; 'represent': 0.38; 'means': 0.39; 'takes': 0.39; 'space': 0.40; 'some': 0.40; 'challenge': 0.61; 'back': 0.62; 'more': 0.63; 'physical': 0.72; 'square': 0.76; 'forth': 0.79; 'accurately': 0.84; 'roots.': 0.84 DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=79oM9t5KP0Hv7KO6fmfFYw1Iu9jDyzccZKUHxGRp9zM=; b=vcRbCntqVxWRqZenlpx6S8cwmWLxg8Es8YwB6hXkmCTxcpwRwd7EkY/FdfZxneGBFc sDdgf/8RRTUz4sTP74KrgYH+1P8skSmr7HyKw6P/4kT+XZoNuKZQNkO+/1ivrhscNrlW EYkzBFm7QwH355MHeuh+LAu2438bxdIbUVouT/rCUTWTOj6H/frq0FeeiMn3gcA/tjYW YfVvK3RF8qLE4rd+hen5zXh/SFymfsJYubYSAoeNi8LWkwJGX5+Y1pQLNQK8GFwbsQv8 6dAwBExYum5N1syuBxXW4/Dhy+zRSbqfIq7C0PGv0ldjiDgAI6TdsfAinzwN9MFaaDLs Ntog== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20130820; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc; bh=79oM9t5KP0Hv7KO6fmfFYw1Iu9jDyzccZKUHxGRp9zM=; b=BuUeHssJWnuDBzbRzc0a30LQziEj5sfobTLKMkfIHNLPDdoDrtmrYwwfoIGJHehPAL sX7jTY5u28pDhyNIka9+8f/XVb1RjDcPlYEwDA7+PgYohaDq6V2rApiA4M+MyGby8GmB kJa51fCrZUDXXr6XMJK39CTHTym4irTTv+sVUejYJukkxYdR4SWKc9CRm8tuEaXIytAl 0+V9cersRWAHgxstadPmo9/sT56DPhFlDiWYfF1f8vdSYePo34afgsz6yF7DZcB0bAGa mhEjx2UsQJLTD6hn0Digw8qmca7KNikaG6YoYQmK4GoKx+ArOp85+FOf1tVRz5cx46gc IJCQ== X-Gm-Message-State: ALyK8tIe1V5d4t9jcb8Pqm8R9SsM19uLknCNCIN3awNA1O2VKW8vT5wLMODDjIng0D8Zl86gdbmQuOsdM8f7UA== X-Received: by 10.36.200.131 with SMTP id w125mr15320065itf.80.1468260559057; Mon, 11 Jul 2016 11:09:19 -0700 (PDT) In-Reply-To: X-BeenThere: python-list@python.org X-Mailman-Version: 2.1.22 Precedence: list List-Id: General discussion list for the Python programming language List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Mailman-Original-Message-ID: X-Mailman-Original-References: Xref: csiph.com comp.lang.python:111277 On 11 July 2016 at 20:52, wrote: > What kind of statistic law or mathematical conjecture or is it even a physical law is violated by compression of random binary data? > > I only know that Shanon theorised it could not be done, but were there any proof? Compression relies on some items in the dataset being more frequent than others, if you have some dataset that is completely random it would be hard to compress as most items have very similar number of occurrances. > What is to say that you can not do it if the symbolic representation is richer than the symbolic represenatation of the dataset. > > Isn't it a fact that the set of squareroots actually depict numbers in a shorter way than their actual representation. A square root may be smaller numerically than a number but it definitely is not smaller in terms of entropy. lets try to compress the number 2 for instance using square roots. sqrt(2) = 1.4142 the square root actually takes more space in this case even tho it is a smaller number. so having the square root would have negative compression in this case. with some rounding back and forth we can probably get around the fact that sqrt(2) would take an infinite amout of memory to accurately represent but that neccesarily means restricting the values we are possible of encoding. for sqrt(2) to not have worse space consumprion than the number 2 itself we basically have to trow away precision so sqrt(2) ~= 1 now i challenge you to get that 2 back out of that 1..