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Palindrome Day 20200202

The year 2020 is definitely a very special one for all those who have a sense of symmetry – and this disposition was given to us by the evolution. Depending on the date format used, there are several palindrome days this year, i.e. dates that are symmetrical (or palindromic).

When written in the international ISO 8601 format YYYYMMDD, 2020-02-02 is the first palindromic date since 2011-11-02. In between there are 3014 days (more than 8 years). Of course, this is also a symmetrical date when written in the American format MMDDYYYY, i.e. 02/02/2020.

Moreover, that date is also palindromic in the long German date format DDMMYYYY, this is 02.02.2020. This format is also used in many other countries. It is the first such date since 21.02.2012 (2903 days ago). Please note: the symmetry is evaluated neglecting the delimiter symbol.

What’s next?

In February there are two additional palindromic dates in the short American format MMDDYY. These are 02/11/20 and 02/22/20. Depending on the used format we will experience further palindromic dates in the next year. In ISO YYYYMMDD format this will be 2021-12-02 which is also palindromic in the American format (12/02/2021). In the German DDMMYYYY format there will be two such dates in the near future, one in 2021: 12.02.2021 (same date as indicated for the ISO format), and another one in 2022: 22.02.2022 (which is not palindromic in the ISO format).

People who use the short German date format DDMMYY will encounter another symmetry this year on 02.11.20 (2020-11-02 = November 2nd, 2020). The previous symmetrical date in this format was 21.11.12 (2012-11-21) which is almost 8 years ago (2903 days). The closest future symmetrical dates in this format will be 12.11.21 and 22.11.22. A little bit later on 12/11/21 and 12/22/21 we see further symmetrical dates in the short American format MMDDYY.

Is it going on like this?

Why, no. After this accumulation of palindromic dates we will experience a long lasting „dry spell“ which will only end on 2030-03-02 (ISO format), 03/02/2030 (American format), 03/11/30 (short American format), 03.02.2030 (long German format), and 03.11.30 (short German format), respectively. See the tables below.

By the way

The very first palindromic date in ISO YYYYMMDD format after 1000-01-01 (Jan 01 1000) was 1001-10-01 (Oct 01 1001).

2020-02-02 is the 47th palindromic date in the YYYYMMDD format after the reference date 1000-01-01. In total, 372579 days have passed since then. The 331st and very last such date before the year 10000 is 9290-09-29 (Sep 29 9290). This will be the 3028132nd day after 1000-01-01 and therefore is still 2655553 days away (after 2020-02-02).

It is a little bit different in the DDMMYYYY format. The following applies here: 02.02.2020 is the 67th palindromic date after the reference date 01.01.1000. The last possible symmetrical date before the year numbers become five digits long one is 29.09.9092 which is the 335th such date in the list. It’s just the 2955814th day after 01.01.1000.

Hint: Because of the Gregorian Calendar Reform of 1582, the numbers of days after 1001-01-01 are fictitious, strictly spoken. They are valid only then, if we adopt the reform for dates before 1582, subsequently. To get the real number of days after ‘Jan 1 1000’ for years after 1582 subtract 5 from each term representing a date after 1582. This applies to all palindromic dates after the 43rd in YYYYMMDD format, and after the 61st in DDMMYYYY format. The value 5 comes from the 10 skipped “Gregorian” dates between 1582-10-04 (Oct 4 1582) and 1582-10-15 (Oct 15 1582) minus the 5 additional Julian leap days in the years 1000, 1100, 1300, 1400 and 1500 which are not Gregorian leap years.

Useless knowledge?

Do not ask about the benefits of these considerations and let me quote Bertolt Brecht: „Thinking is one of the greatest pleasures of the human race“. Jean-Baptiste le Rond d’Alembert (you should know him; possibly you remember the convergence criterion for infinite series that was named after him) says it even more clearly: „Mathematics is a kind of toy that nature has thrown at us for comfort and entertainment in the darkness“. – In Praise of Idleness.

Tables

Altogether, there are 331 palindromic dates in the YYYYMMDD format and 335 such dates in the DDMMYYYY format (between the years 1000 and 9999). The following two tables show excerpts from the complete lists of dates for both formats. In both cases the symmetry is evaluated neglecting the delimiter symbol.


Excerpt of palindromic dates in the YYYYMMDD format.

# Date # of days after 1000-01-01
1 10011001 638
2 10100101 3652
3 10111101 4321
4 10200201 7335
44 20011002 365882
45 20100102 368896
46 20111102 369565
47 20200202 372579
48 20211202 373248
49 20300302 376260
50 20400402 379944
51 20500502 383626
52 20600602 387310
326 92400429 3009717
327 92500529 3013399
328 92600629 3017083
329 92700729 3020765
330 92800829 3024449
331 92900929 3028132

Excerpt of palindromic dates in the DDMMYYYY format.

# Date # of days after 01.01.1000
1 10011001 374
2 20011002 749
3 30011003 1124
4 01011010 3652
65 11022011 369301
66 21022012 369676
67 02022020 372579
68 12022021 372955
69 22022022 373330
70 03022030 376233
71 13022031 376608
72 23022032 376983
73 04022040 379886
330 08099080 2951410
331 18099081 2951785
332 28099082 2952160
333 09099090 2955063
334 19099091 2955438
335 29099092 2955814

Finally, here are the complete lists of symmetrical dates in the DDMMYY and in the MMDDYY format: The symmetry is valid with and without the delimiter symbol.


All palindromic dates in the DDMMYY format.

# Date # of days after 01.01.00
1 101101 619
2 201102 994
3 301103 1369
4 011110 3897
5 111111 4272
6 211112 4648
7 021120 7551
8 121121 7926
9 221122 8301
10 031130 11204
11 131131 11579
12 231132 11955
13 041140 14858
14 141141 15233
15 241142 15608
16 051150 18511
17 151151 18886
18 251152 19262
19 061160 22165
20 161161 22540
21 261162 22915
22 071170 25818
23 171171 26193
24 271172 26569
25 081180 29472
26 181181 29847
27 281182 30222
28 091190 33125
29 191191 33500
30 291192 33876

All palindromic dates in the MMDDYY format.

# Date # of days after 01/01/00
1 101101 589
2 102201 600
3 011110 3603
4 012210 3614
5 111111 4272
6 112211 4283
7 021120 7255
8 022220 7297
9 121121 7955
10 122221 7966
11 031130 10967
12 032230 10978
13 041140 14651
14 042240 14662
15 051150 18333
16 052250 18344
17 061160 22017
18 062260 22028
19 071170 25699
20 072270 25710
21 081180 29383
22 082280 29394
23 091190 33066
24 092290 33077

Autonomous driving – How to achieve functional safety in highly complex traffic scenarios?

(switch to german)

To anticipate the answer: The decisive advantage in functional safety results from the constructive cooperation of on-board systems and IT back ends.

Emission-free mobility and highly automated driving are the determinant future topics for automotive OEMs and suppliers. Embedded systems (ES) in the vehicle (on-board) together with high-performance back end IT systems (off-board) are the enablers in order to achieve these ambitious goals. The key lies in the intelligent connection of both worlds.

On the way to accomplish highly automated and autonomous driving functions, established OEMs, suppliers and engineering service providers are faced with the task of implementing innovative and highly complex customer functions economically. At the same time, the market is rapidly changing. New and unconventional acting market players such as Google, Apple, Tesla, Faraday, Uber, and others, are radically breaking new ground, both technologically and in terms of business models. This competition comes mainly from the IT world, not from the engineering world. These companies understand the vehicle mainly as a sort of „software on the road„.

The well proven technology access, which has been tried and tested by premium OEMs and their suppliers, is based on a more or less self-sufficient functional representation using on-board sensors and on-board embedded systems in the vehicle. Remember, a little bit more than 20 years ago, vehicles have been largely mechanical, mechatronic and electronic systems with a marginal share of software. Meanwhile, vehicle systems have been technologically expanded by more and more electronics and a rapidly growing share of software. This technological change has been extremely successful: many vehicle functions have been gradually realized completely as embedded systems with integrated software. Today, the functionalities at the cutting edge are complex driver assistance systems up to highly automated driving (level 3 automation / conditional automation). As mentioned before, all on-board and essentially without active communication with the outside world!

Even more challenging is the implementation of functions with the required higher levels of automation (Level 4 and higher / High and Full Automation or Autonomous Driving). Particularly, in the urban environment, e.g. safe passage of a multi-lane urban intersection, there are extremely difficult tasks that cannot be handled safely by state-of-the-art closed on-board solutions.

Provided, we must rely on the exclusive basis of a self-sufficient on-board system solution. Would we gain the confidence to entrust our preschool children (without accompany of adults) to an autonomous vehicle, which should them take to the grandparents living at the other end of the city? That’s hard to imagine!

To implement such highly complex and highly critical applications in a functionally reliable manner, new solutions are needed. One promising approach is to remove definite sub functions of the overall task from the vehicle and outsource them to an IT back end, or implement them at the IT back end, redundantly. This may comprise, for example, the computationally intensive parts of the representation and interpretation of the digital world view, the processing of large amounts of data, the determination of alternative courses of action in the driving strategy using AI methods (AI = Artificial Intelligence), the continuous expansion of the scenario knowledge base (Continuous Learning), the anticipation of the behavior of other road users, the analysis and verification of the ego vehicle’s driving trajectory in view of the traffic rules and quite simply the monitoring of the vehicle and the route from a distant location.

Certainly, it is no coincidence that the new market players mentioned above have recognized the benefits of IT solutions in automotive scenarios right from the start. They take advantage of the resulting flexibility in the technical development and especially they apply IT proven procedures for the validation of driving functions. Also, they adopt the perspectives for potential disruptive changes in mobility concepts.

Enormous pressure on established OEMs, suppliers and engineering service providers results from this situation. Both technological approaches, the classical automotive one and the merely IT based one have their strengths and weaknesses. With respect to future mobility solutions, the benefits of the IT world (including the capability to process large amounts of data, rapid updates, usage of AI methods, deep learning) must be combined with the benefits of the ES world (including the close union of HW and SW, high efficiency, compact algorithms, real-time capability).

The decisive technological requirement arising from this is the connectivity capability of the different subsystems inside the car and the interconnection of the vehicle system with the overall network. The core requirement is the availability of highly secure and operationally reliable data connections with a high-bandwidth. Provided this is ensured, functionally safe applications (Safety) distributed over a heterogeneous system environment of IT and ES systems can be established. At the same time, of course, the highest standards must be applied on data security (IT security). Finally, functional safety is ruled by the simple precept „without security, there is no safety„.

The technological cornerstones for maintaining the functional safety of IT back ends are:

    • Function-dependent end-to-end latency < 20 ms … < 1sec
      (transit time measured from on-board to IT back end, and backwards)
    • 24/7 availability and third-level technical support
    • Protection of data integrity from cyber attacks
    • Anonymization of the data
    • Continuous updating of protective measures
    • Scalability of services

With the advent of the cellular standard 5G, the foundations have been laid for high-security data links with low latencies („signal propagation time„, delay between triggering and the effective execution of an action or response). The highly secure networking between the embedded systems in the vehicles on the one hand and the corresponding IT back ends on the other will thus provide a significant contribution to the further evolutionary steps in driver assistance towards reliable higher automation functions and autonomous driving.

Nevertheless, there can be no doubt that even with this holistic approach the way to the driverless car that rules the full variety of traffic scenarios („autonomous drivingin the truest sense of the word) is still far away. There may be people who are saying, what’s the matter, that’s possible, Google has done it already. Others have also shown that cars can maneuver in real world traffic scenarios without driver intervention. Yes and no! Here we have to put into perspective, that all of these examples are far away from the required technological maturity and readiness for mass use under arbitrary real traffic conditions. – Let’s do the litmus test and remind ourselves again of the scenario mentioned above: Would we gain the confidence to entrust our preschool children to an autonomous vehicle (without accompany of adults) which should them take to the grandparents living at the other end of the city? – Provided, we can answer in the affirmative without hesitation we have reached the goal, not earlier.

In the medium to long term there will be an extensive technological convergence of the IT world and the ES world. We already see the beginnings of this process. For example, there are more and more dedicated AI chips used in both environments, ES and IT. Among other things this is the progression that is driving and pioneering the convergence. This process has the power to bring together the still separated worlds of ES and IT. An additional transformation pressure comes from those highly complex new automation functions with multiple cross system dependencies. Paradoxically, precisely the use cases that are easy to describe (for example, the car should drive from address A to address B, completely independent from any driver interaction) are calling for a holistic view, thus driving the convergence process.